notebooks/more_kernel_estimation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Scipy vs our code\n",
    "\n",
    "The `scipy` Gaussian kernel density estimation method is [documented here](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gaussian_kde.html#scipy.stats.gaussian_kde).  From reading the source code, and comparing with [\"Density Estimation for Statistics and Data Analysis\" by Silverman](https://books.google.co.uk/books?id=e-xsrjsL7WkC&lpg=PR9&ots=iwStts0DZr&dq=density%20estimation%20for%20statistics%20and%20data%20analysis&lr&pg=PP1#v=onepage&q=density%20estimation%20for%20statistics%20and%20data%20analysis&f=false) see equation 4.7 for example, the method is as follows.\n",
    "\n",
    "- Input is $(X_i)_{i=1}^n$ points in a $d$-dimensional space, say each $X_i = (X^{(i)}_j)_{j=1}^d$\n",
    "- Compute the covariance matrix from this sample:\n",
    "$$ S_{j,k} = \\frac{1}{n-1} \\sum_i (X^{(i)}_j - \\overline{X}_j)(X^{(i)}_k - \\overline{X}_k) $$\n",
    "where $\\overline{X}_j = \\frac{1}{n} \\sum_i X^{(i)}_j$ is the sample mean of the $j$th coordinate.\n",
    "- Letting $S^{-1}$ be the inverse matrix and $|S|$ the determinate of $S$, choose $h$, a \"bandwidth\", and $K$, a \"symmetric kernel\".  Then our density estimation is\n",
    "$$ f(x) = \\frac{1}{|S|^{1/2} h^d n} \\sum_{i=1}^n K\\big( h^{-2}  (X_i-x)^t S^{-1} (X_i-x) \\big) $$\n",
    "- For example, the Gaussian kernel gives $K(t) = (2\\pi)^{-d/2} \\exp(-t/2)$\n",
    "- As stated by Silverman, this procedure is equivalent to applying a linear transformation to the input data so that it has unit covariance, forming the standard KDE, and then transforming back.\n",
    "- The bandwidth can be chosen by eye, or we can use a \"rule of thumb\".  Here we follow `scipy` and use Scott's rule, which is $h = n^{-1/(4+d)}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Some matrix algebra\n",
    "\n",
    "The [covariance matrix](https://en.wikipedia.org/wiki/Covariance) $\\Sigma(X)$ satisfies that if $A\\in\\mathbb M_n$ is a matrix, then $\\Sigma(AX) = A \\Sigma(X) A^T$.  As $\\Sigma(X)$ is positive definite and invertible, we can find an invertible square-root $L$ with $L L^T = \\Sigma(X)$ (e.g. use the [Cholesky Decomposition](https://en.wikipedia.org/wiki/Cholesky_decomposition)).  Thus $\\Sigma(L^{-1}X) = L^{-1} \\Sigma(X) L^{-T} = L^{-1} L L^T L^{-T} = I$.\n",
    "\n",
    "Now apply our KDE method to $Y = L^{-1}X$ to get say\n",
    "$$ g(x) = \\frac{1}{n h^d} \\sum_{i=1}^n k(h^{-1}(x-Y_i)). $$\n",
    "For example, $k(x) = (2\\pi)^{-d/2} \\exp(-x^Tx/2)$ the Gaussian kernel.  Then finally we set\n",
    "$$ f(x) = |L^{-1}| g(L^{-1}x) = \\frac{1}{n h^d} \\sum_{i=1}^n k(h^{-1}(L^{-1}x-L^{-1}X_i)). $$\n",
    "The $|L^{-1}|$ factor occurs to make sure that $f$ is a _normalised_ density.  Notice that $|L^{-1}| = |L|^{-1} = |\\Sigma(X)|^{-1/2}$.  Assuming that $k(x) = K(x^Tx)$ for some $K$ (which is true for the Gaussian) we see that\n",
    "$$ f(x) = \\frac{|\\Sigma(X)|^{-1/2}}{n h^d} \\sum_{i=1}^n K(h^{-2} (x-X_i)^T \\Sigma(X)^{-1} (x-X_i)), $$\n",
    "as we claimed above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy.stats\n",
    "import scipy.linalg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class GaussianKernel():\n",
    "    \"\"\"Expect input as array of shape `(d,N)` of `N` samples in `d`-dimensional space.\"\"\"\n",
    "    def __init__(self, data, bandwidth=None):\n",
    "        self.data = np.asarray(data)\n",
    "        if len(self.data.shape) == 0:\n",
    "            raise ValueError(\"Cannot be a scalar\")\n",
    "        if len(self.data.shape) == 1:\n",
    "            self.data = self.data[None,:]\n",
    "        \n",
    "        self.space_dims, self.num_data_points = self.data.shape\n",
    "        if bandwidth is None:\n",
    "            bandwidth = self._scott()\n",
    "        \n",
    "        self.covariance = np.atleast_2d(np.cov(data, rowvar=1, bias=False))\n",
    "        self.inv_cov = scipy.linalg.inv(self.covariance) / (bandwidth**2)\n",
    "        cdet = np.sqrt(scipy.linalg.det(self.covariance))\n",
    "        \n",
    "        self.normalisation = cdet * (2 * np.pi * bandwidth * bandwidth) ** (self.space_dims/2)\n",
    "        self.normalisation *= self.num_data_points\n",
    "        \n",
    "    def _scott(self):\n",
    "        return self.num_data_points ** (-1 / (4 + self.space_dims))\n",
    "        \n",
    "    def __call__(self, t):\n",
    "        t = np.asarray(t)\n",
    "        if len(t.shape) == 0:\n",
    "            if self.space_dims != 1:\n",
    "                raise ValueError(\"Expect {} dimensional input\".format(space_dims))\n",
    "            t = t[None]\n",
    "        if len(t.shape) == 1:\n",
    "            t = t[None,:]\n",
    "\n",
    "        x = self.data[:,:,None] - t[:,None,:]\n",
    "        x = np.sum(x * np.sum(self.inv_cov[:,:,None,None] * x[:,None,:,:], axis=0), axis=0)\n",
    "\n",
    "        return np.sum(np.exp(-x / 2), axis=0) / self.normalisation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = np.random.random(size=(2,20))\n",
    "k = GaussianKernel(data)\n",
    "kernel = scipy.stats.kde.gaussian_kde(data, bw_method=\"scott\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.random.random(size=(2,100))\n",
    "np.testing.assert_allclose(kernel(x), k(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = np.random.random(size=20)\n",
    "k = GaussianKernel(data)\n",
    "kernel = scipy.stats.kde.gaussian_kde(data, bw_method=\"scott\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.random.random(size=100)\n",
    "np.testing.assert_allclose(kernel(x), k(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = np.random.random(size=(3,20))\n",
    "k = GaussianKernel(data)\n",
    "kernel = scipy.stats.kde.gaussian_kde(data, bw_method=\"scott\")\n",
    "\n",
    "x = np.random.random(size=(3,100))\n",
    "np.testing.assert_allclose(kernel(x), k(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stocastic declusting\n",
    "\n",
    "To convert the \"stocastic declusting\" algorithm into a more \"EM-like\" algorithm, I would like to do the following:\n",
    "\n",
    "- Start with data $(X_i)_{i=1}^m$ and a probability distribution on $\\{1,2,\\cdots,m\\}$.\n",
    "- Using the probability distribution, sample from the data, giving $(Y_i)_{i=1}^n$ say.\n",
    "- Form the density estimate $f$ using $(Y_i)$.\n",
    "- Thus $f$ is a random variable, and it makes sense to ask what the expectation of $f$ is (with respect to our probability distribution on $\\{1,2,\\cdots,m\\}$).\n",
    "\n",
    "This unfortunately seems rather computationally difficult:\n",
    "\n",
    "- The covariance matrix is non-linear\n",
    "- The normalisation factor $1/m$ is non-linear.  Even this alone seems hard to deal with: [Math.Stackoverflow question](https://math.stackexchange.com/questions/2357192/expectation-of-repeated-sampling)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Is this even correct?  Suppose we really have a _parametric_ distribution, for simplicity\n",
    "$$ f(x; \\mu) = \\frac{1}{\\sqrt{2\\pi}} e^{-(x-\\mu)^2/2} $$\n",
    "i.e. a Gaussian with unknown mean.  The EM algorithm would look at log likelihood and in general boils down to calculations like\n",
    "$$ \\sum_{i=1}^n p_i \\frac{\\partial f / \\partial \\mu}{f} (x_i) = 0, $$\n",
    "where $(x_i)$ are points, and we deem $x_i$ to have been chosen from the distribution with probability $p_i$ (and chosen from some other distribution with probability $1-p_i$).  What makes this work is that here we have linearity and so can use linearity of the expectation.\n",
    "\n",
    "Continuing the example, we find that\n",
    "$$ \\sum_i p_i(x_i-\\mu) = 0 \\quad\\Leftrightarrow\\quad \\mu = \\sum_i p_ix_i. $$\n",
    "So we end by estimating as the weighted sum of the $(x_i)$.\n",
    "\n",
    "Alternatively, imagine sampling from the $(x_i)$ as before to get $(y_i)_{i=1}^k$ and then using the $(y_i)$ to estimate $\\mu$: we get $\\mu = \\frac{1}{k} \\sum_i y_i$.  Suppose we repeat this many times, and then take the average $\\mu$.  What is this?  Well,\n",
    "$$ \\mathbb E(\\mu) = \\sum_{A\\subseteq [n]} \\prod_{i\\in A} p_i \\prod_{i\\not\\in A} (1-p_i) \\frac{1}{|A|} \\sum_{i\\in A} x_i, $$\n",
    "i.e. exactly what I asked in the Math.SO question.\n",
    "\n",
    "Simple case: $n=2$.  Then we get\n",
    "$$ (1-p_1)(1-p_2) 0 + p_1(1-p_2) x_1 + p_2(1-p_1) x_2 + \\frac12 p_1p_2(x_1+x_2) \n",
    "= x_1 p_1\\big(1-\\frac12 p_2\\big) + x_2 p_2\\big(1-\\frac12 p_1\\big) $$\n",
    "\n",
    "**Moral of the story:** These are simply not the same!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example: 1D mixture model\n",
    "\n",
    "Sample $(X_i)_{i=1}^n$ where each $X_i$ is chosen from $N(\\mu_0,1)$ or $N(\\mu_1,1)$.\n",
    "\n",
    "The EM algoritmn is to iterate these two steps:\n",
    "\n",
    "1. Set, using the current estimates for $\\mu_0, \\mu_1$,\n",
    "$$ p_{i,0} = \\frac{e^{-(x_i-\\mu_0)^2/2}}{e^{-(x_i-\\mu_0)^2/2} + e^{-(x_i-\\mu_1)^2/2}},\n",
    "\\qquad\n",
    "p_{i,1} = \\frac{e^{-(x_i-\\mu_1)^2/2}}{e^{-(x_i-\\mu_0)^2/2} + e^{-(x_i-\\mu_1)^2/2}}. $$\n",
    "2. Choose new estimates by\n",
    "$$ \\mu_0 = \\frac{\\sum_i p_{i,0} x_i}{\\sum_i p_{i,0}},\n",
    "\\qquad\n",
    "\\mu_1 = \\frac{\\sum_i p_{i,1} x_i}{\\sum_i p_{i,1}}. $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = 20\n",
    "mu0, mu1 = 1, 5\n",
    "actual0 = [i for i in range(N) if np.random.random() < 0.5]\n",
    "\n",
    "x = []\n",
    "for i in range(N):\n",
    "    if i in actual0:\n",
    "        x.append(np.random.normal(loc=mu0))\n",
    "    else:\n",
    "        x.append(np.random.normal(loc=mu1))\n",
    "x = np.asarray(x)\n",
    "x.sort()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Via parameter estimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0272444383208252, 4.6669915189066877)"
      ]
     },
     "execution_count": 159,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def make_p(x, mu0, mu1):\n",
    "    p0 = np.exp(-(x-mu0)**2/2)\n",
    "    p1 = np.exp(-(x-mu1)**2/2)\n",
    "    return np.vstack([p0 / (p0+p1), p1 / (p0+p1)])\n",
    "\n",
    "def estimate_mu(x, p):\n",
    "    return np.sum(p[0] * x) / np.sum(p[0]), np.sum(p[1] * x) / np.sum(p[1])\n",
    "\n",
    "hatmu0 = 0\n",
    "hatmu1 = 10\n",
    "\n",
    "for _ in range(20):\n",
    "    p = make_p(x, hatmu0, hatmu1)\n",
    "    hatmu0, hatmu1 = estimate_mu(x, p)\n",
    "\n",
    "hatmu0, hatmu1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ldXy57yizRiUR4OOlO45TuGdcNywGzN2QqzuKcEaN1ZDxNvS7DsITdadxDoOnQ2Bn2PSy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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f12c93f0710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = make_p(x, hatmu0, hatmu1)\n",
    "class0 = p[0] < p[1]\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10,5))\n",
    "\n",
    "x0 = x[class0]\n",
    "ax.scatter(x0, [0]*len(x0), color=\"red\")\n",
    "x1 = x[~class0]\n",
    "ax.scatter(x1, [0]*len(x1), color=\"blue\")\n",
    "\n",
    "xx = np.linspace(-2, 7, 100)\n",
    "ax.plot(xx, np.exp(-(xx-hatmu0)**2/2) / np.sqrt(2*np.pi))\n",
    "ax.plot(xx, np.exp(-(xx-hatmu1)**2/2) / np.sqrt(2*np.pi))\n",
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stocastic declustering\n",
    "\n",
    "At each stage, we use the current estimates of the kernels to build the probability density of the \"hidden variables\", and then sample: this makes a random choice for which class each point is in, given the current kernels.\n",
    "\n",
    "Using this random choice, we use `scipy.kde` to build new estimates for kernels, and then repeat.\n",
    "\n",
    "This actually doesn't perform as well as we might hope: it does fine for small datasets, but tends to converge to the kernels being equal sometimes..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x0 = [x < np.mean(x)]\n",
    "x1 = [x >= np.mean(x)]\n",
    "\n",
    "for _ in range(1000):\n",
    "    k0 = scipy.stats.kde.gaussian_kde(x0)\n",
    "    k1 = scipy.stats.kde.gaussian_kde(x1)\n",
    "    \n",
    "    p0, p1 = k0(x), k1(x)\n",
    "    p = np.vstack([p0/(p0+p1), p1/(p0+p1)])\n",
    "    \n",
    "    choice = np.random.random(size=len(x)) <= p[0]\n",
    "    x0 = x[choice]\n",
    "    x1 = x[~choice]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cl0FaUoLrKFGpQJsxywGlD0F6bxh6vuskkSc+ASZMhc0fQsVi12kkBDotrIwx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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f12c8ce4710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,5))\n",
    "\n",
    "ax.scatter(x0, [0]*len(x0), color=\"red\")\n",
    "ax.scatter(x1, [0]*len(x1), color=\"blue\")\n",
    "\n",
    "xx = np.linspace(-2, 7, 100)\n",
    "ax.plot(xx, k0(xx))\n",
    "ax.plot(xx, k1(xx))\n",
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stocastic declustering with repeatition\n",
    "\n",
    "At each stage, instead of taking one sample, we take many samples, compute many kernels, and then take the average.\n",
    "\n",
    "This suffers from the problem above, but only more so: if there is not a good \"gap\" between the two sets, we tend to find poor convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def combine(kernels):\n",
    "    def kernel(t):\n",
    "        return np.mean(np.asarray([k(t) for k in kernels]), axis=0)\n",
    "    return kernel\n",
    "\n",
    "def make_kernels(x, p, samples=100):\n",
    "    k0, k1 = [], []\n",
    "    for _ in range(samples):\n",
    "        choice = np.random.random(size=len(x)) <= p[0]\n",
    "        x0 = x[choice]\n",
    "        x1 = x[~choice]\n",
    "        k0.append(scipy.stats.kde.gaussian_kde(x0))\n",
    "        k1.append(scipy.stats.kde.gaussian_kde(x1))\n",
    "    return combine(k0), combine(k1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p0 = np.array(x < np.mean(x), dtype=np.int)\n",
    "p1 = np.array(x >= np.mean(x), dtype=np.int)\n",
    "p = np.vstack([p0/(p0+p1), p1/(p0+p1)])\n",
    "\n",
    "for _ in range(1000):\n",
    "    k0, k1 = make_kernels(x, p)\n",
    "    \n",
    "    p0, p1 = k0(x), k1(x)\n",
    "    p = np.vstack([p0/(p0+p1), p1/(p0+p1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RCOjKitUMYIu1tsRa2wI8BnxgMpy1tt7+93xBJqBzBxJW+xtaKKs5qMb1MNLI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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f12c945a898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,5))\n",
    "\n",
    "xx = np.linspace(-2, 7, 100)\n",
    "ax.plot(xx, k0(xx))\n",
    "ax.plot(xx, k1(xx))\n",
    "\n",
    "None"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mixed KDE\n",
    "\n",
    "Here we try our rather tentative idea of using the probability \"weights\" directly in the KDE construction.  This suffers from the same problem: we converge to the case of no mixture."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def kde(x, p, training):\n",
    "    # `training` used only for bandwidth selection.\n",
    "    s = np.var(training, ddof=1)\n",
    "    scott = len(training) ** (-1 / 5)\n",
    "    band = 1 / (s * scott * scott)\n",
    "    norm = np.sqrt(band / (2 * np.pi)) / np.sum(p)\n",
    "    def kernel(t):\n",
    "        t = np.asarray(t)\n",
    "        if len(t.shape) == 0:\n",
    "            t = t[None]\n",
    "        xx = (x[:,None]-t[None,:])**2 * band\n",
    "        return np.sum(p[:,None] * np.exp(-xx/2), axis=0) * norm\n",
    "    return kernel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p0 = np.array(x < np.mean(x), dtype=np.int)\n",
    "p1 = np.array(x >= np.mean(x), dtype=np.int)\n",
    "p = np.vstack([p0/(p0+p1), p1/(p0+p1)])\n",
    "\n",
    "for _ in range(10000):\n",
    "    k0 = kde(x, p[0], x[p[0] > 0.1])\n",
    "    k1 = kde(x, p[1], x[p[1] > 0.1])\n",
    "\n",
    "    p0, p1 = k0(x), k1(x)\n",
    "    p = np.vstack([p0/(p0+p1), p1/(p0+p1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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E3iUCDB6s9VRz5ji3wu+JJ4A//9TR8r179W8rq6NgRF7AxIqyRkTfLFu3zv4ZaDAS4epJ\nCg7GaP3lhQtaM+WU0FBg0iSgQgXg7bc1qRo/nn9X5HOY7lPWxMRor5kOHWxH4h8OHtSVTZMm2Y6E\nyLM2bAAeeEBrMIsXdzapSmUM8NZbwKBB2iOOC0PIB3HEirKmVCntRcPlz+4pVQo4coQF7BTYYmKA\nzp21d9vx455JqtJ66y3gvvuAevU8+zhE2cDEirImdUorTx7bkfiHkBB98+eZNQWq+Hjgjjt0dHbx\nYs8nVYC+B6UmVd9/rzWfHTt6/nGJ3MCpQHLf2bPaFPS772xH4l/q19cRK65kokDUr59uxv7VV9p3\nypuSkoB33gHuvVe3xyHyAUysyH0LFui+XiVL2o7EvzRoABw7pmf0RIFk/35g8mTgxRdd3dO9KSQE\n+PFHIF8+oEsX4NQp78dAdAkmVuS+OXN0364WLWxH4l+aNdOi3gsXbEdC5Kzy5YG1a7XmyZZKlYDp\n0/Wkr3dvjgyTdUysyD2pbRbatNFlz+S+xo2Br7/W1YFEgSApCfjpJ31fqF7d/nvCDTdoE9KpU4E/\n/rAbCwU9Jlbkns2bdTVgu3a2I/FPIrr5LFEgGDNGC9YXLrQdicugQVrI3qaN7UgoyDGxIvc98ABw\n2222o/BP3boBt9xiOwqinNu5ExgyRFfh3Xyz7WhcQkKA7t11xWB0NFvCkDVMrMg9depwOisnqlTR\nVUvJybYjIco+Ed1aJiRE9+7zxa7ne/YA4eHAe+/ZjoSCFBMrylxiIrBtG4tCc6JuXSA2Vt/0ifzV\nxIm6OnjkSN1axhdVrgy0bQsMGwZs3Gg7GgpCTKwoc2vWALVqATNm2I7Ef9Wtq5cbNtiNgygn8ucH\n7rxTR6182bhxwFVXAT17ckqQvI6JFWVu3jy9vOEGu3H4s/BwvWRiRf7s3nu1tUEuH//oKFVKk6tV\nq/SSyIt8/K+DfMK8ecC11wIlStiOxH8VKaKrlq67znYkRFn399/A2LH+Nfpz991A+/YaO5EXGbFU\nNxMRESFRUVFWHpuyIDYWKFoUePZZrasgouCSnKyj1du3A1u26EmCv4iL067sRA4wxqwRkYjMbscR\nK7qyyEjtGN66te1I/F9CAlcGkv+ZNg1YvhwYMcK/kirAlVRt2QKsWGE3FgoaTKzoyho2BL74AmjZ\n0nYk/u+rr7TWavdu25EQuef8eWDwYH0fePhh29FkjwjQowfw4INAfLztaCgIMLGiKytVCnj0UaBA\nAduR+L/UlYFcAk7+YuxYbREycqTvF6xnxBgdbduxQ58PkYf56V8KecWZM8CECcDhw7YjCQxcGUj+\n5uqrgaee8v9SgLZttZD9jTeAmBjb0VCAY2JFGYuMBHr1Atavtx1JYChSBChXjokV+Y/OnYHx421H\n4Yz33wfOngVee812JBTgmFhRxhYvBvLkAZo1sx1J4Khbl1OB5Puio4HhwzURCRR16gB9+mjLCO4i\nQR6U250bGWPaARgFIATA5yIyIoPbXQdgBYAeIjLdsSjJjsWLte9S/vy2Iwkczz2nS8CJfNkbbwBf\nfgncfz9QsKDtaJwzapRv7m9IASXTxMoYEwJgHIA2AKIBrDbGzBKRjenc7h0Av3siUPKys2eB1auB\nAQNsRxJYOna0HQHRlW3frnsC9u4deJuupyZVUVHaRqZ5c7vxUEByZyqwCYDtIrJTRC4AmAqgazq3\newbADwCOOBgf2bJ6NZCUBNx0k+1IAktCAvDnn8DevbYjIUrfa69pCcCQIbYj8YykJB2Je+IJ/+ok\nT37DncSqPIB9aa5Hp3zvP8aY8gC6Afj4SndkjOlljIkyxkTFcGWGb7v5ZmDXLiZWTjt3Drj+euDb\nb21HQnS5jRuBb74BnnkGKFPGdjSeERICvPOOPtfPPrMdDQUgp4rXPwIwUESu2FJaRD4TkQgRiShZ\nsqRDD00eU6UKkDev7SgCS5EiQPnyXBlIvikuTk+q+ve3HYlnde2qz3PYMOD0advRUIBxJ7HaD6Bi\nmusVUr6XVgSAqcaY3QC6AxhvjLndkQjJ+2Jjdah85UrbkQSm8HAmVuSbGjcG5s8P/A3XjdFRq6NH\ngQ8/tB0NBRh3EqvVAGoaY6oaY0IB9AAwK+0NRKSqiFQRkSoApgPoIyIzHI+WvOPPP3U64Ngx25EE\nprp1uWcg+Z7p04OreeZ11wH33ce/Q3JcpomViCQCeBrAXACbAHwnIhuMMb2NMb09HSBZEBmpZ3Rc\nMeMZdevqlAv3DCRfsWuX7qc3It1OOoFryhTg9ddtR0EBxq0+ViIyB8CcS773SQa3fSTnYZFVy5bp\nh3/RorYjCUxt2wKzZuk+jES+YMQILeru1892JN6V2n5h3jxtIFq+/JVvT+QGdl6niyUlAcuXAy1b\n2o4kcFWsqFuFBFLjRfJf+/ZpM9DHHgvOxOLgQaBDB+D//s92JBQgmFjRxQ4cAIoXZ2LlaZGRwNy5\ntqMgAt59V7d4GTjQdiR2lC0LPPkk8MUXwLZttqOhAGDE0p5JEREREhUVZeWxyQ3JyUAu5t0e07at\nrkhas8Z2JBTMRLT1QKlSwOef247GnsOHgWrVgC5d2GOOMmSMWSMiEZndjp+clD4mVZ4VHs6VgWSf\nMVrv9/EVezsHvtKlgeefB6ZOBdautR0N+Tl+etLFmjYFPvrIdhSBjysDybbjx11bK+XJYzcWX9C/\nvzZF3rrVdiTk55hYkcvevcCqVUButxaLUk7UrauXGzde+XZEnvLRR0CtWsARbu8KQHdF2LYNuPtu\n25GQn2NiRS6RkXrZooXdOIJBeLhesgM72XDuHDBuHNC+Pdt+pJU7t07PL1liOxLyY0ysyCUyErjq\nKqBePduRBL7ChbWtxZNP2o6EgtHEiToVOGCA7Uh8zxdf6ObzK1bYjoT8FFcFkkvDhkDJksAff9iO\nhIg8JTERqFFD+6ktXWo7Gt9z7pzWWjVqxJYodBGuCqSsEQEiIoBu3WxHEjzWrgXefJMrA8m7IiOB\nPXs4WpWRAgX0Z/P77zqqTJRFHLEisuWzz3QqcPduoHJl29FQMNm8WQvX2VYlfefOaV+rBg00wSIC\nR6woq06f1lEr8p7UAnauDCRvSUzUy9q1mVRdSeqo1bp1XDVJWca/LFIPPgg0b247iuBSp45eMrEi\nb+ncGXj2WdtR+Ie+fYGdO7lqkrKMiRXpSNWKFcDVV9uOJLgUL65v2ps22Y6EgsHatcBvvwHlytmO\nxD/kzQvkzw8kJOhGzURuYidIAnbtAmJigGbNbEcSfMLDOWJF3jFyJFCwINC7t+1I/MvNNwNhYcD8\n+bYjIT/BESty9Wu5/nq7cQSj//2Pb9jkeXv2ANOmAb16aYdxct+ddwILFrBpKLmNiRUBK1dqseY1\n19iOJPiUKwfky2c7Cgp0H36oGy4//7ztSPxP795AmTLAsGG2IyE/wcSKgHbtgP/7PyAkxHYkwefg\nQeDFF4G//7YdCQWyZ57RjuIVK9qOxP/kywcMGgQsWqRfRJlgHysimw4dAsqWBUaP1g8/IvI9cXFA\n9epAq1bAN9/YjoYsYR8rcs/Bg7oRMLt/21G6NFC0KAvYyTPi4oAHHgD++cd2JP4tXz5g3jxg0iTb\nkZAfYGIV7KZM0dqqo0dtRxKcjOHKQPKcyZN1gcTx47Yj8X/h4UCePEB8PJsp0xUxsQp2K1fqEDeb\n4NlTpw4TK3JeUhLw/vu6B2irVrajCQz//ANUrcpaK7oiJlbBLLUxKNss2BUeDsTGAidP2o6EAsnM\nmcC2bUD//joySjmX2kT5tdc4akUZYmIVzPbt0xorNga1q08f4MwZ9hci54gA776rGwnfcYftaAJH\n3rzA4MHa04qjVpQBJlbBjI1BfUNYGDfEJWclJAAtWwJDhgC5ucGGo554QvvPcdSKMsB382B28826\ndLh+fduR0AsvAKNG2Y6CAkVoKPDee8Cjj9qOJPCkHbVatsx2NOSDmFgFs1KlgHvv1ZUuZNeyZcDP\nP9uOggLB9u3AH39wNMWTHn8cmD4daN7cdiTkg9xKrIwx7YwxW4wx240xg9I53tUYs84Ys9YYE2WM\nael8qOSo+Hhg3Dhg717bkRDAlgvknLffBrp2ZYsFT8qbV/cQ5BQ+pSPTV4UxJgTAOADtAYQDuNcY\nE37JzeYDaCAiDQE8CuBzpwMlh/31F/D008CaNbYjIUATq4MHuTKQcubAAeDrr3UKsHhx29EEvvHj\nNYnl6CCl4U663QTAdhHZKSIXAEwF0DXtDUTkrLj2xikAgK8yX7dypV6ycN03hKecq2zaZDcO8m+j\nR2v/qn79bEcSHESAWbOAhQttR0I+xJ3EqjyAfWmuR6d87yLGmG7GmM0AfoGOWl3GGNMrZaowKiYm\nJjvxklNWrAAqV9Z96si+8HCgTBlO31D2nT4NfPwx0L27tlkgz3vsMaB8ea4QpIs4NkEsIj+JSG0A\ntwN4I4PbfCYiESISUbJkSacemrJj5UqOVvmSatV0KrBjR9uRkL9atw4ICdGGoOQdqSsEly7lqBX9\nx53Eaj+AimmuV0j5XrpEZAmAasaYEjmMjTzl4EFtDsrGoESBo2VLYP9+3cKGvIejVnQJdzrHrQZQ\n0xhTFZpQ9QBwX9obGGNqANghImKMaQQgDMAxp4Mlh5Qtq2/AYWG2I6G0Ro8GZs8Gfv/ddiTkb/bt\n0w/3fPlsRxJ88uYFxowBChSwHQn5iEwTKxFJNMY8DWAugBAAE0VkgzGmd8rxTwDcCeAhY0wCgDgA\n96QpZidfVK6c7QjoUmfOaP+hs2eBggVtR0P+IikJaNMGaNAAmDbNdjTBqVs32xGQD3GrxkpE5ohI\nLRGpLiLDU773SUpSBRF5R0TqikhDEWkmIpGeDJpyaOhQvgH7otSVgZs3242D/MvMmcCWLdwT0LYz\nZ7S+jbVWQY/dzYLNhQu61cWff9qOhC5Vp45eslEouUsEGDECqF5dG1aSPaGhwLffAq++ylqrIMfE\nKtisWwecP8/CdV9UvbpuL8TEity1cCGwejUwYAA3W7YtLAx4+WUgMhJYsMB2NGQRE6tgw8agvitP\nHuC224DChW1HQv7ik0+0/9lDD9mOhACuECQA7q0KpECyYoUWrleoYDsSSs/s2bYjIH8yaZLWV+XN\nazsSAlyjVn376qjVrbfajogsYGIVbGJidEd2Y2xHQkQ5IaLtFRo2tB0JpfXYY3oCy70agxanAoPN\n779rgSX5puXLgYoVtW6GKCNbtgC1armm9sl3hIXpRthMeIMWE6tgxCJX31WqFBAdDaxfbzsS8mUj\nR+rrpGpV25FQRvbs0RWbrLUKOkysgsmIEbpBK//QfVfVqjq9w8SKMhIdDUyeDDz6KFC6tO1oKCO/\n/KL7CM6fbzsS8jImVsFkzhx9U2Z9le8KCdF+VkysKCPvvKMnR9xs2bdxhWDQYmIVLBIStG6H/at8\n3zXXMLGi9B04AEyYADz8MFCliu1o6EpSVwguWwbMm2c7GvIiJlbBYu1abQzavLntSCgzbdroV0KC\n7UjI15QqBXz6KTBkiO1IyB2PPQZUqqS/L45aBQ0mVsFi+XK95IiV73vgAeCrr7RhKFFauXPraBWL\n1v1DWJhOBVapopurU1BgYhUsChTQrt5sDOofRIC4ONtRkC95801g1CjbUVBW9ewJfPcdcNVVtiMh\nL2FiFSwefxyYO9d2FOSuqlWBl16yHQX5ikOHgOHDdUqf/NPGjcDixbajIC9gQ6NgkJCgq81yMY/2\nG+XLs4CdXN59V/+OWVvln0R0P8cTJ4BNm4DQUNsRkQfxkzYYzJgBFCsGbN1qOxJyV+rKQBa80uHD\nutny/fcDNWrYjoaywxjg9deBnTuBiRNtR0MexsQqGCxfDly4wIJXf3LNNcDx4zoFRMFt5EggPh54\n5RXbkVBOdOigq7LfeIP1kwGOiVUwWL4cuO46rjLzJ/Xq6eW6dXbjIPtatQKGDQNq1rQdCeWEMcBb\nb2kvsvHjbUdDHsTEKtDFxQF//cX+Vf6mQQPg6aeBMmVsR0K2deoEvPqq7SjICTfdpCNXR47YjoQ8\niMXrgS4qCkhMZGLlb4oWBcaMsR0F2bRrl9bj9O8PFCpkOxpyyqxZupiIAhZHrAJd8eLAM8+wMag/\nSkjggoNpk4d9AAAgAElEQVRgNnQo8P77wJkztiMhJ6UmVStXAseO2Y2FPIKJVaALDwdGjwZKlLAd\nCWXV66/r7+/8eduRkLf9/Tfwv/8Bzz+vrTcosOzbB7RooRtqU8BhYhXIRPQNOjHRdiSUHfXrA0lJ\n2veGgsvgwdoiZcAA25GQJ1SsqFtXjRmjxewUUJhYBbIdO4BGjYAvvrAdCWVHgwZ6+c8/duMg75o/\nX3dJGDIEKFLEdjTkKa+9pidOb75pOxJyGBOrQLZihV6ycN0/1agB5MvHxCrYFC4MdO8O9OljOxLy\npKpVgSeeACZMALZvtx0NOYiJVSBbvlxXE4WH246EsiMkRPtZMbEKLhERwPffA3nz2o6EPG3oUF0B\nHBVlOxJyENstBLLly4Hrr+fSXn82aBB/f8EiIUG7cvftC5QubTsa8oYyZYA9e3RkmgKGWyNWxph2\nxpgtxpjtxphB6Ry/3xizzhjzrzFmuTGmgfOhUpacPq17zXEa0L916wZ06WI7CvKGTz7RxGrNGtuR\nkDfly6cLjZYu5d6gASLTxMoYEwJgHID2AMIB3GuMuXRuaReAm0SkHoA3AHzmdKCURXny6HTCPffY\njoRyIiFBa+X27LEdCXnS0aPaXb11a6B9e9vRkLfNnAnceCPw88+2IyEHuDNi1QTAdhHZKSIXAEwF\n0DXtDURkuYicSLm6EkAFZ8OkLMuXD7jjDqB2bduRUE7Exemo4//+ZzsS8qShQ7UR6KhRuqccBZdO\nnYCrrwYGDmR7nADgTmJVHsC+NNejU76XkccA/JreAWNML2NMlDEmKiYmxv0oKeumTgX+/dd2FJRT\nhQrp6iEWsAeuf/4BPvtMa6u40CQ45c6tzUI3b2Z7nADg6KpAY8zN0MRqYHrHReQzEYkQkYiSJUs6\n+dCU1oULwKOPAp9/bjsSckLDhrqRNgWmAgWAu+7SvkYUvLp0AVq2BIYNA86etR0N5YA7idV+ABXT\nXK+Q8r2LGGPqA/gcQFcR4QZINq1Zo1NIN95oOxJyQkSE9rk5dcp2JOQJNWroCHPRorYjIZuMAUaO\n1BPjdetsR0M54E5itRpATWNMVWNMKIAeAGalvYExphKAHwE8KCLcNda2JUv08oYb7MZBzmjcWC85\nahVYjh0DHnkEiI62HQn5iuuv130EuZrbr2WaWIlIIoCnAcwFsAnAdyKywRjT2xjTO+VmrwIoDmC8\nMWatMYbdzmxaskSL1kuVsh0JOaFZM+CXX3R7IgocgwYBU6YAx4/bjoR8SYECQHKytl8gv2TEUt+M\niIgIiWK3WeclJwPFiwN33w18+qntaIgoPZGROqLcvz/w7ru2oyFf89FHwAsvAKtWAdddZzsaSmGM\nWSMiEZnejolVADp2TGusKrDrRcBYtw5Ytgx46inbkVBOxcXpgoT4eGDDBh2hIErr9GmgVi2genVN\nwtmCwye4m1hxr8BAVLw4k6pA88svuinviROZ35Z82/DhwNatumqXSRWlp1AhfZ0sX64LG8ivcK/A\nQPPWW1pb9fjjtiNxXHKyNiBftw7YtAnYu1fzjFOn9ATv7FkdDLh0ENYY3c+2QAGgYEHgqquAwoU1\n96xRQ1sHhYcD+fPbeV5uiUg5SfrrL+DWW+3GQjnTty9QsaJ2WSfKyCOPAOPGAQMGaCsGJuF+g4lV\nIBHRufkOHfw2sUpM1JO0JUuAv//WE/v9+7UptTsNiXPlunzUXMT1dSXGaMP64sX1c+/qq4Frr9XP\nvzp1sv+cHJFauB4VxcTKX8XHayPIsmWBJ5+0HQ35upAQ7cTfowewbZtOH5NfYGIVSDZsAGJigJtu\nsh2JWxITgd9/B2bPBv78E9ixI/1WTQUKAOXLAyVL6mXlyjrSVKOGXi9TBihRQpOqK0lO1lGtw4eB\ngwf18bZvB3bvBg4c0O8fOaLH9u3TBO/LL/X/5sqlbYaqVtXuB23bAh07AqGhjv9Y0le8uD44N+j1\nX/366VDr3Lm6lydRZm64Adi5EwgLsx0JZQETq0Ayf75e3nKL3TgycOEC8N13ujf0qlWayKQdRSpY\nEKhXT0eJrrsOuPlmHSnKLGFyV65cWrpQqBBQs+aV+6fGxgIrV+r+x6tXa866f78OGEVFuRZcFimi\nMbZqBdx/P1C3rjOxpqtxY/ay8lc//wyMHw+8+CKTKsqasDB98/zjDz2bI5/HVYGBpEsXYONGHYbx\nEStWAGPHAgsWAIcOub6fJ48OwLRooe8VHTtqHZSvO3/eNcq2YoWeTMbGuo6HhelinvbtgV69dFGP\nY/bt06ywcGEH75Q87uBBoH59LepbuZKjD5R1778PvPSS9rZq2dJ2NEGL7RaCUatWOnzy8cfWQkhM\n1P1kJ08G1q7VshJAS0tq1NB6pYcfdtViB4Ljx4Fp04CZM3U061iaDZ3y5dNfSceOuqivTBl7cZIF\niYnAbbdpQvXXX9q4lyirzp3TFTaFCunriKOeVjCxClbJyc7NnbnpwgWdGpswQafMkpP1+0WL6ojU\nk09qPb2Xw7Lm7FlNLH/4Qd8DT550HStWTKcg+/QB2rTJ4h2LAG++CVSrpvOO5Pu2bdM6mXffBR56\nyHY05M9mzAC6ddPRq379bEcTlJhYkUclJwNffw188AGwfr0rmSpbFrjzTmDgQLbSSnX8OPDFFzqq\n9e+/mogCetJZty5wzz2aaBUq5Mad1a8PlCsH/PabR2MmB506xelbyjkRoHNnYPFiXQTBN1ivY2IV\nbG6/XZfLjRrl0YdZvRoYOhRYuNCVIJQrp8nUoEH6b7qyRYu0Pc3ixbqIM1XFinpCOnDgFX6OvXtr\nw8Djx4NnCNAfbdigqzSGDtVl8wHu9Gl9ylu3aklZTIy+RE+e1Lzy/HkgIQFIStLZ0cREbW+SJ4/r\nKzRUp86LFdNVvqVK6dR5pUpAgwbc+hSAFnV266bLlbl3qNcxsQomcXE679a3rw4TO+zsWeDVV4FJ\nk1z7xRYqBHTtCrzxhuZzlD1Hj2px/7Rp+qGUOvJXqpQWwA8ceEkPrcmTtUht/XoPL0GkbDt8GGja\nVAsM//pLh3H9WGKitkNZvVpfdjt2ANHR+tqNjdWEKSsfI+n1mXNXaKi2XyleXN936tYFmjTRDjNB\nM4Ajwi1uLGFiFUzmz9eq8NmzHV2Ou2gRMHiwvqmK6Il3y5aaZPloRwe/duGC7nIycSLwzz+uhqhF\niujPe8AAoGnx7dor4rPPgCeesBswXS4uTvuErFunXW79aJVGbKyu3k1tzrttm/Z1i4u7/La5cmmC\nU6iQjjCVKqU95SpV0tHW1NGmcuU0r3RnxW9ysiZr0dH6dfCgriTev193WTh4UBeGnDqlsaaehKSN\nqUgRXW0cEaF/Mx06aBuXgHPuHDBmDPD88/6xnDpAMLEKJi+/rMWxJ07ofi05kJioW1SNGeNa3Vam\njM5ADR7sxYaYQS45WWeSxo3Tnl+pqyvz5xPsSa6AU3c9gepfv2Y1RrpEYiJw991aZPzjjzo976OO\nHAF++klbI61dq8nL+fMX3yYkRBOVSpV0QVqDBtpKrUkT30hWjhzRJHDVKq1d3L5dG/2mbX8CaAJY\no4auIbjrLj059PtZ9AULdAeG11/XM13yCiZWweTaazWhWrIk23dx6JCe/Pz4ow7t58qlq9fefVeb\ndZJdc+fqbkVLlwLx5xKQiDzImxe4/nrg2Wd1WtbvPyz83ZIlOlr10UfAM8/YjuY/sbE61fzzzzoS\nun+/K1EH9HVTvLj2XGvQAGjeXDtE+GtrkPPngXnzNGn8809gy5aLV+YaoyNpLVvqQs127fz0b6dH\nD03i16/XzJE8jolVsEhO1jmi8HDg0Uez/N9XrACee077L4no2V3PnsA77/j4psRB7M8/9fczf74W\nDQNa/BsRoasL77vPTz8oAsHmzdZ7VR09qqV4s2drIpVaFwno66JECa3ba9FC66AbNQr818v589pn\nbuZM/fvZs0cL6QF97ql7Yj/7rC689QsHDugvslEjfTMI9F+iD2BiRVf02WdaeB4drdcrVgReeUX3\nbubfp4/bu1dPtQcNwrpy7TBihI5opX6A5s6tIw9PPAE89pheJw9JTtah3tatdecDC3bt0kVic+fq\nxgtnz7qO5c2rJXm33qqtz/yo5MujkpO1hnTSJF2du2+fq2YrXz6d8nzgAT3J9OnyhwkTdIuHTz7h\nxt5e4G5iBRGx8tW4cWMhB2zcKHLhgls3TUoSef11kcKFRQARY0SaNBFZvtzDMZKzYmNFcucWGTTo\nom9v3SrSs6dIqVL6+wVEcuUSqVdP5P33ReLiLMUbqBISRB58UH/QQ4Z47WHXrBF59ln9vebN6/pd\nAyJXXSXStKnIsGEiu3d7LSS/l5QkMnWqyG23iRQq5Pp5GiNSu7bIW2+JnDtnO8p0JCeL9O0rEhVl\nO5KgACBK3MhvOGLlzxITdVz/3nuvuI3N+fM6Wzhhgv47JET7zH38sf/WUQS9pk11OGLx4nQP792r\n04UzZuiMAaC1JTVr6shFv36+UYDst86e1R/krFm62mPwYI8sgU9O1lmeb74BIiOB3btdq0UBXZHX\nsKH+PT/0kF6nnNu1S0vlfvpJR7MA/fVWq6Zvty++qIX9FFw4YhUMlizR06rp09M9fOKEyH336eAG\nIBIaqiMaZ854OU5yXr9+ImFhOnqVicOHRV56SaRy5YtHNypWFHnySZHNmz0fbkA5flykYUMdDhw7\n1tG7jo/XkZM77xSpUEEfIu3oSdmyIl26iHz1FUcgveXYMZGXXxapVk1/B6m/j0qVRIYO9ZGRrHPn\nRB57TOTrr21HEtDg5ogVEyt/NmiQZk0nT1707cOHRTp1cr0pFyggMmCAzlxQgPjlF/3lzpuXpf92\n4oR+GNSsefGH9lVX6TTI9Ok6LUJXkJws0quXyJw5Ob6rU6dExo8XadtWpGTJixPfkBCRKlX05Gjm\nTP79+oIzZ0TefFOnB1OTLGN0WnbCBIt/O4mJIs2bixQrJnLokKUgAp+7iRWnAv1Zw4a6B1nKdNCR\nI7owcM4cfWsuWhQYMgR44QUWpAecM2e0NfuwYdnYzVklJuoU08SJ2lU7tf9PSAhQq5b2mu3dW5fh\nB72kJGDkSKB79xwtbd+xA5gyRVsBrF+vzS5ThYbqVFOrVlo43aJFzsMmz4mNBUaMAL76yjVdmCeP\n/t5eeUUXDHjV5s2ueeHvv/fygwcHTgUGun379HTp7bfl8GGRDh1cZ1DFiomMG2c7QPI3a9aIPPSQ\nSJkyF4+c5M+vBdHvvKPTIkFn+3aRVq30hzFsmNv/LSlJB7V69hS5+mqdir/059qokY4mb9zoufDJ\n8/bt099z0aKu32/BgiKPPCJy8KAXA3nrLX3w777z4oMGD3DEKsDFx+PEtN/x/JcN8PXiShDRJn/D\nh3PVbVCJjdV+Cg6vCY+NBb7+WhtLrlnj6pcF6Ehogwa6XciDDwbwAojERK1gfvVV/Rl/9JGuv8+g\nSH3PHuCHH4Dff9ctYWJiXPvgGaPrTBo21J/bffdxU+FAtXq1DiTPn+/aqP7qq4H+/fXl49HZg8RE\n7fB64IAOj4aFefDBgg/7WAWwQ4f0D3TuXPyXUL31lrYzoSDy99/aen36dB3+96BDh7T32axZwIYN\nF29/ki+frjZs0QLo1Em7dgdE76w33wSGDtX+VOPH62Z4KbZt0yRq8WKd0jt06OLVeqGhuklw8+Y6\ne9iuXYD8TMhtycnAp58CH3yg2+0Amue0b69TiFdf7aEH3rFDW+uHh3voAYIXE6sAdOCA1lCtmXsU\nfTEWPxZ9HM++WwGPP247MrLi/HkdPnrySR1N8aI9e3REa+5cTbROnLj4eKFCWorUqJFuHdK2rR+M\nbIloppS6V9DRozjyYyRmSFesWGmwfr0+7+PHXV27AU2YSpcG6tbVbaC6d/fghyb5pehoYNAgbX9y\n7px+r3JlbYPTu7cHR7F8YCeAQMLEKoBER2tCNW+evvc/W3AiRp19DPjrL90nkIJXmzY6XPLvv1bD\nOH8e+OUX4NdfdVPcXbsu7gAOaFF8sWLa5b9qVT2hjojQUZ0SJezEnZwMbFqXgMMTZqHqT++j6sEV\nmH9VV9yVewZOnXJ1406VN69O4dWtq9sC3nEHi/spa6ZP110v1q3T62FhurXQ++/rHoaOGTtWG9at\nXKlnOJRjjiZWxph2AEYBCAHwuYiMuOR4bQBfAmgEYIiIvJfZfTKxylx0tE75zZ+vCVXJktr0secP\nnXSYYOdOjzQlJD/y9tvAyy9rclW6tO1oLnL+vA4ALVig5wDbtgGHD188jZjKGJ0+K1BAF7oWL66v\n9yJF9N/Fi2vyVby4JjdhYfqVN6+OGMXF6df581ofdu4ccOyY1jkdO6ajTCdP6j56J0/qosr4eKBX\n4jgMwXCUw0HsQhW8iwH4Cj0RUiAvypbVKc7GjTWJatnSx7c3Ib9y5IjWXX3/vb52AU3YX38duPNO\nBx7g+HHd+LBgQf0D5OavOeZYYmWMCQGwFUAbANEAVgO4V0Q2prlNKQCVAdwO4AQTq5yJjgYeeUQ/\nkET0DPndd4GHH4ZWEZcsCTz9tJ7iUHBbtUq7sH/zjbaE9gPJybqn3cqVWia2dSuwf78r4Tl//uJ6\nJecI6mAzbs89G19e9SzyFQnDwPOvIyJ5FTbc+BTy39keTZqFoFIlTzw2UfqSk3Wvx7ff1vIoQKfS\nH3hAv1eoUA7ufOFC7fuQup8g5YiTiVUzAK+JSNuU64MBQETeTue2rwE4y8Qqe/bu1RGqhQtdCdXI\nkbpVxX+mTtUP0MhINrohLfZ57TVdZlanju1oHJOcrGf0hw4BBw/qv48c0VquhAQdbUq9TErSkaS8\neV2X+fLp+UeFsBjU3jkHZbYtRf5VC2F27tQHWLBAh6FEOOpLPmPbNp29mztXX9/G6HnTe+/l4O1+\n4EA9M//xR51zpGxzN7FyZ51KeQD70lyPBtA0m0H1AtALACrxtPA/e/boaFTqtm+lS+sf0gMPpHPj\n7duBChWAZs28GiP5qJAQLdgIMLlyabF7mTLaosAtyck6Rb50qf59XHstsGgD0PMRLfJv2VLnXjp1\n0r8hgEkV+ZSaNYGff9YR2/feA0aP1pHdli31b+HZZ/UlnKUVpm+8oXeS3hw8eYQ7I1bdAbQTkcdT\nrj8IoKmIPJ3ObV8DR6zctmuXTvktWaLXy5bV2b1MZ3RiYzlfTi6JiZqVly8ffCuAzpzR3cSXLgWW\nLXMtT3zjDW1/ff68noyEh3P7AfJLK1ZoMrV8uQ6w5smjuyJ88IEuAnELR2Yd4e6IlTvvNPsBVExz\nvULK9yibtm3TM5Bq1TSpKldOZ/gOHMgkqUpI0EsmVZTW+fP6ThvoNRSxsboXzKuvAhMm6Pfy5NHr\n27Zpxe+kSbqoY8gQPZ43L3DNNUyqyG81a6aVHydPAn366Et6xgz9/KhdW5v4Zio1qZo0SadHLHUD\nCBbuvNusBlDTGFPVGBMKoAeAWZ4NKzBt2aJLy2vV0pPr8uV1Rcj+/cA997hxBzffDPTt6/E4yc8U\nLAi0bq3dOwPxDXPUKH1+RYtq99Hhw/U0HtBPmUOHtF/PhAlakFi1Ks/OKeAUKgSMG6frl6ZO1V5p\nW7YAPXrosb59L94hIV1HjgCTJ+twF3lMpomViCQCeBrAXACbAHwnIhuMMb2NMb0BwBhTxhgTDaAf\ngFeMMdHGmJysZQgomzZpv8HatfXzoGJFrSOMjtZmgm7Ztk2zsSpVPBkq+asuXXRuecMG25HkzIUL\nuov4O++4vjdrln4gPPOMNso6cUJ3jk5VpIj34ySy6J579Fxi507g9tt10Hr8eP1TaNEC+PPPDP7j\nSy/ph86AAbqAgzyCDUI9aO1aXeW6erVer1RJixG7ds3Gnb36qp6p79vncBc5CggHD+rr4s03XdNg\n/iI+Xqf4vv8emDkTOHVKO4nu3auNreLjuecZ0RUkJuoK8tGjdQAX0Jrd55/XXOqimfAzZ3SpYUyM\n9reqWDHd+6TLOVljRVm0YIHWyl57rSZVlSvrSo89e7KZVCUn6/4hrVszqaL0lS0LNGmiOwD7mxEj\ndK/DWbP09Hv2bC04LFBAjzOpIrqi3LmBwYP1/CoyUmdIDh3STgv58mn54d69KTe+6iqdMomP1zlF\nchwTKwdNm6ZJ1K236vRf7dq6Dc3u3brCO9sWLdI7efBBZwKlwPTtt9oAx5fFxelJwo036tkGADz2\nmO6Hc/gw8NVXWojPZIooW1q00JKT48d1H8LQUM2jKlfWVnfTp0M/nP75R4ezyHFMrHIoORkYM0ab\nefbooWcF112nHaU3bdIkK8dq19apQEf2OaCAVa2aFnP7opgYbWRaqZIWmB865GqvXqEC0KED94sh\nclCRItqJ5MwZYMoU7ZG1eTNw1126bdSzH1bF2XMGWL8+IHvh2cQaq2xKTNQ9nUaN0heuMTpT9+mn\nWegtQuS0qVN1f4xff/WdFgPJyZr07dmjU34vvAC0asWVe0RetmOH1l399pt+huXKBXxV/mU8uO9t\nXTAyYIDtEH0aa6w85ORJ3XamYEGtE46N1TOAI0e0vMXxpOqrr3SVFJE7EhP1hRgZaTeODRu0TXRS\nkr57jxmjGwTOmqVtQ5hUEXld9eo6Ax8XpwMDJUoAD+97E9+iBzBwIObeMxHJybaj9H9MrNy0fr2e\nZBcrprmOMTp/ffo08N13+gJ1XFwc8OKLFy8tJ7qSbt0065882c7jb9mi+xbWq6cjZ5s36/c7dw6o\nvQyJ/Fnu3FpdcvgwsGhxLoyNmIS5uA2tv3sC94T+hPbtgXXrbEfpv5hYZeK773Ruul493TWkZEnd\nz/LcOZ2/9mgT9G++0QrEZ57x4INQQClQQPvUfPedDqd6y7Fj2tE5PFxHpQYO1AUXdet6LwYiyrIb\nbwSWrQ5F030/YE/J6/AcPsJvvwkaNNDFxi+/7N23kkDAxCodFy5oK6BixbQR2/btmlj99ptm+P37\ne6F8JSlJu+PWr6+vfCJ3PfywFv799JPnHyt13qBgQe1K2K+fdi18+22geHHPPz4ROaJIhYKotvU3\ntDz+M+bMMWjaVEtc3n5bOzQ0baqlm5Q5JlZprF2rBej58wNvvaXTfO3b6+fEunVA27ZeDOb777Um\n5eWXWY9CWXPjjTpqVbq05x7j3DldSdSggbZ9DgvT+fKRI3WJLBH5nyJFgEKF0P6mWKws2RlxP/6K\nV17RP+lVq3TxbqFCwKOPuhqR0uWCPrFK7VhboYI29Jw/X5ei9u+vidWcOZZW+cXG6gfkXXdZeHDy\na7lyaWLeurXz952YqHvy1aypRRo1a7o2KMud2/nHIyLvi4sDDhxA6F1d8Ub973HwoLa96tBB+4p+\n+aVOE1atqou4zp+3HbBvCdrEassW7YKeP7+uMD1wAIiI0Iaex45pHZVH66cy8+ij2hjUV5bMk/85\nfly71jpl716dmu7VS99Rly3TzoMcoSIKLMWL6xYiTZtqg8YvvkD9+trHNy5O9yWsXVs7qAwdqp+V\nDRsCkyaBqwoRZIlVbKzOrJUrpy+KWbO0n2Lv3voZtHq1Qw09cyIxEZgxQ1+dnAKknBgzRt8UN23K\n2f0cO6aX5coBV1+ttVuRkUDz5jmPkYh8U+HCupNDmzbA448D778PQM/1n3pK31ZOngQGDdK3hn/+\nAR55RD9Tb7nF9zeB8KSgSKymTdNpvoIFtRDv8GGgcWNt7X/6tK7uK1LEdpQpPv9cl8z7455v5Fv6\n9NF3uQ8+yN7/37pVp6Jr19aNkXPn1qTq9tuZ9BMFg/z5tfHVU08BN9102eFChfQzNTpaFwE//LAu\nTF64EGjXTvcpbN06+FoxBmxitWOHvv/ny6cn7WvXalY9bJjW3UZF+eAOMYcP606at9zi5Up5Ckgl\nS+op5OTJ+q7nrv37gSef1NYJv/4KPP0066eIglWePDr3F5HScHzcON3t+RKVK2uPxxMntNC9Wzf9\nr/Pn6/afqSNZs2Z5N3wbAnZLm+nT9WS7QAHdAHn4cO0669Meeki3JFm3TkcJiHJq3z6dvuvUSXtb\nZWbTJqBRI2330bs3/lsSRES0b582+i1USD9k3SgHiIoCRowA/vjDtc4lLExnkXr21HM/f9kmNOi3\ntOneXQvRz57VXMXnk6pFi4Cvv9ZKeiZV5JSKFbVZ55EjGS/diY11bYFTu7befvNmYPRoJlVE5FKx\nIrBihU4R3nSTrvLKpFo9IkJzsFOngDVrdMAjXz5g5UodGM+bVxcXDxgQOC0cAnbEyu/88osOq82f\nr686IqckJgIhIZfXRcXH63ZJb7yhp5LR0T5UbEhEPuvkSV0d/P33Oho+a1aW6y737NF6+FmzdMFx\naipSooRuH/f441o370sL490dsWJi5UtEWBRMnnPggI5ENWumvajefVfrqVq00ArUG26wHSER+QsR\n4Isv9MStd29XZpSNz7DYWOCzz4ApU7QSJiFBvx8SAtSooY26+/TRkS2bmFj5iwkTNPt/8UXfSs0p\n8HTurMt1JkzQjZJvvFGb0Nx6KxN6IsqZqVO1kdXYsTmuvVmwQBfIL16s54OpUvtlde2qtVnerlQI\n+horv7Bqla64mj/fdiQUyKKjdbVphQpa0DBiBLB8ub5rtW7NpIqIci61VjM8XE/Yzp3L9l3dcgvw\nzTc6oB4Xp+eCN9+si5OXL9cy0NKldQ/DZs20+3vaBMw2Jla2/Puvjm+WL6/jnxytIqetXKm9RqpU\n0Wm/s2f1jHLdOl0oQUTklEcf1S1N7rpLM50aNYBvv83x3ebNq/VWCxZoAfz+/VoWev31ek64cqXm\ncTfe6MBzcAg/zW3YulWr8vLl09GqEiVsR0SB5o039FTut9+AF17Qxm5ff60NZfr31664kybZjpKI\nAkm5cjpQEBmp04Gxsfr9+HjgwgXHHuKVV3Rx4unTQEyMnje+/rojd+8Idv2zYeFCLfSbN8/SDs8U\nUB4Djo0AAA5fSURBVJKSNEH/8kut1YuI0ASqaFEtRChY8OLbv/WWNpLp1MlKuEQU4Fq0AJYudRW0\nf/opMHIk8NxzOrJVrJhjD1WihJ4r+hKOWHlTdLRePvmkNmJkvyrKrsREHRt/5hltedy2rW7OtWOH\nHm/USOv3Lk2qAC1UeOMN3Wg1Pl6bzFhaxEJEAcoYV4lL/fpAtWqaAVWooHN7S5bYjc+DmFh5w4kT\nmkxdfTWwcaN+z8GMnYLE6dPAtm367/PngQ4ddOlMRIR2VT9wALjnnqzd50cfaU3EvfcCZ844HzMR\nUatWulhm7VrggQe09urFF13Hd+0KqJM7TgV6UnKyLkHt108ngl94QQv6iNxx7hywbJlOHS9YoG2L\nGzXS1aQFC+r3GjTQfZuyq39/fUMbMgT46y/dB6xNG+eeAxFRqgYNtGHVhx+6ZnBOn9ZtcipW1AVd\nrVtrV/fChe3GmgMcsfKU8+eBevWA++/XF8zq1cB77/nPpkjkXRcuaGKTdj+/O+/UKb733tPdTF9+\nWas0UzVvnrOkCtCh+kGDNHlLSABuu01bMxAReUqBAjqDA2hpwrhxWuz++efapKp4cV1gA2i/hf37\n/WpEy63EyhjTzhizxRiz3RgzKJ3jxhgzOuX4OmNMI+dD9XHnzukKrLff1ut58+r23lOn6nrQRr77\nI/nf/3RFfq5cevm//2X//2X3vtx9jD59Mr5/dx7b6fj69NH3BWNcXxnerwhw9KjrDeL773Uarl49\nbcjSuLFOyaX2f3nhBeDXX3UqOTIS+L//0yF1T7jxRq37e+894I479Htbt+qbWzo72XuF07+sQODU\nz8TWz7ZPH33M1D+Wq65yPXZOY/L0c/L0m1uwvr7z5wcee0w/P0+c0H1zBw8GmjTR40uXal1W6dJA\nu3Z6bPJk4PBhq2FfkYhc8QtACIAdAKoBCAXwD4DwS27TAcCvAAyA6wH8mdn9Nm7cWPxSYqJIcrL+\ne/FikRdeEGnWTCR3bhFApEgRkVOn7MaYBVOmiOTPr6GnfuXPr9/P6v/Lk0ckNDTr95WVx7j0K/X+\n3Xke2X2uGXnqKRGDJCmC41IDW6UpVkhH/Cx5ESv584vMGzhXpGdPkdatRWrVEsmXTx/0yBG9g+HD\n9fudO4sMGCAybZrIjh2u15dtI0a4flDXXCPy9NMin38ucu6c5x/b6V9WIHDqZ2LrZ/vUU+n/EefO\nrcdyEpOnn5PT98/Xt/v27hUZM0bfSxs2dH3WLlmix3/6SeS227wSCoAoySS3EZHMt7QxxjQD8JqI\ntE25PjglIXs7zW0+BbBIRL5Nub4FQCsRyfBU1ytb2ixYAPzxh75sk5NdX/36aQY8Zw7w888XH0tK\n0pGBSpV0g9rJk7UXx4kTrq9164C6dbU+ZfRoPduoW9f11aEDUKiQFhqvW3d5XG3auI6vXXv58bZt\n9fjWrRkfL1xYm7H9/fflx9u31+ObN+v00qU6dvzv+HMt1+DosYsPz0YnFK1cGLt/3QSk9zvq3BlV\nGhZBvj2bcB1WX3Z4FrrgFIqgDjaiCVahRHEdCPnP7bfrZr8bNmi9EHDxMG+3bkDRorit3HpUPPjn\nZff/I+7ASRRFXaxHM6xA8ZR1AMeO6+V0dMdJFMU1+Bediq34bxBx8GDg5PEkTEUPnERRNMGfaIu5\nKFE4Ac/2TtCpsIQErTcqXVpHi6ZM0aHos2d1JOnsWd01tHJlvJjrQ7wrLyEEF+/uXhNbsR01Mazo\naLyW7x19LVWs6Lp8+GH/2OxYRF+/c+fq39GKFa6fRb58uh39999rY5ly5fQ5FSgAfPCBnoUvXKij\nYCEhej0kRIf3HnpI73/1at2JNXWD6NSvLl30b2rPnstjKlkSOHJE//3338C+fRcfN0a37nHn+Nq1\n6R9PbUOR2fF//kn/eMeOnjn+6KNaq3mpkiX1vcrd++/bN+Of7Zdfei7+rl31PTY9uXKlfyztc7vS\n/bvzs8lJ/E7fvzuvb2+/vvzleJs2wO7d+lkcE6OfcRs2ANOmwdPc3dLGnRGr7gA+T3P9QQBjL7nN\nbAAt01yfDyAinfvqBSAKQFSlSpU8nVyKdO2a/hnSzJl6/Pbb0z8+Y4Yev+ee9I8vXqzH33kn/eMb\nNujxDz/0y+N1sEGMufL/N0bkOWT8/4GMj7sb3/PZvP/Mjodj/UXHk2B0qK1AAR1x3LRJ45s4UaRG\nDZF69USuv17k1ltFunQR2bNHRERaYKn8H16R5/ChPIDJ0g5zJAKrJAxxAoj+DANJUpLI7t2u619/\nLfLAAyK33CJSu7ZI2bIiJUq4jj/88OU//5AQ1/FHHsn4uDHpvzYA1//v2fPK9x+IxzP7cuf+r/Sz\ntR1/Tp+fEz8fb9w/X9/OHq9TR7wBDo5YdQfQTkQeT7n+IICmIvJ0mtvMBjBCRCJTrs8HMFBEMhyS\n8sqI1fr1unVMrlyur5AQ3XSocGFg505g+/aLj4WEaD1U/vx65pDeBkS1a2sNVUxM+vUntWrp8aNH\n0z9es6breHrzxNWr6/FjxzI+HhYGHD/uOrtJq2pVPZ6a0V+qcuX/jre65ij2X/IU96ISylYOw+61\nJzWGS1WsiCq1QnFyz0kUw/HLDkejAhIQikI4haI4gQrltUToP+XKaRH/6dMaY6rUPevKlgXy5EHd\nSmdwet/Jy+7/EMogEXlQEGdQCKdRoXzK4+7XyyMohUTkQQGcRXj50/8NijVpAuzdnwtHUQJJyI1c\nSNKnUzkEu3df/jQzkzu3DnBmpHJlZOt+A8aZMzramzoSnJSk/05tirt/v76GU0eLU117bcZn9GXL\nuv4m9+xJ//WZWs+Y2fHdu9M/3rixe8d37Ur/eESEZ4537gwcOnT57cuU0ZF3d++/e/f0f7ap9+Op\n+Js2zfqI1aXPLaP7d/dnk934nb7/jF7fZcq4PjO8/fry5+N58wLXXHP5bR3m5IhVMwBz01wfDGDw\nJbf5FMC9aa5vAVD2SvfrtzVWAYY1VjmrscosLsom1qBcjjVW9p4Ta6xI3B+xciexyg1gJ4CqcBWv\n173kNh1xcfH6qszul4mV75gyRaRyZR2drlw5a+9ll/6/7N6Xu4/x1FMZ3787j+10fE89paPTad8f\nnbhfEud/WYHAqZ+JrZ/tU09dPA1WsKDrsXMak6efk6ff3Pj69nnuJlaZTgWmDH91APARdIXgRBEZ\nbozpnTLi9YkxxgAYC6AdgFgAPeUK04CAl6YCiYiIiBzg7lSgW53XRWQOgDmXfO+TNP8WAH2zGiQR\nERFRIGHndSIiIiKHMLEiIiIicggTKyIiIiKHMLEiIiIicggTKyIiIiKHMLEiIiIicggTKyIiIiKH\nMLEiIiIicggTKyIiIiKHMLEiIiIicggTKyIiIiKHuLUJs0ce2JgYAHu88FAlABz1wuP4Ij734BXM\nzz+YnzsQ3M+fzz14eeP5VxaRkpndyFpi5S3GmCh3dqMORHzuwfncgeB+/sH83IHgfv587sH53AHf\nev6cCiQiIiJyCBMrIiIiIocEQ2L1me0ALOJzD17B/PyD+bkDwf38+dyDl888/4CvsSIiIiLylmAY\nsSIiIiLyCiZWRERERA4J+MTKGHOXMWaDMSbZGOMTSzE9zRjTzhizxRiz3RgzyHY83mSMmWiMOWKM\nWW87Fm8zxlQ0xiw0xmxMec0/ZzsmbzLG5DXGrDLG/JPy/F+3HZO3GWNCjDF/G2Nm247F24wxu40x\n/xpj1hpjomzH403GmCLGmOnGmM3GmE3GmGa2Y/IGY8zVKb/v1K/TxpjnrccV6DVWxpg6AJIBfArg\nJREJ6D84Y0wIgK0A2gCIBrAawL0istFqYF5ijLkRwFkAk0XkGtvxeJMxpiyAsiLylzHmKgBrANwe\nRL97A6CAiJw1xuQBEAngORFZaTk0rzHG9AMQAaCQiHSyHY83GWN2A4gQkaBrkmmMmQRgqYh8bowJ\nBZBfRE7ajsubUj779gNoKiLeaD6eoYAfsRKRTSKyxXYcXtQEwHYR2SkiFwBMBdDVckxeIyJLABy3\nHYcNInJQRP5K+fcZAJsAlLcblfeIOptyNU/KV2CfOaZhjKkAoCOAz23HQt5jjCkM4EYAXwCAyP+3\ncz8vNoUBGMe/T0k0ko0ko8ZCsx0WSqwMQlJ2o1gpG5SV8g9Yys6GbExTfpZSJqKkhEaI2Fi5irGR\nshE9Fueoqyyv8477Pp+63XvO6rmde7vPfX8cf6+tVLUmgXelSxVUUKwqtAZ433fco6If12hIGgM2\nAI/LJulWOxX2HJgH7tiu6f2fBU7SjNDXyMBdSXOSjpQO06F1wGfgYjsNfF7SSOlQBUwBM6VDwJAU\nK0l3Jb36y6OakZqI3yQtA64BJ2x/LZ2nS7Z/2p4ARoFNkqqYDpa0F5i3PVc6S0Fb22u/GzjaLguo\nwSJgI3DO9gbgG1Db2trFwD7gSuks0FyQ/57t7aUzLCAfgLV9x6PtuahAu7boGjBt+3rpPKXY/iLp\nPrALqGEjwxZgn6Q9wBJguaRLtg8WztUZ2x/a53lJN2iWRTwom6oTPaDXNzp7lcqKFU2Zfmb7U+kg\nMCQjVvGHp8B6SevaFj8F3CycKTrQLt6+ALyxfaZ0nq5JWilpRft6Kc0GjrdlU3XD9inbo7bHaL7z\n92oqVZJG2g0btNNgO6mjUGP7I/Be0nh7ahKoYsNKnwMskGlAqKBYSdovqQdsBm5Jmi2d6V+y/QM4\nBszSLF6+bPt12VTdkTQDPALGJfUkHS6dqUNbgEPAtr7tx3tKh+rQauC+pJc0fzDu2K7utgOVWgU8\nlPQCeALcsn27cKYuHQem28/+BHC6cJ7OtEV6B7BgRuiH/nYLEREREV0Z+hGriIiIiK6kWEVEREQM\nSIpVRERExICkWEVEREQMSIpVRERExICkWEVEREQMSIpVRERExID8Agmb1GwL9NmqAAAAAElFTkSu\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f12c8db5710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,5))\n",
    "\n",
    "class0 = p[0] < p[1]\n",
    "x0 = x[class0]\n",
    "ax.scatter(x0, [0]*len(x0), color=\"red\")\n",
    "x1 = x[~class0]\n",
    "ax.scatter(x1, [0]*len(x1), color=\"blue\")\n",
    "\n",
    "xx = np.linspace(-1, 7, 200)\n",
    "ax.plot(xx, k0(xx), color=\"blue\")\n",
    "ax.plot(xx, k1(xx), color=\"blue\")\n",
    "\n",
    "kk0 = scipy.stats.kde.gaussian_kde(x0)\n",
    "ax.plot(xx, kk0(xx), linestyle=\"--\", color=\"red\")\n",
    "kk1 = scipy.stats.kde.gaussian_kde(x1)\n",
    "ax.plot(xx, kk1(xx), linestyle=\"--\", color=\"red\")\n",
    "None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}