{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "241ec99a-6825-4d61-b90b-5d255a9b1764",
   "metadata": {},
   "source": [
    "(marginalizing-models)=\n",
    "# Automatic marginalization of discrete variables\n",
    "\n",
    ":::{post} Jan 20, 2024\n",
    ":tags: mixture model\n",
    ":category: intermediate, how-to\n",
    ":author: Rob Zinkov\n",
    ":::\n",
    "\n",
    "PyMC is very amendable to sampling models with discrete latent variables. But if you insist on using the NUTS sampler exclusively, you will need to get rid of your discrete variables somehow. The best way to do this is by marginalizing them out, as then you benefit from Rao-Blackwell's theorem and get a lower variance estimate of your parameters.\n",
    "\n",
    "Formally the argument goes like this, samplers can be understood as approximating the expectation $\\mathbb{E}_{p(x, z)}[f(x, z)]$ for some function $f$ with respect to a distribution $p(x, z)$. By [law of total expectation](https://en.wikipedia.org/wiki/Law_of_total_expectation) we know that\n",
    "\n",
    "$$ \\mathbb{E}_{p(x, z)}[f(x, z)] =  \\mathbb{E}_{p(z)}\\left[\\mathbb{E}_{p(x \\mid z)}\\left[f(x, z)\\right]\\right] $$\n",
    "\n",
    "Letting $g(z) = \\mathbb{E}_{p(x \\mid z)}\\left[f(x, z)\\right]$, we know by [law of total variance](https://en.wikipedia.org/wiki/Law_of_total_variance) that\n",
    "\n",
    "$$ \\mathbb{V}_{p(x, z)}[f(x, z)] = \\mathbb{V}_{p(z)}[g(z)] + \\mathbb{E}_{p(z)}\\left[\\mathbb{V}_{p(x \\mid z)}\\left[f(x, z)\\right]\\right] $$\n",
    "\n",
    "Because the expectation is over a variance it must always be positive, and thus we know\n",
    "\n",
    "$$ \\mathbb{V}_{p(x, z)}[f(x, z)] \\geq \\mathbb{V}_{p(z)}[g(z)] $$\n",
    "\n",
    "Intuitively, marginalizing variables in your model lets you use $g$ instead of $f$. This lower variance manifests most directly in lower Monte-Carlo standard error (mcse), and indirectly in a generally higher effective sample size (ESS).\n",
    "\n",
    "Unfortunately, the computation to do this is often tedious and unintuitive. Luckily, `pymc-experimental` now supports a way to do this work automatically!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e40e8a9d-7516-4ad2-af1e-09fb85f77639",
   "metadata": {},
   "outputs": [],
   "source": [
    "import arviz as az\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pymc as pm\n",
    "import pytensor.tensor as pt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "495efc5b-a0c0-45f0-a723-3278495e1ace",
   "metadata": {},
   "source": [
    ":::{include} ../extra_installs.md\n",
    ":::"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8d802429-a250-4c22-9ecd-0dcb6778d876",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pymc_extras as pmx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d686f41b-d55c-417d-8ef4-772c421a47cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = 'retina'  # high resolution figures\n",
    "az.style.use(\"arviz-darkgrid\")\n",
    "rng = np.random.default_rng(32)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f646c49f-41af-4004-a2c4-63d6ead8e007",
   "metadata": {},
   "source": [
    "As a motivating example, consider a gaussian mixture model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "314c7fb7-3339-4e82-abe2-1d0aebf85242",
   "metadata": {},
   "source": [
    "## Gaussian Mixture model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0eecdf9b-4527-45fe-84d5-8a776086cb0c",
   "metadata": {},
   "source": [
    "There are two ways to specify the same model. One where the choice of mixture is explicit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2e7b84e4-1323-4508-93e6-1f00fe21f90d",
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = pt.as_tensor([-2.0, 2.0])\n",
    "\n",
    "with pm.Model() as explicit_mixture:\n",
    "    idx = pm.Bernoulli(\"idx\", 0.7)\n",
    "    y = pm.Normal(\"y\", mu=mu[idx], sigma=1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "63c63f01-8a34-4ef1-a316-384c721a3966",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABbcAAAPXCAYAAAAYJXYaAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8fJSN1AAAACXBIWXMAAB7CAAAewgFu0HU+AAB1/UlEQVR4nOzde3yU5Zk38GtCIIIIQapBAalYREGiQLVWqVhRq6tbpVa7WlexWrdFWw/tWrcnd33d1dZadV1tP1uPy/ux1e5HKYq1iwd0qVSwUEFAwBNWlIhCEDmGZN4/+jplEhImIYe5k+/3r1zP3M99XxN4MswvD/dkstlsNgAAAAAAICElHd0AAAAAAAA0l3AbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABITmlHN0DT1q5d29EttFgmk4ny8vKIiKiuro5sNtuxDUEn55qD9uWag/blmoP25ZqD9uWao6vo169fq87nzm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSU9rRDQAAAACtb9yxdbs4w/ut0sf2Zs10jx0ArcerCgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJKW3vBaurq2PZsmWxYsWKqK6ujmw2G3379o199903DjvssNhjjz1aZZ0333wzFi9eHKtWrYq6urqoqKiIYcOGxYEHHtgq80dELFiwIN54442oqqqKnj17RkVFRVRWVkZFRUWrrQEAAAAAQENtHm7X1dXFCy+8EDNmzIg//OEPsWzZskbHZjKZ+PSnPx2TJk2K8ePHt2i9Z599Nu64446YP3/+Dh8fPnx4fPWrX42//du/bdH82Ww2pkyZElOmTIk333yzweMlJSVx1FFHxeWXXx6jRo1q0RoAAAAAADQtk81ms225wIknnhgrVqxo9nmnnHJKXHvttdG7d++Cxmez2bjhhhvivvvui0Ke0qmnnhrXX3999OjRo+Ceqqur4/LLL4/Zs2fvdGz37t3j29/+dkyaNKng+Xdk7dq1u3R+R8pkMlFeXh4RkbtLH2g7rjloX645aF+uOWi+ccfWdXQLDcyaaXdU2BGvc3QV/fr1a9X52vzO7TVr1jQ49vGPfzwqKyvjYx/7WJSVlcWqVati9uzZsWrVqtyY6dOnx+rVq+POO++MsrKyna5zyy23xL333pt3bMyYMTFq1Kjo1q1bvPzyyzF79uzcD4dHH300unfvHjfccENBz6Ompia+8Y1vxJw5c3LHunfvHsccc0wccMABsWHDhnjhhRdi6dKlufHXX3997LHHHnHGGWcUtAYAAAAAAIVptz23Bw4cGGeeeWZMnDgxBgwY0ODx2traePDBB+P666+PLVu2RETEnDlz4pZbbonvfOc7Tc79zDPPxM9//vNc3adPn/j3f//3+PSnP503bvHixfH1r389F6I//PDDMWbMmDjrrLN22v8tt9ySF2wfeOCB8bOf/SwGDRqUN27atGnx3e9+N2pqaiIi4pprronKysoYNmzYTtcAAAAAAKAwbf7/gfbdd9/4t3/7t5gxY0Z8/etf32GwHRHRrVu3OPvss+O2226LkpK/tjVlypSoqqpqdP5sNhs33XRTrs5kMnHHHXc0CLYjIkaMGBH33ntv3p3gt912Wy5Mb0xVVVVMmTIlV/fv3z/+67/+q0GwHRHx+c9/Pq677rpcXVNTE7feemuT8wMAAAAA0DxtHm4/9NBDccYZZ0S3bt0KGj9+/Pg45ZRTcnVNTU08+eSTjY5/8sknc1uBREScdtppcfjhhzc6fv/9948LL7wwV7/77rvx61//usme7rrrrrwA/Fvf+laT+8OcfvrpeT3MmDGjyQ/SBAAAAACgedo83C4tbf7OJ9uH2xERCxcubHTsb3/727z6y1/+8k7n/7u/+7u8sP3xxx9vcvz2j/ft2zdOPfXUna5x9tlnNzoHAAAAAAC7pig/pni//fbLq997770djtu2bVv87//+b67eZ599orKycqfzV1RUxGGHHZar582bF2vXrt3h2JdeeilvW5Rjjz22oA+4nDBhQnTv3j1XN3X3OQAAAAAAzVOU4faGDRvy6sbu/l6+fHmsW7cuV48ePbrgNbYPt2tra2PevHk7HPfCCy/k1YWusdtuu8VBBx2Uq19++eVYv359wf0BAAAAANC4ogy3t99DOyIa/RDKV199Na8++OCDC15j5MiRTc71kddeey2vHjFiRMFr1B9bfy4AAAAAAFqmKMPtadOm5dVHHnnkDsfVD4v33XffgtfYZ5998urXX3+9oDXqn9eU+v0ItwEAAAAAWkfRhdtz5syJOXPm5Oo99tgjxo0bt8Ox2++FHdH4Hd47Un/sqlWrdrpGaWlpfOxjH2v1NQAAAAAAaJ4db2bdQTZu3Bg/+MEP8o5dcMEFsfvuu+9wfP29uRsbtyP1x27cuHGna/Ts2TNKSgr/fUChazQlk8k0+5xisX3vKT8PSIVrDtqXaw7al2sOOgfXL+yY1zlomaIKt//5n/853njjjVw9dOjQuOiiixodv2nTpry6R48eBa9VVlaWVzcWPG+/Rv1zdqZ+Py0Jt8vLy5t9TjHq27dvR7cAXYprDtqXaw7al2sOCvV+RzfQQGd5jwttyescFK5otiW555574je/+U2u7tGjR9x4441NBsqbN2/Oq5sTbtcfW3+uHR1vzvzNWQMAAAAAgOYpiju3H3vssfjxj3+cd+zaa6+NQw45pMnz6gffNTU1Ba+5devWJufa/vhHd283Z/7mrNGU6urqZp9TLDKZTO63jevWrYtsNtvBHUHn5pqD9uWag/blmoPOIeX3uNCWvM7RVbT2/+Dp8HD7ueeei6uuuirq6upyx771rW/FxIkTd3pur1698uotW7YUvG79sfXn2v74R+F2c++8rh9uN7ZGUzrLD7NsNttpngukwDUH7cs1B+3LNQfpcu3Cznmdg8J16LYkL774YlxyySV5d0RfeOGFcfHFFxd0fv2wuP4HTDal/timwu2PbNq0qVk/XApdAwAAAACA5umwcHvZsmVx8cUX533I4plnnhlXXXVVwXNUVFTk1atWrSr43PpjBwwYsNM1tm3bFqtXr271NQAAAAAAaJ4OCbfffPPN+MpXvpK319bJJ58c1157bbPmGTp0aF799ttvF3zuO++80+RcjR2vf15T6vfT2BoAAAAAADRPu4fbVVVVMWnSpLw7oMePHx833nhjlJQ0r50DDjggr16yZEnB5y5atCivbix4rr/G4sWLC16j/ljhNgAAAABA62jXcHvNmjUxadKkWLlyZe7YEUccEbfddlt079692fMdeOCB0adPn1w9f/78gs/dfmy3bt1izJgxOxw3duzYRs9ryubNm+Pll1/O1cOHD8/rFQAAAACAlmu3cPvDDz+Miy66KF577bXcsUMPPTR+/vOfR1lZWYvmLC0tjWOOOSZXv/POO/Hiiy/u9Lyqqqr405/+lKtHjx4de+655w7HHnLIIXn7bj/99NOxZcuWna7xxBNP5H1Q5oQJE3Z6DgAAAAAAhWmXcHvz5s3xta99LW8rkIMOOih+8YtfxO67775Lc5900kl59f3337/Tc371q19FXV1do3NsL5PJxIknnpirP/jgg3j00UcLWmN7n/vc53Z6DgAAAAAAhWnzcHvbtm1x2WWXxdy5c3PH9t9//7j77rujb9++uzz/hAkT4sADD8zVv/nNb/LWqu/111+Pu+66K1fvtddeceaZZza5xkUXXRQ9evTI1TfddFOsXbu20fFTp07N62HChAlx0EEHNbkGAAAAAACFa9NwO5vNxtVXXx0zZ87MHRs0aFDcd9990b9//1ZZo6SkJK688sq8NSdPnhyzZ89uMHbx4sUxadKkvG1FLr300thtt92aXGPAgAFx7rnn5ur3338/zjvvvHjrrbcajJ02bVp8//vfz9Xdu3ePyy67rFnPCQAAAACApmWy2Wy2rSZfuXJlHHfccXnHSkpKIpPJNGuegQMHxowZM5oc85Of/CR+8Ytf5B0bO3ZsjBo1KkpKSmLp0qXx3HPPxfZP9/Of/3zceOONBfWwdevWuOCCC+KFF17IHevevXuMHz8+hg4dGhs3boy5c+fG0qVL88677rrrdnpneFOaukO82GUymSgvL4+IiOrq6mjDv2pAuOagvbnmoH255qD5xh1bt/NB7WzWzHb76C9Iitc5uop+/fq16nylrTpbPTu6ELff67pQtbW1Ox1z5ZVXxubNm2PKlCm5Y3/84x/jj3/84w7H/83f/E1cd911BffQo0ePuO222+Kyyy6LOXPmRERETU1NPPHEEzscX1paGldeeeUuBdsAAAAAAOxYp/mVaUlJSXz/+9+P//zP/4zDDjus0XEHHnhg/PjHP46bb745ysrKmrXGnnvuGffdd1/80z/9UwwePLjRPo466qj45S9/GRdeeGGz5gcAAAAAoDBtui1JR1qxYkUsWrQo3n333aitrY2KiooYNmxYDB8+vFXmz2azsXDhwnj99dfj3Xffjd122y0qKiri0EMPjYqKilZZI8K2JEDhXHPQvlxz0L5cc9B8tiWBdHido6tIaluSjjRkyJAYMmRIm82fyWSisrIyKisr22wNAAAAAAB2zK9MAQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDklLbXQhs2bIjFixfHggULYsGCBbFw4cJYuXJl7vGBAwfGU0891aw5jzvuuLw5Wur666+PL3zhCzt87K233ooJEya0aN6Kiop49tlnd6U1AAAAitC4Y+s6uoUGZs10/xoAXUubh9v33HNPPPTQQ/HKK69EXV3xvfhHRPTq1aujWwAAAAAAoBnaPNyeO3duLFu2rE3m7tatW3Tr1q1Z52Sz2byQvVevXvGZz3ym4PNLSkoik8kUNLa0tN1ujAcAAAAA6FI6JH3t1atXjBw5MhYtWhQbN25s8TwzZsxo9jn33ntvXH/99bn6xBNPjN13373g8//1X/+10S1MAAAAAABoH20ebpeVlUVlZWWMGjUqRo0aFYccckgccMABUVJSEscdd9wuhdst8fDDD+fVEydObNf1AQAAAADYdW0ebt98881tvUTBlixZEi+//HKuHjhwYHzqU5/qwI4AAAAAAGiJLvVRyvXv2j799NML3j8bAAAAAIDi0WXC7W3btsWjjz6aqzOZjC1JAAAAAAAS1WXC7WeeeSbef//9XD127NgYPHhwB3YEAAAAAEBLdZlwe+rUqXm1u7YBAAAAANLV5h8oWQzWrl0bTz/9dK7u2bNnnHTSSS2a63e/+1089thj8eqrr8batWujrKwsysvLY9iwYXH44YfHySefHHvvvXdrtQ4AAAAAwA50iXB7+vTpUVNTk6tPPPHE6N27d4vmmjlzZl69adOmqK6ujjfeeCNmzJgRP/nJT+KLX/xifPvb347dd999V9qOiEj6Ay+37z3l5wGpcM1B+3LNQftyzcHOpXBtpNAjdASvc9AyXSLcfvjhh/PqttySZOvWrXH//ffHH/7wh/j5z38eQ4YM2aX5ysvLW6exDta3b9+ObgG6FNcctC/XHLQv1xzF4f2dD2lnDd8/ptAjUJ/XOShcpw+3ly9fHi+99FKuHjhwYBx55JHNnmf48OFx/PHHx9ixY+MTn/hElJeXRzabjffeey9efPHFmDp1ajz77LO58a+99lp89atfjQceeCD69evXKs8FAAAAAIC/6PThdv27tk877bRm/feO8vLy+NWvfhWjR4/e4eODBg2KQYMGxSmnnBLPPPNM/OM//mOsW7cuIiJWrFgR1113Xdx0000t7r+6urrF53a0TCaT+23junXrIpvNdnBH0Lm55qB9ueagfbnmYOdSeP+YQo/QEbzO0VW09v/g6dThdm1tbUybNi1XZzKZZm9J0rt370aD7frGjx8fd9xxR5x//vmxbdu2iPjLft//8A//EAceeGCz1v1IZ/lhls1mO81zgRS45qB9ueagfbnmYMdSuC5S6BE6mtc5KFxJRzfQlmbNmhWrV6/O1WPHjo399tuvTdf85Cc/GWeccUauzmaz8dvf/rZN1wQAAAAA6Go6dbg9derUvLotP0hye1/84hfz6tmzZ7fLugAAAAAAXUWnDbfXr18fTz75ZK7u2bNnnHTSSe2y9iGHHBLdu3fP1W+//Xa7rAsAAAAA0FV02nB7+vTpsWXLllx9wgknRO/evdtl7ZKSkrzN0deuXdsu6wIAAAAAdBWdNtyuvyXJF77whXZdf/Pmzbmvy8rK2nVtAAAAAIDOrlOG26+//nrMnz8/V++7775x5JFHttv6a9eujfXr1+fq/v37t9vaAAAAAABdQacMt+vftX3aaadFJpNpt/WfffbZvPqggw5qt7UBAAAAALqCThdu19XVxW9+85u8Y+25JUlNTU384he/yDs2bty4dlsfAAAAAKAr6HTh9vPPPx/vvPNOrh47dmzst99+LZqrqqoqqqurCx5fV1cXP/zhD2P58uW5Y3vttVeccsopLVofAAAAAIAd63Th9kMPPZRXT5w4scVzLVy4MI477rj40Y9+FIsXL25y7JIlS2LSpEkN1r/yyiujV69eLe4BAAAAAICGStt6gZUrV8YJJ5yww8dqa2vzxo0YMWKH4+6999444ogjdrrWhx9+GDNmzMjVPXv2jJNPPrmZHefbsGFD3H333XH33XfHXnvtFSNGjIjBgwfHHnvsEdlsNt5///148cUXY9myZQ3OvfDCC9t1SxQAAAAAgK6izcPtbDabF2I3pbFx2Wy2oPN/97vfxaZNm3L1CSecEL179y7o3EKsXr06nnnmmZ2O22233eLqq6+Os88+u9XWBgAAAADgr9o83G5PU6dOzat39a7p4cOHxznnnBNz5syJ1157Lerq6pocv9dee8XEiRPjy1/+cgwYMGCX1gYAAAAAoHFtHm4PGjQoli5d2tbLRETElClTWnW+wYMHxzXXXBMRERs3boxXXnkl3nrrrXjvvfdi48aNkclkYo899og999wzRo4cGYMHD27V9QEAAAAA2LFOded2W+rVq1dUVlZGZWVlR7cCAAAAANDllXR0AwAAAAAA0FzCbQAAAAAAkmNbEgAAAIrOuGPrOrqFPLNmujcMAIqNV2cAAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJJT2tENpGrBggXxxhtvRFVVVfTs2TMqKiqisrIyKioqOro1AAAAAIBOr93C7Q0bNsTixYtjwYIFsWDBgli4cGGsXLky9/jAgQPjqaeeava8w4cPb3FPixYtitLSwr8F2Ww2pkyZElOmTIk333yzweMlJSVx1FFHxeWXXx6jRo1qcV8AAAAAADStzcPte+65Jx566KF45ZVXoq6urq2XazPV1dVx+eWXx+zZsxsdU1dXF7NmzYrnn38+vv3tb8ekSZPar0EAAAAAgC6kzcPtuXPnxrJly9p6mYiIyGQyUVJS+DbimUymoHE1NTXxjW98I+bMmZM71r179zjmmGPigAMOiA0bNsQLL7wQS5cuzY2//vrrY4899ogzzjijeU8CAAAAAICd6pA9t3v16hUjR46MRYsWxcaNG1tt3ksuuSS+8Y1vtNp8H7nlllvygu0DDzwwfvazn8WgQYPyxk2bNi2++93vRk1NTUREXHPNNVFZWRnDhg1r9Z4AAAAAALqyNg+3y8rKorKyMkaNGhWjRo2KQw45JA444IAoKSmJ4447rlXD7bZQVVUVU6ZMydX9+/eP//qv/4p+/fo1GPv5z38+6urq4jvf+U5E/OUO7ltvvTX+4z/+o936BQAAAADoCto83L755pvbeok2ddddd8WWLVty9be+9a0dBtsfOf300+O///u/Y+7cuRERMWPGjFi2bFkceOCBbd4rAAAAAEBX0SHbkqTk8ccfz33dt2/fOPXUU3d6ztlnn50Ltz+aQ7gNAAAA+cYdW9fRLeSZNbPwz/ECoOP5qd2El156KaqqqnL1scceG2VlZTs9b8KECdG9e/dc/eSTT7ZJfwAAAAAAXZVwuwkvvPBCXj169OiCztttt93ioIMOytUvv/xyrF+/vlV7AwAAAADoyoTbTXjttdfy6hEjRhR8bv2x9ecCAAAAAKDlOtWe288//3wsWbIkli5dGmvWrInS0tLo169fDBkyJA4//PA46aSTYr/99it4vvqB9D777FPwufvuu2+DuQ499NCCzwcAAAAAoHGdKtze/kMcP/LBBx/EihUr4tlnn41bbrklTj755Pjud78b/fv33+l82++3XVpaGh/72McK7mXAgAF59apVqwo+FwAAAACApnWqcHtnamtr49FHH405c+bE7bffHpWVlU2O37BhQ+7rnj17RklJ4bu47L777nn1xo0bm9fs/5fJZFp0XjHYvveUnwekwjUH7cs1B+3LNUdHS+HvnR53XbH3R+fldQ5aplOE20OGDIkJEybEkUceGZ/4xCdizz33jG7dusWaNWvipZdeisceeywef/zxqK2tjYiId999Ny6++OJ48MEHm9ymZNOmTbmvy8rKmtVTjx498uqWhtvl5eUtOq/Y9O3bt6NbgC7FNQftyzUH7cs111W839EN5Gn43qy4+ovQY2voLO/BSZvXOShc8uH2XXfdFUcfffQOf6s1YMCAGDBgQBx//PExadKk+OY3vxnvvPNORESsXbs2rrrqqvjVr37V6NybN2/OfV0/rN6Z+uO3nwsAAAAAgF2TfLg9bty4gsZVVlbG3XffHWeddVasX78+IiLmz58fzzzzTIwfP36H55SVleXu3q6pqWlWX1u3bm0wV0tUV1e36LxikMlkcr9tXLduXWSz2Q7uCDo31xy0L9cctC/XHB0thfdmetx1xd4fnZfXObqK1v4fMsmH280xdOjQuPjii+Omm27KHZs+fXqj4XavXr1y4XZz77yuH2736tWrmd3+RWf5YZbNZjvNc4EUuOagfbnmoH255ugIKfyd0+OuK/b+6Bq8zkHhCv+ExE7ijDPOyNvCZPbs2Y2O3T6Q3rRpU7N+sGz/YZT15wIAAAAAYNd0uXC7f//+MXjw4Fz97rvvNrrlSEVFRe7rbdu2xerVqwteZ9WqVXn1gAEDmtkpAAAAAACN6XLhdsRfAu7tNban1tChQ/Pqjz6MshBvv/12k3MBAAAAANByXTLc/mgf7Y809mGPBxxwQF69ePHigteoP1a4DQAAAADQerpcuF1XV5d3V3X37t2jT58+Oxw7duzYvHr+/PkFrbF58+Z4+eWXc/Xw4cMbXQMAAAAAgObrcuH2vHnz4oMPPsjVBx10UKNjDznkkLx9t59++unYsmXLTtd44okn8vbxnjBhQgu7BQAAAABgR7pcuP2zn/0srx43blyjYzOZTJx44om5+oMPPohHH310p2v86le/yqs/97nPNbNLAAAAAACakmy4XV1dHVVVVc0659///d9j1qxZuXq33XaLs88+u8lzLrrooujRo0euvummm2Lt2rWNjp86dWrMnTs3V0+YMKHJu8MBAAAAAGi+ZMPtd955J44//vj44Q9/GH/84x8jm802OvbNN9+Myy67LG6//fa84xdddFHetiM7MmDAgDj33HNz9fvvvx/nnXdevPXWWw3GTps2Lb7//e/n6u7du8dll11W6FMCAAAAAKBApW29wMqVK+OEE07Y4WO1tbV540aMGLHDcffee28cccQRDY5v3bo1HnjggXjggQeivLw8RowYER//+MejT58+UVJSEmvXro2XXnopFi1aFHV1dXnnnnzyyXHppZcW9ByuuOKKWLBgQbzwwgsREbFs2bI46aSTYvz48TF06NDYuHFjzJ07N5YuXZp33jXXXBPDhw8vaA0AAAAAAArX5uF2NpvNC7Gb0ti4pu7K/kh1dXU899xz8dxzzzU5rlu3bjF58uT4+te/HplMpqC+evToEbfddltcdtllMWfOnIiIqKmpiSeeeGKH40tLS+PKK6+MM888s6D5AQAAAABonmS3JRkwYEBccMEFMXLkyCgt3XlG37dv3zjnnHPi0UcfjUsvvTS6devWrPX23HPPuO++++Kf/umfYvDgwTscU1JSEkcddVT88pe/jAsvvLBZ8wMAAAAAULg2v3N70KBBDbbraA39+vWLq6++OiL+sj3JK6+8Em+99Va8++67sWHDhqirq4s+ffpEeXl5DB8+PA444ICC79RuTElJSUyaNCnOP//8WLhwYbz++uvx7rvvxm677RYVFRVx6KGH7nQPbwAAAAAAdl2bh9vtoUePHjFixIhG9+xubZlMJiorK6OysrJd1gMAAAAAIF+y25IAAAAAANB1CbcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5JR2dAMAAAAAxWjcsXUd3UIDs2a6TxHgI34iAgAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAySnt6AZa0+rVq2P58uXx5ptvxgcffBCZTCbKy8tj8ODBUVlZGb169eroFgEAAAAAaAXtFm5v2LAhFi9eHAsWLIgFCxbEwoULY+XKlbnHBw4cGE899VSz5qypqYnnnnsunnzyyfjDH/4QK1asaHRsaWlpfPazn42vfOUrMWbMmILXeP755+O8885rVl8fGTNmTPzyl79s0bkAAAAAADSuzcPte+65Jx566KF45ZVXoq6urtXm3bBhQ3z2s5+NdevWFTR+27ZtMWPGjHjiiSfi3HPPje985zvRvXv3VusHAAAAAID20+bh9ty5c2PZsmWtPm9tbW2DYDuTycSwYcPikEMOif79+0e3bt3irbfeit///vexdu3aiIjIZrMxZcqUWLNmTfzkJz+JkpLmbTteUlISmUymoLGlpZ1q1xcAAAAAgKLRIelrr169YuTIkbFo0aLYuHHjLs934IEHxplnnhmnnnpq7Lnnng0e37JlS/ziF7+I22+/PXf3+PTp02PMmDFx7rnnNmute++9Nz71qU/tcs8AAAAAALRcm4fbZWVlUVlZGaNGjYpRo0bFIYccEgcccECUlJTEcccdt0vh9rBhw+Lyyy+P448/fqc9XHrppfGxj30srrnmmtzx2267Lc4666zo0aNHi3sAAAAAAKD9tXm4ffPNN7fJvL17945p06Y1a1uRv/u7v4vf/OY3MW/evIiIqK6ujtmzZ8f48ePbpEcAAAAAANpG8zacLiIlJSXN3i87IuKUU07JqxcuXNhaLQEAAAAA0E6SDbdbar/99sur33vvvQ7qBAAAAACAlupy4faGDRvy6tLSDvlMTQAAAAAAdkGXC7eXLl2aVw8YMKCDOgEAAAAAoKW61G3L2Ww2Hn300bxjRx55ZLPmeOCBB+I//uM/YsWKFbFu3bro1atX9OvXLw4++OA4/PDD42/+5m+iT58+rdk2AAAAAAD1dKlwe+rUqfHnP/85V++3334xcuTIZs0xffr0vHrz5s2xZs2aePXVV+PRRx+NG2+8Mc4777yYPHlydO/evVX6BgAAAAAgX5cJt1evXh0/+tGP8o5dcsklkclkWnWdDz/8MO64446YPXt23HHHHbHnnnvu0nyt3V972r73lJ8HpMI1B+3LNQftyzVHR0vh750ed12x9xeRRo80n9c5aJkuEW5v27YtvvWtb8XatWtzxz71qU/FaaedVvAco0ePjuOOOy4OO+ywGDp0aPTp0ydqampi9erVMW/evPj1r38d8+bNy42fP39+TJ48Oe67774oKytrce/l5eUtPreY9O3bt6NbgC7FNQftyzUH7cs111W839EN5Gn43qy4+ovQY2so9v4iOk9OQOO8zkHhukS4fcMNN8Tzzz+fq8vLy+OGG24o6DdhH//4x+PRRx+NYcOGNXisR48esfvuu8fHP/7x+MIXvhAPP/xwXHPNNbFly5aI+EvAfccdd8QVV1zRek8GAAAAAIDOH27fddddMWXKlFzdvXv3uPnmm2Pfffct6PyKioqoqKgoaOzEiROjR48eceWVV+aO/dd//Vecf/75Ld6epLq6ukXnFYNMJpP7beO6desim812cEfQubnmoH255qB9ueboaCm8N9Pjriv2/iLS6JHm8zpHV9Ha//ukU4fbDz/8cNx44425OpPJxA033BBHHXVUm615yimnxEMPPRSzZs2KiIiNGzfGU089FV/84hdbNF9n+WGWzWY7zXOBFLjmoH255qB9ueboCCn8ndPjriv2/iLS6JFd43UOClfS0Q20lSeeeCK+973v5f0w+MEPfhCnnnpqm69dP8iePXt2m68JAAAAANCVdMpwe/bs2XHFFVdEbW1t7thll10WX/7yl9tl/dGjR+fVb7/9drusCwAAAADQVXS6cHvBggUxefLk2Lp1a+7YV77ylZg8eXK79VB/f+21a9e229oAAAAAAF1Bpwq3ly5dGhdddFFs3Lgxd+yss86K73znO+3ax+bNm/PqsrKydl0fAAAAAKCz6zTh9ooVK+LCCy+MdevW5Y6deuqp8S//8i/t3suf//znvLp///7t3gMAAAAAQGfWKcLtqqqquOCCC2L16tW5YxMmTIgf/ehHUVLS/k/xmWeeyasPOuigdu8BAAAAAKAzSz7cXrt2bVxwwQWxcuXK3LGjjz46brnlligtLW33ftavXx9TpkzJO/aZz3ym3fsAAAAAAOjMkg63P/zww7jooovi1VdfzR0bO3Zs3H777dGjR49dnv/NN9+MTZs2FTx+y5Ytcfnll8eaNWtyxw466KA48sgjd7kXAAAAAAD+Ktlwe+vWrTF58uR46aWXcscOOeSQ+M///M/o2bNnq6zx1FNPxYQJE+I//uM/4vXXX29y7Ny5c+NLX/pSzJo1K3espKQkrr766shkMq3SDwAAAAAAf9Hm+3asXLkyTjjhhB0+VltbmzduxIgROxx37733xhFHHJF37E9/+lM8//zzeccWL17cYNzOHH744XHfffc1+vj7778ft912W9x2220xcODAOPjgg2OfffaJPn36xLZt22L16tUxb968eOONNxqc+/3vfz8+/elPN6sfAAAAAAB2rs3D7Ww2mxdiN6WxcdlstqBjdXV1zWuumeesXLkyb2/vxpSXl8d1113XaKgPAAAAAMCuaf9PXEzIpz71qTjjjDNi7ty58eabb+50/KBBg+Kss86Ks846K/r169cOHQIAAAAAdE1tHm4PGjQoli5d2urzfupTn2qTebd38MEHx7/9279FRMT69etj+fLl8fbbb8d7770XmzZtim7dukWfPn3iYx/7WIwaNSoqKiratB8AAAAAAP7CndsF2mOPPWLMmDExZsyYjm4FAAAAAKDLK+noBgAAAAAAoLmE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJKe0oxsAAAAAoGXGHVvX0S00MGumeymB9uGnDQAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAySnt6AYAAABoX+OOrevoFhqYNdO9VwBA8/jXAwAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkJzSjm6gLVRVVcWCBQuiqqoqNm3aFBUVFbH//vvHqFGjWm2NZcuWxfLly6OqqipKSkpiwIABMWLEiNhvv/1abQ0AAAAAAHas3cLtDRs2xOLFi2PBggWxYMGCWLhwYaxcuTL3+MCBA+Opp57apTUWLFgQt956azz33HNRV1fX4PEhQ4bE3//938e5554bmUymRWtMmzYt7rzzzli6dOkOHx89enRccskl8ZnPfKZF8wMAAAAAsHNtHm7fc8898dBDD8Urr7yyw8C5tdx1113x05/+NLZt29bomBUrVsR1110XTz/9dNx8883Rt2/fguffsmVL/NM//VNMnz69yXHz58+Pr371q3HBBRfEVVdd1eIQHQAAAACAxrV5uD137txYtmxZm67x4IMPxo9//OO8YwcffHCMHTs2evbsGa+++mo8++yzueD797//fVx22WVx5513RmlpYd+C733ve3nBdiaTiaOPPjqGDx8eNTU1sXDhwpg/f35ERGSz2bj77rujZ8+e8c1vfrOVniUAAAAAAB/pkD23e/XqFSNHjoxFixbFxo0bd2mul19+Oa699tpc3aNHj/i3f/u3+Nu//du8cX/+859j8uTJuaB99uzZcdttt8UVV1yx0zXuv//+eOSRR3L1PvvsEz/72c/i4IMPzhv3UWi+fv36iIi44447YsyYMTFu3LgWPz8AAAAAABoqaesFysrKorKyMr785S/HDTfcEI8++mj88Y9/jP/7f/9v9OvXb5fnv+WWW6KmpiZX/5//838aBNsREYMHD4777rsv+vfvnzt23333xerVq5ucf9OmTXH77bfnPZ977rmnQbAdEXH00UfHHXfckduKJJvNxk9/+tNmPycAAAAAAJrW5uH2zTffHL/+9a/jhz/8YUycODGGDRsWJSWts+ySJUvi6aefztWHH354nH766Y2O33PPPePKK6/M1Zs2bYq77767yTUefPDBeO+993L1RRddFPvvv3+j44844oj4/Oc/n6sXLVqU1yMAAAAAALuuzcPttvT444/n1eecc85Oz/nbv/3b6NOnT67+3e9+1+T43/72t7mvu3XrFl/60pd2ukb9Pur3CQAAAADArkk63H7qqadyX3fv3j0mTJiw03PKysri2GOPzdUrV66MJUuW7HDsmjVr4sUXX8zVo0ePjoqKip2ucdhhh8WAAQNy9cyZM6O2tnan5wEAAAAAUJhkw+0PPvgg9+GQEREjRoyIsrKygs497LDD8uq5c+fucNy8efOirq4uV48ePbrg/rZfo7q6OpYvX17wuQAAAAAANC3ZcPvVV1/Nq3f0AY+NGTlyZJNzNXZ8xIgRLV7jtddeK/hcAAAAAACalmy4XT8s3nfffQs+d5999mlyrsaO1z+vNdYAAAAAAKD5kg23q6qq8upC9sL+yF577RXdunVrdK7Gjm+/j/bO1B+7atWqgs8FAAAAAKBppR3dQEtt2LAhr+7du3fB55aUlETPnj3jww8/jIiIjRs3FrTG7rvvXvAa9cc2tsbOZDKZFp1XDLbvPeXnAalwzUH7cs1B+3LNdX7F/uda7P1F6LE1FHt/EXrsrLzOQcskG25v2rQpr+7Ro0ezzi8rK8uF2/VD7MbWKPQDK3c0tqXhdnl5eYvOKzZ9+/bt6BagS3HNQftyzUH7cs21hvc7uoEGGr73Ka4ei72/CD22hmLvLyLVHmkOr3NQuGS3Jdm8eXNe3dxwe/vxW7ZsafU16o+tPxcAAAAAAC2X7J3b9e+Mrqmpadb5W7dubXSuptYoNODefv6m1tiZ6urqFp1XDDKZTO63jevWrYtsNtvBHUHn5pqD9uWag/blmuv8iv29T7H3F6HH1lDs/UXosbPyOkdX0dr/syPZcLtXr155dWN3Xzdm+/H152rs+ObNmwsOt+v309gaO9NZfphls9lO81wgBa45aF+uOWhfrrnOqdj/TIu9vwg9toZi7y9Cj12B1zkoXLLbktQPixvbN3tH6urq8rYJKTTcbs6+2fX7aWm4DQAAAABAQ8mG2xUVFXn1qlWrCj539erVsW3btlw9YMCAgtZ45513Cl6jfj+NrQEAAAAAQPMlG24PHTo0r3777bcLPrd+SL3//vsXtEZzwu36Y+vPBQAAAABAyyUbbh9wwAF59ZIlSwo+d9GiRU3O1djxxYsXt/oaAAAAAAA0X7Lhdt++fWPYsGG5evHixQV/qOT8+fPz6sMPP3yH48aMGRMlJX/9FtU/ryl/+tOfcl+Xl5fHJz7xiYLPBQAAAACgacmG2xERxx13XO7rmpqaePLJJ3d6zpYtW+KZZ57J1fvuu2+MGDFih2P79+8fhx56aK6eP39+VFVV7XSN+fPn5+25PX78+CgtLd3peQAAAAAAFCbpcPukk07Kq++///6dnvPII4/EBx98kKs/97nPFbxGbW1tPPDAAztd45e//GWTfQIAAAAAsGuSDrdHjBgR48ePz9Vz586NqVOnNjp+zZo18dOf/jRX77bbbvGVr3ylyTXOOuus6N+/f66+88474/XXX290/Jw5c2LatGl5PX72s59tcg0AAAAAAJon6XA7IuKKK67I2/LjBz/4QTz66KMNxv35z3+O888/P95///3csfPOOy/23nvvJufv1atXTJ48OVdv2bIlLrjggh1+gOXvf//7mDx5cmSz2bz+MplMs54TAAAAAABNa/ONoFeuXBknnHDCDh+rra3NG9fY3tf33ntvHHHEETt87OCDD47vf//78c///M8REbF169b41re+FXfeeWd88pOfjN122y1effXVePbZZ2Pbtm2584444oj45je/WdBzOPfcc2PevHkxffr0iIh45513YuLEiXH00UfH8OHDY9u2bbFgwYIGHzj5ta99LY455piC1gAAAAAAoHBtHm5ns9m8ELspjY3b/k7oHTn77LNj/fr1ceutt+YC7CVLluzw7uqIiCOPPDJuvfXW6N69e0F9RURcf/31UVtbG48//niup1mzZsWsWbMajM1kMnHeeefF5ZdfXvD8AAAAAAAULvltST5y8cUXx/333x9HHXVUlJTs+GkNHjw4vvvd78a9994b5eXlzZq/rKwsbr311vjRj34UBx54YKPjDjvssPjP//zP+O53v2s7EgAAAACANtLmd24PGjQoli5d2tbLRETEoYceGvfcc09UVVXFiy++GFVVVbF58+bYe++9Y//994/KyspdXuP000+P008/PZYuXRrLly+Pqqqq6NatW+y9994xcuTIGDJkSCs8EwAAAAAAmtLm4XZHqKioiBNPPLFN1xg+fHgMHz68TdcAAAAAAGDHOs22JAAAAAAAdB3CbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAklPa0Q0AABAx7ti6jm6hgVkz3QcBAAAUL+9YAAAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5JR2dAMAAKRh3LF1Hd1Cnlkz3acBAABdmXcEAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcko7ugEAAIDOZNyxdR3dQgOzZrqvCQDofPwLBwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5JR2dAMAAAAAdF7jjq3r6BYamDXT/Z7QGbiSAQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOPbcBgF1iD0UAAAA6gnd+AAAAAAAkR7gNAAAAAEByhNsAAAAAACQn+T23//7v/z7mzJmzy/Nceuml8Y1vfGOHjw0fPrzF8y5atChKS5P/NgNA0tpuX/D3W3ymfcEBAAB2jXdV/1+vXr06ugUAAAAAAAqU/C3FJSUl0a1bt2afV1tbm/s6k8nEiSeeWNB5mUwmSkoK/51AJpNpdm8AAAAAADQt+XD7vvvua/Y5M2bMiEsvvTRXf/KTn4zBgwcXdO4ll1zS6PYlAAAAAAC0jy65LclDDz2UV0+cOLGDOgEAAAAAoCW6XLi9Zs2a+N///d9c3atXrzjppJM6sCMAAAAAAJqry4XbjzzySNTU1OTqE088MXbfffcO7AgAAAAAgObqcuH2ww8/nFfbkgQAAAAAID1dKtx++eWXY8mSJbl64MCB8alPfaoDOwIAAAAAoCW6VLg9derUvPq0006LTCbTMc0AAAAAANBipR3dQHvZtm1bPPLII7k6k8m0aEuS559/PpYsWRJLly6NNWvWRGlpafTr1y+GDBkShx9+eJx00kmx3377tWbrAAAAAADU02XC7f/93/+N9957L1ePHTu2RSH03LlzGxz74IMPYsWKFfHss8/GLbfcEieffHJ897vfjf79++9SzxGR9J3l2/ee8vOAVLjm4K9SuAb0uOuKvT9al9e5XZPC96zYeyz2/iL02BqKvb8IPbaWYuvR6xy0TJcJt9vrgyRra2vj0UcfjTlz5sTtt98elZWVuzRfeXl56zTWwfr27dvRLUCX4pqjfb3f0Q000PD1U48tUew9dpZ/J9F8xf86V1zXSkTxX88Rxd9jsfcXocfWUOz9ReixtRTzvyOK/3UOikeXCLerq6vj6aefztU9e/aMk046qVlzDBkyJCZMmBBHHnlkfOITn4g999wzunXrFmvWrImXXnopHnvssXj88cejtrY2IiLefffduPjii+PBBx+0TQkAAAAAQCvrEuH29OnTY+vWrbn6xBNPjN69exd8/l133RVHH330Dv9byIABA2LAgAFx/PHHx6RJk+Kb3/xmvPPOOxERsXbt2rjqqqviV7/6VYt7r66ubvG5HS2TyeR+27hu3brIZrMd3BF0bq45+KsUXj/1uOuKvT9al9e5XZPC9VLsPRZ7fxF6bA3F3l+EHltLsfXodY6uorX/10SXCLenTp2aVzd3S5Jx48YVNK6ysjLuvvvuOOuss2L9+vURETF//vx45plnYvz48c1a8yOd5YdZNpvtNM8FUuCao6tL4e+/HnddsfdH2/E613wpfL+Kvcdi7y9Cj62h2PuL0GNrKeYevc5B4Uo6uoG29uqrr8aCBQty9cCBA+PII49ss/WGDh0aF198cd6x6dOnt9l6AAAAAABdUacPt+t/kORpp53W5p86e8YZZ+StMXv27DZdDwAAAACgq+nU4XZdXV1MmzYt71hztyRpif79+8fgwYNz9bvvvhs1NTVtvi4AAAAAQFfRqcPt3//+91FVVZWrx44dG/vtt1+7rN2/f/+8utg+qAAAAAAAIGWdOtze1Q+S3BWbNm3Kq8vKytptbQAAAACAzq7ThtsffvhhPPHEE7m6Z8+ecfLJJ7fL2nV1dfH222/n6u7du0efPn3aZW0AAAAAgK6g04bbjz32WGzevDlXn3DCCdG7d+92WXvevHnxwQcf5OqDDjqoXdYFAAAAAOgqOm24/fDDD+fVX/jCF9pt7Z/97Gd59bhx49ptbQAAAACArqBThtsrVqyIefPm5ep99903jjzyyGbPU11dnfeBlIX493//95g1a1au3m233eLss89u9toAAAAAADSuU4bb9e/aPu200yKTyTR7nnfeeSeOP/74+OEPfxh//OMfI5vNNjr2zTffjMsuuyxuv/32vOMXXXRRVFRUNHttAAAAAAAaV9rRDbS2bDYb06ZNyzu2K1uSbN26NR544IF44IEHory8PEaMGBEf//jHo0+fPlFSUhJr166Nl156KRYtWhR1dXV555588slx6aWXtnhtAAAAAAB2rNOF288//3ysXLkyV48dOzb222+/Vpm7uro6nnvuuXjuueeaHNetW7eYPHlyfP3rX2/RHeMAAAAAADSt04XbU6dOzasnTpzY4rkGDBgQF1xwQcyZMyeWLl0a27Zta3J8375945RTTom///u/j6FDh7Z4XQAAAAAAmtbpwu0bbrghbrjhhlaZq1+/fnH11VdHxF+2J3nllVfirbfeinfffTc2bNgQdXV10adPnygvL4/hw4fHAQcc4E5tAAAAAIB20OnC7bbSo0ePGDFiRIwYMaKjWwEAAAAA6PJKOroBAAAAAABoLuE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkp7egGAAAACjXy0Pc7uoUGZs10zxAAQEfwrzAAAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSU9rRDaRs2bJlsXz58qiqqoqSkpIYMGBAjBgxIvbbb7+Obg0AAAAAoFPrNOH2cccdFytXrmzRuf/zP/8TQ4YMKXj8tGnT4s4774ylS5fu8PHRo0fHJZdcEp/5zGda1A8AAAAAAE2zLUkzbNmyJa688sr4x3/8x0aD7YiI+fPnx1e/+tX40Y9+FNlsth07BAAAAADoGjrNndvby2QyUVJSeG6fyWQKGve9730vpk+fnnfe0UcfHcOHD4+amppYuHBhzJ8/PyIistls3H333dGzZ8/45je/2bwnAABAs407tq6jW2hg1kz3kgAAQFvplOH26aefHjfccEOrznn//ffHI488kqv32Wef+NnPfhYHH3xw3rjf//73cdlll8X69esjIuKOO+6IMWPGxLhx41q1HwAAAACArsytJAXYtGlT3H777bm6rKws7rnnngbBdkTE0UcfHXfccUfubvBsNhs//elP261XAAAAAICuQLhdgAcffDDee++9XH3RRRfF/vvv3+j4I444Ij7/+c/n6kWLFsXTTz/dpj0CAAAAAHQlwu0C/Pa3v8193a1bt/jSl76003POOeecvPrxxx9v9b4AAAAAALoq4fZOrFmzJl588cVcPXr06KioqNjpeYcddlgMGDAgV8+cOTNqa2vbpEcAAAAAgK5GuL0T8+bNi7q6ulw9evTogs897LDDcl9XV1fH8uXLW7M1AAAAAIAuS7i9E6+++mpePWLEiILPHTlyZF792muvtUpPAAAAAABdXWlHN9AWXn755bjiiiti0aJF8f7770dERHl5eQwaNCgOP/zwOP744+Oggw4qaK76gfQ+++xTcB/1xwq3AQAAAABaR6cMt5csWRJLlizJO/bhhx/GW2+9FX/4wx/itttui2OOOSa+//3vx5AhQ5qcq6qqKq/efh/tnak/dtWqVQWfCwAAAABA4zpluF2IZ599Ns4444z4yU9+Escee2yj4zZs2JBX77777gWvUX/sxo0bm9VjREQmk2n2OcVi+95Tfh6QCtcc/FUK14Aed12x9xeRRo+pKObvZTH39hE97rpi7y9Cj62h2PuL0GNrKbYevZ+DlulU4XZFRUVMmDAhjjrqqBg+fHj0798/evToEdXV1bFkyZJ44okn4uGHH46tW7dGRMT69evjm9/8ZkyZMiUOPfTQHc65adOmvLqsrKzgfuqPbUm4XV5e3uxzilHfvn07ugXoUlxztK/3O7qBBhq+fuqxJYq9x2LvL6Lz/FuOpqX5d1GPzVXs/UXosTUUe38Remwtxfwa7f0cFK7ThNv/+q//GocffniUljZ8SnvttVfstddeccwxx8SFF14Yl156aSxbtiwiIrZs2RJXXHFFPP7449GjR48G527evDmv3tGYxtQfW38uACjEyEOL683Aohf7d3QLAAAA0HnC7U9/+tMFjRsyZEjce++98cUvfjHefvvtiIhYuXJl/PrXv44vf/nLDcbXv/u6pqam4ID7ozvEG5urENXV1c0+p1hkMpncbxvXrVsX2Wy2gzuCzs01R3tJ4bVJj62j2Hss9v4i0ugxFdu/zhWbFP6c9bjrir2/CD22hmLvL0KPraXYevR+jq6itf/XRKcJt5ujf//+8e1vfzuuvPLK3LHHHntsh+F2r1698urNmzcXHG5v2bKlybkK0Vl+mGWz2U7zXCAFrjnaUgp/t/TYOoq9x2LvLyKNHtl1Kfw563HXFXt/EXpsDcXeX4QeW0sx9+j9HBSupKMb6Cif+9znonfv3rn6T3/6U4P9tSMaBtLN2Te7/odRtiTcBgAAAACgoS4bbpeWlsaoUaNy9bZt2+Ldd99tMK6ioiKvfueddwpeY9WqVXn1gAEDmtklAAAAAAA70mXD7Yi/bE+yvbVr1zYYM3To0Ly6OeF2/bH15wIAAAAAoGW6dLhdfxuSHX3g4wEHHJBXL168uOD5Fy1a1ORcAAAAAAC0TJcOt//85z/n1XvuuWeDMWPGjImSkr9+m+bPn1/w/H/6059yX5eXl8cnPvGJ5jcJAAAAAEADXTbcfuedd2L58uW5un///rH33ns3GNe/f/849NBDc/X8+fOjqqpqp/PPnz8/b8/t8ePHR2lp6S52DQAAAABARBcOt++4447IZrO5+uijj45MJrPDsSeddFLu69ra2njggQd2Ov8vf/nLRucAAAAAAGDXJB9ub926NV577bVmnfPf//3f8eCDD+bqTCYT559/fqPjzzrrrLwPn7zzzjvj9ddfb3T8nDlzYtq0abl6xIgR8dnPfrZZPQIAAAAA0Ljkw+3NmzfHqaeeGldeeWXMmjUrtm3b1ujY1atXx7/8y7/E9773vbzjp59+ehxyyCGNnterV6+YPHlyrt6yZUtccMEFsWTJkgZjf//738fkyZPz7gq/4oorGr0rHAAAAACA5usUm0DX1tbG9OnTY/r06dG7d+84+OCDY+jQodG3b9/o3r17rFu3Ll5++eV48cUXo6amJu/cT37yk3HttdfudI1zzz035s2bF9OnT4+Iv+zZPXHixDj66KNj+PDhsW3btliwYEGDD5z82te+Fsccc0zrPVkAAAAAADpHuL29Dz/8MObOnRtz587d6dhzzjknvvOd70SPHj0Kmvv666+P2traePzxxyMiIpvNxqxZs2LWrFkNxmYymTjvvPPi8ssvb1b/AAAAAADsXPLh9m677RZf+9rX4vnnn49FixbF1q1bmxzfq1evOP744+O8886LUaNGNWutsrKyuPXWW2Pq1Klx1113xbJly3Y47rDDDotLLrnEHdsAAAAAAG0k+XC7R48eccUVV0RExLZt2+L111+PN998M1atWhUbNmyIbdu2xR577BF9+vSJYcOGxfDhw6Nbt267tObpp58ep59+eixdujSWL18eVVVV0a1bt9h7771j5MiRMWTIkNZ4agAAAAAANCL5cHt7paWlMWzYsBg2bFi7rDd8+PAYPnx4u6wFAAAAAMBflXR0AwAAAAAA0FzCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACS06k+UBIAmmvcsXUd3UIDs2b63TMAAADsjHfPAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHJKO7oBAADoKsYdW9fRLTQwa6b7XQAASJN/yQIAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQnNKObgAAAAAAOtK4Y+s6uoWIeD/31ayZ7keFQrhSAAAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5JR2dAMAdF7jjq3r6BYamDXT73UBAACgM/AOHwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDklHZ0A22huro6li1bFitWrIjq6urIZrPRt2/f2HfffeOwww6LPfbYo6NbBAAAAABgF3SKcLuuri5eeOGFmDFjRvzhD3+IZcuWNTo2k8nEpz/96Zg0aVKMHz++oPnfeuutmDBhQot6q6ioiGeffbZF5wIAAAAAsGOdItw+6aSTYsWKFQWNzWaz8dxzz8Vzzz0Xp5xySlx77bXRu3fvNu4QAAAAAIDW1CnC7TVr1jQ49vGPfzwqKyvjYx/7WJSVlcWqVati9uzZsWrVqtyY6dOnx+rVq+POO++MsrKygtcrKSmJTCZT0NjS0k7xLQYAAAAAKCqdKnkdOHBgnHnmmTFx4sQYMGBAg8dra2vjwQcfjOuvvz62bNkSERFz5syJW265Jb7zne8UvM6//uu/xhe+8IVW6xsAAAAAgObpFOH2vvvuG+eff36cfvrp0a1bt0bHdevWLc4+++zYd99942tf+1rU1dVFRMSUKVNi0qRJUVFR0V4tAwAAAACwCzpFuP3QQw81a/uP8ePHxymnnBKPPPJIRETU1NTEk08+Geecc05btQgAAEkYd2xdR7eQZ9bMko5uAQA6XLG9Pkd4jaY4dIq/hS3Z1/qUU07JqxcuXNha7QAAAAAA0MY6RbjdEvvtt19e/d5773VQJwAAAAAANFeXDbc3bNiQV7fk7m8AAAAAADpGlw23ly5dmlcPGDCggzoBAAAAAKC5uuztytOmTcurjzzyyILP/d3vfhePPfZYvPrqq7F27dooKyuL8vLyGDZsWBx++OFx8sknx957793aLQMAAAAA8P91yXB7zpw5MWfOnFy9xx57xLhx4wo+f+bMmXn1pk2borq6Ot54442YMWNG/OQnP4kvfvGL8e1vfzt233331mobAAAAAID/r8uF2xs3bowf/OAHeccuuOCCVg2ht27dGvfff3/84Q9/iJ///OcxZMiQFs+VyWRara/2tn3vKT8PSIVrrjApfG+Kvcdi7y9Cj62l2Hss9v4i9NgaPuqvmPss5t4+osddV+z9ReixNRR7fxF6bC3F3mOx9xeRRo90fl0u3P7nf/7neOONN3L10KFD46KLLiro3OHDh8fxxx8fY8eOjU984hNRXl4e2Ww23nvvvXjxxRdj6tSp8eyzz+bGv/baa/HVr341HnjggejXr1+L+i0vL2/RecWmb9++Hd0CdCnFc82939ENNNDw56oem6vY+4vQY2sp9h6Lvb8IPbaGFP49XOzfwwg9toZi7y9Cj62h2PuL0GNrKfYei72/iDReo+n8ulS4fc8998RvfvObXN2jR4+48cYbo6ysrMnzysvL41e/+lWMHj16h48PGjQoBg0aFKeccko888wz8Y//+I+xbt26iIhYsWJFXHfddXHTTTe13hMBAAAAAOjiuky4/dhjj8WPf/zjvGPXXnttHHLIITs9t3fv3o0G2/WNHz8+7rjjjjj//PNj27ZtERExffr0+Id/+Ic48MADm913dXV1s88pFplMJnf36Lp16yKbzXZwR9C5ueYKk8LP1WLvsdj7i9Bjayn2Hou9vwg9toaP+tv+da7YFPv3MEKPraHY+4vQY2so9v4i9Nhair3HYu8vIo0eKT6tfcd/lwi3n3vuubjqqquirq4ud+xb3/pWTJw4sU3W++QnPxlnnHFGPPDAAxERkc1m47e//W2Lwu3OEk5ls9lO81wgBa65xqXwfSn2Hou9vwg9tpZi77HY+4vQY2so9v4i9Nhair3HYu8vQo+todj7i9Bjayn2Hou9v4g0eqTzK+noBtraiy++GJdccknU1NTkjl144YVx8cUXt+m6X/ziF/Pq2bNnt+l6AAAAAABdSacOt5ctWxYXX3xxbNy4MXfszDPPjKuuuqrN1z7kkEOie/fuufrtt99u8zUBAAAAALqKThtuv/nmm/GVr3wlb/+fk08+Oa699tp2Wb+kpCRvD5m1a9e2y7oAAAAAAF1Bpwy3q6qqYtKkSbF69ercsfHjx8eNN94YJSXt95Q3b96c+7qsrKzd1gUAAAAA6Ow6Xbi9Zs2amDRpUqxcuTJ37Igjjojbbrstb5uQtrZ27dpYv359ru7fv3+7rQ0AAAAA0Nl1qnD7ww8/jIsuuihee+213LFDDz00fv7zn7f7ndPPPvtsXn3QQQe16/oAAAAAAJ1Zpwm3N2/eHF/72tdi0aJFuWMHHXRQ/OIXv4jdd9+9XXupqamJX/ziF3nHxo0b1649AAAAAAB0Zp0i3N62bVtcdtllMXfu3Nyx/fffP+6+++7o27fvLs1dVVWV96GUO1NXVxc//OEPY/ny5blje+21V5xyyim71AcAAAAAAH+VfLidzWbj6quvjpkzZ+aODRo0KO67775W2ed64cKFcdxxx8WPfvSjWLx4cZNjlyxZEpMmTYqHHnoo7/iVV14ZvXr12uVeAAAAAAD4i9KObmBXvf322/HII480OPbZz362WfMMHDgwZsyYscPHNmzYEHfffXfcfffdsddee8WIESNi8ODBsccee0Q2m433338/XnzxxVi2bFmDcy+88ML4whe+0KxeAAAAAABoWvLhdjabbXCsrq6u2fPU1tYWNG716tXxzDPP7HTcbrvtFldffXWcffbZze4FAAAAAICmJR9ut7Xhw4fHOeecE3PmzInXXnttp8H5XnvtFRMnTowvf/nLMWDAgHbqEgAAAACga0k+3B40aFAsXbq0zeYfPHhwXHPNNRERsXHjxnjllVfirbfeivfeey82btwYmUwm9thjj9hzzz1j5MiRMXjw4DbrBQAAAACAv0g+3G5PvXr1isrKyqisrOzoVgAAAAAAurSSjm4AAAAAAACaS7gNAAAAAEByhNsAAAAAACTHntsACRt3bF29I+93SB8fmTXT70wBAACA9iGFAAAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDmlHd0AQLEad2xdR7eQZ9ZMv48EAAAA+IikBAAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOSUdnQDQNc07ti6jm6hgVkz/b4PAAAAWsL7fDqCP2EAAAAAAJIj3AYAAAAAIDnCbQAAAAAAkmPPbQAAAACg0yu2fcHtCb7rfAcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASE5pRzeQsurq6pg3b16sWrUqPvzww9h7771j0KBBMWbMmCgp8XsDAAAAAIC2ItxugTfeeCNuuummePrpp6OmpqbB43vvvXd86Utfiosvvjh69OjRAR0CAAAAAHRubi9upmnTpsXEiRPjf/7nf3YYbEdEvPvuu3HbbbfF3/3d38XK/9fevUfXdOZhHH9OSaLiEhGibhUxFmZK61KCNXFpZ1FaUgvLsqaidQlR1tBxmckhxTStjmlHMBpanbZTLZ24swyKThVBxnRcxqWurSYSkZDIheTMH5Y9dhJyjp5kn5N8P3/lt7Pf42lIz96/8+73/eGHCk4IAAAAAAAAAJUfM7dd8NVXX2nmzJkqLCw0jrVo0UJdu3ZVQECALl68qF27dikvL0+SdOzYMUVFRWnVqlWqVauWVbEBAAAAAAAAoNKhue2ktLQ0TZ061Whs22w2zZgxQ6NGjTKtr52RkaEpU6YoKSlJknTq1CnNmTNHCxcutCQ3AAAAAAAAAFRGLEvipGXLlunGjRtG/eqrr2r06NElNo4MDAzUihUrFBoaahzbvHmz/vvf/1ZYVgAAAAAAAACo7GhuO+Hq1atavXq1UTdv3lzjxo277/l+fn6y2+1G7XA4tHTp0nLNCAAAAAAAAABVCc1tJ+zcuVMFBQVGPWzYMPn4+DxwTFhYmEJCQox6z549ys3NLbeMAAAAAAAAAFCV0Nx2wpdffmmq+/Xr59S4e8/Ly8vT3r173ZoLAAAAAAAAAKoqmttOOHTokPF1UFCQmjVr5tS4p556ylQfPHjQrbkAAAAAAAAAoKqiuV2GK1eumDaSbNu2rdNj27VrZ6q/++47t+UCAAAAAAAAgKqsutUBPN3Zs2dNdePGjZ0eGxQUJB8fH926davU10LpevYqsjpCCV/vNn8O5GkZi+cDAAAAAAAAKjs6YmVITU011cHBwU6PtdlspvOLvxYAAAAAAAAA4OEwc7sMOTk5ptrf39+l8feef/v2bRUUFMjX19fp8TabzaU/z5Pcm92b/zskz8/v6fm8haf/HD09n0RGd/H0jJ6eTyKju3h6Rk/PJ5HRHe7m8+ScnpztLjL+dJ6eTyKjO3h6PomM7uLpGT09n0RGd/D0fN6A5nYZcnNzTbWfn59L44ufn5OT41JzOyAgwKU/z1PVrVvXhbOvlluOh1Xy78GzMnrnvxPP+hlK3vr37OkZPSufREZ38PR8EhndxdMzeno+iYzu4A3XOZ7+M5TI6A6enk8iozt4ej6JjO7i6Rk9PZ9ERnfwhuscT2dzOBwOq0N4siVLlmjRokVG/cYbb2jIkCFOjx85cqQOHTpk1Hv27FGjRo3cmhEAAAAAAAAAqhrW3C5D8ZnXdzeHdFZBQYGpdmXWNgAAAAAAAACgdDS3y1CzZk1TnZeX59L4/Px8U+3qmt0AAAAAAAAAgJJobpeheHP75s2bLo2/d0PK6tWru7xmNwAAAAAAAACgJJrbZQgODjbVKSkpTo91OBxKTU2972sBAAAAAAAAAB4Oze0ytGzZ0lRfvnzZ6bHp6emmNbpDQkLclgsAAAAAAAAAqjKa22UIDg5W7dq1jfrEiRNOjz1+/LipDg0NdVsuAAAAAAAAAKjKaG47oVOnTsbX6enpunTpklPjkpOTTXWXLl3cmgsAAAAAAAAAqiqa207o06ePqd66datT47Zt22Z87efnpx49erg1FwAAAAAAAABUVTS3ndC3b1/5+PgY9Zo1a0xraZdm3759OnfunFGHh4erZs2a5ZYRAAAAAAAAAKqS6lYH8AZBQUEaOnSoPv30U0nSxYsXlZCQoOjo6FLPz8/P1/z5843aZrNpwoQJFZK1MikqKtKxY8d0+vRppaenq7CwUP7+/mrcuLF+9rOf6fHHH7c6IgAATnM4HLp48aJOnz6tlJQUZWdny8/PTwEBAWrdurXatGmjatWqWR0T8EiZmZlKTk42fncaNmyopk2bqmPHjnrkEebrAO6UmZmpU6dO6cKFC8rMzJTD4VDdunXVuHFjPfnkk6Y9qQAAsBrNbSdFRUVp/fr1ysnJkSTFx8fL399fL730kumCOiMjQ1OmTNGZM2eMY88995zatWtX4Zm9VUZGhpYvX661a9fq2rVr9z2vXr166tmzp2JiYhQQEFBxAYFKLjs7WwMGDFBKSorp+EcffaSuXbtalArwTjdu3NCOHTu0e/duHThw4IHva7Vq1VJERIQiIyPVtGnTCkwJeK7z589r4cKF2rVrV6lPTjZs2FDDhw/XuHHj5Ovra0FCwPsVFRXp0KFD2r59u/bv369Tp07d91ybzaawsDBFRkYqPDy8AlMCVc/8+fP18ccfm45FRETozTfftCgR4JlsDofDYXUIb7F7925NmDBBRUVFxrEWLVqoW7duCggI0IULF7Rr1y7l5eUZ32/VqpU+//xz1apVy4rIXmfLli2aPXu2bty44dKY0NDQckwFVC2xsbFatWpVieM0twHX7N+/X2PGjClzKbPiatasqZiYGA0ZMqSckgHeYcOGDZozZ45u3rxZ5rk///nPFR8fryZNmlRAMqBy+dWvfqULFy64PG7AgAGaO3cu97pAOThy5IhGjBhh6j9JNLeB0jBz2wW9evVSXFycYmNjlZubK+nObJLz58+Xen7btm21ePFi3uyd9P7772vBggWmY7Vr11ZYWJgee+wx+fv76/r16zp16pSOHj3q1I0OANccPnxYn332mdUxgEohOzu7RGPb19dXHTp0UMuWLRUYGKiCggKdPn1aBw4cUH5+viTp5s2b+t3vfqe8vDyNHDnSiuiA5b766ivNnDlThYWFxrEWLVqoa9euCggI0MWLF02TSo4dO6aoqCitWrWKa2/ARRkZGSWOtWjRQu3bt1dQUJD8/PyUkpKiffv2mZ7s27x5s9LS0rRixQr5+flVZGSgUrt165bsdnuJxjaA0tHcdtHgwYPVvn17LVy4UHv27Cl1NlaDBg00bNgwRUVF8XikkzZt2mRqbNepU0fTpk3Tiy++WOrPMD8/X//85z/16aefymazVWRUoNIqKCiQ3W7X3Qd6GjRooLS0NItTAd7v7iPcw4cPV+/evUttAKSlpWnevHnatm2bcWz+/Pnq1KmT2rRpU5FxAculpaVp6tSpRmPbZrNpxowZGjVqVKnLASYlJUmSTp06pTlz5mjhwoWW5Aa8XZMmTTR06FBFRESoUaNGJb5fWFio1atXKy4uzvhANikpSe+++65mzJhR0XGBSishIcFYHoh7MqBsLEvyE1y7ds3Y2CYnJ0dBQUFq1qyZOnbsyIZQLrh69ar69++vrKwsSXc28Pzkk08UEhJicTKgaomPj9fixYslSb/85S9Vv359rV271vg+y5IArtmxY4c+//xzTZs2zakGtcPh0GuvvaZNmzYZx8LDw5WQkFCeMQGPM2/ePH3yySdGPXny5Adu5B4REaHvvvtO0p1G+Lp16/hQCHDBCy+8oFGjRmnw4MFO3cfu2bNHUVFRxqxSHx8f7dy5U8HBweUdFaj0zp49q0GDBqmgoECPPvqoZs+erVmzZhnfZ1kSoCS2Fv8J6tWrp759+2rkyJEaN26cXnzxRXXp0oXGtovi4uKMxrbNZtOiRYtobAMV7MyZM3rvvfckSTVq1NDs2bMtTgR4v169emn58uVON9lsNpvsdrv8/f2NY998842ys7PLKyLgca5evarVq1cbdfPmzTVu3Lj7nu/n5ye73W7UDodDS5cuLdeMQGWTmJioIUOGOH0fGx4ergEDBhj1rVu3tHPnzvKKB1QZDodDdrtdBQUFkqSJEyeylwTgBJrbsNTly5e1efNmox4wYIA6depkYSKg6ikqKlJMTIyxzFJ0dLSaNWtmcSrA+1Wv7vrqbwEBAerZs6dR37p1S8ePH3dnLMCj7dy507ipl6Rhw4bJx8fngWPCwsJMEyP27Nlj7I8DoGwP8351b3Nbkv7zn/+4Kw5QZX322Wc6dOiQJKl169YaPXq0xYkA70BzG5ZKTEw0bZIwfPhwC9MAVdOqVav0r3/9SxIXUYAnaN68ualOT0+3KAlQ8b788ktT3a9fP6fG3XteXl6e9u7d69ZcAMx4rwLcKzU11dgzwmaz6fXXXy/zw10Ad9DchqU2btxofB0YGKjOnTtbmAaoelJSUkwXUbGxsVxEARbLyckx1fxOoiq5O2NNkrGfjTOeeuopU33w4EG35gJgVvy96mFmfwP4v3nz5unGjRuS7jy11LFjR4sTAd6D5jYsk5WVpfPnzxt1u3bt9Mgj/JMEKlJsbKxxczJ06FCWBQI8wMmTJ001G3Shqrhy5YpxYy9Jbdu2dXpsu3btTPXdDSYBlI/i71WNGjWyKAng/f7xj39o+/btkqT69etr2rRpFicCvAsfr8IyR48eNdWtWrUyvj58+LDWrl2rI0eO6Mcff1S1atVUr149PfHEEwoPD1f//v2ZHQD8RFu2bNGuXbsk3bmIeu211yxOBODSpUtKTk426jp16pRo2gGV1dmzZ01148aNnR4bFBQkHx8fY/+I4q8FwL02bNhgqrt162ZREsC73bhxQ3PnzjXqmTNnqm7duhYmArwP3UFY5syZM6a6fv36ysrK0uuvv27aZPKuuzO9N27cqPj4eMXGxqp79+4VFReoVLKysvSHP/zBqGfMmMFFFOABli5dKofDYdTPPvssH+aiykhNTTXVrjy1YLPZFBwcrO+//77U1wLgPklJSUpKSjLq2rVrmzZDBuC8BQsWKC0tTZLUvXt3vfDCCxYnArwPa0DAMllZWabaZrNp9OjRpTa2i7tw4YLGjh2rtWvXllc8oFJ76623jI1/wsLCNGjQIIsTAdi7d68SExON2sfHR+PHj7cwEVCxiq/h6+/v79L4e8+/ffu2CgoK3JILwP/dvHlTdrvddGz06NEu/74CuLM/xJo1ayRJfn5+io2NtTYQ4KWYCgTL3LumoiQlJCTo+vXrkqQWLVooKipK3bt3V7169ZSZmamkpCQtW7ZMp0+flnTnpsVutys0NFTt27ev8PyAt9q/f7/+/ve/S5J8fX25iAI8QGpqqqZPn246Nn78eD3++OMWJQIqXm5urqn28/NzaXzx83NycuTr6/uTcwH4v9jYWNO+SS1bttSYMWOsCwR4qYKCAtntduOJPa77gIfHzG1Y5ubNm6b6bmO7W7duWrdunSIiIhQcHCxfX181bNhQAwcOVGJionr37m2MuXXrlmbPnl2huQFvlp+fb/qdGT9+vFq0aGFdIADKy8vTpEmTjKcpJOnJJ59UVFSUhamAipeXl2eqXW1MFz8/Pz//J2cC8H8rV67U+vXrjdrX11dvv/22yx9EAZCWLFmic+fOSZJCQkI0duxYixMB3ouZ21CfPn30ww8/lNvrT58+Xa+88kqJ46XdsNSrV0/vvPOOHn300VJfy9fXV3/84x81cOBA/fjjj5KkEydOaO/everRo4d7gwPlxKrfOUmKj4/XhQsXJN25iBo3bly55QA8hZW/c2UpLCzU1KlT9e233xrHHnvsMS1atEg+Pj7uigh4heINsrubQzqr+DIkzNoG3GfLli1asGCB6djcuXP1i1/8wqJEgPc6efKk3n//faN+/fXXec8CfgJmbsMyNWvWLHFsxIgRCgwMfOC4WrVqKTIy0nRs165d7owGVEonTpzQypUrjZqLKMB6drtdO3fuNOqAgACtWLHCpY30gMqi+LVh8ZncZSk+U5s1gAH3+OabbzR9+nQVFRUZx6ZNm6aIiAgLUwHeqaioSDExMcYHuBEREeratavFqQDvRnMblinthuPeJUcepE+fPqY6OTnZLZmAyqqwsFAxMTG6ffu2JC6iAE/w1ltvGevfS3caewkJCWrVqpWFqQDrFG9uF1/Criz3bkhZvXp1lkoA3ODf//63oqOjTU9SvPLKKzz9Bzykjz/+2HhiLyAgoMSeKwBcx7Ik0J///OdyXZOwWbNmpR5v1KhRiWOtW7d26jWbN2+uGjVqGDN6rly58vABgQpmxe/cpk2bdPToUUlcRKHqsep97kH+8pe/6IMPPjBqX19fLVmyRB06dHBnNMCrFH9iISUlxemxDodDqamp930tAK47deqUxo0bZ/qgaejQoVxHAg8pLy9P7777rlFPnz69zCfXAZSN5jb0xBNPWPLnFp+Z5uvrqxo1ajg9vk6dOkZzOzMz053RgHJlxe/ctWvXjK+zsrLUs2fPMsfc++ipJEVGRspmsxn1hx9+qKefftp9IYFyYtX73P387W9/M93YVKtWTe+88466d+9uXSjAA7Rs2dJUX7582emx6enpppmlISEhbssFVEUXL17Uyy+/bLrP6t+/v+bOnWtdKMDLFRQUmD4sstvtstvtDxzjcDhM9bp167RhwwajHjx4sN544w33BgW8DM1tWCY0NFQ2m834n/Xt27flcDhMzbMHuXfTIB47BZzncDhUWFjo8rjize7iF1oAyrZu3TrNmzfPqG02m+Li4vTMM89YmArwDMHBwapdu7Zu3Lgh6c5eEc46fvy4qQ4NDXVrNqAqSU1NVWRkpNLS0oxj4eHhevvtt/XII6xsCrjLw9yTFb+XK36PBlRFvDPBMv7+/mrXrp1RFxUVOb28SG5urq5fv27UPMoDAPB0O3bs0O9//3vTB0Nz5szRoEGDLEwFeJZOnToZX6enp+vSpUtOjSu+/0qXLl3cmguoKjIyMhQZGakffvjBOPb0008rPj5ePj4+FiYDAKB0zNyGpZ599lkdO3bMqJOTk9W/f/8yxx05csT0CWXbtm3LJR9QWURGRioyMtKlMTNnztTatWuN+qOPPmITSuAh7du3T7/5zW+MTV0l6be//a1GjBhhYSrA8/Tp00e7d+826q1btzq1cd22bduMr/38/NSjR4/yiAdUatnZ2RozZozOnj1rHOvQoYOWLVvGk7KAG9SpU0cnT550acyBAwf00ksvGXVERITefPNNd0cDvBozt2Gpfv36mR5t++KLL5wat2bNGlPNDQwAwFN9++23mjhxomk5rejoaI0ZM8bCVIBn6tu3r2l26Jo1a0xraZdm3759OnfunFGHh4erZs2a5ZYRqIzy8vIUFRVlmnjUpk0bLV++XP7+/hYmAwDgwWhuw1IhISF6/vnnjfrrr7/W1q1bHzjm66+/1pYtW4w6ICBAAwcOLLeMAAA8rNOnT2vs2LGmzYMiIyM1efJkC1MBnisoKEhDhw416osXLyohIeG+5+fn52v+/PlGbbPZNGHChHLNCFQ2t2/f1pQpU3Tw4EHjWEhIiD744APVrVvXwmQAAJSN5jYsN3nyZNPsmunTpysxMbHUc7ds2aJXX33VtF7ppEmTmE0AAPA433//vV5++WVlZmYax4YPH65Zs2ZZFwrwAlFRUaZru/j4eH344YclNs3KyMjQmDFjdObMGePYc889Z9rTBcCDORwOzZw507QcUNOmTfXXv/5V9evXty4YAABOYs1tWK5p06ZauHChoqOjVVRUpIKCAs2aNUvvvfeewsLCFBgYqMzMTB04cMB08yJJAwYM0K9//WuLkgMAcH/r1q0rsVHyF1984fQSXHdNnDhRkyZNcmc0wKMFBwfrT3/6kyZMmKCioiI5HA7FxcVp1apV6tatmwICAnThwgXt2rVLeXl5xrhWrVpp7ty5FiYHvM/ly5e1cePGEsd69+7t0us0adJE27dvd2c0AACcQnMbHqFPnz5asGCB5syZo5ycHEnS+fPndf78+fuOGTFihGJiYiooIQAArrn3KaO7CgsL3fI6QGXXq1cvxcXFKTY2Vrm5uZIefG3Ytm1bLV68WLVq1arAlID3K+09pvhTEs54mPc3AADcgWVJ4DGef/55rV+/XgMHDlSNGjVKPcdms6lz585auXKlYmNjVb06n88AAABURoMHD1ZiYqKeeeYZ0yaT92rQoIGio6O1evVqNW3atIITAgAAwGo2B9OB4IGys7N1+PBhpaSk6Nq1a6pVq5YaNmyozp07KzAw0Op4AAAAqEDXrl1TcnKyUlJSlJOTo6CgIDVr1kwdO3ZUtWrVrI4HAAAAi9DcBgAAAAAAAAB4HZYlAQAAAAAAAAB4HZrbAAAAAAAAAACvQ3MbAAAAAAAAAOB1aG4DAAAAAAAAALwOzW0AAAAAAAAAgNehuQ0AAAAAAAAA8Do0twEAAAAAAAAAXofmNgAAAAAAAADA69DcBgAAAAAAAAB4HZrbAAAAAAAAAACvQ3MbAAAAAAAAAOB1aG4DAAAAAAAAALwOzW0AAAAAAAAAgNehuQ0AAAAAAAAA8Do0twEAAAAAAAAAXofmNgAAAAAAAADA69DcBgAAAAAAAAB4HZrbAAAAAAAAAACvQ3MbAAAAAAAAAOB1aG4DAAAAAAAAALwOzW0AAAAAAAAAgNehuQ0AAAAAAAAA8Do0twEAAAAAAAAAXofmNgAAAAAAAADA69DcBgAAAAAAAAB4HZrbAAAAAAAAAACv8z8zpwU8WQkqogAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 491,
       "width": 731
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(pm.draw(y, draws=2000, random_seed=rng), bins=30, rwidth=0.9);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e1b1cab-56ce-4ddd-95d3-6454c8d0aae0",
   "metadata": {},
   "source": [
    "The other way is where we use the built-in {class}`NormalMixture <pymc.NormalMixture>` distribution. Here the mixture assignment is not an explicit variable in our model. There is nothing unique about the first model other than we initialize it with {class}`pmx.MarginalModel <pymc_extras.MarginalModel>` instead of {class}`pm.Model <pymc.model.core.Model>`. This different class is what will allow us to marginalize out variables later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "27852bef-f23b-4151-bc41-1af26f934e61",
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model() as prebuilt_mixture:\n",
    "    y = pm.NormalMixture(\"y\", w=[0.3, 0.7], mu=[-2, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e318f820-9a2c-4b7d-bdfd-34cb1a9eecff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABbcAAAPXCAYAAAAYJXYaAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8fJSN1AAAACXBIWXMAAB7CAAAewgFu0HU+AAB2HklEQVR4nOzde3yU9Zk3/mtCIIIIQaqgglQsoiAoUK1VKlbU6upWqdWuratYrdui9dSudXty18ddba1V19X2tfW4PC9b7b6UUrH2hwd0qVSwUEFAwBNWlIhCEDkGMr8/+jjL5MQkmSTzTd7vv3Ld8z1cE71nyCd37slks9lsAAAAAABAQso6ugEAAAAAAGgu4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJCc8o5ugKatW7euVfMzmUxUVlZGRER1dXVks9kidAW0hvMSSpNzE0qP8xJKk3MTSo/zklT069evqOu5chsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDklHd0AwAAAEDxjT+utg1Xf79Fs2bPco0dAMXjXQUAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5JS394bV1dWxfPnyWLlyZVRXV0c2m42+ffvGvvvuG4cffnjsscceRdnnzTffjCVLlsTq1aujtrY2BgwYEMOGDYuDDjqoKOtHRCxcuDDeeOONqKqqip49e8aAAQNi9OjRMWDAgKLtAQAAAABAfW0ebtfW1sYLL7wQM2fOjD/+8Y+xfPnyRsdmMpn49Kc/HZMnT44JEya0aL9nn3027rzzzliwYEGDjw8fPjy+9rWvxd/+7d+2aP1sNhtTp06NqVOnxptvvlnv8bKysjj66KPjiiuuiFGjRrVoDwAAAAAAmpbJZrPZttzgpJNOipUrVzZ73qmnnhrXXXdd9O7du6Dx2Ww2brzxxrj//vujkKd02mmnxQ033BA9evQouKfq6uq44oorYs6cObsc27179/j2t78dkydPLnj9hqxbt65V8zOZTFRWVkZE5K6UBzqW8xJKk3MTSo/zElpn/HG1Hd1CPbNnuTsqtAXvmaSiX79+RV2vza/cXrt2bb1jH//4x2P06NHxsY99LCoqKmL16tUxZ86cWL16dW7MjBkzYs2aNXHXXXdFRUXFLve59dZb47777ss7Nnbs2Bg1alR069YtXn755ZgzZ07u5H700Ueje/fuceONNxb0PGpqauKb3/xmzJ07N3ese/fuceyxx8aBBx4YGzdujBdeeCGWLVuWG3/DDTfEHnvsEWeeeWZBewAAAAAAUJh2u+f2fvvtF2eddVZMmjQpBg4cWO/xHTt2xEMPPRQ33HBDbN26NSIi5s6dG7feemt85zvfaXLtZ555Jn7+85/n6j59+sS///u/x6c//em8cUuWLIlvfOMbuRD9kUceibFjx8bZZ5+9y/5vvfXWvGD7oIMOip/97GcxaNCgvHHTp0+P7373u1FTUxMREddee22MHj06hg0btss9AAAAAAAoTJv/PdC+++4b//Zv/xYzZ86Mb3zjGw0G2xER3bp1i3POOSduv/32KCv737amTp0aVVVVja6fzWbj5ptvztWZTCbuvPPOesF2RMSIESPivvvuy7sS/Pbbb8+F6Y2pqqqKqVOn5ur+/fvHf/3Xf9ULtiMiPv/5z8f111+fq2tqauK2225rcn0AAAAAAJqnzcPthx9+OM4888zo1q1bQeMnTJgQp556aq6uqamJJ598stHxTz75ZO5WIBERp59+ehxxxBGNjj/ggAPiwgsvzNXvvvtu/PrXv26yp7vvvjsvAP/Wt77V5P1hzjjjjLweZs6c2eQHaQIAAAAA0DxtHm6Xlzf/zic7h9sREYsWLWp07O9+97u8+itf+cou1/+7v/u7vLD98ccfb3L8zo/37ds3TjvttF3ucc455zS6BgAAAAAArVOSH1O8//7759Xvvfdeg+O2b98e//M//5Or99lnnxg9evQu1x8wYEAcfvjhuXr+/Pmxbt26Bse+9NJLebdFOe644wr6gMuJEydG9+7dc3VTV58DAAAAANA8JRlub9y4Ma9u7OrvFStWxPr163P1mDFjCt5j53B7x44dMX/+/AbHvfDCC3l1oXvstttucfDBB+fql19+OTZs2FBwfwAAAAAANK4kw+2d76EdEY1+COWrr76aVx9yyCEF7zFy5Mgm1/rIa6+9llePGDGi4D3qjq27FgAAAAAALVOS4fb06dPz6qOOOqrBcXXD4n333bfgPfbZZ5+8+vXXXy9oj7rzmlK3H+E2AAAAAEBxlFy4PXfu3Jg7d26u3mOPPWL8+PENjt35XtgRjV/h3ZC6Y1evXr3LPcrLy+NjH/tY0fcAAAAAAKB5Gr6ZdQfZtGlT/OAHP8g7dsEFF8Tuu+/e4Pi69+ZubFxD6o7dtGnTLvfo2bNnlJUV/vuAQvdoSiaTafacxua3di2gOJyXUJqcm1B6nJfQ+TiXoW14z6SrKqlw+5//+Z/jjTfeyNVDhw6Niy66qNHxmzdvzqt79OhR8F4VFRV5dWPB88571J2zK3X7aUm4XVlZ2ew5jenbt2/R1gKKw3kJpcm5CaXHeQkt8X5HN1BPMX/GBRrmPZOupGRuS3LvvffGb37zm1zdo0ePuOmmm5oMlLds2ZJXNyfcrju27loNHW/O+s3ZAwAAAACA5imJK7cfe+yx+PGPf5x37LrrrotDDz20yXl1g++ampqC99y2bVuTa+18/KOrt5uzfnP2aEp1dXWz5+wsk8nkfmO3fv36yGazrVoPaD3nJZQm5yaUHucldD6t/RkXaJj3TFJR7L/g6fBw+7nnnourr746amtrc8e+9a1vxaRJk3Y5t1evXnn11q1bC9637ti6a+18/KNwu7lXXtcNtxvboynFfDHKZrNe3KDEOC+hNDk3ofQ4L6FzcB5D2/OeSVfSobclefHFF+OSSy7JuyL6wgsvjIsvvrig+XXD4rofMNmUumObCrc/snnz5ma9OBS6BwAAAAAAzdNh4fby5cvj4osvzvuQxbPOOiuuvvrqgtcYMGBAXr169eqC59YdO3DgwF3usX379lizZk3R9wAAAAAAoHk6JNx+880346tf/WrevbZOOeWUuO6665q1ztChQ/Pqt99+u+C577zzTpNrNXa87rym1O2nsT0AAAAAAGiedg+3q6qqYvLkyXlXQE+YMCFuuummKCtrXjsHHnhgXr106dKC5y5evDivbix4rrvHkiVLCt6j7ljhNgAAAABAcbRruL127dqYPHlyrFq1KnfsyCOPjNtvvz26d+/e7PUOOuig6NOnT65esGBBwXN3HtutW7cYO3Zsg+PGjRvX6LymbNmyJV5++eVcPXz48LxeAQAAAABouXYLtz/88MO46KKL4rXXXssdO+yww+LnP/95VFRUtGjN8vLyOPbYY3P1O++8Ey+++OIu51VVVcWf//znXD1mzJjYc889Gxx76KGH5t13++mnn46tW7fuco8nnngi74MyJ06cuMs5AAAAAAAUpl3C7S1btsTXv/71vFuBHHzwwfGLX/widt9991atffLJJ+fVDzzwwC7n/OpXv4ra2tpG19hZJpOJk046KVd/8MEH8eijjxa0x84+97nP7XIOAAAAAACFafNwe/v27XH55ZfHvHnzcscOOOCAuOeee6Jv376tXn/ixIlx0EEH5erf/OY3eXvV9frrr8fdd9+dq/faa68466yzmtzjoosuih49euTqm2++OdatW9fo+GnTpuX1MHHixDj44IOb3AMAAAAAgMK1abidzWbjmmuuiVmzZuWODRo0KO6///7o379/UfYoKyuLq666Km/PKVOmxJw5c+qNXbJkSUyePDnvtiKXXnpp7Lbbbk3uMXDgwDj33HNz9fvvvx/nnXdevPXWW/XGTp8+Pb7//e/n6u7du8fll1/erOcEAAAAAEDTMtlsNttWi69atSqOP/74vGNlZWWRyWSatc5+++0XM2fObHLMT37yk/jFL36Rd2zcuHExatSoKCsri2XLlsVzzz0XOz/dz3/+83HTTTcV1MO2bdviggsuiBdeeCF3rHv37jFhwoQYOnRobNq0KebNmxfLli3Lm3f99dfv8srwpjR1hXghMplMVFZWRkREdXV1tOF/bqBAzksoTc5NKD3OS2id8cfV7npQO5s9q90++gu6FO+ZpKJfv35FXa+8qKvV0dCJtPO9rgu1Y8eOXY656qqrYsuWLTF16tTcsT/96U/xpz/9qcHxf/M3fxPXX399wT306NEjbr/99rj88stj7ty5ERFRU1MTTzzxRIPjy8vL46qrrmpVsA0AAAAAQMM6za9My8rK4vvf/37853/+Zxx++OGNjjvooIPixz/+cdxyyy1RUVHRrD323HPPuP/+++Of/umfYvDgwY32cfTRR8cvf/nLuPDCC5u1PgAAAAAAhWnT25J0pJUrV8bixYvj3XffjR07dsSAAQNi2LBhMXz48KKsn81mY9GiRfH666/Hu+++G7vttlsMGDAgDjvssBgwYEBR9ohwWxLojJyXUJqcm1B6nJfQOm5LAl2H90xSkdRtSTrSkCFDYsiQIW22fiaTidGjR8fo0aPbbA8AAAAAABrmV6YAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkp7yjGwAAAAC6pvHH1XZ0C3lmz3INIEBKvGoDAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAySnv6AYAAAAgNeOPq+3oFuqZPcv1awB0Ld75AAAAAABIjnAbAAAAAIDkCLcBAAAAAEhOu91ze+PGjbFkyZJYuHBhLFy4MBYtWhSrVq3KPb7ffvvFU0891aw1jz/++Lw1WuqGG26IL3zhCw0+9tZbb8XEiRNbtO6AAQPi2WefbU1rAAAAAAA0oM3D7XvvvTcefvjheOWVV6K2tvQ+cCMiolevXh3dAgAAAAAAzdDm4fa8efNi+fLlbbJ2t27dolu3bs2ak81m80L2Xr16xWc+85mC55eVlUUmkylobHl5u10YDwAAAADQpXRI+tqrV68YOXJkLF68ODZt2tTidWbOnNnsOffdd1/ccMMNufqkk06K3XffveD5//qv/9roLUwAAAAAAGgfbR5uV1RUxOjRo2PUqFExatSoOPTQQ+PAAw+MsrKyOP7441sVbrfEI488kldPmjSpXfcHAAAAAKD12jzcvuWWW9p6i4ItXbo0Xn755Vy93377xac+9akO7AgAAAAAgJYo6+gG2lPdq7bPOOOMgu+fDQAAAABA6egy4fb27dvj0UcfzdWZTMYtSQAAAAAAEtVlwu1nnnkm3n///Vw9bty4GDx4cAd2BAAAAABAS3WZcHvatGl5tau2AQAAAADS1eYfKFkK1q1bF08//XSu7tmzZ5x88sktWuv3v/99PPbYY/Hqq6/GunXroqKiIiorK2PYsGFxxBFHxCmnnBJ77713sVoHAAAAAKABXSLcnjFjRtTU1OTqk046KXr37t2itWbNmpVXb968Oaqrq+ONN96ImTNnxk9+8pP44he/GN/+9rdj9913b03bERGt/sDLnef78EwoDc5LKE3OTSg9zktonhTOk1LvsdT7g8Z4z6Sr6hLh9iOPPJJXt+UtSbZt2xYPPPBA/PGPf4yf//znMWTIkFatV1lZWZzGIqJv375FWwsoDucllCbnJpQe5yWl5/1dD2ln9X9+1GNzFfNncOgo3jPpSjp9uL1ixYp46aWXcvV+++0XRx11VLPXGT58eJxwwgkxbty4+MQnPhGVlZWRzWbjvffeixdffDGmTZsWzz77bG78a6+9Fl/72tfiwQcfjH79+hXluQAAAAAA8FedPtyue9X26aef3qw/z6isrIxf/epXMWbMmAYfHzRoUAwaNChOPfXUeOaZZ+If//EfY/369RERsXLlyrj++uvj5ptvbnH/1dXVLZ4b8dc/RfnoN3br16+PbDbbqvWA1nNeQmlybkLpcV5C87T258f2UOo9lnp/0BjvmaSi2H8h06nD7R07dsT06dNzdSaTafYtSXr37t1osF3XhAkT4s4774zzzz8/tm/fHhF/vd/3P/zDP8RBBx3UrH0/UswXo2w268UNSozzEkqTcxNKj/MSdi2Fc6TUeyz1/qAQ3jPpSso6uoG2NHv27FizZk2uHjduXOy///5tuucnP/nJOPPMM3N1NpuN3/3ud226JwAAAABAV9Opw+1p06bl1W35QZI7++IXv5hXz5kzp132BQAAAADoKjptuL1hw4Z48sknc3XPnj3j5JNPbpe9Dz300OjevXuufvvtt9tlXwAAAACArqLThtszZsyIrVu35uoTTzwxevfu3S57l5WV5d0cfd26de2yLwAAAABAV9Fpw+26tyT5whe+0K77b9myJfd1RUVFu+4NAAAAANDZdcpw+/XXX48FCxbk6n333TeOOuqodtt/3bp1sWHDhlzdv3//dtsbAAAAAKAr6JThdt2rtk8//fTIZDLttv+zzz6bVx988MHttjcAAAAAQFfQ6cLt2tra+M1vfpN3rD1vSVJTUxO/+MUv8o6NHz++3fYHAAAAAOgKOl24/fzzz8c777yTq8eNGxf7779/i9aqqqqK6urqgsfX1tbGD3/4w1ixYkXu2F577RWnnnpqi/YHAAAAAKBhnS7cfvjhh/PqSZMmtXitRYsWxfHHHx8/+tGPYsmSJU2OXbp0aUyePLne/ldddVX06tWrxT0AAAAAAFBfeVtvsGrVqjjxxBMbfGzHjh1540aMGNHguPvuuy+OPPLIXe714YcfxsyZM3N1z54945RTTmlmx/k2btwY99xzT9xzzz2x1157xYgRI2Lw4MGxxx57RDabjffffz9efPHFWL58eb25F154YbveEgUAAAAAoKto83A7m83mhdhNaWxcNpstaP7vf//72Lx5c64+8cQTo3fv3gXNLcSaNWvimWee2eW43XbbLa655po455xzirY3AAAAAAD/q83D7fY0bdq0vLq1V00PHz48vvzlL8fcuXPjtddei9ra2ibH77XXXjFp0qT4yle+EgMHDmzV3gAAAAAANK7Nw+1BgwbFsmXL2nqbiIiYOnVqUdcbPHhwXHvttRERsWnTpnjllVfirbfeivfeey82bdoUmUwm9thjj9hzzz1j5MiRMXjw4KLuDwAAAABAwzrVldttqVevXjF69OgYPXp0R7cCAAAAANDllXV0AwAAAAAA0FzCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAklPe0Q0AAAAAlKLxx9V2dAv1zJ7lOkWAj3hFBAAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOeUd3UCqFi5cGG+88UZUVVVFz549Y8CAATF69OgYMGBAR7cGAAAAANDptVu4vXHjxliyZEksXLgwFi5cGIsWLYpVq1blHt9vv/3iqaeeava6w4cPb3FPixcvjvLywr8F2Ww2pk6dGlOnTo0333yz3uNlZWVx9NFHxxVXXBGjRo1qcV8AAAAAADStzcPte++9Nx5++OF45ZVXora2tq23azPV1dVxxRVXxJw5cxodU1tbG7Nnz47nn38+vv3tb8fkyZPbr0EAAAAAgC6kzcPtefPmxfLly9t6m4iIyGQyUVZW+G3EM5lMQeNqamrim9/8ZsydOzd3rHv37nHsscfGgQceGBs3bowXXnghli1blht/ww03xB577BFnnnlm854EAAAAAAC71CH33O7Vq1eMHDkyFi9eHJs2bSraupdcckl885vfLNp6H7n11lvzgu2DDjoofvazn8WgQYPyxk2fPj2++93vRk1NTUREXHvttTF69OgYNmxY0XsCAAAAAOjK2jzcrqioiNGjR8eoUaNi1KhRceihh8aBBx4YZWVlcfzxxxc13G4LVVVVMXXq1Fzdv3//+K//+q/o169fvbGf//zno7a2Nr7zne9ExF+v4L7tttviP/7jP9qtXwAAAACArqDNw+1bbrmlrbdoU3fffXds3bo1V3/rW99qMNj+yBlnnBH//d//HfPmzYuIiJkzZ8by5cvjoIMOavNeAQAAAAC6isJvUN1FPf7447mv+/btG6eddtou55xzzjmNrgEAAAAAQOsJt5vw0ksvRVVVVa4+7rjjoqKiYpfzJk6cGN27d8/VTz75ZJv0BwAAAADQVQm3m/DCCy/k1WPGjClo3m677RYHH3xwrn755Zdjw4YNRe0NAAAAAKArE2434bXXXsurR4wYUfDcumPrrgUAAAAAQMu1+QdKtqfnn38+li5dGsuWLYu1a9dGeXl59OvXL4YMGRJHHHFEnHzyybH//vsXvF7dQHqfffYpeO6+++5bb63DDjus4PkAAAAAADSuU4Xb8+bNq3fsgw8+iJUrV8azzz4bt956a5xyyinx3e9+N/r377/L9Xa+33Z5eXl87GMfK7iXgQMH5tWrV68ueC4AAAAAAE3rVOH2ruzYsSMeffTRmDt3btxxxx0xevToJsdv3Lgx93XPnj2jrKzwu7jsvvvuefWmTZua1+z/k8lkWjSvofmtXQsoDucllCbnJpQe5yU0TwrnSan3WOr9RaTRI+3PeyZdVacIt4cMGRITJ06Mo446Kj7xiU/EnnvuGd26dYu1a9fGSy+9FI899lg8/vjjsWPHjoiIePfdd+Piiy+Ohx56qMnblGzevDn3dUVFRbN66tGjR17d0nC7srKyRfMa0rdv36KtBRSH8xJKk3MTSo/zktLzfkc3UE/9nx/12Fyl3l9EcXMCOifvmXQlyYfbd999dxxzzDEN/lZq4MCBMXDgwDjhhBNi8uTJcdlll8U777wTERHr1q2Lq6++On71q181uvaWLVtyX9cNq3el7vid1wIAAAAAoHWSD7fHjx9f0LjRo0fHPffcE2effXZs2LAhIiIWLFgQzzzzTEyYMKHBORUVFbmrt2tqaprV17Zt2+qt1RLV1dUtmveRTCaT+43d+vXrI5vNtmo9oPWcl1CanJtQepyX0Dyt/fmxPZR6j6XeX0QaPdL+vGeSimL/9Uny4XZzDB06NC6++OK4+eabc8dmzJjRaLjdq1evXLjd3Cuv64bbvXr1ama3f1XMF6NsNuvFDUqM8xJKk3MTSo/zEnYthXOk1Hss9f4i0uiRjuU9k66k8E9I7CTOPPPMvFuYzJkzp9GxOwfSmzdvbtYLw84fRll3LQAAAAAAWqfLhdv9+/ePwYMH5+p333230VuODBgwIPf19u3bY82aNQXvs3r16rx64MCBzewUAAAAAIDGdLlwO+KvAffOGrtf1dChQ/Pqjz6MshBvv/12k2sBAAAAANByXTLc/ug+2h9p7MMeDzzwwLx6yZIlBe9Rd6xwGwAAAACgeLpcuF1bW5t3VXX37t2jT58+DY4dN25cXr1gwYKC9tiyZUu8/PLLuXr48OGN7gEAAAAAQPN1uXB7/vz58cEHH+Tqgw8+uNGxhx56aN59t59++unYunXrLvd44okn8u7jPXHixBZ2CwAAAABAQ7pcuP2zn/0srx4/fnyjYzOZTJx00km5+oMPPohHH310l3v86le/yqs/97nPNbNLAAAAAACakmy4XV1dHVVVVc2a8+///u8xe/bsXL3bbrvFOeec0+Sciy66KHr06JGrb7755li3bl2j46dNmxbz5s3L1RMnTmzy6nAAAAAAAJov2XD7nXfeiRNOOCF++MMfxp/+9KfIZrONjn3zzTfj8ssvjzvuuCPv+EUXXZR325GGDBw4MM4999xc/f7778d5550Xb731Vr2x06dPj+9///u5unv37nH55ZcX+pQAAAAAAChQeVtvsGrVqjjxxBMbfGzHjh1540aMGNHguPvuuy+OPPLIese3bdsWDz74YDz44INRWVkZI0aMiI9//OPRp0+fKCsri3Xr1sVLL70Uixcvjtra2ry5p5xySlx66aUFPYcrr7wyFi5cGC+88EJERCxfvjxOPvnkmDBhQgwdOjQ2bdoU8+bNi2XLluXNu/baa2P48OEF7QEAAAAAQOHaPNzOZrN5IXZTGhvX1FXZH6muro7nnnsunnvuuSbHdevWLaZMmRLf+MY3IpPJFNRXjx494vbbb4/LL7885s6dGxERNTU18cQTTzQ4vry8PK666qo466yzClofAAAAAIDmSfa2JAMHDowLLrggRo4cGeXlu87o+/btG1/+8pfj0UcfjUsvvTS6devWrP323HPPuP/+++Of/umfYvDgwQ2OKSsri6OPPjp++ctfxoUXXtis9QEAAAAAKFybX7k9aNCgerfrKIZ+/frFNddcExF/vT3JK6+8Em+99Va8++67sXHjxqitrY0+ffpEZWVlDB8+PA488MCCr9RuTFlZWUyePDnOP//8WLRoUbz++uvx7rvvxm677RYDBgyIww47bJf38AYAAAAAoPXaPNxuDz169IgRI0Y0es/uYstkMjF69OgYPXp0u+wHAAAAAEC+ZG9LAgAAAABA1yXcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOeUd3QAAAADUNf642o5uIc/sWa4NA4BS490ZAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOSUd3QDxbRmzZpYsWJFvPnmm/HBBx9EJpOJysrKGDx4cIwePTp69erV0S0CAAAAAFAE7RZub9y4MZYsWRILFy6MhQsXxqJFi2LVqlW5x/fbb7946qmnmrVmTU1NPPfcc/Hkk0/GH//4x1i5cmWjY8vLy+Ozn/1sfPWrX42xY8cWvMfzzz8f5513XrP6+sjYsWPjl7/8ZYvmAgAAAADQuDYPt++99954+OGH45VXXona2tqirbtx48b47Gc/G+vXry9o/Pbt22PmzJnxxBNPxLnnnhvf+c53onv37kXrBwAAAACA9tPm4fa8efNi+fLlRV93x44d9YLtTCYTw4YNi0MPPTT69+8f3bp1i7feeiv+8Ic/xLp16yIiIpvNxtSpU2Pt2rXxk5/8JMrKmnfb8bKysshkMgWNLS/vVHd9AQAAAAAoGR2Svvbq1StGjhwZixcvjk2bNrV6vYMOOijOOuusOO2002LPPfes9/jWrVvjF7/4Rdxxxx25q8dnzJgRY8eOjXPPPbdZe913333xqU99qtU9AwAAAADQcm0ebldUVMTo0aNj1KhRMWrUqDj00EPjwAMPjLKysjj++ONbFW4PGzYsrrjiijjhhBN22cOll14aH/vYx+Laa6/NHb/99tvj7LPPjh49erS4BwAAAAAA2l+bh9u33HJLm6zbu3fvmD59erNuK/J3f/d38Zvf/Cbmz58fERHV1dUxZ86cmDBhQpv0CAAAAABA22jeDadLSFlZWbPvlx0Rceqpp+bVixYtKlZLAAAAAAC0k2TD7Zbaf//98+r33nuvgzoBAAAAAKCluly4vXHjxry6vLxDPlMTAAAAAIBW6HLh9rJly/LqgQMHdlAnAAAAAAC0VJe6bDmbzcajjz6ad+yoo45q1hoPPvhg/Md//EesXLky1q9fH7169Yp+/frFIYccEkcccUT8zd/8TfTp06eYbQMAAAAAUEeXCrenTZsWf/nLX3L1/vvvHyNHjmzWGjNmzMirt2zZEmvXro1XX301Hn300bjpppvivPPOiylTpkT37t2L0jcAAAAAAPm6TLi9Zs2a+NGPfpR37JJLLolMJlPUfT788MO48847Y86cOXHnnXfGnnvu2ar1WtvfzvOL/VyBlnFeQmlybkLpcV5SSlL4f1CPrVfq/UWk0SPtz3smXVWXCLe3b98e3/rWt2LdunW5Y5/61Kfi9NNPL3iNMWPGxPHHHx+HH354DB06NPr06RM1NTWxZs2amD9/fvz617+O+fPn58YvWLAgpkyZEvfff39UVFS0uPfKysoWz62rb9++RVsLKA7nJZQm5yaUHudlV/R+RzeQp/7PZqXVX4Qei6HU+4sobk5A5+Q9k66kS4TbN954Yzz//PO5urKyMm688caCfpP18Y9/PB599NEYNmxYvcd69OgRu+++e3z84x+PL3zhC/HII4/EtddeG1u3bo2Ivwbcd955Z1x55ZXFezIAAAAAAHT+cPvuu++OqVOn5uru3bvHLbfcEvvuu29B8wcMGBADBgwoaOykSZOiR48ecdVVV+WO/dd//Vecf/75Lb49SXV1dYvmfSSTyeR+Y7d+/frIZrOtWg9oPecllCbnJpQe5yWlpLU/m7UHPbZeqfcXkUaPtD/vmaSi2H990qnD7UceeSRuuummXJ3JZOLGG2+Mo48+us32PPXUU+Phhx+O2bNnR0TEpk2b4qmnnoovfvGLLVqvmC9G2WzWixuUGOcllCbnJpQe5yUdLYX///TYeqXeX0QaPdKxvGfSlZR1dANt5Yknnojvfe97eSfzD37wgzjttNPafO+6QfacOXPafE8AAAAAgK6kU4bbc+bMiSuvvDJ27NiRO3b55ZfHV77ylXbZf8yYMXn122+/3S77AgAAAAB0FZ0u3F64cGFMmTIltm3bljv21a9+NaZMmdJuPdS9v/a6devabW8AAAAAgK6gU4Xby5Yti4suuig2bdqUO3b22WfHd77znXbtY8uWLXl1RUVFu+4PAAAAANDZdZpwe+XKlXHhhRfG+vXrc8dOO+20+Jd/+Zd27+Uvf/lLXt2/f/927wEAAAAAoDPrFOF2VVVVXHDBBbFmzZrcsYkTJ8aPfvSjKCtr/6f4zDPP5NUHH3xwu/cAAAAAANCZJR9ur1u3Li644IJYtWpV7tgxxxwTt956a5SXl7d7Pxs2bIipU6fmHfvMZz7T7n0AAAAAAHRmSYfbH374YVx00UXx6quv5o6NGzcu7rjjjujRo0er13/zzTdj8+bNBY/funVrXHHFFbF27drcsYMPPjiOOuqoVvcCAAAAAMD/Sjbc3rZtW0yZMiVeeuml3LFDDz00/vM//zN69uxZlD2eeuqpmDhxYvzHf/xHvP76602OnTdvXnzpS1+K2bNn546VlZXFNddcE5lMpij9AAAAAADwV21+345Vq1bFiSee2OBjO3bsyBs3YsSIBsfdd999ceSRR+Yd+/Of/xzPP/983rElS5bUG7crRxxxRNx///2NPv7+++/H7bffHrfffnvst99+ccghh8Q+++wTffr0ie3bt8eaNWti/vz58cYbb9Sb+/3vfz8+/elPN6sfAAAAAAB2rc3D7Ww2mxdiN6WxcdlstqBjtbW1zWuumXNWrVqVd2/vxlRWVsb111/faKgPAAAAAEDrtP8nLibkU5/6VJx55pkxb968ePPNN3c5ftCgQXH22WfH2WefHf369WuHDgEAAAAAuqY2D7cHDRoUy5YtK/q6n/rUp9pk3Z0dcsgh8W//9m8REbFhw4ZYsWJFvP322/Hee+/F5s2bo1u3btGnT5/42Mc+FqNGjYoBAwa0aT8AAAAAAPyVK7cLtMcee8TYsWNj7NixHd0KAAAAAECXV9bRDQAAAAAAQHMJtwEAAAAASI5wGwAAAACA5LjnNgAAAECixh9X29Et1DN7lmspgfbh1QYAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5JR3dAMAAAC0r/HH1XZ0C/XMnuXaKwCgefzrAQAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDklHd0A22hqqoqFi5cGFVVVbF58+YYMGBAHHDAATFq1Kii7bF8+fJYsWJFVFVVRVlZWQwcODBGjBgR+++/f9H2AAAAAACgYe0Wbm/cuDGWLFkSCxcujIULF8aiRYti1apVucf322+/eOqpp1q1x8KFC+O2226L5557Lmpra+s9PmTIkPj7v//7OPfccyOTybRoj+nTp8ddd90Vy5Yta/DxMWPGxCWXXBKf+cxnWrQ+AAAAAAC71ubh9r333hsPP/xwvPLKKw0GzsVy9913x09/+tPYvn17o2NWrlwZ119/fTz99NNxyy23RN++fQtef+vWrfFP//RPMWPGjCbHLViwIL72ta/FBRdcEFdffXWLQ3QAAAAAABrX5uH2vHnzYvny5W26x0MPPRQ//vGP844dcsghMW7cuOjZs2e8+uqr8eyzz+aC7z/84Q9x+eWXx1133RXl5YV9C773ve/lBduZTCaOOeaYGD58eNTU1MSiRYtiwYIFERGRzWbjnnvuiZ49e8Zll11WpGcJAAAAAMBHOuSe27169YqRI0fG4sWLY9OmTa1a6+WXX47rrrsuV/fo0SP+7d/+Lf72b/82b9xf/vKXmDJlSi5onzNnTtx+++1x5ZVX7nKPBx54IH7729/m6n322Sd+9rOfxSGHHJI37qPQfMOGDRERceedd8bYsWNj/PjxLX5+AAAAAADUV9bWG1RUVMTo0aPjK1/5Stx4443x6KOPxp/+9Kf4v//3/0a/fv1avf6tt94aNTU1ufr//J//Uy/YjogYPHhw3H///dG/f//csfvvvz/WrFnT5PqbN2+OO+64I+/53HvvvfWC7YiIY445Ju68887crUiy2Wz89Kc/bfZzAgAAAACgaW0ebt9yyy3x61//On74wx/GpEmTYtiwYVFWVpxtly5dGk8//XSuPuKII+KMM85odPyee+4ZV111Va7evHlz3HPPPU3u8dBDD8V7772Xqy+66KI44IADGh1/5JFHxuc///lcvXjx4rweAQAAAABovTYPt9vS448/nld/+ctf3uWcv/3bv40+ffrk6t///vdNjv/d736X+7pbt27xpS99aZd71O2jbp8AAAAAALRO0uH2U089lfu6e/fuMXHixF3OqaioiOOOOy5Xr1q1KpYuXdrg2LVr18aLL76Yq8eMGRMDBgzY5R6HH354DBw4MFfPmjUrduzYsct5AAAAAAAUJtlw+4MPPsh9OGRExIgRI6KioqKguYcffnhePW/evAbHzZ8/P2pra3P1mDFjCu5v5z2qq6tjxYoVBc8FAAAAAKBpyYbbr776al7d0Ac8NmbkyJFNrtXY8REjRrR4j9dee63guQAAAAAANC3ZcLtuWLzvvvsWPHefffZpcq3GjtedV4w9AAAAAABovmTD7aqqqry6kHthf2SvvfaKbt26NbpWY8d3vo/2rtQdu3r16oLnAgAAAADQtPKObqClNm7cmFf37t274LllZWXRs2fP+PDDDyMiYtOmTQXtsfvuuxe8R92xje2xK5lMpkXzGprf2rWA4nBeQmlybkLpcV52LaX+37jU+4vQYzGUen8ReqRh3jPpqpINtzdv3pxX9+jRo1nzKyoqcuF23RC7sT0K/cDKhsa2NNyurKxs0byG9O3bt2hrAcXhvITS5NyE0uO8LLb3O7qBeur/7FNaPZZ6fxF6LIZS7y8i1R5pT94z6UqSvS3Jli1b8urmhts7j9+6dWvR96g7tu5aAAAAAAC0XLJXbte9MrqmpqZZ87dt29boWk3tUWjAvfP6Te2xK9XV1S2a95FMJpP7jd369esjm822aj2g9ZyXUJqcm1B6nJddS2t/9mlrpd5fhB6LodT7i9AjDfOeSSqK/ZcdyYbbvXr1yqsbu/q6MTuPr7tWY8e3bNlScLhdt5/G9tiVYr4YZbNZL25QYpyXUJqcm1B6nJedX6n/9y31/iL0WAyl3l+EHtk175l0JcnelqRuWNzYfbMbUltbm3ebkELD7ebcN7tuPy0NtwEAAAAAqC/ZcHvAgAF59erVqwueu2bNmti+fXuuHjhwYEF7vPPOOwXvUbefxvYAAAAAAKD5kg23hw4dmle//fbbBc+tG1IfcMABBe3RnHC77ti6awEAAAAA0HLJhtsHHnhgXr106dKC5y5evLjJtRo7vmTJkqLvAQAAAABA8yUbbvft2zeGDRuWq5csWVLwh0ouWLAgrz7iiCMaHDd27NgoK/vfb1HdeU3585//nPu6srIyPvGJTxQ8FwAAAACApiUbbkdEHH/88bmva2pq4sknn9zlnK1bt8YzzzyTq/fdd98YMWJEg2P79+8fhx12WK5esGBBVFVV7XKPBQsW5N1ze8KECVFeXr7LeQAAAAAAFCbpcPvkk0/Oqx944IFdzvntb38bH3zwQa7+3Oc+V/AeO3bsiAcffHCXe/zyl79ssk8AAAAAAFon6XB7xIgRMWHChFw9b968mDZtWqPj165dGz/96U9z9W677RZf/epXm9zj7LPPjv79++fqu+66K15//fVGx8+dOzemT5+e1+NnP/vZJvcAAAAAAKB5kg63IyKuvPLKvFt+/OAHP4hHH3203ri//OUvcf7558f777+fO3beeefF3nvv3eT6vXr1iilTpuTqrVu3xgUXXNDgB1j+4Q9/iClTpkQ2m83rL5PJNOs5AQAAAADQtDa/EfSqVavixBNPbPCxHTt25I1r7N7X9913Xxx55JENPnbIIYfE97///fjnf/7niIjYtm1bfOtb34q77rorPvnJT8Zuu+0Wr776ajz77LOxffv23LwjjzwyLrvssoKew7nnnhvz58+PGTNmRETEO++8E5MmTYpjjjkmhg8fHtu3b4+FCxfW+8DJr3/963HssccWtAcAAAAAAIVr83A7m83mhdhNaWzczldCN+Scc86JDRs2xG233ZYLsJcuXdrg1dUREUcddVTcdttt0b1794L6ioi44YYbYseOHfH444/nepo9e3bMnj273thMJhPnnXdeXHHFFQWvDwAAAABA4ZK/LclHLr744njggQfi6KOPjrKyhp/W4MGD47vf/W7cd999UVlZ2az1Kyoq4rbbbosf/ehHcdBBBzU67vDDD4///M//jO9+97tuRwIAAAAA0Eba/MrtQYMGxbJly9p6m4iIOOyww+Lee++NqqqqePHFF6Oqqiq2bNkSe++9dxxwwAExevToVu9xxhlnxBlnnBHLli2LFStWRFVVVXTr1i323nvvGDlyZAwZMqQIzwQAAAAAgKa0ebjdEQYMGBAnnXRSm+4xfPjwGD58eJvuAQAAAABAwzrNbUkAAAAAAOg6hNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHLKO7oBAIC2Nv642gJHvt+mfexs9izXGAAAALSGn6oAAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOSUd3QDAAAAAHRe44+r7egW6pk9y/We0Bk4kwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASE55RzfQWn//938fc+fObfU6l156aXzzm99s8LHhw4e3eN3FixdHeXny32YAaNT442o7uoV6Zs/y+3sAAIDOzk9+/0+vXr06ugUAAAAAAAqU/CXFZWVl0a1bt2bP27FjR+7rTCYTJ510UkHzMplMlJUV/juBTCbT7N4AAAAAAGha8uH2/fff3+w5M2fOjEsvvTRXf/KTn4zBgwcXNPeSSy5p9PYlAAAAAAC0j+TD7ZZ4+OGH8+pJkyZ1UCcAAH/l3uUAAADN0+V+Ylm7dm38z//8T67u1atXnHzyyR3YEQAAAAAAzdXlwu3f/va3UVNTk6tPOumk2H333TuwIwAAAAAAmqvLhduPPPJIXu2WJAAAAAAA6elS4fbLL78cS5cuzdX77bdffOpTn+rAjgAAAAAAaIkuFW5PmzYtrz799NMjk8l0TDMAAAAAALRYeUc30F62b98ev/3tb3N1JpNp0S1Jnn/++Vi6dGksW7Ys1q5dG+Xl5dGvX78YMmRIHHHEEXHyySfH/vvvX8zWAQAAAACoo8uE2//zP/8T7733Xq4eN25ci0LoefPm1Tv2wQcfxMqVK+PZZ5+NW2+9NU455ZT47ne/G/37929VzxHR6ivLd57vKnUoDc5LaHspnFt6hF3zntm1lPp/41LvL0KPxVDq/UXosVhS6LE5vGfSVXWZcLu9Pkhyx44d8eijj8bcuXPjjjvuiNGjR7dqvcrKyuI0FhF9+/Yt2lpAcTgv6Rze7+gG6qn//qnHlijmv0OgtbxnFlsKrzml1WOp9xehx2Io9f4i9FgsnfnfOd4z6Uq6RLhdXV0dTz/9dK7u2bNnnHzyyc1aY8iQITFx4sQ46qij4hOf+ETsueee0a1bt1i7dm289NJL8dhjj8Xjjz8eO3bsiIiId999Ny6++OJ46KGH3KYEAAAAAKDIukS4PWPGjNi2bVuuPumkk6J3794Fz7/77rvjmGOOafDPOgYOHBgDBw6ME044ISZPnhyXXXZZvPPOOxERsW7durj66qvjV7/6VYt7r66ubvHciL/+KcpHv7Fbv359ZLPZVq0HtJ7zEtpea98/24MeYde8Z3Ytpf6aU+r9ReixGEq9vwg9FksKPTaH90xSUey/mugS4fa0adPy6ubekmT8+PEFjRs9enTcc889cfbZZ8eGDRsiImLBggXxzDPPxIQJE5q150eK+WKUzWa9uEGJcV5C20jhvNIjNI/3zM6v1P/7lnp/EXoshlLvL0KPxZJCjy3lPZOupKyjG2hrr776aixcuDBX77fffnHUUUe12X5Dhw6Niy++OO/YjBkz2mw/AAAAAICuqNOH23U/SPL0009v80+NPfPMM/P2mDNnTpvuBwAAAADQ1XTqcLu2tjamT5+ed6y5tyRpif79+8fgwYNz9bvvvhs1NTVtvi8AAAAAQFfRqcPtP/zhD1FVVZWrx40bF/vvv3+77N2/f/+8urN9UAEAAAAAQEfq1OF2az9IsjU2b96cV1dUVLTb3gAAAAAAnV2nDbc//PDDeOKJJ3J1z54945RTTmmXvWtra+Ptt9/O1d27d48+ffq0y94AAAAAAF1Bpw23H3vssdiyZUuuPvHEE6N3797tsvf8+fPjgw8+yNUHH3xwu+wLAAAAANBVdNpw+5FHHsmrv/CFL7Tb3j/72c/y6vHjx7fb3gAAAAAAXUGnDLdXrlwZ8+fPz9X77rtvHHXUUc1ep7q6Ou8DKQvx7//+7zF79uxcvdtuu8U555zT7L0BAAAAAGhcpwy36161ffrpp0cmk2n2Ou+8806ccMIJ8cMf/jD+9Kc/RTabbXTsm2++GZdffnnccccdeccvuuiiGDBgQLP3BgAAAACgceUd3UCxZbPZmD59et6x1tySZNu2bfHggw/Ggw8+GJWVlTFixIj4+Mc/Hn369ImysrJYt25dvPTSS7F48eKora3Nm3vKKafEpZde2uK9AQAAAABoWKcLt59//vlYtWpVrh43blzsv//+RVm7uro6nnvuuXjuueeaHNetW7eYMmVKfOMb32jRFeMAAAAAADSt04Xb06ZNy6snTZrU4rUGDhwYF1xwQcydOzeWLVsW27dvb3J8375949RTT42///u/j6FDh7Z4XwAAAAAAmtbpwu0bb7wxbrzxxqKs1a9fv7jmmmsi4q+3J3nllVfirbfeinfffTc2btwYtbW10adPn6isrIzhw4fHgQce6EptAAAAAIB20OnC7bbSo0ePGDFiRIwYMaKjWwEAAAAA6PLKOroBAAAAAABoLuE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkJzyjm4AAACgMxl/XG1Ht1DP7FmuawIAOh//wgEAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnlHd0AANC08cfVdnQLeWbP8rvxrsr/iwAAQCnxEwEAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkJzyjm4AADrS+ONqO7qFembP8rtnAAAA2BU/PQMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJCc8o5uIGXLly+PFStWRFVVVZSVlcXAgQNjxIgRsf/++3d0awAAAAAAnVqnCbePP/74WLVqVYvm/n//3/8XQ4YMKXj89OnT46677oply5Y1+PiYMWPikksuic985jMt6gcAAAAAgKa5LUkzbN26Na666qr4x3/8x0aD7YiIBQsWxNe+9rX40Y9+FNlsth07BAAAAADoGjrNlds7y2QyUVZWeG6fyWQKGve9730vZsyYkTfvmGOOieHDh0dNTU0sWrQoFixYEBER2Ww27rnnnujZs2dcdtllzXsCAAAAAAA0qVOG22eccUbceOONRV3zgQceiN/+9re5ep999omf/exnccghh+SN+8Mf/hCXX355bNiwISIi7rzzzhg7dmyMHz++qP0AAAAAAHRlbktSgM2bN8cdd9yRqysqKuLee++tF2xHRBxzzDFx55135q4Gz2az8dOf/rTdegUAAAAA6AqE2wV46KGH4r333svVF110URxwwAGNjj/yyCPj85//fK5evHhxPP30023aIwAAAABAVyLcLsDvfve73NfdunWLL33pS7uc8+Uvfzmvfvzxx4veFwAAAABAVyXc3oW1a9fGiy++mKvHjBkTAwYM2OW8ww8/PAYOHJirZ82aFTt27GiTHgEAAAAAuhrh9i7Mnz8/amtrc/WYMWMKnnv44Yfnvq6uro4VK1YUszUAAAAAgC5LuL0Lr776al49YsSIgueOHDkyr37ttdeK0hMAAAAAQFdX3tENtIWXX345rrzyyli8eHG8//77ERFRWVkZgwYNiiOOOCJOOOGEOPjggwtaq24gvc8++xTcR92xwm0AAAAAgOLolOH20qVLY+nSpXnHPvzww3jrrbfij3/8Y9x+++1x7LHHxve///0YMmRIk2tVVVXl1TvfR3tX6o5dvXp1wXMBAAAAAGhcpwy3C/Hss8/GmWeeGT/5yU/iuOOOa3Tcxo0b8+rdd9+94D3qjt20aVOzeoyIyGQyzZ7T2PzWrgUUh/OSXSn1/y9Kvb8IPRZLqfdY6v3Ret4ziyeF71+p91jq/UXosRhKvb8IPRZLCj02h/dMuqpOFW4PGDAgJk6cGEcffXQMHz48+vfvHz169Ijq6upYunRpPPHEE/HII4/Etm3bIiJiw4YNcdlll8XUqVPjsMMOa3DNzZs359UVFRUF91N3bEvC7crKymbPaUzfvn2LthZQHM7LUvB+RzdQT/3X/tLqsdT7i9BjsZR6j8X8dxKlL633zNI6VyJK/3yOKP0eS72/CD0WQ6n3F6HHYunM/45I6z0TWqfThNv/+q//GkcccUSUl9d/SnvttVfstddeceyxx8aFF14Yl156aSxfvjwiIrZu3RpXXnllPP7449GjR496c7ds2ZJXNzSmMXXH1l0LAAAAAICW6TTh9qc//emCxg0ZMiTuu++++OIXvxhvv/12RESsWrUqfv3rX8dXvvKVeuPrXn1dU1NTcMD90RXija1ViOrq6mbP2Vkmk8n9xm79+vWRzWZbtR7Qes5LdqW1r/1trdT7i9BjsZR6j6XeH63nPbN4UjhfSr3HUu8vQo/FUOr9ReixWFLosTm8Z5KKYv/VRKcJt5ujf//+8e1vfzuuuuqq3LHHHnuswXC7V69eefWWLVsKDre3bt3a5FqFKOaLUTab9eIGJcZ5SUNK/f+JUu8vQo/FUuo9lnp/FJf3zNZJ4XtX6j2Wen8ReiyGUu8vQo/FkkKPLeU9k66krKMb6Cif+9znonfv3rn6z3/+c737a0fUD6Sbc9/suh9G2ZJwGwAAAACA+rrkldsREeXl5TFq1KiYM2dORERs37493n333RgyZEjeuAEDBuTV77zzTgwcOLCgPVavXp1XFzoPAIDmG39cbUe3UM/sWV32WhIAAGhzXfpf2/3798+r161bV2/M0KFD8+p33nmn4PXrjq27FgAAAAAALdOlw+26tyFp6AMfDzzwwLx6yZIlBa+/ePHiJtcCAAAAAKBlunS4/Ze//CWv3nPPPeuNGTt2bJSV/e+3acGCBQWv/+c//zn3dWVlZXziE59ofpMAAAAAANTTZcPtd955J1asWJGr+/fvH3vvvXe9cf3794/DDjssVy9YsCCqqqp2uf6CBQvy7rk9YcKEKC/vsrc4BwAAAAAoqi6btt55552RzWZz9THHHBOZTKbBsSeffHLuiu0dO3bEgw8+GJdddlmT6//yl7+stwYAAAAApafUPpjah1JDYZI/U7Zt2xavvfZas+b893//dzz00EO5OpPJxPnnn9/o+LPPPjvvwyfvuuuueP311xsdP3fu3Jg+fXquHjFiRHz2s59tVo8AAAAAADQu+XB7y5Ytcdppp8VVV10Vs2fPju3btzc6ds2aNfEv//Iv8b3vfS/v+BlnnBGHHnpoo/N69eoVU6ZMydVbt26NCy64IJYuXVpv7B/+8IeYMmVK3lXhV155ZaNXhQMAAAAA0Hyd4rYkO3bsiBkzZsSMGTOid+/eccghh8TQoUOjb9++0b1791i/fn28/PLL8eKLL0ZNTU3e3E9+8pNx3XXX7XKPc889N+bPnx8zZsyIiL/es3vSpElxzDHHxPDhw2P79u2xcOHCeh84+fWvfz2OPfbY4j1ZAAAAAAA6R7i9sw8//DDmzZsX8+bN2+XYL3/5y/Gd73wnevToUdDaN9xwQ+zYsSMef/zxiIjIZrMxe/bsmD17dr2xmUwmzjvvvLjiiiua1T8AAAAAALuWfLi92267xde//vV4/vnnY/HixbFt27Ymx/fq1StOOOGEOO+882LUqFHN2quioiJuu+22mDZtWtx9992xfPnyBscdfvjhcckll7hiGwAAAACgjSQfbvfo0SOuvPLKiIjYvn17vP766/Hmm2/G6tWrY+PGjbF9+/bYY489ok+fPjFs2LAYPnx4dOvWrVV7nnHGGXHGGWfEsmXLYsWKFVFVVRXdunWLvffeO0aOHBlDhgwpxlMDAAAAAKARyYfbOysvL49hw4bFsGHD2mW/4cOHx/Dhw9tlLwAAAAAA/ldZRzcAAAAAAADNJdwGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnCbQAAAAAAkiPcBgAAAAAgOcJtAAAAAACSI9wGAAAAACA5wm0AAAAAAJIj3AYAAAAAIDnlHd0AAAB0FeOPq+3oFuqZPcv1LgAApMm/ZAEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOSUd3QDAAAAhRp/XG1Ht1DP7FmuGQIA6Aj+FQYAAAAAQHKE2wAAAAAAJEe4DQAAAABAcoTbAAAAAAAkR7gNAAAAAEByhNsAAAAAACRHuA0AAAAAQHLKO7oBADqv8cfVdnQL9cye5fe6AAAA0Bn4CR8AAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABITnlHN9AWqqurY/ny5bFy5cqorq6ObDYbffv2jX333TcOP/zw2GOPPTq6RQAAAAAAWqFThNu1tbXxwgsvxMyZM+OPf/xjLF++vNGxmUwmPv3pT8fkyZNjwoQJBa3/1ltvxcSJE1vU24ABA+LZZ59t0VwAAAAAABrWKcLtk08+OVauXFnQ2Gw2G88991w899xzceqpp8Z1110XvXv3buMOAQAgDeOPq+3oFvIsfrGjOwAAoFR1inB77dq19Y59/OMfj9GjR8fHPvaxqKioiNWrV8ecOXNi9erVuTEzZsyINWvWxF133RUVFRUF71dWVhaZTKagseXlneJbDAAAAABQUjpV8rrffvvFWWedFZMmTYqBAwfWe3zHjh3x0EMPxQ033BBbt26NiIi5c+fGrbfeGt/5zncK3udf//Vf4wtf+ELR+gYAAAAAoHk6Rbi97777xvnnnx9nnHFGdOvWrdFx3bp1i3POOSf23Xff+PrXvx61tX/9k8upU6fG5MmTY8CAAe3VMgAAAAAArVDW0Q0Uw8MPPxxnnnlmk8H2ziZMmBCnnnpqrq6pqYknn3yyrdoDAAAAAKDIOkW43ZL7Wu8cbkdELFq0qFjtAAAAAADQxjpFuN0S+++/f1793nvvdVAnAAAAAAA0V5cNtzdu3JhXt+TqbwAAAAAAOkaXDbeXLVuWVw8cOLCDOgEAAAAAoLm67OXK06dPz6uPOuqoguf+/ve/j8ceeyxeffXVWLduXVRUVERlZWUMGzYsjjjiiDjllFNi7733LnbLAAAAAAD8P10y3J47d27MnTs3V++xxx4xfvz4gufPmjUrr968eXNUV1fHG2+8ETNnzoyf/OQn8cUvfjG+/e1vx+67716stgEAAAAA+H+6XLi9adOm+MEPfpB37IILLihqCL1t27Z44IEH4o9//GP8/Oc/jyFDhrR4rUwm06pedp7f2rWA4nBedqwUvuel3mOp9xehx2Ip9R5Lvb8IPRZTKfdZyr19RI+tV+r9ReixGEq9vwg9Fkup99jc/vycSVfV5cLtf/7nf4433ngjVw8dOjQuuuiiguYOHz48TjjhhBg3blx84hOfiMrKyshms/Hee+/Fiy++GNOmTYtnn302N/61116Lr33ta/Hggw9Gv379WtRvZWVli+Y1pG/fvkVbCyiOzn9evt/RDdRT/3VVj81V6v1F6LFYSr3HUu8vQo/F9L/vmaXXXwrfQz22Xqn3F6HHYij1/iL0WCyl3mNr8qDO/3Mm/K8uFW7fe++98Zvf/CZX9+jRI2666aaoqKhocl5lZWX86le/ijFjxjT4+KBBg2LQoEFx6qmnxjPPPBP/+I//GOvXr4+IiJUrV8b1118fN998c/GeCAAAAABAF9dlwu3HHnssfvzjH+cdu+666+LQQw/d5dzevXs3GmzXNWHChLjzzjvj/PPPj+3bt0dExIwZM+If/uEf4qCDDmp239XV1c2es7NMJpP7jd369esjm822aj2g9ZyXHau1r6vtodR7LPX+IvRYLKXeY6n3F6HHYirl98wUvod6bL1S7y9Cj8VQ6v1F6LFYSr3H5vbn50xSUcy7VER0kXD7ueeei6uvvjpqa2tzx771rW/FpEmT2mS/T37yk3HmmWfGgw8+GBER2Ww2fve737Uo3C7mi1E2m/XiBiXGedn+Uvh+l3qPpd5fhB6LpdR7LPX+IvRYTKX8nlmqfe1Mj61X6v1F6LEYSr2/CD0WS6n32Jr+Svk9E4qtrKMbaGsvvvhiXHLJJVFTU5M7duGFF8bFF1/cpvt+8YtfzKvnzJnTpvsBAAAAAHQlnTrcXr58eVx88cWxadOm3LGzzjorrr766jbf+9BDD43u3bvn6rfffrvN9wQAAAAA6Co6bbj95ptvxle/+tW8exSdcsopcd1117XL/mVlZXn3kFm3bl277AsAAAAA0BV0ynC7qqoqJk+eHGvWrMkdmzBhQtx0001RVtZ+T3nLli25rysqKtptXwAAAACAzq7Thdtr166NyZMnx6pVq3LHjjzyyLj99tvzbhPS1tatWxcbNmzI1f3792+3vQEAAAAAOrtOFW5/+OGHcdFFF8Vrr72WO3bYYYfFz3/+83a/cvrZZ5/Nqw8++OB23R8AAAAAoDPrNOH2li1b4utf/3osXrw4d+zggw+OX/ziF7H77ru3ay81NTXxi1/8Iu/Y+PHj27UHAAAAAIDOrFOE29u3b4/LL7885s2blzt2wAEHxD333BN9+/Zt1dpVVVV5H0q5K7W1tfHDH/4wVqxYkTu21157xamnntqqPgAAAAAA+F/Jh9vZbDauueaamDVrVu7YoEGD4v777y/Kfa4XLVoUxx9/fPzoRz+KJUuWNDl26dKlMXny5Hj44Yfzjl911VXRq1evVvcCAAAAAMBflXd0A6319ttvx29/+9t6xz772c82a5399tsvZs6c2eBjGzdujHvuuSfuueee2GuvvWLEiBExePDg2GOPPSKbzcb7778fL774Yixfvrze3AsvvDC+8IUvNKsXgEKNP662o1vIM3tW8r8zBQAAABKRfLidzWbrHautbX7Ys2PHjoLGrVmzJp555pldjtttt93immuuiXPOOafZvQAAAAAA0LTkw+22Nnz48Pjyl78cc+fOjddee22Xwflee+0VkyZNiq985SsxcODAduoSAAAAAKBrST7cHjRoUCxbtqzN1h88eHBce+21ERGxadOmeOWVV+Ktt96K9957LzZt2hSZTCb22GOP2HPPPWPkyJExePDgNusFAAAAAIC/Sj7cbk+9evWK0aNHx+jRozu6FQAAAACALs0nfwEAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJKe/oBgBK1fjjattw9febPWP2LL+PBAAAAPiIpAQAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOQItwEAAAAASI5wGwAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEhOeUc3AAAAAAA0bvxxtQWMer/N+9jZ7FmumaXj+b8QAAAAAIDkCLcBAAAAAEiOcBsAAAAAgOS45zYAAAAA0CqF3Re8fbkveOfnvzAAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkBzhNgAAAAAAyRFuAwAAAACQHOE2AAAAAADJEW4DAAAAAJAc4TYAAAAAAMkRbgMAAAAAkJzyjm4AAAAAAKCtjT+utqNbyDN7luuOW8t3EAAAAACA5Ai3AQAAAABIjnAbAAAAAIDkCLcBAAAAAEiOD5Rsherq6pg/f36sXr06Pvzww9h7771j0KBBMXbs2Cgr83sDAAAAAIC2ItxugTfeeCNuvvnmePrpp6Ompqbe43vvvXd86Utfiosvvjh69OjRAR0CAAAAAHRuLi9upunTp8f/3969R9d05n8c/5ySBHGJCFG3JmIszJTWpa5r4tLOorSkFsaypqIl4lLW0HGZySHFNK2OaUcwilan7VRLJ+4sRdGpumdMx2WEukRpIhEhIheS8/vDzx47CTlpT7LPyXm//jrfnf0cn+qKs/f3PPt5IiIi9MUXX5TY2JakK1euKD4+Xr/+9a916dKlCk4IAAAAAAAAAJUfM7fL4KuvvtKMGTNUUFBgHAsJCVHnzp0VEBCg5ORk7dq1S7m5uZKk48ePKzo6WqtWrVLNmjWtig24pR49C62OUMzXu/m+DwAAAAAAwFPQ3HZSWlqapkyZYjS2bTabpk+frpEjR5rW187IyNDkyZN18OBBSVJSUpJmz56tBQsWWJIbAAAAAAAAACojpik6aenSpcrKyjLqV155RaNGjSq2cWRgYKBWrFihsLAw49jmzZv13//+t8KyAgAAAAAAAEBlR3PbCVevXtXq1auNulmzZoqKinrg+X5+frLb7UbtcDi0ZMmScs0IAAAAAAAAAN6EZUmcsHPnTuXn5xv10KFD5ePj89AxXbt2VWhoqM6dOydJ2rNnj3JyclS9evVyzQpIrGcNAAAAAACAyo9ukxO+/PJLU923b1+nxt1/Xm5urvbu3evSXAAAAAAAAADgrWhuO+Hw4cPG66CgIDVt2tSpcU8++aSpPnTokEtzAQAAAAAAAIC3orldiitXrpg2kmzdurXTY9u0aWOqv/vuO5flAgAAAAAAAABvxprbpTh79qypbtSokdNjg4KC5OPjo9u3b5f4XiiZJ6wX7W4ZWc8aAAAAAAAA3oaOWClSU1NNdXBwsNNjbTab6fyi7wUAAAAAAAAA+HGYuV2K7OxsU+3v71+m8feff+fOHeXn58vX19fp8TabrUx/3sPG/9T38mbu/nfn7vkkMrqCu+eTyOgq7p7R3fNJZHQVd8/o7vkkMrqSO+d052z3kPGnc/d8Ehldwd3zSWR0FXfP6O75JDK6grvn8wQ0t0uRk5Njqv38/Mo0vuj52dnZZWpuBwQElOnPe5g6deq47L3K11WrAxRT/P+De2V093wSGV2h5H8P3D2je+WTyOgK7p5PIqOruHtGd88nkdGV/nct6375POHvkIw/nbvnk8joCu6eTyKjq7h7RnfPJ5HRFVzZ9/NWNofD4bA6hDtbvHixFi5caNSvv/66Bg8e7PT4ESNG6PDhw0a9Z88eNWzY0KUZAQAAAAAAAMDbsOZ2KYrOvL63OaSz8vPzTXVZZm0DAAAAAAAAAEpGc7sUNWrUMNW5ubllGp+Xl2eqy7pmNwAAAAAAAACgOJrbpSja3L5161aZxt+/IWXVqlXLvGY3AAAAAAAAAKA4mtulCA4ONtUpKSlOj3U4HEpNTX3gewEAAAAAAAAAfhya26Vo3ry5qb58+bLTY9PT001rdIeGhrosFwAAAAAAAAB4M5rbpQgODlatWrWM+uTJk06PPXHihKkOCwtzWS4AAAAAAAAA8GY0t53QoUMH43V6erouXrzo1LjExERT3alTJ5fmAgAAAAAAAABvRXPbCb179zbVW7dudWrctm3bjNd+fn7q3r27S3MBAAAAAAAAgLeiue2EPn36yMfHx6jXrFljWku7JPv27dO5c+eMOjw8XDVq1Ci3jAAAAAAAAADgTapaHcATBAUFaciQIfrkk08kScnJyVq2bJkmTJhQ4vl5eXmaN2+eUdtsNo0bN65CsrpSYWGhjh8/rtOnTys9PV0FBQXy9/dXo0aN9LOf/UyPPfaY1REBALCEw+FQcnKyTp8+rZSUFN28eVN+fn4KCAhQy5Yt1apVK1WpUsXqmIBHy8zMVGJiovE71qBBAzVp0kTt27fXI48wRweoaJmZmUpKStKFCxeUmZkph8OhOnXqqFGjRnriiSdMe1UBAFBRaG47KTo6WuvXr1d2drYkKT4+Xv7+/nrxxRdNF9cZGRmaPHmyzpw5Yxx79tln1aZNmwrP/GNlZGRo+fLlWrt2ra5du/bA8+rWrasePXooJiZGAQEBFRcQgCTp5s2b6t+/v1JSUkzHP/zwQ3Xu3NmiVEDllZWVpR07dmj37t06cODAQz8ja9asqYiICEVGRqpJkyYVmBLwfOfPn9eCBQu0a9euEp+WbNCggYYNG6aoqCj5+vpakBDwDoWFhTp8+LC2b9+u/fv3Kykp6YHn2mw2de3aVZGRkQoPD6/AlAAeZN68efroo49MxyIiIvTGG29YlAgoHzaHw+GwOoSn2L17t8aNG6fCwkLjWEhIiLp06aKAgABduHBBu3btUm5urvHzFi1a6LPPPlPNmjWtiFxmW7Zs0axZs5SVlVWmMWFhYeWYCkBJYmNjtWrVqmLHaW4Drrd//36NHj261GXJiqpRo4ZiYmI0ePDgckoGVC4bNmzQ7NmzdevWrVLP/fnPf674+Hg1bty4ApIB3udXv/qVLly4UOZx/fv315w5czzmHhiojI4eParhw4eb+lcSzW1UTszcLoOePXsqLi5OsbGxysnJkXR3Zsn58+dLPL9169ZatGiRx3yov/fee5o/f77pWK1atdS1a1c9+uij8vf3140bN5SUlKRjx445ddMBoHwcOXJEn376qdUxAK9x8+bNYo1tX19ftWvXTs2bN1dgYKDy8/N1+vRpHThwQHl5eZKkW7du6fe//71yc3M1YsQIK6IDHuOrr77SjBkzVFBQYBwLCQlR586dFRAQoOTkZNNEkuPHjys6OlqrVq3ymOttwJNkZGQUOxYSEqK2bdsqKChIfn5+SklJ0b59+0xPEm7evFlpaWlasWKF/Pz8KjIyAEm3b9+W3W4v1tgGKiua22U0aNAgtW3bVgsWLNCePXtKnMFVv359DR06VNHR0R7zqOSmTZtMje3atWtr6tSpeuGFF0r8b8jLy9M///lPffLJJ7LZbBUZFfB6+fn5stvtuvfgTf369ZWWlmZxKsA73HvsetiwYerVq1eJN+1paWmaO3eutm3bZhybN2+eOnTooFatWlVkXMBjpKWlacqUKUZj22azafr06Ro5cmSJSwAePHhQkpSUlKTZs2drwYIFluQGvEHjxo01ZMgQRUREqGHDhsV+XlBQoNWrVysuLs74cvfgwYN65513NH369IqOC3i9ZcuWGcsIca8Ib8CyJD/BtWvXjE1usrOzFRQUpKZNm6p9+/YetYnU1atX1a9fP12/fl3S3Q00P/74Y4WGhlqcDEBJ4uPjtWjRIknSL3/5S9WrV09r1641fs6yJIDr7dixQ5999pmmTp3qVIPa4XDo1Vdf1aZNm4xj4eHhWrZsWXnGBDzW3Llz9fHHHxv1pEmTHrp5e0REhL777jtJdxvh69at48sjwMWef/55jRw5UoMGDXLq/nbPnj2Kjo42Zov6+Pho586dCg4OLu+oAP7f2bNnNXDgQOXn56t69eqaNWuWZs6cafycZUlQGbHN+E9Qt25d9enTRyNGjFBUVJReeOEFderUyaMa25IUFxdnNLZtNpsWLlxIYxtwU2fOnNG7774rSapWrZpmzZplcSLAO/Ts2VPLly93unlms9lkt9vl7+9vHPvmm2908+bN8ooIeKyrV69q9erVRt2sWTNFRUU98Hw/Pz/Z7XajdjgcWrJkSblmBLxRQkKCBg8e7PT9bXh4uPr372/Ut2/f1s6dO8srHoAiHA6H7Ha78vPzJUnjx49nXwp4BZrbXu7y5cvavHmzUffv318dOnSwMBGAByksLFRMTIyxHNKECRPUtGlTi1MB3qFq1bKv5BYQEKAePXoY9e3bt3XixAlXxgIqhZ07dxo34pI0dOhQ+fj4PHRM165dTZMx9uzZY+yJA8A1fsxn3/3NbUn6z3/+46o4AErx6aef6vDhw5Kkli1batSoURYnAioGzW0vl5CQYNpkYNiwYRamAfAwq1at0r/+9S9JXKwAnqJZs2amOj093aIkgPv68ssvTXXfvn2dGnf/ebm5udq7d69LcwEoOz73AGukpqYa+0/YbDa99tprpX5RDFQWNLe93MaNG43XgYGB6tixo4VpADxISkqK6WIlNjaWixXAA2RnZ5tqfm+B4u7NMpNk7GHjjCeffNJUHzp0yKW5AJRd0c+9HzP7G0DZzZ07V1lZWZLuPgHVvn17ixMBFYfmthe7fv26zp8/b9Rt2rQx7UYPwH3ExsYaNwtDhgxh+SDAQ5w6dcpUs6kWYHblyhXjZlySWrdu7fTYNm3amOp7G0wCsE7Rz72GDRtalATwHl988YW2b98uSapXr56mTp1qcSKgYvE1qhc7duyYqW7RooXx+siRI1q7dq2OHj2qH374QVWqVFHdunX1+OOPKzw8XP369eNbeKCCbNmyRbt27ZJ092Ll1VdftTgRAGdcvHhRiYmJRl27du1izTjA2509e9ZUN2rUyOmxQUFB8vHxMfaiKPpeACrehg0bTHWXLl0sSgJ4h6ysLM2ZM8eoZ8yYoTp16liYCKh4dCe92JkzZ0x1vXr1dP36db322mumTSbvuTfTe+PGjYqPj1dsbKy6detWUXEBr3T9+nX98Y9/NOrp06dzsQJ4iCVLlsjhcBj1M888wxfDQBGpqammuixPN9hsNgUHB+v7778v8b0AVKyDBw/q4MGDRl2rVi3TxsoAXG/+/PlKS0uTJHXr1k3PP/+8xYmAiscaFF7s+vXrptpms2nUqFElNraLunDhgsaMGaO1a9eWVzwAkt58801jI56uXbtq4MCBFicC4Iy9e/cqISHBqH18fDR27FgLEwHuqej6vP7+/mUaf//5d+7cUX5+vktyASibW7duyW63m46NGjWqzL/TAJx36NAhrVmzRpLk5+en2NhYawMBFmH6kBe7f31DSVq2bJlu3LghSQoJCVF0dLS6deumunXrKjMzUwcPHtTSpUt1+vRpSXdvIOx2u8LCwtS2bdsKzw9Udvv379c//vEPSZKvry8XK4CHSE1N1bRp00zHxo4dq8cee8yiRID7ysnJMdV+fn5lGl/0/OzsbPn6+v7kXADKJjY21rSfU/PmzTV69GjrAgGVXH5+vux2u/GUINea8GbM3PZit27dMtX3GttdunTRunXrFBERoeDgYPn6+qpBgwYaMGCAEhIS1KtXL2PM7du3NWvWrArNDXiDvLw80+/W2LFjFRISYl0gAE7Jzc3VxIkTjScuJOmJJ55QdHS0hakA95Wbm2uqy9qYLnp+Xl7eT84EoGxWrlyp9evXG7Wvr6/eeuutMn9ZBcB5ixcv1rlz5yRJoaGhGjNmjMWJAOswc9sN9O7dW5cuXSq39582bZpefvnlYsdLunmoW7eu3n77bVWvXr3E9/L19dWf/vQnDRgwQD/88IMk6eTJk9q7d6+6d+/u2uCAxaz63ZSk+Ph4XbhwQdLdi5WoqKhyywF4Eit/L0tTUFCgKVOm6NtvvzWOPfroo1q4cKF8fHxcFRGoVIo2v+5tDumsosuQMGsbqFhbtmzR/PnzTcfmzJmjX/ziFxYlAiq/U6dO6b333jPq1157jc8/eDVmbnuxGjVqFDs2fPhwBQYGPnRczZo1FRkZaTq2a9cuV0YDvNrJkye1cuVKo+ZiBfAMdrtdO3fuNOqAgACtWLGiTBvkAd6m6PVo0ZncpSk6U5v1fYGK880332jatGkqLCw0jk2dOlUREREWpgIqt8LCQsXExBhfBkdERKhz584WpwKsRXPbi5V08X//kiMP07t3b1OdmJjokkyAtysoKFBMTIzu3LkjiYsVwFO8+eabxhr50t2G3bJly9SiRQsLUwHur2hzu+iyeaW5f0PKqlWrsgwCUEH+/e9/a8KECaanLV5++WWeNgTK2UcffWQ8JRgQEFBsnxfAG7EsiRv4y1/+Uq7rAzZt2rTE4w0bNix2rGXLlk69Z7NmzVStWjVjds2VK1d+fEDATVnxu7lp0yYdO3ZMEhcrQEms+sx8mL/+9a96//33jdrX11eLFy9Wu3btXBkNqJSKPtmQkpLi9FiHw6HU1NQHvheA8pGUlKSoqCjTl1FDhgzhuhUoZ7m5uXrnnXeMetq0aaU+eQ94A5rbbuDxxx+35M8tOpvM19dX1apVc3p87dq1jeZ2ZmamK6MBbsGK381r164Zr69fv64ePXqUOub+R0ElKTIyUjabzag/+OADPfXUU64LCVjIqs/MB/n73/9uusmoUqWK3n77bXXr1s26UIAHad68uam+fPmy02PT09NNs0ZDQ0NdlgtAyZKTk/XSSy+Z7v/69eunOXPmWBcK8BL5+fmmL5XsdrvsdvtDxzgcDlO9bt06bdiwwagHDRqk119/3bVBgQpGc9uLhYWFyWazGf/Y3blzRw6Hw9QUe5j7N/DhEVDA9RwOhwoKCso8rmizu+gFDQDXWLdunebOnWvUNptNcXFxevrppy1MBXiW4OBg1apVS1lZWZLu7jvhrBMnTpjqsLAwl2YDYJaamqrIyEilpaUZx8LDw/XWW2/pkUdY8RSoaD/mXrHoPWbRe0fAE/EJ5MX8/f3Vpk0boy4sLHR6eZGcnBzduHHDqHkUBgDgTXbs2KE//OEPpi+PZs+erYEDB1qYCvBMHTp0MF6np6fr4sWLTo0ruudLp06dXJoLwP9kZGQoMjJSly5dMo499dRTio+Pl4+Pj4XJAADejpnbXu6ZZ57R8ePHjToxMVH9+vUrddzRo0dN3/C1bt26XPIB3iYyMlKRkZFlGjNjxgytXbvWqD/88EM2oQTK0b59+/Tb3/7W2PhVkn73u99p+PDhFqYCPFfv3r21e/duo966datTm9Jt27bNeO3n56fu3buXRzzA6928eVOjR4/W2bNnjWPt2rXT0qVLeYIXqEC1a9fWqVOnyjTmwIEDevHFF406IiJCb7zxhqujAZZi5raX69u3r+kRss8//9ypcWvWrDHV3EwAALzBt99+q/Hjx5uW5powYYJGjx5tYSrAs/Xp08c083PNmjWmtbRLsm/fPp07d86ow8PDVaNGjXLLCHir3NxcRUdHmyZEtWrVSsuXL5e/v7+FyQAAuIvmtpcLDQ3Vc889Z9Rff/21tm7d+tAxX3/9tbZs2WLUAQEBGjBgQLllBADAHZw+fVpjxowxbeQTGRmpSZMmWZgK8HxBQUEaMmSIUScnJ2vZsmUPPD8vL0/z5s0zapvNpnHjxpVrRsAb3blzR5MnT9ahQ4eMY6GhoXr//fdVp04dC5MBAPA/NLehSZMmmWa6TJs2TQkJCSWeu2XLFr3yyiumNUYnTpzIt/YAgErt+++/10svvaTMzEzj2LBhwzRz5kzrQgGVSHR0tOl6Mj4+Xh988EGxja4yMjI0evRonTlzxjj27LPPmvaRAfDTORwOzZgxw7RkUJMmTfS3v/1N9erVsy4YAABFsOY21KRJEy1YsEATJkxQYWGh8vPzNXPmTL377rvq2rWrAgMDlZmZqQMHDphuJCSpf//++s1vfmNRcgAAKsa6deuKbbr8+eefO72c1z3jx4/XxIkTXRkNqBSCg4P15z//WePGjVNhYaEcDofi4uK0atUqdenSRQEBAbpw4YJ27dql3NxcY1yLFi00Z84cC5MDldPly5e1cePGYsd69epVpvdp3Lixtm/f7spoAACY0NyGpLsb+cyfP1+zZ89Wdna2JOn8+fM6f/78A8cMHz5cMTExFZQQAADr3P/E0j0FBQUueR8Ad/Xs2VNxcXGKjY1VTk6OpIdfj7Zu3VqLFi1SzZo1KzAl4B1K+rwq+iSFM37MZyUAAGXBsiQwPPfcc1q/fr0GDBigatWqlXiOzWZTx44dtXLlSsXGxqpqVb4fAQAAgGsMGjRICQkJevrpp02bTN6vfv36mjBhglavXq0mTZpUcEIAAAC4E5uDKUQowc2bN3XkyBGlpKTo2rVrqlmzpho0aKCOHTsqMDDQ6ngAAACo5K5du6bExESlpKQoOztbQUFBatq0qdq3b68qVapYHQ8AAABugOY2AAAAAAAAAMDjsCwJAAAAAAAAAMDj0NwGAAAAAAAAAHgcmtsAAAAAAAAAAI9DcxsAAAAAAAAA4HFobgMAAAAAAAAAPA7NbQAAAAAAAACAx6G5DQAAAAAAAADwODS3AQAAAAAAAAAeh+Y2AAAAAAAAAMDj0NwGAAAAAAAAAHgcmtsAAAAAAAAAAI9DcxsAAAAAAAAA4HFobgMAAAAAAAAAPA7NbQAAAAAAAACAx6G5DQAAAAAAAADwODS3AQAAAAAAAAAeh+Y2AAAAAAAAAMDj0NwGAAAAAAAAAHgcmtsAAAAAAAAAAI9DcxsAAAAAAAAA4HFobgMAAAAAAAAAPA7NbQAAAAAAAACAx6G5DQAAAAAAAADwODS3AQAAAAAAAAAeh+Y2AAAAAAAAAMDj0NwGAAAAAAAAAHic/wMYsRsgcXNqFAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 491,
       "width": 731
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(pm.draw(y, draws=2000, random_seed=rng), bins=30, rwidth=0.9);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "363b907c-8146-4694-a821-7a2ebacbcab6",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 2 jobs)\n",
      "NUTS: [y]\n",
      "/home/zv/upstream/miniconda3/envs/pymc-dev/lib/python3.11/multiprocessing/popen_fork.py:66: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.\n",
      "  self.pid = os.fork()\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "eed05e43a889410ba40cf6d59bac8990",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/zv/upstream/miniconda3/envs/pymc-dev/lib/python3.11/multiprocessing/popen_fork.py:66: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.\n",
      "  self.pid = os.fork()\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 14 seconds.\n",
      "The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details\n",
      "The effective sample size per chain is smaller than 100 for some parameters.  A higher number is needed for reliable rhat and ess computation. See https://arxiv.org/abs/1903.08008 for details\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>0.854</td>\n",
       "      <td>2.059</td>\n",
       "      <td>-3.214</td>\n",
       "      <td>3.704</td>\n",
       "      <td>0.137</td>\n",
       "      <td>0.097</td>\n",
       "      <td>288.0</td>\n",
       "      <td>1919.0</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "y  0.854  2.059  -3.214    3.704      0.137    0.097     288.0    1919.0   \n",
       "\n",
       "   r_hat  \n",
       "y   1.02  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with prebuilt_mixture:\n",
    "    idata = pm.sample(draws=2000, chains=4, random_seed=rng)\n",
    "\n",
    "az.summary(idata)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e6d9a596-af22-4074-bc96-85a91cd35a64",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (4 chains in 2 jobs)\n",
      "CompoundStep\n",
      ">BinaryGibbsMetropolis: [idx]\n",
      ">NUTS: [y]\n",
      "/home/zv/upstream/miniconda3/envs/pymc-dev/lib/python3.11/multiprocessing/popen_fork.py:66: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.\n",
      "  self.pid = os.fork()\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "939c0be727cd4e2794601e6ffd9f7d93",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/zv/upstream/miniconda3/envs/pymc-dev/lib/python3.11/multiprocessing/popen_fork.py:66: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.\n",
      "  self.pid = os.fork()\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 19 seconds.\n",
      "The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details\n",
      "The effective sample size per chain is smaller than 100 for some parameters.  A higher number is needed for reliable rhat and ess computation. See https://arxiv.org/abs/1903.08008 for details\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>idx</th>\n",
       "      <td>0.738</td>\n",
       "      <td>0.440</td>\n",
       "      <td>0.00</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.027</td>\n",
       "      <td>0.019</td>\n",
       "      <td>263.0</td>\n",
       "      <td>263.0</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>0.953</td>\n",
       "      <td>2.015</td>\n",
       "      <td>-3.18</td>\n",
       "      <td>3.714</td>\n",
       "      <td>0.116</td>\n",
       "      <td>0.082</td>\n",
       "      <td>404.0</td>\n",
       "      <td>1229.0</td>\n",
       "      <td>1.02</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "idx  0.738  0.440    0.00    1.000      0.027    0.019     263.0     263.0   \n",
       "y    0.953  2.015   -3.18    3.714      0.116    0.082     404.0    1229.0   \n",
       "\n",
       "     r_hat  \n",
       "idx   1.02  \n",
       "y     1.02  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with explicit_mixture:\n",
    "    idata = pm.sample(draws=2000, chains=4, random_seed=rng)\n",
    "\n",
    "az.summary(idata)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "043b1591-ff13-4dde-880a-aee4572a0b19",
   "metadata": {},
   "source": [
    "We can immediately see that the marginalized model has a higher ESS. Let's now marginalize out the choice and see what it changes in our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e9a84902-73af-4485-a40b-72200411a500",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 2 jobs)\n",
      "NUTS: [y]\n",
      "/home/zv/upstream/miniconda3/envs/pymc-dev/lib/python3.11/multiprocessing/popen_fork.py:66: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.\n",
      "  self.pid = os.fork()\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "295d70c281df4c4389160d474cc924f5",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/zv/upstream/miniconda3/envs/pymc-dev/lib/python3.11/multiprocessing/popen_fork.py:66: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.\n",
      "  self.pid = os.fork()\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 2_000 draw iterations (4_000 + 8_000 draws total) took 21 seconds.\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>0.837</td>\n",
       "      <td>2.062</td>\n",
       "      <td>-3.154</td>\n",
       "      <td>3.711</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.063</td>\n",
       "      <td>742.0</td>\n",
       "      <td>2676.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  ess_tail  \\\n",
       "y  0.837  2.062  -3.154    3.711       0.09    0.063     742.0    2676.0   \n",
       "\n",
       "   r_hat  \n",
       "y    1.0  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "explicit_mixture_marginalized = pmx.marginalize(explicit_mixture, [\"idx\"])\n",
    "\n",
    "with explicit_mixture_marginalized:\n",
    "    idata = pm.sample(draws=2000, chains=4, random_seed=rng)\n",
    "\n",
    "az.summary(idata)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4034eb4d-83f9-4543-992f-0f68bf47fb68",
   "metadata": {},
   "source": [
    "As we can see, the `idx` variable is gone now. We also were able to use the NUTS sampler, and the ESS has improved.\n",
    "\n",
    "But {class}`MarginalModel <pymc_extras.MarginalModel>` has a distinct advantage. It still knows about the discrete variables that were marginalized out, and we can obtain estimates for the posterior of `idx` given the other variables. We do this using the {meth}`recover_marginals <pymc_extras.MarginalModel.recover_marginals>` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a6c4457a-0af5-4ba8-89c9-e2c8267f0336",
   "metadata": {},
   "outputs": [],
   "source": [
    "idata = pmx.recover_marginals(explicit_mixture_marginalized, idata, random_seed=rng);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "627f23bf-c871-4b81-bbf7-14f411604eb3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>0.837</td>\n",
       "      <td>2.062</td>\n",
       "      <td>-3.154</td>\n",
       "      <td>3.711</td>\n",
       "      <td>0.090</td>\n",
       "      <td>0.063</td>\n",
       "      <td>742.0</td>\n",
       "      <td>2676.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>idx</th>\n",
       "      <td>0.706</td>\n",
       "      <td>0.456</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.021</td>\n",
       "      <td>0.015</td>\n",
       "      <td>457.0</td>\n",
       "      <td>457.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lp_idx[0]</th>\n",
       "      <td>-6.303</td>\n",
       "      <td>5.195</td>\n",
       "      <td>-14.387</td>\n",
       "      <td>-0.000</td>\n",
       "      <td>0.201</td>\n",
       "      <td>0.142</td>\n",
       "      <td>742.0</td>\n",
       "      <td>2676.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lp_idx[1]</th>\n",
       "      <td>-2.109</td>\n",
       "      <td>3.814</td>\n",
       "      <td>-10.204</td>\n",
       "      <td>-0.000</td>\n",
       "      <td>0.159</td>\n",
       "      <td>0.113</td>\n",
       "      <td>742.0</td>\n",
       "      <td>2676.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "y          0.837  2.062  -3.154    3.711      0.090    0.063     742.0   \n",
       "idx        0.706  0.456   0.000    1.000      0.021    0.015     457.0   \n",
       "lp_idx[0] -6.303  5.195 -14.387   -0.000      0.201    0.142     742.0   \n",
       "lp_idx[1] -2.109  3.814 -10.204   -0.000      0.159    0.113     742.0   \n",
       "\n",
       "           ess_tail  r_hat  \n",
       "y            2676.0   1.00  \n",
       "idx           457.0   1.01  \n",
       "lp_idx[0]    2676.0   1.00  \n",
       "lp_idx[1]    2676.0   1.00  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d687f4b-ef2a-4512-8e81-0c0b1bc0d0bc",
   "metadata": {},
   "source": [
    "This `idx` variable lets us recover the mixture assignment variable after running the NUTS sampler! We can split out the samples of `y` by reading off the mixture label from the associated `idx` for each sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "70d23a58-3ebd-4b67-80f5-42dd495dfc81",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABbcAAAPXCAYAAAAYJXYaAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8fJSN1AAAACXBIWXMAAB7CAAAewgFu0HU+AACHUUlEQVR4nOzdd5iV1bk/7mcKVQREZRALUaSIAoIlUROJkkSPGsWoRI+J4lFzorFifiYqRkWM7RgxJGhiicqJ9Rw1ii3qsQRLEEVRegTFwgwYigUGpuzfH37ZmT1M2Rtmz8wL931dXhfrnbWeZ+0ZXsb58LJ2QSqVSgUAAAAAACRIYUtvAAAAAAAAciXcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYpbegP5Mm/evJg/f36UlZVFYWFh9OjRIwYMGBA77bRTk9SvqqqK6dOnx4cffhhLly6NTp06RY8ePWLo0KHRtWvXJukBAAAAAEDdmiXcPvjgg+Pjjz/eoLV//etfo1evXlnPf/TRR+O2226LuXPn1vnxIUOGxM9+9rP41re+tUH7Wbt2bfzhD3+I+++/P5YuXbrex9u0aRMHHXRQ/PznP89p3wAAAAAAZK8glUql8t2kOcLtNWvWxEUXXRSPP/54o3MLCgrilFNOiQsvvDAKCgqy3stHH30UZ599dsyaNavRuR07doxx48bF4YcfnnV9AAAAAACy0+zHkhQUFERhYfZHfWcbPl9yySUZwXZBQUEccMAB0a9fv6ioqIh33nknpk+fHhERqVQq7rjjjujQoUOcc845WdX//PPP4yc/+Um899576WsdOnSIgw46KHbcccdYsWJFvPrqq7Fo0aKIiFi1alVceOGFsdVWW8X++++f7csFAAAAACALzR5ujxgxIq655pomrXnPPffEY489lh5vt912cfPNN8duu+2WMe/ll1+Oc889Nz7//POIiJg4cWIMHTo0vvnNbzba49JLL80Itr/+9a/H+PHjo1u3bulrVVVVceedd8b1118fqVQqKisr49xzz42nn346Yx4AAAAAABsn+0eoW6nVq1fH73//+/S4Xbt28ac//Wm9YDsi4oADDoiJEyemnwZPpVLxm9/8ptEe7777bjz55JPp8a677hq33XbbeoF1UVFRnHrqqXHWWWelr3322Wfxhz/8IefXBQAAAABA/RIfbj/wwAPx6aefpsennXZa7LzzzvXO33fffePII49Mj2fOnBnPP/98gz1uvvnmjPGll14abdu2rXf+f/7nf8ZOO+2UHt97772xbNmyBnsAAAAAAJC9Zj+WpKnVfKK6qKgofvjDHza65t///d/jL3/5S3r81FNPxUEHHVTn3C+//DJeeuml9Lh3797xjW98o8H6bdq0ieOOOy5uuOGGiPjqzS6ff/75OOaYYxrdW23Lly/PeU0+FRQURNeuXSMiYsWKFdEM70cKmwX3FuSHewvyw70FTc99Bfnh3oL82JB7a6uttmryfST6ye1ly5bF22+/nR4PGTIkSkpKGl235557Ro8ePdLjF154IaqqquqcO2XKlFi7dm16fMghh2S1t0MPPTRj/Nxzz2W1DgAAAACAxiU63H7zzTejuro6PR4yZEjWa/fcc8/0r1esWBHz58+vc960adMyxtn22GmnnWLrrbeutw4AAAAAABsu0eH2e++9lzEeMGBA1mt33333jPGCBQvqnFf7ei49ar6p5cqVKzPOBgcAAAAAYMM1+5nbc+bMifPPPz9mzpwZ//znPyMiomvXrrHDDjvEPvvsE9/5zneif//+WdWqHTxvt912We+j9txswu22bdtmPI3dmJ49e65Xa5tttsl6PQAAAAAAdWv2cHv27Nkxe/bsjGtffPFFfPTRR/Haa6/FhAkT4sADD4wxY8ZEr169GqxVVlaWMa55jnZjas8tLS1ttEdJSUkUFBRk3aP2+d/19QAAAAAAIDet8liSl156KY455ph44YUXGpz35ZdfZoy32GKLrHvUnrtq1ar15pSXl2e80WQu9SMiOnXq1GgPAAAAAABy12xPbpeUlMTw4cNj//33j379+sXWW28dbdu2jRUrVsTs2bPj2WefjYcffjjWrl0bERGff/55nHPOOTFp0qQYPHhwnTVXr16dMW7Xrl3W+6k9t67gufa1XOpHfHWMSWM9GpPLk+LNoeZ+WtveIMncW5Af7i3ID/cWND33FeSHewvyo7XcW80Sbl911VWxzz77RHHx+u223Xbb2HbbbePAAw+MU089Nc4666yYN29eRESsWbMmzj///HjqqafWC4ojvnqyuqa65tSn9tzatdb139D62fZoTNeuXXNe01y6dOnS0luATZJ7C/LDvQX54d6Cpue+gvxwb0F+tOS91SzHkuy33351Btu19erVK+68886MN2L8+OOP48EHH6xzfu0nqSsqKrLe07onxOurtbH1s+0BAAAAAEDumv0NJRuz9dZbx89//vMYPXp0+toTTzwRJ5544npzO3bsmDEuLy/P+unq2k9l165VX/1c1A636+rRmBUrVuS8Jp8KCgrSfxuzcuXKSKVSLbwj2DS4tyA/3FuQH+4taHruK8gP9xbkx4bcW/k4oaLVhdsREYccckh06tQpvvjii4iIeOutt2L16tXRoUOHjHm1w+JVq1ZF586ds+pR+80o6wqe27dvH0VFRek3lcz1zOx1+2+oR2Na8x+6qVSqVe8Pksq9Bfnh3oL8cG9B03NfQX64tyA/WvLeapZjSXJVXFwcAwcOTI8rKytjyZIl680rKSnJGC9evDjrHqWlpRnjHj161Dmve/fu6V+XlZXl9IUqKyvLqgcAAAAAALlpleF2xFfHk9S0fPny9ebssssuGeNcwu3ac2vXquv6mjVr4p///GfWPT755JOsegAAAAAAkJtWG26vXr06Y1zXmzH27t07Yzxr1qys68+cObPBWuvUDqRz6TF79uz0rzt37hzbbrtt1msBAAAAAKhfqw23P/zww4xxt27d1pszdOjQKCz810uYPn161vXfeuut9K+7du0au+66a53z9t5774xxtj0++OCDjKe8a9cBAAAAAGDDtcpwe/HixTF//vz0eOutt844+7rm9cGDB6fH06dPX++c67pMnz4948ztYcOGRXFx3e+t+c1vfjPatGmTHj/11FNZvYba84YPH57VOgAAAAAAGtcqw+2JEydmvHHjAQccEAUFBXXOPfTQQ9O/rqqqivvvv7/R+vfee2+9NWrr1KlTfOtb30qPFyxYEK+99lqD9SsqKuJ//ud/0uO2bdvGwQcf3Oi+AAAAAADITl7D7bVr18aCBQtyWvM///M/8cADD6THBQUFcfLJJ9c7f+TIkRlvPnnbbbfFwoUL650/derUePTRR9PjAQMGxEEHHdTgns4444yM8ZVXXhlr166td/4f/vCHWLRoUXp8/PHH13msCgAAAAAAGyav4XZ5eXkcccQRMXr06JgyZUpUVlbWO3fp0qVxxRVXxCWXXJJxfcSIEbHHHnvUu65jx45x5plnpsdr1qyJU045JePNHNd5+eWX48wzz8x4Kvz888+v96nwdQYNGhSHHHJIevyPf/wjTjvttFi2bFnGvOrq6rjjjjvid7/7XfralltuGf/5n//ZYH0AAAAAAHJTkKqZ9Daxzz77LPbZZ5/0uFOnTrHbbrvFLrvsEl26dIk2bdrEypUrY86cOfH2229HRUVFxvq99947/vSnP0Xbtm0b7TV69Oh4/PHH0+OCgoI44IADol+/flFZWRkzZsxY780gf/rTn8b555+f9WsZOXJkxlPhHTp0iIMPPjh23HHHWL58ebz66qsZT2wXFRXFH/7wh4xjTXK1fPnyDV6bDwUFBdG1a9eIiFixYkXk8bcPbFbcW5Af7i3ID/cWND33FeSHewvyY0Pura222qrp99Gc4XYu/v3f/z1+8YtfRPv27bOav2bNmrjwwguzesPHgoKCOOmkk+Kiiy5q9Kntmj788MM466yzYs6cOY3O7dixY1xxxRVx5JFHZl2/LsJt2Dy4tyA/3FuQH+4taHruK8gP9xbkR2sJt/N6LEn79u3jpz/9aQwZMiSrp687duwYRx55ZPzP//xPXHbZZVkH2xER7dq1i5tuuimuvfba6Nu3b73z9txzz/jjH/8YF198cU7BdkTEjjvuGA8++GCceeaZse2229Y5p02bNvHd7343HnrooY0OtgEAAAAAqFten9yuqbKyMhYuXBiLFi2K0tLS+PLLL6OysjK23HLL6Ny5c/Tp0yf69esXRUVFTdJv7ty5MX/+/CgrK4uioqLo3r177L777tGrV68mqV9VVRVvvvlmfPjhh/Hpp5/GFltsET169IihQ4c26d9CeHIbNg/uLcgP9xbkh3sLmp77CvLDvQX50Vqe3C5u8or1NSoujj59+kSfPn2apV+/fv2iX79+eatfVFQU++yzzwYfuwIAAAAAwIbL67EkAAAAAACQD8JtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiFLf0BgAAAACA3E2ePDnGjRuXHj/00EPRs2fPJu0xduzYeOKJJyIiokePHvHII480aX0a99FHH8W8efNiyZIlUVVVFd27d49ddtklevfu3dJba3HCbQAAAACAVubVV1+NO+64I9555506P77rrrvGj3/84zjkkEOaeWeth3AbAAAAYDN19nnVLb2FvCsuXhkREZWVVU1Wc8J4J/2SP6lUKm666aa4//77I5VK1TvvH//4R1x22WXx8ssvx5gxY6Jt27bNuMvWQbgNAAAAANBK3HLLLXHfffdlXBs0aFAMGDAgioqKYt68eTFt2rR08P3Xv/41iouL41e/+lVLbLdFCbcBAAAAIIGOOOKIOOKII1p6GzShV155Je666670eMstt4xf//rXsc8++2TMmzt3bvx//9//F0uWLImIiCeeeCIGDRoUI0aMaM7ttjj/hgIAAAAAoIWlUqmYOHFielxQUBDXXXfdesF2RES/fv3id7/7XbRr1y597fbbb481a9Y0y15bC09uAwAAwCao/QMn56Vu+ci7Gp8EQM7+9re/xT/+8Y/0+N/+7d9iyJAh9c7faaed4sQTT4w77rgjIiKWLl0ajz76aBx33HF532tr4cltAAAAAIAW9uyzz2aMjznmmEbXjBgxIoqKitLj//u//2vyfbVmntwGAAAAgM1MKpWKmTNnxoIFC2LFihXRuXPnKCkpiSFDhkT79u1benubncrKynjttdfS45KSkth9990bXde9e/fYY4894u23346IiBkzZsTKlSujS5cuedtrayLcBgAAAIAEmjx5cowbNy49fuihh6Jnz56Nrnv88cfj1ltvjdLS0vU+1qlTpzj88MPjjDPOyDrkfvDBB+OGG25Ij4cNGxbXXntto+sqKyvjzDPPjBkzZqSvXXnllfHd7343q76bkgULFsRnn32WHg8cODDrtTXD7aqqqnj77bfjwAMPbPI9tkbCbQAAABLHedIAuausrIzLLrssnnvuuXrnfPHFF3H//ffH66+/HjfeeGNWdY877riYPn16+kiMF198Me677744/vjjG1x3yy23ZATbP/jBDzbLYDsi4v33388Y9+3bN+u1/fv3X6+WcBsAAAAA2GRcddVV6wXbvXr1ir322iu6dOkSy5Yti7///e9RWloaCxYsiDFjxmT1JHhExCWXXBLz5s2Ljz76KCIifve738Uee+wRe+yxR53zX3755fjzn/+cHvft2zfOO++8DXthm4APPvggY9yjR4+s15aUlDRYa1Mm3AYAAACATdxzzz0XTz75ZHrcsWPH+OUvfxnf+973MualUqn43//93xg/fny88847MXfu3Kzqb7HFFnHVVVfF6aefHmvXro3KysoYM2ZM3H333dG5c+eMuaWlpXHFFVdEKpXKWNu2bduNfJX/snjx4jj22GObrF5dJkyYEEOHDm2SWkuWLMkYd+/ePeu1tefWrrUpK2zpDQAAAAAA+VNVVRW//e1v0+PCwsK4+uqr1wu2IyIKCgri2GOPjTFjxkRExNq1a7Pu069fv4ynr0tLS2Ps2LHpEDsi0qF3zfOlL7744thxxx1zeUmNSqVSUVVVldf/ar6ujbVq1aqMcceOHbNeW3vu6tWrm2RPSSDcBgAAAIBN2CuvvBJlZWXp8eGHHx5f//rXG1xz6KGHxgEHHJBzr9rnZk+ZMiXuueee9Pj3v/99vPvuu+nxscceG8OHD8+5z6amvLw8Y5zLU+y1525O4bZjSQAAAABgE/biiy9mjEeOHJnVuh/+8Ifx8ssv59zvl7/8ZcydOzcWLVoUERETJ06MgQMHxooVK+Lee+9Nz+vfv3+cc845OdfPRs+ePeO1117LS+18WLNmTcZ4Y8Lt2rU2ZcJtAAAAANiE1XxSunv37tGnT5+s1u29997RsWPH9Y7MaMy6M7RPO+20WLNmTVRVVcWYMWMynk7u1KlTk5+znWS1Pw8VFRVZr619dMzm9Dl1LAkAAAAAbKJSqVT6CeqIyDrYjvjqbO7evXtvUN8+ffrE6NGj0+MlS5asd8729ttvv0G1N0UdOnTIGOfy9HXtcLt2rU2ZcBsAAAAANlFffPFFVFdXp8dbbbVVTuu7deu2wb2POuqoOOSQQ9a7ftxxx8XBBx+8wXU3RbXfFDKXp+VrzxVuAwAAAACJV/vNBdu3b5/T+lzn11bXERnf/OY3N6rmpmjbbbfNGC9ZsiTrtbXndu/evUn2lATO3AYAAACATVTtp3hrnnudjVzn1/Tkk0/GY489tt71K6+8Mu6+++6Neiq8MYsXL45jjz02b/UjIiZMmBBDhw5tklq9evXKGJeWlma9tqysLGP8ta99rSm2lAie3AYAAACATVSnTp2isPBfEeDy5ctzWr9s2bIN6rtw4cK47rrr0uOaIfunn34al19+ecZxKU0tlUpFVVVVXv9LpVJNtt/agfS8efOyXjtnzpwGa23KhNsAAAAAsIkqKCiInXbaKT2eP39+1murq6vjvffey7lneXl5XHLJJekjUYqKiuKGG27IOH976tSpceedd+Zce1PVu3fv2HLLLdPjd955J+u1NecWFRXFoEGDmnRvrZljSQAAAABgE7bHHnvE+++/HxFfnc88f/786NOnT6Pr3njjjZze2HCd66+/PhYsWJAen3rqqTF06NDo379/zJkzJz744IOIiLj99ttj8ODBsddee+XcozE9e/aM1157rcnr5ktxcXHst99+8de//jUivjpq5N1334099tijwXVLliyJd999Nz0eOHBgdO3aNZ9bbVU8uQ0AAAAAm7ADDzwwY/zggw9mte7+++/PudcTTzwRjz/+eHq87777xqhRoyIiomPHjnHVVVdFu3btIiKiqqoqLrvssg0++mRTc/DBB2eMH3rooUbXPPLIIxnHu9SusakTbgMAAADAJuyAAw6IkpKS9Hjy5Mkxbdq0Btc888wzMWXKlJz6LFy4MK6//vr0eJtttonLL78848zvXXfdNUaPHp0ef/rpp3HFFVfk9fztpDjwwAOjd+/e6fGTTz4Z06dPr3f+okWL4s9//nN6vM0228SRRx6Z1z22NsJtAAAAANiEFRUVxdlnn50eV1dXx4UXXhjPPPPMenNTqVQ8/PDDMXbs2IiIaNu2bVY96jpne+zYsdGtW7f15h511FEZ52///e9/d/52RBQWFsYZZ5yRHqdSqbjwwgvj9ddfX2/u3Llz46yzzoo1a9akr5166qnRvn37Ztlra+HMbQAAAADYxH3nO9+JKVOmxFNPPRUREatWrYpLL700brvttth7772jS5cusWzZspg6dWp88sknEfHV+c09e/aMp59+utH61113XZ3nbNfnF7/4xXrnb++5554NrtkcfPOb34wf//jHMWnSpIiI+Pzzz+Pss8+OwYMHx2677RZFRUUxf/78eP311yOVSqXXHXrooXH00Ue31LZbjHAbAAAAADYDY8aMiYqKinjuuefS1z744IN0wFzT1772tRg3blz84Q9/aLTu5MmT44knnkiPa56zXZ9152+feuqpsWbNmvT523fffXdstdVW2b+oTdAZZ5wRa9asiQceeCB97e2334633367zvnf+c534qKLLmqu7bUqwm0AAACAzdSE8Zv2ibUFBQXRtWuXiIhYsWJFxpOum6Pi4uK46qqrYr/99otbb701ysrK1pvTsWPHOOyww+JnP/tZdOjQodGaCxcujP/6r/9Kj+s6Z7s+687fvvrqqyMiYunSpXH55ZfHjTfemNX6TVVhYWGMHj06vvGNb8Qdd9wR7777bp3zevfuHT/60Y/i3/7t35p5h61HQWpzv6tbueXLl7f0FjJ89U2ha0T4pgBNyb0F+eHegvxwb9EatH/g5LzULR95V17qNiYf99Wm9jmCDeF7Vv1SqVS8++678d5778XKlSujc+fOUVJSEkOHDt3szm1u7T788MOYO3duLF26NKqrq2PbbbeNXXbZJXbdddcW29OG3Fv5eCLfk9sAAAAAsJkpKCiIgQMHxsCBA1t6KzRixx13jB133LGlt9Eqbb7P9wMAAAAAkFjCbQAAAAAAEsexJAAAAFAHZ1YDQOvmyW0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiVPc0hsAAACAzVH7B05O/7qgIKKy+Ksf0dtXVkYqteF1y0fetbFbA4BE8OQ2AAAAAACJI9wGAAAAgASaPHlyfOMb30j/98knnzR5j7Fjx6brjxgxosnrw8ZwLAkAAAAAQCuybNmymDVrVvq/2bNnx8qVK9MfP+yww+JXv/pVC+6wdRBuAwAAAGymap79vilqyvPsa3K2PflyxRVXxPTp06O0tLSlt5IIwm0AAAAAgFbgb3/7W3zxxRctvY3EEG4DAAAAQAIdccQRccQRR7T0Nsizbt26Ra9evWL69OktvZVWR7gNAAAAANAKbLnlltG/f/8YMGBA7LbbbjFgwIAoKSmJTz75JH7wgx+09PZaHeE2AAAAAEAr8PDDD7f0FhKlsKU3AAAAAAAAufLkNgAAAABsZlKpVMycOTMWLFgQK1asiM6dO0dJSUkMGTIk2rdv39Lbg6wItwEAAAAggSZPnhzjxo1Ljx966KHo2bNno+sef/zxuPXWW6O0tHS9j3Xq1CkOP/zwOOOMM7IOuR988MG44YYb0uNhw4bFtdde2+i6ysrKOPPMM2PGjBnpa1deeWV897vfzaovOJYEAAAAADYDlZWVcckll8SVV15ZZ7AdEfHFF1/E/fffH//xH/8RZWVlWdU97rjj4uCDD06PX3zxxbjvvvsaXXfLLbdkBNs/+MEPBNvkxJPbAAAAALAZuOqqq+K5557LuNarV6/Ya6+9okuXLrFs2bL4+9//HqWlpbFgwYIYM2ZMVk+CR0RccsklMW/evPjoo48iIuJ3v/td7LHHHrHHHnvUOf/ll1+OP//5z+lx375947zzztuwF8ZmS7gNAAAAAJu45557Lp588sn0uGPHjvHLX/4yvve972XMS6VS8b//+78xfvz4eOedd2Lu3LlZ1d9iiy3iqquuitNPPz3Wrl0blZWVMWbMmLj77rujc+fOGXNLS0vjiiuuiFQqlbG2bdu2G/kq/2Xx4sVx7LHHNlm9ukyYMCGGDh2a1x40zLEkAAAAALAJq6qqit/+9rfpcWFhYVx99dXrBdsREQUFBXHsscfGmDFjIiJi7dq1Wffp169fxtPXpaWlMXbs2HSIHRHp0Puzzz5LX7v44otjxx13zOUlNSqVSkVVVVVe/6v5umgZwm0AAAAA2IS98sorGednH3744fH1r3+9wTWHHnpoHHDAATn3qn1u9pQpU+Kee+5Jj3//+9/Hu+++mx4fe+yxMXz48Jz7QIRjSQAAAABgk/biiy9mjEeOHJnVuh/+8Ifx8ssv59zvl7/8ZcydOzcWLVoUERETJ06MgQMHxooVK+Lee+9Nz+vfv3+cc845OdfPRs+ePeO1117LS21aD+E2AAAATa79AyfnpW75yLvyUhdgU1bzSenu3btHnz59slq39957R8eOHWPVqlU59Vt3hvZpp50Wa9asiaqqqhgzZkyUl5en53Tq1KnJz9lm8+NYEgAAAADYRKVSqfQT1BGRdbAd8dXZ3L17996gvn369InRo0enx0uWLFnvnO3tt99+g2rDOp7cBgAAAHLm6XxIhi+++CKqq6vT46222iqn9d26ddvg3kcddVS8+eab8fTTT2dcP+644+Lggw/e4Lqwjie3AQAAAGATtXr16oxx+/btc1qf6/za6jp25Jvf/OZG1YR1PLkNAAAAAJuoDh06ZIxrnnudjVzn1/Tkk0/GY489tt71K6+8Mu6+++6Neiq8MYsXL45jjz02b/UjIiZMmBBDhw7Naw8a5sltAAAAANhEderUKQoL/xUBLl++PKf1y5Yt26C+CxcujOuuuy49rhmyf/rpp3H55ZdnHJfS1FKpVFRVVeX1v1Qqlbf9kx3hNgAAAABsogoKCmKnnXZKj+fPn5/12urq6njvvfdy7lleXh6XXHJJ+kiUoqKiuOGGG+KQQw5Jz5k6dWrceeedOdeGmhxLAgAAAACbsD322CPef//9iIhYsmRJzJ8/P/r06dPoujfeeCNWrVqVc7/rr78+FixYkB6feuqpMXTo0Ojfv3/MmTMnPvjgg4iIuP3222Pw4MGx11575dyjMT179ozXXnutyevSunhyGwAAAAA2YQceeGDG+MEHH8xq3f33359zryeeeCIef/zx9HjfffeNUaNGRUREx44d46qrrop27dpFRERVVVVcdtllG3z0CQi3AQAAAGATdsABB0RJSUl6PHny5Jg2bVqDa5555pmYMmVKTn0WLlwY119/fXq8zTbbxOWXX55x5veuu+4ao0ePTo8//fTTuOKKK/J6/jabLuE2AAAAAGzCioqK4uyzz06Pq6ur48ILL4xnnnlmvbmpVCoefvjhGDt2bEREtG3bNqsedZ2zPXbs2OjWrdt6c4866qiM87f//ve/O3+bDeLMbQAAAADYxH3nO9+JKVOmxFNPPRUREatWrYpLL700brvttth7772jS5cusWzZspg6dWp88sknERExcODA6NmzZzz99NON1r/uuuvqPGe7Pr/4xS/WO397zz33bHDN5uCJJ56Iq666qtF5Tz75ZL1fl5dffrmpt9VqeXIbAAAAADYDY8aMieHDh2dc++CDD+J///d/44477ohHHnkkHWx/7Wtfi3HjxkVRUVGjdSdPnhxPPPFEelzznO361Hf+9vLly3N8VZuW6urqqKqqqvO/mlKpVFbzNnWe3AYAAADYTJWPvKult5BXBQUF0bVr14iI+GLFikilUi27oRZWXFwcV111Vey3335x6623RllZ2XpzOnbsGIcddlj87Gc/iw4dOjRac+HChfFf//Vf6XFd52zXZ93521dffXVERCxdujQuv/zyuPHGG7NaD8JtAAAAAEigI444Io444ogNWnf44YfHu+++G++9916sXLkyOnfuHCUlJTF06NBo3759eu6vfvWr+NWvflVvrZ133jleeOGFDdl+RHx1/vZRRx21wes3NRv6Nd1cCbcBAAAAYDNTUFAQAwcOjIEDB7b0VmCDeb4fAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASJzilt5AvixatChmzZoVpaWlUV1dHSUlJdGnT5/o27dvk/WYMWNGvP/++1FWVhYdOnSIkpKSGDRoUJSUlDRZDwAAAAAA1tdqwu1x48bFpEmTMq4dffTRcc011+RU56WXXoqJEyfG9OnT6/x4v3794vTTT4/vf//7G7TPVCoVkyZNikmTJsWiRYvW+3hhYWHsv//+cd5558XAgQM3qAcAAAAAAA1rFceSvPXWW/HnP/95o2qkUqm4+uqr4yc/+Um9wXZExNy5c+PnP/95XHDBBbF27dqceqxYsSJOOeWUuOqqq+oMtiMiqqurY8qUKXHCCSfEnXfemVN9AAAAAACy0+JPbldUVMSll14a1dXVG1Vn/Pjx64XJQ4cOjYEDB0ZRUVHMmTMnXn311UilUhERMXny5GjTpk3WT4ZXVFTE2WefHVOnTk1fa9OmTRx44IHRu3fv+PLLL2PatGkxd+7c9Pyrr746ttxyyzjmmGM26rUBAAAAAJCpxcPtP/7xjzFv3ryIiNh2221j6dKlOdd48cUX45ZbbkmPO3fuHL/97W9jv/32y5g3a9asOOOMM6K0tDQiIh5++OEYOnRojBw5stEe48ePzwi2+/btGzfffHPssMMOGfMeffTRuPjii6OioiIiIi677LIYNGhQ9OnTJ+fXBQAAAABA3Vr0WJIFCxakQ+kOHTrE6NGjc66RSqXihhtuSI8LCgpi4sSJ6wXbEREDBgyIO++8M9q1a5e+NmHChFizZk2DPcrKyjLOA996663j7rvvXi/Yjog48sgjY9y4celxRUVF3HTTTTm9JgAAAAAAGtZi4XYqlYpLL700fe71mWeeGdtvv33OdZ577rn0USAREUcddVTss88+9c7feeed49RTT02PlyxZEg8++GCDPW6//faMAPyCCy6Irbbaqt75I0aMyNjDM888k346HQAAAACAjddi4fZ9990X06ZNi4ivjvg45ZRTNqjOk08+mTE+8cQTG11z/PHHR1FRUXr81FNPNTi/5se7dOkSRxxxRKM9TjjhhHprAAAAAACwcVok3C4rK0sfJVJQUBBXXHFFtGnTJuc6lZWV8be//S093m677WLQoEGNrispKYk999wzPX7zzTdj+fLldc599913o6ysLD3+9re/nXGsSX2GDx+e8Zqee+65RtcAAAAAAJCdFgm3r7zyyvj8888jImLkyJExdOjQDaozf/78WLlyZXo8ZMiQrNfWDLerqqrizTffrHPeuqfLc+3Rvn376N+/f3o8Z86c9GsGAAAAAGDjNHu4/de//jWeeeaZiPjqjRkvuOCCDa713nvvZYx32223rNfuvvvuDdZaZ8GCBRnjAQMGZN2j9tzatQAAAAAA2DDNGm5//vnnMXbs2PT4l7/8ZXTp0mWD69UOi3v27Jn12u222y5jvHDhwqx61F7XkNr7EW4DAAAAADSNZg23r7vuuli6dGlEROy///5x5JFHblS9mmdhR0T06NEj67W155aWljbao7i4OLbZZpsm7wEAAAAAQG6Km6vR66+/Hg8++GBERLRr1y4uv/zyja755ZdfZoy32GKLrNfWnrtq1apGe3To0CEKC7P/+4BsezSkoKAg5zX5VHM/rW1vkGTuLcgP9xbkh3uLbOTrt8a633P5rt8cPRqqvzG9m+tz1BxfA9hYvmdBfrSWe6tZwu21a9fGpZdeGqlUKiIi/vM//zN69eq10XVXr16dMW7btm3Wa9u1a5cxri94rtmj9prG1N7PhoTbXbt2zXlNc9mYI2WA+rm3ID/cW5Af7i3qU1mcnx831/2MlO/6zdGjvvrFG9m3uT5HzfE1gKbkexbkR0veW81yLMnvf//79JnWO++8c5x++ulNUre8vDxjnEu4XXtu7Vp1Xc+lfi49AAAAAADITd6f3J47d27cfvvt6fEVV1yRc0hcn9pPUldUVGS9du3atQ3Wqnl93dPbudTPpUdDVqxYkfOafCooKEj/bczKlSvTT+MDG8e9Bfnh3oL8cG+RjfaVlXmp+8X/+xkp3/Wbo0ft+uue2K7cyL7N9Tlqjq8BbCzfsyA/NuTeyse/zMlruF1dXR1jxoxJh8JHH310fP3rX2+y+h07dswYr1mzJuu1tefWrlXz+rpwO9cnr2uH2/X1aEhr/kM3lUq16v1BUrm3ID/cW5Af7i3qk6/fFut+v+W7fnP0qFm/9nGlG9O7uT5HzfE1gKbkexbkR0veW3k9lmTSpEkxY8aMiPgqmb/wwgubtH7tsLj2G0w2pPbchsLtdVavXp3TFyrbHgAAAAAA5CZv4XZ5eXmMHz8+Pb7wwgujW7duTdqjpKQkY1xaWpr12tpze/To0WiPysrKWLp0aZP3AAAAAAAgN3k7lmTt2rWxatWq9PjSSy+NSy+9tME1tZ+KfuSRR+LRRx9Nj0eMGBG//vWv0+NddtklY/4nn3yS9f4WL16cMa5dq+b1adOmZazr3r17Vj1q76e+HgAAAMD62j9wcl7qlo+8Ky91AWheeT2WpKaqqqpG/6uurs5Yk0qlGvx47969M8azZ8/Oej8zZ87MGNcXPNfuMWvWrKx71J4r3AYAAAAAaBrNFm7nQ9++faNz587p8fTp07NeW3NuUVFRDB06tM55e+21V73rGlJeXh5z5sxJj/v165exVwAAAAAANlzejiXp3LlzzJ07N6c1f//73+Okk05Kj48++ui45ppr6p1fXFwcBx54YEyePDkivjoy5O23347Bgwc32KesrCzeeuut9HjIkCH1nge+xx57RElJSZSVlUVExPPPPx9r1qyJdu3aNdjj2WefjYqKivR4+PDhDc4HAAAAACB7iX5yOyLi0EMPzRjfc889ja657777Mo44qV2jpoKCgvje976XHn/22WfpML2xHjUdcsghja4BAAAAACA7iQ+3hw8fHn379k2P//KXv8Trr79e7/yFCxfG7bffnh5vu+22cdxxxzXY47TTTou2bdumxzfccEMsX7683vmPPPJIxh6GDx8e/fv3b7AHAAAAAADZS3y4XVhYGKNHj06PU6lUnHnmmfHqq6+uN3fWrFkxatSoWLNmTfraWWedFe3bt2+wR48ePeJHP/pRevzPf/4zTjrppPjoo4/Wm/voo4/GmDFj0uM2bdrEueeem9NrAgAAAACgYXk7c7s5HXTQQXH66afHrbfeGhFfHR0yatSo2GuvvWLgwIFRWFgYc+fOjVdeeSVSqVR63ZFHHhnHH398Vj3OP//8mDFjRkybNi0iIubNmxeHHnpoDBs2LHbZZZdYtWpVvP766+udM37ZZZdFv379muiVAgAAAAAQsYmE2xERo0ePjvLy8pg0aVL62htvvBFvvPFGnfMPO+ywGDduXNb127ZtGxMmTIhzzz03pk6dGhERFRUV8eyzz9Y5v7i4OEaPHt3okScAAAAAAOQu8ceSrFNYWBhjxoyJP/7xj7HnnnvWO69v375x3XXXxY033hjt2rXLqUe3bt3irrvuiosuuih23HHHevex//77x7333hunnnpqTvUBAAAAAMhOq3py++tf//p6x3rkatiwYTFs2LD44IMPYubMmbFkyZKoqqqKkpKS6NOnz0YfEVJYWBijRo2Kk08+Od55551YuHBhLFmyJNq3bx8lJSUxePDgKCkp2ageAAAAAAA0rFWF202pV69e0atXr7zVLygoiEGDBsWgQYPy1gMAAAAAgLptMseSAAAAAACw+RBuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASp7ilNwAAAEDza//AyXmpWz7yrrzUBQCozZPbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkTnFLbwAAAACgJbR/4OS81C0feVde6gKQyZPbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEKW7OZtXV1bFo0aL44IMPoqysLD777LNYu3ZtdOzYMbp27Rr9+/ePPn36RFFR0Ub3WrRoUcyaNStKS0ujuro6SkpKok+fPtG3b98meCVfmTFjRrz//vtRVlYWHTp0iJKSkhg0aFCUlJQ0WQ8AAAAAANaX93B72bJlcfvtt8ebb74Zs2fPjtWrVzc4v0uXLnHkkUfGqaeeGtttt13O/V566aWYOHFiTJ8+vc6P9+vXL04//fT4/ve/n3PtiIhUKhWTJk2KSZMmxaJFi9b7eGFhYey///5x3nnnxcCBAzeoBwAAAAAADcv7sSQff/xx3HbbbfHmm282GmxHRKxcuTImTZoUhx12WDz00ENZ90mlUnH11VfHT37yk3qD7YiIuXPnxs9//vO44IILYu3atVnXj4hYsWJFnHLKKXHVVVfVGWxHfPV0+pQpU+KEE06IO++8M6f6AAAAAABkp1mPJYmI2GabbaJv377Rq1ev6NKlSxQVFcWKFSti9uzZ8dZbb0V1dXVERKxatSouuuiiqKioiB/+8IeN1h0/fvx6YfLQoUNj4MCBUVRUFHPmzIlXX301UqlURERMnjw52rRpE9dcc01W+66oqIizzz47pk6dmr7Wpk2bOPDAA6N3797x5ZdfxrRp02Lu3Lnp+VdffXVsueWWccwxx2TVAwAAAACA7OQ93C4qKop99tknDjnkkDjggANil112qXfuxx9/HGPHjo0XXnghfe3Xv/517LfffrHTTjvVu+7FF1+MW265JT3u3Llz/Pa3v4399tsvY96sWbPijDPOiNLS0oiIePjhh2Po0KExcuTIRl/H+PHjM4Ltvn37xs033xw77LBDxrxHH300Lr744qioqIiIiMsuuywGDRoUffr0abQHAADAOu0fODkvdctH3pWXugAAzS3vx5IMGDAg/vu//zt+/OMfNxhsR0Rsv/32MXHixDjggAPS18rLy+PPf/5zvWtSqVTccMMN6XFBQUFMnDhxvWB73V7uvPPOaNeuXfrahAkTYs2aNQ3uq6ysLCZNmpQeb7311nH33XevF2xHRBx55JExbty49LiioiJuuummBusDAAAAAJCbvIfbuSoqKooLLrgg49rf/va3euc/99xz6aNAIiKOOuqo2Geffeqdv/POO8epp56aHi9ZsiQefPDBBvd0++23ZwTgF1xwQWy11Vb1zh8xYkTGHp555pmYN29egz0AAAAAAMheqwu3IyJ233336NixY3q8ePHieuc++eSTGeMTTzyx0frHH398FBUVpcdPPfVUg/NrfrxLly5xxBFHNNrjhBNOqLcGAAAAAAAbp1WG2xERW2yxRfrX694EsrbKysqMp7q32267GDRoUKO1S0pKYs8990yP33zzzVi+fHmdc999990oKytLj7/97W9nHGtSn+HDh0ebNm3S4+eee67RNQAAAAAAZKdVhtvl5eWxYsWK9HjHHXesc978+fNj5cqV6fGQIUOy7lEz3K6qqoo333yzznnTpk3LGGfbo3379tG/f//0eM6cOfH5559nvT8AAAAAAOrXKsPtp556KioqKtLjgw46qM557733XsZ4t912y7rH7rvv3mCtdRYsWJAxHjBgQNY9as+tXQsAAAAAgA3T6sLt+fPnx7XXXpseb7XVVnHyySfXObd2WNyzZ8+s+2y33XYZ44ULF2bVo/a6htTej3AbAAAAAKBpFLf0BlKpVHzxxRcxb968+Otf/xr33ntvrFmzJiIiOnbsGBMmTIitt966zrU1z8KOiOjRo0fWfWvPLS0tbbRHcXFxbLPNNk3eAwAAAACA3DR7uL1gwYI44ogj0uPq6uo63zDy29/+dlx00UXxta99rd5aX375Zca45ptQNqb23FWrVjXao0OHDlFYmP3D7tn2aEhBQUHOa/Kp5n5a294gydxbkB/uLcgP91bzyNendt3XTP2G6zdHj4bqb0xvX4PsezTHa6Bl+Z4F+dFa7q1mD7dTqVRUVVXV+/HCwsI48cQT4/TTT4+SkpIGa61evTpj3LZt26z30a5du4xxfcFzzR611zSm9n42JNzu2rVrzmuaS5cuXVp6C7BJcm9Bfri3ID/cW/lTWZyfH9fW/YyhfsP1m6NHffWLN7Kvr0H2PZrjNdB6+J4F+dGS91arO3O7uro6Jk2aFMOHD49rr7021q5dW+/c8vLyjHEu4XbtubVr1XU9l/q59AAAAAAAIDfN/uR27969Y+7cuenx2rVrY8WKFTF79ux46qmn4rHHHouKioqoqKiIO+64I+bNmxc333xzncFy7SepKyoqst5H7dC8vqey27Vrl356O5f6ufRoyIoVK3Jek08FBQXpv41ZuXJlnUfKALlzb0F+uLcgP9xbzaN9ZWVe6n7x/37GUL/h+s3Ro3b9dU9sV25kX1+D7Hs0x2ugZfmeBfmxIfdWPv5VS4u/oWTbtm2je/fu0b179xg2bFicfPLJ8dOf/jQWL14cERFTpkyJ3//+93H++eevt7Zjx44Z43VvRJmN2nNr16p5fV24neuT17XD7fp6NKQ1/6GbSqVa9f4gqdxbkB/uLcgP91b+5OvTuu7rpX7D9ZujR836tY8r3ZjevgbZ92iO10Dr4XsW5EdL3lut7liS/v37x6233hpt2rRJX7vzzjvrfIK5dlhc+w0mG1J7bkPh9jqrV6/O6QuVbQ8AAAAAAHLT6sLtiIg+ffrEYYcdlh6Xl5fHCy+8sN682m84WVpamnWP2nN79OhR57yaPSorK2Pp0qVN3gMAAAAAgNy0ynA7ImL//ffPGNc8p3udXXbZJWP8ySefZF1/3bEn9dWq73rtdQ2pvZ/6egAAAAAAkJtWG25vs802GeMvvvhivTm9e/fOGM+ePTvr+jNnzswY1xc81+4xa9asrHvUnivcBgAAAABoGq023K4dZnfu3Hm9OX379s24Pn369Kzr15xbVFQUQ4cOrXPeXnvtVe+6hpSXl8ecOXPS4379+tX5GgAAAAAAyF2rDbdrP/W83XbbrTenuLg4DjzwwPR48eLF8fbbbzdau6ysLN566630eMiQIdGtW7c65+6xxx4Z524///zzsWbNmkZ7PPvss1FRUZEeDx8+vNE1AAAAAABkp1WG2+Xl5fHYY49lXKt9Bvc6hx56aMb4nnvuabT+fffdF9XV1fXWqKmgoCC+973vpcefffZZTJ48OaseNR1yyCGNrgEAAAAAIDt5DbfXrl2bcTRHNqqrq+Oyyy7LeDPGwYMH13te9fDhw6Nv377p8V/+8pd4/fXX662/cOHCuP3229PjbbfdNo477rgG93TaaadF27Zt0+Mbbrghli9fXu/8Rx55JGMPw4cPj/79+zfYAwAAAACA7OU13C4vL48RI0bEOeecE88//3ysXbu2wflvv/12nHTSSfHII4/8a4OFhXHJJZfUu6awsDBGjx6dHqdSqTjzzDPj1VdfXW/urFmzYtSoURnHipx11lnRvn37BvfVo0eP+NGPfpQe//Of/4yTTjopPvroo/XmPvroozFmzJj0uE2bNnHuuec2WB8AAAAAgNwU57tBKpWKp59+Op5++uno0KFD9O/fP3bdddfo0qVLdOjQIb788ssoLS2Nd955Jz788MOMtQUFBTFu3LgYPHhwgz0OOuigOP300+PWW2+NiK+ODhk1alTstddeMXDgwCgsLIy5c+fGK6+8EqlUKr3uyCOPjOOPPz6r13H++efHjBkzYtq0aRERMW/evDj00ENj2LBhscsuu8SqVavi9ddfj7lz52asu+yyy6Jfv35Z9QAAAAAAIDt5D7drWr16dUyfPj2mT5/e6NySkpK44oor4qCDDsqq9ujRo6O8vDwmTZqUvvbGG2/EG2+8Uef8ww47LMaNG5fdxiOibdu2MWHChDj33HNj6tSpERFRUVERzz77bJ3zi4uLY/To0Y0eeQIAAAAAQO7yGm5vscUWce2118bf/va3eP3116OsrKzRNQMGDIijjz46fvCDH0SnTp2y7lVYWBhjxoyJb33rWzFx4sR466236pzXt2/fOO200+Koo47KuvY63bp1i7vuuivuvvvu+O///u/1njRft49vfOMbcf7558egQYNy7gEAAAAAQOPyGm4XFRXFiBEjYsSIERERsWTJknjvvffio48+is8++yzKy8ujY8eO0alTp9hhhx1i9913j86dO29Uz2HDhsWwYcPigw8+iJkzZ8aSJUuiqqoqSkpKok+fPht9REhhYWGMGjUqTj755HjnnXdi4cKFsWTJkmjfvn2UlJTE4MGDo6SkZKN6AAAAAADQsGY9lqR79+7RvXv3ZunVq1ev6NWrV97qFxQUxKBBgzydDQAAAADQAgpbegMAAAAAAJAr4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASp7ilNwAAAACwKWr/wMl5qVs+8q681AVIGk9uAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASp7ilNwAAkCRnn1ed1/oTxnv2AAAAIBt+egIAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEic4pbeAAAAdTv7vOq81p8w3nMOAABAcvmJBgAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiFLf0BgCA5nX2edV5rT9hvL87BwAAIP/89AkAAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4xS29AQBg03X2edV5rT9hvL+nBwAA2Fz5iRAAAAAAgMQRbgMAAAAAkDjCbQAAAAAAEseZ2wAAAAAJ1P6Bk/NSt3zkXXmpC9DUPLkNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIlT3NIbAADYWGefV13vx4qLV0ZERGVl1QbXnzDe8wAAAACtTbOH2ytWrIh58+bFBx98ECtWrIhUKhVdunSJnj17xp577hlbbrllk/RZtGhRzJo1K0pLS6O6ujpKSkqiT58+0bdv3yapHxExY8aMeP/996OsrCw6dOgQJSUlMWjQoCgpKWmyHgAAAAAArC/v4XZ1dXVMmzYtnnnmmXjttddi3rx59c4tKCiI/fbbL0aNGhXDhg3boH4vvfRSTJw4MaZPn17nx/v16xenn356fP/739+g+qlUKiZNmhSTJk2KRYsWrffxwsLC2H///eO8886LgQMHblAPAAAAAAAalvdw+9BDD40PPvggq7mpVCpeeeWVeOWVV+Lwww+PsWPHRqdOnbJee80118Rdd90VqVSq3nlz586Nn//85/HCCy/E1VdfHW3bts2qfsRXT52fd9558eqrr9Y7p7q6OqZMmRJ///vf4+c//3mMGjUq6/oAAAAAAGQn7+H2smXL1rv2ta99LQYNGhTbbLNNtGvXLkpLS+PVV1+N0tLS9JzHH388li5dGrfddlu0a9eu0T7jx4+PO++8M+Pa0KFDY+DAgVFUVBRz5syJV199NR18T548Odq0aRPXXHNNVq+joqIizj777Jg6dWr6Wps2beLAAw+M3r17x5dffhnTpk2LuXPnpudfffXVseWWW8YxxxyTVQ8AAAAAALLTbGdub7/99nHcccfF0UcfHT169Fjv41VVVfHAAw/E1VdfHWvWrImIiKlTp8b48ePjF7/4RYO1X3zxxbjlllvS486dO8dvf/vb2G+//TLmzZo1K84444x0iP7www/H0KFDY+TIkY3uf/z48RnBdt++fePmm2+OHXbYIWPeo48+GhdffHFUVFRERMRll10WgwYNij59+jTaAwAAAACA7BTmu0HPnj3j17/+dTzzzDNxxhln1BlsR0QUFRXFCSecEBMmTIjCwn9ta9KkSVFWVlZv/VQqFTfccEN6XFBQEBMnTlwv2I6IGDBgQNx5550ZT4JPmDAhHabXp6ysLCZNmpQeb7311nH33XevF2xHRBx55JExbty49LiioiJuuummBusDAAAAAJCbvIfbDz30UBxzzDFRVFSU1fxhw4bF4Ycfnh5XVFTEc889V+/85557Ln0USETEUUcdFfvss0+983feeec49dRT0+MlS5bEgw8+2OCebr/99owA/IILLoitttqq3vkjRozI2MMzzzzT4BtpAgAAAACQm7yH28XFuZ98UjPcjoh455136p375JNPZoxPPPHERusff/zxGWH7U0891eD8mh/v0qVLHHHEEY32OOGEE+qtAQAAAADAxsl7uL0hdtppp4zxp59+Wue8ysrK+Nvf/pYeb7fddjFo0KBG65eUlMSee+6ZHr/55puxfPnyOue+++67GceifPvb387qDS6HDx8ebdq0SY8bevocAAAAAIDctMpw+8svv8wY1/f09/z582PlypXp8ZAhQ7LuUTPcrqqqijfffLPOedOmTcsYZ9ujffv20b9///R4zpw58fnnn2e9PwAAAAAA6tcqw+2aZ2hHRL1vQvnee+9ljHfbbbese+y+++4N1lpnwYIFGeMBAwZk3aP23Nq1AAAAAADYMK0y3H700Uczxt/4xjfqnFc7LO7Zs2fWPbbbbruM8cKFC7PqUXtdQ2rvR7gNAAAAANA0Wl24PXXq1Jg6dWp6vOWWW8Y3v/nNOufWPAs7ov4nvOtSe25paWmjPYqLi2ObbbZp8h4AAAAAAOSm7sOsW8iqVavi0ksvzbh2yimnxBZbbFHn/Npnc9c3ry61565atarRHh06dIjCwuz/PiDbHg0pKCjIeU0+1dxPa9sbJJl7i01Jc/4ebqxX7XsrlUrlpU9T2lR7sWnxfesr7R84qclrlo+8O/3rfH1q133N1G+4fnP0aKj+xvT2Nci+h/oN198U+J4F+dFa7q1WFW5ffvnl8f7776fHu+yyS5x22mn1zl+9enXGuG3btln3ateuXca4vuC5Zo/aaxpTez8bEm537do15zXNpUuXLi29BdgkubfIt+LilY1P2ghdu/7r93Bz9cqmT1FR0Ub3ybbXxmipXrChNufvW5X1vPH9xqj5///5qF+zh/oN12+OHvXVL97Ivr4G2fdQv+H6m5rN+XsW5FNL3lut5liSP/3pT/GXv/wlPW7btm1cf/31DQbK5eXlGeNcwu3ac2vXqut6LvVz6QEAAAAAQG5axZPbTzzxRFx33XUZ18aOHRt77LFHg+tqB98VFRVZ91y7dm2DtWpeX/f0di71c+nRkBUrVuS8Jp8KCgrSfxuzcuXKDf7n3UAm9xbNqbKyKq/1a37vaq5e9fUpKChIP7FdVVW1wfdWS7ym5u4FufB96yvtKyubvOYXNe7LfNSv2UP9hus3R4/a9dc9sV25kX19DbLvoX7D9TcFvmdBfmzIvZWPfxXS4uH2K6+8EhdeeGFUV1enr11wwQVx9NFHN7q2Y8eOGeM1a9Zk3bf23Nq1al5fF27n+uR17XC7vh4Nac1/6KZSqVa9P0gq9xZJ15y/fxvrVfPjG7Ov1vSaktqLTdfm/H0rHy8788+tpq9fs4f6Dddvjh4169c+rnRjevsaZN9D/Ybrb2o25+9ZkE8teW+16LEkb7/9dvzsZz/LeCL61FNPjZ/85CdZra8dFtd+g8mG1J7bULi9zurVq3P6QmXbAwAAAACA3LRYuD1v3rz4yU9+kvEmi8cdd1xceOGFWdcoKSnJGJeWlma9tvbcHj16NNqjsrIyli5d2uQ9AAAAAADITYuE24sWLYr/+I//yDjn8d/+7d9i7NixOdXZZZddMsaffPJJ1msXL17cYK36rtde15Da+6mvBwAAAAAAuWn2cLusrCxGjRqV8QT0sGHD4vrrr4/Cwty207t374zx7Nmzs147c+bMjHF9wXPtHrNmzcq6R+25wm0AAAAAgKbRrOH2smXLYtSoUfHxxx+nr+27774xYcKEaNOmTc71+vbtG507d06Pp0+fnvXamnOLiopi6NChdc7ba6+96l3XkPLy8pgzZ0563K9fv4y9AgAAAACw4Zot3P7iiy/itNNOiwULFqSvDR48OG655ZZo167dBtUsLi6OAw88MD1evHhxvP32242uKysri7feeis9HjJkSHTr1q3OuXvssUfGudvPP/98rFmzptEezz77bMYbZQ4fPrzRNQAAAAAAZKdZwu3y8vL46U9/mnEUSP/+/ePWW2+NLbbYYqNqH3rooRnje+65p9E19913X1RXV9dbo6aCgoL43ve+lx5/9tlnMXny5Kx61HTIIYc0ugYAAAAAgOzkPdyurKyMc889N15//fX0tZ133jnuuOOO6NKly0bXHz58ePTt2zc9/stf/pLRq7aFCxfG7bffnh5vu+22cdxxxzXY47TTTou2bdumxzfccEMsX7683vmPPPJIxh6GDx8e/fv3b7AHAAAAAADZy2u4nUql4pe//GW88MIL6Ws77LBD3HXXXbH11ls3SY/CwsIYPXp0Rs8zzzwzXn311fXmzpo1K0aNGpVxrMhZZ50V7du3b7BHjx494kc/+lF6/M9//jNOOumk+Oijj9ab++ijj8aYMWPS4zZt2sS5556b02sCAAAAAKBhxfks/sknn8Rjjz223rWDDjoopzrbb799PPPMM/V+/KCDDorTTz89br311oj46uiQUaNGxV577RUDBw6MwsLCmDt3brzyyiuRSqXS64488sg4/vjjs9rD+eefHzNmzIhp06ZFRMS8efPi0EMPjWHDhsUuu+wSq1atitdffz3mzp2bse6yyy6Lfv365fR6AQAAAABoWF7D7ZpB8jo1z7rOVlVVVaNzRo8eHeXl5TFp0qT0tTfeeCPeeOONOucfdthhMW7cuKz30LZt25gwYUKce+65MXXq1IiIqKioiGeffbbO+cXFxTF69OhGjzwBAAAAACB3zfKGks2hsLAwxowZE3/84x9jzz33rHde375947rrrosbb7wx2rVrl1OPbt26xV133RUXXXRR7LjjjvXuY//994977703Tj311JzqAwAAAACQnbw+ub3DDjusd0xHvg0bNiyGDRsWH3zwQcycOTOWLFkSVVVVUVJSEn369NnoI0IKCwtj1KhRcfLJJ8c777wTCxcujCVLlkT79u2jpKQkBg8eHCUlJU30agAAAAAAqEtew+2W1KtXr+jVq1fe6hcUFMSgQYNi0KBBeesBAAAAAEDdNpljSQAAAAAA2HwItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEKW7pDQAAADS19g+cnJe65SPvyktdAAByJ9wGgFbg7POq81p/wnj/WAsAAIBNi590AQAAAABIHOE2AAAAAACJI9wGAAAAACBxhNsAAAAAACSOcBsAAAAAgMQRbgMAAAAAkDjCbQAAAAAAEke4DQAAAABA4gi3AQAAAABIHOE2AAAAAACJI9wGAAAAACBxhNsAAAAAACSOcBsAAAAAgMQRbgMAAAAAkDjCbQAAAAAAEke4DQAAAABA4gi3AQAAAABIHOE2AAAAAACJI9wGAAAAACBxhNsAAAAAACSOcBsAAAAAgMQRbgMAAAAAkDjCbQAAAAAAEke4DQAAAABA4gi3AQAAAABIHOE2AAAAAACJU9zSGwAAoGWdfV51XutPGO95CgBIqvYPnJyXuuUj78pLXWDz4icNAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAInjDSUBAGg23rwSAABoKv7vHwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEic4pbeAAC0ZmefV53X+hPG+3tmAAAA2BB+ogYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJE5xS28gH8rKymLGjBlRVlYWq1evjpKSkth5551j4MCBTdZj3rx5MX/+/CgrK4vCwsLo0aNHDBgwIHbaaacm6wEAAAAAQN2aLdz+8ssvY9asWTFjxoyYMWNGvPPOO/Hxxx+nP7799tvH//3f/21UjxkzZsRNN90Ur7zySlRXV6/38V69esWPf/zj+NGPfhQFBQUb1OPRRx+N2267LebOnVvnx4cMGRI/+9nP4lvf+tYG1QegcWeft/6f8U1pwnj/sAkAAABau7yH23/605/ioYcein/84x91Bs5N5fbbb4/f/OY3UVlZWe+cDz74IMaNGxfPP/983HjjjdGlS5es669ZsyYuuuiiePzxxxucN3369Dj99NPjlFNOiQsvvHCDQ3QAAAAAAOqX93D79ddfj3nz5uW1xwMPPBDXXXddxrXddtst9tprr+jQoUO899578dJLL6WD75dffjnOPffcuO2226K4OLtPwSWXXJIRbBcUFMQBBxwQ/fr1i4qKinjnnXdi+vTpERGRSqXijjvuiA4dOsQ555zTRK8SAAAAAIB1WuTM7Y4dO8buu+8eM2fOjFWrVm1UrTlz5sTYsWPT47Zt28avf/3r+P73v58x78MPP4wzzzwzHbS/+uqrMWHChDj//PMb7XHPPffEY489lh5vt912cfPNN8duu+2WMW9daP75559HRMTEiRNj6NCh8c1vfnODXx8AAAAAAOvL+6Gi7dq1i0GDBsWJJ54Y11xzTUyePDneeOON+O///u/YaqutNrr++PHjo6KiIj2+8sor1wu2IyJ23HHHuOuuu2LrrbdOX7vrrrti6dKlDdZfvXp1/P73v894PX/605/WC7YjIg444ICYOHFi+iiSVCoVv/nNb3J+TQAAAAAANCzv4faNN94YDz74YPzqV7+Ko48+Ovr06ROFhU3Tdvbs2fH888+nx/vss0+MGDGi3vndunWL0aNHp8erV6+OO+64o8EeDzzwQHz66afp8WmnnRY777xzvfP33XffOPLII9PjmTNnZuwRAAAAAICNl/dwO5+eeuqpjPG///u/N7rm+9//fnTu3Dk9fvrppxuc/+STT6Z/XVRUFD/84Q8b7VF7H7X3CQAAAADAxkl0uP1///d/6V+3adMmhg8f3uiadu3axbe//e30+OOPP47Zs2fXOXfZsmXx9ttvp8dDhgyJkpKSRnvsueee0aNHj/T4hRdeiKqqqkbXAQAAAACQncSG25999ln6zSEjIgYMGBDt2rXLau2ee+6ZMX799dfrnPfmm29GdXV1ejxkyJCs91ezx4oVK2L+/PlZrwUAAAAAoGHFLb2BDfXee+9ljOt6g8f67L777g3Wqu/6gAEDcupR8ziSBQsWRP/+/bNeDwAAm7L2D5ycl7rlI+/KS10AAFqfxD65vWDBgoxxz549s1673XbbNVirvuu11zVFDwAAAAAAcpfYcLusrCxjnM1Z2Otsu+22UVRUVG+t+q7XPEe7MbXnlpaWZr0WAAAAAICGJfZYki+//DJj3KlTp6zXFhYWRocOHeKLL76IiIhVq1Zl1WOLLbbIukftufX1aExBQcEGrcuXmvtpbXuDJHNvtS7N+TVorl6b4mvKplfteyuVSuWlT1PaFHu1xGs669z8vpn3724qanzSJqwpvm/l67fFuv3ku36+euS7fs0e6jdcvzl6NFR/Y3r7GmTfQ/2G6zdXj3zysxbkR2u5txIbbq9evTpj3LZt25zWt2vXLh1u1w6x6+uR7RtW1jV3Q8Ptrl27btC65tClS5eW3gJsktxbjSsuXpnX+l27/utr0Fy9NsXX1Jy9sulT819tbWifbHttjNb6+WuKPs3Zqzlf0+ZuQ79vVRbn50eRdf//nO/6+eqR7/o1e6jfcP3m6FFf/eKN7OtrkH0P9Ruu31w9mouftSA/WvLeSmy4XV5enjHONdyuOX/NmjVN3qP23Nq1AADYNIw6Nb9B+p23+0EcAADqkthwu/aT0RUVFTmtX7t2bb21GuqRbcBds35DPRqzYsWKDVqXLwUFBem/jVm5cuUG//NuIJN7KzeVlfk9bqDmn73N1WtTfE3N2au+PgUFBekntquqqjb43tpcP39N3ac5e22Kr6k1aYrvW+0rK5t6WxER8cX/+3zlu36+euS7fs0e6jdcvzl61K6/7ontyo3s62uQfQ/1G67fXD3yyc9akB8bcm/l419sJDbc7tixY8a4vqev61Nzfu1a9V0vLy/POtyuvZ/6ejSmNf+hm0qlWvX+IKncWy2vOT//zdVrU3xN2fSq+fGN2Vdrek1J7OU1JafXhtjQ71v5elnr9pLv+vnqke/6NXuo33D95uhRs37t40o3prevQfY91G+4fnP1aC5+1oL8aMl7q7BFujaB2mFxfedm16W6ujrjmJBsw+1czs2uvZ8NDbcBAAAAAFhfYsPtkpKSjHFpaWnWa5cuXZrxz7x69OiRVY/Fixdn3aP2furrAQAAAABA7hIbbu+yyy4Z408++STrtbVD6p133jmrHrmE27Xn1q4FAAAAAMCGS2y43bt374zx7Nmzs147c+bMBmvVd33WrFlN3gMAAAAAgNwlNtzu0qVL9OnTJz2eNWtW1m8qOX369IzxPvvsU+e8oUOHRmHhvz5Ftdc15K233kr/umvXrrHrrrtmvRYAAAAAgIYlNtyOiDj44IPTv66oqIjnnnuu0TVr1qyJF198MT3u2bNnDBgwoM65W2+9dQwePDg9nj59epSVlTXaY/r06Rlnbg8bNiyKi4sbXQcAAAAAQHYSHW4feuihGeN77rmn0TWPPfZYfPbZZ+nxIYccknWPqqqquP/++xvtce+99za4TwAAAAAANk6iw+0BAwbEsGHD0uPXX389HnnkkXrnL1u2LH7zm9+kx+3bt4//+I//aLDHyJEjY+utt06Pb7vttli4cGG986dOnRqPPvpoxh4POuigBnsAAAAAAJCbRIfbERHnn39+xpEfl156aUyePHm9eR9++GGcfPLJ8c9//jN97aSTToru3bs3WL9jx45x5plnpsdr1qyJU045pc43sHz55ZfjzDPPjFQqlbG/goKCnF4TAAAAAAANy/tB0B9//HF897vfrfNjVVVVGfPqO/v6zjvvjH333bfOj+22224xZsyYuPzyyyMiYu3atXHBBRfEbbfdFnvvvXe0b98+3nvvvXjppZeisrIyvW7fffeNc845J6vX8KMf/SjefPPNePzxxyMiYvHixXH00UfHAQccEP369YvKysqYMWPGem84+dOf/jQOPPDArHoAAAAAAJC9vIfbqVQqI8RuSH3zaj4JXZcTTjghPv/887jpppvSAfbs2bPrfLo6IuIb3/hG3HTTTdGmTZus9hURcfXVV0dVVVU89dRT6T1NmTIlpkyZst7cgoKCOOmkk+K8887Luj4AAAAAANlL/LEk6/zkJz+Je+65J/bff/8oLKz7Ze24445x8cUXx5133hldu3bNqX67du3ipptuimuvvTb69u1b77w999wz/vjHP8bFF1/sOBIAAAAAgDzJ+5PbO+ywQ8ydOzffbSIiYvDgwfGnP/0pysrK4u23346ysrIoLy+P7t27x8477xyDBg3a6B4jRoyIESNGxNy5c2P+/PlRVlYWRUVF0b1799h9992jV69eTfBKAAAAAABoSN7D7ZZQUlIS3/ve9/Lao1+/ftGvX7+89gAAAAAAoG6bzLEkAAAAAABsPoTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEKW7pDQCw6Tj7vOq81p8w3t/JAgAAAF+REgAAAAAAkDjCbQAAAAAAEke4DQAAAABA4gi3AQAAAABIHOE2AAAAAACJI9wGAAAAACBxhNsAAAAAACSOcBsAAAAAgMQRbgMAAAAAkDjCbQAAAAAAEke4DQAAAABA4gi3AQAAAABInOKW3gAAAAAAm6f2D5ycl7rlI+/KS12gdfHkNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABKnuKU3AAAAtD7tHzi53o8VFERUFn/1o0T7yspIpbKvWz7yro3dGgAARIQntwEAAAAASCDhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAOD/b+/Ow6Sq7vzxf0qgGwWlWWyMAgFFHzDjhhpFzWDQ+GhQA/FR4uMzsUkAUdxGDJoMrbjEBYeJY6sxqHGJoxEnoEZxjAtqJOLGMCr6E1ABRdlEkK3Zun9/8LWkmoauhqoubvfr9Ved2/ec+ym6i7r1rnvPAUgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAInTvNAFAAAA2bno0qq8jl9xq2tfAABIDuE2QCMnCAEAAAAaI4kEAAAAAACJ48ptAAAAABqlluN/Hhuab4q/Wm7YENXVuRm38qwHcjMQsENcuQ0AAAAAQOIItwEAAAAASBzhNgAAAAAAiWPObQAASKCRpWV5GPXBPIwJAAD54cptAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJE7zQhcA0BRddGnVFtuaN18eEREbNmzc4fErbvXdJQAAANC4CbcBAAAAYDu0HH9uXsatPOuBvIwLjY1L+wAAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABJHuA0AAAAAQOIItwEAAAAASBzhNgAAAAAAiSPcBgAAAAAgcYTbAAAAAAAkTvNCFwAAAOxcLrq0KkaWVm9zn1RqQ0REVFdve7+axlxaFRW3usYGAIAd56wSAAAAAIDEEW4DAAAAAJA4piUBAIAcG1lalrOxWo5Pbda6L2fjAgBA0rlyGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOM0LXQAAAAAAULuW48/N+ZiVZz2Q8zGhEFy5DQAAAABA4gi3AQAAAABIHNOSAAAABTNrdnVOxxtzaVVERIws3TTu/t1TOR0fAICdhyu3AQAAAABIHOE2AAAAAACJI9wGAAAAACBxzLkNsJmL/t88nflScavvFAEAAAByQcoCAAAAAEDiCLcBAAAAAEgc05IAANDkjCwt26H+LcenNhurOv14zKL7d2hcAAAge67cBgAAAAAgcYTbAAAAAAAkjnAbAAAAAIDEEW4DAAAAAJA4wm0AAAAAABKneaELAKjLRZdW5XX8ilt9zwcAAACQNBIdAAAAAAASx5XbO2DZsmUxbdq0WLBgQaxcuTJKS0ujU6dO0atXr9hlF98bAAAAAADki3B7O8yZMyfGjh0bkydPjvXr12/x89LS0hg4cGAMHTo0ioqKClAhAECyjSwt265+Lcen/l//6lp/PmbR/dtZEY3BrNm1/13Ux5jNpkur+Xe2f/fUDo8PAED2XF5cT08++WQMGDAg/va3v9UabEdELFq0KCoqKuJnP/tZzJ8/v4ErBAAAAABo/Fy5XQ+vvPJKXHnllbFx48b0tq5du8ZRRx0VJSUlMW/evJg8eXJUVlZGRMSMGTNi2LBh8cgjj0Tr1q0LVTYAAAAAQKMj3M7S4sWL47LLLksH26lUKq644oo499xzM+bXXrp0aVxyySXxxhtvRETEzJkz4+qrr46xY8cWpG4AAAAAgMZIuJ2lu+66K1asWJFuX3TRRTFo0KAt9mvXrl3cc889MWDAgPjoo48iIuLpp5+OIUOGRI8ePRqsXgAAAABo7FqOPzcv41ae9UBexiW3hNtZ+PLLL2P8+PHpdpcuXWLo0KFb3b+4uDjKy8ujrKwsIiKqq6vjzjvvjNtuuy3fpQIAAABA1oTDJJkFJbPwwgsvxLp169Lts846K1q0aLHNPr17945u3bql2y+//HKsWbMmbzUCAAAAADQlrtzOwosvvpjRPvnkk7Pqd/LJJ8fvf//7iIiorKyMKVOmxIknnpjz+qAQLrq0Kq/jV9zquzeAndnI0rKs9205PrVZv+qt7jdm0f07UBEAADsjV4aTT9KjLLz11lvpxx06dIjOnTtn1e+www7LaL/55ps5rQsAAAAAoKkSbtdh0aJFGQtJ9uzZM+u+Bx54YEb7mwUmAQAAAADYMcLtOnz88ccZ7b333jvrvh06dMiYm7vmWAAAAAAAbB9zbtdh4cKFGe2OHTtm3TeVSkXHjh3js88+q3Usmg7zUwMAAAAkUz7mDTdneG4It+uwatWqjHarVq3q1X/z/Tds2BDr1q2LoqKirPunUqm6d2pAm9ezs9XWlDXG30VDPqed4Vg1X1vV1VtfcG1HjpMPjfFYnlPjOVauXls703NK4rEa8m2qoY7VGJ/TpmNle7BUjcf1e22lUim/q62Osfn/Wzs+3raOYfxtj98Qx9jW+DtybL+D7I9h/G2P3xDHaIjnkLk9t+Mn9XfQmH7HjeF3kEQ7S0Yo3K7DmjVrMtrFxcX16l9z/1WrVtUr3C4pKanX8RpSmzZt8jJu2S+X52Xcb9x/77d1N9SxmjfP73FKShr3c2qMx9rWcZo1a5az49R1rFzY2f79cnmchjxWY3xODXmsbI6zI68t/35bqs8JbPPm355yplIbstxv+06Qvxlja8f59uc7dgK+teeUq/G3dqxc/Bttyzfnns2bL896/E271e/voaSkTWyo43e1vWr+DrL9+6vv+Jsfo+bPPvj/tv84Y0d8O+aI9rXv07PHtzVsz7G+OcbWxt/asbL1zd/Rhubb93GzrudUn/prU9dz2vwz2PY+h7rU9W/UfAePu6O/g51l/IY4hvG3PX5DHKMhx9/R11Zd4+dSvn8HjfV3nI/x83WMnTnzq698ZYTZSFXv6OWBjdwdd9wRt912W7p9ww03xBlnnJF1/3POOSfeeuutdPvll1+OvfbaK6c1AgAAAAA0NSbqrUPNK6/Xr19fr/7r1q3LaNfnqm0AAAAAAGon3K7DbrvtltGurKysV/+1a9dmtOs7ZzcAAAAAAFsSbtehZri9evXqevXffEHK5s2b13vObgAAAAAAtiTcrkPHjh0z2gsWLMi6b3V1dSxcuHCrYwEAAAAAsH2E23XYd999M9qff/551n2XLFmSMUd3t27dclYXAAAAAEBTJtyuQ8eOHWP33XdPtz/44IOs+77//vsZ7f322y9ndQEAAAAANGXC7Swcfvjh6cdLliyJTz/9NKt+06ZNy2gfeeSROa0LAAAAAKCpEm5noW/fvhntZ555Jqt+zz77bPpxcXFxHHvssTmtCwAAAACgqRJuZ+GEE06IFi1apNuPPfZYxlzatXnttdfik08+Sbf79OkTu+22W95qBAAAAABoSpoXuoAk6NChQ5x55pnx8MMPR0TEvHnzYty4cTF8+PBa91+7dm1cf/316XYqlYrzzz+/QWrd2VVVVcWMGTNi1qxZsWTJkti4cWO0atUq9t5779h///3ju9/9bqFLBKCJqq6ujnnz5sWsWbNiwYIFsXLlyiguLo6SkpI44IADokePHtGsWbNClwkFt2zZspg2bVr6dVJaWhqdOnWKXr16xS67uHYG6mvZsmUxc+bMmDt3bixbtiyqq6ujTZs2sffee8ehhx6asQYUAOxMvvjii3j33Xfj888/j9WrV0dxcXF06NAhunXrFj169IiioqK81yDcztKwYcPiiSeeiFWrVkVEREVFRbRq1Sp+/vOfZ5zEL126NC655JKYPXt2etuPf/zjOPDAAxu85p3J0qVL4+67746JEyfGV199tdX92rZtG8cdd1yMGjUqSkpKGq5AaCRWrlwZ/fr1iwULFmRsf/DBB+Ooo44qUFWw81qxYkU8//zz8dJLL8Xrr7++zfeo1q1bx4ABA6KsrCw6derUgFXCzmHOnDkxduzYmDx5cq13MZaWlsbAgQNj6NChDfJBBpKqqqoq3nrrrXjuuedi6tSpMXPmzK3um0qlonfv3lFWVhZ9+vRpwCqh8br++uvjT3/6U8a2AQMGxE033VSgiiBZqqqq4sknn4wHH3wwZsyYsdX9WrRoEYcddlgMHTo0fvCDH+StnlR1dXV13kZvZF566aU4//zzo6qqKr2ta9eucfTRR0dJSUnMnTs3Jk+eHJWVlemfd+/ePR599NFo3bp1IUreKUyaNCmuuuqqWLFiRb367LfffnmsChqn0aNHxyOPPLLFduE2bGnq1KkxePDgOqcaq2m33XaLUaNGxRlnnJGnymDn8+STT8bVV18dq1evrnPf733ve1FRURH77LNPA1QGyXPSSSfF3Llz692vX79+ce211zbpz5awo6ZPnx5nn312Rq4TIdyGbH322WcxYsSImD59etZ9hgwZEpdffnneanLldj0cf/zxceONN8bo0aNjzZo1EbHpCpY5c+bUun/Pnj3j9ttvb9InH/fee2+MGTMmY9vuu+8evXv3ju985zvRqlWr+Prrr2PmzJnx3nvvZfWBCajd22+/HX/+858LXQYkxsqVK7cItouKiuKQQw6JfffdN9q1axfr1q2LWbNmxeuvvx5r166NiIjVq1fHb37zm6isrIxzzjmnEKVDg3rllVfiyiuvjI0bN6a3de3aNY466qgoKSmJefPmZVzgMWPGjBg2bFg88sgjTfo8GLZm6dKlW2zr2rVrHHzwwdGhQ4coLi6OBQsWxGuvvZZxN97TTz8dixcvjnvuuSeKi4sbsmRoFNavXx/l5eVbBNtAdmbNmhWDBg2KxYsXp7ftsssuceihh8b+++8f7du3j8rKypg/f36888478cUXXzRIXcLteurfv38cfPDBMXbs2Hj55Zdrvdprzz33jLPOOiuGDRvWpG/JfOqppzKC7T322CNGjBgRP/3pT2v9d1m7dm38/e9/j4cffjhSqVRDlgqJt27duigvL49vbsbZc889M95wgK375pbvgQMHxg9/+MNaA4PFixfHddddF88++2x62/XXXx+HH3549OjRoyHLhQa1ePHiuOyyy9LBdiqViiuuuCLOPffcWqfme+ONNyIiYubMmXH11VfH2LFjC1I3JME+++wTZ555ZgwYMCD22muvLX6+cePGGD9+fNx4443pL1jfeOONuPXWW+OKK65o6HIh8caNG5eeBsjnJaifpUuXxuDBgzNeN6effnpcfvnl0bFjx1r7vP/++zFx4sS8X+xgWpId8NVXX6UX01m1alV06NAhOnfuHL169WryC059+eWXccopp8Ty5csjYtOinA899FB069atwJVB41RRURG33357RET88z//c7Rv3z4mTpyY/rlpSWBLzz//fDz66KMxYsSIrALq6urquPzyy+Opp55Kb+vTp0+MGzcun2VCQV133XXx0EMPpdsXX3zxNhdVHzBgQHz00UcRsSkIf/zxx30BBDWcfvrpce6550b//v2z+tz48ssvx7Bhw9JXm7Zo0SJeeOGFrYYJwJY+/vjj+MlPfhLr1q2LXXfdNa666qr49a9/nf65aUlg20aMGJHxOeg3v/lNnHvuuQWs6FuWM98Bbdu2jRNOOCHOOeecGDp0aPz0pz+NI488sskH2xERN954YzrYTqVScdtttwm2IU9mz54df/jDHyIiomXLlnHVVVcVuCJIhuOPPz7uvvvurIO3VCoV5eXl0apVq/S2f/zjH7Fy5cp8lQgF9eWXX8b48ePT7S5dusTQoUO3un9xcXGUl5en29XV1XHnnXfmtUZIogkTJsQZZ5yR9efGPn36RL9+/dLt9evXxwsvvJCv8qDRqa6ujvLy8li3bl1ERFxwwQXWhYB6mDJlSkawPXDgwJ0m2I4QbpMHn3/+eTz99NPpdr9+/eLwww8vYEXQeFVVVcWoUaPSUyQNHz48OnfuXOCqIBmaN6//7GwlJSVx3HHHpdvr16+P999/P5dlwU7jhRdeSAcBERFnnXVWtGjRYpt9evfunXFBw8svv5xeqwbYZHvefzYPtyMi3n333VyVA43en//853jrrbciIuKAAw6IQYMGFbgiSJa77747/bh169Zx6aWXFq6YWgi3ybkJEyZkLNAwcODAAlYDjdsjjzwS//u//xsRTtSgoXTp0iWjvWTJkgJVAvn14osvZrRPPvnkrPptvl9lZWVMmTIlp3VBU+S9B7bPwoUL0+s/pFKpuOaaa+r8ohb41qeffhpTp05Nt0866aRo165dASvaknCbnPvrX/+aftyuXbs44ogjClgNNF4LFizIOFEbPXq0EzVoAKtWrcpoe93RWH1zlVtEpNeWycZhhx2W0X7zzTdzWhc0RTXfe7bn6m9oiq677rpYsWJFRGy6A6lXr14FrgiSZdKkSbH5co0nnXRSAaupnXCbnFq+fHnMmTMn3T7wwANjl138mUE+jB49Ov1B58wzzzT9DzSQDz/8MKNtQS8ao0WLFqXDgIiInj17Zt33wAMPzGh/s8AksP1qvvfstddeBaoEkuNvf/tbPPfccxER0b59+xgxYkSBK4LkmT59ekb7e9/7XmEK2QZf95JT7733Xka7e/fu6cdvv/12TJw4MaZPnx5ffPFFNGvWLNq2bRsHHXRQ9OnTJ0455RRXIECWJk2aFJMnT46ITSdql19+eYErgqbh008/jWnTpqXbe+yxxxZBHjQGH3/8cUZ77733zrpvhw4dokWLFun1IGqOBdTfk08+mdE++uijC1QJJMOKFSvi2muvTbevvPLKaNOmTQErgmTaPOdr06ZNlJaWRsSmCyEef/zxePHFF+Ozzz6LVatWRdu2baNz585x7LHHxumnn95gX8RKEsmp2bNnZ7Tbt28fy5cvj2uuuSZjkclvfHOl91//+teoqKiI0aNHxzHHHNNQ5UIiLV++PH7729+m21dccYUTNWggd955Z8ZteT/60Y98MUujtHDhwox2fe5QSKVS0bFjx/jss89qHQuonzfeeCPeeOONdHv33XfPWNwY2NKYMWNi8eLFERFxzDHHxOmnn17giiB5VqxYEYsWLUq327dvHxERjz32WNxwww2xevXqjP1Xr14d8+fPj6lTp8btt98egwYNiosvvjiaNWuW1zrNF0FOLV++PKOdSqVi0KBBtQbbNc2dOzeGDBkSEydOzFd50CjcfPPN6UWEevfuHT/5yU8KXBE0DVOmTIkJEyak2y1atIjzzjuvgBVB/tSc37dVq1b16r/5/hs2bIh169blpC5oalavXh3l5eUZ2wYNGlTv1yQ0JW+++WY89thjERFRXFwco0ePLmxBkFDLli3LaLdq1SruuuuuGDVq1BbBdk1r166Nu+66Ky644IK8nwcKt8mpzedmjIgYN25czJgxIyIiunbtGjfddFO88sor8e6778bf//73GDt2bOy///7p/Tds2BDl5eXxzjvvNGjdkBRTp06Nv/zlLxERUVRU5EQNGsjChQtj5MiRGdvOO++8+O53v1ugiiC/1qxZk9EuLi6uV/+a+9cMy4HsjB49OmNNo3333TcGDx5cuIJgJ7du3booLy9P32nnfA2238qVKzPan3zySdx6660RsSmPGDJkSDzxxBMxffr0eOutt+Lhhx+O/v37RyqVSvd56aWX4pZbbslrncJtcqrmNzdff/11RGyaE+7xxx+PAQMGRMeOHaOoqChKS0vj1FNPjQkTJsQPf/jDdJ/169fHVVdd1aB1QxKsXbs247Vx3nnnRdeuXQtXEDQRlZWVceGFF6bvmIiIOPTQQ2PYsGEFrAryq7KyMqNdVFRUr/4191+7du0O1wRNzX333RdPPPFEul1UVBS33HJLvb9sgqbkjjvuiE8++SQiIrp16xZDhgwpcEWQXDUvTli5cmVUV1dH69at46GHHorLL788evToEbvuumvsvvvucfjhh8fNN98ct9xyS+yyy7eR84MPPhjvv/9+3uo0SWQj1bdv35g/f37exh85cmT88pe/3GJ7bR982rZtG7/73e9i1113rXWsoqKi+Pd///c49dRT44svvoiIiA8++CCmTJkSxx57bG4Lhx1UqNdWRERFRUXMnTs3IjadqA0dOjRvdUBDKuTrqi4bN26Myy67LOOOou985ztx2223RYsWLXJVIux0aoZn3ywOma2at5/WNxyHpm7SpEkxZsyYjG3XXntt/NM//VOBKoKd34cffhj33ntvun3NNdd4/4EdsLXXz6hRo+KQQw7Zar/TTjst3n333XjggQfS2+69994YO3ZszmuMcOU2Obbbbrttse3ss8+Odu3abbNf69ato6ysLGPb5MmTc1kaJNoHH3wQ9913X7rtRA0aRnl5ebzwwgvpdklJSdxzzz31WlwPkqjmOV3NK7nrUvNKbfMDQ/b+8Y9/xMiRI6Oqqiq9bcSIETFgwIACVgU7t6qqqhg1alT6y9gBAwbEUUcdVeCqINlqO3/bZ599slr3a+jQoRkXA73yyisZ72u5JNwmp2r7w998ypFt6du3b0Z72rRpOakJkm7jxo0xatSo2LBhQ0Q4UYOGcvPNN6fnuI/YFPaNGzcuunfvXsCqoGHUDLfrWjSops1vY23evLlpFCBL//d//xfDhw/PuFvil7/8pTv2oA5/+tOf0nfalZSUbLFWClB/tWV8ffr0yZhyZGs6dOgQBx98cLr99ddfx+zZs3Na3zdMS9JI/ed//mde5zbs3Llzrdv32muvLbYdcMABWY3ZpUuXaNmyZfrKoEWLFm1/gZAnhXhtPfXUU/Hee+9FhBM1GqdCvWdty+9///v44x//mG4XFRXFHXfcsc3b76AxqXl3woIFC7LuW11dHQsXLtzqWEDtZs6cGUOHDs34MunMM8907gd1qKysTC9yF7FpSrq67h4H6ta+ffto0aJFxheu+++/f9b9DzjggHj77bfT7YULF2adEdaHcLuROuiggwpy3JpXsxUVFUXLli2z7r/HHnukw+1ly5blsjTIiUK8tr766qv04+XLl8dxxx1XZ5+at/uUlZVlrFh8//33x/e///3cFQk7oFDvWVvzX//1XxkfkJo1axa/+93v4phjjilcUdDA9t1334z2559/nnXfJUuWZHwI6tatW87qgsZq3rx58Ytf/CLjM9App5wS1157beGKgoRYt25dxpdC5eXlUV5evs0+1dXVGe3HH388nnzyyXS7f//+ccMNN+S2UEiYFi1aRJcuXeKjjz5Kb2vTpk3W/Wvuu3z58pzVtjnhNjm13377RSqVSr9RbNiwIaqrqzNCtW3ZfPEht6/Clqqrq2Pjxo317lcz7K55Mgds8vjjj8d1112XbqdSqbjxxhvjxBNPLGBV0PA6duwYu+++e6xYsSIiNq39kK33338/o73ffvvltDZobBYuXBhlZWWxePHi9LY+ffrELbfcktWt30Cm7fm8VPNzVr7mBoak6d69e0a4XXPR8G2puW++cj7vlORUq1at4sADD0y3q6qqsp5eZM2aNfH111+n224jAqAhPf/88/Fv//ZvGV/+XH311VktmAKN0eGHH55+vGTJkvj000+z6ldz3ZQjjzwyp3VBY7J06dIoKyuL+fPnp7d9//vfj4qKioyFuACgEGre8b351HN1qTmtXdu2bXNSU02u3CbnfvSjH8WMGTPS7WnTpsUpp5xSZ7/p06dnfDvas2fPvNQHSVNWVhZlZWX16nPllVfGxIkT0+0HH3zQIpSwDa+99lr867/+a3rh1oiIX/3qV3H22WcXsCoorL59+8ZLL72Ubj/zzDNZLWr37LPPph8XFxfHsccem4/yIPFWrlwZgwcPjo8//ji97ZBDDom77rrLXaxQD3vssUd8+OGH9erz+uuvx89//vN0e8CAAXHTTTflujRIvBNPPDGuv/769AVANS9i2Jrq6uqYPn16ut2sWbPo0aNHPkp05Ta5d/LJJ2fcPvff//3fWfV77LHHMto+CAHQEN5555244IILMm6bGz58eAwePLiAVUHhnXDCCRlXjj722GMZc2nX5rXXXotPPvkk3e7Tp0/stttueasRkqqysjKGDRuWcVFQjx494u67745WrVoVsDIA+NZee+0VvXr1SrenTJmS1ULjr776asaaLQcffHC0bt06LzUKt8m5bt26xWmnnZZuv/rqq/HMM89ss8+rr74akyZNSrdLSkri1FNPzVuNABARMWvWrBgyZEjGIkRlZWVx8cUXF7Aq2Dl06NAhzjzzzHR73rx5MW7cuK3uv3bt2rj++uvT7VQqFeeff35ea4Qk2rBhQ1xyySXx5ptvprd169Yt/vjHP9ZroS4AaAgXXXRR+vGGDRti9OjR25yXftWqVfHb3/42Y9u//Mu/5K0+4TZ5cfHFF2dcpTNy5MiYMGFCrftOmjQpLrrooow5Ti+88EJXLACQV5999ln84he/iGXLlqW3DRw4MH79618XrijYyQwbNizjnKyioiLuv//+LT7QLF26NAYPHhyzZ89Ob/vxj3+csRYLsOk27SuvvDJjyp9OnTrFAw88EO3bty9cYQCwFb17947jjz8+3Z48eXKMGDEi43PUN+bNmxeDBg3KuJPvoIMOymq64u2Vqt48UYQcevHFF2P48OEZH366du0avXv3jnbt2sWyZcvi9ddfz/gQFBHRr1+/+I//+I+GLhcaFXNuQ91uv/32qKioyNjWrFmzeo9zwQUXxIUXXpirsmCn89JLL8X555+/xTnd0UcfHSUlJTF37tyYPHlyVFZWpn/evXv3ePTRR/N2+ykk1fz586Nv374Z23bZZZdIpVL1GmefffaJ5557LpelQZNizm2on2XLlsXPfvazjNC6VatW8YMf/CC6du0a69evj5kzZ8bUqVMzprFr165d/OUvf4m99947b7VZUJK86du3b4wZMyauvvrqWLVqVUREzJkzJ+bMmbPVPmeffXaMGjWqgSoEoCmr7fv9jRs35mQcaEyOP/74uPHGG2P06NGxZs2aiNj2OV3Pnj3j9ttvF2xDLWp7z9jWrd1bsz3vVwCwvUpKSuKee+6Jiy++OL1exKpVq+J//ud/ttpn3333jT/84Q95DbYjTEtCnp122mnxxBNPxKmnnhotW7asdZ9UKhVHHHFE3HfffTF69Oho3tx3LgAAO5P+/fvHhAkT4sQTT8xYZHJze+65ZwwfPjzGjx8fnTp1auAKAQDIp06dOsWjjz4al112Weyzzz5b3a+0tDR+9atfxcSJE6NLly55r8u0JDSYlStXxttvvx0LFiyIr776Klq3bh2lpaVxxBFHRLt27QpdHgAAWfjqq69i2rRpsWDBgli1alV06NAhOnfuHL169dquqX0AAEiW6urqePfdd+OTTz6JxYsXRyqVinbt2kXPnj2jR48eDVqLcBsAAAAAgMQxLQkAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHGE2wAAAAAAJI5wGwAAAACAxBFuAwAAAACQOMJtAAAAAAASR7gNAAAAAEDiCLcBAAAAAEgc4TYAAAAAAIkj3AYAAAAAIHH+fx7POR+VwCDBAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 491,
       "width": 731
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fmt: off\n",
    "post = idata.posterior\n",
    "plt.hist(\n",
    "    post.where(post.idx == 0).y.values.reshape(-1),\n",
    "    bins=30,\n",
    "    rwidth=0.9,\n",
    "    alpha=0.75,\n",
    "    label='idx = 0',\n",
    ")\n",
    "plt.hist(\n",
    "    post.where(post.idx == 1).y.values.reshape(-1),\n",
    "    bins=30,\n",
    "    rwidth=0.9,\n",
    "    alpha=0.75,\n",
    "    label='idx = 1'\n",
    ")\n",
    "# fmt: on\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fe000d6-9e6a-4ae7-9cae-3d0eed952410",
   "metadata": {},
   "source": [
    "One important thing to notice is that this discrete variable has a lower ESS, and particularly so for the tail. This means `idx` might not be estimated well particularly for the tails. If this is important, I recommend using the `lp_idx` instead, which is the log-probability of `idx` given sample values on each iteration. The benefits of working with `lp_idx` will explored further in the next example."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b458c9e-3b2d-4ba3-a657-5d7db1c046c5",
   "metadata": {},
   "source": [
    "## Coal mining model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8dd6e73-6d3b-4ee0-9bff-eb0a581399af",
   "metadata": {},
   "source": [
    "The same methods work for the {ref}`Coal mining <pymc:pymc_overview#case-study-2-coal-mining-disasters>` switchpoint model as well. The coal mining dataset records the number of coal mining disasters in the UK between 1851 and 1962. The time series dataset captures a time when mining safety regulations are being introduced, we try to estimate when this occurred using a discrete `switchpoint` variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9086c01b-5da7-4744-96ba-8d0b52e088c4",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/zv/upstream/miniconda3/envs/pymc-dev/lib/python3.11/site-packages/pymc/model/core.py:1288: RuntimeWarning: invalid value encountered in cast\n",
      "  data = convert_observed_data(data).astype(rv_var.dtype)\n",
      "/home/zv/upstream/miniconda3/envs/pymc-dev/lib/python3.11/site-packages/pymc/model/core.py:1302: ImputationWarning: Data in disasters contains missing values and will be automatically imputed from the sampling distribution.\n",
      "  warnings.warn(impute_message, ImputationWarning)\n"
     ]
    }
   ],
   "source": [
    "# fmt: off\n",
    "disaster_data = pd.Series(\n",
    "    [4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6,\n",
    "    3, 3, 5, 4, 5, 3, 1, 4, 4, 1, 5, 5, 3, 4, 2, 5,\n",
    "    2, 2, 3, 4, 2, 1, 3, np.nan, 2, 1, 1, 1, 1, 3, 0, 0,\n",
    "    1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1,\n",
    "    0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2,\n",
    "    3, 3, 1, np.nan, 2, 1, 1, 1, 1, 2, 4, 2, 0, 0, 1, 4,\n",
    "    0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1]\n",
    ")\n",
    "\n",
    "# fmt: on\n",
    "years = np.arange(1851, 1962)\n",
    "\n",
    "with pm.Model() as disaster_model:\n",
    "    switchpoint = pm.DiscreteUniform(\"switchpoint\", lower=years.min(), upper=years.max())\n",
    "    early_rate = pm.Exponential(\"early_rate\", 1.0)\n",
    "    late_rate = pm.Exponential(\"late_rate\", 1.0)\n",
    "    rate = pm.math.switch(switchpoint >= years, early_rate, late_rate)\n",
    "    disasters = pm.Poisson(\"disasters\", rate, observed=disaster_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20d95bc6-ac70-427f-9bf4-c5b42cdf09fe",
   "metadata": {},
   "source": [
    "We will sample the model both before and after we marginalize out the `switchpoint` variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "77b71716-a585-49b8-b31a-43e54211a385",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "CompoundStep\n",
      ">CompoundStep\n",
      ">>Metropolis: [switchpoint]\n",
      ">>Metropolis: [disasters_unobserved]\n",
      ">NUTS: [early_rate, late_rate]\n",
      "/home/zv/upstream/miniconda3/envs/pymc-dev/lib/python3.11/multiprocessing/popen_fork.py:66: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.\n",
      "  self.pid = os.fork()\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "16985d7e91914eb992eeddab48900b48",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/zv/upstream/miniconda3/envs/pymc-dev/lib/python3.11/multiprocessing/popen_fork.py:66: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.\n",
      "  self.pid = os.fork()\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 13 seconds.\n",
      "We recommend running at least 4 chains for robust computation of convergence diagnostics\n",
      "The rhat statistic is larger than 1.01 for some parameters. This indicates problems during sampling. See https://arxiv.org/abs/1903.08008 for details\n",
      "The effective sample size per chain is smaller than 100 for some parameters.  A higher number is needed for reliable rhat and ess computation. See https://arxiv.org/abs/1903.08008 for details\n",
      "/home/zv/upstream/pymc-extras/pymc_extras/model/marginal/distributions.py:297: NonSeparableLogpWarning: There are multiple dependent variables in a FiniteDiscreteMarginalRV. Their joint logp terms will be assigned to the first value: [4 5 4 0 1 ... 0 0 1 0 1].\n",
      "  warn_non_separable_logp(values)\n",
      "/home/zv/upstream/pymc-extras/pymc_extras/model/marginal/distributions.py:297: NonSeparableLogpWarning: There are multiple dependent variables in a FiniteDiscreteMarginalRV. Their joint logp terms will be assigned to the first value: [4 5 4 0 1 ... 0 0 1 0 1].\n",
      "  warn_non_separable_logp(values)\n",
      "/home/zv/upstream/pymc-extras/pymc_extras/model/marginal/distributions.py:297: NonSeparableLogpWarning: There are multiple dependent variables in a FiniteDiscreteMarginalRV. Their joint logp terms will be assigned to the first value: [4 5 4 0 1 ... 0 0 1 0 1].\n",
      "  warn_non_separable_logp(values)\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "CompoundStep\n",
      ">NUTS: [late_rate, early_rate]\n",
      ">Metropolis: [disasters_unobserved]\n",
      "/home/zv/upstream/miniconda3/envs/pymc-dev/lib/python3.11/multiprocessing/popen_fork.py:66: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.\n",
      "  self.pid = os.fork()\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "40d4acddd307467991eb13f288dd45b4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/zv/upstream/miniconda3/envs/pymc-dev/lib/python3.11/multiprocessing/popen_fork.py:66: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.\n",
      "  self.pid = os.fork()\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 36 seconds.\n",
      "We recommend running at least 4 chains for robust computation of convergence diagnostics\n",
      "The effective sample size per chain is smaller than 100 for some parameters.  A higher number is needed for reliable rhat and ess computation. See https://arxiv.org/abs/1903.08008 for details\n"
     ]
    }
   ],
   "source": [
    "with disaster_model:\n",
    "    before_marg = pm.sample(chains=2, random_seed=rng)\n",
    "\n",
    "disaster_model_marginalized = pmx.marginalize(disaster_model, [\"switchpoint\"])\n",
    "\n",
    "with disaster_model_marginalized:\n",
    "    after_marg = pm.sample(chains=2, random_seed=rng)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "55b108e7-c49a-40f1-afd7-c3890587a917",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>early_rate</th>\n",
       "      <td>3.090</td>\n",
       "      <td>0.278</td>\n",
       "      <td>2.594</td>\n",
       "      <td>3.630</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1022.0</td>\n",
       "      <td>1049.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>late_rate</th>\n",
       "      <td>0.937</td>\n",
       "      <td>0.117</td>\n",
       "      <td>0.718</td>\n",
       "      <td>1.151</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1239.0</td>\n",
       "      <td>1443.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>switchpoint</th>\n",
       "      <td>1889.785</td>\n",
       "      <td>2.581</td>\n",
       "      <td>1885.000</td>\n",
       "      <td>1894.000</td>\n",
       "      <td>0.204</td>\n",
       "      <td>0.145</td>\n",
       "      <td>164.0</td>\n",
       "      <td>275.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 mean     sd    hdi_3%   hdi_97%  mcse_mean  mcse_sd  \\\n",
       "early_rate      3.090  0.278     2.594     3.630      0.009    0.006   \n",
       "late_rate       0.937  0.117     0.718     1.151      0.003    0.002   \n",
       "switchpoint  1889.785  2.581  1885.000  1894.000      0.204    0.145   \n",
       "\n",
       "             ess_bulk  ess_tail  r_hat  \n",
       "early_rate     1022.0    1049.0    1.0  \n",
       "late_rate      1239.0    1443.0    1.0  \n",
       "switchpoint     164.0     275.0    1.0  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(before_marg, var_names=[\"~disasters\"], filter_vars=\"like\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "fb62001a-3b80-4923-96e2-064d411ff523",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>early_rate</th>\n",
       "      <td>3.078</td>\n",
       "      <td>0.284</td>\n",
       "      <td>2.577</td>\n",
       "      <td>3.653</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.005</td>\n",
       "      <td>2036.0</td>\n",
       "      <td>1344.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>late_rate</th>\n",
       "      <td>0.929</td>\n",
       "      <td>0.115</td>\n",
       "      <td>0.714</td>\n",
       "      <td>1.146</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1303.0</td>\n",
       "      <td>1228.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "early_rate  3.078  0.284   2.577    3.653      0.006    0.005    2036.0   \n",
       "late_rate   0.929  0.115   0.714    1.146      0.003    0.002    1303.0   \n",
       "\n",
       "            ess_tail  r_hat  \n",
       "early_rate    1344.0    1.0  \n",
       "late_rate     1228.0    1.0  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(after_marg, var_names=[\"~disasters\"], filter_vars=\"like\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66532abc-38a6-4796-ab4d-9252159663fc",
   "metadata": {},
   "source": [
    "As before, the ESS improved massively"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e058dba7-9b6b-4002-8360-2fae6fe71306",
   "metadata": {},
   "source": [
    "Finally, let us recover the `switchpoint` variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "19459eaa-a781-4baf-8360-77dad3c15217",
   "metadata": {},
   "outputs": [],
   "source": [
    "after_marg = pmx.recover_marginals(disaster_model_marginalized, after_marg);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b306de49-12b1-44f1-90e7-2d2320567afb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>early_rate</th>\n",
       "      <td>3.078</td>\n",
       "      <td>0.284</td>\n",
       "      <td>2.577</td>\n",
       "      <td>3.653</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.005</td>\n",
       "      <td>2036.0</td>\n",
       "      <td>1344.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>late_rate</th>\n",
       "      <td>0.929</td>\n",
       "      <td>0.115</td>\n",
       "      <td>0.714</td>\n",
       "      <td>1.146</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1303.0</td>\n",
       "      <td>1228.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>switchpoint</th>\n",
       "      <td>1889.812</td>\n",
       "      <td>2.434</td>\n",
       "      <td>1885.000</td>\n",
       "      <td>1893.000</td>\n",
       "      <td>0.108</td>\n",
       "      <td>0.077</td>\n",
       "      <td>494.0</td>\n",
       "      <td>1302.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 mean     sd    hdi_3%   hdi_97%  mcse_mean  mcse_sd  \\\n",
       "early_rate      3.078  0.284     2.577     3.653      0.006    0.005   \n",
       "late_rate       0.929  0.115     0.714     1.146      0.003    0.002   \n",
       "switchpoint  1889.812  2.434  1885.000  1893.000      0.108    0.077   \n",
       "\n",
       "             ess_bulk  ess_tail  r_hat  \n",
       "early_rate     2036.0    1344.0    1.0  \n",
       "late_rate      1303.0    1228.0    1.0  \n",
       "switchpoint     494.0    1302.0    1.0  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(after_marg, var_names=[\"~disasters\", \"~lp\"], filter_vars=\"like\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fc7e742-67b4-4152-8ec5-4bd8c4f7c640",
   "metadata": {},
   "source": [
    "While `recover_marginals` is able to sample the discrete variables that were marginalized out. The probabilities associated with each draw often offer a cleaner estimate of the discrete variable. Particularly for lower probability values. This is best illustrated by comparing the histogram of the sampled values with the plot of the log-probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "798d9cbf-5eda-4625-8c9b-84995318bb15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 491,
       "width": 731
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "post = after_marg.posterior.switchpoint.values.reshape(-1)\n",
    "bins = np.arange(post.min(), post.max())\n",
    "plt.hist(post, bins, rwidth=0.9);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "3338722f-a0c6-4277-b458-8ff8dcb59434",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 491,
       "width": 731
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lp_switchpoint = after_marg.posterior.lp_switchpoint.mean(dim=[\"chain\", \"draw\"])\n",
    "x_max = years[lp_switchpoint.argmax()]\n",
    "\n",
    "plt.scatter(years, lp_switchpoint)\n",
    "plt.axvline(x=x_max, c=\"orange\")\n",
    "plt.xlabel(r\"$\\mathrm{year}$\")\n",
    "plt.ylabel(r\"$\\log p(\\mathrm{switchpoint}=\\mathrm{year})$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad3cc13c-f2e7-4789-aac2-3e3e9dfe58cc",
   "metadata": {},
   "source": [
    "By plotting a histogram of sampled values instead of working with the log-probabilities directly, we are left with noisier and more incomplete exploration of the underlying discrete distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c675ae7f-2c91-4ead-90c2-ab0bd78a02ed",
   "metadata": {},
   "source": [
    "## Authors\n",
    "* Authored by [Rob Zinkov](https://zinkov.com) in January, 2024"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7073a737-5f30-44bc-ac6c-bc85b8955391",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    ":::{bibliography}\n",
    ":filter: docname in docnames \n",
    ":::\n",
    "\n",
    "* [STAN manual section on marginalization](https://mc-stan.org/docs/stan-users-guide/latent-discrete.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f14213a-651e-4271-9a2d-71954e84605c",
   "metadata": {},
   "source": [
    "## Watermark"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "57fd6d30-cfd8-4fc4-85df-1f4361ed7015",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Sat Jan 04 2025\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.11.6\n",
      "IPython version      : 8.22.2\n",
      "\n",
      "pytensor: 2.26.4\n",
      "xarray  : 2024.3.0\n",
      "\n",
      "arviz      : 0.18.0\n",
      "numpy      : 1.26.4\n",
      "pymc_extras: 0.2.1\n",
      "matplotlib : 3.8.4\n",
      "pymc       : 5.19.1\n",
      "pytensor   : 2.26.4\n",
      "pandas     : 2.2.2\n",
      "\n",
      "Watermark: 2.4.3\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w -p pytensor,xarray"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47987baa-2f8d-4efd-9c43-12f76e2659e2",
   "metadata": {},
   "source": [
    ":::{include} ../page_footer.md\n",
    ":::"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.6"
  },
  "myst": {
   "substitutions": {
    "extra_dependencies": "pymc-experimental"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}