{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "861823e7",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "(Normalizing_Flows)=\n",
    "\n",
    "# Normalizing Flows in PyTensor\n",
    "\n",
    ":::{post} August 17, 2025 \n",
    ":tags: Graph rewrites \n",
    ":category: avanced, explanation \n",
    ":author: Jesse Grabowski, Ricardo Vieira\n",
    ":::\n",
    "\n",
    "\n",
    "A hip new algorithm for doing machine learning on distributions is called *normalizing flows*. \n",
    "\n",
    "The idea begins with the change of variables formula. We begin with a random variable $X \\sim N(0, 1)$. Suppose we know the PDF for $X$ (because we do!). What if we instead wanted the PDF for $ Y = \\exp(X)$. Do we know that? \n",
    "\n",
    "The answer is yes! We know it because of the *change of variable* formula, which states:\n",
    "\n",
    "$$\n",
    "g(y) = (f \\circ G^{-1})(y) \\left | \\frac{\\partial}{\\partial x} G^{-1}(y) \\right |\n",
    "$$\n",
    "\n",
    "Where:\n",
    "\n",
    "- $g(\\cdot)$ is the (unknown!) PDF of the variable $Y$\n",
    "- $f(\\cdot)$ if the (known!) PDF of the variable $X$\n",
    "- $G(\\cdot)$ is a function with nice properties.\n",
    "\n",
    "The \"nice properties\" require (in the most general case) that $G(x)$ is a $C^1$ diffeomorphism, which means that it is 1) continuous and differentiable almost everywhere; 2) it is bijective, and 3) its derivaties are also bijective. \n",
    "\n",
    "A simpler requirement is that $G(x)$ is continuous, bijective, and monotonic. That will get us 99% of the way there. Hey, $\\exp$ is continuous, bijective, and monotonic -- what a coincidence!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d61e7e32",
   "metadata": {},
   "source": [
    "## Prepare Notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "327c0f12",
   "metadata": {},
   "outputs": [],
   "source": [
    "from abc import ABC\n",
    "\n",
    "import arviz as az\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import preliz as pz\n",
    "import pymc as pm\n",
    "from scipy.optimize import minimize\n",
    "\n",
    "import pytensor\n",
    "import pytensor.tensor as pt\n",
    "from pytensor.graph.basic import explicit_graph_inputs\n",
    "from pytensor.graph.replace import vectorize_graph\n",
    "from pytensor.graph.rewriting import rewrite_graph\n",
    "from pytensor.tensor.basic import TensorVariable\n",
    "\n",
    "\n",
    "plt.style.use(\"seaborn-v0_8\")\n",
    "\n",
    "%config InlineBackend.figure_format = \"retina\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70d3acdd",
   "metadata": {},
   "source": [
    "## Simple Example: Change of Variables Formula"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f318527d",
   "metadata": {},
   "source": [
    "Let's visualize this result through a concrete example. We look at the transformation of a normal distribution to a lognormal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "99ba1913",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/wj/wjy2vm8d7_j9v43bv29zcgl80000gq/T/ipykernel_79672/3343765610.py:11: RuntimeWarning: invalid value encountered in log\n",
      "  return np.where(x > 0, np.log(x), 0)\n"
     ]
    },
    {
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      "text/plain": [
       "<Figure size 800x550 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 466,
       "width": 669
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = pz.Normal(0, 1)\n",
    "Y = pz.LogNormal(0, 1)\n",
    "\n",
    "x_grid = np.linspace(-3.1, 3.1, 100)\n",
    "\n",
    "f_values = X.pdf(x_grid)\n",
    "\n",
    "\n",
    "# This is just a convenient trick: setting the value to 0 if x <= 0\n",
    "def G_inv(x):\n",
    "    return np.where(x > 0, np.log(x), 0)\n",
    "\n",
    "\n",
    "def d_G_inv(x):\n",
    "    return np.where(x > 0, np.reciprocal(x), 0)\n",
    "\n",
    "\n",
    "g_values = (X.pdf(G_inv(x_grid))) * np.abs(d_G_inv(x_grid))\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x_grid, Y.pdf(x_grid), c=\"C0\", label=\"LogNormal PDF\")\n",
    "ax.plot(\n",
    "    x_grid, g_values, c=\"C1\", ls=\"--\", label=r\"$f(\\ln x) \\left | \\frac{1}{x} \\right |$\"\n",
    ")\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9ba9923",
   "metadata": {},
   "source": [
    "## Normalizing Flows Fundamentals\n",
    "\n",
    "In this section, we will explore the core concepts of normalizing flows. along this notebook, we will work one complete example: sampling from a log-normal distribution using normalizing flows.\n",
    "\n",
    "Before going into the actual example, let us understand the overall strategy."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a4a265c",
   "metadata": {},
   "source": [
    "The change of variables procedure above, is basically all we need to understand normalizing flows. The logic goes like this:\n",
    "\n",
    "1. Suppose we have some data $\\mathcal{D} \\sim D(\\cdot)$, where $D$ is totally unknown.\n",
    "2. We would like to sample from $D$, which seems hard since we don't know it.\n",
    "3. Instead of sampling from $D$, let's instead sample $F(\\cdot)$, where we get to choose $F$ to be as simple as possible. Say it's just $N(0, 1)$\n",
    "4. Then, we'll use a change of variables to make draws from $F$ _look like_ draws from $D$. \n",
    "5. We just need a function $G(x)$ that makes *samples* $x \\sim N(0, 1)$ look like our data.\n",
    "6. $G$ needs to have the nice properties we want: monotonic, bijective, and invertible. And, we'd  like it to have some parameters to learn!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc400f29",
   "metadata": {},
   "source": [
    "Let's define a simple base class to represent normalizing flows in PyTensor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "75a89714",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Flow(ABC):\n",
    "    __slots__ = (\"parameters\",)\n",
    "\n",
    "    def transform(self, x: TensorVariable) -> TensorVariable:\n",
    "        \"\"\"Apply function F to the distribution x, along with the jacobian correction\"\"\"\n",
    "        ...\n",
    "\n",
    "    def inverse_transform(self, x: TensorVariable) -> TensorVariable:\n",
    "        \"\"\"Apply inverse function F^{-1} to the distribtuion x\"\"\"\n",
    "        ..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a6e041f",
   "metadata": {},
   "source": [
    "We can now specify two concrete examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b4770d35",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Exp(Flow):\n",
    "    \"\"\"Exponential transformation\"\"\"\n",
    "\n",
    "    def transform(self, x: TensorVariable) -> TensorVariable:\n",
    "        return pt.exp(x)\n",
    "\n",
    "    def inverse_transform(self, x: TensorVariable) -> TensorVariable:\n",
    "        return pt.log(x)\n",
    "\n",
    "\n",
    "class Affine(Flow):\n",
    "    \"\"\"Affine transformation\"\"\"\n",
    "\n",
    "    __slots__ = (\"loc\", \"scale\", \"parameters\")\n",
    "\n",
    "    def __init__(self, loc: float = 0.0, scale: float = 1.0) -> None:\n",
    "        self.loc = pt.as_tensor_variable(loc)\n",
    "        self.scale = pt.as_tensor_variable(scale)\n",
    "\n",
    "    def transform(self, x: TensorVariable) -> TensorVariable:\n",
    "        return self.loc + self.scale * x\n",
    "\n",
    "    def inverse_transform(self, x: TensorVariable) -> TensorVariable:\n",
    "        return (x - self.loc) / self.scale\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be5d7585",
   "metadata": {},
   "source": [
    "As the composition of two flows is itself a flow, we can define a class that composes them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "09e1c0dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compose(*fns):\n",
    "    def f(x):\n",
    "        for fn in fns:\n",
    "            x = fn(x)\n",
    "        return x\n",
    "\n",
    "    return f"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d93829f7",
   "metadata": {},
   "source": [
    "## Understanding the Forward Pass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66e7f3b2",
   "metadata": {},
   "source": [
    "Let's use these classes to generate a normalizing flow computational graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ace905a5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exp [id A]\n",
      " └─ Add [id B]\n",
      "    ├─ loc [id C]\n",
      "    └─ Mul [id D]\n",
      "       ├─ scale [id E]\n",
      "       └─ normal_rv{\"(),()->()\"}.1 [id F]\n",
      "          ├─ rng [id G]\n",
      "          ├─ NoneConst{None} [id H]\n",
      "          ├─ 0 [id I]\n",
      "          └─ 1 [id J]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<ipykernel.iostream.OutStream at 0x1055e99c0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Random number generation\n",
    "rng = pytensor.shared(np.random.default_rng(), name=\"rng\")\n",
    "# Sample from a normal distribution\n",
    "x = pt.random.normal(0, 1, rng=rng)\n",
    "\n",
    "# Define the parameters of the affine transformation\n",
    "loc, scale = pt.dscalars(\"loc\", \"scale\")\n",
    "# Define the transformations\n",
    "transforms = [Affine(loc=loc, scale=scale), Exp()]\n",
    "# Compose the transformations\n",
    "flow = compose(*[x.transform for x in transforms])\n",
    "# Apply the transformations to the random variable\n",
    "z = flow(x)\n",
    "\n",
    "# Print the resulting graph\n",
    "z.dprint()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "501932bf",
   "metadata": {},
   "source": [
    "We can now compute the log-density of the transformed variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "975b389d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Switch [id A] 'z_values_logprob'\n",
      " ├─ Isnan [id B]\n",
      " │  └─ Mul [id C]\n",
      " │     ├─ [-1.] [id D]\n",
      " │     └─ Log [id E]\n",
      " │        └─ z_values [id F]\n",
      " ├─ [-inf] [id G]\n",
      " └─ Add [id H]\n",
      "    ├─ Switch [id I]\n",
      "    │  ├─ Isnan [id J]\n",
      "    │  │  └─ Mul [id K]\n",
      "    │  │     ├─ [-1.] [id D]\n",
      "    │  │     └─ Log [id L]\n",
      "    │  │        └─ Abs [id M]\n",
      "    │  │           └─ Alloc [id N]\n",
      "    │  │              ├─ scale [id O]\n",
      "    │  │              └─ Squeeze{axis=0} [id P]\n",
      "    │  │                 └─ Shape [id Q]\n",
      "    │  │                    └─ Sub [id R]\n",
      "    │  │                       ├─ Log [id E]\n",
      "    │  │                       │  └─ ···\n",
      "    │  │                       └─ ExpandDims{axis=0} [id S]\n",
      "    │  │                          └─ loc [id T]\n",
      "    │  ├─ [-inf] [id G]\n",
      "    │  └─ Add [id U]\n",
      "    │     ├─ Check{sigma > 0} [id V]\n",
      "    │     │  ├─ Add [id W]\n",
      "    │     │  │  ├─ [-0.91893853] [id X]\n",
      "    │     │  │  └─ Mul [id Y]\n",
      "    │     │  │     ├─ [-0.5] [id Z]\n",
      "    │     │  │     └─ Pow [id BA]\n",
      "    │     │  │        ├─ True_div [id BB]\n",
      "    │     │  │        │  ├─ Sub [id R]\n",
      "    │     │  │        │  │  └─ ···\n",
      "    │     │  │        │  └─ ExpandDims{axis=0} [id BC]\n",
      "    │     │  │        │     └─ scale [id O]\n",
      "    │     │  │        └─ [2] [id BD]\n",
      "    │     │  └─ True [id BE]\n",
      "    │     └─ Mul [id K]\n",
      "    │        └─ ···\n",
      "    └─ Mul [id C]\n",
      "       └─ ···\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<ipykernel.iostream.OutStream at 0x1055e99c0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z_values = pt.dvector(\"z_values\")\n",
    "# The funtion `pm.logp` does the magic!\n",
    "z_logp = pm.logp(z, z_values, jacobian=True)\n",
    "# We do this rewrite to make the computation more stable.\n",
    "rewrite_graph(z_logp).dprint()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "911e0bd9",
   "metadata": {},
   "source": [
    "From the log-density graph, we can extract the inputs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9ca6e924",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[z_values, scale, loc]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inputs = list(explicit_graph_inputs(z_logp))\n",
    "inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "49ef5ec0",
   "metadata": {},
   "outputs": [],
   "source": [
    "z_values, scale, loc = inputs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "448fa2fe",
   "metadata": {},
   "source": [
    "We proceed to compile the graph into a function so we can do actual computations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a27b4303",
   "metadata": {},
   "outputs": [],
   "source": [
    "f_logp_pymc = pytensor.function([z_values, loc, scale], z_logp)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cd883ba",
   "metadata": {},
   "source": [
    "Let's verify that the resulting log-density of the transformed variable is the same as the log-density of a `LogNormal` distribution, which is precisely what we expect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "24bb63d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
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pk72Y52ee56sz1jTo62kCCBNMHngxoaapXjVVVrfddou9ranOMsFQRSYYNMxtTX/WigKBQHn1qQmjqmNCwzZt9gWrpmXAgb7++gtbNWZCkhYtWlbb/7RMdbdraKY/qKk0NUyvxooBaxkTKt166502qDSv1YcfvlspzCsLgEzF4YFMNezvfveHGudhwiRTbXpgRaOpCL3uut+Xn7r+44+VT2GuD6ai8aKLLgsaN8GS6blqmN6bVTHVlKGUVSSaEO/aa38X8jamMvqEE8aWV/PW1Fahtsp+LiYgD3VMm+rpqgK6+nxt6qJ79x6VAtYyptdt2anuFR9737H5nr1u+rVWDFgrMv82mHDXnEpf9jrVhqnYLdt3qB7BvXv3sb1Va2L+bSgLWCsy/56dfvpZ9oME87sUqsrYBNT9+g2w16sLyM2/dxUD1orHatncTduEUMzjmg9MDmReM9MPuiF/5gAAAABgUMmKStal71Fzsi49p0H3b/qplp36XR0TQtx119/Uu3ffoApUc5qxCVZMoFqxMs/0OCzrsVhTyGpODf7FL36hKVOmaPr06Zo8+bKQfV2rW5THMAskVexHGi6mr6UJp8oCv6rsWwBrmD19vKxauOLp5CNHnlDlAkjHHHOc/bmY/qTVLehVVcsEU6loForKz8/XggXf67jjRqk+9e8/IOTp6karVq3s18LC0BXJxoHHWpmy12nUqNFV7r/s2DSVgWaRJ3Mqvlnsqy5MVfDSpT/9/NhjqrydOR384Yfvb9DXpi4GDdoX4oaSktLKVmOa51pm48YNtl9yWeBZVRW55FDPnr1t64ElS/a9TjUxC8GZ3qnGCSdU/Zqa1gSmBUR1+vQJfbyYDyRChZsVF/MyPVHLnmN1gXx1rUpGjhxtj81Vq1baRfoOXASrY8fO9ve9qtfdqPi6AwCA+i8uKSr1qtBbqsJSr4pLvCouLSm/eEtLVewz173yBfz2vbw/ELBf7UUBdfB0l8vhln2bH5DdbjidDjkcfm0tXm/Xr3A5nHI5nfar2+m0Y+ary+lSjDtKMW6PYj3RivV4FOuOVny0Rx53cLshAKhvhKyopFfHFtqVU3Wo1NT06hieakyPJ9r2mezWrYcN40xfTHPK9oHM6dnHHjvShlkmCK0YspZVdA0YMMj2Aq3JySefbENW0zLAhC9dunSz4yaoNeGWqfiqLojZN58kG0qaN1FmEaRw2blzR/n1bt26V3vbbt262VDV9NQ0TJ9IU11qVPe67euP28UGRFUx1YlVMZV1JoBds2a1du7cqfpWXSVx2eJp5udUFdN/9kAFBfk2NDXMivDVqbjdvLZ1DVl37cooD+Cq+7mYClsT7JXNsyFem7po2bK6x3YGBY0Vqysfe+xhe6nJgQtYVWX79u3l1zt3rrq9R9eu+/4tONTnVcb0nDWtOEzrA1N5bwJl0+u3YiuCsg9HDvb3qXPnzuX3NwsBHhiy1uZ1b6ifOQAAkc5bWqLd+XnKzMtVdkGesov2KrcoX3neAhWUFKhlaQ+5ShJU5PVVuJSq+OfrxX2myxFVfeuh2ihaPEYBb2zojS6vYod9dcj7DgQckt8phy9KsRt+oSiXU9Eel2I9bsWYr9H7vspTpEzXOhvOxrpjFO+JUZwnRkkx8UqJS1Sr+CS1ik+Q27XvPSUAVETIikpMj1JTMbVic1Yz6MmaoktO6tOgj2NOcX388WfrtI9Jk06xIatZDMhcTF9RUx1mVsuubsGrAw0ZMlQdO3ZUenq6vvrqi/J+nF9++bkNLo4//oQaF6cyp9536NDRhicHti+oiQk4qqoaPVimOrSMWSioOjExsZWq2Ewf1/3bql9pvKZ9m9PSq1O2kFTFNgv1JdTiPwcjVI/Yiq9rXFxsrV+b+qgKrRja1/xzias2ZK3ra1MX1VX/hmKC7YNV8edUH69pTcd52QdDVTG/U/ff/3/65puvgkJU82/KsGHDlZm5237gcKi/T2W/S1X9Ph3s6w4AQFNm/n9cWOzT5uwMbc/drd35e5RVmKs9xbnKK81ToT9fJYFC+RxeBVxeyVVa7f6K1/vkz25X5faYQL3NvOpN1a97WiOHIyC5fAoEnMrKrToQdibtVnS/BZL5TNzcLMTbLvN2x4S1Dr9H7oBHbkeMoh0xinHFKs4dq/ioOKXEJGtAcn8lxXvspUWL2JCL2QJoWvirBJWYT/CuPn1f7zw0DuY088TEJO3dm2tbBvTo8Vu7WJYJUEy15YQJ1Z/iX7GyctKkSXrhhRdsD9aykPWrr2bUqlVAxf6uJmQ1C8mYirXaVMEZJih+6KF/2cpd0y+zLpWPJmQrY8JTU9lYlbLTr8tCpophTUFB9acPFxVVv72mxYLKgt1w9q891Ne1ptemYjhYFmTXllng6EAVQ8CaQtumdNp3xePxwQcfLe8fWh8qvqZVtyEwx/mhn71gPvC5+eYbyhcsMx8sDR8+Qj169LJV5KYa3Hy48re/3VVjyGp+n6oKfCv+zCPl9wkAgIaSnZ+nTZk7lV8QUElBtDJzi5WVW6TduUXK2VusPflelZT65emzQK6Wu+ucADic1fffD/hcdc1Af36g6rbVUwGQv4ags4bA2U7FzNNdooBKVKJ8mSZq5e9UzDSLJd+uZE373FvpPolxHrVMiFZ8jFtK2ilvTIYSoxLUIiZRreKS1CY+WZ1SUtUusUW9FacAOLwIWYFGzlSPmoVfzOI4c+Z8Y/sfmpXRy/qG1uY03jKnnHKKDVnXr19nWwa4XG6tXLnChpTHHTeyVvsYN26iPv304/JFdapaHOlAX3wxQ1lZmTYovvzy/W0PDoVZsKrMpk0bNWjQ4Cpvu2nThkr3MacZt2jRwobUW7duqbYCwFT9Vqe6hXRM5W56elrQfBsz00PWVBPm5e3V5s0bq72ted3LVHx+ZW8ITR/hqoRqNdG+fUf7QYB53dPS9r1uoeTk5Nj5NRVt2+6vCtmxY1//1KqY1ybUwlJV6dRpf79gc6ybnq+hVPd7UBNTFV8WsF5//R904YWXVPlzq4n5faoqQDX/XpVVrKam7lvEDwCApqqoxKt1O7drY9YOpefu1K7CTO0t3aMi7ZXPVVAeBJZs667SraH7phuBkqrPRDkoNQWP/vqKFeqtJLbqR/BXf5q/w1U/C7oe+Nqb6tfcfK+9GO5OGxTVYaNkXlpzkk7ZiTobzRwdcpbGKioQp1hnghKjEtXS00Kt45PVNiFFHVu2UqeWrRQdxrO3AIRGyApEALPqtglZTThqFrKZN+/bWi14daBBg/b1b01L26Kvv/7SVsIao0ePs2FubZhg1/SSNeHlm2++rtNOO7PKxZ/KrFy5XLNmfV1e6Waq3OrCrBBf1hvWtE2oKmQ1i+2YBcKMQYOOKB831bQzZ36lefPmVhlcLVq0sMZTuRcvXmQr7EJV35nFrsqq744/vn4XvWoo5nUwlcpz587WnDmzdNNNt1Z5Graphi47HbxiL82y16KqVeRN5eOqVcuDxk3Q36dPP61evdI+/kUXXRry/mZbOBxMuHkwevXqXb5A2uzZs3TWWeeFvJ2pRL3ggrPs76mpOv/tb2+ocd/m99QsBmV+D+bOnWM/IAnl228P/TVdtmz/IlxnnnlulZWyy5cvqbEv6nffzbWLyYVijsey392a2kkAABAJSv0+rd+1Q6t2pil9T4Z2F2Yq15ejIuXKH1Wwr1qyjPkMO8RbdUd09WejBEpq9/6+JtUFj26X0waCDm+pHHLJGTBVrS45zX8O89UsVGUubnNNLqdbTodTjrL/HOXX1OXI7op2xtmCVvP8neYDePv+IaBif5E2+YcoIH+FhbP8Mv/tv+6TP+BTqUrlD5Tu+14+BRz7Lw6fx+67yjbxtahkrZUaXvvqetg6nAEFPAXyylx2y5QnbDXZrLmYt9hpP7csKI1Wi7xB6uIeqFYtYtS6Raxa268xapUUI08UfWOBw42QFYgAJvgyvVBNpdd///ucXfjFhFs1LVRV1QJYzz77jL755uvy4Ki2rQIME27+4Q9/1E03/c6e3nvjjb/VAw/8R92796iy4vHOO/+fXezHBHam2q2ukpOT7XM3z+G9996y8+/Xr3+l25gw56GH7rMVleZ5mjC4zBlnnGND1u3b0/XWW6/rggsuDjqd/amnHq1xHua09ueff0o33HDzAeOFevLJfffv0qWrBg6sutI2FBN+m9erumrQhnLGGWfbINP00HzmmSf0u9/dGHQbU0k9e/Y35T2DKwaxnTp1th8GLFmy2O7DLFRVkVnFvqqeouaxH3hgpV1F3vxsx4wZF9T788UX69bj+FCVfSBRFhTXF/PanXLKGXr77f9p/vy5tjLUVK4f6Nlnn7RhaVkwW9vfVXPcT5nyX82Y8ZnOPvs8u1BeRaa3snnsQ2Wq4cuYD14ODEnN7+G///2v8p95da+d+dDm5JNPC6r8nj79Uy1bti+kPfnk0w95rgAAhIMJCHflFGrb7nyl787Xtsx8bShcodyUhXI4K3z4aN5q/Px2o7Yf7To81bdQqqmStareotGuGMW742xv0XhPnDoM76D28W3tQlExHrdiPS57PTrKZUNWaawOj3pqa3e6VOrzly/gVVS8fzGv7fntta2gkwpKi1RkLr5iFfuK5fUXqzhQqNJAse1l63d55agmkK3ptXdE7W8lcCjsn3FRxdqVXawdu0Mvsmt6wbq7LpUnOqCkqBZqHZusdomt1S25rXq1aa+YqPoJ4QHsR8gKRFA1qwlYP/tsqv1+7Njxlfo5HmzIumbNKvu9qXQbNuzog9qH6bn429/+Xk8++R+7ovhVV11qq2pN2GlCNjMvcwqyCTLff/9tG1qaoPPmm29Tv3718+bouutu1MKFC+yp4zfe+BtdfvlVNpQzFZEm5Hv55Re1cOH39rbmFOaK4c+IEcfahb5MmPj4449o586dNuAzrRfWrl1jw0XTRqE2VYwmGNq7d68uvPBiGyiavpNPPfWY1q1bY+/3xz/ecdA9lcwp06a1gmkPYaqMnU7HYetDOWrUaHsxlYMmEN25c4cmT77Yru5uqlOnT/9Mr732sr2tCf4PbBcxZsx4G5B6vV7dcsvvdcMNN6lnz97atStDH3zwrq3ILusxfKBTTz1DH3zwjv0Z3HPPn3T55b/W+eefo8TEBC1YsFAPPPCAPd4auro0lKSkpEpVvPtCfUel8UN1xRW/totG7dyZYZ+3qfw++eRT7fFkKtffeedN25qj7AOXCRNOqvW+L7nkcntf00P55puv19VXX2c/oDCh8Q8/zNfTTz9eaRGxg31Nze9SWUj717/+yf68+/UbKJ/PVCyv1JtvvmYD9zLVVYeb3+XrrrtK1133ew0bNsLe1sz9lVdeLK9iPemkSQc1PwAADqfMvFwtTt+ozZm7FMjqoC0787Q9s8AGehU5kwKKbl33HqMOT+hK1oTYKLVI8MiT1EHFpV7FuxOU5ElQckwLtYpvobYJLdUuKVmtE5LkrvBBcnNiwuGEWHOpfMr9ILWSVLl4oyrFJSXKzN9rL1kFucopzFducZ7yigsU0zVVSm25r0VAgVd5haXKySu2vXLrI2QtE/BWvTaCeewYzzYVRhXbatg0k8mby04psEpylsQpWolKciWrdWwrdUxKVbeUDurTpp3iPJw5BBwKQlYgQpgQ04SsZat3H2yrgDJ9+/a1i1WZRauMceMmVKrSqy1zOnerVq30yCMP2sDs448/sJdQTJBrwsYDKxPrwrQo+Pe/H9Mdd9yizMxMG/iay4FMwBqqb+zdd9+rP/zhOttP0gRB5lLRKaecbvvHmoC4qtfHhIemd5TpUVvWp7aMOa37jjvu1lFHDT/o52bCJPPYpi3E6aefaCv73nmn8v4b0t13/11/+9ufbdD65Zef28uBzKn99957n+LjKy86ZgLAzz+fZudugmZT6VyRadtgql8ffPC+kFWd9933b91ww7W2avu5556yl4rM6fQmiDUO5bg9VOaDA1ORvHz50vJj3bS+ePzxulfWmgD9kUee0K233mw/nDDhtrkcyHxQ8I9/PHBQob35+dx//yO66abrbF/Uhx++317KmH2deeY5Nvw+lNfU9HI2P3NzvJqq2NtvvyXoNq1bp9rg3oTspnWAqcQ3Ywc68cRJ+uKL6TasPZB5rc1zBwCgsTBB6uL09dqQnaaMwh3KU6Y9xdsI+J0qWmbOTAn9/2x/YdWLttbE7NtVGq9oxSvB3UJHjupmTxM3p4entIhRckK0otwsmnQ4mJ6oHVqm2EtNUlLibeHE3nyvNqfnaE1mO+3My1JW4Z59wWzpXuX78uQNFKjU9N111y6EDRRXswCtaY/gCd2WwLZM8BSoSOaSoZ1eaYVZI223FFgt2wLC409UkrulWsW00ojWx6hTagu1TY79uXoZQCiErECEML1Uy0Ies/DLoYR3ZcaPP9EGtsaECbVvFRCqunbkyNGaPv0T20/RVJDu2ZNjT3VPSmphe3WOHHmCPQX4wDCuPphTn19//V29++5b9vT1tLTN9hT71NS2Gjr0SBseVdXj0VS8Pv30i7bdwIwZ07Rly2YFAn7bL/acc863z82cYm14PKFP9zGLaJlWCabSzoRMJjwyPxtT6WvCXfMzOxS33HKbDRy/++5b23rAVBeasDc6up4WL6hBXFycDTtnz55pw+MVK5YpNzfXhoHdunW3r42pWo4K0WzfhHTmvlOnfmirrjdsWG8/GDCvhQlXzzlnsn2tqlsI6qWX/qc33njV9ts1lZwmCDR9d88770L17t23PGStbR/h+nLPPf/UI4/cb9sZeL0lNjCsL126dNPLL/9PU6d+YCvAN2xYZytMze+NaQ9gAkgT/B9KsGwWvJoy5W1bgfztt7OUkZFhjyXT2/iyy660x31ZyFrVsV6dv/71H/bfo7Kfd3FxkZ23aZVh/n0wv4emp+xHH71v2weYqt1zz70gaD+nn36WrSg37Q3Mv3NOp8u2ITHj5vlX1R8YAICGlp2frwVpa7Vy5walF6Qrz7FLiqrwPuCAtySmDYAjNl+BwsTQOyyJVqDULYe7itPNS6IV7U9SgssEXCnqkNhGnVu2UbeUNmrDyvMRy7ynj4+NUruUOLVLqf7svgJvkdKyM7VtT6Z27DVhbI6yi/cov3SvCv35KnUWyO8qUsBbdcWpI7rwEOcpBaIKVaxC7dJO7Sx2aNGH5lg2fXYdSk2OVfuUOLVvHaf2KfFKTfaodXKUWiXU/QwvINI5AmVlcYgYu3Y1nZW1cXB++9srtXTpEltFak6XPxjm01OXyymfz6+srOoXdMK+vqwTJoy01//853s0adKp5duuv/4aG7TVVyUjan/cmgrsiy/etzjUE088pyFDjgz3FCOe+YDkj3/8vb3+7rtTbdB9uPz44wL9/ve/sdcfffTpOn141Fjwby0iDccsIlFDHrdmQaolWzdp8bZ12py7Rdn+DJVG5VZeiKoWvOuPkC+zQ5XbY/r/oCiPX0muFKXGpNogtVtKW/Vu00EtYuPr/kTQ5I/Z4tIS7c0rVWZukXbvKbsUKvPn69naKk/fBXV+HH9RnIqXjK5yuzMpU9H9fvj5w4EWaulOUZu4Nurasp36te2srimpfDAQoZrDe4TU1Co+DDtElIUAEcKcPm0CVqNi4IeDZ1oDpKWl2WrXqhb9Mv0ky5j2Cmh4pheuqdw99tjj7SUU096hYvUnqvevf/1D8fHxtoezadVQ3WsaGxtnK7EBAGhOTL/UzTv2as3WHK3ZkqM1sVOluD2V/lo+lC7wjrhcKbODXSCqQ6t4dWwdrw72Eme/T2kxzlYFAocq2h2l6JZRat0yVn1DbPeWligte7Q2Z2UoPXe3dhVkKbs4W/m+PSp25tqFs2ojUBRX7XZHzM/9/aOKVaydpvmAMopXaWmGNDVDCvhc8pS2UAtXK7WLb6ceKR01sH03dWyRfFjXWAAOB0JWIEKYU2gN0zLAnNKOQ2dOwzannH/++WcaMeK4oMWLTLuDl19+wV5v2TLZnqKOhmfaLZhTzufNm6NXX307qB2BOT3/f/97tfwU+OTk5DDNNHKYFhqm6toEqaGqrrOzs22vVMO0uaDKAADQ1JkV5Ddu36s1aTn2sn7bHnlL9i9CFdU9Qe6ykPVglcQoLpCiNtFt1X9QX404pZ8NwAhTEQ4ed5R6prazl1D2FOZr3a4d2pi5Xdvzdml3Uab2lub8HMDub4cRKK4+ZHXGVl/h6HD5VOLK0m5laXfxWi3bLn1k1rIt9Sja11LJUa3VMaG9BrXppcEduyo2mpgKkYujF2ikTO/CJ5981K4wvmTJIttz1LjoosvCPbWIZxbqMX1U8/Pz7eJXv/71tTa0MwHTpk0b9frrU/T99/PsbX/72xvoBXmYmJXjTchqFlAyp6+bfqFDhw6U3+/TihUr9cQTT9rFtMwn3tdff1O4pxsRzAJ5JmQ1l7vuul0XXHCROnbsrMLCAttr1/RmNuG26cUaaoE4AAAinanm+37zWi3YukJbCjaqIDdG3o2he/Yb/r3JUmp6jft1eOOU5Gij9nHt1btVFx3RoXutFkACGgvTlmJYl572cqC8oiKt27VNG7J2qDgmSsUtE7U9M1/bMwuUV1hS6baOmEM8jdztVbF7p3Zop3YUrNB3325SaXpvtUqKVsfUBHVMjVfn1AR1bpuodimxclEMgAhAcgA0UibwmzZtql0RvMzo0eM0Zsy4sM6rKTCLN/3hD/9PjzzygNasWaXbbrsp5Ot/xRVX6dRTzwjLHJujo48+Vpde+itbtb1w4Q/2ciCz2JX52Q0bdnRY5hhpTjvtTP3004+aPv0zff31F/YSahG4P//5b/b3AgCAplCosCojXXM3LdW6Peu117Vdcv28wFS05EisZjX2spD1QKVRivW3UrvojurbupuGdemjDi04owZNV0JMjIZ27mEvB9pb4LVh646sAhu8Li5ao73eQvmjCg66d3FF/oJ9vTEzc4vtZcn6zPJtUW6nEvusVkKsW50S2qtPalcN7dhDSbHV/z4DhxshK9CIHXXU0ZozZ5YSExM0ceIkKs3q0dlnn2dXV3/nnTdsld/OnRlyudxKTU3VkCFH2RXR+/XrH+5pNjvmGDf9WN9//x0tXfqTsrIyFRMTo7Zt22rYsBH250Iv1tozHxbcdde9GjfuRH3yyYdasWK59uzJUVxcvH1NR44crTPOOFtt2rQN91QBADhk2fn5+mrtYi3ZtVKZ/jS7MrrlCb6tM6Zw36nQJaFXZTenRrsLU9UqurV6tOiioR16qV/7TnI7XQ38LIDIkBjnsZc+nVva7y9Qb/u1wFukVTvStW53urbuzVBm0W7l+bNVYhaOc+5vyVGVQGFCldtKSn0qiNmsQlepdhWu1qIt0hubJVdJghIdrdUutp16teqsIzr2VCcqyhFGjkAgEAjnBHDwdu3aG+4pIAI1h5UB0fRw3CLScMwi0nDMIlKP25XbturTpd9peeZKFbgz5HDW/s9a77oh8mW1t9dNv9Ru7RPVp1NLGxr16tRCCbGV+8IDddWc/601LTvWZGzTqp1p2rwnXbuKdyk/kCVfVF555WvA71TRgonmNzLkPhyeAsUMnVW7ByyJVuzPvZF7tOysIR162r60rD1w8JrDcZuauq+Cur5QyQoAAAAAaNR8fr9mrV2u+elLtM27UT5P7r4NHulgzlAO+B1q08aho/t3U+/OLdWzQ5JiPPxZDDTkAlyDOna1lwP7vq7YvkVrdqcpY+8eOXukauuuPGXvLQ7ahyPuIArNoopVqO3aHNiuzdmL9XV2WcuP1moX3V7jOoxX9/ZJSk6Mtms9APWJ/5sAAAAAABodb4lPyzdmacHqXVqyfrdKun0rV1J2yDYA1XF5k9QuqquOaNtXo3sOpo8j0Ej6vo7o3sdeKiooKlH67nxt3ZmnLeaSkad01/q6PZi7xAav6/P3asX7bexQUrxH3dol7ru0T1L3dolqkRBdt8dBs0fICgAAAABoFIq8pVq6IUsLV+/UT+szVez1lW9z57TZF7LWpCRGKY6O6p/SR6N7DFanlNYNO2kA9SYuJkq9O7W0lzLe0iFauSNdK3Zs0qbcrcr07lShM0tyew9q3/78FuXXc/O9dnGtigtsJXbaoZjWu9U+toN6t+qq4V36qG3S/vsANSFkBQAAAACEdeGqz1Z+rzU7MrR9VTuVlIZeJMeXk6qoLquDxgMBh2K8rdUjoZdGdRuiIzp2o/8i0MRaDgzp1M1eyvj9fqVlZ2rJtg1an52mjMId2hvIVMCTX6uQNZSi6AyVerZrrW+r1u78Xp/ulJzeeLVwtFOXxE46on0vHdmph6Kj6NuM0AhZAQAAAACHVaHXq89WLtAPOxZpjyvNrj4eiHapxN/KnOAf8j6Bonj5i2LljCm0PRZTHF00IKWvJvQ+Um2oNgOaFfNBStdWqfYiHVM+np2fp8XpG7R61xZtzUvXnsBO+aL22kW2/PlJ1e8zfk/QmN+Tr2ytV3bRev208Ru9st6p6JIUpXraq1dyVw3r3EfdW7Xhgx1YhKwAAAAAgAZX6vPp6zU/aU7aQu12bJRcpVLU/oWrHC6fnC12yZ/dLuT927eKV6eYE3RUn046adBQuZyuJrviNYBDkxyfoHF9jrCXitXyi7auU1F8ktIyCrRpe64ysgsr39FVImdMQY37Nx8IeaN3K127lZ6zVN/kmBYl0UoItFHHuI4a0KaHju3Wz/acRfNDyAoAAAAAaDALNq/VjHXzlF661q78Xd1foa7kjEoha5c2CRrWN1XD+rZRh9bxdiwlJV4ul1M+X+i2AgBQUXJ8vMb3HRK0wNbmHXu1acdebdyxV+tzNqroUB8gqlh5StPq0jSt3vad/vfZGHVMSlWPDknq1bGFendqoTbJsXKYclo0aYSsAAAAAIB6lZG7Rx8sna0VuUtUGp2zr1y1Fm0MXS13qVOHBA3v21bD+qSqTXLc4ZgugGa4wFb/bin2ss8gZeSO1o9pa7U6c5O2F2xTnnPnQS+uFfBGK1Aco6278uxl1k/b7HhSXJR6dmyhrh1j1LJ1iY7u0luxHk8DPDOEEyErAAAAAKDOvKUlmr7yR83d9sPPfVYDUnTt7htVnKy+iQM16Yhj1L1124aeKgAEaZvUQicPHK6TNbx8ca31u3Zo4da1Wp+zWbu82+WNyrYtA6rizzP9oYMrVnMLSrRo7W4tydwuT6+f9Mamfb1d20Z3VP/WPW2LgbZJLRv0+aHhEbICAAAAAA7ZzuwCTV38kxZ6P93XDqBCn9XqOL0J6hHbX5P6Hqv+7TofhpkCQO2Zxax6t+1gLxUX7VuUtkFLM9Zpy96t2hPIUMCzvze0P7/6oNSZkF2pt2uaditt90+asXvfv4kpzvbq0aKbhnXqowHtO7OgVoQhZAUAAAAAHBSf36+f1mXq60XpWr4xyy4aE3NkSc3hakmMOkX10YTuIzS8ay8CBAARxZzif3zPfvZSZtuebC3cskardm9SSXyq0qNdKiz2hby/M9GslBWa35On3Vqr3flr9f3qz6XlHiX426hLQlcd2aGvhnfpKY+7Fn1XEDaErAAAAACAWsneW2x7DJqLuV7OFyVfVlu5W28Puk/A71SKv5vGdB6hcX2HyO10Hd5JA0AD6tAiWR0GH6PTdYz93h8IaHtmgdan79HarTlat3WPMrILJWepHHF7a79jt1d52qoV3q1aselbvbrepThfqjrFddGoTkdrSJdOinLz72ljQsgKAAAAAKiS6Utoeq0uWZettavcNkAIxbe7Y6WQNaq4lY5IHqozB41Uq4SEwzhjAAgfp8Ohjq3j7WX0kH2tBnILvFq+ebtmbt+pncXpKo7K2te3+iA4XD4VunZobekOLf3EKVfRRvXokKQ+nVuqb+eW6tkxSTEeYr5w4tUHGsCoUfsaZZ988mn605/+qkhx/fXXaPHiH+31hx9+XEcffWyN9/nHP/6qzz6bqnbt2uuddz4+DLOMDOedd7p27Nh+0MfACy88o//+97kqt7tcLnk8HiUnp6hPn34aN26Cxo8/UQ6Ho8rjsOr9RCslJUW9e/fRuHETNWbMeLnd7lodH7UVab8DAABgv71FhXpr8TdanPOD/J698qml/IGq3x/6c1vJUZBsq6xO7TtKgzt2PazzBYDGKinOo+P6d7UXo8BbpB82r9WSHeu0NT9Nec6dtnK1NgI+lwIFSSoN+LUmLcdepv4c7nZtl6heneMV13qPju8xQKkJSQ38zFARISuAkO677++aMuVNxcXFh3sqqMDn86mwsFCFhenati1dM2d+qffff0f/+te/FR+fcJD7KVB6urls1cyZX6lnz166++6/268AAKD52rg7Q28t+VJbSpdL7hLJs2/clZgjR+xeBQoTK93efNQ7sEeKxg3tqCN6jZOLPqsAUK04T4zG9B5sL2VnDKzYsVULt67WhpxNyvLvsB9uheLPaykFgv+dNWcZbNyeq835GxTdb4Gm73pPbm8LpUZ1VL9WPTWy+0B1aJnS4M+tOSNkBRBSRsYOPf74I7r11j+FeyrN1pQpb6lt23YHjAZUVFSktLQteu65p2xlqbk88MA/9de//iPkfk466WT98Y93BIWs+fl52rJls778coY+/fRjrV+/Tjfe+Fs99dQL6ty5S5XzMnMyc6uN6ipjAQBA4zJn/Qp9um6mctyb5XAEQv616G6TppLNA+z1xLgojTqivcYM7ag2LWMP/4QBoIkwiwAO6tDFXsrs2JOt7zat1Ird65ThTVeJJ1vmBEb/3uTq95WYbb+a2/qi92iH9mhH9grNzP5YTm+iUt2dNKBVb43qMVDtWlS/Lxwc/voFUKWPPnrfnoo+fPiIcE+lWYqJiVFcXFzQuKkuTklppYceekzXXvsrrVu3Rl98MV1XXnm1unTpFrI1QKj9JCYm2jYPI0Ycq+OPH6W7775DOTnZuv32m/XKK2/a+4ViWhOE2h8AAIg8pX6fpi6dr5nbZqskOlOK2leZWhVX63R19Y/Q+CO7aFifNopyU7UKAA3BBKBnDTleZ+l4+312fp7mbVypTKdLW537qlZLfcF9XZ2JWVXu01THZmilMrJX6uuFH8nlTVIbd2f1b91LJ/QYpDZJLRr0OTV1hKwAgrRv31FZWbtVXFys++671wZuhGqNT3R0tC688GL9/e9/sd/PmTNLF10UHLLWhunHetllV9p+sJs3b7J9dk877cx6njEAAGgsikq8emvRLP2QNW/fKanR1d8+4HeqbaC3zuw3TkNP7HG4pgkA+FlyfIJOGXR0+ffeEp8NWlf/3Jd1XfoeeUtL5UzYU+t9+jy52q7l2p61XF9mfqgob0u18XTSwNTeOv2oY9QumdD1YBCyAo2U6ZP5zjtv6ocfvrMLKJnqwbZtTdXhMbrggotDnEa+X27uHr377lv65puvbd9Oc8r20KFDdNVVV2n48KM1fvzx8nq9evTRp3XUUcGLI7Vt21bnnTdZjz32sH3sJ5/8T9Dp5gfjp58W64MP3tGSJYuVlZWpmJhYdenSVaNHj9U550xWbGxslYssmeDPBID//ve/tHbtanvbvn376777/m2rN//v/+4pX3Rr0aKF+t//XtWKFctUVFSodu06aNKkU3ThhZfY16C4uMhuN/fbtm2brRQdPPgIXXnlterbt1/IuRcU5Ovjjz/Qd9/N1YYN6+1r63ZH2QWjBg8eonPOOV8DBgxSuPTu3bf8+vbt+1fzPRQXXXSZPeb27s3Vu+++ScgKAEATtKcwX6//+JWW5f0gRRWV91utUkmM+sYO1QVDJ6gtFU4A0Gh4olzq2yXZXoxSn19rt+3WF5v2Ki1/s/JdOyVXaa33Z9oLlEbnaJtytG33Mn3y+BYNbjNAV50xUHGctVArhKxAIzR16gf6978fkNdbXGl806YN9vLBB+/p9tvv0kknTQq6r6lCvOmm32nnzoxK47NmzdLs2bP1xz/+v1rN4fzzf2kXQ1q69Cd9+OF7dvX5YcP2f2pWG6Z590MP3WfvX1FJSYmWL19qL++997YNTM0K91WFzTfe+Bvl5eXZ7004bHg8lf8iePPN12wP2UBg/+kS5rV6+unHbTh700232f2YvqNlzOv77bez9cMP3+uJJ55V//4DK+1z1aoVuvXWm2wwfOD8yxaMmj79U91225/DFkia8L2My1W3//GZANu0DTDPad26tcrJyVHLli3rYZYAACDcMvfm6aWFn2iDd8m+xayiqr99VHGKjmt7nM4afLyio2q4MQAg7Nwup/p3bqP+nc+235f6fFqUtkEL01dp095N2uvcse/f/1oIBBzy5SZrcc4uPfDqQt112XA5ndU1k4H9GfAyAI2LWS3+X//6hw0LO3bspKuu+o2OPHK4/VRp4cIFdrGj7dvTde+9d9memscdN7L8vmbV+bKANTY2Tldf/VuNHTveNtFetGi+/vOfR/TAA/fXah7mPnfccbd+9auLytsGvPzyGwfVNuDRRx8qD1iHDRuhyy+/Uj169LILLn399Rd6+eUX7AJbN910nV588TW1adM2aB9mUab4+Hjde+99Gjr0KFtNGnXAG/3MzN02YO3Vq7euvfZ6W5W6dWuaHnzwnzZU/fLLz7V27Rpblfub31xv+8yaKlYTIj/++MM2bH322Sf18MNPVKpgve22m23AavqfXnPNdfbxzWu+c+dOzZ49U6+//opdhOo//3lIEyacFLIit6GtXLm8/HrXrt3rvD9TJWxCVnP8LVu2RKNGja7zPgEAQPjkFng1ff4WffnjFjkGrJAzuuo/sM1n1S1Ku+qUnuN0Qq99i1sBACKT2+XS0d1620tZD+5FWzZogQ1dNyrPtaPKStdAfpLk3xcZbt6xV8UlPsVGEyHWhFcIIc3Y/LU+3zyzzvv5RbfxmthlTJXbn13ystbmbKjz41x7xBXq1bLqgOn2OX+Tz+8r//7ErmN1UtdxamxMlaYJ7EzAZVZ3f+aZ/yqpwmlZpnL16KOP0bXXXmHbADzwwP/pzTc/KA8dTehnAlazYNEDDzxiQ8EyF1xwgY466khNnjzZhqa1YU7pN0GtCTC3b9+mJ598VH/84+21uq8JN03LAsOEmmblexPcGqY68pJLrrDzu+GGa23FpGlNYILUUK6//iZbSWsMG5YStN1Ulpr2CU888ZxdFMpITk6x1b5XX325/X7Lls26557/s2FoGXOqvwlezev200+LVFpaatsKGNOmfWrDW+Pvf/+XjjhiaPn9WrRoaStvExISbZBcWFhgK37NAlKHU0FBgV577WV73RwD9RGImtYLZbKzQzdMN8eneeyamCC77GcOAADCFa5ulbfEb8dc27vL021FyH6r7QJ9NHnwSerXrlMYZgsAaGhu5wGhq8+nhVvWa0H6Sm3K22jbCzh+Dl19ufv/7u7cNkHRUaEXRUZlhKwIqcRXooLSwnrYT/X9P4p8xfXyOP7AvjeOVSksKVRpwFfp+TVG8+Z9q127dpYHixUD1jLJycm64YabdMcdf7SB6rffztLYsRPstmnTPrFfJ078RaWAtUy/fv100UUX67//fbHWc5o8+SJ9841pG7BEH374rsaPnxiyj+uBTB9TE8aZ0/pvvvm2kGHboEFH6Oyzz9Nbb/3PPoYJ9Uw4euDp8GXPrzomMC0LWMuY0/89nmhbqWrCw4oBa8U5lAXcJuxt3bq1/d5U1Zp9+v2BSgFrRUceOaz8ek5OtuqbqZI9MMz0+Xz2sUyoawJWEx4b559/oVJT29T5MStW4+7ZkxPyNqb6+KSTag50//vf1yr1jAUAAOEJV8v4dnVUoOM6OaL2tV+Sz62u7kG66KiT1Cll33sgAEDzqXQ9pnsfezG8pSVasGW9FqavVF5cC+1tFad2KfH69RkDaRVQS4SsQCNiFnoqqwA89tjjq7zd8cefYG9jQjhzHxNCbtmyyVabGiecUHX18EknnXhQIWtZ24ArrrjYhpX//Oe9euWVN2o8Nb7suQwdOqzavp7jx59kQ1bTv9UsjGUWuaqoffsO9hT9mlS1+JR5bBNGVxX2mVYEZUpKfv6DQ7JVodVVhpo2AsuXL6kUfta3Sy+dXKvb/eIXp+iaa35XL49pqoJD9XsFAACN27Y92Xp94Rdat6iVvFXVEwRcKt3RVVHttqhf3FG6aMSJapWQcJhnCgBojDzuKB3fo5+9GCkp8XbdD5/Pr6ys/HBPLyIQsgKNyM6dO+xX0yrAnPJfFbPN3Mb0GTVVhQeuLN+5c9cq79u9e4+DnleXLt1s24AnnjBtA9L11FOP2urU6p/LvoW3unXrVu3tunXb3+ah7LlU1LLlvpUSa2JO4Q+lrII2oYo/IGoKEk0LgUWLFmrNmlXaunWrtm3bahcX2717V6XbVVxwqyGZn72p2DXtEUyl7qRJp2jIkCPrbf9lC4wZph1CKKYq+J13Pq63xwQAAIcuOz9PL/7widaXLJbD5ZOvxSBpd+hT/lOSovWLwSdq5KB2ivPEHPa5AgDQlBGyIqQoV5Ti3HVfxCfKVf0hFuOKrpfHcTqq7/sYGxVbqSereX6NUX7+vk+HzKJVNYmJ2fe6FRTsa7ewZ8+eCtuqftN8MAtXVXTBBfvaBpjFkN5//x3bI7Xi6fIHMotb1ea5VJxrqD6fpt1AbTTEolNfffWF/vOfB8t7s1YMZrt27WarZz/7bKoayttvf2QreQ8nEyKX6dCh42F9bAAAUHuFXq9e+mG6luXPl9xeOX7+fN7dYYN8u837B2elcPW047pp5OD2inLTLx0AgIZAyIqQzKJQh2NhqGuO2LcoUUO7b9TdigRlgaRZSKkmZYFkbGxMrcLKMoWFh9YD11SE3nlnxbYBf9PLL79R7XPJy9tb43OpONeGCEoPlQmU//KXO2yFqqmmHTNmnPr27a+uXburR4+etoXB1q1pDRqyhsOKFcvKg2RTKQsAABoXs1DJ/36cqflZsxSIKgz6i84ZUyBX623y7e5EuAoAwGFEyAo0ImUru6elbbE9PqtqGWBOYTe3qXifTp32nxa2desW9e69r3n1gTZv3rdQ0qEwbQOuuupaPfnko9q2LV1PP/1Ytc9l3bq92rRpU7X73LRpQ6X7NBZPPfW4DVjbt++o559/OWQ7ArNQVlNins+CBd/b66YFQVUtFgAAwOFn+td/vOx7fbntC/k8uVI1J2bFtN2hc4dNIFwFAOAw4v+4QCMyZMi+VezNglbffTe3ytvNnTvHVpMagwYdYb9269ZDyckp5durMnPmzDrN8YILLtbAgYPt9ffee7u88rGq57J48cJqw8ivv/6yvHJy4MB9zyXczHxNUG2MHTu+yn6vCxfuCyTL/vCJdK+//oq83n2Lf51xxjnhng4AAPjZ3A2rdMv0BzVj93v7AtaqlERrSMwY3f+LP2jskR0JWAEAOIz4vy7QiIwcOVqtWrW21x9//GHl5ga/id6zJ8cuQGWY09hHjRpTfjr/aaedaa/PmPFZyPAzLS1NU6a8Uqc5muraO+/8izyeaFvpaRaBCuX008+2X01o9+9//ytkCGnm+MEH79jrxx03Uq1b73vu4VaxgrhipW1F69at1auvvlz+fWlpVcv4RoaZM7/UG2+8aq/36zdAJ574i3BPCQCAZm/j7gz9efozem3Ti/JGV+4RX4nPrT7uY/TP0XfqmuNPVWwte9oDAID6Q7sAoAGZasiPP/6gxtuZylDT5zMqKko333yr/vSnW207gGuuuVxXXfWb8gWmFi/+Uc8++6TS0/ctTnTHHXdX6sV6ySWXa9q0T7Rr107dfPP1uvrq63TCCWNsaDhnzhf697//rb1795bf3lSPHgqz6NOvf32Nnnqq6nYBvXr11nnnXaB33nlTX331uXJz9+iyy65Uz5697AJfM2d+pZdeel4lJSVKTEzSLbfcrsbC9Fs1/UhXrlyuefO+1SOPPKizzjpXycnJ2rlzpw0k33zzNVtxXJs+uOFmWk8cOD8TfpueuevXr9UXX8ywz2lf/9mWuuee/zvkYwMAANRdbmGhnpv/sdaX/ihHVNVnywT8TnV2DtKVx5yutkktDuscAQBAZYSsQANaunSJvdTk97+/2Yasxpgx43XbbX+21Z9mYaW//vVPQbc3C0T9v//3J40ceUKl8fj4BN1//yO66abr7CnvDz98v72UMdWukydfoLfeetN+X1XP19q48MJL9M03X1fZLsC4/vqbbJj30Ufv216fZf0+KzIr2N9777/Utm07NSa33HKbbrjhN3bhrnfeecNeDmQqh81z2rFju60SbqxMZbO51KRXrz7629/+qY4d9/f3BQAAh0+p36c3Fs7UvKxvpKgiOao47zAQkFJ9vXXFUWeoe+u2h3uaAAAgBEJWoBE6/fSzdNRRw/X22//TDz/MV0bGDhuImkWYTLB6xhlnVxlKmgWvpkx5W6+99rK+/XaWMjIyFB0drWHDjtJvf/tblZb6ykNWc8p/XdsGXHnlxeV9PA/kdrt1661/0kknnawPPnhXS5YsVnZ2lhISEtW5cxdNnPgLTZp0quLi4tTYmFPmX3zxVU2Z8l8bpGZm7rbPx7RzMFWuZ555jv0Z3XffvZo69UPNnTvbLkhmbhMJzM/PhPVt2rRVnz79bO/Z448/wQbxAADg8Fu3dY9e+2K1drT+Vs64/WfLHCjB20kXDzpDR3TqdljnBwAAqucImPNDEVF27dp/ujdQWykp8XK5nJo58xtde+01duzdd6c2ugpSINRx6/P5lZWVH+7pADXimEWk4ZgNv9x8r97+ep2+XbbDfu9M2q3ofguCbucqbqHTu52sE/sfpeaO4xaRhmMWkag5HLepqYn1ur/IKLkCUCv/+tc/FB8fb6sSBw06IuRtli/fd3p/bGycUlPbHOYZAgAAwPD7A/p6Ubren7VBBcWl+8dzW8uXnSpX8q59AyXRGt7yBF06ZoLcdWj1BAAAGhYhK9CEpKVttotjrVq1Qo8//mzQ9qysLL3xxr7eosOHj+DUcAAAgDBYn75HU2as1paMvJDbS9L6yZmUpW7uwbp61JlKjo8/7HMEAAAHh5AVaEJM71MTsprLXXfdrgsuuEgdO3a2izd9991aPfnkk9q5c6ftxXrttb8L93QBAACalW17svXM/He0Ld0lX0bVPVWHd+uu048apU6tkg/r/AAAwKEjZAWaELPa/U8//ajp0z/T119/YS8HSkxM1J/+dI+6deseljkCAAA0N6V+n175/gstzJ0luUsU1cklX1Y7qSSm0u06to7XJSf1Ud8uhKsAAEQaQlagCTGn/991170aN+5EffLJh1qxYrn27MlRXFy8OnTooPHjx+m8886Xx1O/zZ0BAAAQ2rL0zXpxyVsqjt5V/teXw+VTVJfVKlk/xH4f7XHpzJHdNXF4J7ldtHMCACASEbICTdCoUaPtpbmtDAgAANBYFJV49fTcj7Sm5Ac5ogNB292ttsu3s5OGd+qvC8b3VnJidFjmCQAA6gchKwAAAADUo9nrVujtde/J58mVo4rCVKc3Ub+c0FcT+g063NMDAACRGLKuXr1azz//vObPn29XNm/ZsqUGDRqkiy66SKNHV660Oxhbt27Vc889pzlz5igjI0MJCQnq27evzj//fJ122mnV3jc3N1evvPKKPv/8c23evFkOh0OdOnXSuHHjdPHFF6tt27YN9tgAAAAAmqbs/Hw9Pu9tbXeskMMT+jYBv1P9o4/R1SecqpioKm4EAAAijiMQCASfu1JPvvzyS914440qKSkJuf3SSy/Vn//854Pe75IlS3TFFVcoPz/0Kc8nnXSSHn74YbndwRny2rVrddVVV2nHjh0h75uUlKQHH3xQY8aMqffHri+7du1tsH2j6aJdACIRxy0iDccsIg3HbP2Zuux7TUv/RIGowipvE+Ntq2uOvFB923Y8rHNrajhuEWk4ZhGJmsNxm5pav+vVNFhX9RUrVujmm2+2AevgwYM1ZcoUfffdd3rnnXc0ceJEexsz9tprrx3Ufk04es0119iQs1u3bnrmmWc0b948TZ06VZMnT7a3mTFjhh566KGg++bl5enaa6+1+zDVp7fffrumTZumWbNm6T//+Y+6dOliq1z/8Ic/aOPGjfX62AAAAACanuz8PP1lxnP6bOc7VQespVE6NvEXeuCkmwhYAQBoohosZDWhZVFRkbp27aqXX35ZI0aMUHJysg1cH3/8cU2aNMne7tFHH7XhZ209++yzys7OthWnJqQdO3asUlJS1Lt3b91777268sor7e3MNnNaf0VvvPGG0tPTbXsAU236q1/9St27d7ftAcx8XnrpJcXHx6ugoED//e9/6/WxAQAAADQt01f+qLvmPKDd7rVV3qZlSXf9acQtuvToCXI6G+zPLwAAEGYN8n/59evXa+bMmfa6qRw1wWVFJuQ0VaTmTUZOTo7tjVobpsrUVMKWtRpo06ZN0G2uv/56G4KaCtoPPvig0rayxzFBb6h+sB07dtTw4cPL2wLU52MDAAAAaBoKi0t07xcv6aPtb1RZveooidXJbc7VP37xW3VomXLY5wgAAJpAyDp79uzyMNUsJhVK+/bt1b9/f3v9iy++qNV+zeJZxcXF9vqECRNC3sYEuscdd1zI/ZoK048//lh///vfa3ysA3uq1vWxAQAAAES+NWk5uue/C7Q1c0/I7WbFi/b+gfrH6Ft12qBjDvv8AABAEwpZV65cab926NDBnk5flQEDBtivy5cvP6j9mgC0X79+Vd6uLLxds2aNvF5v+bjH41GfPn3Ut2/fkPcztzc9Vo2RI0fW62MDAAAAiFzeEp/e+HKt/vXaj9qZU6iSLf3kL46pdBuHN07ndbpYf554uVrEVj6bDwAANG2VyzXriel7anTq1Kna25kQtmxBqdLS0qDq0ar2265dO7lcrhr36/P57L7NglahBAIB22N127Ztmj59ul5//XUbjJog9qqrrmrQxwYAAAAQGdJ25umZj5Zr2+4Kqyv7olSycZCi+y2w37b19dONYy4gXAUAoJlqkJDVBJdGixYtqr1dYmJiedhpep5WV/V6KPs19uwJfRqPYRanmjhxYqWxk08+Wffcc0+lfTTEYwMAAABo3MzfKV8s2Kq3Z65TqS8QtN2f21ruXX118uChmjRgWFjmCAAAmnDIWta7NDo6utrbxcTsP72mNqfWH8p+y+4TSll1akWml2pUVJT+8pe/KCEhocEeuy6Sk+Nsv1vgYDidjvKvKSlUWCAycNwi0nDMItJwzFZty+7deuizj7R5aWqVt5kwvLOuPH2S4mOjDuvcmjuOW0QajllEIo7bRhKyVnc6fWPar+nNahbpatmypdLS0vTyyy/rzTff1EcffaQNGzbojTfesIFrQzx2XbjdjWcuiDwmoHe5COkRWThuEWk4ZhFpOGYre+O7WXpv/btSrFeuVkfIl7mvJViZ5MRoXT95qEYMaBe2OYLjFpGHYxaRiOM2zCFrbGxsrapTi4qKyq/XVCFacb81VYhW3G/FytIDJScnl1/v2bOn/va3v9mWBU899ZSWLVum999/X5MnT26Qx66L0lIflaw4aObTJ3PcmNPe/P7g092AxojjFpGGYxaRhmO2sr1Fhbrnk5eUHlhW/pdSVNcV8u9tqYA3zn5/zMB2+t15Q5QU75HP5w/vhJspjltEGo5ZRKLmcNy6XM7GH7KW9SXdu3dvtbczfVjLqkRr6nVqJCUl2a95eXm12u+BQWpt/Pa3v9Urr7yi/Px8ffnll+Uh6+F47NrKzi5okP2iaTPl/ebTJ/OPY1ZWhUUbgEaM4xaRhmMWkYZjdr/FaRv04vLX5fPsfz9vONyliuq5RFp7rC6c2FdjhnRQaXGJsopLwjbX5o7jFpGGYxaRqDkct6mplddjqqv6jWx/1r17d/t127Zt1d5u+/bt9mvbtm3ldNY8lW7dupXfzyTpNe3X7XYrNbXqHkqhmIraXr16lS+MdTgfGwAAAMDh98r3X+jZ1c8GBaxloj3SzRcP1NihHTmjDAAAHL6QtU+fPvar6XNaXeXnihUr7Nf+/fsf1H5NG4J169bVuF8Tlno8nvIK0+uvv15nnnmmPvzww1qd8l+xhUFdHhsAAABA42wPcNeMZzU/b4YcztCn/nfSEbpvwh/Vp33bwz4/AADQzEPWMWPG2K8+n08zZ86ssuJz5cqV9voJJ5xQq/2OGDGivDfqV199FfI2BQUF+u6774L2a1oYzJ8/X6tWrdLUqVOrfIwdO3aUh6iDBg2ql8cGAAAA0LgsTd+sP818SFnuKgooSqJ1ersLdMf4SxRL8QQAAAhHyNq5c2cNGzbMXn/ssceCerOa0+3vu+8++f1+27fUVJfWRnx8vE488UR7/cUXXwzZjsA8nqlajYqK0iWXXFI+bk7rOfXUU+31WbNmad68eUH3LS0t1V//+lcbDpvbn3/++fXy2AAAAAAaj/8t+FpPrXi6yvYA8d6OuuvYmzVpwL6/aQAAAMISshp33HGH7bO6adMmXXTRRZozZ46ysrK0fPly3XDDDZo2bZq9nbkeF7dvpc4ykyZNspdbb701aL8333yzvX1OTo4uvvhiTZ8+3e53/fr1uvvuu20Aalx66aVq165dpfuadgEpKSnlC1w9/fTT9n7m/t9++60uu+wyff3113b7FVdcocGDB9fbYwMAAAAIrwJvkf76+Quak/uZHC5f0PZAwKEBnuN130k3qF2LhlnEFgAANE2OQHWrONXRe++9p7vuustWiIbyq1/9SrfffnvQeN++fctP0Z8yZUrQ9tmzZ9twtrCwMOR+TUD78MMPh1xMy/RMNQGraQtQFROw3nbbbSHvX5fHri+7dlWuDAZqvzKgUz6fv8muDIimh+MWkYZjFpGmOR2zq3Zs1VOLXlFpdE7oG5TEaHKP8zWmd+VCCzQ+zem4RdPAMYtI1ByO29TUxHrdn1sN6JxzztHAgQP1wgsv2H6omZmZthLU9Do11a0TJ048pP2afqeffPKJnn32WVshm5GRYReZ6tevn84991z7uFWt+jlgwAB9/PHHeu211/T5559r48aNNgROTU3V0UcfbStUjzjiiAZ5bAAAAACH39Rl3+uzbR9K0SUht8d62+uPx11B9SoAAGiclaxoGFSy4lA0h0+h0PRw3CLScMwi0jT1Y9b8qTN17iZ9kvG2XC13h9gu9Y06Rr8bdZbcTldY5oiD19SPWzQ9HLOIRM3huE2NpEpWAAAAAAiHwuJSvfjJSi1cs0tyHaHogfPkjKnQ8qskWud0PVcT+w0N5zQBAEATQcgKAAAAoEnZnpmvx99bqu2ZBfsGfB551x6l6AHf2QWvoovb6ObjrlSnlvsWxQUAAKgrQlYAAAAATcbitbv13NTlKiz2VRoPFCaqZOMgde/p0x9P/KU87qiwzREAADQ9hKwAAAAAIp4/ENDH327Sh3M2htzucTt1xcgJOnZgu8M+NwAA0PQRsgIAAACIaLmFhfq/b17U7o2tzTIWQdtbt4jR9ecMVpe29bvABQAAQBlCVgAAAAARa+PuDD3ywwsqjc6Rp2e6ilccq0BRQvn2gd2Sde2Zg5QQS3sAAADQcAhZAQAAAESkb9ev1OvrXpeii+33DnepPH1+tEGrSj06+ZguOmdMD7mcznBPFQAANHGErAAAAAAizhsLv9Gs7M/kiPJXGnfGFCim51Jd0e8yjejfNmzzAwAAzQshKwAAAICIUer36T+z3tEG/0I5QhWolsToiqFnakR3AlYAAHD4ELICAAAAiAh5RUX6xzcvKDdqc8jtUcUpuvmYq9QlxSyABQAAcPgQsgIAAABo9Lbtydb9c59VSXRmyO0tSrrpznFXKiEm5rDPDQAAgJAVAAAAQKO2ckeanlj8ogLR+SG393QdrT+MPVdOFrgCAABhQsgKAAAAoNGatW653tzwuuQpCdoW8Ds1rtWpOv/IE8IyNwAAgDKErAAAAAAapXcWzdFXmVPlcPuDN5ZE65LeF+v4Hv3CMTUAAIBKCFkBAAAANDpPffuxlhbNliNEBwCnN1G/P/LX6t22QzimBgAAEISQFQAAAECj4Q8E9K+vXtdWx09yOIK3Rxen6o4TrlVqQlI4pgcAABASISsAAACARqGk1K8XPlmh9ekeefo45HAGKm1vWdJdf57wa8V6PGGbIwAAQCiErAAAAADCrrC4VE+8v1QrNmVLaiXv+iHy9FpcXs3a1TFUN594gdxOV7inCgAAEISQFQAAAEBY5RZ49Z+3f9LG7XvLx/zZ7VSyeYCiuq7UsPhx+vWxk8I6RwAAgOoQsgIAAAAIm917CvXQmz8pI6sgaJsrq5suPO54je7fJyxzAwAAqC1CVgAAAABhkb4rTw+9uVg5ed6gbfExbt143hD16tQiLHMDAAA4GISsAAAAAA67WWuX683l01RYcISpWa20LTkxWjdPHqKOqQlhmx8AAMDBcB7UrQEAAACgjqat+FFvbHpVSsqQp+diyeEv39YuJU53XHIUASsAAIgohKwAAAAADpsPlszTR9velMPls9+7kncpqttySQF1b59oA9bWLWLDPU0AAICDQrsAAAAAAIfFGwu/0aycT+VwBiqNu1PT1S66o/7fKWMU4+FPFAAAEHl4BwMAAACgwb08/3PNz/tcDkfwtqSSrrrj1DMUE8WfJwAAIDLxLgYAAABAg3r626laWjwrZMDaqrS37p54pdyuyotfAQAARBJCVgAAAAAN5j+z3tWa0vkht7XzD9AdEy+V20nACgAAIhshKwAAAIB65/f79dA3b2pTYFHI7V0dQ/XH8RfK6WQtXgAAEPkIWQEAAADUe8D64DdvaHNgccjtfdzH6MbR5x72eQEAADQUQlYAAAAA9Rqw3j/zf0rTTyG3D44erd+MPO2wzwsAAKAhEbICAAAAqLeA9V8zX9dWLQnaFghIIxIm6opjTgrL3AAAABoSISsAAACABg9Yj0/6hS45ekJY5gYAANDQCFkBAAAA1EkgENCjX3+qrY7QAevIFpN08fDxYZkbAADA4cBSngAAAADqFLC+8eU6LVkQLV9O6wO2SaNanEzACgAAmjxCVgAAAACHHLC++dU6fb4gTQq45F17ZHnQagLWE1qeoouGjwv3NAEAABocISsAAACAQwpY35u1QTN+SKswWBa0pmpM8qn65bCx4ZwiAADAYUNPVgAAAAAH7eO5m/TJvM1B40659at+l+qYAe3CMi8AAIBwIGQFAAAAcFA+m79ZH8zeGDTucEjXnjlQR/drE5Z5AQAAhAshKwAAAIBae3bup/p+Ub6kVpXGHZKuOm0AASsAAGiW6MkKAAAAoFZe/G66fiqaKU/fhXK22FVp2xUn99NxA2kRAAAAmidCVgAAAAA1mvLDl1qQ/6W97nD65en9o5wtM+z3l5zURycM6RDmGQIAAIQPISsAAACAar2zaI7m5U63PVfLOJwBeXot1mljW2n8UZ3COT0AAICwI2QFAAAAUKVpK37UV5kfVwpYy/T1jNA5xw4Jx7QAAAAaFUJWAAAAACHNWb9CH6W/batWD9TdcZRuHH1uWOYFAADQ2BCyAgAAAAiyOG2D/rf+NTlcvqBtHQODdfOYyWGZFwAAQGNEyAoAAACgkjUZ2/Tcipckd0nQttalvXX7uIvldPKnBAAAQBneGQEAAAAotzVrtx5d9JwUVRS0LdHbRX8afwUBKwAAwAF4dwQAAADAyszL1f3zn1HAkx+0Laa4rf4y/hp53FFhmRsAAEBjRsgKAAAAQHlFRfr77Kfli94TtC2qOEV3j/2NYj2esMwNAACgsSNkBQAAAJo5b2mp7p35rLzRu4O2Ob2JumPkb9UiNj4scwMAAIgEhKwAAABAM+b3+3X7B08rz7M1aJvDG6c/Hv0btU1qEZa5AQAARApCVgAAAKAZe37GXG3zrwreUOrR74b+Wl1bpYZjWgAAABGFkBUAAABopr78YYs+/jxT3rVHKeBzlY+b65f1vkz923UO6/wAAAAiBSErAAAA0AwtWZ+pJ95dYq/796SqeOUIBUo8CvgdOr3DuTqme59wTxEAACBiuMM9AQAAAACH18btuXryg6Xy+wPlY4GCFipecaxOPCFJJw8cHtb5AQAARBpCVgAAAKAZycgu0CNv/yRviT9o27nHDdYpw7uGZV4AAACRjHYBAAAAQDOxt8Crh9/6SXsLSoK2TTiqk04+pktY5gUAABDpCFkBAACAZqDQ69U/Z7ylnTn5QduOG9xev5zYWw6HIyxzAwAAiHSErAAAAEAT5/f79fevX9CepCXy9FkgufZXsg7s0Uo3XXiknE4CVgAAgENFyAoAAAA0cQ/Pels5URvtdVeLLEUP+E6O6AJ1apOgP/9qhDxRrnBPEQAAIKIRsgIAAABN2JQfvtQG/8JKY87YfMX0XaQ7rxiuhDhP2OYGAADQVBCyAgAAAE3Ul6t/0rw9M4LGA36nLuhzjjq0TgzLvAAAAJoaQlYAAACgCVqWvlnvbX5LDmcgaNvYlFM0utfAsMwLAACgKSJkBQAAAJqYHXuy9fTSlyT3/gWuyvR1H6vJR40Oy7wAAACaKkJWAAAAoAkpKvHq/rnPK+DJD9rWurS3rh91VljmBQAA0JQRsgIAAABNhN/v1z9nvqLi6F1B22KK2+rOcVfI6eRPAAAAgPrGOywAAACgiXh23qfa7VoTNO70JurOE65WdFRUWOYFAADQ1BGyAgAAAE3AZ8sXaknRrOANpVG6/sgr1SohKRzTAgAAaBYIWQEAAIAIt3zbFk1Nf08OR+XxgN+hc7pOVt+2HcM1NQAAgGaBkBUAAACIYJl5uXp6yUuSuyRo2/CEcZrQd0hY5gUAANCcELICAAAAEcpbWqJ/znlBfk9e0LZ2/gG68thJYZkXAABAc0PICgAAAESot79Zp7w8f9B4THFb3Tb24rDMCQAAoDkiZAUAAAAi0Jwl2/XlD9vlXTdUJek9y8cd3njdNvIqedxRYZ0fAABAc+IO9wQAAAAAHJyN23P1yvTVP3/nUGl6bwUKE+TpukrXDr5CbZJahHmGAAAAzQshKwAAABBBcvO9euL9pSr1VW4T4M9ur1+Pm6DBHduFbW4AAADNFe0CAAAAgAjh8/v19IfLlJVbHLTtvLE9dVRvAlYAAIBwIGQFAAAAIsTbX6/Xqi05QeMj+rfRpBFdwjInAAAA0C4AAAAAiAhvLPxGX6xLl1S5WrVTarx+dXJ/ORyOsM0NAACguaOSFQAAAGjkfti0VrOyP1N078VydzILXgXseFy0W9efM1jRHle4pwgAANCsEbICAAAAjVhG7h69vOo1OZz7FrqK6rBRnr4L5HB5de2ZA9UmOS7cUwQAAGj2aBcAAAAANFKlPp8emPuCAp6CSuOuFpkadIxXg3u0CtvcAAAAsB+VrAAAAEAj9fCst1Xo2RE0nujtrOtGnRaWOQEAACAYISsAAADQCE1d9r02BX4MGnd6E3XbCVfK6eStPAAAQGPBOzMAAACgkVm3c7s+2/Zh0HjA59a1gy9Tcnx8WOYFAACA0AhZAQAAgEak0OvV4wtfltwlQdsmpJ6iQR27hmVeAAAAqBohKwAAANCIPDjrdZVEZwWNdwwM1rlDR4VlTgAAAKgeISsAAADQSLyx8BvtcK4IGvcUt9Itoy8My5wAAABQM0JWAAAAoBFYsnWTZmVNC95Q6tEfRlyp6KiocEwLAAAAtUDICgAAAIRZbmGhnls2RQ6Xr9J4ICCd3ukcdW2VGra5AQAAoGaErAAAAEAY+f1+3T/7Zfk9e4O29XYfrUkDjgrLvAAAAFB7hKwAAABAGE354UtluzcEjcd62+uGE84Jy5wAAABwcAhZAQAAgDBJ25Wr+ZnfBo07SmL1x+OukNvpCsu8AAAAcHAIWQEAAIAw8Jb49OxHK1W04hj5clqXjwf8Dl3Q8wK1a5Ec1vkBAACg9ghZAQAAgDB448u1St+VL5VGy7tmmEq29LEB68CY43VCrwHhnh4AAAAOgvtgbgwAAACg7n5YtVMzF2+rMOJQ6Y4e6pnUW9eOHxXGmQEAAOBQELICAAAAh9HOnEK99NnKoPGWCR5dN2kEfVgBAAAiUIOHrKtXr9bzzz+v+fPnKysrSy1bttSgQYN00UUXafTo0Ye8361bt+q5557TnDlzlJGRoYSEBPXt21fnn3++TjvttGrvm5eXpzfffFOff/651q9fr8LCQiUlJWnAgAE666yzdMopp8jpDN1J4aWXXtI///nPGud35ZVX6rbbbjvk5wcAAICmp9Tn1zMfLlNhsa/SuMMhXXvGQCXGecI2NwAAADTSkPXLL7/UjTfeqJKSkvKxXbt26euvv7aXSy+9VH/+858Per9LlizRFVdcofz8/PKx7Oxsfffdd/Yyffp0Pfzww3K7g5+eCVWvueYaG9JWlJmZqdmzZ9vL+++/r8cff1yxsbFB91+2bNlBzxcAAAAw3vxmpTZu3xs0fsbI7urbhYWuAAAAIlWDLXy1YsUK3XzzzTZgHTx4sKZMmWID0HfeeUcTJ060tzFjr7322kHtd8eOHTYkNQFrt27d9Mwzz2jevHmaOnWqJk+ebG8zY8YMPfTQQ0H3LSgo0NVXX20D1piYGN1yyy02kJ07d66dR9m8THXsnXfeWeXzMswcfvzxxyovN91000G/ZgAAAGi6pi6br29LX5ezZUal8X5dWur047uFbV4AAABoxCHrf/7zHxUVFalr1656+eWXNWLECCUnJ9vA1VSJTpo0yd7u0Ucftafv19azzz5rq1bN6f0mpB07dqxSUlLUu3dv3XvvvfY0fcNsO7Ba1QSp6enp9vqTTz5pg1IT1LZq1UrDhw/XE088ocsvv9xu//TTT7V06dKgkHbjxo32+pFHHqn4+PgqLx4Pp3oBAABgn61Zu/XZto/lcJcous8iRXVZITn8SoiN0tWnD5TT6Qj3FAEAANDYQlZzSv7MmTPt9WuvvdaGjhU5HA7dfvvttu9pTk6O7Y1aG7m5ubYS1jCtBtq0aRN0m+uvv94GsKaC9oMPPqi0zVStGibwHTlyZMjHuOGGG8rbDHzzzTeVtq1cuVJ+v99eN2ExAAAAUJNSv0+PfD9FcnvLx9zttih6wHe64tQ+Sk6MDuv8AAAA0EhDVtPXtCxMHTduXMjbtG/fXv3797fXv/jii1rt1yyeVVxcbK9PmDAh5G1MoHvccceF3K8JdE2wO2TIkCofIzEx0VbcGjt37gzZKsDMPTU1tVZzBgAAQPP2/LzPVOjZHjTeJb6rjurVNixzAgAAQAQsfGUqPo0OHTrYU/mrMmDAAC1fvtxeDma/ptK0X79+Vd7OhLemanXNmjXyer3lp+6b0LW0tLTSQlwHMq0LTDsCw1TEVlQ2z0GDBtl2Au+++65tKWDaCLRr106jR4/WVVddZZ83AAAA8OOW9VpSOEeOA0ob3MUtddPEC8I1LQAAAERCJWtZ39NOnTpVe7uyMNIsZmXCz9ru1wSaLperxv36fD6774pMQBsbG1vlfd9+++3yuQwbNixkyGpaIZiFrcwCWXv27LGhbVpamu35esopp+jLL7+s8bkAAACgacsrKtJLK/4nh3Nfu6kyAb9TVx1xsWKi6OEPAADQVDRIJWtZJWiLFi2qvZ05Nd8IBAK232p1Va+Hsl/DhKC1tXnzZrsol2EW7Bo1alT5NtOmYMOGDfa6CVXNwl2XXXaZunfvbuc+Y8YMPfXUU7aq9cYbb7SBa3VtCeoiOTnOtmIADkbZghrma0pK5T7JQGPFcYtIwzGLiv753hT5PLlB48enTNCYwQPUGHDMIhJx3CLScMwiEnHcNpKQtaxvanR09U38Y2Jiyq+b0/obYr9l96nJ7t277SJdpl2ACTDvuusuRUVFlW/ftm2b2rZtaytjr7vuOrvAVhkTDl9zzTV2Qa1LLrnEhrB/+9vfbDuBhuB2V13FC9TEHN8uFyE9IgvHLSINxyzemj9HW/1Lg8aTSjvrxhPPsusENCYcs4hEHLeINByziEQct2EOWas7lb8x7jcjI0NXXnmlNm7caL83AeoJJ5xQ6TamYvWrr76yAWrF8LWioUOH6oILLtCrr76qZcuWadWqVdX2jj1UpaU+Kllx0MynT+a4MZXjfn8g3NMBaoXjFpGGYxbGlszdemfdO8HvtEuj9ZdfXK1AwLS1qtxCIFw4ZhGJOG4RaThmEYmaw3Hrcjkbf8ha1vO0purUoqKi8us1VadW3G9N1akV91uxqjWU9evX6+qrry7v93rFFVdUqlI9UFUBa5kJEybYkNVYsmRJg4Ss2dkF9b5PNH2mvN98+mT+cczKyg/3dIBa4bhFpOGYhd/v1z0znpE8we9XT+t4pmICMY3q2OCYRSTiuEWk4ZhFJGoOx21q6v52o402ZC3ribp3795qb2d6mZZVqNbUZ9VISkqyX80p/bXZr5GcnFzl7ebOnavf//735fM0bQBMP9W6aN++ffn1rKysOu0LAAAAkeXF+dNU4NkWNN4xMEgnDxweljkBAACg4TVIMyhzan1ZH9PqbN++3X41vU5r05eqW7du5fcz5co17dftdis1NTXkbUy/VNNH1QSsJuS95557ahWwVve4hmkncGDlLQAAAJq+FdvT9GP+rKBxV3EL3XTChWGZEwAAACI4ZO3Tp4/9mpaWVm3V6YoVK+zX/v37H9R+TRuCdevW1bjfXr16yePxBG1/7rnndOedd9pANC4uTk8++aQuvLD6N74PPPCAjjvuOB111FHVtiuoOK+yUBgAAABNm7e0RM8ufl0OZ+VeqwG/U1cO+qViQ7wnBQAAQNPRICHrmDFj7Fefz6eZM2dWWW26cuVKe/3ARaaqMmLEiPLqULMIVSgFBQX67rvvqtzva6+9pgcffNBeb9WqlaZMmaKxY8fW+Nim7YA5/b/i/kP5+OOP7VcT3g4bNqxWzwsAAACR7am5H6kkOjNo/IjYURrauUdY5gQAAIAID1k7d+5cHjA+9thjQb1ZzSn39913n10YwISXZ555Zq32Gx8frxNPPNFef/HFF0O2IzCPZ3qymgWqLrnkkkrbzEJU//znP+31lJQUG7gOGjSoVo998sknly96df/994dc1Gvq1Knl4a+pjE1ISKjVvgEAABC51m/P0uqCxUHjMcVtddVxJ4dlTgAAAGgCIatxxx132D6rmzZt0kUXXaQ5c+bYStDly5frhhtu0LRp0+ztzHVT9VnRpEmT7OXWW28N2u/NN99sb5+Tk6OLL75Y06dPt/tdv3697r77bhu+GpdeeqnatWtX6b6m76ppEeBwOHTvvfeqTZs2ys/Pr/JSMUjt2LGjrrzyyvKWAJMnT9Y333yj3bt328c21bG33Xab3d6zZ0/7vAAAANC0lZT69dKna1W07Hj5strs3+Bz6/qjL5Hb6Qrn9AAAAHCYOAI1reRUB++9957uuusulZaWhtz+q1/9SrfffnvQeN++fcvbA5jT+Q80e/ZsG2IWFhaG3K8JaB9++OFKi2ktWLDAhrIH4+yzz7YVt2VM5e1f//pXvfnmm1Xex/SXfeaZZ+xiXg1l167KlcFAbaSkxMvlcsrn8ysrKz/c0wFqheMWkYZjtvl5++t1+mz+lp+/C8jVapuiuq7U8ckTdMnRE9TYccwiEnHcItJwzCISNYfjNjU1sV7351YDOuecczRw4EC98MILmj9/vjIzM20VqjlF31S3Tpw48ZD2a3qtfvLJJ3r22WdthWxGRoZd4Kpfv34699xz7eOaatWKfvrppzo/HxPa/u1vf7OtA/73v/9p0aJFys7Otm0MevfurVNPPVXnn3++3O4GfVkBAADQCKxJy9G08oDVcMiX2VGDWvfVRROHh3FmAAAAaFKVrGgYVLLiUDSHT6HQ9HDcItJwzDYfhcWl+suL32v3nqJK40lxUfrbVccoKc6jSMAxi0jEcYtIwzGLSNQcjtvUeq5kbbCerAAAAEBT9dbX64ICVuPyk/tFTMAKAACA+kPICgAAAByEn9bt1jeLtwWNjxrcXkf2Tg3LnAAAABBehKwAAABALWXm5em51c/K2XJnpfFWSTH65cTeYZsXAAAAwouQFQAAAKilR+e+oUBsjqL7/KioHkskl9eO//rU/oqNZvFTAACA5op3ggAAAEAtfLZ8gXa715R/7269Ta6kTA11naJ+XZPDOjcAAACEF5WsAAAAQA2y8/P0ydaPg8adcunCUUPDMicAAAA0HoSsAAAAQA3+M/dNBaIKg8bP7n62kmJjwzInAAAANB6ErAAAAEA1pq34Ubtcq4PG2/kHaELfIWGZEwAAABoXQlYAAACgCtn5+Zqa9mHQuMMbp9+PPD8scwIAAEDjQ8gKAAAAVOGxKtoEnNntLLWIjQ/LnAAAAND4ELICAAAAIXy+8kdluFYFjbf19deJ/VjsCgAAAPsRsgIAAAAHyC0s1IebPwoad5TE6vcjJ4dlTgAAAGi8CFkBAACAAzw+920FPAVB46d3OVMt42gTAAAAgMoIWQEAAIAKvl2/Ulu1LGi8ja+vftH/qLDMCQAAAI0bISsAAADws+KSEr259l05HAdsKInR74+/IEyzAgAAQGNHyAoAAAD87Ol5H8nnyQ0aP6nDKUqOTwjLnAAAAND4EbICAAAAkpalb9Zq7w9B4y1KuunMwceGZU4AAACIDISsAAAAaPb8gYA+/CZN/pzUyhtKo3T9MReGa1oAAACIEO5wTwAAAAAIt1mLt2n9Fq+kI+VM3iFP15VyeIp1bPI4dWiZEu7pAQAAoJEjZAUAAECzlr23WG/PXFf+vT+7nYpyW6ljnyxdPHZ8WOcGAACAyEC7AAAAADRbgUBAr85YrcJiX6VxjyNaN4w5S04nb5cBAABQM941AgAAoNlauHqXFq3dHTR+1gk91KZlbFjmBAAAgMhDyAoAAIBmqaCoVK99viZovGu7RJ14dKewzAkAAACRiZAVAAAAzdJrsxZpT75Z7Go/p8OhX53cTy7aBAAAAOAg8O4RAAAAzc7cDau0yPW2onoskdz7g9ZJx3RRl7aJYZ0bAAAAIo873BMAAAAADidvaYneXP2eHNGSu/U2uVruUklaH7X09tLpI7uFe3oAAACIQISsAAAAaFZenD9NpdE55d873CXydF+uiW2HKDrKFda5AQAAIDLRLgAAAADNxubMXVpSMDdoPKmkq34xcGhY5gQAAIDIR8gKAACAZuPpBW/K4fJVGgv43PrN8MlhmxMAAAAiHyErAAAAmoWpy+YrN2pL0PgRccera6vUsMwJAAAATQMhKwAAAJq8vUWFmrb1s6Bxd3FL/frYSWGZEwAAAJoOQlYAAAA0eU/Ne18BT0GlsUBAurDvOYpysRYsAAAA6oaQFQAAAE3a4rQN2uT7KWi8fWCAjuvRLyxzAgAAQNNCyAoAAIAmq9Tv0yvL3pXDGai8oSRa1x17XrimBQAAgCaGkBUAAABN1msLvlJx9K6g8dGpE9UqISEscwIAAEDTQ8gKAACAJmln7h59nzMzaDzW207nDz0hLHMCAABA00TICgAAgCbp6e/fk9wllcYCfqeuGjpZTidvgwEAAFB/eHcJAACAJueHTWu1w7EyaLxX1DD1a9cpLHMCAABA00XICgAAgCbF7/fr9ZXvy+GoPO7wxuk3x50ermkBAACgCSNkBQAAQJMyb/kO5aW3V6DEU2n8xI6TFOeJCdu8AAAA0HS5wz0BAAAAoL4UFpfq7Zkb5MvvKF92G0V1XCdX2y2KL2mvMwcfG+7pAQAAoIkiZAUAAECT8eGcjcrN9+77xhelki39FcjsrKvOHxbuqQEAAKAJo10AAAAAmoT0XXn6YsHWoPFJQwapb7uOYZkTAAAAmgdCVgAAAES8QCCg1z5fI38gUGm8VVK0Tj2ua9jmBQAAgOaBkBUAAAAR74dVO7VqS07Q+IUTeis6yhWWOQEAAKD5IGQFAABARNtTWKA3Zq4MGh/YLVlH9UkNy5wAAADQvBCyAgAAIKI9Pe8DFXX/Qq5W6aZxgB1zOR266MQ+cjgc4Z4eAAAAmgFCVgAAAESs5du2aLP/Jzk8Xnl6LpWn/3w54nJ10tGd1b5VfLinBwAAgGaCkBUAAAAR66Ul78nh3L/YlSsxRzF9F+nkYzuHdV4AAABoXghZAQAAEJGmLvteBZ5tQeOjWo9TQmx0WOYEAACA5omQFQAAABGnuKRE07dODxqPLk7VBUeODsucAAAA0HwRsgIAACDi/Pf76fJ79lYaCwSkX/Y/S04nb3EBAABwePEOFAAAABElI3ePlubPCxpv4++jo7v1DsucAAAA0LwRsgIAACCiPPP9e5K7pNJYwOfWNUefE7Y5AQAAoHkjZAUAAEDEWJy2QTscq4LGB8QcrQ4tU8IyJwAAAICQFQAAABHB7/fr1eUfyOEIVBp3eOP162NODdu8AAAAAEJWAAAARISPl3+vQs+OoPEJ7U9UrMcTljkBAAAABiErAAAAGr2iEq++SJ8RNB5T3FZnDj42LHMCAAAAyhCyAgAAoNH77/xp8nvyKo0FAtJFA8+S08lbWgAAAIQX70gBAADQqG3bk61lhd8Fjbf199OwLj3DMicAAACgIkJWAAAANGrPf/++5CqtPOhz6+oRZ4drSgAAAEAlhKwAAABotNIy9mpbdm7Q+IDYY9ShRXJY5gQAAAAciJAVAAAAjdZbM9fLu+EIFa84Rv68FnbM6U3Qr485OdxTAwAAAMq5918FAAAAGo9lGzK1fGOWve7PS1bximPlarVNZx7bXzFRnnBPDwAAAChHyAoAAIBGx+8P6K2v1x0w6lCfhEE6ddDQMM0KAAAACI12AQAAAGh0vl26XVt35Vcac0i6YHwvORzmGgAAANB4ELICAACgUSn2+vT+7A1B48cPaqcubRPDMicAAACgOoSsAAAAaFRm/LBFOXneSmNRbqfOHt0jbHMCAAAAqkPICgAAgEZja06WPtv2sRyegkrjJx3dWSlJMWGbFwAAAFAdFr4CAABAo/HCDx/I0WqropPTVZrRVaXbeioxOk6nHNs13FMDAAAAqkTICgAAgEZhydZNynCutgtcOZwBRbXfJHdqusYmn6/YaN62AgAAoPGiXQAAAAAahVeXfSiHI1BpzOWP1ilDB4ZtTgAAAEBtELICAAAg7L5YtVj5nvSg8fHtJyo6KioscwIAAABqi5AVAAAAYVXq9+njjZ8FjUcXp+rMwceGZU4AAADAwSBkBQAAQFi9/eMslUZnB42f2+c0OZ28XQUAAEDjx7tWAAAAhE2Bt0jfZs4MGm9R0k0je/YPy5wAAACAg0XICgAAgLD57/fTFIgqrDQW8Dt0xdCzwjYnAAAA4GARsgIAACAsMvNytaLgh6Dxzs5B6tO2Q1jmBAAAABwKQlYAAACExQs/fCK5SyoPlkbpqhFnhmtKAAAAwCEhZAUAAMBhtyVrtzaVLgka7x87XKkJSWGZEwAAAHCoCFkBAABw2L208CM5XL7KgyUxuuLok8M1JQAAAOCQEbICAADgsFq5I007HKuDxoe3HKWEmJiwzAkAAACoC0JWAAAAHFZTfvpYDmeg0pjTm6CLh40L25wAAACAuiBkBQAAwGHz/aa12hO1KWh8TNtx8rijwjInAAAAoK4IWQEAAHDYzPohRyXpPRXwucrH3MXJOmfIyLDOCwAAAKgLd53uDQAAANTSqs3ZWrF+r6TeKs3ooqgO6+Vqk6ZTuv1CTief/QMAACByEbICAACgwQUCAb3zzfr9A6XRKtkyQD3cR+oXE48K59QAAACAOqNkAAAAAA3uxzW7tWFbbtD4BaMHh2U+AAAAQH0iZAUAAECD8vn9em9WhSrWnx3dr426tUsKy5wAAACA+kTICgAAgAY1d9kObc8sqDTmdDh09ugeYZsTAAAAUJ8IWQEAANBgirxefTBnQ9D46CHt1S4lLixzAgAAAOobISsAAAAazH+/n6aCzl/L2WKXWf7KjnncTp0+snu4pwYAAADUG3f97QoAAADYb09hvpYVfC9nvFfRfRfKl5uskrS+mjh4iJITo8M9PQAAAKDeUMkKAACABvHyD9Mlt7f8e1dStmL6LtSEo9uFdV4AAABAfSNkBQAAQL3LzMvT6qKFQeO9Y45Ucnx8WOYEAAAANBRCVgAAANS7lxZ8IrlLKg+WenT5sJPDNSUAAAAgcnuyrl69Ws8//7zmz5+vrKwstWzZUoMGDdJFF12k0aNHH/J+t27dqueee05z5sxRRkaGEhIS1LdvX51//vk67bTTqr1vXl6e3nzzTX3++edav369CgsLlZSUpAEDBuiss87SKaecIqfT2SCPDQAA0NRl5O7R+pKf5HBVHh8QdzRVrAAAAGiSHIFAYN8yrw3gyy+/1I033qiSkgOqGH526aWX6s9//vNB73fJkiW64oorlJ+fH3L7SSedpIcfflhud3CGbELVa665xgalVRk1apQef/xxxcbG1utj15ddu/Y22L7RdKWkxMvlcsrn8ysrK/TxCzQ2HLeINByz+9z31WtK00+VB0uidd+YO5UYE/z+CuHDMYtIxHGLSMMxi0jUHI7b1NTEyGgXsGLFCt188802YB08eLCmTJmi7777Tu+8844mTpxob2PGXnvttYPa744dO2xIakLObt266ZlnntG8efM0depUTZ482d5mxowZeuihh4LuW1BQoKuvvtoGrDExMbrllls0ffp0zZ07186jbF6mQvXOO++s18cGAABoDrbmZGmLb1nQ+JDEYwlYAQAA0GQ1WMj6n//8R0VFReratatefvlljRgxQsnJyTZwNVWikyZNsrd79NFH7en7tfXss88qOzvbnt5vQtqxY8cqJSVFvXv31r333qsrr7zS3s5sO7Ba1QSp6enp9vqTTz5pA1MTlrZq1UrDhw/XE088ocsvv9xu//TTT7V06dJ6e2wAAIDm4OWFU+Vw+SqNOUpidenwE8M2JwAAACAiQ1ZzSv7MmTPt9WuvvVbxB/Tecjgcuv32223f05ycHNsbtTZyc3NtJWxZq4E2bdoE3eb666+3IaipoP3ggw8qbTNVq4YJfEeOHBnyMW644YbyU/2/+eabentsAACApm7j7gylB1YEjQ9rOVKxHk9Y5gQAAABEbMg6e/bs8jB13LhxIW/Tvn179e/f317/4osvarVfs3hWcXGxvT5hwoSQtzGB7nHHHRdyvybQNcHukCFDqnyMxMREW3Fr7Ny5s94eGwAAoKl7ZdEncjj9lcYc3jhddFTo94MAAABAU9EgIevKlSvt1w4dOtjT6asyYMAA+3X58uUHtV9TadqvX78qb1cW3q5Zs0Zer7d83ASfpgXA7373uyrva1oXmJYAhqlKra/HBgAAaMrWZGxThmN10PixrU5QdFRUWOYEAAAARHTIWtb3tFOnTtXezoSwZQtKlZaW1nq/7dq1k8vlqnG/Pp/P7rsiE5LGxla96MLbb79dPpdhw4bV62MDAAA0Va/+ZKpYA5XGnN5EXXjU2LDNCQAAAIjokLWsErRFixbV3s6cmm8EAgHb87S+92vs2bNHtbV582a7KJdhFuwaNWrUYXtsAACASLV82xbtdq0NGh/ddqzc1Xw4DQAAADQV+1Z4qmdlvUujo6OrvV1MTEz59dqcWn8o+y27T012795tF+ky7QJML9m77rpLURVObWvIxz5Yyclxdo7AwXA6HeVfU1IqL0YHNFYct4g0zfWYfePzT+U4IEt1e1vo12NPJGRt5JrrMYvIxnGLSMMxi0jEcdtIQtbqTqdvjPvNyMjQlVdeqY0bN9rvr7/+ep1wwgmH5bEPhdvdeOaCyGMCepeLkB6RheMWkaY5HbPfr1+rTOcGHfhsT+05SdEeerFGiuZ0zKLp4LhFpOGYRSTiuA1zyFrW87Sm6tSioqLy6zVViFbcb00VohX3W7GyNJT169fr6quvLu+5esUVV9iQ9XA89qEqLfVRyYqDZj59MseNac/h91fumQc0Vhy3iDTN8Zj9Yk6mSrYeIXfH9XLG5tuxKG+KJh89Sj6fP9zTQw2a4zGLyMdxi0jDMYtI1ByOW5fL2fhD1rK+pHv37q32dmV9WE2VaE29To2kpCT71ZzSX5v9GsnJyVXebu7cufr9739fPs/rrrtON95442F57LrIzi5okP2iaTPl/ebTJ/OPY1bWvj+CgcaO4xaRprkds1t35em7JRkKqIN8We3lStkhd8d1OqnbBOXkFIZ7eqiF5nbMomnguEWk4ZhFJGoOx21q6v51lRrtwlfdu3e3X7dt21bt7bZv326/tm3bVk5nzVPp1q1b+f1Mkl7Tft1ut1JTU0Pe5t1339U111xjA1YT8t5zzz1VBqz1/dgAAABNwcffbtL+d0UOG7R2zDpZk/oPC+u8AAAAgMOtQULWPn362K9paWnVVn6uWLHCfu3fv/9B7de0IVi3bl2N++3Vq5c8Hk/Q9ueee0533nmnSkpKFBcXpyeffFIXXnjhYXlsAACApiB9V54WrNoZNH7WqJ61+vAcAAAAaEoa5B3wmDFj7Fefz6eZM2dWWfG5cuVKe/3ARaaqMmLEiPLeqF999VXI2xQUFOi7776rcr+vvfaaHnzwQXu9VatWmjJlisaOHXtYHhsAAKCp+HhuxSrWfXp2SNLAbilhmhEAAADQxELWzp07a9iwfaeJPfbYY0G9Wc3p9vfdd5/8fr/tW3rmmWfWar/x8fE68cQT7fUXX3wxZDsC83imL2pUVJQuueSSStuWLFmif/7zn/Z6SkqKDVwHDRp0WB4bAACgqUjfna8fVgZXsZ45qjuLcwIAAKBZarBzue644w57qtimTZt00UUXac6cOcrKytLy5ct1ww03aNq0afZ25ro5Zb+iSZMm2cutt94atN+bb77Z3j4nJ0cXX3yxpk+fbve7fv163X333TYANS699FK1a9eu0n1N31XTIsC8+b/33nvVpk0b5efnV3kxrQHq67EBAACaio/nbgiqYu1hqli7U8UKAACA5skRqG4Vpzp67733dNddd6m0tDTk9l/96le6/fbbg8b79u1bfoq+OZ3/QLNnz7bhbGFh6FVrTUD78MMPV+oHtmDBAhuMHoyzzz7bVtzW9bHr265dlSuDgdqvDOiUz+dvsisDounhuEWkaQ7H7JKtm/T0sudVuqObSnd2kfxuO/6H84foiJ6twj09HKTmcMyi6eG4RaThmEUkag7HbWpqYr3ub9+74gZyzjnnaODAgXrhhRc0f/58ZWZm2kpQc4q+qW6dOHHiIe3X9Dv95JNP9Oyzz9oK2YyMDLvIVL9+/XTuuefaxz3wVLWffvqpXp7ToTw2AABAU/Hm8s/k8HgV1WWN3O03qnRHd3V0DNTgHlSxAgAAoPlq0EpWNAwqWXEomsOnUGh6OG4RaZr6Mbs0fbOeWvWEDvw8+eQ25+q0QceEa1qog6Z+zKJp4rhFpOGYRSRqDsdtaj1XsjbcOe0AAABoUt4wVawHBKxRxck6ZcDR4ZoSAAAA0CgQsgIAAKBGy9I3K9u1IWh8QqfxDdqLHgAAAIgEvCMGAADAIVWxuouTdepAqlgBAAAAQlYAAABUa/m2LcoKUcU6vtM4qlgBAAAAQlYAAADU5H9LQ1exnj5wRLimBAAAADQqhKwAAACo0ortacpyrw8aH9+RKlYAAACgDO+MAQAAUKU3lk4LUcXaUqcPoooVAAAAKEPICgAAgJDW79qh3c51QePjOoylihUAAACogHfHAAAACOm1nz6TwxmoNObyJum0wceEbU4AAABAY0TICgAAgCBbs3Zrh1YHjY9sc4LcTldY5gQAAAA0VoSsAAAACDJl8TQ5nP5KY05vgs4dMipscwIAAAAaK0JWAAAAVJKRu0dpvuVB48NTjpPbRRUrAAAAcCBCVgAAAFTy6o/T5HD5Ko05SmJ14ZFjwzYnAAAAoDEjZAUAAEC5wuJSbVgZr9LMdgpUWPNqSNIxio6KCufUAAAAgEbLHe4JAAAAoPH46setKtwTJ+0ZqtL0PLk7bJA7KVsXjxof7qkBAAAAjRYhKwAAAKziEp9m/JBW/n2gKEElG47QGWO7Kc4TE9a5AQAAAI0Z7QIAAABgzfppm/YWlFQai49xa8JRXcI2JwAAACASELICAABAJaV+TZu/JWj8pKM7K8bDyU8AAABAdQhZAQAAoLnLtit7b3GlsdholyYM6xS2OQEAAACRgpAVAACgmfP5/fr0u81B4+OP6qS4mKiwzAkAAACIJISsAAAAzdxbP85STsr3csTklY953E6deHTnsM4LAAAAiBQ02AIAAGjGSv0+zd09W+7We+VqtU2+rHYq3d5DYwYMVFKcJ9zTAwAAACICISsAAEAz9tHS+fJ79trrDofkbrVDruSdGj1sTLinBgAAAEQM2gUAAAA0U36/X7O2zQoabxvorY7JyWGZEwAAABCJCFkBAACaqa/XLlVJdFalsUBAuvCISWGbEwAAABCJCFkBAACaqc82fhU01rK0m/q27RiW+QAAAACRipAVAACgGVqwea0KPduDxs/ue2JY5gMAAABEMkJWAACAZuj9VV8EjcV62+vobr3DMh8AAAAgkhGyAgAANDOrM9KV7d4YND6p27iwzAcAAACIdISsAAAAzcybS2fI4ag8FlWcovF9jgjXlAAAAICIRsgKAADQjKTnZGmHVgeNn9D+BDmdvDUEAAAADgXvpAEAAJqR1xZNl8PprzTm9CbozCOODducAAAAgEhHyAoAANBMZOfna3PJsqDx4cnHye10hWVOAAAAQFNAyAoAANBMvL7oC8ldUnmwJEaTjxwTrikBAAAATQIhKwAAQDNQ6PVqRf7CoPEB8cMU6/GEZU4AAABAU0HICgAA0Ay8uWimFFVUebA0ShcdOTFcUwIAAACaDEJWAACAJs7vD2jpxt0KlEZVGu8WNVjJ8fFhmxcAAADQVLjDPQEAAAA0rEVrdyl7UztpS2u5Urcqqv1G25v14uEnhXtqAAAAQJNAyAoAANCEBQIBffrd5n3f+N3yZXSTb2cXDT8yWh1apoR7egAAAECTQLsAAACAJmxNWo42bt9bacwpl84fMTxscwIAAACaGkJWAACAJmza/C1BY0f3b6PUlrFhmQ8AAADQFBGyAgAANFHbdufrp/WZQeOTRnQJy3wAAACApoqQFQAAoIma8UNwFWv/rsnq2i4xLPMBAAAAmipCVgAAgCZoa3am5m1ZYpa+qjQ+6RiqWAEAAID65q73PQIAACDs/rf4c7l7/yhnQYJKd3STL7ODOrZO1KDuKeGeGgAAANDkUMkKAADQxOQWFmpTyVJ73RmXJ0+PZYoZ8o2OOTJODocj3NMDAAAAmhxCVgAAgCbmjUVfSe6SSmMmW504uG/Y5gQAAAA0ZYSsAAAATUipz6cluT8EjfeNO1IxUZ6wzAkAAABo6ghZAQAAmpAPlsxTwFNQaSzgc+miIyeGbU4AAABAU0fICgAA0ET4/X7N2TEnaLyjs79aJySFZU4AAABAc0DICgAA0ETMXr9cJdFZlcYCAYcmD6KKFQAAAGhIhKwAAABNxKfrZwaNtSztqt5tO4RlPgAAAEBzQcgKAADQBCzftkV7o9KCxk/vPT4s8wEAAACaE0JWAACAJuCd5V/I4ag8Fl3cRsf16BeuKQEAAADNBiErAABAhNu2J1sZjjVB4+M6nRCW+QAAAADNDSErAABAhHtj8edyOP2VxpzeRJ08cHjY5gQAAAA0J4SsAAAAESyvqEjri5cEjQ9LPkZupysscwIAAACaG0JWAACACPb2T7Mkt7fyYEm0Jh85OlxTAgAAAJodQlYAAIAI5ff7tSj7+6Dx3jFDFOeJCcucAAAAgOaIkBUAACBCzVi1WD5PbqWxgN+pC4dOCNucAAAAgOaIkBUAACBCrVjmUPGao+TLTSkfaxPopXYtksM6LwAAAKC5cYd7AgAAADh423bna9mGbBOrypvTRo64XLnbbdJZx1PFCgAAABxuVLICAABEoC8WpFX6PlCQpD6BsRraqXvY5gQAAAA0V4SsAAAAESavsERzl+0IGj/p6M5hmQ8AAADQ3BGyAgAARJiZi9LlLfVXGmvfKk6Duu/vzQoAAADg8CFkBQAAiCClPr++/HFr0PiJR3eWw+EIy5wAAACA5o6QFQAAIIL8sGqn9uR5K40lxEbp+IHtwjYnAAAAoLkjZAUAAIgQfr9fb216Te5Oa6SoovLxsUd2kCfKFda5AQAAAM2ZO9wTAAAAQO18s26ZvLEZioqV3O02ypfVXoGd3TTuyE7hnhoAAADQrBGyAgAARIjpG76RPPuuO5wBuVtvU3LLGCUnRod7agAAAECzRrsAAACACLA6I125UWlB46f3Hh+W+QAAAADYj5AVAAAgAryz7Es5HJXHootTdUz3PuGaEgAAAICfEbICAAA0ctn5eUr3rwoaH9VhZFjmAwAAAKAyQlYAAIBG7o1FX8nhKq005vDG6YxBx4RtTgAAAAD2I2QFAABoxEp9Pi3P+zFofFDiMLldrrDMCQAAAEBlhKwAAACN2NRl8xXwFFQe9Ll1wVAWvAIAAAAaC0JWAACARmz2tnlBYx2d/ZQcHx+W+QAAAAAIRsgKAADQSC1O26Ci6IxKY4GAdO6gCWGbEwAAAIBghKwAAACN1Iervg4aSyjpqL5tO4ZlPgAAAABCI2QFAABohHbl5SpD64LGx3cZFZb5AAAAAKgaISsAAEAj9Nbir+Vw+SqNOb2JOqnfkWGbEwAAAP5/e3cCJldV543/13v2DbInJCzZyAIBDSD7pqAICoLKMq/AiI4j4vA6CK/Lf14cR5zRl1EZR1FwAcfRQQUBZd8ShCAIhOwQtuxk39P7/7kXu0mnujud9HK7uj+f5+mnKqdunftrPFZXfevcc6BxQlYAgE6mqro6Fmx9Pqf9sP5HRmGht28AANDZeJcOANDJ3DNvdtSWbm/YWF0c5x9+YlYlAQAAzRCyAgB0Ms++9nrU1hQ0aBtZODH69+ydWU0AAEDTipt5DACADrZ87bZYsWBYRMnAKB68NIqHLI0oKY9zJ5+SdWkAAEAThKwAAJ3Iw88te/tOZVlUrTgkqlYeFOPGV8fEYaOyLg0AAGiCkBUAoJPYtrMy/jR3ZcPG2sI4+/AjsioJAABoAWuyAgB0ErPmrIyKypoGbcP36xWHjh2YWU0AAMCeCVkBADqBmprad5YK2MWpR46KgoKGm2ABAACdi5AVAKATeHHJ2li7aWeDtp5lRfGeKcMyqwkAAGgZISsAQCdw3wsLctqOmzoiepRaQh8AADo779oBADL2wrLXY9l+90Rp6cCoWjUmajYOiYLawjjlyJFZlwYAALSAkBUAIGN3LXgkoiiiqO+G9Ke2oiyGl787hg7slXVpAABACwhZAQAytG7r5lgdL8euW1sVlJbHu0aPyLAqAABgb1iTFQAgQ7964dEoKKpu0FZY0SdOnzQ9s5oAAIC9I2QFAMhIVU11zN/6fE771H5HRnFhUSY1AQAAe0/ICgCQkfvmPxu1pdsbNlYXx/mHnZRVSQAAQGdck3XRokXx4x//OGbPnh3r16+PAQMGxJQpU+LCCy+ME044YZ/7XbZsWfzoRz+KWbNmxerVq6NPnz4xYcKEOP/88+Oss87aq762bt2aPmflypVpvc356U9/Gt/4xjf22Odll10WX/ziF/eqDgCge3l82VMRpQ3bhhdMiIG9e2dVEgAA0NlC1ocffjiuuuqqqKysrG9bs2ZNPProo+nPJZdcEl/+8pf3ut85c+bEJz7xidi2bVt924YNG+Lpp59Of+6///648cYbo7h4z79eTU1NfOlLX0oD1paYO3fuXtcLALC7RauXx7aSFQ02vEp8aJJZrAAAkG/aLWSdP39+XH311WnAOnXq1Ljmmmti3Lhx6QzUH/zgB/HQQw/FbbfdFgceeGBcdNFFLe531apVccUVV6QB69ixY+O6666LadOmxbp16+LnP/95/PrXv44HHnggvv3tb+9xJmlSWxLy3nfffXv1eyWSGj796U83eVxJSUmL+wQAup/fzns0CnZLWHtUDI0pI8dkVRIAANDZ1mT9zne+Ezt37owxY8bEz372s5gxY0YMHDgwDVxvuummOOOMM9Ljvvvd76aX67fUzTffnM5a7devXxrSnnTSSTFo0KA0wP3a176WXqafSB5LAt3mwtpkJu2dd97Z4nNv3749XnvttfT+9OnTo3fv3k3+lJbudu0fAMBfbd25M5ZVLchpf8+wozOpBwAA6IQh65IlS+Kxxx5L73/qU59KQ8ddFRQUxLXXXhuFhYWxcePGePDBB1vU7+bNm+OOO+5I7ycB6ZAhQ3KO+exnP5sGsMks1cYC1CT4/f73vx9nnnlmPP/88+mSAhMnTmzR+RcsWJAuL5BIwmIAgH3xu5dmRRS/s5xSqrJnfHDKjKxKAgAAOlvIOnPmzPow9eSTT270mOHDh8ekSZPS+8nSAS2RbJ5VXl6e3j/11FMbPSYJdI855pgm+/3DH/6QzrJNZqWOHj06fvKTn8Rpp522V0sFJLUPHjy4Rc8BANjdc2ufzWkb12NqlBZbbggAAPJRu4SsyYzPxIgRI9JL+Zty6KGHprfz5s3bq373NPu0LrxdvHhxVFRU5DyezHT9/Oc/H3fffXe6jEFL1dU5ZcqUNKy9/PLL0+cn/06C2uuvvz5WrFjR4v4AgO7nqVcXRmXZ+gZttTUF8ZHDTsmsJgAAoBNufLV8+fL0dtSoUc0el4SwdeujVlVVpeFpS/odNmxYFBUV7bHf6urqtO8DDjig/rFjjz02Hn/88ejVq1fsrbqQNVkKYfclDpYuXRq/+MUv4re//W266VZTM20BgO7tj688kfMObGD12Bg1oOkvpgEAgG4YsiYbUyX69+/f7HF9+/ZNb2tra9P1Vpub9bov/SY2bdrU4LGhQ4fGvkiWKXj11VfT+8l6r8nGXX/zN38TBx54YFr7Aw88EP/5n/+ZLkNw1VVXpYHrYYcdFu1h4MBe6VIMsDcKCwvqbwcNarhOMnRWxi1dbcyu2LAh1ha+Grv/FT9nyinGOJnwOks+Mm7JN8Ys+ci47SQha926qWVlZc0e16NHj/r7jV3W3xb91j2ntZJlAJKANpkZ+5nPfCbdYKtOEg5fccUV6dIBF198cRrCJksH/OY3v4n2UFzc9Cxe2JMkoC8qEtKTX4xbusqYvW32A1FQ+PYmmnWKK/rHmdOOSDcEhax4nSUfGbfkG2OWfGTcZhyyNncpf2fstyWSGauPPPJIGqCWlDS+KcXhhx8eH/3oR+P222+PuXPnxsKFC5tdO3ZfVVVVm8nKXku+fUrGTTJzvKamNutyoEWMW7rSmE3+veiVnVHTr08U9tpa3/7uIUdFbW2yzFHD8BU6gtdZ8pFxS74xZslH3WHcFhUVdv6QtWfPni2anbpz5876+3uanbprv3uanbprv7vOam0LTQWsdZK1WJOQNTFnzpx2CVk3bNje5n3S9SXT+5Nvn5IXx/Xrt2VdDrSIcUtXGrNzlqyL9W8mSyMdG4V9NkTR0DejuP/6+OCkY4xvMuN1lnxk3JJvjFnyUXcYt4MHv7PcaKcNWevWRN2yZUuzxyVrmdbNUN3TOquJfv36pbdbt25tUb+JgQMHRkcaPnx4/f316xvuHAwAdF+P/mXZX+8VRM3WQenPsUcOi/49rXEFAAD5rrC9Lq2vW8e0OStXrkxvk7VOW7IO2dixY+ufl0xX3lO/xcXFMXjw4GhLzZ03kSwnsPvMWwCge1uzcUc6k3V3px8xJpN6AACAPAhZx48fn94uXbq02Vmn8+fPT28nTZq0V/0myxC88sore+z3kEMOidLS0mgL//Zv/xbHHHNMHHHEEc0uV7BrXXWhMADQvT32wvLY/WvaSWMGxvD9zGIFAICuoF1C1hNPPDG9ra6ujscee6zJ2aYLFixI7x9//PEt6nfGjBn1s0OTTagas3379nj66af3qt+WSJYdSC7/37X/xtx9993pba9eveLII49ss/MDAPmpsqo6Zr749lU2uzrliJGZ1AMAAORJyDp69Oj6gPF73/teztqsySX3N9xwQ9TU1KTh5TnnnNOifnv37h2nn356ev/WW29tdDmC5HzJmqzJBlUXX3xxtJUzzzyzftOrf/3Xf210U6977rmnPvz92Mc+Fn369Gmz8wMA+enPC9+KrTveWU4oMbBvWRw+bv/MagIAAPIgZE1cd9116Tqrr7/+elx44YUxa9asdCbovHnz4sorr4z77rsvPS65n8z63NUZZ5yR/lxzzTU5/V599dXp8Rs3boyLLroo7r///rTfJUuWxFe/+tU0fE1ccsklMWzYsDb7fUaOHBmXXXZZ/ZIAF1xwQTz++OOxdu3a9Nzf+ta34otf/GL6+MEHH5z+XgAA9y54KqKwqkHbiYePiKIWrEcPAADkh+L26njq1Knx9a9/Pb7yla/E4sWL4/LLL8855tJLL02D0t299tpr6W1jm1YNHz48vvvd76YhZjKT9XOf+1zOMUlA+4//+I/R1j7/+c+n4e6vfvWrdKmDK664IueYZH3ZH/7whznBMQDQ/Tz92qLYuN/T0WNAUVSvHRFVbx0QheX94sTDRmRdGgAAkA8ha+Lcc8+NyZMnxy233BKzZ8+OdevWpeHjlClT0tmtp5122j71m6y1eu+998bNN9+czpBdvXp1usHVxIkT47zzzkvPW1BQ0Oa/TzIz9/rrr0+XDvjlL38Zzz//fGzYsCFdxmDcuHHxgQ98IM4///woLm7X/6wAQJ74w8tPpO+2Coqqo3jo0vRnSPm06N+nLOvSAACANlRQmyyQSl5Zs6bhGrfQEoMG9Y6iosKorq6J9eu3ZV0OtIhxSz6P2UVvroz/7+l/iYLCmgbHfGTUxXHy+GmZ1Qi78jpLPjJuyTfGLPmoO4zbwYP7tml/FgMDAGgHv3nxiZyAtaiiX5x4yJTMagIAANqHkBUAoI3V1NTEvC3P57RP639EuvwQAADQtXiXDwDQxu576fmoKW24vE9tdVGcN+2EzGoCAADaj5AVAKCN3bvwsZy2IXFIDOzdJ5N6AACA9iVkBQBoQ2+uXRvrCl7LaX//IcdnUg8AAND+hKwAAG3o508/EAWFtQ3aSsoHxYwDx2dWEwAA0L6ErAAAbaSqujrmbvxLTvv0QUdmUg8AANAxhKwAAG3k7hf+HDUl2xo2VhfHh6cdl1VJAABABxCyAgC0kftffiKnbVjB+OjXs2cm9QAAAB1DyAoA0AbeWLcmNha9mdP+wQknZFIPAADQcYSsAABt4LdzH4uCgoYbXpWVD47DRx+UWU0AAEDHELICALRSRVVlvLLzpZz2dw9+Vyb1AAAAHUvICgDQSn+c/1xEyc6GjVWl8aFpx2ZVEgAA0IGErAAArbTo5aqoWn1A1FYV17eNKp4YPUtLM60LAADoGO98EgAAYK+t3bgjFr1cEbVxaFQuHR9Fg1ZF8ZClcc67T8y6NAAAoIMIWQEAWuGJOSuifrurmuKoXjsqpgw8PA4dPjrbwgAAgA5juQAAgH1UVV0TT7y4Mqf9fUePyaQeAAAgG0JWAIB99MLLa2PztooGbQP7lsWMQ4dlVhMAANDxhKwAAPvo0eeX57S996gxUVzkLRYAAHQnPgEAAOyDVeu3x4I3NjRoKyyIeK+lAgAAoNsRsgIA7INfv/B4FPZdF/HOtldxxMShMWRgr0zrAgAAOl5xBucEAMhr2yt2xqKqWVE2qTJqdvSOqrdGR/XaEXGGWawAANAtmckKALCX7nrp6YjiyvR+Yc9tUTpmYfSa8kwcPn5w1qUBAAAZELICAOylP7/1bE7bwb0m2fAKAAC6KZ8EAAD2wryVS6O87K0GbbW1EedOOSmzmgAAgGwJWQEA9sLdC57IaetTOTLG7GepAAAA6K6ErAAALbSzsiKWVi3IaT925FGZ1AMAAHQOQlYAgBa6Z+7siOKKho2VPeLMSUdmVRIAANAJCFkBAFro6dV/zmk7qGxylBaXZFIPAADQOQhZAQBaYPHqFbGjdFXOhlfnHHpCZjUBAACdg5AVAKAF7pz/eE5b78rhcciQ4ZnUAwAAdB5CVgCAPSivqow3KubntB89bEYm9QAAAJ2LkBUAYA/+MO/PESXlDRsry+KsyUJWAABAyAoAsEd/WvlMTtuY0klRVmLDKwAAQMgKANCsJWtWxbaSFTntZ0+y4RUAAPA2ISsAQDPunPd4FBQ0bOtRMTQmDhuVVUkAAEAnI2QFAGhCVXV1vFqeu+HVUUPenUk9AABA5yRkBQBowkuvrouKN8ZH9ab93mmsKo2zpx6dZVkAAEAnU5x1AQAAndXMF1dF9frh6U9B2fYoGrwsxo/YP3qUlGZdGgAA0ImYyQoA0IgNW8pjzpJ19f+uLe8VVcvGx8WHvz/TugAAgM5HyAoA0IhZL62MmtraBm0TRg+IYYN6ZVYTAADQOQlZAQB2k4SrM19ckdN+4uEjMqkHAADo3ISsAAC7mf/6+li7aWeDtt49iuPICYMzqwkAAOi8hKwAALt5/IXcWazHTBkWJcVFmdQDAAB0bkJWAIBdLNu4PuZsfTqipOFM1hMPs1QAAADQuOIm2gEAuqXfvfR4FI98OYpGvBw1GwdH1ZrRcWDvg2Pk4D5ZlwYAAHRSQlYAgL+qqqmORdvmRJRGFBREFA1ck/6M6Tsk69IAAIBOzHIBAAB/9ejil6K2dFvDxuriOGfqMVmVBAAA5AEhKwDAXz325tM5bUMLxkXfHj0zqQcAAMgPQlYAgIhYt3VzbCh8Paf9jEOOy6QeAAAgfwhZAQAi4rcvzYqCwpoGbcXlA2LG2HGZ1QQAAOQHISsAQETM3fhCTtuUAYdnUgsAAJBfhKwAQLf3zGuLo6psY4O22prCOHeqpQIAAIA9E7ICAN3efUuezGkbVDM29uvTL5N6AACA/CJkBQC6ta07d8bqmldy2k864OhM6gEAAPKPkBUA6NZ+P/epiOLKBm0FFb3jlPHTMqsJAADIL0JWAKBbe3bNczlt43pNicJCb5MAAICW8ekBAOi2Fq5aFuVlbzVoq62N+NDkEzKrCQAAyD9CVgCg27p7wcyctj6VI2PMfoMzqQcAAMhPQlYAoFuqqKqM1ysW5LQfPfzdmdQDAADkLyErANAt3b/gLxElOxs2VpbFBw4VsgIAAHtHyAoAdEuvvBJRueyQqCnvUd82umRilJWUZFoXAACQf4qzLgAAoKNt2lYR81/eHtU1h0TVioOjsN+6KBq8LM56z3FZlwYAAOQhISsA0O08NXdVVNfU/vVfBVGzef84uN/BMWXkmIwrAwAA8pHlAgCAbqW2tjaeeHFFTvvx00ZkUg8AAJD/hKwAQLfyyvJNsWr99gZtPUqL4t0Th2RWEwAAkN+ErABAtzLzxZU5bTMmDY2y0qJM6gEAAPKfkBUA6DZ2lFfFMwtX57SfcJilAgAAgH0nZAUAuo3fv/hMVPVZEVFQU982cnDvOHB430zrAgAA8ltx1gUAAHSUp9Y9EWXj1kdtZUlUrxsRVWtGxfHTxkVBQUHWpQEAAHlMyAoAdAsvLH01KsvWp/cLSiqjeNgbUTTkzTh8wklZlwYAAOQ5ywUAAN3CHxbPymnrX31ADOnXP5N6AACArkPICgB0eTsqKmJ59aKc9hNGHZVJPQAAQNciZAUAurx75s2OKK5s0FZQ2TNOnzQ9s5oAAICuQ8gKAHR5s1c/m9N2YNmhUVxYlEk9AABA1yJkBQC6tCVrVsX2kpUN2mprI8459ITMagIAALoWISsA0KXdNX9mFBQ0bOtVOSwOGTI8q5IAAIAuRsgKAHRZVTXV8eqOeTntM4a8K5N6AACArknICgB0WY8tfilqS7c3bKwqiQ9OOTqrkgAAgC5IyAoAdFmPvzk7p21Y4bjoWVqaST0AAEDXJGQFALqkDdu2xbqC13Pa33vwezKpBwAA6LqErABAl3TX3CejoKi6QVtRef9495hDMqsJAADomoSsAECX9OL6F3LaJvWbFoWF3v4AAABty6cMAKDLmbvizagoW9ugrbamIM6ZclxmNQEAAF2XkBUA6HLuXTgrp61f1agY0X9gJvUAAABdm5AVAOhSampqY+XrvaNq3fCorXnnrc4xI96daV0AAEDXVZx1AQAAbWnua+tj81t9I946LCqLKqNo0Moo239tnHnCkVmXBgAAdFFmsgIAXcqsl1a+84/qkqhec0Cc0O9DUVpckmVZAABAFyZkBQC6jK07KuOFl9fktB83dXgm9QAAAN2DkBUA6DJmz18dVdW1DdoOGtEvRuzfO7OaAACArk/ICgB0GTPnrMhpM4sVAABob0JWAKBLeHP1lnhz9dYGbSXFhTFj0tDMagIAALoHISsA0CXc9dJTUdBzS4O2IycMjl49ijOrCQAA6B586gAA8t7OyopYWPNE9JhaETXb+kXVmpFRvW64pQIAAIAOIWQFAPLevfOeiSiuSO8X9t4cpb03R8HwpTHhgPdmXRoAANANWC4AAMh7s1c9l9N2YM8JUVTorQ4AANAFZrIuWrQofvzjH8fs2bNj/fr1MWDAgJgyZUpceOGFccIJJ+xzv8uWLYsf/ehHMWvWrFi9enX06dMnJkyYEOeff36cddZZe9XX1q1b0+esXLkyrbcjzw0AtM6y9Wtja8mKKNit/YOTjs+oIgAAoLtp15D14YcfjquuuioqKyvr29asWROPPvpo+nPJJZfEl7/85b3ud86cOfGJT3witm3bVt+2YcOGePrpp9Of+++/P2688cYoLt7zr1dTUxNf+tKX0oC1o88NALTenfNmRkFBbYO2svIhMX7oiMxqAgAAupd2u4Zu/vz5cfXVV6cB69SpU+O2225LQ8g77rgjTjvttPSYpO0Xv/jFXvW7atWquOKKK9KQc+zYsfHDH/4wnnrqqbjnnnviggsuSI954IEH4tvf/vYe+0pqu+666+K+++7r8HMDAK2XfFm6aNvcnPbp+0/PpB4AAKB7areQ9Tvf+U7s3LkzxowZEz/72c9ixowZMXDgwDRwvemmm+KMM85Ij/vud7+bXq7fUjfffHM6c7Rfv35pSHvSSSfFoEGDYty4cfG1r30tLrvssvS45LHksv7mAtNkJu2dd97Z4ecGANrGk68ujJrSLQ3aaquL45wp78msJgAAoPtpl5B1yZIl8dhjj6X3P/WpT0Xv3r0bPF5QUBDXXnttFBYWxsaNG+PBBx9sUb+bN29OZ8ImkoB0yJAhOcd89rOfTUPQZJZqYwFqEvx+//vfjzPPPDOef/759LL+iRMndsi5AYC29fBrT+W0DY6Dol/PnpnUAwAAdE/tErLOnDmzPkw9+eSTGz1m+PDhMWnSpPT+Qw891KJ+k82zysvL0/unnnpqo8ckge4xxxzTZL9/+MMf0lm227dvj9GjR8dPfvKT+uUL2vvcAEDb2bJzR6yJJTntp459+28xAABAXoesCxYsSG9HjBiRXk7flEMPPTS9nTdv3l71u6fZp3Xh7eLFi6OioiLn8WS26ec///m4++6702UMOvLcAEDbuHvu0xFFVQ3aCiv6xHEHv/23GAAAoKMUt0eny5cvT29HjRrV7HFJCFu3PmpVVVUaYLak32HDhkVRUdEe+62urk77PuCAA+ofO/bYY+Pxxx+PXr167cVv1DbnBgDaznNr/hJR1rBtXK8p6XJEAAAAHaldPoUkm0Ml+vfv3+xxffv2TW9ra2vTNU/but/Epk2bGjw2dOjQvQ5Y2+rcAEDbePmtFbGjdHWDttraiHMmH59ZTQAAQPfVLjNZ69YuLSvbbXrJbnr06FF/vyWX1u9Lv3XPaa0sz727gQN7pevdwt4oLCyovx00qOFmdNBZGbc05b4nn4rd/xT2qRoZ08eNjSwZs+QbY5Z8ZNySb4xZ8pFx20lC1uYup++M/Xb2c++uuLjz1EL+SQL6oiIhPfnFuGVXVdXVsWjrSxElDdtPGHNUFBV1jqUCjFnyjTFLPjJuyTfGLPnIuM04ZO3Zs2eLZqfu3Lmz/v6eZoju2u+eZoju2u+uM0tbI8tz766qqtpMVvZa8u1TMm6S5TlqamqzLgdaxLilMfc8/2zUlmxv2FhVEh858tiorq6JLBmz5Btjlnxk3JJvjFnyUXcYt0VtPEGjXULWunVJt2zZ0uxxdeuwJrNE97TWaaJfv37p7datW1vUb2LgwIEtqrkzn3t3Gzbs9sESWiCZ3p98+5S8OK5fvy3rcqBFjFsa88eFM3NmsQ4rHBc7t1XHzm3ZjhNjlnxjzJKPjFvyjTFLPuoO43bw4Hf2VWoL7XJN3YEHHpjerlixotnjVq5cWb8ZVUt2Ah47dmz985IkfU/9FhcXx+DBg/eq9s54bgDgbTvKq2Ld8t5Rs7Xhl7PvO/g9mdUEAADQLiHr+PHj09ulS5c2O/Nz/vz56e2kSZP2qt9kGYJXXnllj/0ecsghUVpaule1d8ZzAwBv+/PCt6L8rRFRPv+Y2PnSsVG5cmyU7BgaMw58++80AABAlwlZTzzxxPS2uro6HnvssSZnfC5YsCC9f/zxx7eo3xkzZtSvjfrII480esz27dvj6aef3qt+O/u5AYC3zZrz9hUjidodfaNq6cT4wJALMq0JAACgXULW0aNHx5FHHpne/973vpezNmtyuf0NN9wQNTU16bql55xzTov67d27d5x++unp/VtvvbXR5QiS8yXropaUlMTFF1/cJr9P1ucGACJWrtsWryzf1KCtqLAgjp48NLOaAAAA2i1kTVx33XXpOquvv/56XHjhhTFr1qxYv359zJs3L6688sq477770uOS+7169Wrw3DPOOCP9ueaaa3L6vfrqq9PjN27cGBdddFHcf//9ab9LliyJr371q2kAmrjkkkti2LBhbfo7ZXluAOjunnxpVU7b4YfsH317WZ4HAADIVnF7dTx16tT4+te/Hl/5yldi8eLFcfnll+ccc+mll6Zh5e5ee+219LaxjaOGDx8e3/3ud9NwNplN+rnPfS7nmCSg/cd//Mc2+106w7kBoDurrqmJJ+e+s1RAnWOnDc+kHgAAgA4JWRPnnntuTJ48OW655ZaYPXt2rFu3Lp0JOmXKlHR262mnnbZP/Sbrnd57771x8803pzNkV69enW4yNXHixDjvvPPS8xYUFLT575P1uQGgu5r32vrYtLWiQVv/3qUx9aBBmdUEAABQp6A2WSCVvLJmTcM1bqElBg3qHUVFhVFdXRPr12/LuhxoEeOWOt+8+75YtLAgorqkvu3Mow6I808+JDoTY5Z8Y8ySj4xb8o0xSz7qDuN28OC++TOTFQCgtVZv3hRv9Hw0ekwviOoNQ6J67cio2bR/HGepAAAAoJMQsgIAndqdc2dGQWFy4U1tFO+3Kv3psWNEDN/v1KxLAwAASBW+fQMA0DnN3zQnp23yfhMzqQUAAKAxQlYAoNN69o2Xo6psY4O22prCOGfKcZnVBAAAsDshKwDQad338p9y2gbWjI39+vTJpB4AAIDGCFkBgE5pZ2VFrKx5Oaf9hNEzMqkHAACgKUJWAKBTumfuMxHFFQ3aCip7xqkTDsusJgAAgMYIWQGATmn26mdz2g4sOzSKC4syqQcAAKApQlYAoNN5c/3a2FayIqf9g5OOz6QeAACA5ghZAYBO5655M6OgoGFbWfmQGD90RFYlAQAANEnICgB0KjU1NbF429yc9iP2n55JPQAAAHsiZAUAOpUnX10YNaVbGrTVVhfHOVPfk1lNAAAAzRGyAgCdysOvPZXTNiQOir49emZSDwAAwJ4IWQGATmPLzh3xVizJaT9l7DGZ1AMAANASQlYAoNO4e+7TUVBU1aCtsKJPHHfwpMxqAgAA2BMhKwDQaTy35i85beN6TYnCQm9ZAACAzssnFgCgU1izYXtsWd8raitL69tqayPOmXx8pnUBAADsSfEejwAA6AB/mrc6qpZOiKpl46Kw/5ooHrw8+vUujTH7Dc66NAAAgGYJWQGAzNXU1saTL618+x+1hVGzcWhUbBwa558zOevSAAAA9shyAQBA5ha9uTHWbtrZoK13j+I4fJxZrAAAQOcnZAUAMjdrzoqctqMnD4uSYm9VAACAzs8nFwAgU9t3VsVzi9bktB83dXgm9QAAAOwtISsAkKk/L1wdFVU1DdpGD+kTY4b1zawmAACAvSFkBQAy9cjCucluVw3azGIFAADySXHWBQAA3dfc5W/E2iEPR1n/HlG9dkRUrx0ZhZV94ujJQ7MuDQAAoMWErABAZu5ZNCu9LSzbGYUjX42Ska/G/junRt9epVmXBgAA0GKWCwAAMlFRVRlLKxfmtL9r9PhM6gEAANhXQlYAIBMPLPxLREl5w8bKsnjfpCOyKgkAAGCfCFkBgEzMWv7nnLbRJROjtLgkk3oAAAD2lZAVAOhwqzZtiM1FS3Pa3z/+2EzqAQAAaA0hKwDQ4e6c+2QUFNY2aCsp3y+mjRqbWU0AAAD7SsgKAHS4+VtezGmbNvDwTGoBAABoLSErANChnnltcVSXbmrQVltTGB+eaqkAAAAgPwlZAYAOdf+SP+W0Dao+MAb27pNJPQAAAK0lZAUAOsyOiopYVfNyTvuJY47KpB4AAIC2IGQFADrMPfNmRxRXNmgrqOgVJ4+fmllNAAAArSVkBQA6zDOrn8tpO6jn5CguLMqkHgAAgLYgZAUAOsQb69bEtpIVDdpqayPOnnRcZjUBAAC0BSErANAh7pz3RBQUNGzrWTE0DhkyPKuSAAAA2oSQFQBodzU1NfHK9rk57e8afEQm9QAAALQlISsA0O7mL30rKrf1jtraXaayVhfHB6cck2VZAAAAbaK4bboBAGjaM/M2RMXLR0QUl0fx/iuiaP/lMaxsVPTp0SPr0gAAAFpNyAoAtKvyiur488K33v5HVVlUrTowqlaNjY9dfHjWpQEAALQJywUAAO3q2UVvpUHrrkbs3yfGjxyUWU0AAABtScgKALSrmXNW5rQdN3V4FBTssj4rAABAHhOyAgDt5q0N22Px0o0N2goLCuKYKcMyqwkAAKCtCVkBgHYz66VVOW3TDt4v+vcuzaQeAACA9iBkBQDaRVV1dcxc+EpO+/HThmdSDwAAQHspbreeAYBu7cGFz0fFIQ9F6eaBUb12ZFSvHxb9evSMqQfvl3VpAAAAbUrICgC0i5nLnokoiSjqtyH9qR2zIA4uPDGKi1xIAwAAdC0+5QAAbW7N1s2xsejNBm0FRdVx3PjxmdUEAADQXoSsAECbu/OlWVFQWNOgraR8YEwffVBmNQEAALQXISsA0Obmbnwxp23KgMMyqQUAAKC9CVkBgDb1/JuvRlXZhgZttTWF8aGpx2VWEwAAQHsSsgIAbeqPLz+Z0zawekzs36dfJvUAAAC0NyErANBmyisrY3n1opz240fPyKQeAACAjiBkBQDazL3z/xxRXNGgraCyZ5w24fDMagIAAGhvQlYAoM3MXvlsTtvY0kOjuKgok3oAAAA6gpAVAGgTy9avjS0ly3PaP3ioDa8AAICuTcgKALSJu+bPioKC2gZtZeVDYsLQkZnVBAAA0BGErABAq9XU1MTCrS/ltE/ff3om9QAAAHQkISsA0Gp/em1h1JRuadBWW10c50x5T2Y1AQAAdBQhKwDQag+/+lRO2+A4KPr17JlJPQAAAB1JyAoAtMqWnTvirViS037q2GMyqQcAAKCjCVkBgFZ5cuGrUVPeo0FbYUWfOO7gSZnVBAAA0JGKO/RsAECX88K88ihfemwU9N4cxYOXRtF+K2N876lRWOi7XAAAoHsQsgIA+2z1+u2xeOnGiCiI2m39o3Jb/6heOik+esVRWZcGAADQYUwxAQD22cw5K3PaDjtoaAzp3y+TegAAALIgZAUA9kl1TU08+VJuyHr8YSMyqQcAACArQlYAYJ/MWbIuNm2raNDWv09pTD1oUGY1AQAAZEHICgDsk5kv5s5iPW7q8Ciy4RUAANDN+BQEAOy1VZs2xZzXVue0HzdteCb1AAAAZEnICgDstf+Z80iUHv5IlBz4UhT22RARtTHxgAExdGCvrEsDAADocMUdf0oAIJ/V1NTE4m1zoqC0OooHL09/anb0jmkjP5J1aQAAAJkwkxUA2CuPvfxS1JRua9BWWFoex008OLOaAAAAsiRkBQD2yqNvPJ3TNjQOiT49emRSDwAAQNaErABAi63bujXWFb6W0/6+Q47LpB4AAIDOQMgKALTY7+bOjILCmgZtxeUDYsbYcZnVBAAAkDUhKwDQYi9teCGnbXL/w6KgoCCTegAAADoDISsA0CLPvvFyVJVtaNBWW1MYH552fGY1AQAAdAZCVgCgRf748pM5bQOrx8TgPv0yqQcAAKCzELICAHu0vWJnrKp5Oaf9pAOOyqQeAACAzkTICgDs0e9fmh1RXNmgraCiV5w84bDMagIAAOgshKwAwB79ec2zOW2H9JwSxYVFmdQDAADQmQhZAYBmLV69InaWrm7QVlsbcc5kG14BAAAkhKwAQLN+P39mTlvvyhFx4P5DM6kHAACgsxGyAgBNqqqujtcq5uW0Hz3sXZnUAwAA0BkJWQGAJv1x/rMRJTsbNlaVxgcmz8iqJAAAgE5HyAoANOmF11ZEbVVJg7ZRxROjR0lpZjUBAAB0NsVZFwAAdE4btpTH6wv6R22cFEUDV0fRkGVR2Hd9nD3phKxLAwAA6FSErABAo2bOWRG1tcm9oqhePyL9OWRsSUw+9YCsSwMAAOhULBcAAOSoqamNmS+uyGk/ddr4TOoBAADozISsAECOua+tj3Wbyxu09elZEkeMH5xZTQAAAJ2VkBUAyPH4C8tz2o6dOixKir11AAAA2J1PSgBAzoZXL76yLqf9hMNGZFIPAABAZydkBQAaeHDO4qiprWnQNmH0gBi+X+/MagIAAOjMirMuAADoPKpqquOJrXdE2bSI6jWjomrtqIjKsjjxcLNYAQAAMgtZFy1aFD/+8Y9j9uzZsX79+hgwYEBMmTIlLrzwwjjhhBP2ud9ly5bFj370o5g1a1asXr06+vTpExMmTIjzzz8/zjrrrGafW1tbG3fddVfccccdsWDBgqisrIxhw4bFiSeeGJdddlkMHz68yef+9Kc/jW984xt7rC/p54tf/OI+/W4AkJUHFvwlakt2RGFJROHol6N45CtRsGFUHDnhxKxLAwAA6J4h68MPPxxXXXVVGmLWWbNmTTz66KPpzyWXXBJf/vKX97rfOXPmxCc+8YnYtm1bfduGDRvi6aefTn/uv//+uPHGG6O4OPfXq6mpiS984Qtx7733Nmh/44034uc//3n87ne/i5tuuimOPvroRs89d+7cva4XAPLFE0tnR5S+8++CwtoYOah/lBQXZVkWAABA9wxZ58+fH1dffXUasE6dOjWuueaaGDduXDoD9Qc/+EE89NBDcdttt8WBBx4YF110UYv7XbVqVVxxxRVpwDp27Ni47rrrYtq0abFu3bo0JP31r38dDzzwQHz7299udCZpEr7WBayXXnppfPSjH41+/frFM888E9/85jdj5cqVceWVV8bdd9+dzm5t7PdKJDV8+tOfbrLOkpKSFv9OANAZvLl+bWwuXhoFu7WfNWHfrzwBAADoDtpt46vvfOc7sXPnzhgzZkz87Gc/ixkzZsTAgQPTwDWZKXrGGWekx333u9+NrVu3trjfm2++OZ21mgSjSUh70kknxaBBg9IA92tf+1p6mX4ieSwJdHeVLCvwk5/8JL3/yU9+Mq699to05N1vv/3izDPPjF/84hfpcgabN2+O//iP/8g59/bt2+O1115L70+fPj169+7d5E9p6S7TgAAgD/xu7uPpzNVdlZUPjmmjxmZWEwAAQLcNWZcsWRKPPfZYev9Tn/pUGjruqqCgIA04CwsLY+PGjfHggw+2qN8k/EzWUU0kSw0MGTIk55jPfvazaQCbzKC98847Gzx2++23p+29evVqdBbqyJEj02UIEslM1h07djR4PFm/NVluIJGExQDQlTa8enn7SzntRw4+MpN6AAAAoruHrDNnzqwPU08++eRGj0k2l5o0aVJ6P1k6oCWSzbPKy8vT+6eeemqjxySB7jHHHNNov48//nh6e9RRR6UbZTWmrt8kYH3yyScbXSogqX3w4MEtqhkA8sFDC1+I2tLtDRurSuKcKe/JqiQAAIDuHbImMz4TI0aMSC/lb8qhhx6a3s6bN2+v+k02tJo4cWKTx9WFt4sXL46Kior0fjKDNZlhm5gyZUqTz02WHahbT3X3uur+nTz/D3/4Q1x++eXpMgjJv0877bS4/vrrY8WKFS36XQCgM3l86VM5bcOLxkefHj0yqQcAACC6e8i6fPny9HbUqFHNHpeEsHWbWVVVVbW432RDqqKioj32W11dnfa9+zmaqyuZfZvMVE3svqZrXciaLIXwD//wDzFr1qzYtGlTGuAuXbo0XdP1/e9/fzz88MN7/F0AoLNYtnF9bCpamtN+1vjjM6kHAAAg3xS3R6fJxlSJ/v37N3tc375909va2tp0vdXmZr3uS7+JJATd9bmJZM3Wljw/qalOskzBq6++mt5PQtVk466/+Zu/STfOSo574IEH4j//8z/TzbGuuuqqNHA97LDDoj0MHNgrDYNhbxQWFtTfDhrUcJ1k6KyM247xg6d/n7vhVcX+ccph1h/fW8Ys+caYJR8Zt+QbY5Z8ZNx2kpC1bt3UsrKyZo/rscsliHWX9bd1v3XP2bX/XR9vTF3/dc9NJMsADB06NJ0R+5nPfCbdYKtOEg5fccUV6dIBF198cRrCJksH/OY3v4n2UFzc9Cxe2JMkoC8qEtKTX4zb9lNVXR3zNj0f8fZKOfXeM+roKCpqlwteugVjlnxjzJKPjFvyjTFLPjJuMw5Zm7uUP6t+Cwtb90ExmbH6yCOPpAFq3Zqtuzv88MPjox/9aNx+++0xd+7cWLhwYbNrx+6rqqpqM1nZa8m3T8m4SWaO19Q0nLEGnZVx2/5+++xTUVOyrWFjdUl8fMZJUV1dk1VZecuYJd8Ys+Qj45Z8Y8ySj7rDuC1q40kl7RKy9uzZs0WzU3fu3Fl/f0+zU3ftd9cZpnvqt27Waq9everb9vT8uscbm/HaVMBa59RTT01D1sScOXPaJWTdsGG33Z+hBZLp/cm3T8mL4/r1uwUq0EkZt+3vvsWPR5Q2bBteMD4qt9fE+u3+m+8tY5Z8Y8ySj4xb8o0xSz7qDuN28OB3lhttC+1yHWDdmqZbtmxp9ri6NU+TGap7Wmd117VUt27d2qJ+EwMHDmxQ097UVffcvVG3aVZi/fr1e/18AOgoS9asii0lDTd5TJw98cRM6gEAAMhX7RKyJpfW161j2pyVK1emt8lapy25nH/s2LH1z0umK++p3+Li4hg8eHB9+Fk3M7W5upJ+k3VX657T2OPNSZYT2H3mLQB0Rr+d+2jsvvpMWfmQmDbq7b+3AAAAZBiyjh8/Pr1dunRps7NO58+fn95OmjRpr/pNliF45ZVX9tjvIYccEqWlb18DmYS4Bx98cIPHG7N48eL6oPTQQw+tb/+3f/u3OOaYY+KII45odrmBXeuqC4UBoLPZWVkRr1fOy2k/ZthRmdQDAACQz9olZD3xxLcvM6yuro7HHnusydmmCxYsSO8ff/zxLep3xowZ9bNDk02oGrN9+/Z4+umnG+23rq7k8eS4xtT1m4SzyfnqJEsHJJf/79p/Y+6+++76NWCPPPLIFv1eANDRZi9aFtWbB0aDCzQqy+LsKUdnWBUAAEB+apeQdfTo0fUB4/e+972cNVCTS+5vuOGGqKmpScPLc845p0X99u7dO04//fT0/q233troZf/J+ZI1VZMNqi6++OIGj5199tnp+q+bNm2Km266Kee5SX8//elP0/vnnXde/RqwiTPPPLN+06t//dd/bXRTr3vuuac+pP3Yxz4Wffr0adHvBQAd7akXN0bFK9Nj5wsnReXyg6O2oiwOLJ0SZXvY4BEAAIAOClkT1113XXqJ/uuvvx4XXnhhzJo1K50JOm/evLjyyivjvvvuS49L7iezPnd1xhlnpD/XXHNNTr9XX311evzGjRvjoosuivvvvz/td8mSJfHVr341DV8Tl1xySQwbNixnrdiklsQtt9ySHp88L3l+0k/SX9LvgAED4oorrmjw3JEjR8Zll11WvyTABRdcEI8//nisXbs27eNb3/pWfPGLX0wfT5YlSH4vAOiMlq/ZGouXbnz7H5U9omr5uKiYc1JcdPgZWZcGAACQlwpq97STUyv89re/ja985StRVVXV6OOXXnppXHvttTntEyZMSG+Ty/Vvu+22nMdnzpyZhpg7duxotN8koL3xxhsb3UwrWU/1c5/7XJPLGCQBbhLUTp8+PeexZObtP/3TP8WvfvWraEqyvuwPf/jDdDOv9rJmTcOZwdASgwb1jqKiwqiuron167dlXQ60iHHbPn7xwOJ4+C/LGrRNH7d/XHnetMxq6iqMWfKNMUs+Mm7JN8Ys+ag7jNvBg/u2aX/F0Y7OPffcmDx5cjprdPbs2bFu3bo0xJwyZUo6o/S0007bp36TtVbvvffeuPnmm9MZsqtXr07XUJ04cWJ6mX9y3oLdt0v+q7KysvjBD34Qd955ZxoCL1y4MA1rhwwZEscdd1x88pOfTJc7aEwS2l5//fXp0gG//OUv4/nnn48NGzakyxiMGzcuPvCBD8T5558fxcXt+p8VAPbZzoqqeHLuypz2U44YlUk9AAAAXUG7zmSlfZjJyr7oDt9C0fUYt23vsReWx8/vW9SgbcjAnvEvVxwdhU18QUnLGbPkG2OWfGTckm+MWfJRdxi3g9t4Jmu7rckKAHQuyfeqj/5leU77ydNHClgBAABaQcgKAN3Ec6+/Hss2r2rQVlJcGMdOHZ5ZTQAAAF2BxUMBoJu48+X7o8e0V6N6035R9dboqNkwJGZMHBZ9epZkXRoAAEBeE7ICQDewatOGWF/4WiSLAhT1X5f+1FaUxYxD/y7r0gAAAPKe5QIAoBv4nzmPRUFhw70uS2p7xuRRwzKrCQAAoKsQsgJAF1dVXR2Ltr+Q0z590LuisNBbAQAAgNbyyQoAurjfz50dtSU7GjZWF8e5047PqiQAAIAuRcgKAF3ckyueymkbVTQp+vXsmUk9AAAAXY2QFQC6sOeXvho7y1Y3aKutjTh38imZ1QQAANDVCFkBoAu7a+GjOW19K0fFhKEjM6kHAACgKxKyAkAXtWbr5nir4OWc9pMPOC6TegAAALoqISsAdFG/fuGRKCisadBWWNE33jvx8MxqAgAA6IqErADQBVVVV8eCrS/ktB824F1RWOjPPwAAQFvyKQsAuqB75s6O2tLtDRuri+P8w07IqiQAAIAuS8gKAF3QzBVP5bSNLJwU/Xv2zqQeAACArkzICgBdzAtLX42dZasbtNXWRpw35ZTMagIAAOjKhKwA0MXctfCxnLY+lSNjwtCRmdQDAADQ1QlZAaALWbN1c6yOl3PaTznguEzqAQAA6A6ErADQhTzz0tqofOPQqNnet76tsKJvvHfi9EzrAgAA6MqKsy4AAGgbVdU18chfVkb1lpFRvXZEFPZbF8XDXo/Dh0+JwkLfqwIAALQXISsAdBHPLnwrNmwp/+u/CqJm8/5RUjEsLvnAezKuDAAAoGszrQUAuoDa2tq4/5mlOe0nTR8ZPcp8pwoAANCehKwA0AUsXrox3li9pUFbUWFBnHLEqMxqAgAA6C6ErADQBTQ2i/WoQ4fGwL5lmdQDAADQnQhZASDPrVq/PV54ZW1O+3vfPTqTegAAALobISsA5LmfPPf7KB72WkRRZX3bpDED44ChfTOtCwAAoLuwEwYA5LHVmzfF0oIXouSAmige+UpUrxkVVavGxPtmTMu6NAAAgG5DyAoAeeyXLzwYBYU16f2CouooHvZGlA7aEJMPfH/WpQEAAHQblgsAgDy1o6IiXt7xYk779AHviqJCf+IBAAA6ik9gAJCn/ueFJyJKyhs2VpXGBYeflFVJAAAA3ZKQFQDyUE1NTTy7/umc9oNKp0afHj0yqQkAAKC7ErICQB66d96fo7p0c4O22prC+Ojhp2dWEwAAQHclZAWAPPTIssdz2gbXHhKjBgzKpB4AAIDuTMgKAHnm0cUvRUXZ2gZttbURF0x+b2Y1AQAAdGdCVgDIM3989ZGctv5VB8TkEQdkUg8AAEB3J2QFgDzy/NJXY1vp8pz2s8edlkk9AAAACFkBIK/8Zv6DOW09yofGMQdNzKQeAAAAhKwAkDdeeWtlrC9+Naf99DEnZ1IPAAAAbxOyAkCe+OWc+6OgoLZBW3H5wHjvxMMzqwkAAAAhKwDkhRWbNsTKWJjTfvyw46Kw0J9zAACALPlUBgB54Pa//DEKCmsatBVW9I4PTXtPZjUBAADwNiErAHRyW3dUxuurN0dtTUGD9iMGHhPFRUWZ1QUAAMDbiv96CwB0Ug/+eWnsfH18FKwYHcXDX4uiwUujoLosPjb9pKxLAwAAQMgKAJ3b9p2V8dBzS9P7tRU9o/KNQ6NyxUHxvuP2i56lpVmXBwAAgOUCAKBze+jZZbGjvLpBW/+yfnHuke/KrCYAAAAaErICQCe1o7wqHvjz27NYd/X+o8ZESbG1WAEAADoLISsAdFIPP7cstpdXNWjr17s0Tjh8RGY1AQAAkEvICgCddBbr/c+8mdN+xowDoqzELFYAAIDORMgKAJ3QL//8RGwvWtugrU/Pkjh5+sjMagIAAKBxxU20AwAZ2bBtWzy3/ZHoMbkiqjftF1XLD4marQPjjKMOiLJSs1gBAAA6GyErAHQyP332DxHFFen9ov7r0p/YODxOnn5C1qUBAADQCMsFAEAnsnrzpnil4vmc9vH7HxA9y3w3CgAA0BkJWQGgE/nJs/dEFFU1bKwqjUvf/f6sSgIAAGAPhKwA0Em8sW5NvFnzUk77tD5HR7+ePTOpCQAAgD0TsgJAJ/Gz5++JgsKaBm0FlT3jb9713sxqAgAAYM+ErADQCSxavTxWxcKc9ncPOC56lpZmUhMAAAAtI2QFgE7g9heTWay1DdoKK/rEx488KbOaAAAAaBkhKwBk7IVlr8e6oiU57ccPOSlKi0syqQkAAICWE7ICQMb+a+5dUVDQsK24fECce/ixWZUEAADAXhCyAkCGHlzwl9hWujyn/bRRp0ZxYVEmNQEAALB3hKwAkJGqmuq45/X7ctrLygfHBya/O5OaAAAA2HtCVgDIyH8/91hUlW3MaT9/wgejsNCfaAAAgHzhExwAZGDrzp3x1PrHc9oHVB0Uxxw0MZOaAAAA2DdCVgDIwC3P3BtRsrNBW21NYVx6+DmZ1QQAAMC+EbICQAfbsKU8Fs4rippt/Rq0H1A4NQ4ZMjyzugAAANg3xfv4PABgH/360VeifFO/iE3HRNHgZVEyanEUFBTEJ99jFisAAEA+ErICQAda9OaGmD1/9V//VRDVa0ZH9fphccaJA2O/Pn0yrg4AAIB9YbkAAOgg1TU18YsHF+e0H7D/wPjIu96dSU0AAAC0npAVADrIY8+viGVrtuW0X3T6+CgsLMikJgAAAFpPyAoAHWDztor43ROv5rQfM3lojBs1IJOaAAAAaBtCVgDoAD975C+xvbyqQVtZaVGcf/IhmdUEAABA2xCyAkA7u3fun2NBr99GyQELIgrfCVrPPnZsDOhTlmltAAAAtF5xG/QBADRh844d8cdl90ZBaUTxsDeicODqqHzj0BhecmCc/q7RWZcHAABAGzCTFQDa0X889ZuoLd1e/+/Csp1ROu4vcc4pg6O4yJ9hAACArsCnOwBoJ8+8tjiW1r6U0z689tB414EHZVITAAAAbU/ICgDtYEdFRdy+6NdRUFDb8IHKHvHZYz6SVVkAAAC0AyErALSD78z6n6gu3ZzTfuqwM2Jg7z6Z1AQAAED7ELICQBt74uV58WbtizntfSsPiHMPe08mNQEAANB+hKwA0IY279gRv15yRxQU7PZAVWl87uiLMqoKAACA9iRkBYA29O9P/nfUlm7LaT996PtjRP+BmdQEAABA+xKyAkAbueP5WbG6cEFO+6Cqg+NDlgkAAADosoSsANAGFq1eHo+u/UPuA5U94vPv+XgWJQEAANBBhKwA0Eo7Kiri+3/5eURRVYP22tqIsw/4UOzXp19mtQEAAND+hKwA0ErfnvnLqCrbkNN+UOGR8b5JR2RSEwAAAB1HyAoArfDLZx+NlQXzctrLygfH50/4SCY1AQAA0LGErACwj15dsTkef+nNdFmABqpK46oZn4jioqKMKgMAAKAjCVkBYB9s2FIe3/vtnKhYPToqFr0raquK0/YkcD1r5IdizH6Dsy4RAACADiJkBYC9VF5ZHd/7zZzYtLUi/XfN5v2jfP7RUbOjV4wvnhFnTn5X1iUCAADQgd6edgMAtEhVdU388K558fqqLQ3aa3f2iSlV58TfHX9YZrUBAACQDTNZAaCFampr4yd/WBAvvLI257Gxw/rGJ98/LQoL/WkFAADobsxkBYAWqKmpidsfWhhPzVud89iAPqVx5XnTorTERlcAAADdkZAVAFoQsH7r8f+OV7e9GVF4RETNO38+e5QWxVUfOSwG9i3LtEYAAACy45pGANhDwHrDo7fHG7UvRFH/9VE28c8RxW9veFVSXBhXfWRajBnWN+syAQAAyJCQFQCaUFFVGdc/fGssL5hb31bYZ1OUTXwmisrK4zMfmhITDhiYaY0AAABkz3IBANCIDdu2xb/M/FFsL12R81hBz61x+ol94rBD9s+kNgAAADoXISsA7Gbx6hVx0/M/ierSTTmP1dYWxLH93xcXHHF8JrUBAADQDUPWRYsWxY9//OOYPXt2rF+/PgYMGBBTpkyJCy+8ME444YR97nfZsmXxox/9KGbNmhWrV6+OPn36xIQJE+L888+Ps846q9nn1tbWxl133RV33HFHLFiwICorK2PYsGFx4oknxmWXXRbDhw9vt3MD0LndNefpeGDV3RGllTmP1dYUxKn7fzDOO/y4TGoDAACgcyqoTRLHdvLwww/HVVddlYaYjbnkkkviy1/+8l73O2fOnPjEJz4R27Zta/Tx9773vXHjjTdGcXFxoxuYfOELX4h777230ef27ds3brrppjj66KPb/NxtZc2aLe3WN13XoEG9o6ioMKqra2L9+sbHL3Tncbt5x474zpO/ilWF8xs/oLo4PjjyvDjj0CPbtQ7ym9da8o0xSz4ybsk3xiz5qDuM28GD++bHxlfz58+Pq6++Og1Yp06dGrfddls8/fTT6ezR0047LT0mafvFL36xV/2uWrUqrrjiijTkHDt2bPzwhz+Mp556Ku6555644IIL0mMeeOCB+Pa3v93o85MAtC5gvfTSS+O+++6LP/3pT/Hv//7v6QzWLVu2xJVXXpmep63PDUDn9Md5z8b/efybTQasBZU9428n/q2AFQAAgI6dyfqpT30qHnvssRgzZkz87ne/i969e9c/lpzy85//fBpwJssHJDNek0vuW+L6669Pg9l+/fqlYemQIUMaPP7Nb34zbr311igpKUn7HzVqVP1jyaX9p556ahr8fvKTn0xntO5q+fLlce6558bGjRvT0PRrX/tam527LZnJyr7oDt9C0fW097idu/yNuO2lu2Jr6bImjykrHxxXH3VpjBpkkyv2zGst+caYJR8Zt+QbY5Z81B3G7eB8mMm6ZMmSNGCtC1t3DVgTBQUFce2110ZhYWEaaD744IMt6nfz5s3pTNi6pQZ2DzkTn/3sZ9MQNAlS77zzzgaP3X777Wl7r1694tOf/nTOc0eOHJkuBZC4++67Y8eOHW12bgA6jzlL34z/c//34/sL/6PZgHV0HBY3nP55ASsAAAAdH7LOnDmzPkw9+eSTGz0muTR/0qRJ6f2HHnqoRf0mm2eVl5en95MZqY1JAt1jjjmm0X4ff/zx9Paoo45qcuZsXb9JwPrkk0+22bkByNbm7RXx+AvL4+s/fza+89vnY1PJ61FQEE0uD3DW0Avi2lMuitLiko4uFQAAgDzTLrszLViwIL0dMWJEDBo0qMnjDj300Jg3b176szf9JptKTZw4scnjkvD2/vvvj8WLF0dFRUWUlpams0uTGbaJKVOmNPnccePGpZf7J8cnddWtH9uacwPQsZJNDt/avDXWrq+Mxcs2xaI3N8QryzfFOwvk9I2arf2jsM+mBs9LHh9SMz6uPPZjsV8Ll7EBAACAdglZk7VNE3takzQJYes2lKqqqkoDzJb0O2zYsCgqKtpjv9XV1WnfBxxwQP059lRXMvs2mWX75ptvxrJly9rk3LTc2o074qnXF8b6irV7PngPqwnvVzw8+hU3HfIvK38lymt3tvgkTa1ePKr04Cgr7NloWTW1NfF6efNfIrRkUeSCKIwDyyY3+fj26s2xsvK1ZvsoKS1Ox3eyJnJFxdv/X9hdr8K+Maz4wCb7WF+1MjZUvxUtVdvEbzeoaFgMLBq6y3ENLa98JXbWbG3xeRqe8x0jig+JnoVNBGW1tbGk4sU9/i/Q1O+wq4NKpjf5WPJ7LK9e3Pw5Gpyi8fP1KOwTI4vHN3nYhupVsa5mxb79Lrs0DygcGvsVjWyyj5XVS2JbzcZoraGFh0Tvwv5NPv5a1QtRE8nfhaJ0tmny36iqsrrJ4ytqKmJb1fbYWb0jymu3RmXxlqje2j8qFr27yedUvTU6SncJWUvL94sLJpwTxxzU9BdpAAAA0GEh64YNG9Lb/v2b/gCd6Nv37QVmk9AnWfO0uVmv+9JvYtOmTQ2em0jWTW3J85Oa2uLctMwzC1bHD38/L4pHL4jiYW+0ur+K1ydF9Vtjmny8bPKforD3O/8b76snZ++I2h1NjKnC6uj5rkdafY7a6qKY9VjT/3ct7L8myiY813wn7ywx3KTqjftHxeLKJh8vHvlylIx8e0Z4a1QuHRdVKw9u8vHSibOjqN87/5/dV889Xx41W5t+Xenx7llRUND6vf+endX0YtmFfTZE2aGzW32O6i0D4k8Lmv6Cp3jYa1FywKJWn6dyxYFRteztpVEaUzru+Sga2PKgvSkvLaqMmk25a1vX6XHEn6OguDKi8e8DGpf859nlP1Fhz+aD+ur1w6L2gIVRWt0vTh51Unxw8ox0rXAAAADoFCFr3dqlZWVlzR7Xo0eP+vvJpfXt0W/dc3btf9fHG1PXf91zW3vutjZwYK90RmJX8/snX29ytijA3iooLY8orIqoyf1TV1xUEEdPOSDePfUzcfykccJV2kxhYUH9bbIjK3R2xiz5yLgl3xiz5CPjtpOErM1dTp9Vv639AN1ev9O+SC6f7Yoqq2uyLgHoYgp6bovabf3rg9Vp4wbHMVOGxzFTh0f/Ps1/aQatkXwZWlTU9b4QpesyZslHxi35xpglHxm3GYesPXv2bNHs1J0731kPc08zRHftd08zRHftt25maa9everb9vT8usd3nZXamnO3taqq6i45k/VDJxwcP7prbtZlAF1AbU1hFFf1jSmHDIgpQ8fHoQcOivEHDIyykne+pKr2xQ7tIPmmv27965oal2fQ+Rmz5CPjlnxjzJKPusO4LSoq7Pwha926pFu2bGn2uLo1T5NZonta63TXtVS3bm1+nb1d11IdOHBgg5r2pq6657b23G1tw4bt0RUdM2lIDO53ZPzp9ZJYX/3Opkj7avD4A6L/xCHppjmNWVpVHuW1e/5vWRC7dNBIX6NnTIiygndC/F0Pq6mtjler9ryBU/OReUEUlhbFQScf0uQR22uGxMrq5kP9kpKiKExeIJNZw01sfNVzWL8YMergJutZV907NlYPb0Hhzf9G+00YFgMPHdbkU5ZXFsTOmm177rmg+f/NRhx1cNMbX0XEkvLkS5E9/7HY05caB50+Lv1v25jk91heucv4aOH3I7sf1qN37xh5wMFNHrSxalCsr2p6w6qWFJD8CgMmDo79pu72v80uVlX0jO01W1pwluZ/0aFHHRC9i5tey/b1nRE1UR09ykrq/7CXlze9QGtJYVEM6Nk39uvVLwb37R+jB+4fxbtdgbBty85ofFRB20kupUq+6U/eiK5fb8TR+Rmz5CPjlnxjzJKPusO4HTy46c+knSZkPfDAA+OZZ56JFSua3+l65cqV6e3QoUNbdDn/2LFj65+XfOBuKvio67e4uDgGDx6c3h8+fHg6szSZadpcXUm/q1atqn9OW5ybljtkZP84ZOTxHXS2t/83bX8HddB5prTgBbIwnb237y+QB0THGN0hZzk1RnXIeSImdMA5WhKwtoURHXKW4/96nrYZtwAAANC+2mWnj/Hjx6e3S5cubXbm5/z589PbSZMm7VW/yTIEr7zyyh77PeSQQ6K0tDS9n4S4Bx98cIPHG7N48eKorHx7d/VDDz20Tc4NAAAAAHRd7RKynnjiieltdXV1PPbYY03O+FywYEF6//jjWzZzccaMGfVroz7yyCONHrN9+/Z4+umnG+23rq7k8eS4xtT1mwSkyfna6twAAAAAQNfULiHr6NGj48gjj0zvf+9738tZAzW53P6GG26ImpqadN3Sc845p0X99u7dO04//fT0/q233troZf/J+ZJ1UUtKSuLiiy9u8NjZZ5+drv+6adOmuOmmm3Kem/T305/+NL1/3nnn1a/D2hbnBgAAAAC6pnYJWRPXXXddeon+66+/HhdeeGHMmjUr1q9fH/PmzYsrr7wy7rvvvvS45H6vXg03DTrjjDPSn2uuuSan36uvvjo9fuPGjXHRRRfF/fffn/a7ZMmS+OpXv5oGoIlLLrkkhg0blrNWbFJL4pZbbkmPT56XPD/pJ+kv6XfAgAFxxRVXtOm5AQAAAICuqaA2mVbaTn7729/GV77ylaiqanxH6EsvvTSuvfbanPYJEybUX6J/22235Tw+c+bMNJzdsWNHo/0mAe2NN97Y6GZa5eXl8bnPfa7JZQySEDUJS6dPn97o4605d1tZs2bPO3vD7mwgRD4ybsk3xiz5xpglHxm35BtjlnzUHcbt4MF927S/4mhH5557bkyePDmdNTp79uxYt25dGmJOmTIlnVF62mmn7VO/yXqn9957b9x8883pDNnVq1ena6hOnDgxvcw/OW9BQUGjzy0rK4sf/OAHceedd6Yh8MKFC9PAdMiQIXHcccfFJz/5yXS5g/Y4NwAAAADQ9bTrTFbah5ms7Ivu8C0UXY9xS74xZsk3xiz5yLgl3xiz5KPuMG4Ht/FM1va7ph0AAAAAoBsQsgIAAAAAtIKQFQAAAACgFYSsAAAAAACtIGQFAAAAAGgFISsAAAAAQCsIWQEAAAAAWkHICgAAAADQCkJWAAAAAIBWELICAAAAALSCkBUAAAAAoBWErAAAAAAArSBkBQAAAABoBSErAAAAAEArCFkBAAAAAFpByAoAAAAA0ApCVgAAAACAVhCyAgAAAAC0gpAVAAAAAKAVhKwAAAAAAK0gZAUAAAAAaAUhKwAAAABAKwhZAQAAAABaQcgKAAAAANAKQlYAAAAAgFYQsgIAAAAAtIKQFQAAAACgFYSsAAAAAACtUFBbW1vbmg4AAAAAALozM1kBAAAAAFpByAoAAAAA0ApCVgAAAACAVhCyAgAAAAC0gpAVAAAAAKAVhKwAAAAAAK0gZAUAAAAAaAUhKwAAAABAKwhZAQAAAABaQcgKAAAAANAKQlYAAAAAgFYQsgIAAAAAtIKQFQAAAACgFYSsAAAAAACtIGQFAAAAAGgFISsAAAAAQCsIWQEAAAAAWkHICgAAAADQCsWteTKQ315++eW47bbbYvbs2bFq1aq0bejQoXHUUUfF3/zN38S4ceOyLpFuaNGiRfHjH/84HZfr16+PAQMGxJQpU+LCCy+ME044IevyoFGPP/54/OY3v4kXXnghHbelpaUxZsyYOPHEE9PX00GDBmVdIjRr+/bt8eEPfzhef/31+OxnPxtXXnll1iVBA1u3bo2f//zn8dBDD8Wbb74Z5eXlMWLEiPR19vLLL0/fw0Jn89RTT8Xtt98eL774YmzcuDF69+4dEydOTF9vzz777CgsNO+NbP3zP/9zmgl84xvfiHPPPbfZYysrK+OXv/xl/P73v48lS5ZEbW1tjBw5Mk477bS49NJL089t3V1BbfJfBeh2khfSG264Iaqqqhp9vLi4OL785S/Hxz/+8Q6vje7r4Ycfjquuuir9A96YSy65JB2X0Fkkr6HXXntt3H333U0es99++8V//Md/xPTp0zu0NtgbX/3qV+NXv/pVel/ISmezcOHC+OQnPxlvvfVWo48nH+x/9KMfxbRp0zq8NmjKN7/5zbj11lubfPy4445L3x/06NGjQ+uCOsmXVsnf+5qamj2GrMkXW3/7t38bzzzzTKOPDxkyJG655ZYYP358dGe+NoFu6JFHHkm/sUrCgeRFMPnj/uSTT6Yvst/+9rfTb6OSx/7v//2/6ews6Ajz58+Pq6++Og1Yp06dmn4R8PTTT8cdd9yRfjuaSNp+8YtfZF0q1EteM+sC1lNPPTX9dj8Zt0nbF77whejVq1esW7cuPv3pT8fq1auzLhca9dhjj9UHrNDZrFmzJv7X//pfacDat2/f9AuB5L3sAw88ENddd1307NkznSH493//9+lsV+gM/ud//qc+YD388MPjpz/9afp5K7nq5ayzzkrbZ82aFddff33GldJdJa+jn//859OAtSWS19skYC0pKYl/+Id/SCfHzJw5M80V+vfvn75Gf/rTn06vjOnOzGSFbugDH/hAvPLKK3HggQemf+iTy1Z2tWnTpvRbrGXLlqVLBtxzzz2Z1Ur38alPfSr9oJ9cYv273/2uwbhM/lQlbwLuu+++dLZK8ke9T58+mdYLSWh6yimnpF9KffCDH4xvfetbOce89NJL8bGPfSw95qKLLkrDAehMkuUtkvG7du3a+jYzWelM/vf//t/pe9HkS6tkuYDki9hdJe8dkvcQieQ1Nnmthaydfvrp6bIWyYSWZMJAWVlZo+O6oKAgndRiuQs6ShKq3nTTTfGf//mfDQLW5mayJu9nP/KRj6T3/+mf/innatdksswFF1yQTpZJAtgkbO2uzGSFbiYJV5OfRPKGdPeANZF8E3XZZZfVr9u6fPnyDq+T7iVZ0yf5kNTUuEzegCaXZCfrViWzVR588MGMKoV3JLP/65ZcSd5QNiYJA+pmYteNcehMkiVYkoB1T+uwQRaSsfnHP/4xvf93f/d3OQFr4qSTToqxY8ems6vmzZuXQZXQUPJeNQlYE8m6q7sHrIm6kCqZSDBnzpwOr5HuKZl5es4556RXsiYB6+TJk1v0vJ/85Cfp7ahRo9IwdXeHHnpofOhDH6qfxd2dCVmhm0lmp9bNAGxu3apkNmGdpta/grb8g18Xpp588smNHjN8+PCYNGlSfbgFWUteG5N11Pbff/90mZU9vZ56LaWzST4IJVcGJOP3S1/6UtblQI77778/qqur0yUBLr744iaPSzZhmTt3bvzLv/xLh9YHjdl1M6um9r9IvhRo7HhoT8maqosXL07HX3LFyr//+7/v8TnJFwF1n9WSz2lFRUWNHpcsm1WXNyTraHdX/t8M3Uzybf9zzz0Xf/nLX9Jv/Zvyxhtv1N/v169fB1VHd7VgwYL0NtkluLld2JNvSRNmqtAZJLNXk92CkxCgOXWvp8lVAtBZJLOskkAq+XIruUTQEix0RnUz/JIZrMlyAbvadZPMxmYKQlaSz051n7PuvffeqKioyDkmWbItkYRdjc3QhvaQ/M1/73vfG3fddVe6NFBLAv4kNN28eXN6v7mZr3Wf0xLJl17dVXHWBQDZaGyZgDrJpQO//vWv63fFTtZuhfZUtyRFcglKc5IQNrFq1ap0ZkBxsT9jZK+5cCpZt/XRRx9N7x955JEdWBU0LZkZeM0116SbUyQbCh111FFZlwSNSpatStQFVsnM69tvvz1eeOGFdPwOHjw4XZIlWUrAmpZ0Jsmaq1dddVU6hi+99NJ01mCy10WykVuyiWvdZ61k7Ca7skNHSJZf2dvP9rsuHdjcZ7Xk9bikpCT9AiwJZrsrn06BHLfcckv9FP9kwxaXsNDeNmzY0KKZfsmuwnWXrSTfqDY36xWylozTZBOW8vLy9N8XXnhh1iVB6oc//GE8//zzcfDBB6dBAHRWdcusJO8PktfTX/3qVw0eTwKrX/7yl2lw8IMf/CCmT5+eUaXQUDJbMNlc6F//9V/j2WefTb/Q2n0ZrGRT17p1LKEj7MvkqbrPaXu6wjXJDHr37p2uSVw387U7ErJCHvr+978f3/nOd/bqOR/+8Ifjhhtu2ONxyWWvN954Y/2sgcsvv3yf64SWqguh9nS5X7L+ZZ3GLr2CziS5BLtus6uzzjorjj766KxLgvQSvuR9RHIlQPLh32XWdGbbtm1Lb++88840UH3Xu96VLtWSXF6dPJaEq9/61rfSD/Wf+cxn0ktgzQqks9i6dWvOMhd11q1bly7fdsIJJ5g0QF58Ttv9s1hjyv76nmLX53Q3pqcB9ZI3qsmMluQywuTy1+9973vNLisAbaWpBdQhX2ewJgHrz372s/Tf48ePj+uvvz7rsiB27twZ//iP/5heypdcojplypSsS4I9jtlEErAmy1r89Kc/TYPW5IN8EkxddNFFcfPNN6czqNavX5/eh87gn//5n9NlWebPnx8f//jH4w9/+EO89NJL8cQTT8SXv/zlKC0tTWdmJxu6rV27NutyoUk+p+0dM1khDyV/qN/3vvft1XPqLrNuSrK+1de//vV0PdYkWE0uJUyCAegIya7BLZmdWvdhK2H2FZ1RMoaTXdqTna4TyeXYt956qy+s6BSSmauvvvpqOgvw05/+dNblwB4ls6aStVcT1157bYMd2eu8+93vjhNPPDFd//qBBx5IAyzI0p/+9Ke47bbb0vvJBJYrrrii/rFk7eBLLrkkHbfJZ7olS5bE//t//y/diBA68+e0lsxQLf/r43ua8dqVCVkhDw0cODD9aQtJqJr8Ua97IzBgwID40Y9+FNOmTWuT/mFvvgTYsmVLs8fVre+TfKNqp3Y6m+Ry1WSn1j//+c/1O7D++Mc/dhkgncLMmTPTzVaSL6i++c1v2jiQvJB8QZWErMn7hF13rt7djBkz0pA12WwwuUS7uQ0Job3VbWqVrLva1NJrEydOTPe+SL6ITZa5+MpXvtIgzILOYtd1WJv7rJbkCtv+usRLW2UV+chyAdCN7dixI/7+7/++PmAdPXp0/Pd//7eAlcwWYV+xYkWzx61cubJ+FoAN2ehM3nzzzfjoRz9aH7Aef/zx6WurgJXO4t57762fZfL+978/JkyYkPNTJ9mspa6tO+8QTPbqdrLe09Uru4aqu171All4/fXX09vDDjus2Uutky8HElVVVen7COiMkn1a6jT3WS1Z1qWysrL+C4buyidU6KaSb/mTXS4feeSR+jcBybpA+7LjILRW3dIUS5cuTcdmU5J1rRKTJk3qsNpgT15++eU0YK37UHXBBReku1xbIgCgder+3ifrrTb3/qBuTctkOQFfbpG1uqBpbzZptaErnVWymWByteuun8UaM2/evPr7zV150NUJWaEbSv6IJ2sDvfjii+m/Tz755Pj5z38e++23X9al0U0la6klkk3X6nZjb2wW64IFC+pnCUJnkHwxcOmll6YBQOKqq66Kr33tay7FptNJNl9LdrJu7qfOpz71qfq2kSNHZlo33dtJJ51UfxnqQw891ORxTz75ZHqbXI3lSheyVjdpJXkNbS48ffbZZ9Pb5D3DmDFjOqw+2NfPasnntGSD18bUTd4aPHhwuhxGd+UvEHTTjS+ee+659H6ygVZyWWB3Xpya7CVLVRx55JHp/e9973s56/0kf8xvuOGG9ENWssbPOeeck1Gl0HCmyuc///n08qjEddddF5/5zGeyLgsalexkncyubu6nTjIbsK6toKAg07rp3o499tj6oP/GG29sdBf2++67rz6s+vCHP9zhNcLukiVZ6tZqT8ZtY1555ZX4r//6r/T+CSec0GDdS+hs6l5bk80z68btrpIZrnfeeWd6P7latju/dxCyQjezaNGiuP3229P7yTemX/3qV9P12ZJFqpv6SWYXQntLAqpk9klyyfWFF14Ys2bNSmcHJpeeXHnllemHqERyv1evXlmXC+kSK3Pnzk3vn3nmmXH++ec3+1patxkAAC2TzPBLZmEn7w9WrVqVLseSbBKUbHC1fPnydGmWL3zhC+mxhx9+eJx77rlZlwzpe4Kjjz46vZ9sbJW8d03WbE/e1ybrXCdrtifvdes2dbvmmmuyLhmadcwxx8Qpp5yS3v/617+efnmQXM2VTDS444470qu6kskHo0aNio9//OPRnRXUNjXXF+iSvvSlL6UvhHsjWUrgqKOOareaoM5vf/vbdHfVZAOAxiR/wK+99toOrwsac/rpp+/1RhXJF13QWdVtfvXZz342DQWgM23c9n/+z/9pclOryZMnx/e///0YNmxYh9cGjdm8eXO6hNCf/vSnJo/Zf//947vf/W791VzQ0ZLQ/9RTT03vf+Mb32j2i6pNmzbF5ZdfHi+99FKT4/m//uu/uv3SFxYMg26mbh1W6IySP+zJB6VbbrklZs+eHevWrUtnrU6ZMiX9xv+0007LukRIJbNR7AQM0DE+8IEPxPTp0+MnP/lJPPHEE+ms1rKysnTty7PPPjvOO+88S1/RqSSX/yfvZx944IH0Murkypdk+YBknCa7tSezAi+66KLo379/1qVCiyRj9Ze//GX6c/fdd8eSJUvSNYeTJV2SPV4++clP2uPFTFYAAAAAgNaxJisAAAAAQCsIWQEAAAAAWkHICgAAAADQCkJWAAAAAIBWELICAAAAALSCkBUAAAAAoBWErAAAAAAArSBkBQAAAABoBSErAAAAAEArCFkBAAAAAFpByAoAAAAA0ApCVgAAAACAVhCyAgAAAAC0gpAVAAAAAKAVhKwAAAAAAK0gZAUAAAAAaAUhKwAAAABAKwhZAQAAAABaQcgKAAAAANAKQlYAAAAAgFYQsgIAAAAAtIKQFQAAAACgFYSsAAAAAACtIGQFAAAAAGgFISsAAAAAQOy7/x9Aeav3rajOdAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 800x550 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 466,
       "width": 684
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_grid = np.linspace(-3, 10, 1000)\n",
    "plt.plot(\n",
    "    x_grid,\n",
    "    np.exp(f_logp_pymc(z_values=x_grid, loc=3, scale=1.0)),\n",
    "    c=\"C0\",\n",
    "    label=\"PyMC logp through the graph\",\n",
    ")\n",
    "plt.plot(\n",
    "    x_grid,\n",
    "    pz.LogNormal(mu=3, sigma=1).pdf(x_grid),\n",
    "    ls=\"--\",\n",
    "    c=\"C1\",\n",
    "    label=\"LogNormal PDF\",\n",
    ")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0a3d904",
   "metadata": {},
   "source": [
    "## Learning the `loc` and `scale` parameters\n",
    "\n",
    "Suppose now, we just have samples from some \"unknown\" lognormal distribution, we can learn parameters `loc` and `scale` by maximizing the log likelihood of the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "88dba68c",
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = pz.LogNormal(mu=2.234, sigma=0.99354).rvs(5_000)\n",
    "\n",
    "objective = -pm.logp(z, z_values, jacobian=True).mean()\n",
    "\n",
    "# We can use pytensor for automatic differentiation\n",
    "grad_objective = pt.stack(pt.grad(objective, [loc, scale]))\n",
    "# We compile the graph to make actual computations\n",
    "f_obj_grad = pytensor.function([z_values, loc, scale], [objective, grad_objective])\n",
    "\n",
    "# Next, we compute the Hessian matrix\n",
    "# It would be nicer to just use the hessian function, but pytensor is fussy and doesn't like\n",
    "# scalar inputs\n",
    "hess = pt.stack(\n",
    "    pytensor.gradient.jacobian(\n",
    "        pt.stack(pt.grad(objective, [loc, scale])), [loc, scale]\n",
    "    ),\n",
    "    axis=0,\n",
    ")\n",
    "\n",
    "f_hess = pytensor.function([z_values, loc, scale], hess)\n",
    "\n",
    "f_sample = pm.compile([loc, scale], z)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "446f2d5c",
   "metadata": {},
   "source": [
    "We can use the `scipy.optimize.minimize` function to find the maximum likelihood estimates of the `loc` and `scale` parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6704f27e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       " message: Optimization terminated successfully.\n",
       " success: True\n",
       "  status: 0\n",
       "     fun: 3.6165369785017196\n",
       "       x: [ 2.232e+00  9.664e-01]\n",
       "     nit: 10\n",
       "     jac: [ 1.643e-13 -4.547e-13]\n",
       "    nfev: 12\n",
       "    njev: 12\n",
       "    nhev: 10"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = minimize(\n",
    "    lambda x, *args: f_obj_grad(*args, *x),\n",
    "    jac=True,\n",
    "    hess=lambda x, *args: f_hess(*args, *x),\n",
    "    method=\"Newton-CG\",\n",
    "    x0=[0.8, 0.8],\n",
    "    args=(samples,),\n",
    "    tol=1e-12,\n",
    ")\n",
    "res"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79aa4f16",
   "metadata": {},
   "source": [
    "We see that we have recovered the parameters of the lognormal distribution. Let's compare the samples from the learned distribution with the original samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "feb5b9db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 557,
       "width": 860
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 6))\n",
    "az.plot_kde(\n",
    "    np.r_[*[f_sample(*res.x) for _ in range(5_000)]],\n",
    "    plot_kwargs={\"c\": \"C0\", \"label\": \"Samples from Learned Distribution\"},\n",
    "    ax=ax,\n",
    ")\n",
    "az.plot_kde(\n",
    "    samples,\n",
    "    plot_kwargs={\"c\": \"C1\", \"label\": \"Samples from Original Distribution\"},\n",
    "    ax=ax,\n",
    ")\n",
    "ax.legend(fontsize=12)\n",
    "ax.set_xlabel(\"x\", fontsize=14)\n",
    "ax.set_ylabel(\"Density\", fontsize=14)\n",
    "ax.tick_params(labelsize=12)\n",
    "ax.set_title(\n",
    "    \"Samples from LogNormal(mu=2.234, sigma=0.99354)\", fontsize=18, fontweight=\"bold\"\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f9a7a50",
   "metadata": {},
   "source": [
    "Theese distribution are essentially the same."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e8ce3cb",
   "metadata": {},
   "source": [
    "## Reproducing what PyMC does\n",
    "\n",
    "Most of the heavy lifting here was done by PyMC. It already knows how to handle the change-of-variables formula for a wide variety of functions, including $\\exp$ and affine shifts. That's why things just sort of magically worked up until now. \n",
    "\n",
    "Recall the formula for change of variables:\n",
    "\n",
    "$$\n",
    "g(x) = (f \\circ G^{-1})(x) \\left | \\frac{\\partial}{\\partial x} G^{-1}(x) \\right |\n",
    "$$\n",
    "\n",
    "Right now in the graph of $z$, we just have draws from $x$, passed through the function $G$. Or:\n",
    "\n",
    "$$\n",
    "z = G(x) \n",
    "$$\n",
    "\n",
    "To get to where we want to go, we need to:\n",
    "\n",
    "1. Iterate backwards over all the flows, applying the inverse function to the incoming samples\n",
    "2. At the same time, we also need to compute $\\left | \\frac{\\partial}{\\partial x} G^{-1}(x) \\right | $ and accumulate their products\n",
    "3. We need to get the logp of the original random variable, $f(x)$, and plug in the result of (1) as the value\n",
    "4. Finally, add the log of the product of the determinant corrections. \n",
    "\n",
    "Since in the end we need the log of the determinant, it will be easier to modify step (2) to accumulate the sum of the log determinant of the transformations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "207209eb",
   "metadata": {},
   "source": [
    "### In detail\n",
    "\n",
    "We have two transformations, $H(x) = \\exp(x)$ and $J(x) = a + bx$. Define $G$ as their composition, $G \\equiv (H \\circ J)(x) = \\exp(a + bx)$\n",
    "\n",
    "For inverses, we have $H^{-1}(x) = \\ln(x)$ and $J^{-1}(x) = \\frac{x - a}{b}$\n",
    "\n",
    "So, the inverse of their composition is $G^{-1} \\equiv (J^{-1} \\circ H^{-1}) = J^{-1}(H^{-1}(x)) = J^{-1}(\\ln(x)) = \\frac{\\ln(x) - a}{b}$\n",
    "\n",
    "For the correction term, we need the determinant of the jacobian. Since $G$ is a scalar function, this is just the absolutel value of the gradient:\n",
    "\n",
    "$$\\left | \\frac{\\partial}{\\partial x}G^{-1} \\right | = \\left | \\frac{\\partial}{\\partial x} \\frac{\\ln(x) - a}{b} \\right | = \\left | \\frac{1}{b} \\cdot \\frac{1}{x} \\right | $$\n",
    "\n",
    "We we will compute $g(z) = f(\\frac{\\ln(z) - a}{b}) \\left | \\frac{1}{b} \\cdot \\frac{1}{z} \\right |$, where $f(x) = \\frac{1}{\\sqrt{2\\pi}}\\exp(-\\frac{x^2}{2})$ is a standard normal PDF.\n",
    "\n",
    "Of course we'll work with the logp, so we will actually have:\n",
    "\n",
    "$$\\ln g(z) = -\\frac{1}{2}\\ln{\\sqrt{2\\pi}} - \\frac{1}{2}\\left (\\frac{\\ln z - a}{b} \\right )^2 - \\ln{\\left | b \\right |} - \\ln{\\left | z \\right |}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05bc8bd2",
   "metadata": {},
   "source": [
    "### Solution by hand\n",
    "\n",
    "We now implement theis analytic procesure in PyTensor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ea6f42c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def standard_normal_logp(x):\n",
    "    x = pt.as_tensor_variable(x)\n",
    "\n",
    "    kernel = -(x**2) / 2\n",
    "    normalizing_constant = -0.5 * pt.log(2 * np.pi)\n",
    "    return normalizing_constant + kernel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f1736b90",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get the parameters of the first transform (affine)\n",
    "loc, scale = transforms[0].loc, transforms[0].scale\n",
    "z_star = (pt.log(z_values) - loc) / scale\n",
    "analytic = (\n",
    "    standard_normal_logp(z_star) - pt.log(pt.abs(scale)) - pt.log(pt.abs(z_values))\n",
    ")\n",
    "# Compile the function\n",
    "f_analytic = pytensor.function([z_values, loc, scale], analytic)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "786f3be8",
   "metadata": {},
   "source": [
    "We can pass specific value now and evaluate the analytic function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "85d583bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.06681489, -3.42976537, -3.42097081, ..., -3.73252572,\n",
       "       -4.26441774, -3.43616604], shape=(5000,))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_analytic(samples, loc=3, scale=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcd081d3",
   "metadata": {},
   "source": [
    "We can verify these values are exaclty what we are expecting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7eb42be1",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.testing.assert_almost_equal(\n",
    "    actual=f_analytic(samples, loc=3, scale=1),\n",
    "    desired=pz.LogNormal(mu=3, sigma=1).logpdf(samples),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10633413",
   "metadata": {},
   "source": [
    "### Solution using autodiff\n",
    "\n",
    "Now we do it again using autodiff. We need the absolute value of the gradient through the whole composite transformation. We do it on a dummy scalar $x$, then vectorize back up to `z_values`, since that's the behavior we want.\n",
    "\n",
    "We could also do `pt.grad(f_inverse(z_values).sum(), z_values)`, and rely on the fact that the sum function introduces no cross-terms in the gradient expression. This would be the same, but would require you to grok this math fact. We also like that the vectorize way shows off `vectorize_graph`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "1e6e9c07",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = pt.dscalar(\"x\")\n",
    "# Get the inverse of the flows\n",
    "inverse_flows = [f.inverse_transform for f in reversed(transforms)]\n",
    "\n",
    "f_inverse = compose(*inverse_flows)\n",
    "# Use autodiff to compute the log jacobian determinant\n",
    "log_jac_det = pt.log(pt.abs(pt.grad(f_inverse(x), x)))\n",
    "# Vectorize the graph\n",
    "log_jac_det = vectorize_graph(log_jac_det, {x: z_values})\n",
    "\n",
    "# Compute the logp of the inverse flow\n",
    "inverse_flow = standard_normal_logp(f_inverse(z_values)) + log_jac_det\n",
    "# Compile the function\n",
    "f_logp_flow = pytensor.function(list(explicit_graph_inputs(inverse_flow)), inverse_flow)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46834a6f",
   "metadata": {},
   "source": [
    "As above let's verify taht the results are consistent and correct:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "8323642a",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.testing.assert_almost_equal(\n",
    "    actual=f_logp_flow(samples, loc=3, scale=1),\n",
    "    desired=f_logp_pymc(samples, loc=3, scale=1),\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abeea690",
   "metadata": {},
   "source": [
    "### Re-do optimization using our new implementation\n",
    "\n",
    "Finally, we can re-do the optimization using our new implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "4f6f537b",
   "metadata": {},
   "outputs": [],
   "source": [
    "objective = -inverse_flow.mean()\n",
    "\n",
    "grad_objective = pt.stack(pt.grad(objective, [loc, scale]))\n",
    "f_obj_grad = pytensor.function([z_values, loc, scale], [objective, grad_objective])\n",
    "\n",
    "hess = pt.stack(\n",
    "    pytensor.gradient.jacobian(\n",
    "        pt.stack(pt.grad(objective, [loc, scale])), [loc, scale]\n",
    "    ),\n",
    "    axis=0,\n",
    ")\n",
    "f_hess = pytensor.function([z_values, loc, scale], hess)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6f1f5acb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       " message: Optimization terminated successfully.\n",
       " success: True\n",
       "  status: 0\n",
       "     fun: 3.616536978501722\n",
       "       x: [ 2.232e+00  9.664e-01]\n",
       "     nit: 10\n",
       "     jac: [ 1.643e-13 -4.357e-13]\n",
       "    nfev: 12\n",
       "    njev: 12\n",
       "    nhev: 10"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = minimize(\n",
    "    lambda x, *args: f_obj_grad(*args, *x),\n",
    "    jac=True,\n",
    "    hess=lambda x, *args: f_hess(*args, *x),\n",
    "    method=\"Newton-CG\",\n",
    "    x0=[0.8, 0.8],\n",
    "    args=(samples,),\n",
    "    tol=1e-12,\n",
    ")\n",
    "res"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "854383a5",
   "metadata": {},
   "source": [
    "We get the expected results 🚀!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea866a18",
   "metadata": {},
   "source": [
    "## Authors\n",
    "\n",
    "- Authored by Jesse Grabowski and Ricardo Vieira in August 2025"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2a10b15",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    ":::{bibliography} :filter: docname in docnames"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbb49ec8",
   "metadata": {},
   "source": [
    "## Watermark "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "29f26df2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Sun Aug 17 2025\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.12.11\n",
      "IPython version      : 9.4.0\n",
      "\n",
      "pytensor: 2.31.7\n",
      "\n",
      "numpy     : 2.2.6\n",
      "pytensor  : 2.31.7\n",
      "arviz     : 0.22.0\n",
      "preliz    : 0.20.0\n",
      "pymc      : 5.25.1\n",
      "scipy     : 1.16.1\n",
      "matplotlib: 3.10.5\n",
      "\n",
      "Watermark: 2.5.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w -p pytensor"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3e24733",
   "metadata": {},
   "source": [
    ":::{include} ../page_footer.md \n",
    ":::"
   ]
  }
 ],
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