16. Poiseuille channel flow.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b881bae0",
   "metadata": {},
   "source": [
    "Step 14: Channel Flow with Navier–Stokes\n",
    "----\n",
    "***\n",
    "\n",
    "The only difference between this step and the previous step is that we are going to add a source term to the $u$-momentum equation, to mimic the effect of a pressure-driven channel flow. Here are our modified Navier–Stokes equations:\n",
    "\n",
    "$$\\frac{\\partial u}{\\partial t}+u\\frac{\\partial u}{\\partial x}+v\\frac{\\partial u}{\\partial y}=-\\frac{1}{\\rho}\\frac{\\partial p}{\\partial x}+\\nu\\left(\\frac{\\partial^2 u}{\\partial x^2}+\\frac{\\partial^2 u}{\\partial y^2}\\right)+F$$\n",
    "\n",
    "$$\\frac{\\partial v}{\\partial t}+u\\frac{\\partial v}{\\partial x}+v\\frac{\\partial v}{\\partial y}=-\\frac{1}{\\rho}\\frac{\\partial p}{\\partial y}+\\nu\\left(\\frac{\\partial^2 v}{\\partial x^2}+\\frac{\\partial^2 v}{\\partial y^2}\\right)$$\n",
    "\n",
    "$$\\frac{\\partial^2 p}{\\partial x^2}+\\frac{\\partial^2 p}{\\partial y^2} = \\rho\\left(\\frac{\\partial}{\\partial t}\\left(\\frac{\\partial u}{\\partial x} +\\frac{\\partial v}{\\partial y} \\right) - \\frac{\\partial u}{\\partial x}\\frac{\\partial u}{\\partial x}-2\\frac{\\partial u}{\\partial y}\\frac{\\partial v}{\\partial x}-\\frac{\\partial v}{\\partial y}\\frac{\\partial v}{\\partial y} \\right)$$\n",
    "\n",
    "The initial condition is $u, v, p=0$ everywhere, and at the boundary conditions are:\n",
    "\n",
    "$u, v, p$ are periodic on $x=0,2$\n",
    "\n",
    "$u, v =0$ at $y =0,2$\n",
    "\n",
    "$\\frac{\\partial p}{\\partial y}=0$ at $y =0,2$\n",
    "\n",
    "$F=1$ everywhere.\n",
    "\n",
    "Let's begin by importing our usual run of libraries:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5ba4088b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt, cm\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f1b0cf4",
   "metadata": {},
   "source": [
    "In step 13, we isolated a portion of our transposed equation to make it easier to parse and we're going to do the same thing here.  One thing to note is that we have periodic boundary conditions throughout this grid, so we need to explicitly calculate the values at the leading and trailing edge of our `u` vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4147ca9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_up_b(rho, dt, dx, dy, u, v):\n",
    "    b = np.zeros_like(u)\n",
    "    b[1:-1, 1:-1] = (rho * (1 / dt * ((u[1:-1, 2:] - u[1:-1, 0:-2]) / (2 * dx) +\n",
    "                                      (v[2:, 1:-1] - v[0:-2, 1:-1]) / (2 * dy)) -\n",
    "                            ((u[1:-1, 2:] - u[1:-1, 0:-2]) / (2 * dx))**2 -\n",
    "                            2 * ((u[2:, 1:-1] - u[0:-2, 1:-1]) / (2 * dy) *\n",
    "                                 (v[1:-1, 2:] - v[1:-1, 0:-2]) / (2 * dx))-\n",
    "                            ((v[2:, 1:-1] - v[0:-2, 1:-1]) / (2 * dy))**2))\n",
    "    \n",
    "    # Periodic BC Pressure @ x = 2\n",
    "    b[1:-1, -1] = (rho * (1 / dt * ((u[1:-1, 0] - u[1:-1,-2]) / (2 * dx) +\n",
    "                                    (v[2:, -1] - v[0:-2, -1]) / (2 * dy)) -\n",
    "                          ((u[1:-1, 0] - u[1:-1, -2]) / (2 * dx))**2 -\n",
    "                          2 * ((u[2:, -1] - u[0:-2, -1]) / (2 * dy) *\n",
    "                               (v[1:-1, 0] - v[1:-1, -2]) / (2 * dx)) -\n",
    "                          ((v[2:, -1] - v[0:-2, -1]) / (2 * dy))**2))\n",
    "\n",
    "    # Periodic BC Pressure @ x = 0\n",
    "    b[1:-1, 0] = (rho * (1 / dt * ((u[1:-1, 1] - u[1:-1, -1]) / (2 * dx) +\n",
    "                                   (v[2:, 0] - v[0:-2, 0]) / (2 * dy)) -\n",
    "                         ((u[1:-1, 1] - u[1:-1, -1]) / (2 * dx))**2 -\n",
    "                         2 * ((u[2:, 0] - u[0:-2, 0]) / (2 * dy) *\n",
    "                              (v[1:-1, 1] - v[1:-1, -1]) / (2 * dx))-\n",
    "                         ((v[2:, 0] - v[0:-2, 0]) / (2 * dy))**2))\n",
    "    \n",
    "    return b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b787c3b",
   "metadata": {},
   "source": [
    "We'll also define a Pressure Poisson iterative function, again like we did in Step 11.  Once more, note that we have to include the periodic boundary conditions at the leading and trailing edge.  We also have to specify the boundary conditions at the top and bottom of our grid.  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d8899b59",
   "metadata": {},
   "outputs": [],
   "source": [
    "def pressure_poisson_periodic(p, dx, dy):\n",
    "    pn = np.empty_like(p)\n",
    "    \n",
    "    for q in range(nit):\n",
    "        pn = p.copy()\n",
    "        p[1:-1, 1:-1] = (((pn[1:-1, 2:] + pn[1:-1, 0:-2]) * dy**2 +\n",
    "                          (pn[2:, 1:-1] + pn[0:-2, 1:-1]) * dx**2) /\n",
    "                         (2 * (dx**2 + dy**2)) -\n",
    "                         dx**2 * dy**2 / (2 * (dx**2 + dy**2)) * b[1:-1, 1:-1])\n",
    "\n",
    "        # Periodic BC Pressure @ x = 2\n",
    "        p[1:-1, -1] = (((pn[1:-1, 0] + pn[1:-1, -2])* dy**2 +\n",
    "                        (pn[2:, -1] + pn[0:-2, -1]) * dx**2) /\n",
    "                       (2 * (dx**2 + dy**2)) -\n",
    "                       dx**2 * dy**2 / (2 * (dx**2 + dy**2)) * b[1:-1, -1])\n",
    "\n",
    "        # Periodic BC Pressure @ x = 0\n",
    "        p[1:-1, 0] = (((pn[1:-1, 1] + pn[1:-1, -1])* dy**2 +\n",
    "                       (pn[2:, 0] + pn[0:-2, 0]) * dx**2) /\n",
    "                      (2 * (dx**2 + dy**2)) -\n",
    "                      dx**2 * dy**2 / (2 * (dx**2 + dy**2)) * b[1:-1, 0])\n",
    "        \n",
    "        # Wall boundary conditions, pressure\n",
    "        p[-1, :] =p[-2, :]  # dp/dy = 0 at y = 2\n",
    "        p[0, :] = p[1, :]  # dp/dy = 0 at y = 0\n",
    "    \n",
    "    return p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9b10b5fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "##variable declarations\n",
    "nx = 41\n",
    "ny = 41\n",
    "#nt = 10\n",
    "nit = 80 \n",
    "#c = 1\n",
    "H = 2\n",
    "dx = H / (nx - 1)\n",
    "dy = H / (ny - 1)\n",
    "x = np.linspace(0, H, nx)\n",
    "y = np.linspace(0, H, ny)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "\n",
    "\n",
    "##physical variables\n",
    "rho = 2\n",
    "nu = .01\n",
    "mu = nu * rho\n",
    "\n",
    "F = 1\n",
    "dpdx = F * rho \n",
    "dt = .1\n",
    "\n",
    "#initial conditions\n",
    "u = np.zeros((ny, nx))\n",
    "un = np.zeros((ny, nx))\n",
    "\n",
    "v = np.zeros((ny, nx))\n",
    "vn = np.zeros((ny, nx))\n",
    "\n",
    "p = np.ones((ny, nx))\n",
    "pn = np.ones((ny, nx))\n",
    "\n",
    "b = np.zeros((ny, nx))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e57f06c",
   "metadata": {},
   "source": [
    "For the meat of our computation, we're going to reach back to a trick we used in Step 11 for Laplace's Equation.  We're interested in what our grid will look like once we've reached a near-steady state.  We can either specify a number of timesteps `nt` and increment it until we're satisfied with the results, or we can tell our code to run until the difference between two consecutive iterations is very small.  \n",
    "\n",
    "We also have to manage **8** separate boundary conditions for each iteration.  The code below writes each of them out explicitly.  If you're interested in a challenge, you can try to write a function which can handle some or all of these boundary conditions.  If you're interested in tackling that, you should probably read up on Python [dictionaries](http://docs.python.org/2/tutorial/datastructures.html#dictionaries).  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "39cbfa90",
   "metadata": {},
   "outputs": [],
   "source": [
    "udiff = 1\n",
    "stepcount = 0\n",
    "\n",
    "while udiff > 1e-6:\n",
    "    un = u.copy()\n",
    "    vn = v.copy()\n",
    "\n",
    "    b = build_up_b(rho, dt, dx, dy, u, v)\n",
    "    p = pressure_poisson_periodic(p, dx, dy)\n",
    "\n",
    "    u[1:-1, 1:-1] = (un[1:-1, 1:-1] -\n",
    "                     un[1:-1, 1:-1] * dt / dx * \n",
    "                    (un[1:-1, 1:-1] - un[1:-1, 0:-2]) -\n",
    "                     vn[1:-1, 1:-1] * dt / dy * \n",
    "                    (un[1:-1, 1:-1] - un[0:-2, 1:-1]) -\n",
    "                     dt / (2 * rho * dx) * \n",
    "                    (p[1:-1, 2:] - p[1:-1, 0:-2]) +\n",
    "                     nu * (dt / dx**2 * \n",
    "                    (un[1:-1, 2:] - 2 * un[1:-1, 1:-1] + un[1:-1, 0:-2]) +\n",
    "                     dt / dy**2 * \n",
    "                    (un[2:, 1:-1] - 2 * un[1:-1, 1:-1] + un[0:-2, 1:-1])) + \n",
    "                     F * dt)\n",
    "\n",
    "    v[1:-1, 1:-1] = (vn[1:-1, 1:-1] -\n",
    "                     un[1:-1, 1:-1] * dt / dx * \n",
    "                    (vn[1:-1, 1:-1] - vn[1:-1, 0:-2]) -\n",
    "                     vn[1:-1, 1:-1] * dt / dy * \n",
    "                    (vn[1:-1, 1:-1] - vn[0:-2, 1:-1]) -\n",
    "                     dt / (2 * rho * dy) * \n",
    "                    (p[2:, 1:-1] - p[0:-2, 1:-1]) +\n",
    "                     nu * (dt / dx**2 *\n",
    "                    (vn[1:-1, 2:] - 2 * vn[1:-1, 1:-1] + vn[1:-1, 0:-2]) +\n",
    "                     dt / dy**2 * \n",
    "                    (vn[2:, 1:-1] - 2 * vn[1:-1, 1:-1] + vn[0:-2, 1:-1])))\n",
    "\n",
    "    # Periodic BC u @ x = 2     \n",
    "    u[1:-1, -1] = (un[1:-1, -1] - un[1:-1, -1] * dt / dx * \n",
    "                  (un[1:-1, -1] - un[1:-1, -2]) -\n",
    "                   vn[1:-1, -1] * dt / dy * \n",
    "                  (un[1:-1, -1] - un[0:-2, -1]) -\n",
    "                   dt / (2 * rho * dx) *\n",
    "                  (p[1:-1, 0] - p[1:-1, -2]) + \n",
    "                   nu * (dt / dx**2 * \n",
    "                  (un[1:-1, 0] - 2 * un[1:-1,-1] + un[1:-1, -2]) +\n",
    "                   dt / dy**2 * \n",
    "                  (un[2:, -1] - 2 * un[1:-1, -1] + un[0:-2, -1])) + F * dt)\n",
    "\n",
    "    # Periodic BC u @ x = 0\n",
    "    u[1:-1, 0] = (un[1:-1, 0] - un[1:-1, 0] * dt / dx *\n",
    "                 (un[1:-1, 0] - un[1:-1, -1]) -\n",
    "                  vn[1:-1, 0] * dt / dy * \n",
    "                 (un[1:-1, 0] - un[0:-2, 0]) - \n",
    "                  dt / (2 * rho * dx) * \n",
    "                 (p[1:-1, 1] - p[1:-1, -1]) + \n",
    "                  nu * (dt / dx**2 * \n",
    "                 (un[1:-1, 1] - 2 * un[1:-1, 0] + un[1:-1, -1]) +\n",
    "                  dt / dy**2 *\n",
    "                 (un[2:, 0] - 2 * un[1:-1, 0] + un[0:-2, 0])) + F * dt)\n",
    "\n",
    "    # Periodic BC v @ x = 2\n",
    "    v[1:-1, -1] = (vn[1:-1, -1] - un[1:-1, -1] * dt / dx *\n",
    "                  (vn[1:-1, -1] - vn[1:-1, -2]) - \n",
    "                   vn[1:-1, -1] * dt / dy *\n",
    "                  (vn[1:-1, -1] - vn[0:-2, -1]) -\n",
    "                   dt / (2 * rho * dy) * \n",
    "                  (p[2:, -1] - p[0:-2, -1]) +\n",
    "                   nu * (dt / dx**2 *\n",
    "                  (vn[1:-1, 0] - 2 * vn[1:-1, -1] + vn[1:-1, -2]) +\n",
    "                   dt / dy**2 *\n",
    "                  (vn[2:, -1] - 2 * vn[1:-1, -1] + vn[0:-2, -1])))\n",
    "\n",
    "    # Periodic BC v @ x = 0\n",
    "    v[1:-1, 0] = (vn[1:-1, 0] - un[1:-1, 0] * dt / dx *\n",
    "                 (vn[1:-1, 0] - vn[1:-1, -1]) -\n",
    "                  vn[1:-1, 0] * dt / dy *\n",
    "                 (vn[1:-1, 0] - vn[0:-2, 0]) -\n",
    "                  dt / (2 * rho * dy) * \n",
    "                 (p[2:, 0] - p[0:-2, 0]) +\n",
    "                  nu * (dt / dx**2 * \n",
    "                 (vn[1:-1, 1] - 2 * vn[1:-1, 0] + vn[1:-1, -1]) +\n",
    "                  dt / dy**2 * \n",
    "                 (vn[2:, 0] - 2 * vn[1:-1, 0] + vn[0:-2, 0])))\n",
    "\n",
    "\n",
    "    # Wall BC: u,v = 0 @ y = 0,2\n",
    "    u[0, :] = 0\n",
    "    u[-1, :] = 0\n",
    "    v[0, :] = 0\n",
    "    v[-1, :]=0\n",
    "    \n",
    "    udiff = (np.sum(u) - np.sum(un)) / np.sum(u)\n",
    "    #print(udiff)\n",
    "    stepcount += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1decc6d",
   "metadata": {},
   "source": [
    "You can see that we've also included a variable `stepcount` to see how many iterations our loop went through before our stop condition was met.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "95c6a2b0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3159\n"
     ]
    }
   ],
   "source": [
    "print(stepcount)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43aaffeb",
   "metadata": {},
   "source": [
    "If you want to see how the number of iterations increases as our `udiff` condition gets smaller and smaller, try defining a function to perform the `while` loop written above that takes an input `udiff` and outputs the number of iterations that the function runs.  \n",
    "\n",
    "For now, let's look at our results.  We've used the quiver function to look at the cavity flow results and it works well for channel flow, too.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "129d9bd9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lJCRIXFycrFixwua+LVmypDz11FMyZ86cAvk+2B7p6enqsdy7d2+b+TZs2FCGDBkimzdvdtkP+gpqbcAisoAZNGiQzT+GnEbTpk3lgw8+kL///tul/khCQ0MdzjUgIEDuv/9+mTx5spw/f97oFOy2ZMkSp/Zt5cqV5dVXX5U//vjDpT4N79Gjh8O5enh4SPv27eWLL76Q/fv3u8wb07i4OKf2bYkSJeSJJ56QX375Ra5fv250GnYbPXq0U/nWr19fBg8eLBs3bnSpT8Pr1KnjcK6+vr4SExMj3377rZw6dcroFOy2efNmp/ZtuXLl5MUXX5TffvtNbt26ZXQaduvbt6/DuSqKIq1atZJPPvlE/vvvP5c5T4mIeHh4OJxvUFCQPPzww/Lzzz/LlStXjE7BblOnTnXqWK5Zs6a89dZbsmbNGpf6oK99+/YO5+rt7S1dunSR//3vf3L06FGjU7DboUOHnNq3pUqVkmeffVbmz58vN27cMDoNuxXU2oBFZAHj7IFiPTK/2j506JDR6eTKmSLy3hEeHi6jR48u8N9QOltEWo/MttfVq1cbnU6unCki7x3Vq1eXt956Sy5cuGB0OjY5W0Raj8y216lTpxb4D4KcLSKtR2bb665du4xOJ1fOFJH3jsaNG8vHH39c4N+4OFtEWo/MttclS5YYnU6unCki7x0VK1aUV155xSVa55wpIq1HZtvrN998U+ALLGeLSOuR2fa6ZcsWo9PJlTNF5L2jbt26MmTIkALf4utsEWk9MtteZ8+eXeA/CCqotYEjRaQXqEDz8fFB586dYTabYTKZULFiRaND0lXZsmVhMplgNpvRuXNn+Pn5GR2SbhRFQXh4uJpvw4YNjQ5JV4GBgejWrRvMZjNiY2MREhJidEi6qlGjhvp3265dO3h4uO91zLy8vNChQweYzWaYzWZUq1bN6JB0FRoaiu7du8NsNiMyMhJFixY1OiRdNWnSRD1PNWvWzOhwdOXv74/IyEiYzWZ0794dZcqUMTokXVWqVEn9u42IiICXl/u+LfTw8EDbtm3VY7l27dpGh6Sr4sWLIyYmBmazGdHR0ShWrJjRIemqXr166mtuq1atoCiK0SHppqDUBu57tihAWrZsiZdeegkAMGPGjFwv01yqVCn1JNe1a1eXe4PyzDPP4ObNmzh37hwWLVqU6/xmzZqp+TZt2tSl/vArVaqk7ts///wz10uOBwQEICoqSn2DUrp06fwIUzPR0dEICwtDeno6Jk+enNkFkKMqVaqoJ7mIiAj4+PjkU6R55+vrq+7bffv2Yd26dTbne3p6om3btuobslq1auVHmJpp1KiRmu+8efNyvTVCiRIlEBsbC7PZjG7duiE4ODg/wtRMr169cOHCBcTFxWH27Nm5zm/QoIF6LIeHh8PT0zMfotRG6dKl1X27ceNG7Nq1y+Z8X19fdOnSRc23fPny+RGmZjp27Ahvb2+ICH744Ydcb3tRrlw59e+2U6dO8Pf3z6dItdGvXz+ICI4dO4Y//vjD5lxFUdCqVSv1Nbd+/fou9Zpbq1Yt9VheunQpTp06ZXN+UFAQoqOjYTabERMTg5IlS+ZHmJp54IEHUL9+fdy6dQs//fRTrvNr1aql/t22bdvWpT4UCA4OVvft9u3bsW3bNpvzvb29ERERoeZbtWrV/AhTM25RG+T2VaWrDBTgdtZMW7ZsyfEr6UaNGsmQIUNky5YtBb7tzV4vvvhitrn6+fmJyWSSiRMnuvQFhKzFx8dL8eLFs823QoUK0r9/f1m2bFmBb8+1188//5xjW1Tbtm1lxIgRsmfPngLfTmKviIiIbPMNDg6WXr16yYwZM1z2AkL3OnjwYI7tcXXq1JGBAwfK+vXrC3zbm73ee++9HNuioqKiZPz48S59ASFrKSkpUqFChWzzDQsLk759+8qiRYtc9gJC91q6dGmOr7ktWrSQ4cOHy44dO9zmPPXggw9mm2vRokWlZ8+eMnXqVJe+gJC1c+fOiZ+fX7b5VqtWTd544w1ZtWqVy15A6F5jx47NNldPT0/p1KmTjBkzxiWWO9kjIyND6tevn22+JUuWlN69e8vcuXML9Pt9RxS02oBrIguomJiYu96gREdHyzfffOMSay4cdeLEibsu0Vy2bFl54YUXZMmSJW51K5NMn3zyiZqroijSsmVL+fjjj+Xff/91mzcomdLS0qRGjRpqvoGBgfLQQw/JTz/9JJcvXzY6PM2tWbPmrpN6jRo15M0335TVq1e71a1MMj311FNqrl5eXtK5c2f58ssv5ciRI0aHprkrV65I0aJF1XxDQ0PlmWeekXnz5rnVrUwyfffdd3cdy02aNJH3339ftm3b5jYfXmayWCzSokULNVd/f3+57777ZNKkSW53KxMRkf/++++ufVupUiV55ZVXXO7ibfayvmJ25sXbRo4cKfv27XO719zExEQpXbq0mm/x4sXl8ccfl1mzZsm1a9eMDk9zc+fOvetYrlevngwaNEg2bNjgUhdvs1dBqw0cKSIVyaUdzVUoihIEID4+Ph5BQUFGh5PF1q1bcf/996vraArMV9E6eemll7Bt2za1RcjV2lQdkZCQgPr166NZs2Yu26bqiGnTpmHYsGEu26bqqK5duyItLc1l21QdcejQIbRr105du+qKbaqOGDJkCJYsWeKybaqOSE1NRYMGDVC9enWXbVN1xLJly/DCCy+4dJuqIx555BGcPn1azdfV2lQdcf78eTRp0kRtZXTFNlVHfPnll5g4caLLtqk6wmKxoEWLFihRooTLtqk6oiDWBgkJCZmv+8EiYrPHlkVkPrl69SqKFy/u1hfXsHb58mWEhoYaHUa+uHHjBry9vd36IkDWLl++jJCQELd9g2ItIyMD8fHxKFGihNGh5Iu4uDgEBQW57RuUexWm81RiYiIAoEiRIgZHkj+uXLmCkiVLForzlIjg6tWrbn+xskzXr19HQECAW394aa0wnadSUlKQkpJSIN/H66Eg1gYsIgvJwUdERERERKQFR4rIglP6EhERERERUYHncBGpKEoHRVGWKIpyTlEUURTlgVzm/3hn3r1jr9WcZ3KYUzj6A4mIiIiIiFyEM99EFgHwH4BX7Jz/OoAyVqMCgDgAc++Zl3DPvDIikuxEfERERERERKQTh6+eICK/A/gdgF0L1kUkHkB85r/vfHNZHMDUrFPlgqPxEBERERERUf4xYk3kcwBWicjJe35eVFGUk4qinFEU5TdFUZrY2oiiKL6KogRlDgCBukVMREREREREAPK5iFQUpQyAGACT73noAIBnANwH4DEAyQA2KopSw8bmBuP2N5yZ44zW8RIREREREdHd8vubyGcAXAew0PqHIrJFRKaLyH8i8heARwAcAvCqjW2NABBsNdz3rslEREREREQFRL7dUVq5vYCyD4BpIpJqa66IWBRF+RtAjt9EikgKgBSr7WsVKhEREREREeUgP7+JjABQHcCU3CbeKTgbAzivc0xERERERETkAIe/iVQUpShuF4OZqiiK0hhAnIicUhRlBIByItL7nl99DsBWEdmTzTaHAdgC4DCAIACv4XYR+bKj8REREREREZF+nGlnbQ5gjdW/x97570+4veaxDICK1r+gKEowgAdx+56R2SkG4HsAYbh9kZydADqIyDYn4iMiIiIiIiKdKCJidAyauHObj/j4+HgEBQUZHQ4REREREZHLSEhIQHBwMAAEi0iCrblG3CeSiIiIiIiIXBSLSCIiIiIiIrIbi0giIiIiIiKyG4tIIiIiIiIishuLSCIiIiIiIrIbi0giIiIiIiKyG4tIIiIiIiIishuLSCIiIiIiIrIbi0giIiIiIiKyG4tIIiIiIiIishuLSCIiIiIiIrIbi0giIiIiIiKyG4vIAmrUqFH49ddfkZCQYHQoujtz5gzef/99bN26FRaLxehwdDd79mx8//33OHfunNGh6C49PR1Dhw7F8uXLkZycbHQ4uvv7778xcuRI7N27FyJidDi6+/rrrzFz5kxcu3bN6FB0d+3aNbz33nvYsGED0tPTjQ5Hd7/99hu+/vprnDx50uhQdCci+Oijj7B48WLcunXL6HB0d+DAAXz88cfYuXNnoThPTZ06FT/++CMuXbpkdCi6S0pKwnvvvYfVq1cjLS3N6HB0t2bNGowdOxaHDx82OpR8UdBqAxaRBVSlSpXw8MMPIyQkBFFRUfjqq69w/Phxo8PSRfny5bFt2za0atUKZcuWxXPPPYeFCxciMTHR6NB0ER4ejpdffhnlypVD8+bNMXz4cOzYscMtX8y9vLzg4+ODmJgYhISEoEePHvjhhx9w8eJFo0PTRZMmTTBp0iTUr18f1apVw+uvv45Vq1YhNTXV6NB0UadOHTzxxBMIDQ1Fx44dMXr0aBw8eNDosHRRvHhxnDx5Eu3bt0fp0qXx1FNPYc6cOYiPjzc6NF20atUKgwYNQuXKldGwYUMMGTIEW7ZsQUZGhtGhaU5RFISEhOD+++9HyZIlYTKZ8N133+HMmTNGh6aLWrVqYdGiRWjatCkqVqyIl156CcuWLXPbD/oaN26MZ599FmFhYWjTpg0+++wz7N692y1fc/39/ZGYmIguXbogJCQEjz76KKZPn46rV68aHZouwsPD8fnnn6NmzZqoXbs23nnnHaxfv95tP+grcLWBiLjFABAEQOLj48UdZGRkSN26dQXAXaNevXoyaNAg2bhxo6SnpxsdpmY2btyYJVdfX1+JiYmRb775Rk6dOmV0iJrq27dvlnzLli0rL7zwgixZskRu3bpldIiauXbtmhQrVuyuXBVFkZYtW8onn3wi//77r1gsFqPD1MzUqVOz7NvAwEB56KGH5KeffpLLly8bHaJmLBaLtGvXLku+NWrUkDfffFPWrFkjqampRoepmf3794uiKHfl6uXlJV26dJH//e9/cuTIEaND1NSgQYOy7NvQ0FB55plnZN68eXLjxg2jQ9RMcnKylCtXLku+TZo0kQ8++ED+/vtvycjIMDpMzSxZsiRLrgEBAXLffffJpEmT5Ny5c0aHqKkHHnggS76VK1eWV155Rf744w9JTk42OkTNnD17Vnx9fe/K1cPDQ9q3by9ffPGF7Nu3z61ec0eNGpVl3xYvXlwef/xxmTVrlly7ds3oEDWTH7VBfHx85naDJJfaSxE3+SRGUZQgAPHx8fEICgoyOpy7xMfH48aNGw7/3rx58/DGG2/k+HhISAhiY2NhNpsRFRVVYPI+d+6cU22pDz/8MLZs2ZLj440aNYLZbIbZbEbz5s3h4WH8F+lJSUlOfcJ3/PhxRERE5PhJqL+/P7p06QKz2QyTyYSyZcvmNVRNXLlyxalPq0eOHImvv/46x8crVqwIk8kEs9mMjh07ws/PLy9hasJisTjVcpyeno42bdrg/Pnz2T7u4eGB1q1bq/u2bt26UBQlr+Hm2Y0bN5z6Vm316tV4+umnc3y8WLFiiI6OhtlsRkxMDIoXL56XMDVz4cIFpz6tfuGFF/D777/n+HidOnXU81SrVq3g5eWVlzA1kZKSgsuXLzv8e1euXEHLli1z/Cbdx8cHnTp1Uo/lSpUq5TVUTVy7ds2pTpZJkybho48+yvHxMmXKoHv37jCbzejatSsCAgLyEqZmnPnGVEQQGRlps3OgRYsW6r5t3LhxgThPJSYmOtU+v3PnTtx33305Pl60aFFERUXBbDaje/fuCA0NzUuYmrl06ZJTnSyDBg3CjBkzcny8WrVq6nmqffv28Pb2zkuYmkhLS3OqSykxMRHh4eE5tnh6eXmhffv26rFco0aNvIaqiYJaGyQkJCA4OBgAgkXEdt9sblWmqwwU4G8is/s0V+vh7e0tkZGRMm7cODl27Jih+YaGhuqeb+nSpaVPnz6yYMECuXnzpmG5Zvdprh6jWbNm8uGHH8r27dsN/QSxR48euudapEgR6dGjh0yZMkUuXLhgWK5xcXH5sm+rVKkir732mqxcuVJSUlIMy3f06NG65+rp6SkREREyevRoOXDggGG5iojUqVNH93xLlCghTz75pMyePVuuX79uWK6bN2/Ol2O5QYMG8t5778nmzZsN7ZTJrtND6+Hn5yfdu3eXCRMmyOnTpw3LVUTEw8ND93zLly8v/fr1k6VLl0pSUpJhuWbX6aH1UBRFWrduLZ999pns2rXL0Nfc9u3b655vUFCQPPLIIzJt2jS5cuWKYbkeOnQoX85TtWrVkrffflvWrVsnaWlphuVbUGsDR76JNLz402qgkBeR94569erJ559/bsjJPj+KSOuR2fa6evXqfM81v4pI61G2bFl59dVX5eLFi/meb34UkdYjs+11ypQp+d5Kll9FpPUIDAyUhx9+WHbt2pWvuYrkTxF576hRo4YMGzbMkA+C8qOItB6Zba9LlizJ91zzq4i0HqGhofL8888bshQhP4rIe0eTJk3kq6++MuRNaX4UkdYjICBA7r//ftmyZUu+55ofReS9o3LlyjJw4EBD2iLzo4i0Hpltr7Nmzcr34jm/ikjrUbx4cXnqqafk8OHD+ZqrSMGtDRwpIo3vsyFNVa9eXW1RaNeuXYFoUdCLl5cXOnTooLYoVK9e3eiQdBUSEqK2UkVFRSEwMNDokHTVuHFj9Vhu1qxZgWhf1ou/vz8iIyNhNpsRGxtbYNqX9VKxYkV133bs2BG+vr5Gh6QbDw8PtGnTRs23du3aRoekq+LFiyMmJgZmsxndunUrMO3Leqlbt+5d7cuenp5Gh6QbHx8fdO7cWW35LCjty3opU6aMusyiS5cuBaZ9WS/h4eHqsdywYcMC0b6sl8DAQHTr1k1dZlFQ2pf1oldtwCIyH7Rv396ptTenTp3CnDlzbM7x9PRE27Zt1YOjZs2ahv/h9+/f36n1KL/99hsOHDhgc06JEiUQGxsLk8mEbt26oVixYk5GqY2qVavi7bffdvj3UlNTMX78+BzXRGaqX7++um/Dw8MNf4Ny//33o1q1ag7/3s6dO/Hnn3/anOPr66uuA+3evTsqVKjgbJia8PX1dWrfAsDPP/+c6+Xky5Urp75B6dy5M/z9/Z16Lq00b97cqXwvXbqEn3/+2eYcRVHQsmVL9ViuX7++4eepZ5991qlL/v/555/YuXOnzTlBQUHqOtDo6GiEhIQ4G6YmypQp49S+FRGMHz8+1zVZNWvWVPdt27ZtDV8HGhUV5dRrw4EDB/Dbb7/ZnOPt7Y2IiAj1w8uqVas6GaV23nrrrVxfS7Lz66+/4sSJEzbnlCpVSv3wMjIyEkWLFnUySm3Uq1fPqWP5xo0bmDhxYq7zmjZtqh7LTZo0MfzDy169eqFly5YO/97mzZuxceNGm3MCAgLUdaCxsbEICwtzNkxNFCtWzOnX3IkTJ+a6vrBy5crqvo2IiICPj49Tz6UVt6gNcvuq0lUGCnA7q7OeeeaZbL+ODg4Oll69esn06dPl6tWrRoepiatXr0pQUFC2+dauXVveeecdWb9+vaH961qaNGlStrl6e3tLVFSUjB8/Xo4fP250mJqwWCzSqlWrbPMtXbq0PPfcc7Jw4UJD17Zqaffu3Vmu4Jk5mjdvLsOHD5cdO3a4zdXx3nrrrWxzLVKkiPTs2VN++OEHQ1qv9XDr1i0pU6ZMtvlWrVpVXn/9dVm1apWha1u1tGDBgmxz9fT0lI4dO8qYMWPk4MGDRoepGZPJlG2+JUuWlN69e8ucOXPc5j3GqVOnxMfHJ9t8GzZsKEOGDJEtW7a4zRVpR4wYkW2ufn5+YjKZ5LvvvpMzZ84YHaYm0tPTpVatWtnmW6FCBXnppZdk2bJlhq5t1dK6deuyzVVRFGnTpo2MGDFC9uzZ4zavuXrXBlwT6QYOHz4snp6e6sFRvXp1GTBggKxevdqtLpmf6f3331dz9fLyks6dO8uXX35pSJ+63lJSUqRy5cpqviEhIfL000/Lr7/+KgkJCUaHp7nly5ffdaJr3LixvP/++7Jt2za3eYNi7ZFHHlFz9ff3Vy+Zf/bsWaND09yFCxfE399fzbdixYry8ssvy/Lly93qkvmZxo0bp+bq4eEh7dq1k5EjR7rdJfNFbn/407hx47vWDj3++OMyc+ZMiYuLMzo8zf399993nafq1q0r7777rmzYsMGtbqeVqX///mquPj4+Eh0dLd98842cOHHC6NA0l5CQICVLllTzLVOmjDz//POyePFiSUxMNDo8zc2YMeOuYzk8PFw+/vhjt7udVqbOnTuruWbeTuvHH3+US5cuGR2a5vKjNuAtPgrIrS7y4vnnn8ehQ4cKVJuqXuLi4tC8eXO0bdu2wLSp6mny5MkYN25cgWpT1YuIoHPnzggICCgwbap62rNnD2JjY9XLaxeENlU9DRw4EH/99VeBalPVS1JSEpo2bYqGDRsWmDZVPS1cuBDvvvtugWpT1dODDz6IhISEAtWmqpfTp0+jbdu26Nq1a4FpU9XTyJEjMWfOnALVpqqXjIwMtGzZEhUqVCgwbap6Wr9+PZ5++ukC1aaqp/yoDRy5xQeLyAIqISHBLfKwR2JiInx9fd36DYq1wrRv09PTkZKSgiJFihgdSr64ceMGihYt6raF1L0K07GclJQET09Pt36DYq0w7VsRwY0bNwpNvjdv3kRAQIDbFlL3KkzHcmpqKiwWS4G413J+SEhIQGBgIF9zNX4OFpFERERERERkF0eKyMLxMRQRERERERFpgkUkERERERER2Y1FJBEREREREdmNRSQRERERERHZjUUkERERERER2Y1FJBEREREREdmNRSQRERERERHZjUUkERERERER2Y1FJBEREREREdmNRSQRERERERHZjUUkERERERER2Y1FJBEREREREdmNRSQRERERERHZjUUkERERERER2Y1FJBEREREREdmNRSQRERERERHZjUUkERERERER2Y1FJBEREREREdmNRSQRERERERHZjUUkERERERER2Y1FJBEREREREdmNRSQRERERERHZjUUkERERERER2Y1FJBEREREREdmNRaQL+/nnn/HVV1/h+PHjRoeiu7S0NLz11ltYsGABbt68aXQ4utu0aRM+/PBDbN++HSJidDi6GzNmDH744QdcvHjR6FB0d+XKFQwYMAArV65Eamqq0eHobv78+Rg9ejQOHjxodCi6s1gsGDx4MObMmYP4+Hijw9Hd7t278d5772Hz5s3IyMgwOhzdTZgwAd999x3OnDljdCi6S0xMxIABA7B06VIkJSUZHY7uVqxYgc8++wy7d+8uFK+5H330EaZPn46rV68aHYruTp48ibfffhvr1q1Denq60eHoLl9rAxFxaADoAGAJgHMABMADuczveGfevaP2PfMeBLAPQMqd//ZwMK4gABIfHy+FxdGjR8XLy0sASL169WTQoEGyYcMGSU9PNzo0XXz44YcCQHx9fSU6Olq++eYbOXnypNFh6SI1NVWqVq0qAKRs2bLywgsvyJIlSyQxMdHo0HSxatUqASCKokjLli3l448/ln///VcsFovRoeniscceEwASGBgoDz30kPz0009y+fJlo8PSxaVLl6RIkSICQGrUqCFvvvmmrF69WlJTU40OTRdff/21ABAvLy/p3LmzfPnll3LkyBGjw9KFxWKRpk2bCgAJDQ2VZ555RubNmycJCQlGh6aLHTt2qO9hmjRpIu+//75s27ZNMjIyjA5NF6+++qoAkICAALnvvvtk0qRJcu7cOaPD0sXNmzclJCREAEilSpXklVdekeXLl0tycrLRoenil19+EQDi4eEh7dq1k5EjR8q+ffvc9jU3MjJSAEjx4sXl8ccfl1mzZsm1a9eMDksXea0N4uPjM89zQZJb7ZXbhCy/AMQA+ARATweLyJoAwqyGp9Wc1gDSAQwGUPvOf9MAtHQgrkJXRIqIPPfcc1kK9JCQEOndu7fMnTvXrf7/uHbtmgQHB2fJt1GjRjJ06FDZsmWLW72Y//DDD1ly9ff3F5PJJBMnTpSzZ88aHaJmLBaLtGvXLku+FStWlP79+8vvv/8uSUlJRoepmX379omiKHflqiiKtGnTRkaMGCF79uxxqxfzd999N8u+LVasmPTq1UtmzJghV69eNTpEzSQlJUm5cuWy5FunTh0ZOHCgrF+/XtLS0owOUzOLFy/OkquPj49ERUXJ+PHj5cSJE0aHqKn7778/S75hYWHSt29fWbRokdy8edPoEDVz5swZ8fX1zZJv8+bNZfjw4bJjxw63Ok998cUXWXItWrSo9OzZU6ZOnSoXL140OkTNpKenS926dbPkW61aNXnjjTdk1apVbvVB34YNG7Lk6unpKR07dpQxY8bIoUOHjA5RU3mpDRwpIhXJw9f2d94E9RCRhTbmdASwBkBxEbmew5zZd4KNsfrZcgDXROQxO2MJAhAfHx+PoKAge1PIF5cvX0ZcXJwu2z5+/DhiYmJyfNzb2xsREREwm80wm82oUqWKLnFYO3LkiG6tTaNHj8bkyZNzfLx06dLo3r07zGYzunbtiqJFi+oSR6abN2/i7Nmzumw7LS0NnTt3xuXLl3Oc06xZM5hMJpjNZjRt2hSKougSS6azZ8/q1k68Zs0avPTSSzk+XqRIEURGRsJsNqN79+4oXbq0LnFkysjIwJEjR3Tb/ssvv4w///wzx8erVKmi/t126NABPj4+usUCAHFxcTaPtby4fPkyOnXqlGMrkaenJ9q2bavmW6tWLV3isHb8+HHd2omnTJmCUaNG5fh4iRIlEBsbC7PZjG7duiE4OFiXODIlJSXh1KlTumxbRGAymXD06NEc5zRo0EA9T4WHh8PT01OXWDJduHBBt3binTt34rHHcn5b4ufnh86dO8NsNsNkMqF8+fK6xGFNz1bxoUOH4tdff83x8fLly6v7tlOnTvD399ctFgCIj4/HhQsXdNl2YmIiOnTogMTExGwfVxQFrVq1UvOtX7++7q+5p06d0q2deP78+XjvvfdyfDwoKAjR0dEwm82IiYlByZIldYkjU2pqqq4tmI8//jh27NiR4+O1atVS/27btm0LLy8v3WIBCm5tkJCQkPmaFCwiCTafKLcq09aAY99EHgdwHsCfADrdM+cUgAH3/GwAgJMOxFJgv4kcNGhQdu28hoz8aHsNDQ01PE8gf9pelyxZYniemSM/2l579OhheJ5A/rS9xsXFGZ5n5siPttfRo0cbnmfmyI+21zp16hieJ5A/ba+bN282PM/MkR9tr3379jU8z8yRH22vHh4ehucJ5E/b69SpUw3PM3PkR9tr+/btDc8TyJ+210OHDhmeZ+bIj7bXglYbvPvuu7Jhwwbr9z7at7PK3YWbIPcishaA5wE0xe221W8BWAB0sJqTCuDxe37vcQApNrbri9uFY+YoB7CIdGSEhITIyy+/rPmb0oJSRN47GjVqJFOnTtX0hbwgFZHWw9/fX3r06CF79+7VLFeRglNE3jsqVqwow4YN07R4LkhFpPVQFEXatm0ry5Yt0yxXkYJVRFqPYsWKSZ8+feTMmTOa5ltQish7R506dWT8+PGatrwWpCLSevj4+EhMTIz8/fffmuUqUrCKSOsRFhYm77zzjubvUwpKEXnvaN68ucydO1fTgqMgFZHWo2jRovLYY4/J0aNHNctVpOAUkfeOatWqyeeffy4pKSma5VqQikjr4enpKZ06dZJ169ZplqtIwa0NSpQokfm/cy0i9f2uFoCIHARg3WuxWVGUCgDeBrDeeuo9v6pk8zNrgwEM0yTIQqZixYrqV9gdO3aEr6+v0SHpxsPDA23atFHzrV27tu7tJ0YqXrw4YmJiYDKZEB0djeLFixsdkq7q1q2r7ttWrVrp3iZnJB8fH7VNrnv37qhUqZLRIemqTJkyattYly5dEBAQYHRIugoPD1eP5YYNG7r1eSowMBDdunWDyWRCbGwsQkNDjQ5JV9WrV1f3bbt27eDt7W10SLrx8vJChw4d1LbA6tWrGx2SrkJCQtQlNFFRUQgMDDQ6JF01btxYPZabNWsGDw/3vcmDv7+/uoQmNjYWZcuWNTokXVWqVAlmsxmdO3dGz5497fod3YvIHGwB8KTVvy/g9sV2rJUCYOt6/yMAjLX6dyCAAnnd7S5duuhWqCUlJeGLL76wOUdRFLRs2VL9w9e7j/+dd97JcU1BXm3evBkrVqywOce6jz86OhohISG6xAIANWvWxLBh+n2W8e233+a6Tq1mzZrqvtW7j//RRx9Fw4YNddn22bNnba53Be7u4zeZTKhataousQC31zbpuW+XLFlic30GAJQqVQomkwkmkwmRkZG6rvFt3bq1bvlmZGTg888/z/Xy6k2bNlWP5SZNmuj6BuXll1/WbQ3of//9h4ULF9qcExAQgKioKPUNSljYvS+B2ilfvryux/KPP/6IkydP2pxTuXJldd9GRETousbXbDajXLlyumw7Li4O48ePtznn3jW+NWvW1PU194MPPsjs0NLcn3/+iQ0bNtick7nG12QyoVu3bihWrJgusQC3ixi9jmURwZgxY3J9/1K/fn113+q9xvfZZ59F586dddn24cOHMXPmTJtzfH190aVLF/XDywoVKugSC3D7ONLzPDV79mwcOHDA5pxy5cqpH1527txZ1zW+BaE2aNWqlfp+KrM2SEiwvQzyLrl9VWlr4PY3hTbbWXP4vV8BrLb692wAy+6Z8zuAWQ5ss8CuidTT//73v2y/ji5SpIj07NlTfvjhB7e5olhGRoY0bNgw23yrVq0qr7/+uqxatUrT9gojbdu2LcfWiswrih08eNDoMDXz0ksvZZtvyZIlpXfv3jJnzhy3+ftOSEiwbhm5azRs2FCGDBniVlcbnj59era5+vn5iclkku+++07zdlUjderUKdt8K1SoIC+99JIsW7bMba42fPjwYfH09MySq7tebXjo0KHZ7tvg4GDp1auXTJ8+3W2uNpySkiKVKlXKNt/atWvLO++841ZXG/7999+zzdXb21u92vDx48eNDlMzDz/8cLb5li5dWp577jlZuHCh21xt+Pz58+Lv759tvu54teGcagN7rjas9y0+igJofGcIbl8ApzGAinceHwHgZ6v5bwB4AEANAPXuPC4AelrNaYPbt/h4F7dv8fEueIuPXN26dUvCwsLUg6NixYry8ssvu+29jebNm6fmWhjubdS9e3c138xF3jNnzpS4uDijQ9PcqVOnxNvbW823bt266iJvd7zv6Weffabm6uPjo14Ayt1uhyBy+1LyNWvWVPMtU6aMPP/887J48WK3vO/p2rVr73rRDg8Pd+v7nj799NNqrpkXgPrxxx/l0qVLRoemuatXr0pgYKCab/Xq1WXAgAFue9/T77//Xs3V+gJQhw8fNjo0zVksFmnZsqWab0hIiDz99NPy66+/uuV9T3fv3n3Xeapx48Zufd/TN998U83V399fvQCUO90qLVNeawNdb/FhdcuOe/0kIs8oivIjgMoi0vHO/IEAXsDtC98kAdgLYISILLtnuw/h9v0nqwI4CmCIiMx3IK4Ce4sPvYwfPx4zZ87MtzZVI1ksFnTs2FFdJxUTE6Nrm6rR/v77bzz11FNqW0V+XG7aSG+88Qb27t2bL22qRrtx4wZatWqlXipe7zZVo82cORNjxozJtzZVo5nNZnh5eeVLm6rRjhw5gpiYGMTExORLm6rRPvzwQ6xZs0Y9T9WqVcttX3NTU1PRunVr1K1bN1/aVI22fPlyvPPOO/nWpmq03r174+rVq/nSpmq0CxcuoEOHDuo1BfRuUzVaXmsDR27xkaf7RBYkhbGITEpKcus/BGvp6emwWCxu/QbFWmHat0DhyjclJQXe3t5uXUhZK0z71mKxIDU1FX5+fkaHki+SkpLg5+fntoXUvQrTsZyamgoPDw+3/vDSWmHat0DhypfnKcewiCwkRSQREREREZEWHCkiC8dH4URERERERKQJFpFERERERERkNxaRREREREREZDcWkURERERERGQ3FpFERERERERkNxaRREREREREZDcWkURERERERGQ3FpFERERERERkNxaRREREREREZDcWkURERERERGQ3FpFERERERERkNxaRREREREREZDcWkURERERERGQ3FpFERERERERkNxaRREREREREZDcWkURERERERGQ3FpFERERERERkNxaRREREREREZDcWkURERERERGQ3FpFERERERERkNxaRREREREREZDcWkURERERERGQ3FpFERERERERkNxaRREREREREZDcWkW5q+PDh+Pbbb3Hq1CmjQ9HduXPn0K9fPyxZsgS3bt0yOhzdTZ8+HZ988gn+++8/iIjR4egqIyMDr732Gn7++WdcuXLF6HB0988//+DNN9/EmjVrkJaWZnQ4uhs9ejT+97//4ejRo0aHorv4+Hi8+OKLmDdvHm7cuGF0OLpbuHAhPvjgA/z999+wWCxGh6MrEcHAgQMxefJknD9/3uhwdHfw4EG8+uqr+OOPP5CSkmJ0OLr77rvv8MUXX2D//v1u/5qbnJyMl156Cb/88guuX79udDi6W716NQYNGoSNGzciIyPD6HB0p3ltICJuMQAEAZD4+HghkWXLlgkAASCNGjWSoUOHypYtWyQjI8Po0HTx0EMPCQDx9/cXk8kkEydOlLNnzxodli7Onz8v/v7+AkAqVKgg/fv3l2XLlklSUpLRoeniyy+/FACiKIq0adNGRowYIXv27BGLxWJ0aJrLyMiQhg0bCgApVqyY9OrVS2bMmCFXr141OjRdbN26VT1P1alTRwYOHCjr16+XtLQ0o0PTRb9+/QSA+Pj4SFRUlIwfP15OnDhhdFi6iI+PlxIlSggACQsLk759+8qiRYvk5s2bRoemi2nTpqnHcvPmzWX48OGyY8cOtzxPiYh07NhRAEjRokWlZ8+eMnXqVLl48aLRYeni0KFD4uHhIQCkWrVq8sYbb8iqVaskNTXV6NB0MWTIEAEgnp6e0rFjRxkzZowcOnTI6LB0kZKSIhUrVhQAEhISIr1795a5c+e6bS1hT20QHx+fOSdIcqu9cpvgKoNF5N0sFouEh4erB0vmKF26tPTp00cWLFggN27cMDpMzezatStLrgCkWbNmMmzYMPnnn3/c6sX8zTffzJJrkSJF5IEHHpApU6bIhQsXjA5RM7du3ZKwsLAs+VapUkVee+01WbFihaSkpBgdpmbmzZuXJVdPT0/p0KGDjBo1Sg4cOGB0iJqKjY3Nkm+JEiXkySeflNmzZ8v169eNDlEzJ0+eFG9v7yz5NmjQQAYPHiybNm2S9PR0o8PUzKeffpolVz8/P4mNjZUJEybI6dOnjQ5RM2lpaVKzZs0s+ZYvX1769esnS5culVu3bhkdpmbWrFmTJVdFUaR169by6aefyq5du9zqNbd3795Z8g0KCpJHHnlEpk2bJleuXDE6RM1cuXJFAgMDs+Rbq1Ytefvtt2Xt2rVu9UHfxIkTs+Tq7e0tXbt2lXHjxsmxY8eMDlEz9tQG586ds7uIVMRNvppXFCUIQHx8fDyCgoKMDucuZ8+excWLF/P9eVeuXIlBgwbl+Livry86deoEs9kMk8mEihUravK8u3btQnp6uibbcsQrr7yCzZs35/h42bJlYTKZYDKZ0KVLFwQEBOT5OePj4w1pxbtw4QJMJlOOrTWKoiA8PBwmkwlmsxkNGzaEoih5ft5jx44Z0uIyefJkTJgwIcfHAwMD0a1bN5jNZsTGxiIkJCTPz5meno5du3bleTuOslgseOCBB3D27Nkc59SoUUP9u23Xrh28vb3z/LwXL160+Zx6+fvvv9GvX78cH/fy8kKHDh1gNpthNptRrVo1TZ533759SE5O1mRbjhg6dCh+//33HB8PDQ1F9+7dYTabERkZicDAwDw/Z2JiIg4ePJjn7Tjqxo0b6Natm82WxyZNmqjnqWbNmsHDI++rbE6ePImrV6/meTuOmjt3Lj7//PMcHw8ICEDXrl1hNpvRvXt3lClTRpPn3bFjhybbcdSTTz6J/fv35/h4pUqV1PNUx44d4evrm+fnvHr1Kk6ePJnn7Tjq8OHD6NWrV46Pe3h4oG3btuqxXLt2bU1ecw8dOoSbN2/meTuOGj16NGbNmpXj48WLF0dMTAzMZjOio6NRrFixPD9ncnIy9u3bl+ftOCo1NRXR0dGIj4/PcU69evXUY7lVq1bw9PTM8/MW1NrAx8cHqampABAsIgk2N5ZblekqAwX4m8hBgwZl+y1ZQRtatb2GhoYanktuQ6u21yVLlhieiz2jYsWKmrS99ujRw/Bcchtatb3GxcUZnos9w7rtNS4uzul9O3r0aMNzsWdo1fZap04dw3PJbWjV9rp582bDc7FnaNX22rdvX8NzsWe0aNFCk7bXzFbLgjy0anudOnWq4bnYM7Rqe23fvr3hueQ2tGp7PXTokOG52DO0ant1gdqA7awFgQscKFlG6dKl5aOPPnKq4HCFIvLeER4eLqtWrXI4V1cpIq1HkSJFpE+fPk61vLpCEXnvqFKlinz//fcOtwm6ShFpPTw9PSUqKkr+/fdfh/etqxSR1qNEiRLy7rvvOtWa7wpF5L2jUaNGsmjRIocLDlcpIq2Hn5+f9OrVS06ePOnwvnWVItJ6lC9fXsaOHetUweEKRaT1UBRFOnToIJs3b3Y4V1cpIq1HUFCQvPLKK059yOcKReS9o3bt2jJz5kyHz1OuUkRaD29vb7n//vvl4MGDDu9bF6gNci0ivUB0h6IoaNmypdo2Vr9+fU3aMQqqoKAgREdHw2w2IyYmBiVLljQ6JF3VqlVLbcdo27YtvLzc98/f29sbERERar5Vq1Y1OiRdlSpVSm2j6tq1K4oWLWp0SLpq2rSpep5q2rSpW5+nAgICEBUVpbZAli5d2uiQdFWlShX17zYiIgI+Pj5Gh6QbT09PtG3bVj2Wa9WqZXRIuipRogRiY2NhNpvRrVs3BAcHGx2Srho0aKAey+Hh4Zq0QBZUvr6+6NKli5pv+fLljQ5JV+XKlVP/bjt16gR/f3+jQzIE10Tmg3Xr1mHr1q35/ryHDx/G5MmTbc4pWrSo+gYlNjYWpUqVyvPzfv3114bcamPmzJn477//bM6pVq2aepJr3759nt+gHDlyBPPnz8/TNpyRnJyMDz/8MMc1kcDtNyjt27dXT3Q1atTI8/MuWLAAhw8fzvN2HLVp0yYsWrTI5pySJUuqa8mioqLyfB5ITk7GV199ladtOGvcuHE4d+6czTmNGjVSC8cWLVrkeS3Ztm3bsHbt2jxtwxnnzp3DuHHjbM7x8/O7ay1ZuXLl8vy8U6ZMMWTd3KJFi7Bp0yabcypUqKCepzp16gQ/P788Pee5c+cwffr0PG3DGRkZGRg+fLjNNZGKoqB169bqeapu3bp5/lBg+fLlhqxn/vfff22uIwOA4ODgu9aSlShRIs/PO2rUKJuvBXqZNGkSjhw5YnNOnTp11GO5devWef7wcvfu3TbXFOvl+vXrGDFihM05Pj4+6Nixo5pv5cqV8/y8M2fOxJkzZ/K8HUetXLkSq1atsjknLCxMfQ3q0qULihQpkqfnjIuLy/U9qx5EBCNGjLC5JhIAWrRooebbuHHjPJ+nCnJtcEewcE1k4dWrV69sv6KuVKmSvPLKK/LHH39IcnKy0WFq4tKlSxIQEJAlVw8PD2nXrp2MHDlS9u3b5zZXi/v666+z3bfFixeXxx9/XGbNmpWn9XEFicVikSZNmmSbb7169eTdd9+VDRs2uM1VLXfs2JFtrj4+PhIdHS3ffPONUy1+BdUrr7ySbb5ly5aVF154QZYsWSKJiYlGh6mJmzdvSkhISLb5hoeHy8cffyz//vuv25ynZs2alW2ugYGB8tBDD8lPP/0kly9fNjpMzURGRmabb/Xq1WXAgAGyevVqt7ktxNGjR8XT0zNLrl5eXtK5c2f58ssv5ciRI0aHqZkPP/ww230bGhoqzzzzjMybN08SEhKMDlMTqampUqVKlWzzbdKkibz//vuybds2t7ll3MqVK7PN1d/fX+677z6ZNGmSnDt3zugwNZNbbTB//ny721kNL/60Giwi77Z3715RFEWA2+sPWrVq5ZaX3c40cOBA9Q/BXS+7nSkpKUnKlSun5lurVi1566233O6y25kWLVp01/qDzMtuHz161OjQdHH//fer+ZYqVUr69Okj8+fPd6tb8mQ6c+aM+Pj4qPk2bdrULW/Jk+mLL75Qcw0ICFBvyXP+/HmjQ9Ncenr6XetO3fWWPJk2bNig5urOt+TJ1KdPHzVfd70lT6Zr165JcHCwmq+73pIn05QpU9RcfX193fKWPJksFou0bdtWzbdcuXLSr18/+e2339zqljyZ7q0NWrduLZ999tldtYEj94lkO6ubeuGFF3D16lVN21QLqsuXL6Nr167o3LmzZm2qBdnEiRPxyy+/aNqmWlCJCKKjoxEWFqZZm2pBtnPnTvTp00dty9WiTbUgGzhwIPbv369pm2pBlZiYiIiICLRs2VKzNtWCbM6cORg3bpymbaoF2SOPPAJPT09N21QLqmPHjqFHjx6Ijo7WrE21IPv888+xZs0aTdtUC6q0tDR06tRJbUPWok21IPvzzz8xePBgTdtUCzJ7aoOEhITM9crBkks7K4tIN5WWlqbJveNcQVpaGry8vNz6D99aYdq3FosFIuLWFySwVpj2LVC48uV5yn2JCNLT0wtNvoVp3wKFK9/09HR4eHi49YeX1grTvgXsy9eRItJ9Pzoq5ArTH0VhyhUoXPkWlheyTIVp3wKFK9/ClCtQuPJVFKVQ5VuYcgUKV77u/I1ydgrTvgW0z7dwvUMjIiIiIiKiPGERSURERERERHZjEUlERERERER2YxFJREREREREdmMRSURERERERHZjEUlERERERER2YxFJREREREREdmMRSURERERERHZjEUlERERERER2YxFJREREREREdmMRSURERERERHZjEUlERERERER2YxFJREREREREdnO4iFQUpYOiKEsURTmnKIooivJALvN7KoqyUlGUy4qiJCiKsllRlG73zHnmzrbuHX6OxkdERERERET6ceabyCIA/gPwip3zOwBYCSAWQDMAawAsURSlyT3zEgCUsR4ikuxEfERERERERKQTL0d/QUR+B/A7ACiKYs/8N+750XuKotwPwAxg591T5YKj8RAREREREVH+yfc1kYqieAAIBBB3z0NFFUU5qSjKGUVRfsvmm8p7t+OrKEpQ5rizTSIiIiIiItKRERfWeQu3W2LnWP3sAIBnANwH4DEAyQA2KopSw8Z2BgOItxpn9AiWiIiIiIiI/p8iIs7/sqIIgB4istDO+Y8BmAzgfhFZZWOeB4AdANaLyGs5zPEF4Gv1o0AAZ+Lj4xEUFGRnBkRERERERJSQkIDg4GAACBaRBFtzHV4T6SxFUR4FMAXAw7YKSAAQEYuiKH8DyPGbSBFJAZBitX2tQiUiIiIiIqIc5Es7651vIH8E8LiILLVjvgKgMYDz+kZGREREREREjnD4m0hFUYoCqG71oyqKojQGECcipxRFGQGgnIj0vjP/MQA/A3gdwBZFUcLu/F6SiMTfmTMMwBYAhwEEAXgNt4vIl51JioiIiIiIiPThzDeRzXH71hyZt+cYe+d/f3Tn32UAVLSa/yJuF6vf4PY3i5ljnNWcYgC+B7AfwAoA5QB0EJFtTsRHREREREREOsnThXUKkju3+YjnhXWIiIiIiIgc48iFdYy4xQcZYO3atXjllVfwxx9/ICUlJfdfcHEffPABvvjiC+zbtw/u8kFJTi5evIjevXtj1qxZuHbtmtHh6G769OkYNGgQNm7ciIyMDKPD0ZXFYkG/fv3wzTff4NSpU0aHo7sdO3bghRdewJIlS3Dr1i2jw9HdqFGj8Mknn+Dff/91+/NUQkICevfujZ9++gmXL182OhzdLV68GG+++SbWrFmDtLQ0o8PRlYjgzTffxJdffokjR44YHY7ujh49imeffRbz5s3DjRs3jA5HdxMmTMAHH3yAbdu2wWKxGB2OrlJSUtCnTx9MmjQJ58+7/2VZ8lwbiIhbDNxeSynx8fFCWaWlpUnNmjUFgBQpUkR69OghP/zwg1y8eNHo0HSxdu1aASAApGrVqvL666/LqlWrJCUlxejQdNG7d28BIJ6entKxY0cZM2aMHDx40OiwdHH16lUJDAwUAFKyZEl56qmnZM6cOW77t//999+rx3LDhg1lyJAhsmXLFsnIyDA6NM1ZLBZp2bKlABA/Pz8xmUzy3XffyZkzZ4wOTRe7d+9W922FChXkpZdekmXLlklSUpLRoenizTffFACiKIq0adNGRowYIbt37xaLxWJ0aJq7deuWhIWFCQAJDg6WRx99VKZPny5Xr141OjRdzJs3Tz2Wa9euLe+8846sX79e0tLSjA5NF927dxcA4uPjI1FRUfLVV1/J8ePHjQ5LFydPnhRvb28BIGFhYfLcc8/JwoUL5ebNm0aHpovPPvtMPZabN28uw4cPl+3bt7vlecq6NihatKj07NlTvv3228z8gyS32iu3Ca4yWETmbtq0aeofRuZQFEVatWoln376qfz3339u9UfSqVOnLPkGBQXJww8/LD///LNcuXLF6BA1c+jQIfHw8MiSb82aNeWtt96StWvXutWL+dChQ7Pk6u3tLV27dpVx48bJ0aNHjQ5RMykpKVKpUqUs+ZYqVUqeffZZmT9/vty4ccPoMDXz+++/Z8kVgDRt2lSGDRsm//zzj1sV0A8//HCWXAMCAuT++++XyZMny/nz540OUTPnz58Xf3//LPlWqVJFXn31VVmxYoVbfdD3v//9L0uunp6e0qFDBxk1apTs37/fbV5zMzIypGHDhlnyLVGihDzxxBPyyy+/yPXr140OUzPbtm3L9jxVv359GTx4sGzatEnS09ONDlMz/fr1y5Krr6+vxMTEyLfffiunTp0yOkTNJCQkSIkSJbLkW65cOXnxxRflt99+k1u3bhkdpmayqw3sLSK5JjIfnDhxAmfOnDE6DKSnp+PBBx9EXFxcjnMqVaoEk8kEs9mMjh07wtfX1+Hn2bp1a4Fo39m4cSMGDRqU4+MeHh5o06YNzGYzTCYT6tSp4/D9RuPi4rBv3768hqqJwYMHY8OGDTk+XqxYMcTExMBsNiM6OhrFixd3+Dn279+Pq1ev5iVMTcTFxaFHjx42W2vq1q0Ls9kMs9mMVq1awdPT06HnSE9Px5YtW/IaqiZmzZqFb7/9NsfHfXx80LlzZ/Vvt2LFijnOzcnZs2dx/PjxvISpCRHBk08+abN9t2zZsujevTvMZjO6dOmCgIAAh59n+/btSEpKykuomtizZw9eeuklm3PCw8PV81SjRo0cPk8lJCRg165deQlTM59//jmWLs35Tl+BgYHo1q0bTCYTYmNjERoa6vBzHD58GBcvXsxLmJpISkrC/fffb/M4q169unqeateuHby9vR1+Hlvn/fy0dOlSfP755zk+7uXlhQ4dOqjnqerVq+c4NycXL17E4cOH8xKmZvr374/du3fn+HhoaChiY2NhNpsRFRWFwMBAh59j165dSEiwuSwtX5w6dQpPPPGEzTmNGzdWj+VmzZrBw8OxFXNJSUnYvn17XsLUzIQJEzBz5swcH/f390dkZCRMJhNMJhPKlCnj8HO4QG0QLLmsiTT8G0StBgrwN5GDBg3Kqcov0CPzq21H215DQ0MNj92Z4Uzb65IlSwyP25nhbNtrjx49DI/dmeFM22tcXJzhcTs7nGl7HT16tOFxOzOcbXutU6eO4bE7M5xpe928ebPhcTsznG177du3r+GxOzOcbXvNrgvFFYYzba9Tp041PG5nhrNtr+3btzc8dmeGM22vhw4dMjxuZ4czba8uUBuwnbUgcIEDJdehKIrExMTIgQMHcs3XVYtI6xEUFCTDhg3LtWXBVYvIe0eDBg1kxYoVue5bVy0irYe3t7c89dRTcu7cOZu5unIRaT3CwsJkwoQJubZWuWoRee+IiIiQnTt35nosu2oRaT0CAgLkrbfekoSEBJu5umoRee+oUaOGLFiwINc3aa5aRFoPT09P6dmzp10Fh6sWkdajRIkSMmrUKElNTbWZq6sWkfeO8PBw2bhxY6771lWLSOvh6+sr/fr1y3UJkSsXkdajYsWKMm3atFzPUy5QG+RaRHqByAYtWm1cRWarTWbbmDOtNq4kNDQU3bt3h8lkcrrVxpXktdXGlWS22pjNZsTGxqJs2bJGh6SrihUrqvvW2TZ8V2Hdhm82m1G7dm2H21tdSfHixdU2/G7dujnVhu9K8tqG70oy2/DNZjO6d++OSpUqGR2SrsqUKaO28jrbhu9KMtvwzWYzGjZs6Nbnqcw2fLPZjJiYGKfa8F0R10Tmg82bN2PHjh1GhwERwbBhw2yuifT09ETbtm3VP/xatWo5/Dw//PBDgVhrdPDgQYwfP97mnBIlSiA2NhYmkwndunVDsWLFHHqOEydO2Fzfk59+/PFH/PPPPzbn1K9fX9234eHhDr9B+f3333Hs2LG8hKmJ5ORkDBw40OaaSF9fX3Tp0kV9g1KhQgWHn2PKlCl5DVUTf/31F2bPnm1zTrly5dQPQDp37gx/f3+HnmPnzp3YtGlTXsLUzMiRI3H69OkcH1cUBS1btlSP5fr16zv8BmXmzJkF4pY4Z8+exYgRI2zOCQoKQnR0NEwmE2JiYhASEuLQc1y4cAHz5s3LS5iamTt3LtatW2dzTs2aNdV927ZtW3h5OfZ595o1awrEWvWMjAwMGjTI5uuht7c3IiIi1L/dqlWrOvw83377LQrCe7kdO3bghx9+sDmnVKlS6jqyyMhIFC1a1KHn2L9/P1avXp2XMDXzzTffYP/+/TbnNG3aVD2WmzRp4vCHl/Pnzy8Qt5q4fv06hg4danNOQEAAoqKi1A8vw8LCHH6OGTNm5CVMzfz++++5vrerXLmyum8jIiLg4+Pj0HO4QG0QLFwTSZlWrFiR7VfWwcHB0qtXL7e7/HivXr2yzdcdLz9+8eJFCQgIyJKrt7e3REVFyfjx493q8uPjx4/Pdt+GhYVJ37593ery4xaLRZo0aZJtvpnrMHbs2OE2V3ncvn17trlmrtGeOnWqW92a6JVXXsk2X3e8NdGNGzckJCQkS67uemuiWbNmZbtvS5YsKb1793a7WxN17do123zd8dZER48eFU9Pzyy5Zq7RnjhxolvdmmjYsGHZ7lt3vDVRamqqVKlSJUuu1mu09+zZ4zavuTnVBuCaSMpksVikTZs26sFRvXp1GTBggKxevTrXNQiuaO/evaIoigAQLy8v6dy5s3z55Zdy+PBho0PTxTvvvKPu25CQEHn66afl119/zXWtlCtKSkqSsmXLqvk2btxY3n//fdm2bZvbvEGxtmjRIjVXf39/ue+++2TSpEly9uxZo0PTxX333XfX2pKXX35Zli9fLsnJyUaHprkzZ86Ij4+PABAPDw9p166djBw5Uvbt2+c2b1CsjRw5Ut23xYsXl8cff1xmzZolcXFxRoemufT09LvW3datW1feffdd2bBhg1vd+iHTX3/9pebq4+Mj0dHR8s0338iJEyeMDk0Xffr0UfMtU6aMPP/887J48WJJTEw0OjTNXbt2TYKDg9V8w8PD5eOPP5Z///3XLc9TU6ZMUXMNDAyUhx56SH766Se5dOmS0aFpLrvaoH///nYXkWxnLSTWrFmDDz/8UP3qvWbNmm7dn/7KK68gPj7e6TZVV3Lp0iXcd9996toSZ9pUXcnkyZOxYMECp9tUXYmI4IEHHkCZMmVgNpudalN1Jf/++y/69++vrhtypk3VlQwdOhSHDx92uk3Vldy8eRPR0dFo1aqV022qrmT+/PmYMGFCntpUXcmTTz4JHx8fmM1mp9pUXcnx48fx2GOPITo62uk2VVcyatQobNq0yek2VVeSlpaGmJgYdW2yM22qrmT16tUYPny4ep6qVasWbty4geDgYMCOdlYWkYWExWJx65PcvQpTvoUpV6Bw5Zt5fnbnQspaYdq3QOHKtzDlChSufDO/lSgs+RamfQsUrnwtFgsURSnUr7kJCQl2F5Hu+zEg3aWwnAAyFaZ8C1OuQOHKt7C8kGUqTPsWKFz5FqZcgcKVb2F60w0Urn0LFK58C1OuQN7zLVz/bxEREREREVGesIgkIiIiIiIiu7GIJCIiIiIiIruxiCQiIiIiIiK7sYgkIiIiIiIiu7GIJCIiIiIiIruxiCQiIiIiIiK7sYgkIiIiIiIiu7GIJCIiIiIiIruxiCQiIiIiIiK7sYgkIiIiIiIiu7GIJCIiIiIiIruxiCQiIiIiIiK7sYgkIiIiIiIiu7GIJCIiIiIiIruxiCQiIiIiIiK7sYgkIiIiIiIiu7GIJCIiIiIiIruxiCQiIiIiIiK7sYgkIiIiIiIiu7GIJCIiIiIiIruxiCQiIiIiIiK7sYgkIiIiIiIiu7GIJCIiIiIiIruxiCxk1qxZgz59+mDBggW4efOm0eHobvDgwRg2bBj++ecfWCwWo8PR1cWLF/Hwww9jypQpuHDhgtHh6O7nn3/Ga6+9hhUrViAlJcXocHRlsVjQp08fjBo1CgcOHICIGB2Srnbs2IEnn3wSs2fPxvXr140OR3cjRozAe++9h02bNiEjI8PocHR148YNPProo5gwYQJOnz5tdDi6W7hwIfr164elS5ciKSnJ6HB0JSJ49dVX8emnn2LXrl1uf546evQoHn30UUybNg1Xr141Ohzdff3113j77bexdu1apKenGx2OrlJTU/HEE09g3LhxOHbsmNHh6C6zNpg/f75jtYGIuMUAEARA4uPjhXKWkZEhdevWFQDi4+Mj3bp1k6+//lpOnDhhdGi62LhxowAQAFKmTBl5/vnnZdGiRZKYmGh0aLro27evmm94eLh89NFHsnPnTrFYLEaHprlr165JsWLFBIAULVpUHnzwQfnxxx/l0qVLRoemi6lTp6r7tnr16jJgwAD5888/JTU11ejQNGexWKRdu3YCQLy8vKRTp04yduxYOXz4sNGh6WL//v2iKIoAkNDQUHn66afl119/lYSEBKND08WgQYPUY7lx48YydOhQ2bp1q2RkZBgdmuaSk5OlXLlyAkD8/f3FbDbL999/L+fOnTM6NF0sWbJE3bcVK1aUl19+WX7//XdJTk42OjRdPPDAAwJAPDw8pF27dvL555/L3r173fI19+zZs+Lr6ysApFixYvLYY4/JzJkzJS4uzujQdDFq1Cj1WK5bt64MHDhQ/vrrL0lPTzc6NM1Z1wbe3t6ZeQdJbrVXbhNcZbCItN/s2bPVPwzr0aBBA3nvvfdk8+bNbvViHhUVlSVXPz8/6d69u3z33Xdy+vRpo0PUzLFjx8TLyytLvhUqVJCXXnpJli5dKklJSUaHqZnhw4dnyVVRFGndurV89tlnsnv3brd5MU9LS5Nq1aplyTc4OFgeffRRmT59uly5csXoMDWzatWqbM9TtWrVkrffflvWrVsnaWlpRoepmccffzxLrt7e3hIZGSlfffWVHD9+3OgQNXP58mUpUqRIlnzDwsLkueeekwULFsjNmzeNDlMz33zzTbbHcrNmzeTDDz+U7du3u815ymKxSLNmzbLkWqRIEenRo4f88MMPcuHCBaPD1MyOHTuy3bdVq1aV119/XVauXCkpKSlGh6mZ1157LUuunp6eEhERIaNHj5aDBw8aHaJmbt68KaGhoVnyLVmypDz11FMye/ZsuX79utFhaiab2iDXIlIRN2k3UBQlCEB8fHw8goKCjA7nLocOHcLx48eNDkNlsVjw5JNPIi4uLsc5pUqVQmxsLMxmM6KiolC0aFG7t79mzRqkpqZqEaomtm3bhg8++MDmnCZNmsBsNsNsNqNp06bw8LCv0/vSpUvYuXOnFmFq5uOPP8bGjRtzfDwgIACRkZEwm83o3r07wsLC7N72zp07cenSJS3C1ER8fDwee+wxm63KlStXhslkgtlsRkREBHx9fe3adlpaGlavXq1VqJqYN28eJk2alOPjHh4eaNu2rXos16pVC4qi2LXtEydO4ODBg1qFmmcighdffBGnTp3KcU7x4sURExMDs9mM6OhoFCtWzO7tb9iwAYmJiRpEqo0DBw7gjTfesDmnXr166r5t2bIlPD097dr29evXsXXrVg2i1M64cePw+++/5/i4r68vOnfuDLPZDJPJhAoVKti97b179+LMmTNahKmJlJQU9OrVy2Y7a9myZdXzVJcuXeDv72/39v/44w8twtTMqlWrMHr06BwfVxQF4eHh6rHcoEEDu89TZ8+exZ49e7QKVRNvv/22zZiCgoLQrVs3mM1mxMTEICQkxO5tb9u2DdeuXdMiTE2cO3cOffr0sTmnRo0a6r5t27YtvL297dp2YmIiNmzYoEWYmpk6dSpmz56d4+NeXl6IiIhQz1PVqlWze9suUBsEi0iCzV/Krcp0lYEC/E2kdeuOK47Mttfx48fb1faa3Sc3rjTKlCkjffv2tavt1bp1x1VHixYt5KOPPpIdO3bk+ml4jx49DI83L6No0aLSs2dPmTp1qly8eNFmrnFxcYbHm9dRrVo1eeONN+xqex09erTh8eZlZLa9jhkzRg4dOmQzVxGROnXqGB5zXkZISIj07t1b5s6dm+vr3ubNmw2PN6+jUaNGMnToUNmyZUuunTLWbf2uODLbXidOnChnz57N9Vj28PAwPOa8jIoVK0r//v3l999/z7VTxrqt3xWHh4eHtG3bVj7//HPZs2dPrq+57du3NzzmvIxixYpJr169ZMaMGbm2vR46dMjwePM66tSpIwMHDpT169fn2injArUB21kLAhc4UBwakZGRsn///hzzdfUi0nr4+/vLsGHD5NatW9nm6g5FpPWoXbu2rFixIsd96+pFpPVQFEWeeOKJHNcmuUMRaT1KliwpEyZMyHE9h6sXkfeOtm3bys6dO3M8ll29iLQePj4+8tZbb+W4htIdikjrUblyZVmwYEGOb8BdvYi8dzzwwAM225ldvYi0HoGBgTJq1KgcW0BdvYi8dzRp0kQ2btyY47519SLSenh6esqLL76Y47ILdygirUeZMmVk2rRpOZ6nXKA2yLWI9AKRHRo1aqS2JzRv3tzudk9X5O/vj65du6rtnmXLljU6JF1VqFBB3bcdO3aEn5+f0SHpxsPDA61bt1bzrVOnjt1tVK6oWLFiiImJgclkQnR0NEqUKGF0SLqqU6eOum9bt25td7unK/Lx8UGnTp3UNqpKlSoZHZKuypQpA5PJBJPJhK5duyIgIMDokHTVokUL9Vhu1KiRW5+nihYtele7Z6lSpYwOSVfVqlVT92379u3tbvd0RV5eXmjfvr16nqpRo4bRIekqJCQE3bt3h8lkQlRUVIFbXqc1ronMB9u3b8fu3buNDkMlInj77bdtronMy3qUX375BcnJyVqEqom9e/faXJ8B3F6Pkplr586d7X6Dcvr0afz5559ahKmZCRMmYNu2bTk+npf1KKtXr7a5Ri2/3bp1C6+++qrNNZGBgYGIjo52eD1KSkoKZs2apVWomli1ahVmzJhhc46z61H27NmDf/75R4swNTNs2DCbx1te1qMsWLAA8fHxWoSpiZMnT+LDDz+0OadUqVLqG5TIyEgEBgbate3Lly9j6dKlGkSpnenTp+d67nR2rfrGjRtx+PBhLcLURHp6Ol599VWbr4t5Wav+008/oSC9l9u6dSu+++47m3MqVaqk7ltH1qofOXKkwK2bGzVqFPbt25fj43lZq/7777/j4sWLWoWaZ1evXsXbb79tc07x4sURGxurfnhp71r1hIQEzJ8/X4MotbNw4UIsWrTI5hxn16q7QG0QLFwTSfdaunRptl9dly5dWvr06SMLFiyQGzduGB2mZh588MFs83XHK+OdO3dO/Pz8suTqrlfGGzt2bLb7tkqVKvLaa6+51ZXxMjIypH79+tm2CLnjlfG2bNmS7b7NvDLenDlz3OrKeC+88EK2+brjVbPj4+OlePHiWXK1vmr2mTNnjA5TMz/99FO2+7Z8+fLSr18/Wbp0aY5LJlxRREREllzd9arZBw4cyLad2F2vmv3ee+9leyy741WzU1JSpEKFCllytb5q9rFjx4wOUzPZ1AZcE0l3s1gs0qJFC/UgybxYgbveo+u///5Tc7W+R5c9FytwRW+88Yaab4UKFey+WIErSkxMlNKlSwtw98UK3PUeXXPnzlX3beY9umbMmCFXr141OjRdxMTEqPlmXqzAXe/RdeLECfXWPIXh/r2ffPLJXeuG3Pn+vWlpaVK9enU138wLmbnr/XvXrFmj5mp9/97cLmTmqp588kk1X0cuZOaKrly5IkWLFhXg7vv32nMhM1f03Xffqfs2JCREnn76absuZOaK7q0N7C0i2c5ayKxevRqjR492qk3VFb3++utITk6G2Wx2qE3VFV28eBG9evVS13M60qbqiqZMmYI//vgDJpMJsbGxDl023dVYLBY88sgjaguYI22qrmjnzp145513nGpTdUUffPABzpw543Cbqiu6ceMGevbsiTZt2jjcpuqK5s2bh2nTpjnVpuqKnnnmGQQGBjrcpuqKjh49ir59+6q3Q3OkTdUVjRkzBjt37nS4TdUVpaamokePHmjYsKHDbaquKLM2MJlMiIiIQP369QE72llZRBYyIuLWJ7l7FaZ8C1OuQOHKtzDlCjBfd1aYcgUKV76Z7ycLU76FJVegcOVbmHIF7s43ISEBwcHBgB1FJK/OWsgUpj8KoHDlW5hyBQpXvoUpV4D5urPClCtQuPItTLkCzNedFaZcAefzdd8eEiIiIiIiItKcw0WkoigdFEVZoijKOUVRRFGUB+z4nQhFUbYripKsKMoxRVH6ZTPnQUVR9imKknLnvz0cjY2IiIiIiIj05cw3kUUA/AfgFXsmK4pSBcAyAH8BaALgMwBfKYryoNWc1gBmA5gGoNGd/85RFKWlE/ERERERERGRTvJ0YR1FUQRADxFZaGPOSAD3iUgdq599B6CRiLS+8+/ZuH0p2RirOcsBXBORx+yMhRfWISIiIiIicoIjF9bJjzWRrQGsuOdnfwBoriiKdy5z2uS0UUVRfBVFCcocANz3muhEREREREQFRH4UkWEALt7zs4u4fWXYkFzm2Lqh0mAA8VbjTJ4jJSIiIiIiIpvy6+qs9/bMKtn8PLs5tnptRwAIthrl8xIgERERERER5S4/7hN5AVm/USwFIB3A1Vzm3PvtpEpEUgCkZP67sN3ThYiIiIiIyAj58U3kZgCR9/wsCsA/IpKWy5xNOsdGREREREREDnD4m0hFUYoCqG71oyqKojQGECcipxRFGQGgnIj0vvP4dwBeURRlLIBJuH0RnecAWF91dRyA9YqivAtgEYD7AXQF0M7R+IiIiIiIiEg/znwT2RzAzjsDAMbe+d8f3fl3GQAVMyeLyHEAsQA6AvgXwPsAXhOReVZzNgHoBeBZALsAPAPgURHZ6kR8REREREREpJM83SeyIOF9IomIiIiIiJxT0O4TSURERERERG6CRSQRERERERHZjUUkERERERER2Y1FJBEREREREdmNRSQRERERERHZjUUkERERERER2Y1FJBEREREREdmNRSQRERERERHZjUUkERERERER2Y1FJBEREREREdmNRSQRERERERHZjUUkERERERER2Y1FZCHz5ptv4p133sH69euRnp5udDi6On/+PEwmE8aPH48TJ04YHY7upkyZgr59+2LRokVITEw0OhxdZWRk4LHHHsPw4cOxY8cOiIjRIenq77//Rs+ePTF16lRcunTJ6HB0N2zYMLzxxhv4888/kZqaanQ4uoqPj4fZbMaYMWNw6NAho8PR3dy5c9G7d2/MnTsXCQkJRoejKxFB3759MWTIEGzZsgUWi8XokHR16NAhmM1mTJw4EWfPnjU6HN2NHTsW/fv3x++//47k5GSjw9FVcnIyevbsiREjRmDPnj1u/5q7cuVK9OrVCzNmzEBcXJzR4ejO6dpARNxiAAgCIPHx8UI527x5swAQAFKiRAl54okn5JdffpHr168bHZounn/+eTXf+vXry+DBg2Xjxo2Snp5udGiau379uhQvXlwAiK+vr8TExMi3334rp06dMjo0Xfz444/qvi1Xrpy8+OKL8ttvv8mtW7eMDk1zFotFOnToIABEURRp1aqVfPLJJ/Lff/+JxWIxOjzN7d+/Xzw8PASABAUFycMPPyw///yzXLlyxejQdDF48GD1WK5Zs6a89dZbsmbNGklLSzM6NM0lJydL+fLlBYB4e3tLly5d5H//+58cPXrU6NB08dtvv6n7tlSpUvLss8/K/Pnz5caNG0aHposePXqo+TZt2lSGDRsmf//9t2RkZBgdmubOnTsnfn5+AkACAgLk/vvvl8mTJ8v58+eNDk0XY8aMUfdt5cqV5dVXX5U//vhDkpOTjQ5NcxkZGVKvXj0BIB4eHtK+fXv54osvZP/+/W75mmtdG2S+jwQQJLnVXrlNcJXBItJ+0dHR6sGSOby8vKRTp04yduxYOXz4sNEhaub48ePi5eWVJd/Q0FB5+umn5ddff5WEhASjw9TMxx9/nCVXANK4cWMZOnSobN261W1ezNPS0qRatWpZcvX39xez2Szff/+9nDt3zugwNbN69eps923FihXl5ZdfluXLl7vVi/kTTzyRJVcPDw9p166dfP7557J37163eTG/fPmyFC1aNEu+xYoVk8cee0xmzpwpcXFxRoepmW+//TbbY7lu3bry7rvvyoYNG9zmgz6LxSLNmzfPkquPj49069ZNvv76azl58qTRYWpm586d2e7bMmXKyPPPPy+LFy+WxMREo8PUzOuvv55tvuHh4fLRRx/Jzp073eY8lZiYKKVKlcqSa9GiReXBBx+UH3/8US5dumR0mJqZM2dOtvu2evXqMmDAAFm9erWkpqYaHaZmsqkNci0iFXGTr6QVRQkCEB8fH4+goCCjw7nLnj17ClSb0j///IMRI0bYnFO7dm2YzWaYTCa0adMGXl5edm9/6dKlSElJyWuYmhk5ciS2bduW4+Pe3t7o2LEjzGYzzGYzKleubPe2z58/j82bN2sQpTbi4+Px3HPP2Ww1CQsLQ/fu3WE2m9G1a1cUKVLE7u1v2bIF586d0yJUTSxatAg///yzzTnNmzdXj+UmTZpAURS7tp2amorffvtNizA1ISJ4/fXXbbaJFSlSBFFRUTCbzejevTtKlSpl9/YPHz6M3bt3axGqJg4ePIj33nvP5pyqVauqf7ft27eHj4+P3dtfuXIlbty4kdcwNTNhwgSsWrUqx8c9PT3Rvn17mEwmmM1m1KxZ0+5tx8XFYe3atRpEqY2UlBQ8++yzNl8nSpYsidjYWJjNZnTr1s2h1/UdO3YUqCUMa9aswddff21zTsOGDdXzVHh4ODw87F9tNH/+/LyGqKmhQ4di//79OT7u5+eHLl26qPmWK1fO7m2fPHkS27dv1yJMTZw/fx6vvPKKzTkVKlRQ/247deoEPz8/u7e/bt06XL16Na9hamb69OlYsGBBjo8rioLWrVur+darV8/u19ybN29ixYoVWoWaZxaLBc8//zyuX7+e45zg4GBER0fDbDYjJiYGJUqUsHv7LlAbBIuI7TUHuVWZrjJQgL+JHDRoULafZrjKcLTtNTQ01PCY8zIcaXtdsmSJ4fHmZTja9mrdquSKw5G217i4OMPjzcvIbHv99NNP7Wp7HT16tOEx52U42vZap04dw2POy8hse127dm2uba/WrUquOBxte+3bt6/hMedlONr2mtn67arDkbbXqVOnGh5vXoajba/t27c3POa8jMy21xUrVuTaKXPo0CHD483LcLTt1QVqA7azFgQucKDYPfz8/GT48OGSlJSUY76uXkRaj9q1a8uqVatyzNXVi8h7R+/eveXChQs55uvqRaT1KFGihEycODHHDwpcvYi8d7Rr107+/fffHPetqxeR1sPLy0sGDhxos1Xd1YtI61G5cmVZtGhRjm9aXL2IvHc8+OCDNltAXb2ItB6BgYEyZswYm21zrl5EWo8mTZrIpk2bcszV1YtI6+Hh4SH9+/eXq1ev5pivqxeR1iMsLExmzJiR43nK1YvIe0e3bt3k4MGDOe5bF6gNci0i7e9RpEIrODgYMTExMJvNiI6OdujreldUp04dtc2mdevWDrXyuhofHx+1lddkMjnUyuuKwsLC1DabLl26ONTK64patGih7tvGjRvb3VbkiooWLaq28sbGxjrUyuuKqlWrprbytmvXzqFWXlfj6emJDh06qH+7NWrUMDokXYWEhKitvFFRUQVuiY7WGjVqpJ6nWrRo4VArr6vx8/ND165d1SUHjrTyuqIKFSqo56mOHTs61Mrrajw8PO5q5a1bt65bv+YC4JrI/LB7924cOHDA6DBU27dvx8iRI23OqVGjhvqH37ZtW3h7e9u9/cWLFxeoNZGjR4+2uSbSy8sLHTp0UPOtVq2a3ds+d+4cNm7cqEWYmkhISMDzzz9vc01kaGiouiYyMjISgYGBdm9/06ZNBerS7UuWLMG0adNszmnSpIl6Um/WrJndb1BSU1OxaNEiLcLUzIABA2z+/+/v74/IyEj1DUqZMmXs3vbBgwexa9cuLcLUxOHDhzFkyBCbcypVqqT+3UZERMDX19fu7S9fvrxArYmcOHEi/vzzzxwf9/DwQNu2bdVjuXbt2na/Qbl69SpWr16tVah5lpqaiueee87m60Tx4sXv+vCyWLFidm//n3/+wfHjxzWIVBvr1q3DN998Y3NOvXr11GO5ZcuW8PT0tHv7c+fOzWuImho2bJjNNZE+Pj7o3LmzWjhWrFjR7m2fOHECf//9txZhauLChQt47bXXbM4pW7as+nfbuXNnBAQE2L39NWvW4MqVK3kNUzMzZ87EwoULc3xcURSEh4er+TZs2NDu89SNGzewfPlyjSLNO4vFgn79+tlcExkYGIhu3bqpH16GhITYvX0XqA2ChWsi6V4xMTFZvrb29PSUDh06yKhRo+TAgQNGh6iZEydOiLe3d5Z8S5QoIU8++aTMnj3brW5v8sknn2TbltCgQQN57733ZNOmTW5z1cO0tDSpUaNGllx9fX0lNjZWJkyYIKdPnzY6TM2sWbMm231brlw56devnyxdutStbm/y1FNPZclVURRp3bq1fPrpp7Jr1y63uerhlStXJDAwMEu+QUFB8sgjj8i0adPc6vYm3333XbbHcq1ateTtt9+2a52nq7BYLBIeHp4lV29vb+natauMGzfOrW5v8t9//2W7b0uXLi19+vSRBQsWuNXtTQYMGJBtvs2aNZNhw4bJP//84zbnqcTERCldunSWXAMCAuSBBx6QKVOm2FwO42p+/fXXbPdtlSpV5LXXXpMVK1ZISkqK0WFqJpvagGsi6W5bt25VD5Dg4GDp1auXzJgxw2ZPvit78cUX1Xzr1KkjAwcOlPXr17vNGxRr8fHx6v19fHx8JCoqSsaPHy/Hjx83OjRd/Pzzz+q+DQsLk759+8qiRYvk5s2bRoemi4iICDXfFi1ayPDhw2XHjh1u8wbF2sGDB9V1XkWLFpWePXvK1KlT5eLFi0aHposhQ4ao+7ZatWryxhtvyKpVq9zqDUqmlJQUqVChgvrhZadOnWTMmDFy6NAho0PTxbJly9R9W7JkSendu7fMnTvXbd+rPPjgg2q+jRo1kqFDh8qWLVvc5tZS1s6fP6/eJ9LPz09MJpNMnDhRzpw5Y3Rouhg7dqy6bytUqCD9+/eXZcuW2bxGhqvKyMiQBg0aCHB77Wrbtm1lxIgRsmfPHrd8zbWuDYKCguwuItnOWsi88cYb8PDwUNfRONKm6mrOnz+PPn36qK0GjrSpuqLJkydj48aNTrWpupqMjAw88cQTqFmzpsNtqq7o77//xieffOJUm6or+uCDD3Dt2jWn2lRdTXx8PB5//HFEREQ43KbqiubOnYuFCxc61abqakQEffv2RWhoKMxmM1q1auVQm6qrOXToEAYMGIDu3bs73KbqisaMGYNDhw451abqapKTk9GrVy/1llmOtKm6opUrV+L77793qk3VFQ0YMECtDRo0aJCZb7Dk0s7KIpKIiIiIiKiQS0hIQHBwMGBHEem+H90TERERERGR5lhEEhERERERkd1YRBIREREREZHdWEQSERERERGR3VhEEhERERERkd1YRBIREREREZHdWEQSERERERGR3VhEEhERERERkd1YRBIREREREZHdWEQSERERERGR3VhEEhERERERkd1YRBIREREREZHdWEQSERERERGR3VhEEhERERERkd1YRBIREREREZHdWEQSERERERGR3VhEEhERERERkd1YRBIREREREZHdWEQSERERERGR3VhEEhERERERkd1YRBIREREREZHdWEQSERERERGR3VhEEhERERERkd1YRBIREREREZHdWEQWAiJidAj5pjDlCjBfd1aYcgUKV76FKVeA+bqzwpQrwHzdWWHKFdAmXxaRhcDXX3+NJ598Er/88guuX79udDi6Sk9Px/3334/Bgwdj06ZNyMjIMDokXW3cuBGxsbGYMGECTp8+bXQ4uhs4cCBefPFF/Pbbb0hKSjI6HF3FxcWha9eu+PTTT7Fr1y63f4GbMWMGHnnkEfz888+4cuWK0eHo7rHHHsNbb72FtWvXIi0tzehwdLV3715ERkZi3LhxOHr0qNHh6O6TTz7Bs88+i/nz5+PmzZtGh6OrpKQkREdHY9iwYfjnn39gsViMDklXv/32Gx544AFMnjwZFy5cMDoc3fXr1w+vvvoqVqxYgZSUFKPD0dXp06fRpUsXjBo1Cvv373f711xNagMRcXgA6A/gOIBkANsBtLcx90cAks3YazXnmRzm+DkQUxAAiY+PF7rbtWvXJDg4WACIl5eXdOrUScaOHSuHDh0yOjRdTJkyRT2GQkJCpHfv3jJ37ly3PDYsFou0bdtWzbdRo0YydOhQ2bp1q2RkZBgdnub27dsniqIIAPH39xez2Szff/+9nD171ujQdDFw4EB131asWFH69+8vv//+uyQlJRkdmuaSkpKkXLlyAkA8PDykbdu28vnnn8uePXvEYrEYHZ7mFi1apO7bYsWKSa9evWTGjBkSFxdndGi6uP/++9V869SpIwMHDpS//vpL0tPTjQ5Nc2fOnBEfHx8BID4+PtKtWzf5+uuv5cSJE0aHposvvvhC3bdlypSRvn37yqJFiyQxMdHo0DSXnp4uderUUfNt0aKFfPTRR7Jz5063PE9t2LBBzbVo0aLy4IMPytSpU+XSpUtGh6aLPn36qPlWq1ZN3njjDfnzzz8lNTXV6NA0l1NtsGPHjsz/D4Ikt9ortwlZfgF4FEAqgL4A6gD4H4CbACrmMD8YQJjVKA/gKoAPreY8AyD+nnlhDsbFItKGDz/8MLsiXWrVqiVvv/22rFu3TtLS0owOUxOpqalSpUqVLLl6e3tLZGSkfPXVV3L8+HGjw9TMypUrs923pUuXlj59+siCBQvk5s2bRoepmcceeyzbfJs1ayYffvihbN++3W1ezC9duiQBAQFZci1SpIj06NFDpkyZIhcuXDA6TM18/fXX2e7bKlWqyGuvvSYrV66UlJQUo8PUhMVikSZNmmTJ1dPTUyIiImT06NFy8OBBo8PUjNUbk7tGiRIl5Mknn5TZs2fL9evXjQ5TM6+88kq2+TZo0EDee+892bx5s9t80Hfz5k0JCQnJkqufn590795dJkyYIKdPnzY6TM3MmjUr231bvnx56devnyxdutStPuiLjIzMkquiKNK6dWv57LPPZPfu3W7zmnv06FHx9PTMkm9wcLA8+uijMm3aNLly5YrRYWomp9rA3iJSEQe/rlUUZSuAHSLyktXP9gNYKCKD7fj9BwDMB1BFRE7e+dkzAP4nIsUcCubu7QYBiI+Pj0dQUJCzm9HFjh07sHfvXkNjuH79Ol577TWbc4oXL47Y2FiYTCZER0ejWLFiTj3XnDlzDG97WLx4MX799Vebc+rVqwez2Qyz2YyWLVvC09PT4ec5c+YM1qxZ42yYmhARvPPOO7h06VKOc3x9fdG5c2eYzWaYTCZUqFDBqedau3at4W2zBw8exKeffmpzTtmyZWEymWA2m9GlSxf4+/s7/DwpKSmYM2eOs2Fq5vvvv8eGDRtyfFxRFISHh6vHcoMGDaAoisPPs2/fPmzfvj0voeZZcnIy+vfvj/T09BznBAUFoVu3bjCZTIiNjUVISIhTz7V48WLEx8c7G6om1qxZg6lTp9qcU6NGDXXftm3bFt7e3g4/z+XLl7F8+XJnw9TM8OHDbbazenl5ISIiQj1PVatWzann2bx5M44cOeJsmJo4e/YsBg+2/ZaoVKlSiI2NhdlsRlRUFIoWLerUc02fPt3w1ruZM2fmeow1adJEPZabNm0KDw/HV1QdPXoUmzZtcjZMTWRkZODVV1+12aocEBCAyMhImM1mdO/eHWFhYU491x9//GHztT0//PPPP/jqq69szqlcubL6mhsREQFfX1+HnychIQGLFi1yNkzNjBkzBv/991+Oj3t4eKBt27bqsVyrVi2nXnNdoDYIFpEEmxvIrcqUu7/t8wGQDqDHPT8fB2CdndtYAmDFPT975s52TwI4A+A3AE1y2Y4vbn/7mDnKoYB+Ezlo0CBblX6BHHlpew0NDTU8fkeHs22vS5YsMTx2Z4azba89evQwPHZHh7Ntr3FxcYbH7sxwtu119OjRhsfu6MhL26t1S5qrDGfbXjdv3mx47M4MZ9te+/bta3jsjo68tL16eHgYHr+jw9m216lTpxoeuzPD2bbX9u3bGx67o8PZttdDhw4ZHrszw9m2VxeoDbRtZwVQ9s6G29zz8/cAHLTj98vgdrH4yD0/bwXgSQCNALQH8CuAWwBq2NjWh9klzSJS+6Eoijz33HN2nwxcsYi0HqVKlZKpU6faVVy5ahFpPTp16iR79uyxa9+6YhFpPXx9fWXIkCF2vWlx1SLSetSoUUOWLVtm1751xSLy3vHoo4/a3TbnikWk9ShWrJiMHz/ermUIrlpEWo/w8HDZtm2bXfvWFYtI6+Hl5SWvv/663e29rlhEWo8KFSrInDlz7CquXLWItB4mk0mOHDli1751xSLSehQpUkRGjBghycnJuebqqkWk9WjQoIGsW7fOrn3rArVBrkWkF5wj9/xbyeZn2XkGwHUAC+/amMgWAFvUjSnKRgA7ALwKIKfvWUcAGGv170Dc/haTNBAYGIhu3brBbDYjJiYGoaGhRoekq+rVq6utCe3atXOqZcxVeHl5oUOHDmrLWPXq1Y0OSVehoaHo3r07zGYzIiMjERgYaHRIumrSpInaVtSsWTOnWsZchb+/v9oyFhsbi7Jlyxodkq4qVqyonqc6duzoVMuYq/Dw8ECbNm3UfGvXru1Uy5irKF68OGJiYmA2m9GtWzcUL17c6JB0Va9ePfU81apVK6eWk7gKHx+fu5aTVKxY0eiQdJW5nMRkMqFLly4ICAgwOiRdWS8nadiwoVufp+7l0JpIRVF8cPsbwodFZIHVz8cBaCwiETZ+VwFwCMBvIjLAjueaBKC8iMTYGVuBXRN54MABwy9rfvnyZTz77LM251SpUkU9yUVERMDHx8ep51q5ciVSU1Od+l2tzJo1CzNmzMjxcU9Pzyw97c64ePEi/vnnH2fD1ISI4LnnnrO5bqJEiRLq2ptu3bohODjYqefavn274Zc1/++//zBkyBCbcxo0aKC+QQkPD3fqDUpaWhpWrFjhbJiaGTVqFNatW5fj476+vujSpYv6t1u+fHmnnufYsWPYv3+/s2FqIjExEU888YTNNZHlypVTc+3cubNT610BYN26dYbffmHp0qWYMGFCjo8rioKWLVuq56n69es79Qbl2rVrhq8jA4A33njD5lrFoKAgREdHqx9elixZ0qnn2bVrl+Frt48fP45XX33V5pxatWqp56m2bdvCy8u5z/WXLl3q1O9paeLEiViyZEmOj3t7e9+13rVq1apOPc/p06exa9cuZ8PURFpaGp566imb549SpUqphVRkZKTT6103b96MuLg4Z0PVxF9//YWRI0fanNO0adO71rs6c55KTEzE2rVrnYxSO++//z527tyZ4+MBAQGIiopSP7x0dr2rC9QGwaLlmsg7BedWAN/e87N9AEbk8nsdcfvbyvp2PIcC4G8APzgQF6/OasO7776b5atqRVGkTZs2MmLECLe6jL71rQKsR3BwsLqe6OrVq0aHqZnFixdn24pQp04deeedd2T9+vVuc+VdEZEHHnggS64+Pj4SFRUl48ePd6sr7545c0Z8fX2z5BsWFiZ9+/aVhQsXutWVd0eNGpXtsdy8eXMZPny47Nixw23OU+np6VK3bt0suRYtWlR69uwpU6dOlYsXLxodpmY2btyY7b6tWrWqvP7667Jq1Sq3ufKuiMhzzz2XJVdPT0/p2LGjjBkzxq1usXXt2jUpVqxYlnxLliwpvXv3ljlz5rjVe7Mffvgh22O5UaNGMmTIENmyZYvbXHnXYrFIu3btsuTq5+cnJpNJJk6cKGfOnDE6TM1Y30bMelSoUEH69+8vy5Ytc6sr72ZXG1gNXW/x0Qe3b/HxJW7f4qPSncdHAPg5m9+bBmBLDtscBqAbgKoAGgP4AUAagHAH4mIRmYNLly5JkSJFBIAEBgbKQw89JD/99JPb3ufH+jYB1atXlwEDBsjq1avd8j4/FotFmjZtKsDtdTSdO3eWL7/8Ug4fPmx0aLqwvk1AaGioPPPMMzJv3jxJSEgwOjRdvPrqq2q+TZo0kffff1+2bdvmNm9QrN28eVNdT+3v7y/33XefTJo0yW3vAfrLL7+o+7ZixYry8ssvy/Lly+1aO+SKoqKiBLh9MaR27drJyJEjZd++fW7zoYC1o0ePipeXlwCQ4sWLy+OPPy6zZs1y23uADh8+XD2W69WrJ++++65s2LDBLe8BmpqaKlWrVlU/vIyOjpZvvvlGTp48aXRouli1apW6b8uWLSsvvPCCLF682C3vASpy9y3EwsPD5eOPP5Z///3XLc9TOdUGx44d029NpIjMVhSlJIAPcPtCOXsAxMqd23Xc+dldDd+KogQDeBDA6zlsthiA73H7/pDxAHYC6CAi2xyNj7KaN28e+vTpo1562dk2VVeQlpaGTZs2YdSoUXlqU3UVmzZtQt26dfHuu+/mqU3VVcyfPx+DBw/OU5uqq7h69SrOnj2LCRMm5KlN1VUsXrwYPXv2hNlszlObqisQEaxcuRKffvppntpUXcXevXtRrFgxTJs2LU9tqq7i119/xeuvv57nNlVXcOvWLezZswfjxo3LU5uqq1ixYgUiIiIwevToPLWpuoolS5Zg2LBheWpTdRWnTp1CamoqpkyZkqc2VVeRU22QkGC7g9Waw/eJLKgK8ppIIiIiIiKigiwhISHzC4lgyWVNpPteto+IiIiIiIg0xyKSiIiIiIiI7MYikoiIiIiIiOzGIpKIiIiIiIjsxiKSiIiIiIiI7MYikoiIiIiIiOzGIpKIiIiIiIjsxiKSiIiIiIiI7MYikoiIiIiIiOzGIpKIiIiIiIjsxiKSiIiIiIiI7MYikoiIiIiIiOzGIpKIiIiIiIjsxiKSiIiIiIiI7MYikoiIiIiIiOzGIpKIiIiIiIjsxiKSiIiIiIiI7MYikoiIiIiIiOzGIpKIiIiIiIjsxiKSiIiIiIiI7MYikoiIiIiIiOzGIpKIiIiIiIjsxiKSiIiIiIiI7MYikoiIiIiIiOzGItLNWCwWo0PIN4UpV6Bw5SsiEBGjw8g3hWnfAoUr38KUK1C48hWRQpVvYcoVKFz5WiwWvua6Mb3yZRHpZvr3749nnnkG8+bNw40bN4wOR1cXL15EmzZt8MEHH2Dbtm1uf1KYOHEi7rvvPkyaNAnnz583OhxdiQjMZjNeeeUV/PHHH0hJSTE6JF1t374d7du3x8iRI7Fv3z63fzEfPHgwHn/8ccyaNQvXrl0zOhxd3bhxA+3bt8egQYOwceNGZGRkGB2SrubMmYOYmBh88803OHXqlNHh6O7xxx/HCy+8gCVLluDWrVtGh6OrI0eOoE2bNvjkk0/w77//uv15auTIkXjooYfw008/4fLly0aHo6u0tDR07doVb775JtasWYO0tDSjQ9LVqlWr0KVLF3z55Zc4cuSI0eHoTrfaIPMTf1cfAIIASHx8vBRmO3fuFAACQHx8fCQqKkq++uorOX78uNGh6eK1115T8w0LC5PnnntOFi5cKDdv3jQ6NM3dvHlTSpUqpebbvHlzGT58uGzfvl0sFovR4Wlu9uzZaq5FihSRHj16yA8//CAXL140OjRddOvWTc23atWq8vrrr8uqVaskJSXF6NA0d/z4cfHy8hIA4unpKR07dpTRo0fLwYMHjQ5NFx999JG6b0uWLClPPfWUzJkzxy1fr9LS0qRatWpqvg0bNpQhQ4bI5s2bJSMjw+jwNPfnn3+qufr5+YnJZJLvvvtOzpw5Y3RounjiiSfUfCtUqCAvvfSSLFu2TJKSkowOTXOXL1+WIkWKCABRFEXatGkjI0aMkN27d7vla+63336r7tvg4GB59NFHZfr06XL16lWjQ9OcxWKR5s2bq/nWrl1b3nnnHVm3bp2kpaUZHZ7msqsNxo8fn21tEB8fnzk3SHKrvXKb4CqDReT/69Gjh3qwWI/69evL4MGDZePGjZKenm50mJo4e/as+Pr6ZsnV19dXYmJi5Ntvv5VTp04ZHaZmRo8ene2+LVeunLz44ovy22+/ya1bt4wOUxMZGRlSt27dLLkqiiKtWrWSTz/9VP777z+3eTHftGlTtvs2KChIHn74Yfn555/lypUrRoepmb59+2abb82aNeWtt96StWvXus2L+fXr16VYsWJZcvX29pauXbvK//73Pzl69KjRYWpm6tSp2e7bUqVKybPPPivz58+XGzduGB2mJiwWi7Rv3z7bfJs2bSrDhg2Tv//+220K6P3794uHh0eWXAMCAuT++++XyZMny/nz540OUzODBg3Kdt9WqVJFXn31VVmxYoXbfNCXnJws5cuXz5Krp6endOjQQb744gvZv3+/27zmLlmyJNt9W6JECXniiSfkl19+kevXrxsdpmZyqw02bdok6enpDhWRirhJO4KiKEEA4uPj4xEUFGR0OHfZunUr/v3333x7vr1792L8+PE254SGhiI2NhZmsxlRUVEIDAzU7Pl/+uknJCcna7a93Hz//ffYsWOHzTmNGzeG2WyG2WxGs2bN4OGhTSf3yZMnsXz5ck22ZY/ExES8/fbbNtuI/P390bVrV5jNZphMJpQpU0az5//jjz9w4sQJzbaXmz///BNz5861OadSpUowmUwwm83o2LEjfH19NXnulJQU/Pjjj5psy14fffQRzp07l+PjHh4eaNOmjZpvnTp1oCiKJs/933//YcuWLZpsyx4nTpzA559/bnNOsWLFEBMTA7PZjOjoaBQvXlyz5589ezauX7+u2fZyM3PmTKxfv97mnLp166rnqVatWsHT01OT57548SIWLlyoybbskZ6ejjfffBOpqak5zvHx8UHnzp3VY7lixYqaPf+6detw4MABzbaXm61bt2Lq1Kk255QpU0bNtUuXLggICNDs+b///vt8bS0dO3YsDh06ZHNOeHi4eiw3bNhQs/PUwYMHsXbtWk22ZY8rV65g6NChNucEBgYiKioKZrMZsbGxCA0N1ez5Fy1ahAsXLmi2vdwsXrwYy5YtszmnevXq6r5t164dvL29NXnu+Ph4/PLLL5psyx4igkGDBiE+Pj7HOV5eXujQoYP6t1u9enXNnr+g1gaRkZGYOXMmAASLSILNX8itynSVgQL8TWROn2QVlKF122toaKjhOdkaWra95vRJVkEaWra95vRJVkEZWra9xsXFGZ5PbkPLttecvuUuKCOz7XXMmDGatL3WqVPH8JxsDS3bXjdv3mx4PrmNzLbXLVu25Plbu5y+5S4oQ+u21+y+GSxIQ8u215y+5S4oQ+u215y+5S4oQ8u210OHDhmeT24js+11/fr1ee6UKei1AdjOWjC4wIGijqCgIPn444/zdKIv6EWk9WjYsKGsWrXK6VxdoYjMHF5eXvLMM8/IhQsXnM63oBeR1iMsLEwmTZrk9BtSVygirUfHjh3l33//dXrfFvQi0noEBATIu+++m6eWyIJeRFqPmjVryuLFi51+Q+oKRWTm8PDwkIcfflhOnjzp9L4t6EWk9ShRooR8+eWXkpqa6nS+Bb2ItB4tW7aUzZs3O51rQS8irYevr6+8/PLLEhcX53S+Bb2ItB6VKlWSmTNnOn2ecoUiMnMoiiKxsbF5+kDTBWqDXItIL1ChV6VKFbU1oUOHDvDx8TE6JN14enqiXbt2ar41a9Y0OiRdlSxZ8q625eDgYKND0lXDhg3VtpPw8HDN2pYLIj8/P3Tp0kVtWy5XrpzRIemqfPny6t9tp06d4OfnZ3RIulEUBa1atVLzrVevnmbtgAVRcHAwoqOjYTabERMTgxIlShgdkq5q166tnqfatGkDLy/3fSvm7e2Njh07quepKlWqGB2SrkqXLq3u265du6JIkSJGh6SrZs2aqeepJk2auPV5qkiRIne1LZcuXdrokAzHNZH54NixY/l6qfP169dj2LBhOT7u4eGB1q1bq3/4Wq6rAoCNGzfm6+WhBw8ebHMtl57rqq5evYrdu3drtr3cXLlyBY888ojN9S9169ZVX8Rat26t2boqANizZw+uXLmi2fZyM2PGDEyePDnHx318fNCpUyf1DUqlSpU0e+60tDRs3LhRs+3lRkTw5JNP2lwTmbmuymQyoWvXrpquqzp9+jSOHj2q2fZy899//+GNN96wOadFixbqeapRo0aanqe2bduWr7dkGDFiBFasWJHj40WLFkW3bt10WVeVkJCQ67pxLSUmJqJnz54210RmrqsymUxo3769ZuuqgNvr5vLzNkhLlizB2LFjc3zcy8sL7du3V49lLddVAcjXNYLA7dsF7N+/P8fHQ0JC0L17d5jNZkRGRmr6nuzChQv5ut71+PHj6NOnj805jRs3Vl9zmzdvrumHlzt37rS5Zk9r3377rc3rEFhfc6F79+4oW7asZs9969YtbNu2TbPt5SY9PR0PPfSQzf9/K1asqJ6nOnbsqOmHlwW1NoiMjMSHH34IcE1k4ZPTleICAwPVKzxevnzZ6DA1k9OV4mrUqCFvvvmmrFmzJk9tQgVNdu0PXl5e0qVLF/nf//4nR44cMTpEzeR0pbjMKzzOmzdPEhISjA5TMzm1Rjdt2lQ++OADt7rCo0j2rdHueoXHnK4iXblyZXn11Vfljz/+kOTkZKPD1Ex2rdEeHh7Svn17t7vCY05XkS5evLh6hcdr164ZHaZmcrqKdP369WXQoEFudfV3kexbo9316u85XUW6bNmy8uKLL8qSJUvc5urvIiI//vhjtm2qLVu2lE8++cStrv7uSG3AW3wUYtb3rKpSpYq89tprsnLlSre5BPW9Mu9Z5enpKREREW59rznre1ZZX3TDnS5Bbc36nlUNGzaU9957z23vNWexWKRZs2YC3L7oRvfu3d36XnPW96wqX768vPTSS7J06VK3eoNiLfN+toqiSOvWreWzzz5z23vNWd/P1vqiG+50expr1vezrV27trz99ttue685kf+/n623t7dERkbKV199JceOHTM6LF0cO3ZMvZ9t6dKl3fo+1CJ338+2WbNm8uGHH7rtfait72drfUG+vFwzoiBzpDZwpIh030b8QmrVqlX4/PPPdWlTLWjOnTsHRVEwc+ZMzdtUC6LffvsNL7/8si5tqgVNRkYGdu7cia+//lrzNtWC6O+//0bTpk3xwQcfaN6mWhAtW7YMH330kS5tqgXN9evXERcXhx9//BExMTEoVaqU0SHp6o8//sDjjz8Os9mseZtqQSMi2LBhA8aOHatLm2pBc/DgQYSFheHXX3/VvE21IFqyZAkGDRqkS5tqQZOcnIyjR4/i+++/17xNtSBau3atunxA6zbVgkiv2oBrIomIiIiIiAq5hISEzIswBksuayLd92MVIiIiIiIi0hyLSCIiIiIiIrIbi0giIiIiIiKyG4tIIiIiIiIishuLSCIiIiIiIrIbi0giIiIiIiKyG4tIIiIiIiIishuLSCIiIiIiIrIbi0giIiIiIiKyG4tIIiIiIiIishuLSCIiIiIiIrIbi0giIiIiIiKyG4tIIiIiIiIishuLSCIiIiIiIrKbU0Wkoij9FUU5rihKsqIo2xVFaW9jbkdFUSSbUfueeQ8qirJPUZSUO//t4UxsREREREREpB+Hi0hFUR4F8D8AnwJoAuAvAL8rilIxl1+tBaCM1Thstc3WAGYDmAag0Z3/zlEUpaWj8REREREREZF+FBFx7BcUZSuAHSLyktXP9gNYKCKDs5nfEcAaAMVF5HoO25wNIEhEYqx+thzANRF5zM64ggDEx8fHIygoyP6EiIiIiIiICrmEhAQEBwcDQLCIJNia69A3kYqi+ABoBmDFPQ+tANAml1/fqSjKeUVR/lQUpdM9j7XOZpt/2Nqmoii+iqIEZQ4AgblnQERERERERHnhaDtrCABPABfv+flFAGE5/M55AC8AeBBATwAHAfypKEoHqzlhDm4TAAYDiLcaZ+yIn4iIiIiIiPLAy8nfu7cHVsnmZ7cnihzE7cIx02ZFUSoAeBvAeme2eccIAGOt/h0IFpJERERERES6cvSbyCsAMpD1G8JSyPpNoi1bANSw+vcFR7cpIikikpA5ANxw4PmJiIiIiIjICQ4VkSKSCmA7gMh7HooEsMmBTTXB7TbXTJuz2WaUg9skIiIiIiIinTnTzjoWwDRFUf7B7eLvBQAVAXwHAIqijABQTkR63/n3GwBOANgLwAfAk7i9PvJBq22OA7BeUZR3ASwCcD+ArgDaOREfERERERER6cThIlJEZiuKUhLAB7h9v8c9AGJF5OSdKWVwu6jM5ANg9P+1d+fxMV39H8A/J4nEEkTFklpaVUvsSwmC1BJLktGqp4u2dNO91epTSldd6NMW9XShnrZodUNbVGmLopRQFTQ0hDZKbLUlhOzz/f2RzPxGzCR30nvn3ozP+/U6L8ycufl+nZl78p055w6ABgCyUVRMxovIcpdjblRK3QLgFQAvA/gDwM0istn7lIiIiIiIiMgoXn9PpFVdKt8TWVBQgKCg8l4PqeK5lPK9lHIFLq187XY7RASBgYFmh+ITl9LYApdWvgUFBQgMDIRSyuxQfOJSGlsRQWFh4SWT76U0tsCllW9hYSECAgJ4nioHw74nksy3bt06dOvWDZMmTcKOHTvgL28CePLII4/gpptuwscff4wTJ06YHY6hTp8+jU6dOuHf//431q5di/z8fLNDMtTs2bPRv39/TJ8+HX/88YfZ4RhKKYWEhATcdddd+Prrr5GVlWV2SIZKTk5G586d8cILL2DLli2w2+1mh2SoZ599Ftdffz0++OADHD161OxwDJWbm4uoqCg8+uijWLFiBXJzc80OyVCLFi1C79698cYbbyAlJcWv51ylFG6//Xbcdttt+OKLL5CRkWF2SIY6cOAAOnbsiAkTJmDjxo0oLCw0OyRDTZ06FXFxcZgxYwYOHjxodjiGstvtiImJwf33349vv/0W2dnZZodkKNNqAxHxiwagBgDJzMwUf2a32yU6OlpQ9PUn0rhxY3nooYfku+++k+zsbLPD092uXbtEKSUAJCAgQKKjo+U///mP7Ny5U+x2u9nh6W7cuHHOsQ0LC5NbbrlFPv30Uzl16pTZoekuOztbGjRo4Mw3MjJSxo0bJ+vXr5f8/Hyzw9PdkiVLnLkGBwfLwIED5e2335b9+/ebHZohrrvuOme+ERERMmrUKFmyZImcO3fO7NB0l56eLsHBwc58u3TpIi+99JIkJSX55Xnq9ddfd+YaGhoqN9xwg8yZM0f+/vtvs0PTXUFBgURGRjrzbdq0qTz++OPy448/Sl5entnh6e7nn3925hoUFCR9+vSRadOmSWpqqtmhGeLuu+925hseHi4jR46UhQsX+uXvkqdPn5aaNWs6823fvr08++yzsnnzZiksLDQ7PN19+OGHzlyrVKkiNptNZs2aJYcOHTI7NN3pWRtkZmY6jlNDyqq9yupQUdqlUkSKiKxcudL5RHFt1apVk6FDh8qHH34oR48eNTtM3dxyyy1u823SpImMHj1aVq5cKbm5uWaHqYu///5bqlatelGugYGBEhMTI2+88Ybs3r3b7DB1884777gd28suu0xuv/12mT9/vmRkZJgdpi7sdrt07NjRbb5t27aVp59+WhITE6WgoMDsUHWRlJTkNtfKlStLfHy8zJw5Uw4ePGh2mLp55JFH3ObbsGFDeeCBB2TZsmV+80ZfVlaWhIeHX5SrUkq6d+8ukydPluTkZL8poD///HO3Y1ujRg256aabZN68eXLixAmzw9RNbGys23xbtGghTz75pPz0009+80bfH3/8IYGBgRflWqlSJYmNjZX//ve/8ueff5odpm4mTpzodmzr1asnd999tyxatEiysrLMDlMXeXl50qRJE7f5du7cWSZOnChbt271m/OUXrWBN0Uk90T6wPr167FlyxbdjicieOWVV0pdaqKUQteuXWGz2WCz2dC2bVufrQ2fOXOmrksHUlNTMWvWrFL71KhRAwMHDkRCQgLi4uIQHh6u288vzZ9//onFixfresxPPvkE27ZtK7VPs2bNnGMbHR2NSpUq6RqDJ9988w327dun2/FycnLw3HPPlbrcMSgoCDExMbDZbEhISEDTpk11+/llxTZjxgxdj7lhwwZ8/fXXpfapU6cO4uPjYbPZMGDAAISGhuoagye//vor1q1bp+sxp02bhkOHDpXap2PHjs7ncqdOnRAQ4JtdFnPnzsWpU6d0O96hQ4cwbdq0UvtUrVoVsbGxSEhIQEJCAurXL/n1yMY4cuQIPv/8c12PuWjRIvz888+l9rnyyiuRkJAAm82GmJgYhISE6BqDJytWrMDOnTt1O15hYSGee+65UpfuBgQEIDo62nmeatmypc/m3DfffFPX5Wvbt2/HvHnzSu1Tq1YtDB48GDabDYMGDUJYWJhuP780u3btwg8//KDrMWfNmoXU1NRS+7Ru3dp5noqKivLZ/vb58+eXeQ71RkZGBl5++eVS+4SEhKBv377O53KjRo10+/mlOX36NObMmaPrMVesWFHm8+Xyyy93nqf69euHKlWq6BqDJ1atDbzZE2n6J4h6NVj4k8jx48e7fXfAl82Xy17r1Kljaq6+XPa6dOlS08fWl8tehw4danq+vlr2eurUKdNz9eWy1ylTppiery+XvbouUTSr+WrZa2Jioum5+nLZ66hRo0zP15fLXgMCAkzN1ZfLXufMmWP62Ppy2WuvXr1Mz9dXy15TU1NNz9WXy16tWhtwOavFWOGJ4miBgYEyZMgQ2bNnj2H5ml1Eurbw8HB58cUXDSucrVBEurbOnTvLypUrDclVxBpFpKNVrlxZ7rzzTjly5IghuVqhiHRtjRs3llmzZhm23NUKRaSjBQQESP/+/WX79u2G5CpijSLS0WrWrCljx46VM2fOGJKrFYpI19amTRtZsmSJYYWzFYpIRwsODpabbrrJ0DeBzC4iXVv9+vVl6tSphhXOVigiXVvPnj1l48aNhuQqYo0i0tFCQ0Pl4YcflpMnTxqSqxWKSNd29dVXy6effmrYecqqtYE3ReSlca3fS1ytWrUQFxeHhIQEny47MYtZy07M4LrsJD4+Ho0bNy77QRWY67KTvn37omrVqmaHZBgzl6SboXr16hg0aJDPl6Sbxawl6WYwa0m6WerWrYv4+HgkJCQgNjYW1atXNzskQ5m1JN0MjiXpNpsNcXFxiIiIMDskQ11xxRXOsfXlknQzuC5Jt9lsaNGihV/PuZ5qgzNnSl/B6op7In0gPT0dR44c0e14+fn5iI+PL3Xdc8uWLZ2/bPfo0cOn3w20bds2FBQU6Ha81atXY/z48R7vr1SpEq699lrnLyhNmjTR7WeXJSMjA3v37tX1mGPGjMGGDRs83l+vXj3nnqr+/fv7bM8cAOzdu1fXy77//fffGDJkSKl7Ijt37uw8qXfs2NFnJ/WCgoIy96Z6a+7cuaXus6xWrRoGDBjg/AWlXr16uv780hw9elTXy76LCIYNG4b09HSPfZo0aeIc2969eyM4OFi3n1+W5ORk5OTk6Ha8pKQkPPDAAx7vDwwMRM+ePZ35Nm/eXLefXZasrCykpKToesyJEydi+fLlHu+vXbu28xeUgQMHOvbY+ERaWpquXwmVlZWFwYMHl7onsl27ds45t2vXrj4tpPTcVwUU7Xd99dVXPd5fuXJl9OvXz/nmZcOGDXX9+aU5ceIE0tLSdD3mXXfdhV27dnm8v2HDhs7fL/r06eOzPXMAkJKSoutXQv3xxx8YPny4x/uVUujWrZvzPNW6dWufzbk5OTlITk7W9ZjTp0/HZ5995vH+mjVrYtCgQc69vbVr19b155fGqrUB90T6OdfLFjua656EvXv3mh2ibux2u/To0eOifMPDw+WOO+6QL7/80rAlYGZw/UoT19ahQwe/vBT32LFjL8rVsSfhf//7n19dijs7O1suv/zyi/Jt3LixPPzww373NT2LFy++KFfX/cq7du3ym6viiYgMGTLkonzDwsJk+PDh8tlnn/nV1/QcPHjwgq80cbRWrVo59yv7y1WGRURee+21i3J17Fd+5513/OpregoKCqRly5YX5RsRESH33nuv331Nz/r1690u7+vatau89NJLsm3bNr86T911111ul6kOGzZM5s6d61df01PyK00c7eqrr5YxY8b43df06FUbcE+kH3O9ZHGtWrXktttuky+++EJOnz5tdmiGWLFihfPF0KZNG5kwYYJs3LjRr35BceX4OpOQkBAZPHiwzJgxQw4cOGB2WIY4duyY8+tMGjRoIPfff798++23cv78ebNDM8Tbb78tQNHXIHTr1k0mTZokO3bs8KtfUBzsdrt06NBBAEj16tXlxhtvlI8//liOHz9udmiG2Lp1q/M81bx5c/n3v/8ta9eu9atfUFw9/PDDzl9Q+vXrJ9OnT5d9+/aZHZYhzp496/w6k7p168pdd90lX3/9tZw9e9bs0Azx2WefOZ/LnTp1khdeeEG2bNniV29euurfv78AkKpVq8p1110nH3zwgWH77M22b98+59eZXHnllfLoo4/KihUrJCcnx+zQDPHCCy8437zs3bu3vPHGG5KSkuKXc66etQH3RPqxn3/+Gf/6179gs9nQvXt3ny5TNcPGjRvx1ltvwWaz4corrzQ7HEMdPXoU1atXx+LFi9G/f39Uq1bN7JAMtXLlSowbN87ny1TNUFhYiNTUVMyePdvny1TNkJSUhJiYGEyZMgW9evXy6TJVM6xevRpTpkzx+TJVM2RmZiIvLw8LFizAgAEDfLpM1QyrV6/G/fffD5vNhi5duvj1fj8RwbZt2/Dee+8hISEBDRo0MDskQ+3duxfNmjXDE088gT59+qBy5cpmh2SolStX4uWXX/b5MlUz5OTk4OjRo/jkk08wePBgXHbZZWaHZCizagPuiSQiIiIiIrrEebMn0n/fUiMiIiIiIiLdsYgkIiIiIiIizVhEEhERERERkWYsIomIiIiIiEgzFpFERERERESkGYtIIiIiIiIi0oxFJBEREREREWnGIpKIiIiIiIg0YxFJREREREREmrGIJCIiIiIiIs1YRBIREREREZFmLCKJiIiIiIhIMxaRREREREREpBmLSCIiIiIiItKMRSQRERERERFpxiKSiIiIiIiINGMRSURERERERJqxiCQiIiIiIiLNWEQSERERERGRZiwiiYiIiIiISDMWkURERERERKQZi0giIiIiIiLSjEUkERERERERacYikoiIiIiIiDRjEWkROTk5ZofgU5dSvrm5uRARs8PwmUtpbAsLC5Gfn292GD5zKY0tcGnlm5eXB7vdbnYYPnMpja2IXFL55uTkcM71U/n5+SgoKDA7DJ+x+tiyiLSIxMREtGvXDk8//TQSExNRWFhodkiGGj16NOLj4/Hee+8hPT3d7HAMdfbsWbRu3RoPPvggli1bhuzsbLNDMtTHH3+M7t27Y/LkyUhOTvbryTwgIADx8fG4+eab8cknn+DkyZNmh2SoPXv2IDIyEk8++SR++uknv5/MX3jhBcTGxuKtt95CWlqa2eEYqqCgAJ06dcI999yDRYsWISsry+yQDLVs2TJ07twZEydOxNatW/36PKWUwogRIzB06FDMnj0bR48eNTskQx07dgyRkZEYPXo0Vq5ciby8PLNDMtT06dMRExODKVOmYM+ePWaHYyilFHr16oURI0ZgwYIFyMzMNDskQ1m+NhARv2gAagCQzMxMqYjsdrv07t1bAAgAqVOnjtx5553y5ZdfypkzZ8wOT3e7d++WgIAAZ74dO3aU5557Tn755RcpLCw0OzzdTZgwwZlr1apVZciQIfL+++/L4cOHzQ5Ndzk5OdKoUSNnvldccYU88sgj8v3330tOTo7Z4elu2bJlzlwDAgKkZ8+e8tprr8nvv/8udrvd7PB0d8MNNzjzrVWrltx6663y+eefy+nTp80OTXeHDx+WypUrO/Nt3bq1PPXUU/Lzzz9LQUGB2eHpburUqc5cQ0JCZNCgQfLuu+/KX3/9ZXZouissLJQ2bdo487388svlvvvuk2+++UbOnTtndni6S0xMdOYKQLp27Sovv/yybN++3S/PU/fdd58z1+rVq8u//vUv+eijj+T48eNmh6a7jIwMqVWrljPfZs2ayZgxY2T16tWSl5dndni6++ijj5y5BgUFSd++feXNN9+Uffv2mR2a7syoDTIzMx0/r4aUVXuV1aGitIpeRIqIrF69+oKTvKMFBwfLgAED5O2335b9+/ebHaZubr/9drf51q9fX0aNGiWLFy+WrKwss8PUxfHjxyU0NNRtvtdcc428+OKLkpSU5DeT+cyZM93mGhoaKjfccIPMmTNHjh07ZnaYurDb7dKlSxe3+TZt2lQef/xxWbVqld9M5tu3b3eba2BgoFx77bUydepUSU1NNTtM3Tz++ONu8w0PD5eRI0fKggULKvS84+rcuXNSt25dt/m2a9dOnnnmGdm0aZPfvNG3cOFCt7lWqVJFEhISZNasWXLo0CGzw9TNoEGD3ObbqFEjeeihh2T58uWSnZ1tdpi62L9/vwQFBV2Uq1JKevToIa+++qrs3LnTb+bcl19+2e3YhoWFyS233CKffvqpnDx50uwwdZGfny9XX32123wjIyNl7Nixsm7dOsnPzzc7VF34ujbwpohU4idLOJRSNQBkZmZmokaNGmaHc4HVq1djw4YNZfYTEUybNq3Mj+fbtm2LhIQE2Gw2dO3aFYGBgXqFqoupU6fi/PnzZfb7888/MXfu3FL7VK5cGX379oXNZkNCQgIaNmyoU5T6SE1Nxfz58zX1XbhwIZKTk0vt07BhQ+fY9unTB1WqVNEjTN0sXLgQu3fvLrNfbm4uJk+eXOoSMaUUoqKiYLPZYLPZ0KZNGyil9Az3H8nOzsaUKVM09f3ll1/w7bffltqnRo0aGDRoEGw2GwYPHozatWvrEaZuEhMTsWrVKk19Z86ciSNHjpTap0WLFs7ncnR0NIKCgvQIUzczZ87EiRMnyux39OhRzJgxo9Q+lSpVQkxMjPO53KRJE73C1EV6ejrmzJmjqe+yZcuwefPmUvvUq1cP8fHxsNls6N+/P0JDQ/UIUzfffvsttm3bVmY/u92OV199Fbm5uaX269Spk3NsO3XqZKnzFAC88sormpbjJicnY+HChaX2qVatGmJjY2Gz2RAfH4969erpFaYuduzYgW+++UZT348++gh//PFHqX2aNGniPE/FxMQgODhYjzB189FHH+HAgQNl9jtz5kyZ81VgYCCio6Odz+UWLVroFaYuTp48Wea51mHt2rVYvXp1qX0uu+wyxMXFwWazYeDAgahZs6YeYerGqrXBmTNnHP9XNUXkTJnB+UODhT+JHD9+vNt3EfRojo+2v/rqK8sse61Tp45h+Vpt2evSpUsNy9WKy16HDh1qWL5WW/Z66tQpw3K14rLXKVOmGJavFZe9RkZGGpav1Za9llzKqGez4rLXUaNGGZavFZe9um4N0btZbdnrnDlzDMvVistee/XqZVi+zZo1kyeeeMIyy15TU1MNy9WKy16tWhtwOavFGPlEcbTKlSvLsGHDZM+ePWana2gR6WiNGjWSV155xfSlN0YWkY7mKDhWrVplaq4ixhaRjlazZk2599575ejRo6bmamQR6doiIyPl/fffN/1NESOLSEcLDg6W+Ph42b59u6m5ihhbRDpa/fr1ZcKECXL27FlTczWyiHRtXbp0kSVLlphebBhZRDpaaGio3H777ZYonI0sIh2tadOm8uabb5pebBhZRDpaYGCg9OvXTxITE03NVcTYItLRwsPD5bHHHpNTp06ZmquRRaRra9++vXz66aemn6esWht4U0Raa30ReeXyyy93fnTdt29fVK1a1eyQDKOUQteuXZ35tmvXznJLivRUvXp1DBw4EDabDXFxcQgPDzc7JEM1a9bMucQmOjoalSpVMjskwwQFBSEmJsb5XG7atKnZIRmqTp06zqWPsbGxqF69utkhGapjx47Ose3cuTMCAvz3IuhVqlS5YOljRESE2SEZ6oorrnCep2JiYhASEmJ2SIYJCAhAdHS087ncsmVLv55za9WqhcGDB8Nms2HQoEEICwszOyRDtW7d2vlcjoqKsty2KD0FBwdfsC2qcePGZodkKF/WBtwT6QPHjh3TdOn/3Nxc9OnTp9R1z507d3a+EKy4NwMo+hoALZch/u677/Dkk096vN/qezOAoq/vOHjwoKa+o0aNQmJiosf7mzRp4jyp9+7d23J7MwDg4MGDOHv2bJn9Dh8+jAEDBnjcpxMYGIiePXs6T3RW25sBFH0HpNbLpc+cORPvvPOOx/utvjcDKNqPcuzYsTL72e12DBo0CIcOHfLYp23bts7zlBX3bQPAvn37NF36f9OmTbjnnns83h8SEoJ+/fpZdt82AJw/fx779+/X1Hfs2LFYvny5x/sbNGjgPE9Zcd82UHT+ycjIKLNfZmYm+vTp43FPpFIK3bp1c56nrLZv2+H333/X1O+zzz7DpEmTPN5v9X3bAJCRkYHDhw+X2U9EcNNNN5X6f9OiRQvn69aK+7YBYP/+/ZquMbF7924MGzbM4/2u+7YTEhJw1VVX6RmmLnJzc8vcw+owefJkfPrppx7vt/q+bcC6tQH3RFZQ7777rtuPoh1XiUtPTzc7RN3Y7Xbp3LnzRfk6rhL33Xffmb5UVU9JSUkX5RoQECDR0dF+d5U4EZHRo0dflG/NmjX97ipxIiJZWVlur2gZGRkp48aN86urxImIzJ8//6Jcg4ODZeDAgfL2229LWlqa2SHqauDAgRfl67iC9JIlS/zmCtIiIn/++afbK1p26dLF764gLSLy0ksvXZSrP15BWqToipZNmza9KF/XK0jn5uaaHaZufvzxR7fLVPv06eN3V5AWEbn11lsvyrd27doycuRIWbhwYYX+3bik48ePS7Vq1dwuU3322Wf96grSIr6vDbgnsgLKycmRBg0aCPD/G/eXLl1qmY37enPsJVRKSVRUlKU27hvh+uuvF8CaG/f1dujQIQkJCRHg/zfur1mzxvS9NEZx7CUMCgqSfv36WWrjvt4KCwulVatWAljzol5627hxo3PSttpFvYzg2EtYpUoVy13US28ZGRkSFhYmwP9f1OuHH36wxEW9jODYSxgQECC9evWy1EW99Ga32517Ca14US+9paSkiFJKgKKLeo0fP94yF/UygmMvYXBwsOUu6qU3M2oD7omsgDZu3IhRo0ZZ9hLietuxYwc+/PBDyy5T1dPhw4dxxRVXYOXKlZZdpqqntWvX4pVXXrHsMlU9FRYW4siRI5g/f75ll6nqKSkpCddffz0++OADyy5T1dPmzZsxc+ZMyy5T1VNGRgaqVKmCZcuWWXaZqp7WrVuHsWPHWnqZql5EBHv37sW8efMsu0xVT3v37kVUVBRefvllyy5T1dP69esxffp0yy5T1VNOTg6ys7OxaNEiyy5T1ZPVawPuiSQiIiIiIrrEebMn0n8vG0dERERERES6K1cRqZR6SCmVppTKUUptVUr1KqXvDUqplUqp40qpM0qpRKXUwBJ97lRKiZtWuTzxERERERERkTG8LiKVUjcDmA5gEoCOANYD+E4p5emLV3oDWAkgDkBnAGsALFVKdSzR7wyACNcmIjnexkdERERERETG8XpPpFJqM4AkEXnQ5bYUAItFZILGY+wCMF9EXir+950ApotImFfBXHhM7okkIiIiIiIqB8P2RCqlglH0aeKKEnetANBD4zECAFQHcKrEXaFKqb+UUulKqW/dfFJJREREREREJvN2OWs4gEAAx0rcfgxAfY3H+DeAagAWuNy2G8CdAIYAGA4gB8AGpVQzTwdRSoUopWo4GooKUyIiIiIiIjJQeb88p+QaWOXmtosopYYDmAjgOhH523kwkU0ANrn02wAgCcCjAEZ7ONwEAC94FTURERERERH9I95+EnkCQCEu/tSxLi7+dPICxRfk+RDATSKyqrS+ImIHsAWAx08iAbwKoKZL8+9vgiYiIiIiIrIAr4pIEckDsBVAbIm7YgFs9PS44k8g5wK4VUSWlfVzlFIKQAcAR0qJJVdEzjgagLNlJkBERERERET/SHmWs04DME8p9SuARAD3AWgM4D0AUEq9CqCBiIws/vdwAB8DeAzAJqWU41PMbBHJLO7zAoqWs+4FUANFS1g7AHi4fGkRERERERGREbwuIkVkvlKqNoDnUfR9jjsBxInIX8VdIlBUVDrcX/xz3i1uDh+h6GI6ABAG4H8oWiabCWAbgN4i8ou38REREREREZFxvP6eSKvi90QSERERERGVj2HfE0lERERERESXNhaRREREREREpBmLSCIiIiIiItKMRSQRERERERFpxiKSiIiIiIiINGMRSURERERERJqxiCQiIiIiIiLNWEQSERERERGRZiwiiYiIiIiISDMWkURERERERKQZi0giIiIiIiLSjEUkERERERERacYikoiIiIiIiDRjEekD2dnZZofgUzk5OWaH4DO5ubmw2+1mh+Ezl9JzWUQuqedydnY2RMTsMHzmUnou5+XloaCgwOwwfOZSGlvg0so3JyeH5yk/VVBQgPz8fLPD8Bl/GFsWkT6QnJyMli1bYuzYsVi3bp3fT+ZPPfUUBgwYgLfffhv79+83OxxD5ebmom3btrjnnnuwePFinDt3zuyQDPX111/jmmuuwYsvvoikpCS/nsyVUrjxxhtxww03YPbs2Th27JjZIRkqPT0dLVq0wGOPPYZVq1YhLy/P7JAM9dprr+Haa6/F1KlTkZqaanY4houKisKIESOwYMECZGZmmh2OodauXYt27drhmWeewaZNm/z+jb77778fCQkJeO+995Cenm52OIbKyMhAy5Yt8eCDD2L58uV+/0bf+++/jx49euDVV1/Fzp07/XrODQgIQP/+/XHLLbfgk08+wcmTJ80OyVB+URuIiF80ADUASGZmplhRXFycABAAUqtWLbntttvk888/l9OnT5sdmu7++usvqVSpkjPf1q1by/jx42XDhg1SUFBgdni6mzRpkjPXkJAQGTx4sMyYMUMOHDhgdmi6y8/Pl+bNmzvzvfzyy+W+++6TpUuXyvnz580OT3dr1qxx5qqUkqioKHnllVdkx44dYrfbzQ5PdyNHjnTmW6NGDbnxxhvlo48+kuPHj5sdmu5OnDgh1atXd+bbrFkzeeKJJ2TNmjWSl5dndni6mzVrljPXoKAg6devn0yfPl327dtndmi6s9vt0rVrV2e+devWlbvuuku++uorOXv2rNnh6e63335z5gpAOnbsKM8//7xs2bJFCgsLzQ5Pd0888YQz16pVq8p1110nH3zwgRw5csTs0HR3/vx5qV+/vjPfK6+8Uh555BH54YcfJCcnx+zwdPfVV185cw0ICJBevXrJ66+/LikpKX4551qxNsjMzHTEVEPKqr3K6lBRmpWLyMOHD8v7779/wUnedTLv06ePTJs2Tfbu3Wt2qLrYuXOnxMfHu803PDxcRo4cKQsXLrTkWHkrMzNT1q1bJyEhIW7zbd++vTz77LOyefNmv5jM09LS5JlnnnGba5UqVcRms8n//vc/OXTokNmh/mP5+fmyfft2adWqldt8GzduLA899JB89913fjGZHzt2TBYuXOg214CAAImOjpb//Oc/smvXLr+YzFNSUuTWW291m29YWJgMHz5cPvvsMzl16pTZof5jWVlZ8ssvv0hYWJjbfCMjI2XcuHGyfv16v3ij78CBA/LGG2+4zTU4OFgGDhwo77zzjuzfv9/sUHWxfft2iY6OdptvRESEjBo1SpYsWSLnzp0zO9R/7OTJk/L9999LQECA23y7dOkiL730kmzbts0vzlN79+6Vhx9+2G2uoaGhMmzYMJk7d678/fffZof6j+Xk5EhSUpI0bNjQbb5NmzaVxx9/XH788Ue/eKPPqrUBi0iLGT9+vNsnibvWsmVLefLJJ+Wnn36S/Px8s0Mvlzp16mjKtVKlShIbGytvvfWWpKWlmR12uSxdulTz2NavX1/uueceWbRokWRlZZkderkMHTpUc76dO3eWiRMnytatWyvkZH7q1CnNuVarVk2GDh0qs2fPlmPHjpkderlMmTJFc75XXXWVjB49WlauXCm5ublmh14ukZGRmnINDAyUmJgYmTJliuzZs8fssMslMTFR89jWrl1bRowYIfPnz5eMjAyzQy+XUaNGac63Xbt28vTTT0tiYmKFfaPPU0FVslWuXFni4+Plvffek/T0dLPDLpc5c+ZoHtuGDRvKAw88IMuWLZPs7GyzQy+XXr16acpVKSXdu3eXyZMnS3JycoWcc1NTUzWPbc2aNeXmm2+WefPmyYkTJ8wOvVysWhuwiLQYb54ojtaqVSt5/fXXK+QnHFqLSEdzvDO8du1as0P3mjdFpKNFRETI6NGjK+Q7h94UkY7WtWtXmT17doX7Bc2bItLRQkND5cYbb5SdO3eaHb7XvCkiHe3qq6+WiRMnVshPOLQWkY4WFBQkffv2lWXLlpkdute8KSIdLTw8XO699145ePCg2eF7zZsi0tE6dOgg7777boV881ZrEeloVapUkSFDhsgvv/xiduhe86aIdLTGjRvLU089VSHfFNFaRDpaQECA9OzZU+bPn1/hCklvikhHCwsLkxEjRlTIZflWrQ28KSKDQIZr3LgxOnXqhKSkJI99KlWqhJiYGCQkJMBms+Gqq67yYYT6uuaaa5CcnFzqBv+6desiPj4eNpsNsbGxCA0N9WGE+gkLC0O3bt2QlJRU6oVIOnXqBJvNhoSEBHTq1AkBARXzmlbNmzdHZGQkUlJSPPapWrUqYmNjYbPZEB8fj/r16/swQv0EBgaiW7du2Lt3b6kb/K+88krYbDbYbDb07t0bISEhPoxSPxEREejatSt++eUXj30CAgLQs2dP53mqRYsWUEr5MEr9tG/fHtnZ2aVe/KtWrVqIi4uDzWbDwIEDERYW5rP49BQaGopu3brht99+w/nz5z32a9OmjfM8FRUVhcDAQB9GqZ+rrroKbdu2RXJyssc+ISEh6NevHxISEpCQkIBGjRr5MEJ9devWDX/88UepF/9q0KCB83Xbt29fVKlSxYcR6qdOnTqIiorCli1bPF4wSSmFqKgo53O5bdu2FfY81bp1axw5cgT79u3z2Kd69eoYNGgQbDYbBg8ejPDwcB9GqJ/KlSujW7duSElJKfXiX82bN3fOuT169EClSpV8GKV+/KI2KKvKrCgNFv4kUkRkxowZF72j4Fg2tGDBggr5DpkndrtdrrnmmovybdeunTzzzDOyadOmCvepVGm2bdt2Ua7+sGzIk8cee+yifBs2bCgPPvigLF++vMIuG3InKytL6tate0GuSinp0aNHhV425MmCBQsuGlvHsqFPPvlETp48aXaIuho4cOBF+bZs2VLGjh0r69atq5CfSnmSlpYmQUFBF+TquqXgzz//NDtEXb300ksXjW29evXknnvukcWLF1fYLQXu5OfnS9OmTS/K95prrqnQWwo8Wb169UW5um4pOHr0qNkh6uq22267KN+rrrpKHnvsMVm1alWF3VLgzvHjxyU0NPSCXAMDA+Xaa6+t0FsKPLFibcDlrBaTk5Pj3CjcqlUreeqpp/zmAgbufPvttwL45wUM3HEs8YyIiJB7771Xvvnmmwq5vE+Lw4cPS+XKlQXwvwsYuONY4ulvFzBwp7CwUFq3bi1A0TLVMWPG+M0FDNzZuHGjAP55cTN37r33XgGKlqnecccd8uWXX1pyvtRDRkaG8yJCHTp0kOeee85vLm7mzty5c53LVP3p4mbu2O126d27t3OZ6sMPPyzff/+9X7156SolJUUCAgL88uJm7kyYMMG5TNWfLm7mjlVrAy5ntZjt27fjySefREJCApo2bWp2OIb766+/8PXXX1foZapanThxAu3atcPTTz9doZepavXrr7/inXfeqdDLVLUSEeTk5OCHH35ATExMhV2mqlVKSgruuOOOCr9MVavdu3fjiy++qNDLVLU6d+4cIiIisGHDhgq9TFWrrVu3YvLkyRV+mapWx48fx9KlS9GvX78Ku0xVqwMHDji/h7oiL1PVaseOHZg7d26FXqaqVX5+PkJCQrBmzRpER0dX2GWqWvlDbaCk6FO8Ck8pVQNAZmZmJmrUqGF2OERERERERBXGmTNnULNmTQCoKSJnSuvr3x+bEBERERERka5YRBIREREREZFmLCKJiIiIiIhIMxaRREREREREpBmLSCIiIiIiItKMRSQRERERERFpxiKSiIiIiIiINGMRSURERERERJqxiCQiIiIiIiLNWEQSERERERGRZiwiiYiIiIiISDMWkURERERERKQZi0giIiIiIiLSjEUkERERERERacYikoiIiIiIiDRjEUlERERERESasYgkIiIiIiIizVhEEhERERERkWYsIomIiIiIiEgzFpFERERERESkGYtIIiIiIiIi0oxFJBEREREREWnGIpKIiIiIiIg0YxFJREREREREmrGIJCIiIiIiIs1YRBIREREREZFmLCKJiIiIiIhIs3IVkUqph5RSaUqpHKXUVqVUrzL6xxT3y1FK/amUesBNn2FKqd+VUrnFfw4tT2xERERERERkHK+LSKXUzQCmA5gEoCOA9QC+U0o19tC/CYDlxf06ApgM4C2l1DCXPt0BzAcwD0D74j8XKKWivI2PiIiIiIiIjKNExLsHKLUZQJKIPOhyWwqAxSIywU3/1wAMEZFIl9veA9BeRLoX/3s+gBoiMtilz/cATovIcI1x1QCQmZmZiRo1aniVk5GSk5OxZ88etGnTBi1btjQ7HMMtXboUubm5sNlsCAkJMTscQx05cgQbNmxAREQEoqOjzQ7HcImJiTh06BC6d++OBg0amB2OofLy8rB06VJUqlQJQ4YMMTscw6WmpuK3335D8+bN0a5dO7PDMdwPP/yAs2fPYsCAAZaaL4xw8uRJrFmzBrVr10afPn3MDsdwW7duRVpaGjp37owmTZqYHY6hRASLFy+GiOD6669HQIB/71Dav38/fv31V1xxxRXo0qWL2eEYbu3atThx4gRiYmJQp04ds8MxVFZWFr7//nuEhoZi0KBBZodjOCvXBmfOnEHNmjUBoKaInCm1s4hobgCCARQAGFri9v8C+MnDY9YB+G+J24YCyAdQqfjfBwCMKdFnDIC/SoklBEANl9YAgGRmZopVnD9/Xho1aiQApGXLlpKXl2d2SIZasmSJABAAMmnSJLPDMdyQIUMEgFSuXFnS0tLMDsdQBw4ckKpVqwoAiYuLMzscw7322mvO5/KXX35pdjiGKigokNatWwsAadCggWRlZZkdkqHWr1/vHNsxY8aYHY7h7r77bgEggYGBsmPHDrPDMdTJkyflsssuEwDSrVs3sdvtZodkqA8//ND5XJ41a5bZ4RiuZ8+eAkDCwsLk+PHjZodjqJ07d0pQUJAAkJEjR5odjuHGjRvnfC6vXbvW7HAMZfXaIDMz0zEWNaSMutDbt63CAQQCOFbi9mMA6nt4TH0P/YOKj1daH0/HBIAJADJdWnppgZth7969SE9Pd/794MGDJkdkrDVr1rj9uz/Kzc3Fxo0bAQA5OTlITEw0OSJjbd68GefPnwcAbNq0CdnZ2SZHZKxL6bl86NAhpKamOv++Z88ekyMy1tq1a51/9/exBf4/38LCQqxbt87cYAz222+/4dSpUwCAHTt24OTJkyZHZCzX5+/q1atNjMR4p0+fxrZt2wAAGRkZzr/7q/Xr16OgoABA0WtYvFw1WNFcSnOuX9UGZVWZcuGnf5ejqDrtXuL2ZwDs9vCYVAATStwWXXyc+sX/zgMwvESf2wDklBKL5T+JFBF59NFHJTIyUiZMmGB2KIY7fvy4dOjQQSIjI+XXX381OxzDzZkzRyIjIyUuLk4KCwvNDsdQdrtdhgwZIpGRkfL++++bHY7htm/fLq1atZL27dvL0aNHzQ7HcM8//7xERkbKgw8+aHYohjt79qxERUVJZGSkrFy50uxwDLdo0SKJjIyUmJgYyc3NNTscw40YMUIiIyPl9ddfNzsUw6WlpUmbNm2kdevWsnfvXrPDMdy0adMkMjJShg8fbnYohsvLy5M+ffpIZGSkLFy40OxwDLd27VqJjIyULl26yJkzZ8wOx3BWrg28+STSqz2RSqlgAOcB3Cgii1xu/y+ADiIS4+Yx6wBsE5HHXG4bCmABgKoikq+UOgDgTRF506XPGACPi8gVGmOz5J5IIiIiIiIiq/NmT6RXy1lFJA/AVgCxJe6KBbDRw8MS3fQfAOBXEckvo4+nYxIREREREZEJgsrxmGkA5imlfkVR8XcfgMYA3gMApdSrABqIyMji/u8BeEQpNQ3A+wC6A7gHgOtVV/8LYJ1S6ikASwBcB6A/gJ7liI+IiIiIiIgM4nURKSLzlVK1ATwPIALATgBxIvJXcZcIFBWVjv5pSqk4AG8CeBjAYQCjReQrlz4blVK3AHgFwMsA/gBws4hsLl9aREREREREZASvvyfSqrgnkoiIiIiIqHwM2xNJRERERERElzYWkURERERERKQZi0giIiIiIiLSjEUkERERERERacYikoiIiIiIiDRjEUlERERERESasYgkIiIiIiIizVhEEhERERERkWYsIomIiIiIiEgzFpFERERERESkGYtIIiIiIiIi0oxFJBEREREREWnGIpKIiIiIiIg0YxFJREREREREmrGIJCIiIiIiIs1YRBIREREREZFmQWYHoLczZ86YHQIREREREVGF4k0dpUTEwFB8RynVAEC62XEQERERERFVYA1F5FBpHfypiFQALgdw1uxYSqiOouK2IawX26WI42EdHAtr4XhYB8fCOjgW1sLxsA6OhXXoPRbVARyWMopEv1nOWpxoqRWzGYpqWwDAWRHhWluTcTysg2NhLRwP6+BYWAfHwlo4HtbBsbAOA8ZC0zF4YR0iIiIiIiLSjEUkERERERERacYi0ni5AF4s/pPMx/GwDo6FtXA8rINjYR0cC2vheFgHx8I6TBkLv7mwDhERERERERmPn0QSERERERGRZiwiiYiIiIiISDMWkURERERERKQZi0giIiIiIiLSjEVkOSilHlJKpSmlcpRSW5VSvcroH1PcL0cp9adS6gE3fYYppX5XSuUW/znUuAz8hzdjoZS6QSm1Uil1XCl1RimVqJQaWKLPnUopcdMqG59NxefleFzr4f+6ZYl+fG2Ug5djMdfDWOxy6cPXRjkopXorpZYqpQ4X/39dr+ExnDMM4O1YcM4wVjnGg3OGQcoxFpwzDKKUmqCU2qKUOquU+lsptVgp1ULD43w+b7CI9JJS6mYA0wFMAtARwHoA3ymlGnvo3wTA8uJ+HQFMBvCWUmqYS5/uAOYDmAegffGfC5RSUcZlUvF5OxYAegNYCSAOQGcAawAsVUp1LNHvDIAI1yYiObon4GfKMR4OLXDh//del2PytVEO5RiLx3DhGDQCcArAwhL9+NrwXjUAOwA8oqUz5wxDeTUW4JxhNG/Hw4Fzhv68HQvOGcaJAfAugG4AYgEEAVihlKrm6QGmzRsiwuZFA7AZwMwSt6UAeNVD/9cApJS47T0AiS7/ng/guxJ9vgfwudn5Wrl5OxYejrELwPMu/74TQIbZuVXEVo7XxrUABEBYKcfka8MHY+Hm8dcDsAO4wuU2vjb++bgIgOvL6MM5wyJj4eFxnDNMGg/OGdYZCzeP4Zxh3HjUKR6T3qX0MWXe4CeRXlBKBaPo3cgVJe5aAaCHh4d1d9P/BwDXKKUqldHH0zEveeUci5LHCABQHUXvnrkKVUr9pZRKV0p96+ZdZyrhH47HNqXUEaXUj0qpPiXu42vDS3q8NgDcA2CViPxV4na+NozHOcOiOGdYBucM6+GcYZyaxX+WPO+4MmXeYBHpnXAAgQCOlbj9GID6Hh5T30P/oOLjldbH0zGpfGNR0r9RtIRjgcttu1H07tkQAMMB5ADYoJRq9k+CvQSUZzyOALgPwDAANwDYA+BHpVRvlz58bXjvH702lFIRAAYD+KDEXXxt+AbnDOvinGEuzhkWxDnDOEopBWAagJ9FZGcpXU2ZN4LK+8BLnJT4t3JzW1n9S97u7TGpSLn+35RSwwFMBHCdiPztPJjIJgCbXPptAJAE4FEAo3WI199pHg8R2YOiXwIcEpVSjQA8CWBdeY5JFyjv/9udADIALL7gYHxt+BLnDIvhnGE+zhmWdSc4ZxjlHQDtAPTU0Nfn8wY/ifTOCQCFuLhqr4uLq3uHox76FwA4WUYfT8ek8o0FAOdFRz4EcJOIrCqtr4jYAWwBwHfOSlfu8ShhEy78v+Zrw3v/5LWhANwNYJ6I5JXWl68Nw3DOsBjOGZbGOcNEnDOMo5R6G0Wf4vYRkfQyupsyb7CI9ELxC2Qriq6W5CoWwEYPD0t0038AgF9FJL+MPp6Oeckr51g43k2eC+BWEVlW1s8pPkF2QNEyGvKgvOPhRkdc+H/N14aX/uFYxAC4GkW/MJeKrw3DcM6wEM4Zlsc5w1ycM3SmiryDoiXbfUUkTcPDzJk3zL7qUEVrAG4GkIeid14iAbwJIAvFV6QC8CqAj136NwFwDkVrmiOLH5cHYJhLnx4oerfgKQAti//MBxBldr5WbuUYi+HF/68PoejdGEer6dLnBQADAVyFopPd7OLHdDU7X6u3cozH4yi6olszAK2L7xcAN7j04WvDB2Ph8rh5ADZ5OCZfG+Ubi9Di/68Oxc/vMcV/b+xuLDhnWGosOGdYazw4Z1hkLFwexzlD/7GYgaLlwTElzjtVXPpYYt4w/T+rIrbiCWU/gFwUvePf2+W+uQDWlugfg6J14LkA0gA84OaY/0LRJuQ8FF2K/wYjc/CX5s1YAFhbfHIs2ea69HkTwF/Fx/sbRVeu6m52nhWleTke4wDsA5CNoquOrQcQ5+aYfG0YPBbFt9UEcB7AvR6Ox9dG+cbh2tLOO5wzrDsWnDMsNx6cMywyFsW3cc4wZizcjYMAuNOljyXmDVV8UCIiIiIiIqIycU8kERERERERacYikoiIiIiIiDRjEUlERERERESasYgkIiIiIiIizVhEEhERERERkWYsIomIiIiIiEgzFpFERERERESkGYtIIiIiIiIi0oxFJBEREREREWnGIpKIiIiIiIg0YxFJREREREREmrGIJCIiIiIiIs3+D4AEnJolmZBOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1100x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (11,7), dpi=100)\n",
    "plt.quiver(X[::3, ::3], Y[::3, ::3], u[::3, ::3], v[::3, ::3]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3b44812",
   "metadata": {},
   "source": [
    "The structures in the `quiver` command that look like `[::3, ::3]` are useful when dealing with large amounts of data that you want to visualize.  The one used above tells `matplotlib` to only plot every 3rd data point.  If we leave it out, you can see that the results can appear a little crowded.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d56293ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1100x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (11,7), dpi=100)\n",
    "plt.quiver(X, Y, u, v);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e3fc881c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u_ana = -dpdx / (2*mu) * y * (y - H)\n",
    "\n",
    "# Plotting\n",
    "plt.figure(figsize=(10,8))\n",
    "\n",
    "plt.plot(u_ana, y, 'o', label='Analytical') # \n",
    "plt.plot(u[:,int(nx/2)], y, label='CFD') # \n",
    "plt.xlabel('u-velocity')\n",
    "plt.ylabel('y')\n",
    "#plt.title('u-velocity for different y and Re')\n",
    "plt.legend()\n",
    "plt.gca().invert_yaxis()  # To invert y-axis\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ec46fb9",
   "metadata": {},
   "source": [
    "##### What is the meaning of the $F$ term? \n",
    "\n",
    "Step 12 is an exercise demonstrating the problem of flow in a channel or pipe. If you recall from your fluid mechanics class, a specified pressure gradient is what drives Poisseulle flow. \n",
    "\n",
    "Recall the $x$-momentum equation:\n",
    "\n",
    "$$\\frac{\\partial u}{\\partial t}+u \\cdot \\nabla u = -\\frac{1}{\\rho}\\frac{\\partial p}{\\partial x}+\\nu \\nabla^2 u$$\n",
    "\n",
    "What we actually do in Step 12 is split the pressure into steady and unsteady components $p=P+p'$. The applied steady pressure gradient is the constant $ -\\frac{1}{\\rho}\\frac{\\partial p}{\\partial x}=F$ (interpreted as a source term), and the unsteady component is $\\frac{\\partial p'}{\\partial x}$. So the pressure that we solve for in Step 12 is actually $p'$, which for a steady flow is in fact equal to zero everywhere.\n",
    "\n",
    "<b>Why did we do this?</b>\n",
    "\n",
    "Note that we use periodic boundary conditions for this flow. For a flow with a constant pressure gradient, the value of pressure on the left edge of the domain must be different from the pressure at the right edge. So we cannot apply periodic boundary conditions on the pressure directly. It is easier to fix the gradient and then solve for the perturbations in pressure.\n",
    "\n",
    "<b>Shouldn't we always expect a uniform/constant $p'$ then?</b>\n",
    "\n",
    "That's true only in the case of steady laminar flows. At high Reynolds numbers, flows in channels can become turbulent, and we will see unsteady fluctuations in the pressure, which will result in non-zero values for $p'$. \n",
    "\n",
    "In step 12, note that the pressure field itself is not constant, but it's the pressure perturbation field that is. The pressure field varies linearly along the channel with slope equal to the pressure gradient. Also, for incompressible flows, the absolute value of the pressure is inconsequential.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bb091a1",
   "metadata": {},
   "source": [
    "### Try to use Chorin's projection method to solve this problem:\n",
    "\n",
    "Solution strategy:   (Projection Method: Chorin's Splitting)\n",
    "\n",
    "https://www.youtube.com/watch?v=BQLvNLgMTQE&t=106s\n",
    "\n",
    "1. Solve Momentum equation without pressure gradient for tentative velocity\n",
    "   (with given Boundary Conditions)\n",
    "\n",
    "$$\\frac{\\partial \\vec{v}^*}{\\partial t}+(\\vec{v}^*\\cdot\\nabla)\\vec{v}^*= \\nu \\nabla^2\\vec{v}^* + \\vec{F} $$\n",
    "\n",
    "2. Solve pressure poisson equation for pressure at next point in time\n",
    "   (with homogeneous Neumann Boundary Conditions everywhere except for\n",
    "   the top, where it is homogeneous Dirichlet)\n",
    "\n",
    "$$\\frac{\\partial^2 p}{\\partial x^2}+\\frac{\\partial^2 p}{\\partial y^2} = \\rho\\left(\\frac{\\partial}{\\partial t}\\left(\\frac{\\partial u^*}{\\partial x} +\\frac{\\partial v^*}{\\partial y} \\right)  \\right)$$\n",
    "\n",
    "3. Correct the velocities (and again enforce the Velocity Boundary Conditions)\n",
    "\n",
    "$$u = u^* - \\frac{\\Delta t}{\\rho} \\frac{\\partial p}{\\partial x} $$\n",
    "$$v = v^* - \\frac{\\Delta t}{\\rho} \\frac{\\partial p}{\\partial y} $$\n"
   ]
  }
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