3_bbmodel_concordance.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/Users/quanti/Desktop/M_HSC/\n"
     ]
    }
   ],
   "source": [
    "import itertools as itt\n",
    "%matplotlib inline\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as mpatches\n",
    "import numpy as np\n",
    "import os\n",
    "import pandas as pd\n",
    "import pickle\n",
    "import scipy.optimize as spo\n",
    "import scipy.special as spsp\n",
    "import scipy.stats as sps\n",
    "import seaborn as sns\n",
    "\n",
    "from matplotlib.ticker import FixedLocator\n",
    "\n",
    "mpl.rcParams['axes.titlesize'] = 'xx-large'\n",
    "mpl.rcParams['axes.labelsize'] = 'xx-large'\n",
    "mpl.rcParams['xtick.labelsize'] = 'x-large'\n",
    "mpl.rcParams['ytick.labelsize'] = 'x-large'\n",
    "mpl.rcParams['xtick.direction'] = 'out'\n",
    "mpl.rcParams['ytick.direction'] = 'out'\n",
    "mpl.rcParams['legend.frameon'] = True\n",
    "mpl.rcParams['legend.framealpha'] = 0.5\n",
    "mpl.rcParams['legend.fontsize'] = 'large'\n",
    "\n",
    "path_proj = os.getcwd()+ '/'\n",
    "path_sc = path_proj + 'csv/Single_cell/'\n",
    "path_sort = path_proj + 'csv/Sort/'\n",
    "path_plot = path_proj + 'figures/'\n",
    "print(path_proj)\n",
    "\n",
    "#LOAD THE PROCESSED DATA\n",
    "df = pd.read_csv(path_sc+'Pooled_data.csv', sep=';', decimal=',')\n",
    "\n",
    "#GLOBAL VARIABLES FOR ITERATION\n",
    "conds = ['P', 'P+ILs']\n",
    "or_cells = ['SLAM-HSC', 'ST-HSC', 'MPP']\n",
    "\n",
    "#SET A RANDOM SEED TO REPLICATE THE BOOTSTRAP CONFIDENCE INTEVALS\n",
    "#BASED ON RANDOM SAMPLING WITH REPLACEMENT\n",
    "np.random.seed(123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#IMPORTANT: SAMPLING PROBABILITY MUST BE SPECIFIED FROM THE USER! \n",
    "r_sample = 0.71"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "#NOTE: A FULL FAMILY VECTOR IS THE VECTOR OF CELL COUNTS PER GENERATION (ONE GENERATION PER VECTOR ENTRY);\n",
    "#A SAMPLED FAMILY VECTOR IS A FULL FAMILY VECTOR WHERE CELLS WERE NOT NECESSARILY COUNTED/OBSERVED\n",
    "\n",
    "#BELOW ARE THE FUNCTIONS AND CLASSES TO DEFINE FULL AND SAMPLED FAMILY VECTORS\n",
    "\n",
    "#GIVEN A SAMPLED FAMILY VECTOR, POPULATE THE NEXT GENERATION WITH ALL POSSIBLE COUNTS THAT ARE PHYSICALLY POSSIBLE\n",
    "#(HERE IT IS ASSUMED THAT EACH DIVIDING CELLS PRODUCES TWO CELLS IN THE NEXT GENERATION)\n",
    "def add_generation(family):\n",
    "    i = len(family)\n",
    "    past = [family[j] * 2**(i-j) for j in range(i)]\n",
    "    max_val = 2**i - sum(past)\n",
    "    new_fam_list = [family[:]+[k] for k in range(max_val+1)]\n",
    "    return new_fam_list\n",
    "\n",
    "#CREATE ALL SAMPLED FAMILY VECTORS UP TO GENERATION DD\n",
    "def fam_generator(DD):\n",
    "    possible_fam = [[0],[1]]   \n",
    "    for DD in range(DD):\n",
    "        temp = [add_generation(elem) for elem in possible_fam]\n",
    "        possible_fam = list(itt.chain.from_iterable(temp))\n",
    "    return possible_fam\n",
    "    \n",
    "#GIVEN A FULL FAMILY VECTOR, RETURNS ALL SAMPLED FAMILY VECTORS THAT MAY POSSIBLY DESCENT FROM IT  \n",
    "def sub_trees_gen(ft):\n",
    "    res_lst = [[float(k)] for k in range(int(ft[0])+1)]\n",
    "    for max_n in ft[1:]:\n",
    "        new_lst = [vec[:]+[float(k)] for k in range(int(max_n)+1)\n",
    "                                     for vec in res_lst]\n",
    "        res_lst = new_lst\n",
    "    return [Sub_tree(np.asarray(vec), sum(np.subtract(ft,vec)))\n",
    "                for vec in res_lst if sum(vec)!=0.]\n",
    "\n",
    "#CLASS FOR SAMPLED FAMILY VECTORS\n",
    "class Sub_tree(object):\n",
    "    def __init__(self, st, lost_c):\n",
    "        self.st = st\n",
    "        self.lost_c = lost_c\n",
    "        self.range = np.arange(len(st))[st>0].max() - np.arange(len(st))[st>0].min()\n",
    "    def show_st(self):\n",
    "        print( 'ST:', self.st, 'Lc:', self.lost_c)\n",
    "\n",
    "#CLASS FOR FULL FAMILY VECTORS\n",
    "class Full_tree(object):\n",
    "    def __init__(self, ft):\n",
    "        self.ft = ft\n",
    "        self.ebc = cells_arrived_in_gen(ft)\n",
    "        self.st_lst = sub_trees_gen(ft)\n",
    "        self.range = np.arange(len(ft))[ft>0].max() - np.arange(len(ft))[ft>0].min()\n",
    "    def show(self):\n",
    "        print( 'FT:', self.ft)\n",
    "        print( 'Ebc:', self.ebc)\n",
    "        for st in self.st_lst:\n",
    "            st.show_st()\n",
    "\n",
    "            \n",
    "#BETA-BINOMIAL (BB) MODEL FOR CELL DIVISION,\n",
    "#WHERE A FAMILY DEVELOPS FROM A 1 CELL IN GENERATION 0 ITERATIVELY AS FOLLOWS:\n",
    "#THE NUMBER OF CELLS THAT DIVIDE FROM GENERATION i TO i+1 FOLLOWS A BETA-BINOMIAL DISTRIBUTION\n",
    "#PARAMETRISED SO THAT ONE CELL DIVIDES WITH PROBABILITY p, AND THE CELLS IN THE SAME GENERATION\n",
    "#DECIDE TO DIVIDE WITH (INTRACLASS) CORRELATION rho.\n",
    "#IN ACCORDANCE WITH EXPERIMENTAL DATA, THE CELLS FROM FULL FAMILY VECTOR GROWN UNDER THE BB MODEL\n",
    "#ARE THEN SAMPLED (INDEPENDENTLY AND WITH EQUAL DISTRIBUTION) WITH PROBABILITY r.\n",
    "\n",
    "#GIVEN A FULL FAMILY VECTOR m, RETURN THE NUMBER OF CELLS THAT WERE EVER BORN IN EACH GENERATION\n",
    "def cells_arrived_in_gen(m):\n",
    "    nn = np.zeros(len(m))\n",
    "    nn[0] = 1.\n",
    "    for k in range(1, len(m)):\n",
    "        nn[k] = 2.*(nn[k-1] - m[k-1])\n",
    "    return nn\n",
    "\n",
    "#PROBABILITY THAT A BETA-BINOMIAL DISTRIBUTION, WITH PARAMETERS n, a, b, EQUALS k\n",
    "def bb_dist(k, n, a, b):\n",
    "    if a == 0.:\n",
    "        if k==0.:\n",
    "            return 1.\n",
    "        else:\n",
    "            return 0.\n",
    "    elif b == 0.:\n",
    "        if k == n:\n",
    "            return 1.\n",
    "        else:\n",
    "            return 0.\n",
    "    else:\n",
    "        return spsp.binom(n,k) * spsp.beta(k+a,n-k+b) / spsp.beta(a,b)\n",
    "    \n",
    "#PROBABILITY THAT A BINOMIAL DISTRIBUTION, WITH PARAMETERS n, R, EQUALS k    \n",
    "def bino_dist(k, n, r):\n",
    "    if r == 0.:\n",
    "        if k==0.:\n",
    "            return 1.\n",
    "        else:\n",
    "            return 0.\n",
    "    elif r == 1.:\n",
    "        if k == n:\n",
    "            return 1.\n",
    "        else:\n",
    "            return 0.\n",
    "    else:\n",
    "        return spsp.binom(n, k) * r**(k) * (1.-r)**(n-k)\n",
    "    \n",
    "#PROBEBILITY OF OBSERVING THE FULL FAMILY VECTOR m UNDER THE BB MODEL WITH PARAMETERS p, rho\n",
    "def pmf_m(m, p, rho):\n",
    "    nn = cells_arrived_in_gen(m)\n",
    "    if rho==0.0:\n",
    "        res = np.prod([bino_dist(nn[i]-m[i], nn[i], p[i]) for i in range(len(m)-1)])\n",
    "        return res\n",
    "    elif rho==1.:\n",
    "        m_v = [(m[dd] / (2.**dd)) == 1. for dd in range(len(m))]\n",
    "        if sum(m_v) == 1.:\n",
    "            n_dd = next(dd for dd in range(len(m)) if (m[dd]/(2.**dd))==1.)\n",
    "            res = np.prod([p[i] for i in range(n_dd)])*(1.-p[n_dd])\n",
    "            return res\n",
    "        else:\n",
    "            return 0.\n",
    "    else:    \n",
    "        alpha = np.multiply(p, (1.-rho)/rho)\n",
    "        beta = np.multiply(np.subtract(1., p), (1.-rho)/rho)    \n",
    "        res = np.prod([bb_dist(m[i], nn[i], beta[i], alpha[i])\n",
    "                       for i in range(len(alpha)-1)])\n",
    "        return res\n",
    "\n",
    "#PROBABILITY OF OBSERVING THE SAMPLED FAMILY VECTOR v,\n",
    "#SAMPLING EACH CELL FROM THE FULL FAMILY VECTOR m WITH SUCCESS RATE r\n",
    "def pmf_v_given_m(v, m, r):\n",
    "    return np.prod([bino_dist(v[i], m[i], r)\n",
    "                    for i in range(len(v))]) / (1.-((1.-r)**sum(m)))\n",
    "\n",
    "#PROBABILITY OF OBSERVING FRAY/RANGE EQUAL TO k UNDER THE BB MODEL rho, p,\n",
    "#GENERATING FULL FAMILY VECTORS IN Ft_lst, THEN SAMPLED WITH SUCCESS RATE r \n",
    "def fray_dist(k, rho, p, r, Ft_lst):\n",
    "    out = 0.\n",
    "    for Ft in Ft_lst:\n",
    "        out += sum([pmf_v_given_m(St.st, Ft.ft, r) for St in Ft.st_lst\n",
    "                    if St.range==k]) * pmf_m(Ft.ft, p, rho)\n",
    "    return out\n",
    "\n",
    "#NEGATIVE LOG-LIKELIHOOD OF FRAY/RANGE DATA\n",
    "def log_like_data(rho, p, r, Ft_lst, fray_freq):\n",
    "    return -sum([fray_freq[k]*np.log(fray_dist(k, rho, p, r, Ft_lst))\n",
    "                 for k in range(len(fray_freq))])\n",
    "\n",
    "#BELOW ARE THE FUNCTIONS TO CALCLUATE THE DISTRIBUTION AND CONFIDENCE INTERVALS\n",
    "#OF DATA IN A GIVEN SUPPORT (SIMILARLY AS IN NOTEBOOK 2)\n",
    "\n",
    "#TRANSFORM THE PANDAS DATAFRAME OF A FAMILY INTO A FAMILY VECTOR\n",
    "def df_fam_to_vec(dff, max_g):\n",
    "    res = np.zeros(max_g+1)\n",
    "    gens, counts = np.unique(dff.Generation, return_counts=True)\n",
    "    res[gens] = counts\n",
    "    return res\n",
    "\n",
    "def epmf_on_support(data, support, bool_norm=True):\n",
    "    classes, counts = np.unique(data, return_counts=True)\n",
    "    counts_sum = counts.sum()\n",
    "    if counts_sum == 0:\n",
    "        return np.zeros(len(support))\n",
    "    elif bool_norm:\n",
    "        return np.hstack([counts[classes==cl] if any(classes==cl) else np.zeros(1) for cl in support]\n",
    "                        )/counts_sum\n",
    "    else:\n",
    "        return np.hstack([counts[classes==cl] if any(classes==cl) else np.zeros(1) for cl in support])\n",
    "    \n",
    "def stat_bootCI(func, args, data, n_iter=250000, bool_trim01=True):\n",
    "    stat = func(data, *args)\n",
    "    boot_stat = np.array([func(data[boot_index], *args)\n",
    "                          for boot_index in np.random.choice(len(data), size=(n_iter,len(data)))])\n",
    "    boot_per = np.percentile(boot_stat, q=[97.5, 2.5], axis=0)\n",
    "    boot_ci = 2.*stat - boot_per\n",
    "    if bool_trim01:\n",
    "        boot_ci[0,boot_ci[0,:]<0.] = np.zeros((boot_ci[0,:]<0.).sum())\n",
    "        boot_ci[1,boot_ci[1,:]>1.] = np.ones((boot_ci[1,:]>1.).sum())\n",
    "    return stat, boot_ci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " SLAM-HSC P 73\n",
      "\n",
      " SLAM-HSC P+ILs 81\n",
      "\n",
      " ST-HSC P 77\n",
      "\n",
      " ST-HSC P+ILs 63\n",
      "\n",
      " MPP P 48\n",
      "\n",
      " MPP P+ILs 43\n"
     ]
    },
    {
     "data": {
      "image/png": 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cl5aWwt7eHp988km565b9oi1T0d2Xs2fPxtmzZzF58mR06NAB+vr60NDQwObNmxV64bFI\nJJL4vuwaufIIr91oUJHXQx4AXL58GdOnT4ednR2WLFmCFi1aoH79+uKbGso+n1fJ8v4D0sdQkap+\nVq8qLCzEt99+i0GDBkFTU1N8vVFZsHvy5Anu3LmDVq1aQUNDA9u3b0fr1q3FAa2Mk5MTdHV1ceHC\nBamQJuvxvknjxo3h4uICFxcXzJ07F/v378dff/2Fbt26ybyPpKQkpKamAoDE3alljh49WunM6siR\nIzF79mxs3LgR5ubmsLGxKXe90NBQfP/99xJjZbPfNaWpqQlra2tYW1tjwIABGDRoEPbs2YNRo0ZB\nT08PLVq0kNtr6enplRskiUi1MKTJgYuLCxITE3HgwIFKZ8Ze1bp1awAv7657vYdTTbRu3RrPnz+v\n0T/Qz58/x4kTJ+Dn5wd/f3+JZWvXrpVaX9ZQArzsnVY2i/iqtLQ08fLacOjQIWhpaSE8PFwixL1+\nF2BVmZiY4Pbt21Lj5Y3V5LPKz8/H06dPsX//fuzfv19qedmNChcuXEDDhg2lZkPLCIKA0tJSFBcX\nV7mG6rCzs8P+/fur3IajbObtu+++kwruT548weeff45ff/0VY8aMKXf7sjs5z507hzlz5lT4OqNG\njZK6YUcR2rRpAwMDA4n3wcXFBRERETh79myFs6tEpF7YgkMO3NzcYGJigqCgoAqv13p99mHgwIGo\nV68eQkJCyv0F+aZTXRUZOnQo0tLSyv3FXVJSgqdPn75xHxoaGhCJRFKzSefOncOVK1ek1m/QoIHM\nLSP69euHO3fu4MiRI+IxQRAQGhoqXl4bNDU1IRKJUFJSIh4rKSnBtm3barTfPn364ObNm0hISJDY\nb2RkpNS6NfmsdHV1sXbtWqmvCRMmAABmzJiBtWvXik+Xt23bFnfu3JH6/A4fPoyCgoIKZ5aqIyUl\nBZmZmVLjgiDgxIkTAPDGOx1fVVRUhIMHD8LBwQHvv/++eFau7Gv8+PEwNjbG3r17K9yHtrY2li9f\nDj8/P4waNarC9Vq1aoWePXtKfNVERaH/0qVLePr0qcT7MG3aNDRs2BBLliyROu0P/H9LFCJSH5xJ\nkwM9PT1s3LgR06dPx7hx4+Di4oKuXbtKPHHg5MmTEtf4mJqaYsGCBVi5ciVcXV0xePBgNGnSBI8e\nPcL58+chEomwY8eOKtcyZcoUnDhxAvPmzcPx48fRuXNnAC9vv4+Pj8fMmTPfONunp6cHBwcHbN26\nFfn5+TAzM8ONGzfwyy+/oF27dlLX33Xq1An79u3D999/jzZt2qBBgwbidgev8/b2RlxcHGbPni1u\nwXH8+HGcPHkSEyZMkPkRPTXVv39/hIWFYdKkSRg9ejTy8/Nx6NChKp/Ke91HH32E/fv3w8/PT6IF\nR9l79uqsY00+Ky0tLQwaNEhqvOx6qm7dukkEjI8++ginTp2Cl5cXxo8fL75xIDo6GkZGRhg/fnyN\njvtVZ86cwZo1a+Dk5AR7e3s0atQIWVlZOHLkCK5cuYKhQ4eiffv2Ets8evQIGzZskNqXnp4ejI2N\nkZWVVe5pzjLOzs6IjIzE/fv3K5yNHTZsWM0OrBo++eQTNGvWDP369YOZmRkEQcCNGzewd+9e6Orq\nim8cAICWLVsiJCQEfn5+GDZsGIYPH46OHTtCQ0MD//zzDw4fPozs7GwsXry41o+DiOoGQ5qcWFlZ\nYf/+/YiIiMDRo0dx+vRpFBQUwMDAAO3bt8dnn30m9Rf8hx9+CDMzM4SFhWHbtm0oKCiAkZER7Ozs\nZD5t+jptbW38+OOPCA0NxcGDBxEfHw9tbW0YGxtj2LBhMvdg+vbbb7Fq1SrxXabt27fHhg0bEBsb\nK3WX4pw5c/D06VOEhoYiNzcXJiYmFYa0Ro0aYdeuXQgODsbevXuRk5ODVq1aYeHCheU2+1WUbt26\nITg4GBs3bkRQUBAMDAwwaNAgjBs3rka/zJs2bYodO3bgq6++wvbt26Gjo4OBAwfC1dUVbm5uEtcA\nyuuzkkWXLl2we/dubNiwAQcPHkRGRgYMDQ0xdOhQfPrpp2jSpIncXmvgwIHIz8/H6dOnER4ejuzs\nbOjo6MDCwgJLly6VulsXePlc0fJOpZfdkSoSiSqdZe3fvz8iIiIQGxsrEXzq2sqVK3H8+HEcP34c\n0dHRKCwshJGREVxcXODt7S11l2yPHj1w8OBBhIWF4cSJE9i3bx8EQYCpqSmGDBmCiRMn1tGREFFd\nEAk1nTogojc6cuQI/Pz8sHPnTnTp0qWuyyEiIhXAa9KI5Kysp1yZkpISbN++Hfr6+hU+NoyIiOh1\ndXq688KFCwgNDcXff/+NBw8e4NNPP5U6VXHlyhUEBgbi2rVrMDAwwOjRozFz5kyJ9gBPnjzBypUr\nxRfp9unTB0uWLJHrKRwiWY0fPx42NjawsrLCixcv8Ouvv+Lq1atYsGCB0j1wnoiIlFedzqS9ePEC\nFhYWmDdvXrmNFh8+fAgvLy+YmZkhJiYGy5cvR1RUFFavXi1ep7S0FD4+PkhPT0dYWBhCQ0Nx+/Zt\nzJgxo8YXgRNVh7OzMy5duoRvv/1WfPfuihUrMGXKlLoujYiIVIjSXJPm7OyMDz74QGImrezi8uPH\nj4t7I0VGRuKbb77BmTNn0KBBAyQkJGDq1Kk4fPiw+FEzqampGDZsGLZv3y5+lA0RERGRKlHqa9IS\nExPRq1cvieaVjo6OyMvLQ3JysngdU1NTiWcBtmvXDi1atKjwMS1RUVFwdXWFq6urxHMAiYiIiJSF\nUoe0jIwMqdOgTZs2FS+raJ2y9Srqsu7m5oaYmBjExMTwGiEiIiJSSkod0spT1gxUlkcRVeVxRURE\nRETKRKlDmpGRkdRsWNnjZspm1MpbB3j5WKWydYiIiIhUjVKHtC5duuDMmTMSz5A8efIkdHV10aFD\nB/E66enpEg+wTktLw8OHD2vlQclEREREilCnIS03NxcpKSlISUlBYWEhMjMzkZKSgjt37gAAPDw8\n8N///hdLlixBamoqfvvtN6xbtw4TJ05EgwYNAAA9e/ZEx44dMW/ePPz111+4cuUK5s2bh86dO6N7\n9+51eXhERERE1VanIS0pKQmjRo3CqFGjkJGRgcjISIwaNQpLliwB8PKBw6Ghobh58yZcXV2xbNky\njBs3DrNmzRLvQ0NDA5s2bULLli0xadIkeHl54d1338WGDRuU7pq05cuXQyQSSXwtX768rssiIiIi\nJaQ0fdLqiqurK2JiYmr1NUUiERvtEhERUaXq9LFQRERE5SkpKUFWVhaKiorquhQihdDQ0ECDBg2g\nr69f4Zk/hjQiIlI6WVlZ0NHRQdOmTZXu0hWimhIEASUlJXj+/DmysrIqfNa4Ut/dSURE6qmoqAh6\nenoMaPRWEolEqFevHho1aoSCgoIK12NIIyIipcSARm+7N/2MM6S9JQqKSmp1OyIiIlIsXpP2ltDW\n0oTNkiNV3i5pxQAFVENEREQ1xZk0IiJSDfn56vGaRP/DmTQiIlINOjpAbV+nVo2elgsXLsSePXsA\nAJqamtDT04OZmRkcHR0xceJEGBoayryvAQMGYMSIEfD3969yHaT6OJNGREQkZ926dUNCQgKOHTuG\nyMhIjB07FgcOHMCwYcNw69atui6PVARDGhERkZxpaWnByMgIzZs3R7t27fDBBx9g9+7d0NHRwWef\nfQYAuHbtGqZNmwYHBwfY29tjzJgxOHnypHgfnp6euHv3Lr7//ntYWVnBysoK6enpEAQBS5YsgYuL\nC2xtbdG/f38EBwejsLCwrg6XFIQhjYiIqBbo6enBw8MD58+fR1ZWFnJycjB06FDs2LEDMTEx6N27\nN3x9fcUzbSEhITAxMcGUKVOQkJCAhIQEtGzZEoIgoEmTJvjuu+9w6NAhLF68GDExMdi0aVMdHyHJ\nG69JIyIiqiXt2rWDIAhIT0/He++9J7Fs1qxZOHbsGOLi4vDxxx/D0NAQmpqaaNCgAYyMjKTWLWNq\naop79+7hp59+wieffFIrx0G1gyGNiIiolgiv3IiQlZWFdevW4Y8//kBmZiZKSkpQUFCABw8evHE/\n0dHR+Pnnn3H//n3k5eWhuLhYYt/0dmBIU5T8/Jd3IlV1s4Ji6GjzYyEiehulpqZCJBKhVatWWLBg\nAR4+fIh58+bB1NQUOjo6mDVr1hsfKn/48GF88cUXmDNnDv7zn/9AT08PcXFxWL16dS0dBdUWpgFF\nedOt4hUs0xEE6I0Lh2OHFtgxuy88g4/jVPIjqfVeX54TPVlOhRMRkSLk5ORg586dcHBwQKNGjXDh\nwgXMmzcP/fv3BwC8ePEC6enpsLS0FG+jpaWFkhLJJ8NcvHgR1tbW8PLyEo/dv3+/dg6CahVDmhKq\nakAjIiLlUlRUhIyMDAiCgOfPn+Py5cvYunUrCgsLsXz5cgCAmZkZ9u/fj65du6K0tBRr166VCmSm\npqZITEzEgwcPoKOjA0NDQ5iZmWH37t04evQoLC0tcezYMcTHx9fBUZKiMaQpIQY0IqJy5OdXq7ls\njV+zGpeuXLx4Eb1794ampibeeecdmJmZYdiwYfD09ISBgQEAIDAwEJ999hnGjh2Lpk2bYurUqch/\n7QkH/v7++OyzzzBo0CAUFBTgt99+g5ubG27cuIHFixejuLgY/fr1g7+/P7788ku5HDIpD5Gg5lca\nurq6IiYmRjE7r+CUpghAhW+6IGDw8rgqB7Sc6Ml8dicRvTUePHgAY2Pjui6DSOEq+1lnnzQlxBk0\nIiIiYkhTAbJco0ZERERvF4Y0JSfrTQRERET0dmFIU2JVucuTiIiI3i4MaUqKbTiIiIjUG0OaEmJA\nIyIiIoY0JcSARkRERAxptWg5XvZIw//+V/S/sdcxoBERERGfOFCLlqP8UPY6BjQiIiLiTJoKYJ80\nIiIi9cOQpuTYJ42IiEg9MaQpMfZJIyL6f/mFxXXwmiW1/prqIjc3F46Ojvjrr7/qupRKBQcHo2fP\nnrCyskJMTAwWLlyIyZMnv3G7ZcuWISgoqEavzWvSlBTbcBARSdKpXw9648Jr/O9jVZYfXj5IIcci\nTydOnEBwcDDS0tLQrFkzeHp6wsvLq9JtSktLsWHDBsTGxuLx48do3LgxXFxcMHv2bDRo0AAAsHXr\nVhw5cgQ3b96EIAho164dPv74Yzg5OYn3c+HCBYSGhuLvv//GgwcP8Omnn8LX11emurds2QIbGxvY\n2tqKxxYuXIg9e/aIv9fT04OFhQV8fX3Rp0+fqrwtlZo8eTJatGiBVatWVbrelStXsHnzZqxfvx52\ndnbQ19fHgAEDUFpa+sZ9zZgxAwMHDsT48ePRqlWratXJmTQlxIBGRFS+2gxoqvDv69WrV+Hr6wtH\nR0fExsbCz88PwcHB2LlzZ6XbhYaGYtu2bZg7dy4OHTqEL7/8EnFxcRJB448//sCYMWOwfft2REdH\no3PnzvDx8cGff/4pXufFixewsLDAvHnzYGRkJHPdBQUF2LlzJ9zd3aWWdevWDQkJCUhISEB0dDQ6\ndOiAGTNm4O7duzLvX15u374NDQ0NuLi4wMjICDo6OtDX14eBgcEbt23evDl69OiBn376qdqvz5Cm\nhN6mf0CIiORJ1QJaamoqpkyZAnt7e9jZ2WHevHkoLCyUy74BIDw8HJ06dcLcuXNhbm4OV1dXTJw4\nEVu2bKl0u8TERPTu3RsDBw6EqakpHB0dMWzYMIlTj1u3bsW4ceNgbW2Ntm3bYsGCBTA3N8eRI0fE\n6/Tp0wdz5szBkCFDUL9+fZnrPnXqFAoKCtCrVy+pZVpaWjAyMoKRkRHMzc0xZ84cFBUV4fr16xLr\n7dixA4MGDUKnTp3w/vvvY+PGjSgufnlK/OLFi3B3d4e9vT3s7e0xYsQInDp1CsDL2bqzZ89iz549\nsLKygpWVFc6dOydVx8KFCzF//nyUlpaK1ysbLzvd+aZ9DRgwAPv27ZP5fXkdT3cqIQY0IqLyqVJA\nu3z5Mry9veHt7Y2lS5ciKSkJixcvRrt27eDt7S1eb9OmTdi8eXOl+5o+fTp8fHykxhMTEzFmzBiJ\nMScnJ4SGhuLRo0do0aL8u/+7du0qPk3Zvn173Lt3DydOnMD7779fYQ2lpaXIzc1Fo0aNKq1VFufP\nn4e1tTXq1as8hhQWFuLnn39G/fr10aFDB/F4SEgIYmJisHjxYrRv3x43b97EZ599hoKCAvj7+8PX\n1xejR48WzwympqZCV1cXABBWcMbZAAAgAElEQVQQEIB79+7ByMgIAQEBAFDuzFhAQACsra0RFBSE\nEydOlFvfm/ZlZ2eHzMxMpKWlwdzcvArv0EsMaUqIAY2IqHyqEtBKS0sREBCAqVOnYtq0aQAAMzMz\n7Nu3DxcvXpQIae7u7hg8eHCl+6vo9FpGRobUacamTZsCAJ48eVJhSJsyZQry8/Ph6uoKkUiE4uJi\njBs3DjNnzqywhk2bNuH58+cYOXJkpbXKIj09Hc2bNy932fnz52Fvbw8AyMvLg66uLoKCgmBiYiIe\n27p1K0JCQsTXx7Vq1QozZ87EihUr4OXlhWfPnsHZ2Rlt2rQBAPH/AoC+vj60tLSgo6NT6SlafX19\n6OvrA0CF671pX2Xv/7179xjS3lbsk0ZEVD5lDGjAy1m0O3fuYPz48RLj2traEhedA4ChoSEMDQ3l\n9tplRCJRhcvi4uKwc+dOfPXVV7C2tsatW7cQGBiINWvWYNasWVLrR0ZGYvPmzdi4cWOFwa8qCgoK\nxAHodba2tuK7Il+8eIGEhAQsXLgQ+vr6cHR0RGpqKvLz8/HJJ59IHGNJSQkKCgpQUlKCsWPHYurU\nqejRowe6d+8OFxcXtG3btsZ1V1XZKeD8/Pxqbc+QpuTYJ42IqHy1cRNBdZ05cwZt2rSRCiLXrl2D\np6enxFhNTncaGRkhIyNDYiwzM1O8rCJBQUH48MMPMWrUKACAlZUV8vPzERAQAF9fX2hra4vX3bZt\nG0JCQrBx40b07Nmz0jpl1ahRIzx79qzcZTo6OmjdurX4e2tra/zxxx/YtGkTHB0dIQgCAGDt2rUS\nM2RlDAwMsGLFCnz44Yc4ffo0Tp8+jbVr12Lp0qXl3qigSGXH2Lhx42ptz5CmxN6228SJiOSltu7y\nrK6kpCQUFBRIjMXHxyMzMxNDhw6VGK/J6c4uXbogISEBfn5+4rFTp07BxMSk0hmvvLw8aGhI3juo\nqakJQRDEIQh4GYTCw8Pxww8/oHv37pXWWBUdO3ZERESEzOtramoiLy8PAGBhYQFtbW3cu3ev0rYc\nlpaWsLS0hJeXF5YtW4bo6GhxSNPS0kJJiXx64FW2rxs3bkBTU1PierqqYEhTUm/bbeJERPKiCn3S\nkpOTkZOTg9DQUDg7OyMxMRGBgYFYuHCh1LVYNTndOWnSJHh4eGD16tUYMWIErl69ioiICCxatEi8\nTkREBCIiIhAXFyce69+/P0JDQ9G6dWvx6c41a9bAyckJOjo6AICVK1ciKioKwcHBMDMzE8/YlbWh\nAF42pC1rjVFYWIjMzEykpKSgQYMGErNhr3NycsKqVavw8OFDtGzZUmJZUVGR+LXy8vJw6tQpJCQk\nwN/fHwDwzjvvYPr06QgODgYA9OzZEyUlJbhx4waSk5Mxbtw4REdHo1+/fmjZsiWePHmCP//8UyIo\nmZqa4ty5c7h79y709PTE15ZVR2X7On/+PLp27Qo9Pb1q7ZshTQkxoBERlU8V+qRlZWXh8ePHWL9+\nPbZs2YLg4GAYGxtj/vz5GDt2bLX2WRFbW1usX78ewcHB2LZtG4yMjDBr1ix4eHiI18nOzsatW7ck\ntluyZAkMDAywatUqPHnyBE2aNEHfvn0lbhzYvn07gJdNWV/16l2TSUlJ+PDDD8XLIiMjERkZie7d\nu2PHjh0V1m1ubo7u3bsjNjZW6jTuxYsX0bt3bwAvA6GpqSnmzJkj0aB3xowZaNasGSIiIhAUFAQd\nHR20adMGo0ePhq6uLu7cuYPZs2cjKysLhoaG6Nu3LxYsWCDefsqUKbhx4wZGjhyJFy9eYPv27Xjv\nvfcqf7MrUNG+BEHA/v37MXv27GrtFwBEwqvzmmrI1dUVMTExitl5JRdtVkgQkPk8v8r/gORET4bN\nkiNS679J0ooBVa+RiEjBHjx4AGNjY4mx/MIS6NTXrNU68guLoVO/avMZJ0+ehK+vLy5dulTt2Rl1\ncPHiRcyaNQvx8fHi9hhvk0OHDmHjxo3Yu3cvNDUr/rkt72e9DJvZKiHOoBERSavtgPbyNat+wik5\nORkWFhYMaG/QrVs3+Pn5IT09va5LUYjCwkJ89dVXlQa0N+HpTiXEgEZEpLqSk5NhbW1d12WoBDc3\nt7ouQWHK7pytCaUPac7Ozrh//77UuIWFBQ4ePIiYmBiJCyTLhIWFye1W4brGPmlERKpj3bp1dV0C\nvSWUPqTt3r1b4tbWvLw8DB8+HEOGDBGPaWpqSj2yQZaHn6oC9kkjIiJST0of0l5vABcdHY3i4mJ8\n8MEHEuOVNe1TVeyTRkREpL6UPqS9bteuXejXr59En5mSkhL0798fBQUFMDMzw5QpU9CvX786rLLm\n2IaDiIhIvalUSLt69SquXbsm8VwxMzMzBAUFiR9pcejQIfj4+GDFihUV9qOJiopCVFQUgJf9Y5RN\nbQa0wuJS1K9X9Zt8q7sdERERyUalQlpUVBRMTU3FTe4AwN7eHvb29hLfP3v2DFu3bq0wpLm5uYnv\nKHF1dVVs0dVQmzNo9etp4IOwxCpvt9urS41fm4iIiCqmMlMhOTk5OHjwINzc3CSeel8ee3v7cu8I\nVRU8xUlEREQqE9JiY2NRVFQk08xXSkpKpQ+WVXYMaERERKQypzujoqLQv39/NG3aVGI8JCQEtra2\naNOmDQoLC/Hrr7/i559/xpIlS+qoUvljnzQiIiL1oxIh7fLly7h+/Xq5TWtzcnLw+eefIzMzEzo6\nOmjbti3WrFmDgQMH1kGl8sc+aUREROpJJUJa586dcf369XKXLVq0qNzw9jZgnzQiIiL1JfM1aefO\nnUNYWJjE2J49e+Dk5ITOnTtj6dKlKC4ulnuB6op90oiIJBUUlbx5pbfgNYnKyDyTtmHDBhgaGoq/\nv3nzJpYuXYpWrVrB0tISu3fvhrm5OSZPnqyIOtUKAxoRkTRtLU3YLDlSq6+ZtGJArb5edZw4cQLB\nwcFIS0tDs2bN4OnpCS8vr0q3efHiBTZs2IDDhw/jyZMnaNOmDWbMmIFBg3hWRpnIPJP2zz//wM7O\nTvz9gQMHoK2tjejoaGzduhXDhg1DTEyMQopUNwxoREQki6tXr8LX1xeOjo6IjY2Fn58fgoODsXPn\nzkq3W7p0KeLi4vDFF1/g4MGDGDduHGbPno1Tp07VUuUkC5lD2vPnzyUeWn7mzBn07NkT+vr6AIDu\n3bsjPT1d/hWqIQY0IqK3Q2pqKqZMmQJ7e3vY2dlh3rx5KCwslNv+w8PD0alTJ8ydOxfm5uZwdXXF\nxIkTsWXLlgq3KSgoQFxcHGbNmoVevXrh3XffhaenJ/r06YPNmzfLrTaqOZlDmpGREe7evQsAePr0\nKZKSktCjRw/x8tzcXGhoqEzbNaXGgEZEpPouX76MCRMmoGfPnoiJicGKFSsQFxeH8PBwifU2bdok\nfnpORV+bNm0q9zUSExMlnsIDAE5OTrh//z4ePSr/d0VRURFKSkqgra0tMa6jo4PLly+jqKio+gdN\nciXzNWm9e/dGZGQkDAwMcP78eQBA//79xcvT0tLQsmVL+VdI7JNGRKRiSktLERAQgKlTp2LatGkA\nXj5ret++fbh48SK8vb3F67q7u2Pw4MGV7u/VM1mvysjIgJGRkcRYWT/RJ0+elNvYXU9PD126dMHG\njRvRvn17GBsb49SpU/jtt99QVFSE7OxsNGvWrErHS4ohc0ibOXMmbt68ia+//hpaWlqYP3+++MMv\nKCjAr7/+ipEjRyqsUHXFPmlERKrn8uXLuHPnDsaPHy8xrq2tjdLSUokxQ0NDiRvz5KWyRyh+8803\nCAgIgIuLCzQ0NGBmZoaxY8ciIiICmpqacq+FqkfmkNa4cWNEREQgJycH2tra0NLSEi8TBAHbt29X\n6UcxKSP2SSMiUk1nzpxBmzZtxNdtl7l27Ro8PT0lxjZt2vTGa8GmT58OHx8fqXEjIyNkZGRIjGVm\nZoqXVcTExATh4eHIy8vD8+fP0bx5c3z99dfQ09NDo0aNKq2Fak+Vm9nq6elJjeno6KB9+/ZyKYhe\nYhsOIiLVlZSUhIKCAomx+Ph4ZGZmYujQoRLjNTnd2aVLFyQkJMDPz088durUKZiYmMg0caKrqwtd\nXV3xYxXLZtZIOVQppN27dw8hISE4e/YssrOzsWXLFjg4OCArKwvffPMNPDw8YGtrq6ha1QYDGhGR\naktOTkZOTg5CQ0Ph7OyMxMREBAYGYuHChWjevLnEujU53Tlp0iR4eHhg9erVGDFiBK5evYqIiAiJ\nJ/FEREQgIiICcXFx4rHTp0+jqKgI5ubmePjwIdatW4eCggLMnj27egdMCiFzSEtLS4OHhwdKSkrQ\nqVMnnDt3TryscePGuH79Onbt2sWQJgcMaERE0gqKSmq9uWxBUQm0tap2jVZWVhYeP36M9evXY8uW\nLQgODoaxsTHmz5+PsWPHyrU+W1tbrF+/HsHBwdi2bRuMjIwwa9YseHh4iNfJzs7GrVu3JLbLycnB\nd999hwcPHuCdd95B7969ERQUJBUgqW7JHNK+++47NGjQAFFRUdDS0kLPnj0lljs6OkqkdKo+BjQi\nImlVDUt19ZpJSUnQ0tJCnz594OLiooCqJPXt2xd9+/atcLm/vz/8/f0lxgYOHIiBAwcquDKqKZlP\nPF+4cAHjx49H8+bNy71jxMTEBE+ePJFrceqKAY2ISHUlJyfDwsJC4gY7ouqQOaQVFhZK3aXyqufP\nn/NiQwVhnzQiItWRnJwMa2vrui6D3gIyn+40NzfHpUuXJM5zv+rYsWO8w1MB2CeNiEi1rFu3rq5L\noLeEzFNf7u7uOHDgAH766SfxIyNEIhGysrLw2WefITExERMmTFBYoeqoKnd5EhER0dtF5pm0cePG\nITU1FV988QVWrVoFAPj444+Rn58PQRDg5eWFIUOGKKxQdcM2HEREROqtSn3SAgICMGzYMBw6dAi3\nbt1CaWkpWrdujaFDh6JLly6KqlHtMKARERFRlZ84YGdnBzs7O0XUQv/DgEZERES8HVMJMaARERFR\nlWbS7ty5g59//hl3797Fs2fPIAiCxHKRSIQff/xRrgWqIwY0IiIikjmkHT58GHPnzoWGhgbatm2L\nhg0bSq3zemgj+WCfNCIiIvUjc0hbs2YNzM3Nxc8Go9rBPmlERETqSeZr0h4+fAg3NzcGtFrEPmlE\nRETqS+aQ1rp1azx//lyRtdAr2IaDiEhSYXGpWrwmURmZT3f6+/tj5cqVGDNmDJo1a6bImtQeAxoR\nkbT69TTwQVhirb7mbi/l7wF64sQJBAcHIy0tDc2aNYOnpye8vLwq3SYkJATff/+91Hh8fDxat26t\nqFKpimQOaSkpKWjatCkGDRqE/v37w9jYWOqB6iKRCJ988onci1Q3DGhERCSLq1evwtfXF15eXggO\nDsaVK1fw2WefQUdHp8JnbZcxMTFBVFSUxFjjxo0VWS5VkcwhbePGjeL/3r9/f7nrMKTJBwMaEdHb\nITU1FYGBgbh06RJKS0vx/vvvY+XKlahfv75c9h8eHo5OnTph7ty5AABzc3OkpqZiy5Ytbwxpmpqa\nvM5cyckc0n777TdF1kGvYEAjIlJ9ly9fhre3N7y9vbF06VIkJSVh8eLFaNeuHby9vcXrbdq0CZs3\nb650X9OnT4ePj4/UeGJiIsaMGSMx5uTkhNDQUDx69AgtWlTcounRo0dwcnICAFhaWsLX15ePeFQy\nMoc0ExMTRdZBlWCfNCIi1VJaWoqAgABMnToV06ZNAwCYmZlh3759uHjxokRIc3d3x+DBgyvdn4GB\nQbnjGRkZUrNhTZs2BQA8efKkwpBma2uLoKAgtG3bFjk5Odi5cycmTJiArVu3olevXjIfJylWlZ/d\nCbz8oUhPT4dIJIKJiQmnSxWIfdKIiFTP5cuXcefOHYwfP15iXFtbG6WlkneMGhoawtDQUO41iESi\nCpf16dNH4vtu3brh8ePH2LZtG0OaEqlSSLt06RJWrlyJa9euSYx37NgRAQEBsLe3l2tx6q4qd3ke\nXj6oDiokIqLynDlzBm3atIG+vr7E+LVr1+Dp6SkxVpPTnUZGRsjIyJAYy8zMFC+ris6dO+PIkSNV\n2oYUS+aQ9tdff2HSpEmoV68exo4dCwsLCwiCgLS0NBw4cACTJ0/Gjh07YGtrq8h61QbbcBARqa6k\npCQUFBRIjMXHxyMzMxNDhw6VGK/J6c4uXbogISEBfn5+4rFTp07BxMSk0uvRypOSklLlbUixZA5p\na9euRZMmTbBr1y40b95cYtmMGTPg7u6OdevWYevWrXIvUt0woBERqbbk5GTk5OQgNDQUzs7OSExM\nRGBgIBYuXCj1O7QmpzsnTZoEDw8PrF69GiNGjMDVq1cRERGBRYsWideJiIhAREQE4uLixGOBgYHo\n27cvTE1NkZOTg+joaJw+fRobNmyo3gGTQsgc0sruUnn9hwsAmjdvDjc3N2zZskWuxakrBjQiImmF\nxaW13ly2sLgU9evJ/HAeAEBWVhYeP36M9evXY8uWLQgODoaxsTHmz5+PsWPHyrU+W1tbrF+/HsHB\nweJna8+aNUui/UZ2djZu3bolsV1GRgYWLFiArKws6Ovrw8rKCmFhYXBwcJBrfVQzMoe00tJSaGlp\nVbi8fv36UhdDUvUwoBERSatqWKqr10xKSoKWlhb69OkDFxcXBVQlqW/fvujbt2+Fy/39/eHv7y8x\nFhwcrOCqSB5k/umzsrLCL7/8gpycHKllubm5+OWXX2BtbS3X4tQVAxoRkepKTk6GhYVFpRMbRLKQ\neSbt448/ho+PD0aMGAE3Nze0bdsWIpEI//zzD6Kjo/Ho0SNs2rRJkbWqLfZJIyJSHcnJyZy0ILmQ\nOaT16dMH3333Hb766iusXr1a3H9FEAQYGRnhu+++E3cuJvlhnzQiItWybt26ui6B3hJV6pM2ZMgQ\nDBw4EElJSbh//z6Al08isLGxgaampkIKVGfsk0ZERKS+qvzEAU1NTdjZ2cHOzk4R9dD/sA0HERGR\neqv9W2XojVQhoBWXVO9O3upuR0REpG4qnElr3759pc/9Ko9IJEJycnKNi1J3yh7QAKCepga+PpZW\n5e3m9zNXQDVERERvnwpD2owZM6oc0hQhJCQE33//vdR4fHw8WrduDQC4cuUKAgMDce3aNRgYGGD0\n6NGYOXOmyl4np+wBjYiIiBSvwpD2euO7umRiYoKoqCiJscaNGwMAHj58CC8vLwwcOBBffvkl7ty5\ng8WLF0MQBMydO7cuyq0xBjQiIiKq8o0DdUFTUxNGRkblLtu5cyf09PSwcuVKaGhooF27dnj8+DG+\n+eYb+Pr6okGDBrVcrfyxTxoREZH6kfnGgd27d8PPz6/C5f7+/tizZ49cinrdo0eP4OTkBCcnJ0yb\nNg2JiYniZYmJiejVqxc0NP7/UBwdHZGXl/dWXB/HPmlERETqSeaQtmvXLvEpxvI0bdoUO3fulEtR\nr7K1tUVQUBB++OEHBAcHw8DAABMmTMDp06cBvHxI7OuzbE2bNhUvK09UVBRcXV3h6uqK7Oxsudcs\nL1W5y5OIiIjeLjKf7rx9+zZcXV0rXG5paYmDBw/KpahX9enTR+L7bt264fHjx9i2bRt69epV7jZl\nNzxUdOODm5sb3NzcAKDSY6pLqtCGg4ioNhWXlKKeZu12jqqL1yQqI3NIKykpwYsXLypc/uLFCxQW\nFsqlqDfp3Lkzjhw5AgAwMjKSmjHLzMwE8P8zaqqGAY2ISFp1W//UhCq0DTpx4gSCg4ORlpaGZs2a\nwdPTE15eXgrbjmqPzH8eWFhY4Lfffit3mSAIOHr0KNq2bSu3wiqTkpKCFi1eXizfpUsXnDlzBqWl\n/98k9eTJk9DV1UWHDh1qpR55Y0AjIiJZXL16Fb6+vnB0dERsbCz8/PwQHBz8xsuPqrsd1S6ZQ5q7\nuzsuXbqEOXPmID09XTyenp6OefPm4fLly3B3d5d7gYGBgTh79izu3buHlJQUfP755zh9+jQmTZoE\nAPDw8MB///tfLFmyBKmpqfjtt9+wbt06TJw4UWXv7GRAIyJ6O6SmpmLKlCmwt7eHnZ0d5s2bJ9ez\nTuHh4ejUqRPmzp0Lc3NzuLq6YuLEidiyZYtCtqPaJfPpzjFjxuDatWv46aefcOjQIejq6gIA8vLy\nIAgC3N3dMW7cOLkXmJGRgQULFiArKwv6+vqwsrJCWFgYHBwcAAAtW7ZEaGgoVq1aBVdXVzRs2BDj\nxo3DzJkz5V5LbWFAIyJSfZcvX4a3tze8vb2xdOlSJCUlYfHixWjXrh28vb3F623atAmbN2+udF/T\np0+Hj4+P1HhiYiLGjBkjMebk5ITQ0FA8evRIfNZJXttR7apSn7Rly5ZhyJAhiIuLw507dwAArVu3\nxuDBg9G1a1eFFBgcHPzGdTp37oxdu3Yp5PWVAfukERGpltLSUgQEBGDq1KmYNm0aAMDMzAz79u3D\nxYsXJUKau7s7Bg8eXOn+DAwMyh2vrMPBkydPKgxb1d2OaleVm9l269YN3bp1U0QtVA72SSMiUj2X\nL1/GnTt3MH78eIlxbW1tiWuoAcDQ0BCGhoZyr6G6j3ZUhkdC0ksq8cQBdVWVuzwPLx9UBxUSEVF5\nzpw5gzZt2kBfX19i/Nq1a/D09JQYq8npzso6HFT0pJ6abEe1iyFNSbENBxGR6kpKSkJBQYHEWHx8\nPDIzMzF06FCJ8Zqc7uzSpQsSEhIkngh06tQpmJiYVHrKsrrbUe1iSFNCDGhERKotOTkZOTk5CA0N\nhbOzMxITExEYGIiFCxeiefPmEuvW5HTnpEmT4OHhgdWrV2PEiBG4evUqIiIisGjRIvE6ERERiIiI\nQFxcXJW2o7rHkKaEGNCIiKQVl5TWenPZ6jxxICsrC48fP8b69euxZcsWBAcHw9jYGPPnz8fYsWPl\nWp+trS3Wr1+P4OBgbNu2DUZGRpg1axY8PDzE62RnZ+PWrVtV3o7qHkOaEmJAIyKSVhePZ6rOayYl\nJUFLSwt9+vSBi4uLAqqS1LdvX/Tt27fC5f7+/vD396/ydlT3Kvzps7a2xv79+8XfL1q0CFeuXKmV\notQdAxoRkepKTk6GhYUFtLS06roUUnEVhjRNTU0UFxeLv9+zZw/u3r1bK0WRJPZJIyJSHcnJybC2\ntq7rMugtUOHpzlatWiE2NhZWVlbiW4j//fdf3Lt3r9IdtmrVSr4Vqjn2SSMiUi3r1q2r6xLoLVFh\nSPP29kZAQID4sREikQhBQUEICgqqdIcpKSnyrVCNsU8aERGR+qowpI0ePRq2tra4cOECMjMz8f33\n32PAgAGwsrKqzfrUFttwEBERqbdK7+40NzeHufnL252///57vP/++xg+fHitFKbOGNCIiIhI5hYc\nf//9tyLroFcwoBERAYIg8DmS9FYTBKHS5VXuk5aamopjx44hPT0dAGBqaop+/fqhXbt21auQpDCg\nEZG609DQQElJCerVYztPensVFRVBU1OzwuVV+ulfsWIFIiMjpZLf6tWrMWHCBCxZsqR6VZIEBjQi\nUncNGjTA8+fP0ahRI86m0VtHEAQUFRUhKyurwueyAlUIaeHh4YiIiMCAAQMwdepUWFhYAAD++ecf\nhIaGIjIyEq1atcKkSZNqXj1JYJ80IlI3+vr6yMrKwsOHD+u6FCKF0NTUhIGBAXR1dStcR+aQ9vPP\nP8PR0REhISES4507d8a6devw0UcfITo6miFNztgnjYjUkUgkQpMmTeq6DKI6JfNDye7evVvpM776\n9u37xka3VDVVucuTiIiI3i4yh7SGDRuKbxYoT3p6OvT09ORSFLENBxERkbqTOaQ5OjoiMjISR48e\nlVp29OhR/PTTT+jTp49ci1NXDGhEREQk8zVps2bNwrlz5+Dv7493330Xbdu2hUgkQlpaGu7evYuW\nLVti1qxZiqxVbTCgERERkcwzac2bN8eePXvg5eUFDQ0NnD59GgkJCdDQ0ICXlxdiYmLQrFkzRdaq\nNhjQSNGKS0prZRsiIqq+KvVJMzQ0xPz58zF//nxF1UNgnzRSvHqaGvj6WFqVtpnfz1xB1RARUXlk\nnkmjusM+aUREROqHIU3JsU8aERGRemJIU2Lsk0ZERKS+GNKUFNtwEBERqTeGNCXEgEZEREQMaUqI\nAY2IiIiq1ILjVbm5uTh+/DgePXoEIyMj9O3bFw0bNpRnbWqLAY2IiIiqFdKSk5MxZcoU5ObmwsDA\nANnZ2dDT08PmzZvRuXNnedeodhjQiIiIqFqnO7/66isMHDgQFy5cQEJCAk6ePIl27drhyy+/lHd9\nBPZJIyIiUkeVhrTVq1ejoKBAavzOnTtwc3ODjo4OAKBJkyYYMmQIbt++rZAi1Rn7pBEREamnSkPa\nyZMnMXjwYBw9elRivEOHDtiwYQPu37+PoqIipKSkYOfOnejQoYNCi1U37JNGRESkvioNaTExMZg6\ndSoCAgLw0Ucf4e7duwCAJUuWIC0tDS4uLrC1tYWrqyvy8vKwfPny2qhZLbANBxERkXqr9MYBkUiE\nCRMmYPDgwfjmm28wYsQIeHl5wcfHBwcPHsSlS5fw+PFjNGvWDHZ2dtDS0qqtut9qDGhEREQk092d\njRs3RmBgIMaNG4cvvvgCsbGxWLx4MVxcXBRdn1piQCMiIqIq3d1pb2+PX375BVOmTMHixYvh7e2N\ne/fuKao2tcWARkRERJWGtJKSEmzbtg0eHh4YPXo0vvjiCzx9+hQTJ07E4cOH0bhxYwwfPhzr1q1D\nYWFhbdX81mNAIyIiokpDWnBwMFavXo02bdrgvffeQ3x8PHx8fCAIApo0aYJVq1YhNDQUv//+OwYP\nHozff/+9tupWK+yTRkREpH4qvSZt37598Pb2xieffAIAGDhwIMaPH4+bN2/C3NwcANClSxfExMQg\nIiICCxcuxPnz5xVftRphnzQiIiL1VOlMWnFxMfT09MTfv/POOxAEAUVFRZI70dDAhx9+iLi4OMVU\nqabYJ42IiEh9VTqT1h4GWUQAAA8RSURBVK9fP2zcuBEFBQVo2LAhdu3ahdatW8PCwqLc9Rs3bqyQ\nItUR23AQERGpt0pDWkBAALS0tBAZGYn8/Hx07twZixYtQr161XouO8mIAY2IiIgqTVvvvPMOPv/8\nc3z++ee1VY+UrVu34siRI7h58yYEQUC7du3w8ccfw8nJSbxOTEwMFi1aJLVtWFgYevbsWZvlygUD\nGhERESn9lNgff/yBMWPGoFOnTtDW1sbPP/8MHx8f7NixA127dhWvp6mpiRMnTkhsa2BgUNvlygUD\nGhERESl9SNu6davE9wsWLEBCQgKOHDkiEdIAwMjIqDZLUxgGNCIiIlL6kPa60tJS5ObmolGjRhLj\nJSUl6N+/PwoKCmBmZoYpU6agX79+5e4jKioKUVFRAIDs7GyF11xT7JNGRESkflQupG3atAnPnz/H\nyJEjxWNmZmYICgqClZUV8vPzcejQIfj4+GDFihUYO3as1D7c3Nzg5uYGAHB1da212quDfdKIiIjU\nk0qFtMjISGzevBkbN25Eixb/P3tkb28Pe3t7ie+fPXuGrVu3lhvSVEVV7vI8vHxQHVRIREREilKl\nB6zXpW3btuGbb77Bxo0bZbpj097eHvfv36+FyhSDbTiIiIjUm0rMpK1duxbh4eH44Ycf0L17d5m2\nSUlJkZhtUyUMaERERKT0IW3lypWIiopCcHAwzMzMkJGRAQDQ0dGBvr4+ACAkJAS2trZo06YNCgsL\n8euvv+Lnn3/GkiVL6rL0amNAIyIiIqUPadu3bwcAzJgxQ2J89OjRWLVqFQAgJycHn3/+OTIzM6Gj\no4O2bdtizZo1GDhwYK3XKw8MaERERKT0Ie369etvXGfRokXlPnFAVTGgERERkcrcOKDO2CeNiIhI\n/TCkKTn2SaPKFBaX1nUJRESkIEp/ulOdsU8avUn9ehr4ICyxytvt9uqigGqIiEieOJOmpNiGg4iI\nSL0xpCkhBjQiIiJiSFNCDGhERETEkKaEGNCIiIiIIU0JMaARERERQ5oKYJ80IiIi9cOQpuTYJ42I\niEg9MaQpsarc5UlERERvF4Y0JcU2HEREROqNIU0JMaARERERQ5oSYkAjIiIihjQlxICmnJYvXw6R\nSCTxtXz58roui4iI3lJ8wLoSYkBTTsuXLxcHNUEQ6rocIiJ6y3EmTQWwTxoREZH6YUhTcuyTRkRE\npJ4Y0pQY+6QRERGpL4Y0JcU2HEREROqNIU0JMaARERERQ5oSYkAjIiIihjQlxIBGREREDGlKiAGN\niIiIGNJUAPukERERqR+GNCXHPmlERETqiSFNibFPWh3Kz6/d7YhkVFxSWqvbEVHd4bM7lRTbcNQx\nHR1AJKp4eUXL+ExPUrB6mhr4+lhalbeb389cAdUQkSJxJk0JMaARERERQ5oSYkBTXfmFJdXcrljO\nlRARkarj6U4lxICmunTqa2Lw8rgqf3450ZNrqUIiIlIVnElTQgxoqo2fHxERyQNDmgpgnzTVxs+P\niIiqgyFNybFPmmrj50dERNXFkKbE2CdNtfHzIyKimmBIU1Jsw6Ha+PkREVFNMaQpIf6CV238/IiI\nSB4Y0pQQf8Grtup8fgVF1euvRkREby/2SVNCDGiqrTqfn7aWJmyWHKnyayWtGFDtOqluFRaXon49\n/p1MRBVjSFNCDGiqjZ8fyaJ+PQ18EJZY5e12e3VRQDVEpIz4Z5wKYJ8t1cbPj4iIqoMhTcmxz5by\nWA5A9L//Fv3va/kbtuHnR0RE1cWQpsTYZ0u5LAcgvPa1vJL1+fkREVFNvDUh7cSJExg5ciRsbGzg\n7OyMsLCwui6pRtjGQbXx8yMiopp6K0La1atX4evrC0dHR8TGxsLPzw//1979x1Rd73Ecf4F5IZMa\nmaXT40JQ5oQmGmjqMG1toDA0qOOZomLoxH7pqAw3y5VlRbORDEhDmcboFOqp+Ye2tIa29WMyNxNM\n4ziXNBe/lB96PV4594/muR0Pt/Jw9HvO1+djY4zP+Xw/3/c5n7Hz2vfXZ9OmTaqpqTG6NL/wBR/a\nmL/Q9G/Xf27pdgDwd0xxd2dVVZUSExP14osvSpJiY2N16tQpbd26VTabzeDqbhxf8KGN+QtNkf+6\nQ+nr993w/LVV597qUgHcJkwR0urr65Wdne3Vlpqaqm3btuncuXMaNiy07p7jCz60MX+hy5+AzTPu\nANwsYW632210Ef2VkJCgdevWyWq1etpOnTqljIwMffbZZ3rooYe8+tvtdtntdknS6dOnFRMTc0vr\nvZU6OjoUHR1tdBnwA3MXOCdPnlRXV5dXW1RUlMaOHXvT9mn2+YuOjlZlZaXRZQCmZoojaX8lLCzM\np81qtXoFOjN74okntHv3bqPLgB+Yu9DG/AHoL1PcODB06FC1tLR4tbW2tnpeAwAACDWmCGkTJ07U\n4cOHvdoOHTqkESNGhNz1aAAAAJI0YP369euNLqK/hg8frrKyMrlcLt1///2qq6tTSUmJXnjhBSUm\nJhpdnuESEhKMLgF+Yu5CG/MHoD9MceOAJH3zzTfatGmTnE6nhg4dqkWLFikvL8/osgAAAPximpAG\nAABgJqa4Jg0AAMBsCGkAAABBiJBmQmZbbP528uOPP6qgoEAzZ85UfHy8ysrKjC4J/9BHH30kq9Wq\n5ORkPfzww7LZbKqrqzO6LAAhjJBmMmZbbP52c/HiRcXFxemll17iGX8h5rvvvlN2drZ27NihTz/9\nVBMmTNCKFSt05MgRo0sDEKK4ccBkCgsL1dzcrE8++cTT9s4772j//v06ePCggZXhRs2aNUs5OTla\nuXKl0aXAT5mZmZo2bZpeeeUVo0sBEII4kmYy9fX1mj59uldbamqqmpubde4ci3oDt0pvb696enpM\nvX4ngJuLkGYyLS0tPqfJ7rvvPknS77//bkRJwG2poqJCnZ2dysrKMroUACHK9Aus43/6WmweQOBV\nV1frww8/VHl5OUvTAfAbIc1kWGweMFZlZaU2b96s8vJyTZ061ehyAIQwTneaDIvNA8YpKSlRaWmp\ntmzZQkAD0G+ENJNZvHixjh07pvfff19NTU1yOBz6+OOPtWzZMqNLwz/Q09OjxsZGNTY2yuVyqbW1\nVY2NjTpz5ozRpeFvvPnmm6qsrFRxcbFiYmLU0tKilpYWdXV1GV0agBDFIzhMiMXmQ9f333+vRYsW\n+bSnpKRo586dBlSEfyo+Pr7P9nnz5untt9++xdUAMANCGgAAQBDidCcAAEAQIqQBAAAEIUIaAABA\nECKkAQAABCFCGgAAQBAipAEAAAQhQhoAAEAQYu1O4AZd/8DZsLAwRUVFKSEhQfn5+Zo2bZqB1QEA\nzIKQBvgpJydHKSkp6u3t1dmzZ2W325Wfn6/KykrWbQQA9BshDfDThAkTlJWV5fk7LS1NGRkZqqqq\nIqQBAPqNa9KAABkzZoyio6O9FkNvbm7WG2+8oTlz5igpKUlJSUlasGCBDh065LN9bm6uUlNT9dtv\nv2nlypVKSkpSSkqKXn31VblcLp/+DodDaWlpSkxMVHp6uhwOhzZv3tznGpInTpzQM888o8mTJysx\nMVGZmZnatWtXYD8AAEBAcSQNCJDOzk51dnbqwQcf9LQdO3ZM3377rR577DFZLBZ1dXXpiy++0PLl\ny7V9+3ZNmTLFa4zLly9ryZIlSk5O1ssvv6yjR4/Kbrfr3nvv1apVqzz9HA6H1qxZo3HjxqmwsFDd\n3d1699139cADD/jUVV9fr6VLl8pisejpp5/WXXfdpa+//lpr165VR0eH8vPzb9pnAgDwHyEN8FNP\nT4/a29vldrt19uxZlZSU6OrVq5o9e7anz4wZM5SWlua13eLFi5WVlaWtW7f6hLTz58+roKBAS5Ys\nkSTZbDZduHBBdrvdE9KuXLmi4uJijRo1SjU1NbrzzjslSbNnz1ZmZqbXeG63W+vWrVN8fLyqq6t1\nxx1//MsvWLBAzz77rEpLS2W1WhUVFRXQzwYA0H+c7gT8tHHjRj3yyCOaOnWqnnrqKR05ckTPP/+8\ncnNzPX2uBSjpj6NkHR0d6u7uVkpKin766SefMcPDwzV//nyvtilTpqi9vV3d3d2SpOPHj6u1tVVP\nPvmk1/ijR4/W9OnTvbb9+eef9csvvygjI0OdnZ1qb2/3/MyYMUOXLl3S0aNHA/J5AAACiyNpgJ/y\n8vKUmpqqy5cv64cfflBVVZUuXryosLAwT58rV66orKxMn3/+uZqbm722/3O/a4YMGaLIyEivtrvv\nvluSdOHCBQ0ePNgzzp9Pq15zfZvT6ZQkbdiwQRs2bOjzfbS1tf31GwUAGIKQBvgpNjbWcxfnzJkz\nNXjwYH3wwQeaNGmSZs2aJUl66623VFNTI5vNpkmTJumee+7RgAEDtGvXLu3du9dnzPDw/39w2+12\ne/3uK+Rde+36v5977jlNnDixz3Hj4uL+7q0CAAxASAMCJD8/X3a7XcXFxXr00UcVHh6uvXv3au7c\nuXrttde8+tbW1vq9n5EjR0qSTp8+7fPan+8slaRRo0ZJkiIiIngsCACEGK5JAwIkIiJCeXl5cjqd\n2rdvn6Q/joz19vZ69XM6nfrqq6/83s/48eM1ZMgQ1dbW6tKlS17jHj582KdvTEyMduzYofb2dp+x\n+moDAAQHjqQBAWS1WlVRUaGKigqlp6fr8ccfV21trSIjI5WQkKBff/1VNTU1io2NVUNDg1/7GDhw\noAoLC7V27VrZbDbNnTtXPT09qq6u1tixY73GDQ8P18aNG7V06VLNmTNHOTk5slgs6ujoUENDgw4c\nONDnDQwAAOMR0oAAGjRokBYuXKjS0lIdPHhQRUVFioiI0JdffimHw6HRo0fr9ddfV1NTk98hTZKy\ns7MlSVu2bNF7770ni8WiNWvW6MSJE2pqavLqm5SUpNraWpWXl2vPnj06f/68oqOjFRcXp6Kion69\nXwDAzRPmvv5KYwAhq6CgQE6nU/v37ze6FABAP3FNGhCCXC6Xz52cTU1Nqqur0+TJkw2qCgAQSJzu\nBEJQQ0ODioqKlJaWpuHDh+vMmTOy2+2KjIzUsmXLjC4PABAAhDQgBA0bNkxjxozR7t271dbWpkGD\nBik5OVmrV6+WxWIxujwAQABwTRoAAEAQ4po0AACAIERIAwAACEKENAAAgCBESAMAAAhChDQAAIAg\n9F9mzxle3QkRjQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GmpoaateujU8//VTiOmJiYjBhwgSZMb9v5syZZRpBlOXrr7/GjBkzMHjwYFhYWKBLly7o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\ngg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ffPMNmjdvjlOnTmH69OmoW7cuXF1dBc9RRiKRYPv27Vi2bJnCts6dO2PlypUA\ngJycHERFRWHKlCk4fPgw3nnnnXJ/RpXx559/Qk9PD+7u7rIxIyMjQa+1srJCly5d8NNPP2H27NkV\nen9e7tQw9kkjIqq4mhbQUlJSMH78eDg7O8PJyQkzZ85Efn6+WvYNAJGRkejQoQNmzJgBW1tbeHh4\nYMyYMdi4cWOpr2vQoAEsLCxkX+fOnUNhYSE++eQTAK9CVGxsLKZNm4bu3bvjnXfegY+PD3r27IkN\nGzYInqNKfHw8JBIJunfvrrDNwMBAVpetrS2++uorFBQU4NatW3Lztm7digEDBqBDhw744IMPsG7d\nOhQWvrokfunSJXh5ecHZ2RnOzs4YOnQo4uPjAbw6W/fbb79h7969sLe3h729Pc6fP69Qx5w5czBr\n1iwUFxfL5pWMl1zuLGtf/fr1w/79+0v9LErDM2kaxj5pREQVV5MC2pUrV+Dn5wc/Pz8sWLAASUlJ\nmDdvHtq0aQM/Pz/ZvPXr15cZaiZNmgR/f3+F8cTERAwfPlxuzM3NDeHh4Xj8+DEaNxb2D/8dO3ag\nd+/esLKyAgAUFBSgqKgIhoaGcvOMjIwQHx+PgoICQXMMDAyUvt+FCxfQrl071KpVegzJz8/Hrl27\nULt2bbz77ruy8dWrVyMmJgbz5s1D27ZtcefOHSxatAgSiQSBgYEICAjAsGHDZJcgU1JSYGxsDAAI\nCgrC/fv3YWFhgaCgIACAmZmZwnsHBQWhXbt2CA0NxalTp5TWV9a+nJyckJmZidTUVNja2pZ6rMow\npGmYrqyBICLShpoS0IqLixEUFIQJEyZg4sSJAAAbGxvs378fly5dkgtpXl5eGDhwYKn7UxYiACAj\nIwMWFhZyY40aNQIAPH36VFBIu379Om7cuIFp06bJxkxMTODi4oJ169ahbdu2aNq0KeLj43H8+HEU\nFBQgOzsblpaWguYok56eLguEb7pw4QKcnZ0BvLoMa2xsjNDQUFhbW8vGNm3ahNWrV8PNzQ0A0Lx5\nc3z55ZdYvHgxfH198ffff6NPnz5o2bIlAMj+FwBMTU1hYGAAIyMjhc/udaampjA1NQUAlfPK2lfJ\n53///n2GtJpAF9ZAEBFVF9UxoAGvzqKlpaVh1KhRcuOGhoZyi84BwNzcHObm5mp77xIikajsSQCi\no6PRrFkz9OjRQ258+fLlCAoKgru7O/T09GBjY4MRI0YgKioK+vr6gucoI5FIZAHoTY6OjrK7Il+8\neIGEhATMmTMHpqamcHV1RUpKCvLy8vD555/LHWNRUREkEgmKioowYsQITJgwAV26dMF7770Hd3d3\ntGrVStDnoU61a9cGAOTl5VWWKHMPAAAgAElEQVTo9QxpWsaARkRUMZq4iaCizp49i5YtWyoEkRs3\nbsDHx0durDKXOy0sLJCRkSE3lpmZKdtWltzcXBw6dAiTJ09WCHXW1taIjIzEy5cvkZOTAysrKyxb\ntgwmJiaoX7++4DnK1K9fH3///bfSbUZGRmjRooXs+3bt2uHcuXNYv349XF1dIZVKAQCrVq2SO0NW\nwszMDIsXL8ann36KM2fO4MyZM1i1ahUWLFgALy+vMj8TdSo5xgYNGlTo9QxpWsSARkRUMZq6y7Oi\nkpKSIJFI5Mbi4uKQmZmJwYMHy41X5nKni4sLEhISMHXqVNlYfHw8rK2tBV3q3LdvHwoKCuDh4aFy\njrGxMYyNjZGfn49ffvlFdtasvHNe1759e0RFRZVZXwl9fX28fPkSwKs2IYaGhrh//36pbTns7Oxg\nZ2cHX19fLFy4EDt37pSFNAMDA7m7WyujtH3dvn0b+vr6cuvpyoMhTUsY0IiIKqYm9ElLTk5Gbm4u\nwsPD0adPHyQmJiIkJARz5sxRWItVmcudY8eOhbe3N1asWIGhQ4fi+vXriIqKwty5c2VzoqKiEBUV\nhdjYWIXXR0dHo2/fvrJ1bK87c+YMCgoKYGtri0ePHiEsLAwSiQTTp08v1xxl3NzcsHTpUjx69AhN\nmjSR21ZQUCA7O/jy5UvEx8cjISEBgYGBAIC6deti0qRJEIvFAIBu3bqhqKgIt2/fRnJyMkaOHImd\nO3eid+/eaNKkCZ4+fYrff/9dLig1a9YM58+fx71792BiYiJbW1YRpe3rwoUL6NSpE0xMTCq0b4Y0\nLWBAIyKqmJrQJy0rKwtPnjzBmjVrsHHjRojFYjRt2hSzZs3CiBEjKrRPVRwdHbFmzRqIxWJs3rwZ\nFhYWmDZtmlyPtOzsbNy9e1fhtVeuXMGtW7fkAt3rcnNz8f333+Phw4eoW7cuevTogdDQULmQKWSO\nMra2tnjvvfewb98+hcu4ly5dkq2PMzIyQrNmzfDVV1/JNeidMmUKLC0tERUVhdDQUBgZGaFly5YY\nNmwYjI2NkZaWhunTpyMrKwvm5ubo1auXXK+y8ePH4/bt2/joo4/w4sULbNmyBe+//36pNauial9S\nqRQHDhwoM7CWRiQtubj7lvLw8EBMTEzldyRkgaZUioHBsWX+B+JI8AA4zD8q6G2TFvcrb6VERNXe\nw4cP0bRpU7mxvPwiGNVWvRi9KuTlF8KodvnOZ5w+fRoBAQG4fPlyhc/OvA0uXbqEadOmIS4uTtYe\nQ5ccPnwY69atw88//1zqTRTKftdLsJmthrFPGhFRxWg6oL16z/JfcEpOTkbr1q0Z0MrQuXNnTJ06\nFenp6doupUrk5+fju+++KzWglYUhTcOEnGIvj/zC4rInlWMeERFVTnJyMtq1a6ftMmoET09PtGnT\nRttlVImPP/4YHTp0qNQ+qv2atLIeAhsTE6P0enpERAS6deumiRLLRd1rIGrX0sMnEYllztvt61Ku\n/RIRUcWEhYVpuwTSEdU+pAl5CKy+vr7CIxtU3a5c3fAmAiIiIlKm2oe0NxvA7dy5U+4hsCWENO2r\nbhjQiIiISJVqH9Le9OZDYIFXj4Lo27cvJBIJbGxsMH78ePTu3VuLVZaNAY2IiIhKU6NCmrKHwNrY\n2CA0NBT29vbIy8vD4cOH4e/vj8WLF6vsRxMdHY3o6GgAr/rHaBoDGhEREZWlRoU0ZQ+BdXZ2hrOz\ns9z3f//9NzZt2qQypHl6esLT0xMASn0URlWoymfFERERke6oMS04Sh4C6+npqfAQ2Dc5OzsrvSO0\nOmCfNCIiIhKixoQ0IQ+BLXHz5k1BD5bVBnX3SSMiIiLdVGMud6p6COzq1avh6OiIli1bIj8/H7/8\n8gt27dqF+fPna6nS0lXVs+KIiIhIt9SIkFbaQ2Bzc3Px9ddfIzMzE0ZGRmjVqhVWrlyJ/v37a6HS\n8mNAIyIiImVqREjr2LEjbt26pXTb3LlzlYa3moABjYiIiFQRvCbt/PnziIiIkBvbu3cv3Nzc0LFj\nRyxYsACFhYVqL1BXMaAREZWPpKCo7Ek68J5EJQSfSVu7di3Mzc1l39+5cwcLFixA8+bNYWdnh927\nd8PW1hbjxo2rijp1CgMaEVH5GRrow2H+UY2+Z9Lifhp9v4o4deoUxGIxUlNTYWlpCR8fH/j6+pb6\nmhcvXmDt2rU4cuQInj59ipYtW2LKlCkYMGCAhqomIQSfSfvvf/8LJycn2fcHDx6EoaEhdu7ciU2b\nNmHIkCGIiYmpkiJ1CfukERGRuly/fh0BAQFwdXXFvn37MHXqVIjFYmzfvr3U1y1YsACxsbH45ptv\ncOjQIYwcORLTp09HfHy8hionIQSHtJycHLmHlp89exbdunWDqakpAOC9995Denq6+ivUMeyTRkT0\n9khJScH48ePh7OwMJycnzJw5E/n5+Wrbf2RkJDp06IAZM2bA1tYWHh4eGDNmDDZu3KjyNRKJBLGx\nsZg2bRq6d++Od955Bz4+PujZsyc2bNigttqo8gSHNAsLC9y7dw8A8NdffyEpKQldunSRbX/+/Dn0\n9GpM2zWtYZ80IqK3w5UrVzB69Gh069YNMTExWLx4MWJjYxEZGSk3b/369bKn56j6Wr9+vdL3SExM\nlHsKDwC4ubnhwYMHePxY+XKagoICFBUVwdDQUG7cyMgIV65cQUFBQcUPmtRK8Jq0Hj16YNu2bTAz\nM8OFCxcAAH379pVtT01NRZMmTdRfoY5hnzQiIt1XXFyMoKAgTJgwARMnTgTw6lnT+/fvx6VLl+Dn\n5yeb6+XlhYEDB5a6v9evZL0uIyMDFhYWcmMl/USfPn2qtLG7iYkJXFxcsG7dOrRt2xZNmzZFfHw8\njh8/joKCAmRnZ8PS0rJcx0tVQ3BI+/LLL3Hnzh0sW7YMBgYGmDVrluyHL5FI8Msvv+Cjjz6qskJ1\nFQMaEZHuuXLlCtLS0jBq1Ci5cUNDQxQXF8uNmZuby92Ypy6lPUJx+fLlCAoKgru7O/T09GBjY4MR\nI0YgKioK+vr6aq+FKkZwSGvQoAGioqKQm5sLQ0NDGBgYyLZJpVJs2bKl2j6KqbpiQCMi0k1nz55F\ny5YtZeu2S9y4cQM+Pj5yY+vXry9zLdikSZPg7++vMG5hYYGMjAy5sczMTNk2VaytrREZGYmXL18i\nJycHVlZWWLZsGUxMTFC/fv1SayHNKXczWxMTE4UxIyMjtG3bVi0FvS0Y0IiIdFdSUhIkEoncWFxc\nHDIzMzF48GC58cpc7nRxcUFCQgKmTp0qG4uPj4e1tbWgEyfGxsYwNjaWPVax5MwaVQ/lCmn379/H\n6tWr8dtvvyE7OxsbN25E165dkZWVheXLl8Pb2xuOjo5VVavOYEAjItJtycnJyM3NRXh4OPr06YPE\nxESEhIRgzpw5sLKykptbmcudY8eOhbe3N1asWIGhQ4fi+vXriIqKknsST1RUFKKiohAbGysbO3Pm\nDAoKCmBra4tHjx4hLCwMEokE06dPr9gBU5UQHNJSU1Ph7e2NoqIidOjQAefPn5dta9CgAW7duoUd\nO3YwpJWBfdKIiCpGUlCk8eaykoIiGBqUb41WVlYWnjx5gjVr1mDjxo0Qi8Vo2rQpZs2ahREjRqi1\nPkdHR6xZswZisRibN2+GhYUFpk2bBm9vb9mc7Oxs3L17V+51ubm5+P777/Hw4UPUrVsXPXr0QGho\nqEKAJO0SHNK+//571KlTB9HR0TAwMEC3bt3ktru6usqldFKOfdKIiCqmvGFJW++ZlJQEAwMD9OzZ\nE+7u7lVQlbxevXqhV69eKrcHBgYiMDBQbqx///7o379/FVdGlSX4wvPFixcxatQoWFlZKb1jxNra\nGk+fPlVrcbqIfdKIiHRbcnIyWrduLXeDHVFFCA5p+fn5CnepvC4nJ4eLDQVgnzQiIt2WnJyMdu3a\nabsM0gGCL3fa2tri8uXLcte5X3fixAne4VkBDGhERLolLCxM2yWQjhB86svLywsHDx7ETz/9JHtk\nhEgkQlZWFhYtWoTExESMHj26ygrVRQxoREREpIrgM2kjR45ESkoKvvnmGyxduhQAMHnyZOTl5UEq\nlcLX1xeDBg2qskJ1DQMaERERlaZcfdKCgoIwZMgQHD58GHfv3kVxcTFatGiBwYMHw8XFpapq1DkM\naERERFSWcj9xwMnJCU5OTlVRy1uBfdKIiIhICN6OqWHsk0ZERERClOtMWlpaGnbt2oV79+7h77//\nhlQqldsuEonwn//8R60F6hohfdKOBA/QQmVERERUnQgOaUeOHMGMGTOgp6eHVq1aoV69egpz3gxt\npIh90oiIiEgIwSFt5cqVsLW1lT0bjNSDAY2IiIiUEbwm7dGjR/D09GRAUyMGNCIiIlJFcEhr0aIF\ncnJyqrKWtwoDGhFR+eQXFr8V70lUQvDlzsDAQCxZsgTDhw+HpaVlVdak8xjQiIjKr3YtPXwSkajR\n99ztW/17gJ46dQpisRipqamwtLSEj48PfH19S33N6tWr8cMPPyiMx8XFoUWLFlVVKpWT4JB28+ZN\nNGrUCAMGDEDfvn3RtGlThQeqi0QifP7552ovUpewTxoREanL9evXERAQAF9fX4jFYly9ehWLFi2C\nkZGRymdtl7C2tkZ0dLTcWIMGDaqyXConwSFt3bp1sv/7wIEDSucwpJWNfdKIiN4eKSkpCAkJweXL\nl1FcXIwPPvgAS5YsQe3atdWy/8jISHTo0AEzZswAANja2iIlJQUbN24sM6Tp6+tznXk1JzikHT9+\nvCrreGuwTxoR0dvhypUr8PPzg5+fHxYsWICkpCTMmzcPbdq0gZ+fn2ze+vXrsWHDhlL3NWnSJPj7\n+yuMJyYmYvjw4XJjbm5uCA8Px+PHj9G4seqrM48fP4abmxsAwM7ODgEBAXzEYzUjOKRZW1tXZR1v\nDfZJIyLSfcXFxQgKCsKECRMwceJEAICNjQ3279+PS5cuyYU0Ly8vDBw4sNT9mZmZKR3PyMhQOBvW\nqFEjAMDTp09VhjRHR0eEhoaiVatWyM3Nxfbt2zF69Ghs2rQJ3bt3F3ycVLXK/exO4NUvRXp6OkQi\nEaytrXm6tBIY0IiIdM+VK1eQlpaGUaNGyY0bGhqiuFj+jlFzc3OYm5urvQaRSKRyW8+ePeW+79y5\nM548eYLNmzczpFUj5Qpply9fxpIlS3Djxg258fbt2yMoKAjOzs5qLU7XMaAREemms2fPomXLljA1\nNZUbv3HjBnx8fOTGKnO508LCAhkZGXJjmZmZsm3l0bFjRxw9erRcr6GqJTikXbt2DWPHjkWtWrUw\nYsQItG7dGlKpFKmpqTh48CDGjRuHrVu3wtHRsSrr1RkMaEREuispKQkSiURuLC4uDpmZmRg8eLDc\neGUud7q4uCAhIQFTp06VjcXHx8Pa2rrU9WjK3Lx5s9yvoaolOKStWrUKDRs2xI4dO2BlZSW3bcqU\nKfDy8kJYWBg2bdqk9iJ1DQMaEZFuS05ORm5uLsLDw9GnTx8kJiYiJCQEc+bMUfgbWpnLnWPHjoW3\ntzdWrFiBoUOH4vr164iKisLcuXNlc6KiohAVFYXY2FjZWEhICHr16oVmzZohNzcXO3fuxJkzZ7B2\n7dqKHTBVCcEhreQulTd/uQDAysoKnp6e2Lhxo1qL00Xsk0ZEVDH5hcUaby6bX1iM2rUEP5wHAJCV\nlYUnT55gzZo12LhxI8RiMZo2bYpZs2ZhxIgRaq3P0dERa9asgVgslj1be9q0aXLtN7Kzs3H37l25\n12VkZGD27NnIysqCqakp7O3tERERga5du6q1PqocwSGtuLgYBgYGKrfXrl1bYTEkKWKfNCKiiilv\nWNLWeyYlJcHAwAA9e/aEu7t7FVQlr1evXujVq5fK7YGBgQgMDJQbE4vFVVwVqYPg3z57e3vs2bMH\nubm5CtueP3+OPXv2oF27dmotThcJ6ZNWFQqLhAfo8swlIiJ5ycnJaN26daknNoiEEHwmbfLkyfD3\n98fQoUPh6emJVq1aQSQS4b///S927tyJx48fY/369VVZq07QVp+0Wvp6WHYiVdDcWb1tq6QGIqK3\nQXJyMk9akFoIDmk9e/bE999/j++++w4rVqyQ9V+RSqWwsLDA999/L+tcTMLxJgIiIt0SFham7RJI\nR5SrT9qgQYPQv39/JCUl4cGDBwBePYnAwcEB+vr6VVKgLmNAIyIiIlXK/cQBfX19ODk5wcnJqSrq\neWswoBEREVFpNH+rDDGgERERUZlUnklr27Ztqc/9UkYkEiE5ObnSReky9kkjIiIiIVSGtClTppQ7\npFWF1atX44cfflAYj4uLQ4sWLQAAV69eRUhICG7cuAEzMzMMGzYMX375ZbVcJ8c+aURERCSEypD2\nZuM7bbK2tkZ0dLTcWIMGDQAAjx49gq+vL/r3749vv/0WaWlpmDdvHqRSKWbMmKGNckslpE/akeAB\nWqiMiIiIqpNy3zigDfr6+rCwsFC6bfv27TAxMcGSJUugp6eHNm3a4MmTJ1i+fDkCAgJQp04dDVdb\nOm31SSMiIqKaRfCNA7t378bUqVNVbg8MDMTevXvVUtSbHj9+DDc3N7i5uWHixIlITEyUbUtMTET3\n7t2hp/f/h+Lq6oqXL1/WiPVxDGhERESkjOCQtmPHDtklRmUaNWqE7du3q6Wo1zk6OiI0NBQ//vgj\nxGIxzMzMMHr0aJw5cwbAq4fEvnmWrVGjRrJtykRHR8PDwwMeHh7Izs5We81CMaARERGRKoIvd/75\n55/w8PBQud3Ozg6HDh1SS1Gv69mzp9z3nTt3xpMnT7B582Z0795d6WtKbnhQdeODp6cnPD09AaDU\nY6pKDGhEROVTWFSMWvqa7RyljfckKiE4pBUVFeHFixcqt7948QL5+flqKaosHTt2xNGjRwEAFhYW\nCmfMMjMzAfz/GbXqhgGNiKj8yvMMYnWpCc8yPnXqFMRiMVJTU2FpaQkfHx/4+vpW2etIcwT/86B1\n69Y4fvy40m1SqRTHjh1Dq1at1FZYaW7evInGjV/1E3NxccHZs2dRXFws23769GkYGxvj3Xff1Ug9\n5cE+aUREpC7Xr19HQEAAXF1dsW/fPkydOhVisbjM5UcVfR1pluCQ5uXlhcuXL+Orr75Cenq6bDw9\nPR0zZ87ElStX4OXlpfYCQ0JC8Ntvv+H+/fu4efMmvv76a5w5cwZjx44FAHh7e+Off/7B/PnzkZKS\nguPHjyMsLAxjxoypdnd2AuyTRkT0NklJScH48ePh7OwMJycnzJw5U61XnSIjI9GhQwfMmDEDtra2\n8PDwwJgxY7Bx48YqeR1pluDLncOHD8eNGzfw008/4fDhwzA2NgYAvHz5ElKpFF5eXhg5cqTaC8zI\nyMDs2bORlZUFU1NT2NvbIyIiAl27dgUANGnSBOHh4Vi6dCk8PDxQr149jBw5El9++aXaa1EH9kkj\nIno7XLlyBX5+fvDz88OCBQuQlJSEefPmoU2bNvDz85PNW79+PTZs2FDqviZNmgR/f3+F8cTERAwf\nPlxuzM3NDeHh4Xj8+LHsqpO6XkeaVa4+aQsXLsSgQYMQGxuLtLQ0AECLFi0wcOBAdOrUqUoKFIvF\nZc7p2LEjduzYUSXvr27sk0ZEpPuKi4sRFBSECRMmYOLEiQAAGxsb7N+/H5cuXZILaV5eXhg4cGCp\n+zMzM1M6XlqHg6dPn6oMWxV9HWlWuZvZdu7cGZ07d66KWt5KDGhERLrnypUrSEtLw6hRo+TGDQ0N\n5dZQA4C5uTnMzc3VXkNFH+1YHR4JSa/UiCcO6CoGNCIi3XT27Fm0bNkSpqamcuM3btyAj4+P3Fhl\nLneW1uFA1ZN6KvM60iyGNC1hQCMi0l1JSUmQSCRyY3FxccjMzMTgwYPlxitzudPFxQUJCQlyTwSK\nj4+HtbV1qZcsK/o60iyGNC1gQCMi0m3JycnIzc1FeHg4+vTpg8TERISEhGDOnDmwsrKSm1uZy51j\nx46Ft7c3VqxYgaFDh+L69euIiorC3LlzZXOioqIQFRWF2NjYcr2OtI8hTcPYJ42IqGIKi4o13ly2\nIk8cyMrKwpMnT7BmzRps3LgRYrEYTZs2xaxZszBixAi11ufo6Ig1a9ZALBZj8+bNsLCwwLRp0+Dt\n7S2bk52djbt375b7daR9DGkaxj5pREQVo43HM1XkPZOSkmBgYICePXvC3d29CqqS16tXL/Tq1Uvl\n9sDAQAQGBpb7daR9Kn/72rVrhwMHDsi+nzt3Lq5evaqRonSZkD5pRERUcyUnJ6N169YwMDDQdilU\nw6kMafr6+igsLJR9v3fvXty7d08jReky9kkjItJtycnJaNeunbbLIB2g8nJn8+bNsW/fPtjb28tu\nIX727Bnu379f6g6bN2+u3gp1HAMaEZFuCQsL03YJpCNUhjQ/Pz8EBQXJHhshEokQGhqK0NDQUnd4\n8+ZN9VaowxjQiIiISBWVIW3YsGFwdHTExYsXkZmZiR9++AH9+vWDvb29JuvTWQxoREREVJpS7+60\ntbWFre2r251/+OEHfPDBB/jwww81UpguY0AjIiKisghuwfHHH39UZR1vDfZJIyISRiqV8jmSpNOk\nUmmp28vdJy0lJQUnTpxAeno6AKBZs2bo3bs32rRpU7EK3zLsk0ZEVDY9PT0UFRWhVi228yTdVVBQ\nAH19fZXby/Xbv3jxYmzbtk0h+a1YsQKjR4/G/PnzK1blW0RIn7QjwQO0UBkRUfVRp04d5OTkoH79\n+jybRjpHKpWioKAAWVlZKp/LCpQjpEVGRiIqKgr9+vXDhAkT0Lp1awDAf//7X4SHh2Pbtm1o3rw5\nxo4dW/nqdRj7pBERlc3U1BRZWVl49OiRtkshqhL6+vowMzODsbGxyjmCQ9quXbvg6uqK1atXy413\n7NgRYWFh+Oyzz7Bz506GtHJiQCMiUiQSidCwYUNtl0GkVYIfSnbv3r1Sn/HVq1evMhvdkjwGNCIi\nIlJFcEirV6+e7GYBZdLT02FiYqKWot4GDGg1W2FRcZXMJSIiKiH4cqerqyu2bduGTp06wd3dXW7b\nsWPH8NNPP2HQoEFqL1AXMaDVfLX09bDsRKqgubN621ZxNUREpIsEh7Rp06bh/PnzCAwMxDvvvINW\nrVpBJBIhNTUV9+7dQ5MmTTBt2rSqrFUnsE8aERERCSH4cqeVlRX27t0LX19f6Onp4cyZM0hISICe\nnh58fX0RExMDS0vLqqxVJ7BPGhEREQlRrj5p5ubmmDVrFmbNmlVV9eg89kkjIiIiIQSfSSP1YJ80\nIiIiEoIhTcsY0IiIiEgZhjQtYkAjIiIiVRjStIQBjYiIiErDkKYFDGhERERUFoY0DWOfNCIiIhKi\nXC04Xvf8+XOcPHkSjx8/hoWFBXr16oV69eqpszadxD5pREREJESFQlpycjLGjx+P58+fw8zMDNnZ\n2TAxMcGGDRvQsWNHddeoU9gnjYiIiISo0OXO7777Dv3798fFixeRkJCA06dPo02bNvj222/VXZ/O\nYZ80IiIiEqLUkLZixQpIJBKF8bS0NHh6esLIyAgA0LBhQwwaNAh//vlnlRSpyxjQiIiISJlSQ9rp\n06cxcOBAHDt2TG783Xffxdq1a/HgwQMUFBTg5s2b2L59O959990qLVbXMKARERGRKqWGtJiYGEyY\nMAFBQUH47LPPcO/ePQDA/PnzkZqaCnd3dzg6OsLDwwMvX75EcHCwJmrWCQxoREREVJpSbxwQiUQY\nPXo0Bg4ciOXLl2Po0KHw9fWFv78/Dh06hMuXL+PJkyewtLSEk5MTDAwMNFV3jcaARkRERGURdHdn\ngwYNEBISgpEjR+Kbb77Bvn37MG/ePLi7u1d1fTqHfdKIiIhIiHLd3ens7Iw9e/Zg/PjxmDdvHvz8\n/HD//v2qqk0nsU8aERERCVFqSCsqKsLmzZvh7e2NYcOG4ZtvvsFff/2FMWPG4MiRI2jQoAE+/PBD\nhIWFIT8/X1M112hC+qQRERERlRrSxGIxVqxYgZYtW+L9999HXFwc/P39IZVK0bBhQyxduhTh4eH4\n9ddfMXDgQPz666+aqrvGYp80IiIiEqLUNWn79++Hn58fPv/8cwBA//79MWrUKNy5cwe2trYAABcX\nF8TExCAqKgpz5szBhQsXqr5qHcKARkRERMqUeiatsLAQJiYmsu/r1q0LqVSKgoIC+Z3o6eHTTz9F\nbGxs1VSpoxjQiIiISJVSz6T17t0b69atg0QiQb169bBjxw60aNECrVu3Vjq/QYMGVVKkLmJAIyIi\notKUGtKCgoJgYGCAbdu2IS8vDx07dsTcuXNRq1aFnstO/8OARkRERGUpNW3VrVsXX3/9Nb7++mtN\n1aNg06ZNOHr0KO7cuQOpVIo2bdpg8uTJcHNzk82JiYnB3LlzFV4bERGBbt26abLcMrFPGhEREQlR\n7U+JnTt3DsOHD0eHDh1gaGiIXbt2wd/fH1u3bkWnTp1k8/T19XHq1Cm515qZmWm63DKxTxoREREJ\nUe1D2qZNm+S+nz17NhISEnD06FG5kAYAFhYWmiytQoT0STsSPEALlREREVF1Uu1D2puKi4vx/Plz\n1K9fX268qKgIffv2hUQigY2NDcaPH4/evXsr3Ud0dDSio6MBANnZ2VVe8+vYJ42IiIiEqHEhbf36\n9cjJycFHH30kG7OxsUFoaCjs7e2Rl5eHw4cPw9/fH4sXL8aIESMU9uHp6QlPT08AgIeHh8ZqV4YB\njYiIiJSpUSFt27Zt2LBhA9atW4fGjf9/gb2zszOcnZ3lvv/777+xadMmpSGtumBAIyIiIlXK9YB1\nbdq8eTOWL1+OdevWCbpj09nZGQ8ePNBAZRXDgEZERESlqRFn0latWoXIyEj8+OOPeO+99wS95ubN\nm3Jn26oTBjQiIiIqS7UPaUuWLEF0dDTEYjFsbGyQkZEBADAyMoKpqSkAYPXq1XB0dETLli2Rn5+P\nX375Bbt27cL8+fO1WeaDW0kAAA5USURBVLpS7JNGREREQlT7kLZlyxYAwJQpU+TGhw0bhqVLlwIA\ncnNz8fXXXyMzMxNGRkZo1aoVVq5cif79+2u83rKwTxoREREJUe1D2q1bt8qcM3fuXKVPHKiO2CeN\niIiIhKgxNw7oCvZJIyIiIiEY0rSMAY2IiIiUYUjTIga06ie/sFjbJRAREQGoAWvSdBUDWvVUu5Ye\nPolILHPebl8XDVRDRERvM55J0wIGNCIiIioLQ5qGsU8aERERCcGQpmHsk0ZERERCMKRpmJA+aURE\nREQMaRrGPmlEREQkBEOaljGgERERkTIMaVrEgEZERESqMKRpCQMaERERlYYhTQsY0IiIiKgsDGka\nxj5pREREJARDmoaxTxoREREJwZCmYeyTRkREREIwpGkY+6QRERGREAxpWsaARkRERMowpGkRAxoR\nERGpwpCmJQxoZQsODoZIJJL7Cg4O1nZZREREGlFL2wW8jRjQhAkODpYFNalUqu1yiIiINIpn0jSM\nfdKIiIhICIY0DWOfNCIiIhKCIU3D2CeNiIiIhGBI0zD2SSMiIiIhGNK0jAGNiIiIlGFI0yIGNCIi\nIlKFIU1LGNCIiIioNAxpWsCAph55+UUC5xVWcSVERETqx2a2GsY+aepjVFsfJiMj5caUfb65O8dp\nvjgiIqJK4pk0DWOftDLk5VX4pTxDSUREuoQhTcPYJ60MRkaASCT/BSiOlYz/DwMaERHpGoY0DWOf\nNPXj50dERLqIIU3LGDAqh2v8iIhIVzGkaREDWuVxjZ9uKCwqVus8IiJdwLs7tYQBTT2ErPE7EjxA\nC5VRedTS18OyE6llzpvV21YD1RARVQ88k6YFDGjqwzV+RESkqxjSNIxrqKqWss9XUiCs6S0REVF1\nwsudGsY1VFVHVQA2NNCHw/yjgvaRtLhfVZVHRERULjyTpmHsk1Y1eImTiIh0DUOahnENlfrx8yMi\nIl3EkKZlDBiVwzV+pC3BwcEQiURyX8HBwdoui4h0CEOaFjGgVR7X+FVf+YW63dMsODgYUqkUACCV\nSiGVShnSiEitdObGgVOnTkEsFiM1NRWWlpbw8fGBr6+vtstSiQFNPdgnrfqqXUsPn0QkCpq729el\niqshIqp5dOJM2vXr1xEQEABXV1fs27cPU6dOhVgsxvbt27VdmlIMaMIEAyh5jLrof1/Bb8zhGj/S\nqLw89c4jIiqFTpxJi4yMRIcOHTBjxgwAgK2tLVJSUrBx40Z4e3truTp5XEMlXDAUQ1lZGNAqJi+/\nEEa1hf3nIL+gCLUN9Ku4omrKyAgQiRTH3xz732VQIqLK0ImQlpiYiOHDh8uNubm5ITw8HI8fP0bj\nxtUn+HANVdVhQKs4o9q1MDA4VtDvp6mxgRYqpPIoLCpGLf2yL5QInUdE2iGSSmv+P/kcHBywYMEC\neHp6ysZSUlIwZMgQ7Nq1C46OjnLzo6OjER0dDQC4e/cubGxsNFpvRWRnZ6N+/fraLkMnvK2f5e3b\nt/HPP//IjZmamsLOzq5S+31bP89Hjx7h4cOHcmNNmzZFkyZNKrXfmvJ51q9fH5s3b9Z2GUQ6TSfO\npJVGpOTShKenp1ygqwk8PDwQExOj7TJ0Aj9L9eLnqV78PImohE6c57awsEBGRobcWGZmpmwbERER\nUU2jEyHNxcUFCQkJcmPx8fGwtrauVuvRiIiIiITSD9aB7otNmjTB2rVrkZ+fD0tLS5w+fRqrVq3C\nF198gQ4dOmi7PLVxcHDQdgk6g5+levHzVC9+nkQE6MiNAwBw8uTJ/2vv/mOqqv84jj+5lPeKYlNy\n5tbVUIxc4CQETB0mzg1UxATFO38gRi2gmo4tw01dpVjq8AcopJlOY3QX2s35h7bSabqVGVoW2Ra3\nWdLyF+gVZMLk9kfzrit8+36/ePuec/m+Hhtj93M/53Pf525sLz7nc86H0tJS3G43AwcOZOHChaZ+\nmK2IiIjI3+kxIU1ERESkJ+kRa9JEREREehqFNBERERETUkgzsWPHjpGRkUFMTAwpKSns2rXL6JKC\n1ldffUV+fj6TJk0iOjqabdu2GV1SUHv33XfJzs4mISGBMWPG4HA4OH78uNFlBSWXy8WsWbNISEhg\n1KhRpKWl8d5776GVKCLS4x9mG6zubhqfm5tLaWkp33zzDatWrcJms5luP9JgcOvWLaKiokhPT6ek\npMTocoLeF198QWZmJrGxsVitVj788ENefPFF9u7dS3x8vNHlBZWIiAgKCgqIjIykV69enD59mtdf\nf53Q0FBycnKMLk9EDKQbB0yqqKiIhoYGPvjgA1/b22+/zeHDhzly5IiBlQW/lJQUsrKyKCgoMLqU\nHiU9PZ3x48fz2muvGV1K0CssLARg69atBlciIkbS5U6Tqq2tZcKECX5tycnJNDQ08Pvv2jxczKWj\no4OWlpag2HPSzLxeL99++y21tbUkJSUZXY6IGEyXO03qypUrnba0evjhhwG4fPmydlIQU6msrMTj\n8ZCRkWF0KUHp5s2bJCcn097ezp07dygsLGThwoVGlyUiBlNIC0JdbRovYpSqqireeecdKioq9M9D\nN/Xp0weXy0VraytnzpyhtLSUQYMGMXv2bKNLExEDKaSZlDaNl2Cwc+dOysrKqKioYNy4cUaXE7Qs\nFgtDhw4F4IknnsDj8bBp0yaFNJH/c1qTZlLaNF7MbvPmzZSXl7N9+3YFtADr6Oigra3N6DJExGCa\nSTOpnJwcHA4HGzduZMaMGZw7d47333+f4uJio0sLSi0tLfzyyy8AtLW1cfXqVX744QfCwsJ8Mxjy\nn1uzZg1Op5PS0lIiIyN9s742m43w8HCDqwsuW7ZsYcyYMdjtdtrb2zl9+jQ7duxg1qxZRpcmIgbT\nIzhMTJvGB86XX37Z5ULsxMRE9u7da0BFwS06OrrL9meffZa33nrrf1xNcCspKeHo0aNcunQJq9WK\n3W4nMzOTuXPnEhoaanR5ImIghTQRERERE9KaNBERERETUkgTERERMSGFNBERERETUkgTERERMSGF\nNBERERETUkgTERERMSGFNBERERET0o4DIv+lex+MGxISQnh4ODExMeTl5TF+/HgDqxMRkZ5CIU2k\nm7KyskhMTKSjo4OLFy/idDrJy8tj586d2stSRETum0KaSDeNHj2ajIwM3+vU1FSmT5/O7t27FdJE\nROS+aU2aSICMGDGC/v37c+HCBV9bQ0MDb775JtOmTSMuLo64uDjmzZvH559/3un4BQsWkJyczG+/\n/UZBQQFxcXEkJiaycuVK2traOvV3uVykpqYSGxtLWloaLpeLsrKyLvfVPH/+PIWFhSQlJREbG0t6\nejr79u0L7BcgIiIBpZk0kQDxeDx4PB4ee+wxX9u5c+c4efIkkydPxm63c/PmTQ4cOMALL7zArl27\nGDt2rN8Yt2/fZtGiRSQkJPDqq69y9uxZnE4nAwYMYMmSJb5+LpeLZcuWMXLkSIqKimhubmbdunUM\nGjSoU121tbUsXrwYu93Oc889R58+fTh69CjLly+nqamJvLy8f+w7ERGR7lNIE+mmlpYWGhsb8Xq9\nXLx4kc2bN3Pnzh2mTp3q6zNx4kRSU1P9jsvJySEjI4MdO3Z0CmnXr18nPz+fRYsWAeBwOLhx4wZO\np9MX0trb21m/fj1Dhgyhurqa3r17AzB16lTS09P9xvN6vaxYsYLo6Giqqqp44IE//+TnzZvHSy+9\nRHl5OdnZ2YSHhwf0uxERkfuny50i3bR27Vqefvppxo0bx5w5c/j666955ZVXWLBgga/P3QAFf86S\nNTU10dzcTGJiIt99912nMS0WC3PnzvVrGzt2LI2NjTQ3NwPw/fffc/XqVWbPnu03/rBhw5gwYYLf\nsT/++CM//fQT06dPx+Px0NjY6PuZOHEira2tnD17NiDfh4iIBJZm0kS6KTc3l+TkZG7fvs2pU6fY\nvXs3t27dIiQkxNenvb2dbdu28fHHH9PQ0OB3/F/73RUREYHNZvNr69evHwA3btygb9++vnH+eln1\nrnvb3G43AKtXr2b16tVdnse1a9f+/kRFRMQQCmki3TR8+HDfXZyTJk2ib9++bNmyhfj4eFJSUgAo\nKSmhuroah8NBfHw8Dz30EKGhoezbt4+DBw92GtNi+deT216v1+93VyHv7nv3vn755Zd56qmnuhw3\nKirq352qiIgYQCFNJEDy8vJwOp2sX7+eZ555BovFwsGDB5k5cyarVq3y61tTU9Ptz3n00UcB+Pnn\nnzu999c7SwGGDBkCgNVq1WNBRESCjNakiQSI1WolNzcXt9vNoUOHgD9nxjo6Ovz6ud1uPv30025/\nzpNPPklERAQ1NTW0trb6jXvixIlOfSMjI9mzZw+NjY2dxuqqTUREzEEzaSIBlJ2dTWVlJZWVlaSl\npTFlyhRqamqw2WzExMTw66+/Ul1dzfDhw6mrq+vWZzz44IMUFRWxfPlyHA4HM2fOpKWlhaqqKh5/\n/HG/cS0WC2vXrmXx4sVMmzaNrKws7HY7TU1N1NXV8dlnn3V5A4OIiBhPIU0kgMLCwpg/fz7l5eUc\nOXKE4uJirFYrn3zyCS6Xi2HDhvHGG29QX1/f7ZAGkJmZCcD27dvZsGEDdrudZcuWcf78eerr6/36\nxsXFUVNTQ0VFBR999BHXr1+nf//+REVFUVxcfF/nKyIi/5wQ770rjUUkaOXn5+N2uzl8+LDRpYiI\nyH3SmjSRINTW1tbpTs76+nqOHz9OUlKSQVWJiEgg6XKnSBCqq6ujuLiY1NRUBg8ezIULF3A6ndhs\nNp5//nmjyxMRkQBQSBMJQo888ggjRoxg//79XLt2jbCwMBISEli6dCl2u93o8kREJAC0Jk1ERETE\nhLQmTURERMSEFNJERERETEghTURERMSEFNJERERETEghTURERMSE/gAu3qBaNTIEdAAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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iIiJ5MaQpUUXrpBERERFVhCFNiSpaJ42IiIioIgxpKlR6jBoRERFRRRjSVIST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\nRkRERGSDGNKIiIiIbBBDGhEREZEN+j9joVHxy9hLegAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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q1KkYPXo03Nzc0KlTJ4kZBy5cuCBxj4+FhQUWLlyI1atXw93dHQMHDkTjxo3x9OlTXLly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\nTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ADRo0wLp168r9gKzqUldFhgwZgszMzHI/uEtKSvDPP/9UeQ49PT0IBAK53qSzZ8/i0qVL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\ngg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "###FIG 2F\n",
    "df = df[df.Culture_time=='48h']#Use 48h data only\n",
    "boot_iter = 250000\n",
    "for n_oc,oc in enumerate(or_cells):\n",
    "    for n_cnd,cnd in enumerate(conds):\n",
    "        df_temp = df[(df.Original_cell==oc)&(df.Culture_condition==cnd)]\n",
    "        \n",
    "        #SET MAX GENERATION AND ALL SAMPLED FAMILY VECTORS FROM THE DATA \n",
    "        max_g = df_temp.Generation.max()\n",
    "        print('\\n', oc, cnd, len(np.unique(df_temp.Family)))\n",
    "        fam_vec = np.array([df_fam_to_vec(df_temp[df_temp.Family==fam], max_g)\n",
    "                            for fam in np.unique(df_temp.Family)])\n",
    "        \n",
    "        #ESTIMATE p FOR THE BB MODEL, THE PROBABILITY FOR A CELL TO DIVIDE TO NEXT GENERATION \n",
    "        cc_pop = fam_vec.sum(axis=0)*(2.** -np.arange(max_g+1))\n",
    "        p_div = np.array([cc_pop[i+1:].sum()/cc_pop[i:].sum() for i in np.arange(len(cc_pop)-1)] + [0.])\n",
    "        \n",
    "        #CALCULATE THE OBSERVED FRAY/RANGE, AND ITS DISTRIBUTION, FROM THE DATA\n",
    "        fray_data = np.array([df_temp[df_temp.Family==fam].Generation.max()\n",
    "                              - df_temp[df_temp.Family==fam].Generation.min()\n",
    "                              for fam in np.unique(df_temp.Family)])\n",
    "        fray_support = np.arange(max_g)#ALSO np.arange(fray_data.max()+1)\n",
    "        fray_freq = epmf_on_support(fray_data, fray_support, bool_norm=False)\n",
    "        \"\"\"UNCOMMENT TO RECALCULATE THE OPTIMISATION STEP\n",
    "        fray_epmf, boot_ci = stat_bootCI(func=epmf_on_support, args=(fray_support,), data=fray_data)\n",
    "\n",
    "        #Generate all full amily vectors up to max observed depth d\n",
    "        samp_vec = np.array([fam for fam in fam_generator(max_g) if (fam * 2.**-np.arange(len(fam))).sum()<=1.\n",
    "                                                    and (fam * 2.**-np.arange(len(fam))).sum()>=0.])\n",
    "        full_vec = np.array([fam for fam in samp_vec if (fam * 2.**-np.arange(len(fam))).sum()==1.])\n",
    "        Ft_lst = [Full_tree(fam) for fam in full_vec]\n",
    "        \n",
    "        #MLE rho estimation\n",
    "        solution = spo.minimize_scalar(log_like_data, bounds=(0., 1.),\n",
    "                            args=(p_div, r_sample, Ft_lst, fray_freq),\n",
    "                            method='bounded', options={'disp': True})\n",
    "        est_rho = solution.x\n",
    "        \n",
    "        #Fray distribution under the BB model for other values of rho\n",
    "        rho_lst = np.array([est_rho, 0.9, 0.5, 0.0])\n",
    "        fray_pmf = {str(rho):[fray_dist(gen, rho, p_div, r_sample, Ft_lst)\n",
    "                              for gen in fray_support] for rho in rho_lst}\n",
    "        \n",
    "        #LIKELIHOOD-RATIO TEST (EXTRA)\n",
    "        neg_log_like_H0 = log_like_data(0., p_div, r_sample, Ft_lst, fray_freq)\n",
    "        neg_log_like_H1 = log_like_data(est_rho, p_div, r_sample, Ft_lst, fray_freq)\n",
    "        like_ratio_stat = 2. * (neg_log_like_H0 - neg_log_like_H1)\n",
    "        pval = sps.chi2.sf(like_ratio_stat, df=1)\n",
    "        print('LR test pval=', pval)\n",
    "        \n",
    "        #SAVE VARIABLES THAT TAKE A LONG TIME TO CALCULATE\n",
    "        with open('./pickled_data/Fray_ci_'+oc+cnd, 'wb') as fp:\n",
    "            pickle.dump((fray_epmf,boot_ci,est_rho,fray_pmf,pval), fp)\n",
    "        \"\"\"\n",
    "        \n",
    "        with open('./pickled_data/Fray_ci_'+oc+cnd, 'rb') as fp:\n",
    "            fray_epmf,boot_ci,est_rho,fray_pmf,pval = pickle.load(fp)\n",
    "\n",
    "        #PLOTTING CODE\n",
    "        rho_lst = np.array([est_rho, 0.9, 0.5, 0.0])###THIS IS ADDED FOR WHEN THE PART ABOVE IS COMMENTED\n",
    "        width = 0.5/len(rho_lst)\n",
    "        t_cols = sns.color_palette('Blues', n_colors=6)[::-1]\n",
    "        color_dct = {str(est_rho):t_cols[0], '0.9':t_cols[1],\n",
    "                     '0.5':t_cols[2], '0.0':t_cols[3]}\n",
    "        shift_dct = {str(rho_lst[k]):-0.30 + (k+1)*0.125 for k in range(len(rho_lst))}    \n",
    "        sns.set_style(\"ticks\")\n",
    "        fig, ax = plt.subplots()\n",
    "        ax.bar(x=fray_support-0.30, height=fray_epmf, width=width, align='edge',\n",
    "           color='Red', label='Data')\n",
    "        for rho in rho_lst:\n",
    "            if rho == est_rho:\n",
    "                ax.bar(x=fray_support+shift_dct[str(rho)], height=fray_pmf[str(rho)],\n",
    "                       width=width, align='edge', color=color_dct[str(rho)], hatch='///',\n",
    "                       label=r'$\\rho = $'+str(round(rho, 3))+' (Best fit)')\n",
    "            else:\n",
    "                ax.bar(x=fray_support+shift_dct[str(rho)], height=fray_pmf[str(rho)],\n",
    "                       width=width, align='edge', color=color_dct[str(rho)],\n",
    "                       label=r'$\\rho = $'+str(round(rho, 3)))     \n",
    "        xx_fray = np.add(np.arange(len(fray_epmf)), (width/2.)-0.30)\n",
    "        for k in range(len(fray_epmf)):\n",
    "            ax.plot([xx_fray[k]]*2, [boot_ci[0,k], boot_ci[1,k]],\n",
    "                     color='Black', ls='-', lw=1., mfc='Black', mec='Black',\n",
    "                     marker='_', mew=1, ms=5.)\n",
    "        sns.despine(fig=fig)\n",
    "        ax.set_xlabel('Range', fontsize='xx-large')\n",
    "        ax.set_ylabel('% of clones', fontsize='xx-large')\n",
    "        ax.set_xticks(np.arange(max_g))#len(fray_epmf)))\n",
    "        ax.set_xticklabels(np.arange(max_g), fontsize='x-large')# np.arange(len(fray_epmf))\n",
    "        ax.set_yticks(np.arange(0., 1.1, 0.25))\n",
    "        ax.set_yticklabels(('0', '25', '50', '75', '100'), fontsize='x-large')\n",
    "        if oc == 'SLAM-HSC' and cnd == 'P':\n",
    "            ax.set_xlim(-0.5, 2.5)\n",
    "        elif oc == 'SLAM-HSC' and cnd == 'P+ILs':\n",
    "            ax.set_xlim(-0.5, 3.5)\n",
    "        elif oc == 'ST-HSC' and cnd == 'P':\n",
    "            ax.set_xlim(-0.5, 3.5)\n",
    "        elif oc == 'ST-HSC' and cnd == 'P+ILs':\n",
    "            ax.set_xlim(-0.5, 4.5)\n",
    "        elif oc == 'MPP' and cnd == 'P':\n",
    "            ax.set_xlim(-0.5, 2.5)\n",
    "        elif oc == 'MPP' and cnd == 'P+ILs':\n",
    "            ax.set_xlim(-0.5, 4.5)\n",
    "        #ax.set_xlim(-0.5, fray_data.max()+0.5)\n",
    "        ax.set_ylim(bottom=-0.0, top=1.0)\n",
    "        ax.legend(fontsize='x-large', loc='upper left', ncol=1, bbox_to_anchor= (1.05, 1.))\n",
    "        ax.set_title('Generation range 48h '+oc+' '+cnd, fontdict = {'fontsize':'xx-large'})\n",
    "        fig.savefig(path_plot+'/Fray fit 48h '+oc+' '+cnd+'.pdf', bbox_inches='tight')"
   ]
  }
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