{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian Process (GP) smoothing\n",
    "\n",
    "This example deals with the case when we want to **smooth** the observed data points $(x_i, y_i)$ of some 1-dimensional function $y=f(x)$, by finding the new values $(x_i, y'_i)$ such that the new data is more \"smooth\" (see more on the definition of smoothness through allocation of variance in the model description below) when moving along the $x$ axis. \n",
    "\n",
    "It is important to note that we are **not** dealing with the problem of interpolating the function $y=f(x)$ at the unknown values of $x$. Such problem would be called \"regression\" not \"smoothing\", and will be considered in other examples.\n",
    "\n",
    "If we assume the functional dependency between $x$ and $y$ is **linear** then, by making the independence and normality assumptions about the noise, we can infer a straight line that approximates the dependency between the variables, i.e. perform a linear regression. We can also fit more complex functional dependencies (like quadratic, cubic, etc), if we know the functional form of the dependency in advance.\n",
    "\n",
    "However, the **functional form** of $y=f(x)$ is **not always known in advance**, and it might be hard to choose which one to fit, given the data. For example, you wouldn't necessarily know which function to use, given the following observed data. Assume you haven't seen the formula that generated it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "figsize(12, 6);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MWly+vkHto5S1pmpl1nS81aMY2w9TTU30mKpOF2P7Yap2uxlDE0F4AuGiPScR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\n9vJb/gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a48e898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "\n",
    "x = np.linspace(0, 50, 100)\n",
    "y = (np.exp(1.0 + np.power(x, 0.5) - np.exp(x/15.0)) + \n",
    "     np.random.normal(scale=1.0, size=x.shape))\n",
    "\n",
    "plot(x, y);\n",
    "xlabel(\"x\");\n",
    "ylabel(\"y\");\n",
    "title(\"Observed Data\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's try a linear regression first\n",
    "\n",
    "As humans, we see that there is a non-linear dependency with some noise, and we would like to capture that dependency. If we perform a linear regression, we see that the \"smoothed\" data is less than satisfactory:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ONtbCiysKe/W+pV/toLHZz+F5e7Z4BOV4k9iyo57G5tBsWgwqKKkhNsrFXh1M8ghKT47D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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e2fe630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x, y);\n",
    "xlabel(\"x\");\n",
    "ylabel(\"y\");\n",
    "\n",
    "lin = stats.linregress(x, y)\n",
    "plot(x, lin.intercept + lin.slope * x);\n",
    "title(\"Linear Smoothing\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Linear regression model recap\n",
    "\n",
    "The linear regression assumes there is a linear dependency between the input $x$ and output $y$, sprinkled with some noise around it so that for each observed data point we have:\n",
    "\n",
    "$$ y_i = a + b\\, x_i + \\epsilon_i $$\n",
    "\n",
    "where the observation errors at each data point satisfy:\n",
    "\n",
    "$$ \\epsilon_i \\sim N(0, \\sigma^2) $$\n",
    "\n",
    "with the same $\\sigma$, and the errors are independent:\n",
    "\n",
    "$$ cov(\\epsilon_i, \\epsilon_j) = 0 \\: \\text{ for } i \\neq j $$\n",
    "\n",
    "The parameters of this model are $a$, $b$, and $\\sigma$. It turns out that, under these assumptions, the maximum likelihood estimates of $a$ and $b$ don't depend on $\\sigma$. Then $\\sigma$ can be estimated separately, after finding the most likely values for $a$ and $b$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian Process smoothing model\n",
    "\n",
    "This model allows departure from the linear dependency by assuming that the dependency between $x$ and $y$ is a Brownian motion over the domain of $x$. This doesn't go as far as assuming a particular functional dependency between the variables. Instead, by **controlling the standard deviation of the unobserved Brownian motion** we can achieve different levels of smoothness of the recovered functional dependency at the original data points. \n",
    "\n",
    "The particular model we are going to discuss assumes that the observed data points are **evenly spaced** across the domain of $x$, and therefore can be indexed by $i=1,\\dots,N$ without the loss of generality. The model is described as follows:\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "z_i & \\sim \\mathcal{N}(z_{i-1} + \\mu, (1 - \\alpha)\\cdot\\sigma^2) \\: \\text{ for } i=2,\\dots,N \\\\\n",
    "z_1 & \\sim ImproperFlat(-\\infty,\\infty) \\\\\n",
    "y_i & \\sim \\mathcal{N}(z_i, \\alpha\\cdot\\sigma^2)\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "\n",
    "where $z$ is the hidden Brownian motion, $y$ is the observed data, and the total variance $\\sigma^2$ of each ovservation is split between the hidden Brownian motion and the noise in proportions of $1 - \\alpha$ and $\\alpha$ respectively, with parameter $0 < \\alpha < 1$ specifying the degree of smoothing.\n",
    "\n",
    "When we estimate the maximum likelihood values of the hidden process $z_i$ at each of the data points, $i=1,\\dots,N$, these values provide an approximation of the functional dependency $y=f(x)$ as $\\mathrm{E}\\,[f(x_i)] = z_i$ at the original data points $x_i$ only. Therefore, again, the method is called smoothing and not regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's describe the above GP-smoothing model in PyMC3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pymc3 as pm\n",
    "from theano import shared\n",
    "from pymc3.distributions.timeseries import GaussianRandomWalk\n",
    "from scipy import optimize"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create a model with a shared parameter for specifying different levels of smoothing. We use very wide priors for the \"mu\" and \"tau\" parameters of the hidden Brownian motion, which you can adjust according to your application."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "LARGE_NUMBER = 1e5\n",
    "\n",
    "model = pm.Model()\n",
    "with model:\n",
    "    smoothing_param = shared(0.9)\n",
    "    mu = pm.Normal(\"mu\", sd=LARGE_NUMBER)\n",
    "    tau = pm.Exponential(\"tau\", 1.0/LARGE_NUMBER)\n",
    "    z = GaussianRandomWalk(\"z\",\n",
    "                           mu=mu,\n",
    "                           tau=tau / (1.0 - smoothing_param), \n",
    "                           shape=y.shape)\n",
    "    obs = pm.Normal(\"obs\", \n",
    "                    mu=z, \n",
    "                    tau=tau / smoothing_param, \n",
    "                    observed=y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's also make a helper function for inferring the most likely values of $z$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def infer_z(smoothing):\n",
    "    with model:\n",
    "        smoothing_param.set_value(smoothing)\n",
    "        res = pm.find_MAP(vars=[z], fmin=optimize.fmin_l_bfgs_b)\n",
    "        return res['z']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please note that in this example, we are only looking at the MAP estimate of the unobserved variables. We are not really interested in inferring the posterior distributions. Instead, we have a control parameter $\\alpha$ which lets us allocate the variance between the hidden Brownian motion and the noise. Other goals and/or different models may require sampling to obtain the posterior distributions, but for our goal a MAP estimate will suffice.\n",
    "\n",
    "### Exploring different levels of smoothing\n",
    "\n",
    "Let's try to allocate 50% variance to the noise, and see if the result matches our expectations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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sIiKDllKK9Ju6vSVMLPsPS90f58S5R8d7OgNartuF02HCK8UAJ94c/nnaJwCo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\nKKqzkhYVqryKdljgnwsgfgJxs58FlKzf0fHhPZylZwIjnsc0boJ1Nys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/GuPqpLsi9DHi7M5/rmajbvPoFzXgmFH/tIKygWERHJUW9aUkkoL5BVXR6q46UcfstCTuSqRRX0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\n/wOitThxmlZbJwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x121f54390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "smoothing = 0.5\n",
    "z_val = infer_z(smoothing)\n",
    "\n",
    "plot(x, y);\n",
    "plot(x, z_val);\n",
    "title(\"Smoothing={}\".format(smoothing));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It appears that the variance is split evenly between the noise and the hidden process, as expected. \n",
    "\n",
    "Let's try gradually increasing the smoothness parameter to see if we can obtain smoother data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SyxrSclITuiyf6PU0uy5My3aytaIeb3NLl++vN3n8pPlyfN9eB6ffBrW74d6T\nu+xS0Z28jCR27G3o9hkiIiJDWbjKJ6KBBGNMNJAI7AnTfWWYeu7jPcyhkM+W/BsOPRdmnRPpJQ15\nOd1MtevTNLsOpma5aPZbtlZ0vZNbXNNIWmIM8UkpcNjFcPmrEOeC+xbBhhd69Iy8TCctfsuOyoY+\nr1NERCRS+h2KrbW7gT8DO4BioMZa+0rH64wxXzfGrDDGrCgvL+/vY2WIe331Jv6R+E9Myjg49c+R\nXs6wEAjFnQd4hKbZ9W+nuE0Hii4EBne06VGcng+XvwZZM+CRC+DDuw/4jFAHik2qKxYRkWEoHOUT\nacAZwGQgF0gyxlzY8Tpr7V3W2nnW2nkZGRn9fawMYUWlbs6r/DsZLWVqv9YLOSkJeJv97K33tXu9\ndXBHP2qKp6Q7iXaYfR0oOiiu6aJHsTMDLnkepn0BXvw+vPIz8Pu7f0ZGEqC2bCIiMjyFo3ziJGCr\ntbbcWtsEPAUcHYb7yjC1bsl/OTf6LRqPuEbt13oht7VXcfu64tCI575MswuJjXYwOT2JjSVdB9Zu\nRzzHJsFXHoT5/wfv/g2evBxaup5alxgbzbjUBB22ExGRYSkcoXgHcKQxJtEEJgucCKwPw31lGLLu\nUo7fcCNbY/JJOvmnkV7OsJLdTa/i/kyza2tqtqvLnWJPUwuV9T5yu+tR7IiCL/4JTv41fPoUvPDd\nblu2TclI0k6xiIgMS+GoKf4AeAJYCXwSvOdd/b2vDEPW4n78WyTYRtYd+WeIjo30ioaVUCjteNiu\nP9Ps2pqW5WLH3gYafM3tXg/tRLerKe7IGFhwXaDP9MoH4L07urwsL8PJ5rK6TnXRIiIiQ11Yuk9Y\na39hrZ1urT3EWnuRtdYbjvvKMLPqPyTveI0/t5zH0UcuiPRqhp10ZxwxUabLneLMftQTh0zNChy2\nKyxtv5Mbel6Pptkt/AnMOANe+SlseLHT23mZTup9LZTUdt1vWUREZKjSRDsJj71bsS/fwEeOQ9g8\n5ULSkrRL3FsOhyErOZ7i6vY7xWW13n7VE4eEOlB0HOJRUhPaKe7BMxwOOPOfkDsHnrwCite0ezs/\n2IFic5nqikVEZHhRKJb+87fA01fit4ZrGr7OaXPHR3pFw1ZOSjx7ujho15/OEyETxyQSH+NoP+6Z\nXu4UA8QmwvmPQEIq/Pc8cJe0vpWXqQ4UIiIyPCkUS/+9cyvsfJ9nc79NZXQmJx2cFekVDVs5KQnt\naorDMc3Xe8S0AAAgAElEQVQuJMphKMjsfNiupKaRlIQYEmN7MYLblR0Ixo3VgWDsCwzsyHDG4YqP\nVq9iEREZdhSKpX/2rIYlN2EPPp2bds3mhOmZuOL71yVhNMtJjae0xovfHzioFo5pdm1NzXJ1GuCx\np6sexT2RMwvOvjvw38AzV4LfjzEmcNhOO8UiIjLMKBRL33lq4PFLICmDD2f+jIp6H6fNzo30qoa1\nnOR4fC1+KoMDPMIxza6tadlOytxeqtoMCOm2R3FPTD810Kpt3bPw4Z0A5GcqFIuIyPCjUCx9Yy08\nezVU74Rz/s3TGz0kxUaxcFpmpFc2rOWkhnoVB0oowjHNrq19HSj27RZ3Oc2uN46+BvJPgjd+AzW7\nyMtwUlrrxe3pesiHiIjIUKRQLH3z4V2w/jk46Rf4cg/npbUlnDwji4TYqEivbFjL7TDAI9RDODMM\n3SegTQeKYCj2NfupqPOSnbyfHsUHYgycenPgwOWLPyCvddyzOlCIiMjwoVAsvbf7I/jfT2DqKXDU\nNSzbVE5NY5NKJ8IgJzTqOdiWrcztJSbKkNbPaXYh2cnxuOKjWztQhEJ3v3aKAdImwWd/BBtfYFbd\n2wBs1mE7EREZRhSKpXcaq+CxSwPdB878BzgcPP9xMcnx0RxbkBHp1Q17YxJjiY1ytO4Ul9V6yHTF\n93uaXYgxhmlZLgpLAoE1NGQjFMb75airIOsQspb9nFRHo+qKRURkWFEolp6zFp65Ctx74Mv/hsQx\neJpaeOXTEr5wSA6x0frPqb8cDkN2m17FZW5vWKbZtTU128XGUjfWWvYEd6T7vVMMEBUDp92KcRfz\nC+fTCsUiIjKsKMVIz713B2x8AU6+ETt+Hi+vLeH025dR72vhjLkqnQiXnJR4SoIH7UprPWGZZtfW\ntCwXNY1NlLm9babZ9aOmuK3x82D+FZzhe4Go4pXhuaeIiMggUCiWntn5Ibz2C+z0RSwd82XOuOMd\nrnzwI5pbLHd89TCOzkuP9ApHjNzUBPZU7ztoF/ad4mAHig0lboprPLjionHG9WJwx4Gc+HPqY9K5\nuu52mpp8B75eRERkCFAolgOrK4fHLsGbmMPXqi7l4n8vp7LOxx/PnsUr3zmOU2flRHqFI0p2Sjyl\ntR4afM3UeprJClOP4pCpWU4ACkvc/etR3J34ZNbO/gkzHNupWfK38N5bRERkgCgUy/75W/A/eTlN\ndRWcVflNPqk0/PK0Gbzx/eM5d/4EoqP0n1C45abE0+y3rNtTC0BGmKbZhYx1xpHujGNjqZviWk9r\nb+RwSpx1Jq+2HEbaB3+Gqu2d3m/xW1qCU/tERESGAiUa2a/GV27EsfUtfuy7lKMWLGTpDz7LpQsm\nExetfsQDJSdY37t6ZzVA2HeKITDZrrDUTUlNIzkDcP8pmU5+3nQZLRh4/lrw+1vf27m3geP/tIQb\nF68L+3NFRET6SqFYurX7g6dJeP+vPO5fyFFnX8dPF80gMTaMtafSpVA5w8e7aoDwTbNra1pWMoWl\nbsrc3vCXTwCu+Bj8ybk8m/lN2PImrLgXCEzqO//u99lV1cizq3fT3OLf/41EREQGiUKxdOmd5Stw\nvngVG5hM/qX/4KzDxkd6SaNGbmpop7gKCN80u7amZTvxNPmxNkzt2LqQl+HkoaYTIO8EePXnVO5Y\nzwV3f0B1QxNXHp9HVUMTK3dUD8izRUREekuhWNqx1nLX6+tIef5yohww5rJHmDtFB+kGU1piDHHR\nDnbubQzrNLu2Qh0ogAHZKQbIz3SyuaIee/pt+B3RFN9/GaU1Dfz7svlctTCPmCjDa+tLB+TZIiIi\nvaVQLK3cniau/u8qXEt+zCGObcR8+R4yD5oe6WWNOsaY1t3icE6za6ugTSjOCVeP4g7yMpy4Pc1s\n8aVyS8z/cUjLehbPX8P8SWNwxcdw5JSxCsUiIjJkKBQLAGt317DotmUkrXuE86OXYI/5HnEzvxjp\nZY1a2cHDb+HuURzijItmfFogDIdlxHMX8jICrd8uuPsD/r73M5SNO4nJH/8FyjYAcNLBWWwpr9fk\nOxERGRIUikc5ay33vbOVs/7+LhN8W/h93H0w+TjMCT+J9NJGtVBQzQxzO7a2pmW5SIqNwhXOwR1t\n5GUmAVDm9nDreYeRef4/IM4Jz1wJLU2ceHAmAK9rt1hERIYAheJRrKaxiW8+uJJfPr+Ok/MSud95\nB46ENDj7XnCo5Vok5QZLGgaiHVvIJUdP4toTCwakPAMCu92nz87llvPmBga8ODPh1L/AnlWw7K+M\nT0vk4JxkXltfNiDPFxER6Q311xrhyt1etlXW42v242v2421uwdvsp97bwt/f3ERJjYeffnE6l5f+\nBrNzK1yyOBBeJKJCh98GMhQfNzWD46ZmDNj9jTH87fy57V+ceSZsOAfe+gNMPYWTDs7kjiWbqKr3\nkZYUO2BrERERORCF4hHuvLveY3N5fZfvjUtN4PErj2JuyRPw6VNw4i9g0oJBXqF0JTdYPhHuaXZD\nwhf+CFvfhmev4qQvPMNtb2xiycYytf0TEZGIUigewZpb/GyrbOCsueP4yvwJxMVEERvlIC7GQWyU\ng6zkeGJLV8P/fgwFn4MF3470kiVoZm4K41ITmDMhNdJLCb/EMfCF38Pjl3Jo8eNkuvJ5fb1CsYiI\nRJZC8QhWUuuhxW+ZP3kMR0wZ2/mCxip4/BJwZsGX7gSHSsyHiqzkeN750QmRXsbAmXEm5J2IY8lv\nOTP/fh5eV463uUXjw0VEJGKUgkawPdUeIFAm0Ym18My3oLYYzrkvsHsnMliMgS/+CZq9fK3+Huq8\nzXywZW+kVyUiIqOYQvEItru6Adg3Nrid926HjS/C526E8fMGeWUiwNg8OPZ7ZO94gRNi1u63NdvO\nvQ0sK6oYxMWJiMhoo1A8gnW7U7xnFbz2K5i+CI64MgIrEwlacB2MmcJNcfezdN0urLWdLtm5t4Ev\n//NdLrz3A94qLI/AIkVEZDRQKB6imlv8/b7HrqpGxiTFkhDbpk7TVw9PXgFJGXD6bYG/xhaJlJh4\nOPVmspt3c1rd46wvdrd7u6zWwwX3fICnyU9eRhLfeXQ1JTWeCC1WRERGMoXiIeij7XuZ9atXWNrP\nXbHd1Y2dd4n/92Oo3Axn3ak6Yhka8k7AM+1Mrop+lhUrV7S+XN3g4+J/fUhFnZf7LpvPnRfNw9PU\nwrWPrArLHxpFRETaUigegjaUuGnwtXDVQyspKnUf+APd2NMxFK9fDB/dF/gr68nH9X+hImESf+rv\naXFEc8jHN4K1NPiauey+5Wwpr+eui+Yxd2Ia+ZlOfnPmIXy4dS+3vl4U6SWLiMgIo1A8BFXW+QCI\ni4nia/cvp7LO2+t7WGvZXdW475BdbTE8dw3kzIaFPwnnckX6LzmHj6ZcxWFNK6n48DG+8Z+P+Hhn\nNX87fw7HFKS3XnbWYeM5d954bl+yibeLVF8sIiLho1A8BFXUeUlJiOHuiz9DWa2XKx/8CG9zS6/u\nUd3QRGNTC+PSEsDvh2euhGYPnH0vRGucrgw9GSdexVr/JOxLP2JV0Q5+f/YsTjkkp9N1vzr9EAoy\nnXz7kdWU1qq+WEREwkOheAiqqPOS7oxl7sQ0bj53Nsu3VXHDU590eTK/O7urG4Fg54n374Atb8Ip\nv4P0ggFatUj/TMtJ45aEbzHWVvFo/mucO29Cl9clxEZxx1cPo8HXwnWPrKLF3/OvCxERke4oFA9B\nFXU+xjrjAFg0K5fvnjyVp1bu5h9vbe7xPXZVBUJxXsuWfe3XDrtkQNYrEg7GGC740pfYPPl8Zu56\nFHZ/1O21BVkubjzzEN7fovpiEREJD4XiIaiizktGMBQDXHNCPmfMyeWPL2/k5bXFPbrHnupGYmhm\n8tJvQ1K62q/JsLBweiYF5/0eXNnw/Lehpbnba7/8mfF8ae44bn+jiOoG3yCuUkRERqKwhGJjTKox\n5gljzAZjzHpjzFHhuO9oVVnnY6xzX92vMYY/nD2Lwyam8u1HV7OlvO6A99hd3cg3Yl8iunIjLLpF\n7ddk+IhPgVN+DyVr4MM793vpyTOy8FsoVu9iERHpp3DtFN8KvGytnQ7MBtaH6b6jjq/ZT01jE+lt\ndooB4mOiuPW8uXia/D3qX+wp38pVjqcCZRPTThmo5YoMjBlnQMHn4Y3fQs2ubi/LcAW+Tir60KFF\nRESkrX6HYmNMMnAccC+AtdZnra3u731Hq8r6wG/uHUMxwPi0BJLjoykqO/BO8aLi23AYEzhcJzLc\nGANf/BNYP7z4g24vC5UZlbsVikVEpH/CsVM8BSgH/m2MWWWMuccYkxSG+45KoR7FbcsnQowxTM1y\nUVR6gFC88WWO8r3HG1mXQurEAVilyCBIOwg++yPY+EJg8EwXQjvFCsUiItJf4QjF0cBhwD+stXOB\neuBHHS8yxnzdGLPCGLOivFxN97tTXtf9TjEETt0Xlrm7b8/ma8D/4vUU+cexNV/dJmSYO+oqyJwJ\nL/0AvJ2nOybFRZMYG6VQLCIi/RaOULwL2GWt/SD4z08QCMntWGvvstbOs9bOy8jICMNjR6bQTnF6\nFzvFAAWZTqobmqio6+a0/bK/4KjZwc+aLyNnbPJALVNkcETFwGm3QO0eWHJTl5dkuOJa/zApIiLS\nV/0OxdbaEmCnMWZa8KUTgXX9ve9oVXGAneKpWS4Aiso675pRUQTv3ErZpNN53z+D3JSEAVunyKCZ\ncDh85lL44E6o2NTp7QxnnHaKRUSk38LVfeIa4CFjzBpgDtD1lo4cUIXbS0JMFElx0V2+X5DlBOhc\nV2wtvPh9iI7n3bzvAARGPIuMBAt/DNHx8MaNnd7KcCkUi4hI/4UlFFtrVwdLI2ZZa8+01laF476j\nUWW9r8tDdiGZrjiS46MpLO2wU/zpU4FRzif8jM2NSTgMZCXHD+xiRQaLMzNQX7zuGdi9st1bKp8Q\nEZFw0ES7Iaaizttt6QQEOlAUZLnat2WrLYaXb4DsWTD/cnZXN5KdHE9MlP71yghy9DWQMAZe/1W7\nlzOccVQ3NOFtbonQwkREZCRQahpiyt3ebg/ZhUzNclJUGuxA4amFh84Bbx2ccQc4othd1ajSCRl5\n4pPhuO8H/kZk85LWl9ODbdkquzt8KiIi0gMKxUNMZb1vvzvFAPmZLqoamqisrYfHLoaydXDuA5Az\nCwiMeM5NVSiWEWje5ZAyIbBbHGxLqAEeIiISDgrFQ4jfb9nbg1A8NcsJWPzPXQtblgRaVhWcBECL\n31JS42GcQrGMRDHx8NkbYM8qWPcsoAEeIiISHgrFQ0h1YxMtfrvfg3YQaMv2negnydz8JBz/Izjs\n4tb3ytwemv1W5RMycs0+DzKmBzpRtDTvC8U6bCciIv2gUDyEHKhHcUhm0aNcF/0UH435YmAMbht7\nqhsBVD4hI5cjCk78OVRugtUPtv4hUjvFIiLSHwrFQ0hF8Df1/e4UF72KWfwdVsV+hj/HfguMaff2\nrqpAKB6vUCwj2bQvwvjD4c3fE2d9pCbGKBSLiEi/KBQPIRX1gdPzGd3tFJdvhMcugawZPJ1/ExvL\nPZ0u2a2dYhkNjIGTfgnuYvjwLk21ExGRflMoHkJCO8Vdlk80++DJKwIHjb76OAflZrG33tdachGy\np7qR1MSYbifiiYwYkxZA/snw9l+YmNSsmmIREekXheIhpLLeS5TDkJIQ0/nNN2+CkjVw2t8gOYeC\nzK7HPe+ualTnCRk9Ft4AnmoWtbymnWIREekXheIhpMLtY2xSLA5H+zphti2DZbcEukwcvAgIdKAA\nKCprP+55T7VHpRMyeoz7DBx0DCdUP0mVuz4w0EZERKQPFIqHkIo6L2M7lk40VsPTV8KYyfD537W+\nnJUchysumsLSfaHYWsvuau0Uyyhz9DWk+EpZ2PIu9T6NehYRkb5RKB5CKup9nUc8v3g91O6Bs+6G\nOGfry8YYCrKc7conahubqfM2M149imU0Kfgctc4pfD36BcprOx8+FRER6QmF4iGkwu1t33nikyfg\nk8fg+B/C+Hmdri/IdFFUti8Uq/OEjEoOByUzL+cQxza8m96M9GpERGSYUigeIqy1VNZ79/Uort4J\ni78b6MV67Pe6/ExBlpO99T4qg6fuQ6FY5RMy2thDz6XcJjNm9Z2RXoqIiAxTCsVDRL2vBU+TP9CO\nzd8SqCO2LXDWnRDVdXu10GG7wmAJRWianUY8y2iTnprC/c2fJ7N0KZSui/RyRERkGFIoHiL2TbOL\ng9UPwfZlcMrvYcyUbj9TkBWoMd4U7ECxu7qRuGgHY5P2MxFPZARKS4zlv/Zkmhxx8N4dkV6OiIgM\nQwrFQ0RlfSAUZyQAS/8EuYfB3Av3+5ns5PhgB4rATnGoR7HpMPpZZKRzOAzRzrEsTz0V1jwK7pJI\nL0lERIYZheIhotwdGPGcX7wYqnfAZ28IjLLdD2MM+VnO1rZsu6sbdchORq10ZxzPJZwB/mb48K5I\nL0dERIYZheIhorLeSwzNZH18e2AgQcHJPfrc1EwXm4IdKNSjWEazDFccn3rSAwNult8L3roDf0hE\nRCRIoXiIqHD7OCvqbaJrd/ZolzikIMtJZb2P4ppGyt1eHbKTUSvDGRcY9Xz0teCpDtTmi4iI9JBC\n8RBRVVvHtTHPBHaJ80/q8ecKgh0olhaWA+pRLKNXhiuOijov/nHzYcIRgQN3Lc2RXpaIiAwTCsX7\nUe9txlo7KM8qKHmOcZT3apcYoCAz0IHizY2BUKzyCRmtMlxxNPst1Y1Ngd3i6u2w8v5IL0tERIYJ\nheJu1HubOfKm13nu4z0D/7BmHydXPEhRzPRe7RID5KQEOlAsK6oA0IhnGbUyXIFpkOVuL0w/FSYf\nB6/9Sp0oRESkRxSKu1Fc48HtbWZdce3AP+zjh8n0l/FKxmW92iWGfR0o3N5mjIGs5PgBWqTI0BYa\nkV7u9ga+jk79KzR74OUbIrwyEREZDhSKu1ERHJ1cUuMZ2Ac1+2DpzayhgLLMBX26RaiEIssVT2y0\n/pXK6NS6U1wX/JpNz4fjvg+fPgVFr0ZwZSIiMhwoQXWjPDhhrnigQ/Hqh6BmBzf7zmKsq2+7vKFx\nz7mp2iWW0atd+UTIgusgfSq88F3wNURoZSIiMhwoFHdjUHaKm33w9s34sg/jLf8s0oN//dtb+cGd\n4nFpieFcnciw4oyLJj7G0T4UR8fBolsCA3He+kPkFiciIkOeQnE3Qr+xltR4Bq4DxUf3Qc1Ods/5\nDmBId8b26TahnWJ1npDRzBhDhiuufSgGmLQA5l4E794GJWsjszgRERnyFIq7Edop9rX42VvvC/8D\nanbB67+GKQvZlnoEAGP7uFOckxLP1QvzOWNObjhXKDLsZDjjKK/zdn7j5F9DQho8fx34/YO/MBER\nGfIUirvRdrcp7HXF1sLz3wbrh9NupaIuELoz+hiKjTF8//PTODgnOZyrFBl2utwpBkgcA5+/CXav\ngI/+NfgLExGRIU+huBsVdT7GJAXKGcJeV7zmUdj0Kpz4c0g7qDUUj+1j+YSIBHQbigFmnQuTjw/0\nLq4tHtyFiYjIkKdQ3I1yt5dDxqUAUFIbxlBcVwYv/ygwhvbwrwNQWeclISaKpLjo8D1HZBTKcMZT\n1dCEr7mLEgljYNFfodkLL10/+IsTEZEhTaG4C36/paLOy8E5LqIcJrw7xS9eD756OP12cAR++Svq\nvKS7tEss0l+htmyV9d3sFo/Ng4U3wPrnYd2zg7gyEREZ6hSKu1DT2ESz35LliifLFRe+muL1z8O6\nZ+D4H0LG1NaXK+t9jE3qWz2xiOwTCsUV7q4Pxzb4mrm88Egaxx4S+ANqY9VgLk9ERIYwheIuhE6v\nZ7jiyEqJp6S2sf83bayCF74H2YcGBgq0fZ7b2+cexSKyT6epdh0sLazg9cK9PJL7A6ivgFd+OpjL\nExGRIUyhuAsV7n2hOCclPjw7xf/7SeA34TPugKiY9s+r8/W5R7GI7BP6OurusN2bG8sA+F9lJiy4\nFlY9CJuXDNr6RERk6FIo7kJopzjdGUd2ckL/B3hsei0wznnBdZAzu91bfr9lb712ikXCIfR11FUo\nttby5sZyANbsqqH5mOthTF6gd7GvflDXKSIiQ0/YQrExJsoYs8oYszhc94yU8g47xQ2+Fmo9zX28\n2UZ44nJInxaoJe6gqsGH36KdYpEwiI+JIjk+ustQvKHETUmth2Py02nwtVC4twVOvw2qt8OSmyKw\n2r776t3vc8/bWyK9DBGRESWcO8XXAevDeL+IKa/zEhvlIDk+muyUeKCPvYpri+HBsyEqFr76KMTE\nd7qksj7Uo1g7xSLhkOHqeqrdkmDpxLdPKgBg1c6qwAjoeV+D9/8Ouz4a1HX2VaOvhXc3V3Lvsq34\n/QM0gl5EZBQKSyg2xowHTgXuCcf9Iq3C7SPDFYcxhpxgKC6u6eVhO08tPPTlwAG7Cx6HMZO7eda+\nUg0R6b/uBni8uaGcmbnJfOagNMYmxbJqR3XgjZN+Bc5seO5qaB6Ake5htrOqAQhM2nx/a2WEVyMi\nMnKEa6f4FuAHQBcd8wOMMV83xqwwxqwoLy8P02MHRnmdt7WcoU87xc0+ePRCKN8A5z4AuXP2+yxQ\n+YRIuGS44juF4prGJj7aUcXCaZkYY5g7MZXVO4OhOD4ZFv0FytbBGzdGYMW9s6OyofXHT6/cHcGV\niIiMLP0OxcaYRUCZtXa/f/dorb3LWjvPWjsvIyOjv48dUOVub2trp0xXPMbQ8w4Ufj88exVsfSsw\noCP/xP1eXhkc8aydYpHwyHB23ileVlRBi9/y2WmB//fMmZDKprI6ahqbAhdM+0KgjOLdv8HKBwZ7\nyb2yfW8gFJ90cCYvrS2h0dcS4RWJiIwM4dgpXgCcbozZBjwCnGCMeTAM942Yirp93SBiox2kO+N6\nvlP8+i/hk8fgxJ/DnPN79KxohyElIeaA14rIgWW44qj3tVDv3Xc4dsnGMlISYpgzIRWAuRPTAPg4\ntFsM8IU/Qt4JsPg7Q7pN2869DbjiorlswWTqvM28ur400ksSERkR+h2KrbU3WGvHW2snAecBb1hr\nL+z3yiKkxW+prNu3UwwEehXX9iAUf3AnvHMrzLscjvluj55XUedlTFIsDofp65JFpI3WqXbB0iS/\nP9CK7bipGURHBf6XN2t8Csawr64YAv3Dz7kP0qfCYxdD2dA8N7xjbwMTxiRy5JSxZCfH88wqlVCI\niISD+hR3EGqR1jYUZyfHU3Kgg3Zrn8S+9EN8+V+EL/4JTM9CbmWdT6UTImHUOtUuWEKxrriWijov\nn526r2zLFR/D1ExXoANFW/Ep8NXHICYBHjoX6soGbd09tb2ynoljEolyGM6Ym8tbheWtfwAQEZG+\nC2sotta+aa1dFM57DrbyLrpBHHCq3eY34KlvsD5mJhdUXYE1Pf9lrajzMlaH7ETCJqPDAI8lGwLB\n9vhp7c8yhA7bdRrMkzoBzn8E6svhv+eBr4Ghwu+37Kxq5KCxiQCcNXc8LX7L8x/vifDKRESGP+0U\ndxDacWm3U5ySgNvT3K5GsdXulfDIhdiMqVzi+Q7Ld3tY1bZO8YDP87X+Ji4i/de6Uxz8Wl6ysYzZ\n41M6/Y3MnAmpVDc0sa2yi9A77jA4+57A1/fTXw8coB0CSt0efM1+JowJhOJp2S5m5CTztEooRET6\nTaG4g652irNTAj8u6VhXXLEp0Is4aSzbTvkP5U0JADzw7rYePctaGzjU51IoFgmXMUmxOEzga7mq\n3seqndUcPy2z03Whw3ardlR1eg+AgxfB538L65+HV38GbXaU67zNXP3wSr7/+McD8nPoTqgdW2in\nGOCsw8axZlcNm8rqBnUtIiIjjUJxB13uFCcHwm67DhS1xfCfLwEGLnqGtbWBaw6fPIYXPynpcnhA\nR3XeZrzNfsYmqXxCJFyiHIaxwbZsS4vKsRYWTuvcBjI/04kzLrr9YbuOjvwWHP51eO92WPYXIND9\n4ey/v8viNcU89/EemloGbxd5R7Ad28Qx+0Lx6bNzcRh4etWuQVuHiMhIpFDcQbnbS3yMg6TYqNbX\n9k21C4bixurA+ObGvXDhEzA2j/XFtUQ7DL8+Yya+Fj+PLt9xwGepR7HIwAj1Kn5zYzljkmKZNT61\n0zVRDsPsCSmdD9u1ZQyc8gc49Bx4/ddse/k2zrzjHYprGrngiIn4mv0Ulrr7tVa/37J4zR6aexCu\nd+xtIMphyE1NaH0tMzmeYwoyeGbVHo19FhHpB4XiDkKDO0yb7hH7pto1Qum6wA5xRSF85UHInQvA\n+uJa8jKcTM9O5tiCdB76YMcBf5ML7UrroJ1IeGW44ih1e3irsJzjp2YQ1U3Lw7kT0lhf7N7/AAyH\nA878B3uyjmfiez/jzOj3eOaqBVx+TGB0+9rdNf1a6/Jte7n64VW81oN+wzv2NpCbGk9MVPv/dX9p\nbi67qxtZvm1vv9YiIjKaKRR3UNFFi7T4mCgmJPiYu+4P8M9joGproJ9p3sLWa9YXuzk4xwXAxUdN\norjGc8Df5Cq0UywyIDJccXy6p5a99b7WKXZdmTsxlRa/Ze2e7oNti9/yu1c2sXD7ZWyMO4SfNt3K\nlKp3mTQ2CWdcNJ/0MxTvrg60e/x0T+0Br91e2dCudCLk8zOzSYyN0oE7EZF+UCjuoNztbd8Nwu+H\nVQ/xHN/mqIon4DOXwDUrA4dwgqrqfZTUejg4JxmAE6ZnMi41gfvf3b7fZ3VVvywi/ZfujMPaQPXD\ncQXdh+LQhLvuDttZa/nuY6u5860tnHNkPvnXPY/JmgmPXYRj53vMzE3mk90HDrP7EyrLWl984Pvs\n3Nt1KE6MjeaUmdm88EkxniaNfRYR6QuF4g4q2k6z27Ma/vU5ePZbVMbmcJ3rr7Dor5A4pt1nQr+Z\nhUJxlMNw4ZEH8d6Wym7rDffW+/jXO1tJS4xhjA7aiYRV6Gt47oRU0vbz9TXWGcfEMYndHrZ7etVu\nniyEY7MAACAASURBVF29h2+fVMBvzjyUmKQ0uPApSJkAD3+Fk9JKWF9c26/DdsXBwUDrDrBTXOdt\nprLex8QxSV2+/6XDxuH2NPP6+qE3cEREZDhQKG6jucXP3oZg+cSWN+GeE6FqG5z5D/497U7eaRjf\n5efWdQjFAF+ZP4HYaAf/ea/zbnGDr5mv3becXVWN3HnRvE71gSLSP6FQ/NkuWrF1NHdiapehuLTW\nwy+f+5R5B6VxzQkF+95ISoeLn4G4ZC7a/D3GNpdTVNr3dmjF1YGd4j01HqobfN1eF2rH1tVOMcDR\neelkuuJ44RMN8hAR6QulsTb21vuwFvLMbnj0YhhbAFcvhzlfJTslkf9n77zj26rv9f8+kqxhW8t7\nO3F24uxAQkjYe7QUaBkdlNsCpb2ldPfetr9729vdQje0tHRTVoEWCmGvsMkOibMT721JtvY6vz+O\njizbkiU78kj8fb9efiVYR0fHToif89HzeZ4+TzDpW5MN7QMU5RuG2CAK8vRcvqyCR7a10O8PxT8f\nikT5zH3b2NXi5JfXreTU2QUjzicQCI6PJRUWivINXLK0PO2xK6ttdPT74xNbUGwT//XoboKRKD+6\netnIRT1rFXzkEXLkIPfqf8K+xvZxX2u7y09uLO2moT11koUax5aYUZyIViOxrMrG4S7PuK9FIBAI\nZjJCFCfQNRCgEBfnbf9P0Bngww+BSQn4VxMoOocXeKDYJ9Qlu0RuWF+LNxjh0a1Kfqgsy3ztkd28\ntL+b71yxlAuXlE3gVyMQzFzmFOez5RvnMbckP+2xgyUeg9PiR7a18uK+Lr584ULqilOco2Qh0lV/\nYIHUxMK3vjTu1rt2l48Nc4uAwXedktEcE8XVKSbFAJU2I21OX8rHBQKBQJAaIYoT6HP1c4/+Toz+\nbrjuAbDVxB8rtyq5oO2uoaI4FIlyqMvN4gTrhMqyKhvLq2385a1GZFnmh0/v55FtLdx+3jyuX1sz\n4niBQDD5LCq3oNdp2BGrZ+9w+fnWE3s4ZZadG9fPGvW5mgUX8BfrLSx2vQovfWfMr+0PRXB4QyyL\n1VCPtmzX2OfBasrBaspJeUyl3cRAIIzLF0p5jEAgEAiSI0SxSjTKrNe+zGrNQXov+BVUrR7y8GBW\n8VBRfLjbTTASHeInTuSG02o50u3htgd28JtXDnP92ho+d+68pMcKBILJR6/TUF9hYXuTI2ab2EUo\nEuXHVy9HkyLfOJGWeR/jgei5sPkO2PngmF5bvckut5pYVG4eVRQ39flSWidUKm3K42JaLBAIBGNH\niGKVl79HTdsmfhC6lryVV454uGx4q12M4ckTw7lkaTmFeXqe2NnGRUvK+L/31w8pBhEIBFPPyho7\nu1pcPPBuMy/t7+arFy1kVlHylIfhLK2y8Y3gDXgqToPH/xOa38n4dVUfc7nVyOJyCwc73SmTLJp6\nPaNaJwAqbMq/U60OIYoFAoFgrAhRDLDjfnj1x2wrvJy/aq8gV68bcUi+QYfZoBvhKW5oH0Cv1VBX\nnPwHqDFHy1cuWsAVKyr42bUrUjZrCQSCqWNljY1AOMo3//kep84u4IbTZmX83PpKK2F0PF//Y7BU\nwgPXgzN9zTsMJk+U20wsrrAQjEQ53D0yySISlWlx+KhNI4or7YrNq1VMigUCgWDMzGxRHI3CW3fD\n45+F2Wfwl8LbKDYbUx5eZjUO2VAHZVI8rzR/1Fi1a06p4WfXrsSYo83apQsEguyhLtvlaDX8+Opl\nGdkmVOqK8sjTa9nWLcH1D0E4CPd9CAbS1zYnTorVd5uS5RW3u3yEo3LKODaVojwDep1G2CcEAoFg\nHMxcUdx7GP50KTz9NZhzDnzoL3S6o6NWLpdZjSM8xUryRHLrhEAgODGosBq5ZGkZ37uyntrCzGwT\nKhqNxJIKq1L3XDwfrvmrMim+9zzoOTTqc9tdfuy5ORhztNQV5aHXaZL6itNlFCdeS4XVSIsQxQKB\nQDBmZp4ojkbh7XvgNxugcw9ccTdc/yCY7HQnttklodxqHOIp7hrw0+MOClEsEJzgSJLEXR9ezQdW\nJi/oSUd9pZW97f2EI1GoOxM+/gQEvXDv+dCyJeXz2l3+eLKNTqthQak5aVaxmlFck2bRDhQLhZgU\nCwQCwdiZWaLYcQz+8j7Y9GWoXQ+ffhNWXA+xxbeeNKK4zGqi2x2IL8KoP7ySZRQLBIKZw9IqC/5Q\nlMPdseKMytXwiWfBaIE/XQb7n076PEUUD1q2FpWb2dvejyzLQ45r7POi00hxAT0alTaTWLQTCASC\ncTBzRHHDE3DXemjbAe/7FXz4H2CtjD8cDEdxekOj2ifKrUZkWSn5gMHkiWQZxQKBYOawtNIKoFgo\nVArnwCeeg5KFyvLd1j+PeF67y0e5LVEUW+jzBOP/xqg09XmpspsyWtStsJnoGggQCI9s3xQIBAJB\namaOKC5aALPPUKbDqz4anw6r9HqUH0KjT4rVrGJlCtPQ3k+51YgtVz9BFy0QCE4EZhflk6vX8l6i\nKAbIL4Eb/g11Z8ETt8EL34a+oyDL+IIRnN7QkOmveoM9vNmuuc9LTYZe50qbcr7h+w8CgUAgGJ2R\n2WMnK8Xz4foHUj7cHZvMpJsUw2BWsViyEwgEAFqNxJIKy9BJsYohX9lbePw2peBj8x1gsiMXLeOL\nOjurvOdAfx5YylmYkEBx9oKS+Ckae70sq7JmdC2qKG51+Ma8NCgQCAQzmZkjitPQ404/KS63DE5g\n/KEIh7s9XLC4bFKuTyAQTG/qK6088E4zkag80uagzYEr7oJ1n4LWrdC2Hfnou9yq3Yzu3X/Cu8Di\nK7Ce+/+otJmGJFC4vCFcvhC1BRlOimNZxSKBQiAQCMbGzLFPpGFwUpzaCmEx6TDlaGl3+TnU5SYS\nlcWkWCAQAIqv2BeKJC3fABTLVvlyWPMf8L5fsmnDP1gS+APtVz8BG78EB5+DX5/Kd/R/pKO1Mf60\nZoeSPJGuzU6lzGpEkkTVs0AgEIwVIYpjZGKfkCSJ8lhW8d54vbNInhAIBAnLdi1JLBRJ6HD5CKDH\nvuB0OPeb8LkdsPpGzhh4kr+4byH03LfB309jhhnFKgadluJ8g0igEAgEgjEiRHGMHncQs1GXtnVO\nbbVraO/HlKMVnj2BQABAXbGybJfUV5yENpefgjz94L85+SVw6U94/cKneD66ipzX74CfL6fyne+y\nUjpITUHqts3hVNpNtLmEKBYIBIKxIERxjO6B0TOKVdRWu4b2fhaUmTOKSBIIBCc/Wo3E4nLLyASK\nFHS4/JRZRgrdWfOWcVvoszx9+gNQs4761vt5zPA/5N+1AjZ9DRrfVEqIRkFkFQsEAsHYEaI4Rrc7\nQPEo1gmVMouRzoEADe0Dwk8sEAiGUF9pZU9bP5GonPbYNqePCttIUVxlN5Fv0PG6pxquu59PlT/E\nzyxfgvIVsOUP8MeL4M5FsP1vKc9daTPR5vQTzeA6BAKBQKAgRHGMnoEARRlMisutRiJRGZcvxGLh\nJxYIBAmoy3ZHUi3bJdDR749nnyei0UgsLDPHEyj2OyWOVlwG1/0dvnIYrroXCmbDvz4D7/wu6bkr\n7SaCkSg9nkDSxwUCgUAwEiGKY2Q8KU4I2heTYoFAkMjSqiTNdklIVtyRyOIKC/s6BgiGo7Q5/YNL\ndgYzLL0aPvYvWHApPPUleOvuEc9PzCoWCAQCQWYIUQz4QxEG/OGMPMXlCZOdhUIUCwSCBOYU52PK\nSb9s1x5bgitPMikG5YbbHQjz1pFeIlF5ZPKEzgAf/BMsuhye/hq88cshD1fERHGbU7TaCQQCQaYI\nUUxCcUdGk2Llh1hNQS75BtF9IhAIBtFqJBZXpF+2U1sxU02K1XehntnTAaSIY9Pp4eo/wuIr4Nlv\nwOY74w+pBR6tTu+Yv4aZzKPbWnjjUM9UX4ZAIJgihKojIaPYnLq4Q6UgV49eqxH5xAKBIClLK608\ntKWZcCSKTpt87jAoipNPiheUmtFI8OzeTgBqClNkFGtzFI+xNgde+BZEI3Dml7EYczAbdMI+MUbu\nePYA80vzWT+3aKovRSAQTAFiUoySUQxQnJ8+B1Sjkbj9/HnccNqsCb4qgUBwIrKyxoY3GGF/50DK\nY9pjbXPJFu0ATHots4vy6B4IoNdpKDWP8m+TVgcf+C0suxZe+k58YlxpN9Eq7BNjotcTiN+wCASC\nmYeYFDO2STHAp8+aO5GXIxAITmBW19oB2NroYEmFNekx7f3DijuSsKjcwuFuD9V2E5p0eegaLVxx\nF0RD8OL/Qe3pSlaxqHrOGG8wjD8UFfXYAsEMRkyKGRTFhXnpPcUCgUAwGpU2E2UWI1uOOVIe0+70\npbROqCyuUHzFGbdmarRw2c/AWgWP3cIss0yrQ3iKM6XPo7xj2O8P4wmEp/hqBALBVCBEMcqinT03\nB71OfDsEAsHxIUkSq2vtbG0cRRS7/GlFsbpsl3TJLhVGi2KlcBzjqt676feHGfCHMn/+DEYVxYCw\nUAgEM5TjVoGSJFVLkvSSJEkNkiTtkSTpc9m4sMmkeyBAUQbJEwKBQJAJq2vttDp9dKQQV4ooTp48\noVJfYUWnkZhXmj+2F69dD6ffxuK2RzlHs03EsmXIUFEsLBQCwUwkG6PRMPBFWZYXAeuAz0iStDgL\n5500etyBjDKKBQKBIBPWzFJ8xVsa+0Y85g2GcflCKZfsVIrNBp6+fSMfXF099gs4++t47Qv5Yc7v\n6O5oGfvzZyBDRLG4kRAIZiTHLYplWW6XZXlb7PcDQANQebznnUy63WJSLBAIsseicgumHG1SC4X6\n1nyFLX3azdwS8/hsXToDvsvuxoKHmjf+G2R57OeYIt4+0su9rx2d9NdNFMVtYlIsEMxIsmqilSRp\nFrASeDub551oegbEpFggEGSPHK2G5dXW5KI4NoUss4xunzhe7LNX8tPoNdR0vQg7/j6hr5VNfrf5\nKD96eh/yJAv5Pk8QnUaiKF8vJsUCwQwla6JYkqR84BHgdlmW+5M8frMkSVskSdrS3d2drZc9brzB\nMJ5gREyKBQJBVllTW8Cetn68waFJBqpfNZNJ8fGg0Ug8nX8lB03LYdNXwdE4oa+XLXa3OgmEo/Qm\nTG4ngz5PEHuengqbSUyKBYIZSlZEsSRJOSiC+D5Zlh9Ndowsy/fIsrxGluU1xcXF2XjZrNAzECvu\nEJNigUCQRVbX2olEZXY2D618Vu0TpZaJFcUA5fZ87sj7vPIfj94E4cCEv+bx0Nnvp7NfucbJbuPr\n8wQpzNNTbjWmXJCcTjz9XoeopBYIskw20ick4F6gQZblO4//kiaX3a3KD6yJntoIBIKZxaoatcRj\n6LJdu8tPYZrijmxRYTOxc8AC7/sFNL8Nj90C0eiEv+542d0yeAMx2SUafZ4g9lw95VbTCRHJ9r2n\nGvjVS4em+jIEgpOKbEyKTwc+CpwjSdKO2MclWTjvpHDva0eoKchl7ezCqb4UgUBwEmHNzWF+aT5b\nhvmK212+tMkT2aLSbqKz309o0RVw/rdhz2Pw3Dcn5bXHw64WJ1KsvG+y2/j6PEEK8vVU2Iy4A2H6\np3G+czAcpcXhpcc9vSf/AsGJxnHXPMuy/BqQpoN0erK1sY9tTU6+/f4laNPVqAoEAsEYWV1r58ld\n7USjcryqucPlp8o+hkKO46DKZiIqK69Zvf42cLXAm79SWu/W3Top1zAWdrW6mF9ipsXhnXxR7FXt\nE8oCZLvTj6UsZ1KvIVNanT6i8mAbq0AgyA4zusLtd68exWrK4erVVVN9KQKB4CRkdW0B/f4wh7rd\n8c+1ZVDxnC0qbIrAa3X6QJLgoh/Awsvg6f+CPf+clGvIFFmW2d3iYlmVlUq7aVI9xeFIFKc3FLNP\nKH8203nZ7livBwCHN0QwPDF2mD5PkKvufoNjPZ4JOb9AMB2ZsaL4WI+HZ/Z28NF1teTqj3tgLhAI\nBCNYUxsr8TimWCg8gTD9/jDlk7TDUGmPiWJVYGq0cNXvoXotPHozNL4xKdeRCW0uP72eIMuqrFTY\nTJM6KXb6FKtEYb6ectvgpHi60pggVHs9EzMt3tvWz9ZGB8/u7ZiQ8wsE05EZK4rvfe0oORoNH1tf\nO9WXIhAITlJqC3MpzNPH84rVBa7JmhSrrzNEYOaY4Lr7wVYD918LXfsm5VrSsbvFCcDSKhuVNtOk\nLtqpxR32XD2lZgMaCTqm9aTYG/+9mqCUbVSxva3ROSHnFwimIzNSFDs8QR7e2swVKysoMYvUCYFA\nMDFIksTqWns8gaIjLoontrhDxZijpSjfMFJg5hbARx4BnRH+dhU4jk3K9YzGrhYXOo3EwjIzFTYT\nDm9oRMbzRNHrVoRlYZ4enVZDidlI2zROoGjs9aCLedS73RNznT2x78m2JsekF6kIBFPFjBTFf3ur\nEX8oyic31k31pQgEgpOcNbPsHOv10j0QiPtUJ2tSDIqFIqkVwV4LH/4HBN3wx0uh9/CkXVMydre6\nWFhuxpijpSpm+5isabHDqwjAgnw9AOU2Y7xkZTrS2OtlSaUVmLhlu95YskXXQGBa3yAIBNlkxoli\nfyjCn988xlkLiplfap7qyxEIBCc5q2O+4m1NjvikeDKKO1QqbcbU/tzyZfDxf0PIC3+6DHqmJvdW\nlmV2tbhYWmkDBhcEWyZp2U5tzyvIVURxhdU0bT3F4UiUZoc37lefOFE8aMvY3jSyrlwgOBmZcaL4\nn9tb6XEHuVlMiQUCwSRQX2lFr9WwtdFBu8s3acUdKqo/N+Vb4GVLFWEcCcKfLoXuA5N2bSpNfV5c\nvhDLqpTpZ6VNnRRPjjB1qJ7iPEUUl1mNtLlG+Z5NIe0uP6GIzIJSMxajbuJEsSfA/NJ8DDqN8BWf\nYGza3c4tf90yLf/+TndmlCiORmV+/9pRllRYOG2OKOsQCAQTj0GnZWmVNSaK/ZOWPKFSaTPhD0Xj\n09CklC6Bjz8JclQRxl0NY3oNTyDM2u89zyNbW8Z1jbtiTXZLY5aAUosRrUai1ekd7WlZo88TxGzU\nkaNVfiSWW434Q0pM23RDjWOrLcyl2Gyge4IKPHrcQUotRpZVWdnenNmk+O6XD/PGYVE9PdU8tr2V\nZ/Z0ihzrcTCjRPHLB7o41OXmpo11SJIo6xAIBJPDmlo7u1tcNPZ6KbNMzpKdSoUtQ39uyUJFGEsa\nxUrRuSfj19h8sIfO/gDPN3SO6xp3t7rQ6zRxS5tWI1FmMU7apLjXoxR3qKjfs+lY96zmBs8qylNE\n8QROiovyDayqsbOntZ9AODLq8d0DAX70zD4efLd5Qq5HkDk7Y0ku+zoGpvhKTjxmlCi+59UjlFuN\nXLqsfKovRSAQzCBW19oJRqIc7fFQMdmT4uFZxaNRPB9ufAq0ekUY73sqo9dQxfCWxvElFexqcbKo\n3IJeN/gjaTILPByeIAUJolhdhDyeZbtwZGJKNY71ejHmaCgxGyg2G+MpEdmm163cKKysUf7u7mnr\nH/X4l/Z3Ictju5H461uNfO6B7cd7qYIEOlx+OvuVG6X9QhSPmRkjine3uHjrSB//cfrs+FtkAoFA\nMBmsii1FgeJXnUyqbEqldMZlGIVz4MYnwVIJD1ynlHx4+1IeHonKvLivC2OOhu6BwJiX46JRmfda\n+1kWs06oVE5igUfvMFEcn66Pc1L82PYWVnz7OXomwNrQ2OthVmEekiRRlK+fkEmxNxjGG4xQmG9g\nVY2y/LitcXQLxYsNXcBg7GAmvLyvi2f3jO/dBUFydjQrU2JJgoaO0W9kJpOjPZ4x/d2YKmaMOuwa\n8DOvJJ9rTq2e6ksRCAQzjKJ8A7OL8gAl2WAysZh05Om1QwRmNCrzxuEevvKPndz0ly2Ehk81C+rg\nphfhrP+C9x6Bu9alnBpva3LQ5wnyiQ2zAeJFJZlytNeDOxBmadVIUdzR75+wiWsiwyfFRfkGdBqJ\n9nGI8mhU5pcvHMIdCLP5YHc2LxNQJsW1hcqNTrHZgDsQznqeczy3OV9PicVIpc3E9ubUy3aBcCT+\ntXa4/Bm/W9Dm8uMLRfAEJiePeiaws8WJTiNxyqyCaTUpvuPZ/Vz2y9eIRqf38t+MEcXnLirl2c+f\ngcWYM9WXIhAIZiBqNNtkT4olSYpbEfZ19PP9TQ2c/sMXuf53b/PPHW08t7eTF/d1jXyiTg9nfQ1u\negnySpSp8SM3jZgaP7+3kxytxM0b55Bv0LGlMfVUORm7Y0t2y4aJ4gqbiUhUpmuCl4VkWabPE4wn\nT4DiaS61GMflKX6+oZMjMd/v5oPZXTqLRGWaer3MKlRusIrzDUD2W+3UpcyiWG7zyhob20e52Xnn\naB+eYISN84oIRqLxhsB0qPYUsRCWPXY2K1ak5VVWDna5J+WmMh2+YIQX93VxwZJSNJrpvc81Y0Qx\nIJbrBALBlHH63EK0GikuaCaTSpuJ5xs6uehnm7l381EWl1v45XUr2fbN8ym1GHjgnabUTy5fNjg1\n3vMo/HotvP6LuDh+rqGTdXWFWHNzWFljY+sY47t2tbgw5miYW5w/9JpVL/QEWyjcgTDBSHTIoh0o\nvuLxlIf8bvMRKm0mLq4v47WDPVmNxero9xOMRKlVRbFZEcXZbrVTizsK85Tzr6qx0+byp3z7+4UG\nxT5z9eoqIDNfsS8Yiad7TFSCxkwjGlXyvldU21hYZiEYjg6pBJ8qXt7fhTcY4dKl03+fa0aJYoFA\nIJgq3r+8khe/eOakT4oBLq4v59TZBXz7/Ut4+7/P5d6Pn8LlyyvIN+j40JpqXj7QPbr4TJwaF82D\n574Jdy6i/4GbyOvZzXmLSgFFPO3v6GfAn3mU2a4WJ/UVVnTDdj0qYwuJE71s5/Ao12rPHSaKY/aN\nsbCtycG7xxx8YsNszl5QQtdAgAOd7qxda6OaPJFgn4DsT1oT7ROgTIoheYmHLMu8sK+T0+cUxW/4\nMvGOtiUsMfaISXFWONLjxh0Is7zaxoIyJcll3zTwFT+5u53CPD1rZxdM9aWkRYhigUAgmAQ0Gik+\n4ZtsPnRKNQ/cfBofO20WhbG33OOPrVH2LDKK0ipfpqRTfOp1WHE9poNP8IThG1y38wbY8XdOqc4l\nKsP2psymxeFYqsFwPzEMLrtN9KS41xObiuYPFcUVVsU+MZZJ7+83H8Fi1HHNKdVsmFcEkFVfsTr1\nqy0aNinOsqjs8QydFC+psKLXadiWRBQf6nLT3OfjnEUlY0rtSGwMFJPi7LCjWbEirai2MrckH61G\nmnJfsT+kWCcurC8bceM7HZn+VygQCASCCaO6IJeN84p5eEtz5v7Dsnq47Kd8svCv3GW6BX3EC/+8\nlfVPX8YF2i1sPZaZr/hwtwdfKDLCTwyQq9dhz82ZcFHs8MYqnvOG3iyUW40Ew2lKTxJo7PXw9Hsd\nfGRdLXkGHRU2E3OK83g1i77ixl4Pep2G8lhNeGGeAY0E3VmOZet1B8nTazHpleZFvU5DfYUl6c3O\nCzE/+jkLSyhUFxTHOCkWnuLssLPZSb5BR11RPsYcLbOL8qY8q/hEsk6AEMUCgUAw47n+1GraXX5e\nOZD5VLPXHWBzcxD/qk/CZ96B6x9Go9NzT86dnLf1Fujcm/Ycu2IlA0srbUkfr7SbxuXrHQuqVaBg\nmH2iLJYS0p5hgci9rx1Fq5H4+PpZ8c9tnFfMO0d78YdGL77IlGO9HmoKcuPLSlqNREFe9mPZet2B\nEe8orKqxs6vVRTA89MbpxYYullRYKLea4guKmdgn1O+r1ZQjRHGW2NniZFmVNf73Y0GZecrtE0/u\n7qDgBLFOgBDFAoFAMOM5d1EpRfkG7h9t4W4YL+7rIirD+YtKlVDU+RfAra/z78rbqfEfQP7NBnjy\nS6NmHO9udZGn11JXlNxWUmGd+AKP+KR4uH0i5mluy8AK4PAEeWhLM1esqKTEMugZ3zivCH8oOuaY\nulQ09nrjfmKVovzst9r1eoIj7CQra+wEw1Ea2gdFltMbZEtjH+cuLIl/rtyaWWpHu8tHUb6BCptp\nQvKcZxr+UISG9n6WVw/eYC4sNdPc58M9RZF3/lCEFxo6uXDJiWGdACGKBQKBYMaTo9XwwTVVvLiv\nK+OA/ecbOimzGKmvtAx+UptDeM3NnBm4k75FH4Et98IvVsIL/wdt22GYP3dXi4v6SmvKmCZ1UpzN\nBIfh9HqC6LUa8mJWAZXy+KQ4vSj+61uN+ENRbjqjbsjn19UVkqOVshLNJssyx3o9I3zpxWZD1j25\nPe5g3E+ssqo2VuKR4Ct+5UA3URnOiS1aghI5mMmCYpvLT4XNOKFV1ZPBjmYnN/9lC44MbTYTRUN7\nP6GIzPKqBFFcrvy/eaBzaiwUqnXishOoRViIYoFAIBBw7SnVRGV4aEv6hTt/KMKrB3o4b3HJiKjL\n1bV2nJh5qvoLykJe9anw2p1wz1nw03p46itw9FVCoSB72/uT+olVKm0mPMEILl/maRZjpc+tFHcM\n/zoK8/TotRra0wg8fyjCn984xtkLiplfah7yWJ5Bx8oae1aW7boGAvhDUWYVjRTF2U5v6HUH4hnF\nKuVWE+VW4xBf8fMNXRTl64e0ESqT4vQ3Mu1OH+VW44S18k0W/9rRyrN7O7nlb1tHWEsmk52xcpUV\niZPiWALFVC3bnWjWCRCiWCAQCARAbWEeG+YW8eC7zUTStE69ebgXXygSj2JLpMpuosRsYEujA0oX\nw4cfhi8dgvffBeXLYduf4c+XI/1kHj+UfsnF0VdgoCPp61ROQgKFwzu0zU5Fo5EosxrTeoof295K\nryc4Ykqscsa8Iva09R+3ReDYsDg2FXXSmq1pejSqlJkMt0+AEs2mTopDkSiv7O/i7AUlQyb9ZVYT\n/lA07Y1Mu8tPudWkiHp3cELfDZhItjc5KcjT887RPr7xz91T9nXsbHFRajEMiXystJnI02vZ1z75\nvuIT0ToBQhQLBAKBIMZ1p9bQ6vSlnWw+u7eTPL2W0+YUjnhMkiTWzLIP9dHmFcLKD8N1f4evRiZR\nfwAAIABJREFUHIFr/kZz0UY2anazauvX4I4FcNd6eObrcOgFCCkiOB7LNoG+4l5PclEMg1PPVESj\nMr/bfISllVZOqxv5vQBl2Q7g9UPHZ6FojMWxDS9/Kc43EIxE6fdlxzfa7w8Rjsoj7BOgLNu1OHx0\nDfjZ2uig3x/m3GE3RoOxbKlvJvr9IdyBsGKfyPL1TyaBcIS9bf1cvbqK286Zy0NbWvjd5iNTci07\nm51DrBOg3Ngpy3aTPyl+eX/3CZU6oSJEsUAgEAgAOH9xKYV5+lEX7qJRmRcaOjlzQTEGnTbpMap4\n6kxmPdDnwaLLuafwq5wr3YN8y6tw3rcgrwjeuQf+diX8fAU0vR1vtZvIBApHGlHcNsqk+IV9XRzp\n9nDTGXUpG1PrK61YTTnH7Ss+2ushRyvFRafKYKtddiwIPcOKOxIZLPFw8uK+LvRaTTyPWaUsg6xi\ndfquTooh+618k0FD+wDBSJQV1TZuP28+ly4t5/ub9vHc3s5JvQ6XN8SRHs+QJTuVBWUW9ncOTPoE\n+6nd7RTk6VlXd+JYJ0CIYoFAIBDE0OuUqt4XGrroSuGl3d3qomsgkNQ6obJmlvKDcMux5KkLDk+Q\nTe+1c8rsYqTy5bDhdrjhcfhqI1z/EOSY4E+XUrj/AQw6zYTaJ0adFNtMdPb7U9pJ7nu7kXKrkUvq\ny1KeX6uR2DC36Lgrnxt7PVTbc0e8FV2cn90CD7XiuSh/5KR4SYWVHK3E9iYnLzR0sraugHyDbsgx\nFeqC4iiTYvUmR50UK9c/tYtq42FHzEqyssaGRiPxkw8uZ2mllc89sJ29bZNnWdjVOtJPrLKwzIzT\nG6Kzf/J82/5QhOdPQOsECFEsEAgEggSuOaWacFTm4a0tSR9/vqETrUbi7AUlSR8HWFxuwaDTpIwi\n+9Ez+xnwh/nyhQuGPqDPhfkXwk0vwuyNSE/cxg9Nf6bdMTFv/wbDUQb84ZSiuMJqJByVk/qBO/v9\nvHqgmytXVab9wb9hXhEd/X4OdY2/8vlYj5faYX5iyP6kWC0rSTYpNuZoWVxh5d+72jjc7RkSxZZ4\nPVqNNGqKiRpzN3RSfOIt221vdlJqMcSTSkx6Lb//2Bosxhw++ed36RqYnOm3umSXrBlyKuqeT1Tr\nBAhRLBAIBIIE6orzWVdXwAPvNvHS/i62NTk43O2m1x0gFIny3N5O1tTasacQkqBMnJdX29jaODKj\neFeLkwfebeKG02bFf2CPILcArn8Y1n+WK0Kb+FTjF8CdvbpkFWe8zS6VfSL11POf21uJynDVqqq0\nr7Nhrlr5PD4LhSzLNCaJY4PsVz2rk+JknmKAVTU2WmIe7+F+YlAm4yVmw6iT4nanH40EJWZDfCKd\n6fVPp4W8Hc3OEdPZEouR39+wBoc3xM1/2UognJ3iltGvw8Wc4jwsxpwRj01FAsWJap0AIYoFAoFA\nMIyPnTaL5j4fN/7xXa686w3OveMVVn/neeZ9fRP7OgY4f3Fq64TK6lo7e9r68QUHRUE0KvPNf+2h\nMM/A7efPG/0EWh1c8B3ur/omc0MHlEi3th3H+ZUNRZ2KprZPxPyxw+wbsizzj60trKqxUVecn/Z1\nqgtyqSvKG3c0W487iCcYGZE8AUojXI5Wypoo7nEHkSSw544UWKCUeADML82numDk9UAsqzjNpLjU\nYkSn1cSvP5N0ju1NDpb8zzM093kz+Eomlj5PkMZeLyuq7SMeq6+08v0rl7Kj2clrWaz5ToYsy+xo\ndib1EwPYcvWUWYyTtmw3mDpResJZJwB06Q8RCAQCwUzi4voyXvnyWfS4g/T7Qrh8IZzeIC5fmEA4\nwgdXV6c9x5paO3dHZXa2OFkXS2Z4eGszO5ud3Pmh5UmnWsnonv1+rj5s4AnuRvr9ebDqY7DxC2BN\nP6FNhyNRFIeD8PZvwNkIuUWQV0StzsZaqRFPmxFKneBqAVcLXS2HucWxkw3FfrjLDWE/hAODH5EA\naHKg7izFDjLvAjbMK+LhLS0EwpGUC4qpaOxV4thqkzT/SZJEcRZb7Xo9Aey5+pSCZnWtIgLPWZj6\nxqjcahx1Mtnu9MeTRTQaKeNWvp3NTrzBCK8e7ObDa2vTHj8eXL4Q0ag86jsh6rXA4PLhcC5YUopW\nI7Gj2Zl0op4t2l1+etyBpH5ilclMoHjlQDeeYIRLTkDrBAhRLBAIBIJhSJJEbWFe0rfrM2VVbKK4\ntdHBurpCnN4gP3x6P6fMsvOBlZUZn6fCZuI9uY6mqzdRu+tnsO0vsP2vijje8AWwZn6u4aiT4rLA\nMbj389C+E4w28CuCJx940AC8GfuIUYyG9Ro7RaY5YK5TFgO1BtAlfPiccOh52P8kAF+y11Mgz2f/\nVj3LTjkTNJkL42Mp4tji15PFVrted5DCUQRhpc3E7z+2hlNGKWQos5h4eX83siwnTeVod/moTyj8\nyFQUN8dsG+8c7ZswUXz7A9vpcQd54rMbRj1ue5MDjQRLK5OXz+TqdSwsMw8pO5kIVHE+PI4tkYXl\nZt483EsoEiVngqe3T+1ux56bkzKicLojRLFAIBAIso49T8+c4rz4st0dzx7A6Q3yrfetTRlflgy1\nwKMlmEftZT+FDZ+HzXfC1j8rAnnVDcrnxiGO+9x+btRuovYfD4EhH675Gyy6HCJh8PaCt4cv/vF5\n6q0BbtxQB9YqAnnlrP/VXtYvKOOX160c/QVkGbr2woGnydv3NLdpH0Oz6VF4yQo162HWBuWjbOmo\nIrmx14NWI8W/F8MpNhtGjY4bC73u5MUdiZyXxj5TbjXiDUbo94exmoa+IyDLMu0uPxcsGUzsKDYb\nksf3DaPFodwcvH2kL6XgPh4iUZl3jvbhCUY42uNhdpLJvMr2ZifzS83kGVLLqJU1Nv65vY1IVEab\nosr8eNnR4kSv1bCwPIU/H8VXHIxEOdbjYV5p6uOywa4WF6fNKTwhrRMgRLFAIBAIJojVtXae3dvJ\ne60u7nu7kY+uq2VxhWVM56gcXuBhq4HLf6ZYKDbfAVv/qLTk1V8Faz8FFSsyO7GrhbPfuZmanHeJ\n1l2I9L5fgjkm9rQ65ffmUtoLBzgSinDj0tMBeHF3O72+KFevzsC+IUlQugRKl6Dd+EU+cddTLPZu\n5Yvzu+DYa3Bgk3KcwQo168BeC7mFsY8C5VdTAdGWPVxhbkff4AWfQ5lC+52KmF76QYryDexscY3l\n25qSHk+AReVj+zMajurF7nD5R4jiPk+QQDg6JG+5ON/Ae63pr7+5T/k70NHvp8XhS+lpHi8HOgfw\nxDzwm95r59NnzU16XDQqs7PZyaXLRrcIrKi287e3mjjc7R5RAT4WPvfAdroHAvzgymXUDPOV72x2\nsqjCMqolZ0Gp8ufZ0DEwoaI4GpVpdfi4IIOdg+mKEMUCgUAgmBDW1Bbw0JYWPn3fNuy5er5wwYL0\nTxpGmdWIJCWperbVwOU/VywUb/wSdvwddt4PNacp4njhZYq4TSQchN5D0PQGPP9tSkNBviV9iv+5\n/geKgE1CudXEG4cHl6Ue2dZCqcUQT5QYC8sXzOOnz8vceO75io+5vw2OvQ7HNkPz29D8FvhHisMv\nx1884ZM6o+JlfvNXrCq8lYfctqxMJHvdQYry9ND4Brx1t/IaklaZZEsa5VeNDkx2yC+BvBLIL4X8\nYuVXS2VCq51vRMKImkqhJnuAMinu9QSJRuUhldHDaXF4OXV2Ae8c7ePto31ZF8Wq1aHUYuDp9zpS\niuKjvR76/WFWJlmyS0T1G+9och6XKH7lQDdOb4iLf/4q/+/yxXxoTTWSJBGJyuxucaW9QZtTkodO\nI7G/ox+WV4z7OtLR4w4QjESpsid/R+NEQIhigUAgEEwIq2cpoqGpz8uPrl42YmqYCXqdhhKzIXWB\nh70WLv0JnPMN2HEfvP1bePgGsFYrvuNICLr3KR+9h0GOpWFUr+V72s+yudecUhCDUjDR2e8nHIni\n8IZ4aX83N22sG5f4PG9RKXc+d4AfP7OP71+5DCwVsOyDyodKJKRMg7294O1F9vTw2Yf3sHzubG66\ncLUiRo020ObAnkfhuf/lQ3s+jU23GlfzbApqF4/5ulSC4Shmfysfaf4NbH9BEbzWSohGQI7Gfo3E\nrrEvqYCndCm1p38TIGkCRWJxh0pRvp5IVMbhDVKYpDQElAW4fn+YcxaWcKBzgHeO9mY2rR8D25sc\n2HNzuGH9LH709H5aHF6q7COFtyqeV6RYslOZXZiH1ZTD9mYHHzol/XJqMjyBME5viI+uq+VQl5uv\nPrKb5/Z28v0rl+HwKqkkqZInVAw6LXXFeRMey6Z6viuFKBYIBAKBYCh1RXkU5RuoLjBxdQZ5vqmo\ntJlGrXru6vdTYrHBaZ9RpsQHnlamnC99V5lu2mdDySLFL1y8CIoXQGk9B37/DgW50VFfu9xqIipD\n10CAp3a3E4nKXL16fMt9iyss3HrWHO5++TDr6gp5/4ok59HmKBPYfKUYw+kJ8m9/DitqF0Fx3dBj\n66+CBZew/18/4rTdd5P/p42w9mbl+5BXArpBb7AnEKbFMXJyG8ffT+iFH/KC/jdoHTo4++tw2n8q\nhSqpCAfA3QWeLuVXRyO89WuKHv0Qf8xZTnPb14CaIU9JPilWBHK3O5BSFKt+4pqCXE6ZpUyL0yHL\nMt/ftI/Ll1UkLbYYzvZmJytr7FxSX86Pnt7P0+918MmNdSOO29HsIN+gY06aOD6NRmJFte24lu3U\nv/drZtn51vuW8IfXj/KjZ/Zz0c9e5cz5xQBpRTEodc/bUpTpZAv1xjXZjcSJghDFAoFAIJgQJEni\nwVvWUZCrH/Vt8XRU2EzsTuE5fejdZr7yyC6eum2j4lfWaGHhpcrHQCcYrZBjTPrcPk8waUtcIolW\ngH9sbWF5tY25JeN/K/yL58/n3aN9/Peju1lWZRt1mQvgWCyOLVXyBDkmBtZ8lrO3zOPx+leoePs3\n8NZdscfywGQDo40+n54ml445qxahyy9K8C4XgqsZXv4+eZ5uHolupOCi73L2KcvTfzE6A9iqlQ+V\nNTfCO/ew+tnvc+aOD4PmI4rANiuLdW0uH3qtZkjCRWIBycIUjdlqYUiV3cTa2QU8t7eTzn4/pZbk\nf7agiNx7Xj1Cz0CAO68Z3Wvu8oU41OXmihUVzCrKY1G5hU0pRbGTZVXWjN4tWFFt4xcvHsQdCI+o\nxM6EFufg163RSHxyYx1nzC/m8w/u4NHtrZiNOmZnkBKzsMzMEzvbGPCHMGcYhzjma43duKRaCD0R\nEKJYIBAIBBNGumlaJlTaTTy7p3OE57TPE+R7mxoA2NrkGLnEZx594afPG2RV7ehTNnVp7PmGLvZ1\nDPB/718yjq9gEJ1Wwy+uW8klv9jMZ+7bxqOfXo8xZ7TkiVgcW1Fq8V5sNtCDlTcWfZOrL7hdWeJT\nl/F8TvA5GHA0UkM38v5GCPRBNDz0JNXr2Lbht3zxX37+UTy+t/qVL9AA6z/Lp7fM4SOhh7lox/2w\n+xFYcDHkFrLisJ//zNWh2e1SbCDFCyjKVyaeo8WyqYUd1QlTyHeO9nH5KB7Zf+9sB+DVgz1p/co7\n4rnDiuXn4voy7nzuwAjh7QtG2Nc+wC1njhTLyVhZY0OWlSbH9XPG7kNXF0wrbYNf9/xSM499+nR+\n+8ph8gy6jG441Wa7A50DrK6dmKa5VocPe27OyESOaBQOPguOo7Du1gl57WwhRLFAIBAIpjWVNhPB\nSJQed4CSBIHyw037cPvDmHK07G0bW/qCLMs4PEHsuaPHj6lv8//1zUb0Ws2oIixTKmwm7vjgcj7x\n5y1876kGvv3++pTHHu3xIEmjvyWtViX3uAOKTaRk0ZDHg+EoH/jfZwiEo/z8yhW8f3kFBPpjvuU+\nJTquag3HtrcCO1NaGMZCnr2EO3s+zkWf+YZiY2l5B3wuLg64uBjgsXuVAyUNVStuoIC1o7batTh8\n5Om12HJzMBst5Om1o4riaFTmyd1t5Oq19LgD7OsYGDX5ZHuTA0mCZTGbhSqKn9nTwcdOmxU/7r02\nF+GonLTJLhlqqcb2pnGKYqcPnUaKT9NV9DoNnz03SStkf5uyJOl3KcUxsZIb1Tazr2PiRHGLwzfU\nTxwOwnv/gNd/Ad0NUDgPTrlp5ALsNCIrVyZJ0kXAzwEt8HtZln+QjfMKBAKBQBDPKnb64qJ4a2Mf\nD25p5pYz6tjV4mJPW/+YztnvDxOOyikrnlUsRh15ei3uQJhLlpZhSyOiM+XcRaXctHE2v9t8lHV1\nhSkbwBp7PVRYTaNOk/MMOnL12pST1ob2fgJhxTt9sNOtLBYarcpHweDEs9etlJmkyynOhHKriTcO\n9ULhHLj6D/HPn/H959hYo+e7F1UpC4W7HiTn3Xt52fAgbx/8JKz/5hAvtEqLw0t1QS6SJKHTSqxO\n4yt+91gfnf0Bvn7JIr77VAObD3anEcVO5peY49aCeaVm5hTn8dTu9iGieIe6ZFdtU6bwPQeUm4vi\nhWCfNWJp05arp644b9y+4janj3KbMblVQ5ah56CSptL0liKGnY2Djz8JVJ0Ci6+gctHlmA069rVP\n3LJdq9PH3OJ8CLiVmMQ3fw39rVCyBD5wD9RfOa0FMWRBFEuSpAV+DZwPtADvSpL0uCzLe4/33AKB\nQCAQqJXAbU4fq2rshCNRvv7Ye1RYjdx27jx+9vwB/vxm45gau/oSK55HQZIkym0mDnW5s5528OUL\nF/LOMQdf/ccu6iusIzJoQWmzG806oVJsTt0Kt61JWbCy5+ZwoDO1KOrxBNBrNZjH4X0dTrnVyEAg\nPMTDGonKtA6EsBZWK2IZoGoN0ppPsOc3t3J+8y/grn/DBd+BBZcMEZhdfU7qLWHoOwKWKk6dZecn\nsUKYZDcq/97VjjFHw/Vra/jH1hY2H+zhljPnJL3WaFRmR7OTS+uLoXMPDLRDNMJnKxt5dncrA1ua\nMOs14OtjwdbXeCT3CMW//Ty4O4eeyGCF8mVQtkz5tWIVFM9nRbWNVw+kbvgbjVaHb6hHNxyAo5th\n/1OwfxMMtCmfzy2C2lgcYc06MJih4XHY+y949utIz36dR3MW8PahDdDzaShKHjc3XmRZptPRz9fz\nn4SfPqhYd2pPh8t+BvPOHzXhZTqRDcl+KnBIluUjAJIkPQC8HxCiWCAQCATHjfqWrOqv/NMbx9jX\nMcBvPrKaPIOOJRVWguEoh7vdLCzLrHiiz6MIyHSiGKDabsLpDXHGvOJxfgXJ0es0/CrmL/7s/dv4\n1JlzaHX6aHH4aHF4aXH4ONjl5poM4ryKR6lK3tbkpNxqZEW1bdRYLrXNLhtNcWWxBcXOfn9cFHcP\nBIhEZcqHL2KVLORHRd/htMg2viL9FR64Xpm8yjL4ncg+J49HAuACfgFodPyHeTazc+z0/vt1bIvX\nQGFM5IW8RPxuvLve5qsVOvLe6+TWAgdPHPLjPyZhtBQpsXYGqyIoW7bgOvgW90ReYtXeRtg9mHJy\nBXBFDvDvwUtdRS7dxlqYex4UzVeSTEwFSnNhxy6lKnzLvUq+M0DlGj5QeDWPuyvGVTjS6vRx7iw9\n7LhfEcKHX4SgW1minHsOzP2qIj4L544Unhu/qHz0HYG9j2N6/X4+4r4XfnWvcu0LLlZuPqpOGVPt\neDJch97kYem/WNjWrJxzwxeg+pTjOudUkA1RXAk0J/x3C7B2+EGSJN0M3AxQU1Mz/GGBQCAQCJJi\nMeZgNupoc/rocPn56XMHOHtBMRcuURbplsTeFt/T2j8GURwCoDAvvX/2/12+BG8wPCHVtdUFufz4\n6uV86m9bufW+bQDkG3RU2U1U2U2sqyvko6fVpj1PsdnAwS530se2NTpYVWNnTnEez+zpwB+KJLVj\n9LoDWbFOwKAXu93lj6d1tLliGcXWkYkRxfkGXuhdzldu+xRs/ZMiAPX5YLIT0Fn4+evdrF86l40L\nKqDvMIbOBhY7t1G7dwvsHRqrpwXuAOgEnoiJWy3wp0RnpwTIAFg0OeipxbP4Wmzz1is2CI0WWdJy\n41+2U2bP5wdXraQnmMOaX+zmG+cuHplKUZMgeyJh6D0IR1+Fd+5h466v8ZrBjuO5j8Jln4O8zLzF\nIUcLN3l+x0cPvgT7/WAuh2UfUkTnrI0pU1VGUFAHG27n1Zwr+dVjL3GudhsXdW/j1J5fk/P6z+nX\n2DhsP50FZ15D7sLzQJ8+zSJO0AMvfhfrW3fhlexs3/BbVp53bebPn2ZkQxQnu6WUR3xClu8B7gFY\ns2bNiMcFAoFAIEhFpc1Eq9PH/z25l3BU5lvvq49PNOuK8zHmaNjT1s9VqzM7nzoptuelj6dKF5t2\nvFxUX8aznz+DYDhKtT0Xi0k35mltsdnAG4d7R3y+q99Pq9PHjafPotRiJCrDkW5PUn9tryeY0U1C\nJgxG2Q0WeLQ7R2YUqxSZDWxpdCg5zafepHzEONji4u5XX2N5/WqoVzLbtMBXf/smctDLwx8sUYpZ\nNFrIMfGbNzt47uAA9916DsbcPPxeNx/79TNcudDEtfXmWFV2n5LlXLWa/30L/rm7h50fuAASvLsS\nsGCZgXtfO8p/5daytbMXkOJNdSnR6gYXHk+5icjB5zj49++yseEXcOC3sPRqmHcBVK0BS+XICa+j\nEV7/Gbptf+Nj2jDN5Zcx+5LbFTvGcUzxr1xVSa7+PDr6N/DSQIAnXL1U9r7OkoE3WNPzErmPPqk0\nJdadpQjvBRfH87KTcvgleOJz4GykafZ1XNpwLg8tvnDc1zcdyIYobgES39upAtqycF6BQCAQCABF\nFL95uBdPMMIXzp8/xH+r1UgsLLPw3hgSKMYyKZ4MjqcGGJRJq8sXIhCOYNANToG3NQ1Gjak5uQe7\nkicx9LqDzC05/gg9gBKL8n1NbLVrd41ss0u8foc3mNQX3hzLv60uGCqm184u4K6XHbjti8gvWwpA\nKBLlN39/njMXL8FYrtSKG62gn+Xij90Brl1xxojX3tKymRXVtqTRZhfVl/HbV4/wXEMnh7vd5Ggl\nllSkLwKJo9GgXXAhvyy38FDwGL+se1epI99xn/J4filUrobKVVBaD3sfh10PgkZL19yruGr3Wn5w\n1uXMrhx7csVwjDlarlg5vDBmIwAX3vECG/UH+cbco7DvKaUA5wlJua78WHh0oiAPDMDRVxTbxo2b\neKaxFHfDvhO6zQ4gG+8FvQvMkyRptiRJeuBa4PEsnFcgEAgEAkBZtvMEI8wuykuaEbukwkJDWz/R\naGZvRPZ5AhhzNJj0x+elnC4UxSK71AQJle1NDvRaDfWVFmYV5aLVSEoCxTBkWabHHYjHux0vBp2W\nonzDkElxm9OPKUebtO672GxAlgcXIBNRSyGGx9KdOruASFQe0tT2+qEenN4Qly0bGtW2cV4R+zsH\n6OwfWj3tCYTZ39EfzycezopqGxVWI0+/186OJieLyi2jJoGkYmWNjWc6bQQu+jF8tRFuehEu+QnM\nOUdJkHjxO3D/tbDnMVh7C3xuJ68t+AYtcknSm4hsc+HSKv7QVk3Pxm/D7bvgU68rpStaPTiblFQL\nxzHoO6p8eHpg45eU42rX0+LwYTbqxlXlPp047kmxLMthSZL+E3gG5R2NP8iyvOe4r0wgEAgEghhq\n89y3379kyCRUpb7Syn1vN9Hs8FKbQcNXNq0C04Hi/MFWuIqERbZtTQ6WVFri37NZhbkc7Bq5bOcJ\nRgiEo0Oa5o6XcqsxPh0GZVJcbjMmtYYkttoNb6lr7vNhSSK4VtXY0Wok3jnaxxmxyuN/72rHbNRx\nxvyhk9WN84r5/qZ9bD7YMyRFZGeLk6hMSkuEJElcWF/GfW83odNI404gWVlj47evRtnbFhPglauV\nD2I2EZ8TOt9TFgxjnuM250GAIX+eE8XFS8v5xYuHeHZPJ9evrYGyeuXjzC9n9PxWh++ErndWycrW\ngCzLT8myPF+W5TmyLH83G+cUCAQCgUDl2lNreOiW09iYIgEivmyXYV6xwxPMKHniRCFRVKoEw1F2\ntbhYlTAFnVdiTjop7o0VZ2SjuEOlzGocYp9oc/lTVgCrE+ruJAUeLQ5vUsGVZ9BRX2mN5xUHwhGe\n2dPBBYvLRtw4LSwzU5RvYPPB7iGfV/ODV1Sl9glfXF9OMBzFG4zEyzjGilr2kTKv2GSDWRuGLOG1\nOn0U5RvGNZkeKwvLzMwuymPTe+3jen7L8Oi4E5Tsr9IKBAKBQJBl8g06Tp2duolrfqkZrUZiT4a+\n4j5PEPvJKIoTROW+DqW0I1EUzy/N51ivh0A4MuT5PVks7lBRJsWJi3a++ALecEqSiHoVJcosueA6\ndZadHc1O/KEImw/0MOAPc9nykUUoGo3ExnlFvBarfFbZ3uSkrihv1L8Lq2vtcdGeymaRjjKrkXKr\nMV4nnQmtTt+keXQlSeLi+jLeONyLI4mFZTRkWY7duAhRLBAIBALBlGPM0TKvJD/jSXGfN5hVq8BU\no4rZRFGpem1X1Q5ON+eVmuMJFImok+KiLFpKyqxGXL4Q3mCYYDhKtzuQNHkCEibFw0SxIrhSvzV/\n6uxCgpEoO5udPLGrDVtuDhvmJl9KO2N+Eb2eIHvb++Pn3tHsSCt0tRqJK1ZUUGkzMStJwUqmrKyx\nsb3Zkf7AGEpxx8T7iVUuWVpOJCrz3N7O9Acn4PKF8AQjQhQLBAKBQDBdWFxh4b3WDEWxO4g9S5XN\n0wGDTostN2eoKG5yUmYxDhGi80qVdInhzXa9nomZFIOSQNHZ70eWkydPAJj0WvINOnqG2Sd6PUF8\nodSC65RZiqDdfLCH5/d2cnF9WcpWw9NjYnnzwR5A8Sr3uIPpI9aAr168kKdv33hcxSYrq+009/lS\nlqwkIsuyMimeREvCkgoL1QUmnhqjhaIlVqojRLFAIBAIBNOEJRVWetwBuoYlDAzHH4rgCUayKgCn\nA8Nb7bY1OYZMiUHJXNZqJA4NK/pQJ8XZ9FmXWRSR1OHyx20UqSbFkLyqurkvFseWYlLpK3XXAAAQ\nl0lEQVRsy9WzsMzMH18/iicYGZE6kUiJ2ciickvcV6xObTMRxTlaTbyZb7ysiL1OJhaKXk+QQDg6\nqaJYsVCU8/qhHly+UMbPGxTFYtFOIBAIBIJpQX2Gy3YOrzIVPZkmxaBYENRJa9eAnxaHb4ifGJSJ\ncm1h7ohJcY87iNmgy+pSlzoVbnf5R80oVklWVR0XXCk8xaBEs3mCEYry9awdxXcOcMa8IrYcc+AN\nhtne5CRXr2XBcWZEZ0p9hRWdRmJHBhYKtdJ8MpInErm4voxQROaFhswtFGpknli0EwgEAoFgmrA4\nLopHX7ZTs3xPpvQJiE1aY6J4W+Ngacdw5peYR1RC93qCWZ+cq9FqHf1+2kZps1MpMutHpE9kMoVU\nFzAvri9PW8W9cV4xwUiUt4/2sb3JwbIq64TUdyfDpNeyqNySOoEigVan8nVPdhmGmsv81O6OjJ/T\n6vSRp1fsOyc6QhQLBAKB4KTAbMyhtjA340nxSWefSLAfbG8eLO0YzrzSfBp7vUMSKHrdgazGsYGy\n/FiQp6fN6aPNqWQN5xlS1yMU5xvoGW6fcHix5+bE2/iSsXFuMafVFfLR02rTXtOaWXYMOg3P7e1k\nT1vq0o6JYmWNjZ3NTiJpSmbaYqK4yja5lgRJkriovpxXD3Yz4M/MQtHiUFIyjsdvPV0QolggEAgE\nJw1LKixpRbHamnay2SeKzQa8wQieQJjtjc4hpR2JzCs1E4nKHO0ZTKDodU9MGkeZxRjzFPvSWgGK\nzQb6/WH8oUGxPlryhIo1N4f7b16XUVW2MUfL2rpCHtnaQjgqs3KcucPjZUW1DU8wkrRAJZEWh498\ngw6L6bg71sbMJUvLCIajvLivK6PjT5biDhCiWCAQCAQnEUsqrDT1eUddFFJF8ckUyQaDrXbtLh+7\nWp2srE4+BZ0fT6AYtFD0erI/KYbBrOI2pz9lRrGKGsuWmEDR0udNmVE8Xs6YV0QgHAXGnzs8XtTX\nS2ehaHX6qEjR/jfRrKqxU2I2sClDC8XJklEMQhQLBAKB4CRC9RXvHWVa3OcJopEYURt8oqMWeLxy\noAd/KDoieUJFTaA4GFu2i0Rl+jxBiibATlJmNdLR749VPKefFMNgkUg0KtPizP4UUm1FrC4wxV9z\nsphVmEtBnj6eIZ2KtkmOY0tEo1GKPF7a34UnEB712H5/iH5/+KRYsgMhigUCgUBwElFfYQVGX7br\n9SgZxRrNie+BTEQVeM/uUSZ8w5MnVNQECrXu2ekNEpUnZnJeYTPR5wni8IaoSDMpHl5V3e0OEAxH\nqc7yFHJ+aT5VdhNrZxdm9byZIEkSK6ttbGsaXRRPZptdMi6qLycQjvLy/u5Rj2s9ieLYQIhigUAg\nEJxEFJsNlJgNo06KHZ7gSZc8AYP2g3eP9VFmMY7q4Z1Xks+BmK91sLgj+1PTMsugEB4teQJGttqp\nUV/ZFlySJPHorev5n8sXZ/W8mbKq1s7hbg9Ob/I6ZU8gjNMbonKSl+wSOXV2AYV5ejalKfJQ00Gm\nUsBnEyGKBQKBQHBSkW7ZrtcTxH4SiuKCPD0aCaIyKa0TKvNLzfEECtXDOxFpHIk+4vI0lcXq66vX\nowqubHuKAUosxuMu4xgvq9L4itU4ttEynScarUbiwvoyXtzXNWTxcTit8RsXIYoFAoFAIJh2LKmw\ncqjbnfKHucMzMUkLU41WI8WnvamsEyqJCRRqbnPRREyKE0RxRZpJ8fCqarXNbionphPB8morWo2U\n0kKhiuKpFpqX1JfjDUZGtVC0OHwYczQnzf9PQhQLBAKB4KRiSYWFSFRmX0fy2Ku+k3RSDIMJFOmq\ni+eVDCZQqBXPExLJliCKy9J4imFoq12Lw0dRvh6TPnste9OBXL2OhWVmtqZYtlN9ulN9M7CurgBb\nbg5Pj2KhaI0tBJ4MGcUgRLFAIBAITjKWjLJs9/e3m+j1BNMufZ2oFJsN5Gil+PcgFXXFeWgkONQ5\nQG8sjcM2AbnNuXodVlMOhXn6jCqkE6uqmx3ek2aBazira+0pSzxanT50GmnSkzGGo9NqOH9RKS80\ndA0pekkkkxzpEwkhigUCgUBwUlFdYMJs1A3xFYciUb7xz93892O7OXN+MR9bP2vqLnACuWBJKR9e\nW5tWgBp0WmYV5nGg002PW1k81E5QGke51ZjWT6ySWFWtCK6Tw6s6nFU1djzBCPuTvJvR6vBRbjNO\n2J/HWLh4aRkDgTBvHO5N+niLw3vSLNkBTH5VikAgEAgEE4gkSUOW7XrdAW69bxvvHO3jljPr+MqF\nC6eF4JgIPrw2fdWxyrzSfA52DTCnOJ/CvImbSv7HhtnoMvx+q1XVkahMm9PHJUvLJ+y6phLV872t\nyRHP1laZyozi4Zw+twizQcfTuzs4e0HJkMc8gTAOb+ikunERk2KBQCAQnHQsqbCyr72f3S0u3ver\n19nZ7ORn16zgvy5edNIK4rEyv9TMsV4v7S7/hCRPqHxoTTVXrqrK6NiifKWq+miPh1BEPqkEVyLV\nBSaK8g1JSzwUn+70sCQYdFrOWVTCs3s7CEeiQx5TFwKni4DPBkIUCwQCgeCkY0mFhUA4ypV3v04k\nKvPwp07jipWVU31Z04q5JflEojJ72/snJKN4PKg+2u2xZIbqk8ivmogkSayqGVniEYpE6ez3UzmF\ncWzDubi+DIc3xDtH+4Z8/mQr7gAhigUCgUBwErKi2oYkwbIqG4////buLcausgrg+H/NTKfT0A7t\ntJ2pvUJDKy21QimIAQUqlyIoPmjiLSHeeFEDiURBjEYTHoyJ+qCJIUrkQVGiIoQEpCJGfRDkUqAI\nKGCB6YUKtFxLS9vlw9nTTuu0VeZ09p69/7+kmbO/2ZlZyUr3rPlmnfV98XSWzz30NIYmWjwwBWgd\n81yVkVp7i+JnWzN867pTDK1DPNa/8Pre6R8Am196gz1ZrcMwzlzcT8+EDm5bt3m/9cGazSgGi2JJ\nUg0tnDmZOy5/Lzd87jT6p1Rn161Kjp3RmkABMOMItk/8P4biGDrY4lCn8o13+/qK9x3isa8loTq7\nr5O6OzlrcT+/e2Qze4ZNyxjctp3uzo69YwDrwKJYklRLiwam0N3lj7mD6ZnQmkABR+aI57diaKf4\n8c0vM9A78X8a4zZeLZ97NF0HHOIx1JJQ5ml2I7ngHbPY8sqO/WId3Lqd2VN76KhRj75PC0mSGmrR\nQOsQj6q0T0w/auLeo6rr1Ks6kp4JnZwwu3e/N9vtO+K5Wjvkq47vp7tz/xaKDTWbUQwWxZIkNdai\n/lZf8YySD4oY0tkR9BUF+rwa9aoezEnzp/HQ4Eu8WUx22LhtOzMmV2+HfErPBM5YNIPb120ms9VC\nUcc50hbFkiQ11CnH9tHd1VGpKQ8zilaOuu1CjuTkBdPY/uZuHtvUOsRjw7btlXqT3XCrl81iw7bt\nrNvwMm+8uZvnX91Rq3FsYFEsSVJjnbl4Jg9+/bzSjxQebiiWuu1CjmTFgn2HeECrJaFK49iGO3fJ\nAJ0dwW3rNu1t85jbV68cWRRLktRgk7qr9af6oaJ4Xl/9d4pnH93DQO9E7n9mK5lZHNxRzUJz2lHd\nvHvhdG5ft5nBrdWbktEOFsWSJKkyZk5uzk5xRHDygmnc9/RWXnhtJzt27alsUQytFoqnnn+Nux7b\nAtQvRxbFkiSpMlYe08cJs3srN4HhSFkxfxqDW7eztphXPKfCvdTnnTBABNx477N0dQQDvdVs9Xir\nusoOQJIkaci5Swc4d+lA2WGMmZOKQzxufWgjUL0ZxcP1T+nhlAV93LP+Reb1TaKzRjOKwZ1iSZKk\n0iyb00t3Zwdr/v4cAHMr3qd7/rJZQPXjfCssiiVJkkoysauTZXN6eW3nbiZP7KJ3UrX/iL+6KIqr\nOjpuNCyKJUmSSrSiaKGYPbWHiGq3JMyZOomvXbiEj79rftmhtF21fx2RJEmquRULpsFf/lXpyRPD\nffY9C8sO4Yhwp1iSJKlEJxeHeNSxJWE8cadYkiSpRAO9PXzh7OM4+/j+skNptFEVxRHxHeADwE7g\nSeBTmbmtHYFJkiQ1xRXnv73sEBpvtO0Ta4Blmbkc+Adw1ehDkiRJksbWqIrizLwjM3cVl38F5o4+\nJEmSJGlstfONdp8Gbmvj15MkSZLGxGF7iiPi98CsET51dWbeXNxzNbAL+Nkhvs6lwKUA8+fXb7ad\nJEmSxq/DFsWZec6hPh8RlwAXAe/LzDzE17kWuBZg5cqVB71PkiRJGmujnT6xGvgKcGZmvt6ekCRJ\nkqSxNdqe4h8AU4A1EbE2In7UhpgkSZKkMTWqneLMPK5dgUiSJEll8ZhnSZIkNZ5FsSRJkhrPoliS\nJEmNZ1EsSZKkxrMoliRJUuPFIc7bOHLfNOLfwNNj/o1hBvB8Cd9XY8s8N4N5bgbzXH/muBnKzPOC\nzJx5uJtKKYrLEhH3ZubKsuPQkWWem8E8N4N5rj9z3AzjIc+2T0iSJKnxLIolSZLUeE0riq8tOwCN\nCfPcDOa5Gcxz/ZnjZqh8nhvVUyxJkiSNpGk7xZIkSdJ/aUxRHBGrI+LxiHgiIq4sOx61R0RcFxFb\nImLdsLW+iFgTEf8sPk4rM0aNTkTMi4i7IuLRiHgkIi4r1s1zjURET0TcExEPFnn+ZrF+bETcXeT5\nlxHRXXasGr2I6IyIByLi1uLaPNdMRKyPiIcjYm1E3FusVfq53YiiOCI6gR8CFwBLgY9FxNJyo1Kb\n/BRYfcDalcCdmbkIuLO41vi1C/hSZi4BTgM+X/z/Nc/1sgNYlZnvBE4EVkfEacC3ge8Ved4KfKbE\nGNU+lwGPDrs2z/V0dmaeOGwUW6Wf240oioFTgScy86nM3An8Ari45JjUBpn5J+DFA5YvBq4vXl8P\nfGhMg1JbZeamzLy/eP0KrR+kczDPtZItrxaXE4p/CawCflWsm+caiIi5wIXAj4vrwDw3RaWf200p\niucAzw67HizWVE8DmbkJWgUV0F9yPGqTiDgGOAm4G/NcO8Wf1NcCW4A1wJPAtszcVdzis7sevg98\nGdhTXE/HPNdRAndExH0RcWmxVunndlfZAYyRGGHNsRvSOBIRk4FfA5dn5sutzSXVSWbuBk6MiKnA\nTcCSkW4b26jUThFxEbAlM++LiLOGlke41TyPf6dn5saI6AfWRMRjZQd0OE3ZKR4E5g27ngtsLCkW\nHXnPRcTbAIqPW0qOR6MUERNoFcQ/y8zfFMvmuaYycxvwR1o95FMjYmgDx2f3+Hc68MGIWE+rlXEV\nrZ1j81wzmbmx+LiF1i+5p1Lx53ZTiuK/AYuKd7d2Ax8Fbik5Jh05twCXFK8vAW4uMRaNUtFv+BPg\n0cz87rBPmecaiYiZxQ4xETEJOIdW//hdwIeL28zzOJeZV2Xm3Mw8htbP4j9k5icwz7USEUdFxJSh\n18B5wDoq/txuzOEdEfF+Wr+NdgLXZeY1JYekNoiIG4CzgBnAc8A3gN8CNwLzgWeAj2TmgW/G0zgR\nEWcAfwYeZl8P4ldp9RWb55qIiOW03njTSWvD5sbM/FZELKS1o9gHPAB8MjN3lBep2qVon7giMy8y\nz/VS5POm4rIL+HlmXhMR06nwc7sxRbEkSZJ0ME1pn5AkSZIOyqJYkiRJjWdRLEmSpMazKJYkSVLj\nWRRLkiSp8SyKJUmS1HgWxZIkSWo8i2JJkiQ13n8ANB8B+OIIHvAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13193fd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "smoothing = 0.9\n",
    "z_val = infer_z(smoothing)\n",
    "\n",
    "plot(x, y);\n",
    "plot(x, z_val);\n",
    "title(\"Smoothing={}\".format(smoothing));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Smoothing \"to the limits\"\n",
    "\n",
    "By increading the smoothing parameter, we can gradually make the inferred values of the hidden Brownian motion approach the average value of the data. This is because as we increase the smoothing parameter, we allow less and less of the variance to be allocated to the Brownian motion, so eventually it aproaches the process which almost doesn't change over the domain of $x$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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p+z65aBNs/gK2fglFG43ngiONvvb9j4P4IUbSGxINwVEQ4C4kaBfYa6DeCrXl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VBu51iXL/3Y5Q1TYjNg1A0fkKJ24xBuhUAgmAkkkzLfePowZXYj/3D13Cm7Do1GosJhShsWI035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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x131d9ccf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = subplots(2, 2)\n",
    "\n",
    "for ax, smoothing in zip(axes.ravel(), [0.95, 0.99, 0.999, 0.9999]):\n",
    "\n",
    "    z_val = infer_z(smoothing)\n",
    "\n",
    "    ax.plot(x, y)\n",
    "    ax.plot(x, z_val)\n",
    "    ax.set_title('Smoothing={:05.4f}'.format(smoothing))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "This example originally contributed by: Andrey Kuzmenko, http://github.com/akuz"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
