ModelingExamples.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\newcommand{\\ind}[1]{\\left[#1\\right]}$\n",
    "\n",
    "# Model\n",
    "\n",
    "- Data set\n",
    "$$ {\\cal D} = \\{ x_1, \\dots  x_N \\} $$\n",
    "- Model with parameter $\\theta$\n",
    "$$ p(\\cal D | \\theta) $$\n",
    "\n",
    "<img src=\"images/fig13b.png\" width='360' align='center'>\n",
    "\n",
    "\n",
    "## Maximum Likelihood\n",
    "\n",
    "- Maximum Likelihood (ML)\n",
    "$$ \\theta^{\\text{ML}} = \\arg\\max_{\\theta} \\log p({\\cal D} | \\theta) $$\n",
    "- Predictive distribution\n",
    "$$ p(x_{N+1} |  {\\cal D} ) \\approx  p(x_{N+1} |  \\theta^{\\text{ML}})  $$\n",
    "\n",
    "## Maximum Aposteriori\n",
    "\n",
    "- Prior\n",
    "$$ p(\\theta) $$\n",
    "\n",
    "- Maximum a-posteriori (MAP) : Regularised Maximum Likelihood\n",
    "$$\n",
    "\\theta^{\\text{MAP}} = \\arg\\max_{\\theta} \\log p({\\cal D} | \\theta) p(\\theta)\n",
    "$$\n",
    "\n",
    "- Predictive distribution\n",
    "$$ p(x_{N+1} |  {\\cal D} ) \\approx  p(x_{N+1} |  \\theta^{\\text{MAP}})  $$\n",
    "\n",
    "## Bayesian Learning\n",
    "\n",
    "- We treat parameters on the same footing as all other variables\n",
    "- We integrate over unknown parameters rather than using point estimates (remember the many-dice example)\n",
    " - Self-regularisation, avoids overfitting\n",
    " - Natural setup for online adaptation\n",
    " - Model selection\n",
    "\n",
    "\n",
    "- Predictive distribution\n",
    "\\begin{eqnarray}\n",
    "p(x_{N+1} ,  {\\cal D} ) &=& \\int d\\theta \\;\\; p(x_{N+1} |  \\theta) p( {\\cal D}| \\theta) p(\\theta)  \\\\\n",
    " &=& \\int d\\theta \\;\\; p(x_{N+1}|  \\theta) p( {\\cal D}, \\theta)   \\\\\n",
    " &=& \\int d\\theta \\;\\; p(x_{N+1}|  \\theta) p(  \\theta| {\\cal D}) p({\\cal D})   \\\\\n",
    " &=&  p({\\cal D}) \\int d\\theta \\;\\; p(x_{N+1}|  \\theta) p(  \\theta| {\\cal D})  \\\\\n",
    "p(x_{N+1} |  {\\cal D} ) &=& \\int d\\theta \\;\\; p(x_{N+1} |  \\theta) p(\\theta | {\\cal D}) \n",
    "\\end{eqnarray}\n",
    "\n",
    "The interpretation is that past data provides an 'update' to the recent prior to be used for the current prediction.\n",
    "\n",
    "- Bayesian learning is just inference ...\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# Learning the parameter of a (possibly fake) coin\n",
    "\n",
    "Suppose we have a coin, flipped several times independently. A vague question one can ask is if one can predict the outcome of the next flip.\n",
    "\n",
    "It depends. If we already know that the coin is fair, there is nothing that we can learn from past data and indeed the future flips are independent of the previous flips. However, if we don't know the probability of the coin, we could estimate the parameter from past data to create a better prediction. Mathematically, the model is identical to  \n",
    "\n",
    "<img src=\"images/fig13b.png\" width='320' align='center'>\n",
    "\n",
    "Here, $\\theta$ is the parameter of the coin.\n",
    "\n",
    "## Maximum Likelihood Estimation\n",
    "\n",
    "We observe the outcome of $N$ coin flips $\\{x^{(n)}\\}_{n=1\\dots N}$ where $x^{(n)} \\in \\left\\{0,1\\right\\}$. The model is a Bernoulli distribution with parameter $\\pi = (\\pi_0, \\pi_1)$. We have $\\pi_0 = 1 - \\pi_1$ where $0 \\leq \\pi_1 \\leq 1$. \n",
    "\n",
    "\\begin{eqnarray}\n",
    "x^{(n)} & \\sim & p(x|\\pi) = (1-\\pi_1)^{1-x^{(n)} } \\pi_1^{x^{(n)} }\n",
    "\\end{eqnarray}\n",
    "\n",
    "The loglikelihood is \n",
    "\n",
    "\\begin{eqnarray}\n",
    "{\\cal L}(\\pi_1) & = & \\sum_{n=1}^N (1- x^{(n)}) \\log (1 - \\pi_1) + \\sum_{n=1}^N x^{(n)} \\log (\\pi_1)  \\\\\n",
    "& = & \\log (1 - \\pi_1) \\sum_{n=1}^N (1- x^{(n)})  + \\log (\\pi_1) \\sum_{n=1}^N x^{(n)}  \n",
    "\\end{eqnarray}\n",
    "\n",
    "We define the number of $0$'s  \n",
    "\\begin{eqnarray}\n",
    "c_0 = \\sum_{n=1}^N (1- x^{(n)})\n",
    "\\end{eqnarray}\n",
    "and $1$'s as\n",
    "\\begin{eqnarray}\n",
    "c_1 = \\sum_{n=1}^N  x^{(n)}\n",
    "\\end{eqnarray}\n",
    "\n",
    "\\begin{eqnarray}\n",
    "{\\cal L}(\\pi_1) & = & \\log (1 - \\pi_1) c_0  + \\log (\\pi_1) c_1  \n",
    "\\end{eqnarray}\n",
    "\n",
    "We compute the gradient \n",
    "\\begin{eqnarray}\n",
    "\\frac{\\partial}{\\partial \\pi_1} {\\cal L}(\\pi_1) & = & - \\frac{c_0}{1 - \\pi_1} + \\frac{c_1}{\\pi_1}  = 0 \n",
    "\\end{eqnarray}\n",
    "\n",
    "The solution is quite predictable\n",
    "\\begin{eqnarray}\n",
    "\\pi_1 & = &\\frac{c_1}{c_0 + c_1}  = \\frac{c_1}{N}  \n",
    "\\end{eqnarray}\n",
    "\n",
    "## Maximum A-posteriori estimation\n",
    "\n",
    "We need a prior over the probability parameter. One choice is the beta distribution\n",
    "\n",
    "\\begin{eqnarray}\n",
    "p(\\pi_1) & = & \\mathcal{B}(\\pi_1; \\alpha, \\beta) =  \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha) \\Gamma(\\beta) } \\pi_1^{\\alpha-1} (1-\\pi_1)^{\\beta-1}\n",
    "\\end{eqnarray}\n",
    "\n",
    "The log joint ditribution of data is\n",
    "\\begin{eqnarray}\n",
    "\\log p(X, \\pi_1) & = & \\log p(\\pi_1) + \\log \\sum_{n=1}^N \\log p(x^{(n)}|\\pi_1) \\\\\n",
    "& = & \\log \\Gamma(\\alpha + \\beta) -\\log \\Gamma(\\alpha) - \\log \\Gamma(\\beta) \\\\\n",
    "& & + (\\alpha-1) \\log \\pi_1 + (\\beta-1) \\log(1-\\pi_1) \\\\\n",
    "& & + c_1 \\log (\\pi_1)  + c_0 \\log (1 - \\pi_1) \\\\\n",
    "& = & \\log \\Gamma(\\alpha + \\beta) -\\log \\Gamma(\\alpha) - \\log \\Gamma(\\beta) \\\\\n",
    "& & + (\\alpha + c_1 -1) \\log \\pi_1 + (\\beta + c_0 -1) \\log(1-\\pi_1) \n",
    "\\end{eqnarray}\n",
    "\n",
    "The gradient is \n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\frac{\\partial}{\\partial \\pi_1} \\log p(X, \\pi_1)  & = & - \\frac{\\beta + c_0 -1}{1 - \\pi_1} + \\frac{\\alpha + c_1 -1}{\\pi_1}  = 0 \n",
    "\\end{eqnarray}\n",
    "\n",
    "We can solve for the parameter.\n",
    "\\begin{eqnarray}\n",
    "\\pi_1 (\\beta + c_0 -1) & = & (1 - \\pi_1) (\\alpha + c_1 -1) \\\\ \n",
    "\\pi_1 \\beta + \\pi_1 c_0 - \\pi_1 & = & \\alpha  + c_1  - 1 - \\pi_1 \\alpha - \\pi_1 c_1 + \\pi_1 \\\\ \n",
    "\\pi_1  & = & \\frac{\\alpha - 1  + c_1}{\\alpha + \\beta  - 2 + c_0 + c_1}    \\\\ \n",
    "\\end{eqnarray}\n",
    "\n",
    "When the prior is flat, i.e., when $\\alpha = \\beta = 1$, MAP and ML solutions coincide.\n",
    "\n",
    "## Full Bayesian inference\n",
    "\n",
    "We infer the posterior\n",
    "\n",
    "\\begin{eqnarray}\n",
    "p(\\pi_1| X) & = & \\frac{p(\\pi_1, X)}{p(X)} \n",
    "\\end{eqnarray}\n",
    "\n",
    "\n",
    "The log joint density is \n",
    "\\begin{eqnarray}\n",
    "\\log p(X, \\pi_1) & = & \\log \\Gamma(\\alpha + \\beta) -\\log \\Gamma(\\alpha) - \\log \\Gamma(\\beta) \\\\\n",
    "& & + (\\alpha + c_1 -1) \\log \\pi_1 + (\\beta + c_0 -1) \\log(1-\\pi_1) \n",
    "\\end{eqnarray}\n",
    "\n",
    "At this stage, we may try to evaluate the integral \n",
    "$$\n",
    "p(X)  =  \\int d\\pi_1 p(X, \\pi_1) \n",
    "$$\n",
    "\n",
    "Rather than trying to evaluate this integral directly, a simple approach is known as 'completing the square': we add an substract terms to obtain an expression that corresponds to a known, normalized density. This typically involves adding and substracting an expression that will make us identify a normalized density. \n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\log p(X, \\pi_1) & = & \\log \\Gamma(\\alpha + \\beta) -\\log \\Gamma(\\alpha) - \\log \\Gamma(\\beta) \\\\\n",
    "& & - \\log \\Gamma(\\alpha + \\beta + c_0 + c_1) + \\log \\Gamma(\\alpha + c_1) + \\log \\Gamma(\\beta + c_0) \\\\\n",
    "& & + \\log \\Gamma(\\alpha + \\beta + c_0 + c_1) - \\log \\Gamma(\\alpha + c_1) - \\log \\Gamma(\\beta + c_0) \\\\\n",
    "& & + (\\alpha + c_1 -1) \\log \\pi_1 + (\\beta + c_0 -1) \\log(1-\\pi_1) \\\\\n",
    "& = & \\log \\Gamma(\\alpha + \\beta) -\\log \\Gamma(\\alpha) - \\log \\Gamma(\\beta) \\\\\n",
    "& & - \\log \\Gamma(\\alpha + \\beta + c_0 + c_1) + \\log \\Gamma(\\alpha + c_1) + \\log \\Gamma(\\beta + c_0) \\\\\n",
    "& & + \\log \\mathcal{B}(\\alpha + c_1, \\beta + c_0) \\\\\n",
    "& = & \\log p(X) + \\log p(\\pi_1| X)\n",
    "\\end{eqnarray}\n",
    "\n",
    "From the resulting expression, taking the exponent on both sides we see that \n",
    "\\begin{eqnarray}\n",
    "p(\\pi_1| X) & = & \\mathcal{B}(\\alpha + c_1, \\beta + c_0) \\\\\n",
    "p(X) & = & \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)} \\frac{\\Gamma(\\alpha + c_1)\\Gamma(\\beta + c_0)}{\\Gamma(\\alpha + \\beta + c_0 + c_1)}\n",
    "\\end{eqnarray}\n",
    "\n",
    "Predictive distribution: Let $a=\\alpha + c_1$ and $b=\\beta+c_0$\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\int d\\pi_1 p(x|\\pi_1) p(\\pi_1| X) & = & \\int d\\pi_1 \\mathcal{BE}(x; \\pi_1) \\mathcal{B}(\\pi_1; a, b) \\\\\n",
    " & = & \\int d\\pi_1 \\pi_1^{\\ind{x=1}}(1-\\pi_1)^{\\ind{x=0}}\\mathcal{B}(a, b) \\\\\n",
    "\\end{eqnarray}\n",
    "\n",
    "\\begin{eqnarray}\n",
    "p(x) & = & \\frac{\\Gamma(a + b)}{\\Gamma(a)\\Gamma(b)} \\frac{\\Gamma(a + \\ind{x=1})\\Gamma(b + \\ind{x=0})}{\\Gamma(b + a + 1)}\n",
    "\\end{eqnarray}\n",
    "\n",
    "\\begin{eqnarray}\n",
    "p(x=1) & = & \\frac{\\Gamma(a + b)}{\\Gamma(a)\\Gamma(b)} \\frac{\\Gamma(a + 1)\\Gamma(b)}{\\Gamma(b + a + 1)} \\\\\n",
    "& = & \\frac{\\Gamma(a + b)}{\\Gamma(a)\\Gamma(b)} \\frac{a\\Gamma(a)\\Gamma(b)}{(b+a)\\Gamma(b + a)} \\\\\n",
    "& = & \\frac{a}{a+b}\n",
    "\\end{eqnarray}\n",
    "\n",
    "\n",
    "## Alternative Derivation\n",
    "Alternatively, we may directly write\n",
    "\\begin{eqnarray}\n",
    "p(X, \\pi_1) & = & \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)}   \\pi_1^{(\\alpha + c_1 -1)} (1-\\pi_1)^{(\\beta + c_0 -1)} \n",
    "\\end{eqnarray}\n",
    "\n",
    "\\begin{eqnarray}\n",
    "p(X) &=& \\int d\\pi_1 p(X, \\pi_1)  =  \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)} \\int d\\pi_1  \\pi_1^{(\\alpha + c_1 -1)} (1-\\pi_1)^{(\\beta + c_0 -1)} \n",
    "\\end{eqnarray}\n",
    "\n",
    "\n",
    "From the definition of the beta distribution, we can arrive at the 'formula' for the integral \n",
    "\\begin{eqnarray}\n",
    "1 &=& \\int d\\pi \\mathcal{B}(\\pi; a, b) \\\\\n",
    "& = & \\int d\\pi \\frac{\\Gamma(a + b)}{\\Gamma(a)\\Gamma(b)} \\pi^{(a -1)} (1-\\pi)^{(b -1)} \\\\\n",
    "\\frac{\\Gamma(a)\\Gamma(b)}{\\Gamma(a + b)} & = & \\int d\\pi \\pi^{(a -1)} (1-\\pi)^{(b -1)}\n",
    "\\end{eqnarray}\n",
    "Just substitute $a = \\alpha + c_1$ and $b = \\beta + c_0$\n",
    "\n",
    "## An Approximation\n",
    "For large $x$, we have the following approximation\n",
    "\\begin{eqnarray}\n",
    "\\log \\Gamma(x + a) - \\log \\Gamma(x) & \\approx & a \\log(x) \\\\\n",
    "\\Gamma(x + a)  & \\approx & \\Gamma(x) x^a \\\\\n",
    "\\end{eqnarray}\n",
    "\n",
    "When $c_0$ and $c_1$ are large, we obtain:\n",
    "\n",
    "\\begin{eqnarray}\n",
    "p(X) & \\approx & \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)} \\frac{\\Gamma(c_1)\\Gamma(c_0)c_0^{\\beta}c_1^{\\alpha}}{\\Gamma(c_0 + c_1)(c_0+c_1)^{\\alpha + \\beta}}\n",
    "\\end{eqnarray}\n",
    "\n",
    "Let $\\hat{\\pi}_1 = c_1/(c_0+c_1)$ and $N = c_0 + c_1$, we have\n",
    "\\begin{eqnarray}\n",
    "p(X) & \\approx &  \\frac{\\Gamma(c_1)\\Gamma(c_0)}{\\Gamma(c_0 + c_1)} (1-\\hat{\\pi}_1) \\hat{\\pi}_1 \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)} (1-\\hat{\\pi}_1)^{\\beta-1}\\hat{\\pi}_1^{\\alpha-1}\n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Illustration: Bayesian update of a Beta Distribution "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAqYAAAFkCAYAAADys/m9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAIABJREFUeJzs3XmczWX/x/HXNYNsmYhkVxFDNZrRnSWSW6S6i7LcgxYV\nt1J3jTYpUZE21N0dJYWoqdx3SpspJSV0ZwZRIttPI4maTHZmrt8f18g6zBxnznXOnPfz8TgPzXfO\n95y3bJ9zLZ/LWGsREREREfEtxncAERERERFQYSoiIiIiYUKFqYiIiIiEBRWmIiIiIhIWVJiKiIiI\nSFhQYSoiIiIiYUGFqYiIiIiEBRWmIiIiIhIWVJiKiIiISFhQYSoiIiIiYaHQhakxppUxZroxZr0x\nJtcYc0UB7ulpjFlkjNlmjPnJGPOSMaZSYJFFREREpDgKZMS0HLAIuAWwx3qyMaYlMAl4EWgEdAH+\nAowL4L1FREREpJgqUdgbrLUzgBkAxhhTgFuaAWustc/lff1/xpgXgHsK+94iIiIiUnyFYo3pPKCW\nMaYjgDGmKtAVeD8E7y0iIiIiEaLQI6aFZa2da4zpBbxhjCmd957TgVvzu8cYczLQAVgL7CzqjCIi\nIiJSaKWBukCatfbXYLxgkRemxphGwDPAUOAjoBrwFPACcFM+t3UAXi3qbCIiIiJy3HoCrwXjhYq8\nMAUGAl9aa0flfb3UGHML8IUx5n5r7cYj3LMWYMqUKcTHx4cgoviWkpLC6NGjfceQENGvd3TRr3d0\n0a939Fi2bBm9evWCvLotGEJRmJYFdh9yLRe3oz+/zVM7AeLj40lMTCzCaBIu4uLi9GsdRfTrHV30\n6x1d9OsdlYK27DKQPqbljDEJxpgmeZdOz/u6Vt73RxhjJh1wy7vA1caYfsaY0/LaRz0DfGWt/fm4\nfwYiIiIiUiwEMmLaFJiFG/G0wMi865OAG4BTgVr7nmytnWSMKQ/0x60t/R34BDfFLyIiIiICBNbH\ndDZHGWm11vY+wrXngOeO8HQRERERESA0fUxFjik5Odl3BAkh/XpHF/16Rxf9esvxMNYe81TRkDPG\nJALp6enpWkAtIiIiEoYyMjJISkoCSLLWZgTjNTViKiIiIiJhQYWpiIiIiIQFFaYiIiIiEhZUmIqI\niIhIWFBhKiIiIiJhQYWpiIiIiIQFFaYiIiIiEhZUmIqIiIhIWFBhKiIiIiJhQYWpiIiIiIQFFaYi\nIiIiEhZUmIqIiIhIWFBhKiIiIiJhQYWpiIiIiIQFFaYiIiIiEhZUmIqIiIhIWFBhKiIiIiJhQYWp\niIiIiIQFFaYiIiIiEhZUmIqIiIhIWFBhKiIiIiJhodCFqTGmlTFmujFmvTEm1xhzRQHuKWWMGW6M\nWWuM2WmMWW2MuT6gxCIiIiJSLJUI4J5ywCLgJeCtAt4zFagC9AZWAdXQaK2IiIiIHKDQham1dgYw\nA8AYY471fGPMJUAr4HRr7e95l9cV9n1FREREpHgLxajl34AFwL3GmExjzHJjzJPGmNIheG8RERER\niRCBTOUX1um4EdOdQCegMjAWqATcGIL3FxEREZEIEIrCNAbIBXpYa7cCGGMGAFONMbdYa3eFIIOI\niIiIhLlQFKYbgPX7itI8ywAD1MRthjqilJQU4uLiDrqWnJxMcnJyUeQUERERkSNITU0lNTX1oGtb\ntmwJ+vsYa23gNxuTC3Sy1k4/ynP6AKOBU6y12/OuXQn8Byh/pBFTY0wikJ6enk5iYmLA+UREwsXu\n3bv55ZdfOOWUUyhVqpTvOCIixy0jI4OkpCSAJGttRjBeM5A+puWMMQnGmCZ5l07P+7pW3vdHGGMm\nHXDLa8CvwARjTLwxpjXwBPCSpvFFJFosXbqUWrVqsXTpUt9RRETCViC78psCC4F0wAIjgQzgobzv\nnwrU2vdka+024GLgJOBrYDLwDnB7wKlFRCJMvXr1mDFjBvXq1fMdRUQkbAXSx3Q2RylorbW9j3Bt\nBdChsO8lIlJcVKhQgQ4d9NegiMjR6PQlEREREQkLKkxFREREJCyoMBURCYHMzEwGDBhAZmam7ygi\nImFLhamISAhkZ2eTlpZGdna27ygiImErFA32RUSiXqNGjfj22299xxARCWsaMRURERGRsKDCVERE\nRETCggpTEREREQkLKkxFREIgIyMDYwwZGUE5TlpEpFhSYSoiEgK1a9fmxRdfpHbt2r6jiIiELe3K\nFxEJgcqVK3PTTTf5jiEiEtZUmIqIFMauXbBpE/z6K/zxx+GPbdtgzx7Yu3f/Y9/XsbFQosT+R8mS\n7scyZeDEE6F8effjvsdJJ8Epp7j/Nsb3z1xEpMipMBURAdi9G9avhx9/hHXr3OPHH+Gnn+CXX1wx\numkTHK1BfpkyrrgsVerw4rNECcjNPbho3bPHPXbscEWttUd+3VKloEoVV6RWqQJVq0Lt2lCrlvtx\n339XqFA0/29EREJEhamIRI+cHFi7FlascI/ly/f/d2bmwYXhySe7gq96dYiPh9atXVG4r0A8+eSD\nRzfLlXPFZz42btzIq6++Ss+ePalaterhT7AWtm+HrVv3j75mZe0viDdt2l8gr14Ns2e7QjonZ/9r\nnHQS1K8PZ54JDRrs/7F+fZdPRCTMqTAVkeIpKwsWLz748e23bioeoHTp/UVcr15w+ukHjz4GuZDb\nsGEDQ4cOpW3btkcuTI1x71munBsRLYi9e2HDhv0jvGvXwg8/uII7LQ02b97/3NNOg4SEgx9160KM\n9sCKSPhQYSoikW/7dkhPh6++gvnz4euvXaEGcMIJ0LixK8SuvdaNfjZo4IrPEBZlTZo0IftoywAC\nUaKE+3nUqgUtWx7+/d9+c6PB338PS5a44vy55/YXrCeeCImJ0KyZe5x/PlSrFtyMIiKFoMJURCLP\nTz+5qewvvnDF6OLFbkq7bFlo2hS6dYNzz3XFaIMGR51iL9YqVdpfdO5jrRtl3TeK/PXXMHkyPP64\n+37t2q5AbdEC2rSBc87RqKqIhEyU/m0tIhFlXyH62WfusWKFu96woSu6+vZ1xdRZZ0VvEVpQxrh1\ns9WrQ8eO+69nZu4fcZ4/HwYOdMseKlZ062vbtFGhKiJFTn+Di0j42bULPv8cZsyADz+EZcvc9UaN\noF07GDbMFUsFXYspx1azpntcfbX7eudO+N//9n8Y2FeoVqoE7dvDJZdAhw5w6qk+U4tIMaPCVETC\nw5o18MEHrhCdNcutG61RwxVAQ4fChRdGdCG6ZMkSOnbsyIcffsjZZ5/tO86xlS7tiv/WreHBB/cX\nqjNnug8MvXu7ZQHnnutGXjt2hObNXa9WEZEAqTAVET+shW++gWnT3OObb1zPzwsucIXoJZe4qfli\n0lh+38lPlStX9h0lMAcWqg8/7NpWffSR+yAxbhw8+qhrpXXFFdC5M/z1r+4eEZFCMDa/hs4eGWMS\ngfT09HQSExN9xxGRYMnNdesX33rLFaOrV7um8Jdf7oqZDh3cTnGJLLm5bhPVvg8ZK1a4gwYuvdT9\nul5+uftaRIqVjIwMkpKSAJKstRnBeE2NmIpI0do3Mpqa6h7r1rl1iVde6YqWiy5yJxtJ5IqJcZvP\nzj8fRoxwa4L3FanJye5ErCuucP99ySWuhZeIyBGoMBWRorF6tStEX3sNvvvOnZTUtasrTi64QDu7\niytj3Ca1Ro3g/vtd0/833nC/Dzp1cqdTXX019Ojh1g1rTaqIHKDQ/zIYY1oZY6YbY9YbY3KNMVcU\n4t6Wxpg9xpigDPeKSJjZuhUmTnTrEM84w42enXsuvP++6505dqz7XhQWpVlZWUydOpWsrCzfUUKr\nbl24917XM3XpUujfHz791K1BrVsXBg92H2JERAigMAXKAYuAW4ACL1A1xsQBk4CZAbyniIQra2He\nPOjTx50a1Lu3m6p99VXYuBGmTHFrDUuW9J3UqzVr1tCtWzfWrFnjO4o/jRu7Vl+rVrnfM5ddBv/6\nl/sQc9FF7vfK9u2+U4qIR4UuTK21M6y1D1pr3wEKs132eeBVYH5h31NEwlBWFjz9tCs2WrRwO7Tv\nvNO1ffr4YzdVG+Tz5iNZQkICW7ZsISEhwXcU/4xxByM8/7wbSX/lFXf9mmvch5tbbnGjqyISdUIy\nn2aM6Q2cBjwUivcTkSK0aJEbHa1RA+65x50E9PHHriAdOtRNz8phYmNjqVChArFaU3mwsmVdQTpr\nFqxcCbfdBm+/DWef7dagvvEG7N7tO6WIhEiRF6bGmPrAo0BPa21uUb+fiBSBXbvc1HyLFm7N6IwZ\nMGiQ22H/+uvuNKYoXDcqQXbGGW6q///+zxWkxsDf/w516sCQIbB+ve+EIlLEinRXvjEmBjd9P8Ra\nu2rf5YLen5KSQlxc3EHXkpOTSU5ODl5IEcnfr7+66dZ//xt+/tltWHnrLfjb33QmvRSdkiWhWzf3\nWLoUxoyBUaNcE//u3d2SkXPP9Z1SJKqkpqaSmpp60LUtW7YE/X2Oq8G+MSYX6GStnZ7P9+OALGAv\n+wvSmLz/3gu0t9Z+doT71GBfxKeVK9360QkTXPP0666DO+6Ahg19J4tYy5cv5/rrr2fixIk0aNDA\nd5zIk53tfj8+/bRrQXXRRa5A7dhRo/UinhRFg/2i/tOcDZwFNAES8h7PA9/n/fdXRfz+IlIY8+bB\nVVfBmWfCm2+6NaTr1rlRUxWlx6V06dI0btyY0jqmMzAVKsDtt8MPP7jfm9u2uROlzjoLxo93y01E\nJOIF0se0nDEmwRjTJO/S6Xlf18r7/ghjzCQA63x34AP4BdhprV1mrd0RtJ+JiATGWvjkE2jb1q0h\nXbYMXnjBrfMbMsSdfy7HrU6dOowfP546der4jhLZSpRwBzXMnw9ffAENGkDfvm596jPPqN2USIQL\nZMS0KbAQSMf1MR0JZLB/x/2pQK2gpBORomOta3zfooXbvLRli1s/+u23btd9mTK+E4rkzxh3gti0\nae5ksXbt3NR+3brw+ONu6l9EIk4gfUxnW2tjrLWxhzxuyPt+b2tt26Pc/5C1VgtHRXzJzYX//hcS\nE91UaEwMfPABLFjgzq7Xej2JNA0buhPHfvjBLUV58MH9O/mj7aQtkQinf4FEooW18N57kJQEXbq4\ns+tnzYI5c9wGElOY8zKksLZu3cq8efPYunWr7yjF12mnufXQq1fD9dfDk0+6a8OGwR9/+E4nIgWg\nwlSkuLMWZs6E5s1dm6e4OLc2b+ZMaNNGBWmIrFixghYtWrBixQrfUYq/GjVg9Oj9Beojj8Dpp8PI\nkbBDWxtEwpkKU5Hi7MsvXVudiy92BerHH7tR0gsu8J0s6sTHx7N06VLi4+N9R4kep57q2kutXOmm\n+AcOdJukxozRaVIiYUqFqUhxtGwZXHmlK0B//x2mT3e7mNu10wipJ2XKlKFx48aU0aay0KtVy3Wa\n+P5792fg1lshPt6dLnUcvbxFJPhUmIoUJz//DP36uXPGv/kGXnsNMjLcFL4KUol2Z5wBr7ziTpNq\n3Ngdd9qsmVvaIiJhQYWpSHGwbRs8/DDUq+eajz/xhBsdSk7WLnuRQzVq5GYRZs1yXSpat4ZOndyf\nGRHxSv9iiUSy3Fx3TGP9+jB8ONx8M6xaBQMGwAkn+E4nB1i9ejVdu3Zl9erVvqPIPm3awFdfuZmF\nxYvdKVL9+8Ovv/pOJhK1VJiKRKqvvnLTkDfcABdeCMuXu/Y4FSv6TiZHkJOTQ3Z2Njk5Ob6jyIFi\nYtzMwvffu8b8U6a4D3rPPQd79/pOJxJ1VJiKRJoNG+C661xRunevWx+XmupOvJGwVb9+fdLS0qhf\nv77vKHIkJ5zgTo764Qe4+mq47TZ3CMWsWb6TiUQVFaYikWLXLrd29Mwz3UlNL7wAX3+t1k8iwXTK\nKfDii+7PVvny0LYtdO0K//d/vpOJRAUVpiKR4NNPISEBBg1yU/crVkDfvhAb6zuZSPGUlOT6AE+Z\n4n6Mj4cRI9T/VKSIqTAVCWcbN8I118Bf/wpVqsCiRfDMM1pHGoF2795NZmYmu1XYRA5joGdP90Gw\nf38YPBiaNIHPP/edTKTYUmEqEo5yc91UfcOG8OGH8PLLMHu22zUsEWnp0qXUqlWLpUuX+o4ihVW+\nvNtYmJEBJ53kNhv27g2bNvlOJlLsqDAVCTeLF0OLFq5R/lVXud3CvXurH2mEq1evHjNmzKBevXq+\no0igzjkH5sxxa1DfeQcaNIDx490HSREJCv1LJxIudu6E++93a9u2bnXThS+9BJUr+04mQVChQgU6\ndOhAhQoVfEeR4xETAzfd5NqzXXEF9OnjltqsXOk7mUixoMJUJBzMnQvnnuumC4cMcVOGrVr5TiUi\n+alSBSZOhE8+cTv2zz4bnnpKvU9FjpMKUxGftm6Ff/7TtXyKi4OFC90Gi1KlfCcTkYJo2xaWLHGn\nrt1zj1uGs2SJ71QiEUuFqYgvH3/sNjO99BKMGuVa0jRu7DuVFJHMzEwGDBhAZmam7ygSbOXKuT/D\nc+fCtm2uMf+QIWotJRIAFaYiobZ1q9vY1L49nHGGG1254w71JC3msrOzSUtLIzs723cUKSrNmrll\nOPfdB48+CuedB9984zuVSERRYSoSSl984RrlT54MY8bAzJlw+um+U0kINGrUiG+//ZZGjRr5jiJF\n6YQT4OGH3clRubnQtKlrzK+1pyIFosJUJBR27oS773b9D6tVcy2hbr7ZNfAWkeKnSRNYsAAGDIAH\nHnCbGX/4wXcqkbCnwlSkqGVkuFGTf/0LHn/cNcpXL0uR4u+EE+Cxx9xMyaZNbrbk3/9W31ORo1Bh\nKlJUcnLcFN7557td9unpbtRUa0lFokuLFm6WpHdvuO026NgRNmzwnUokLBW6MDXGtDLGTDfGrDfG\n5BpjrjjG8zsbYz4yxvxijNlijJlrjGkfeGSRCPDjj67p9v33u2J0/nwdJxrlMjIyMMaQkZHhO4r4\nUK4cPPccpKW5DVHnnAPvvus7lUjYCWTEtBywCLgFsAV4fmvgI6AjkAjMAt41xiQE8N4i4e8//3FT\ndqtWwaefut256ksa9WrXrs2LL75I7dq1fUcRn9q3d4Vps2bu5Kj+/WHHDt+pRMJGoQtTa+0Ma+2D\n1tp3gGPu3LDWplhrn7LWpltrV1lr7wd+AP4WQF6R8LVtmzuqsGtXN1q6eDG0aeM7lYSJypUrc9NN\nN1FZR8xKlSowfbobQX35ZbcGXW2lRAAPa0yNMQY4Efgt1O8tUmQWLnRNtVNTYfx4ePNNqFTJdyoR\nCVfGwC23uJ37sbHwl7+4DZK2IBORIsWXj81Pd+OWA7zp4b1Fgsta14+0WTO3hiwjA268UW2gRKRg\nGjeG//0P/vEPuP12uOoqyMrynUrEm5AWpsaYHsBgoKu1dnMo31sk6LZsge7d3Rqxvn1h3jxo0MB3\nKglTGzduZNSoUWzcuNF3FAk3pUvDM8/AtGnw2Wdu9uXrr32nEvGiRKjeyBjzd2Ac0MVaO6sg96Sk\npBAXF3fQteTkZJKTk4sgoUghZGRAt26uN+HUqdCli+9EEuY2bNjA0KFDadu2LVWrVvUdR8JRp06u\nMX/37tCyJTz1lGsvpRkYCQOpqamkpqYedG3Lli1Bfx9jj2M9izEmF+hkrZ1+jOclA+OB7tba9wrw\nuolAenp6OomJiQHnEwk6a2HsWEhJce2f3nzTnXcvIhIsu3fDwIEwejR07uw2SJ10ku9UIofJyMgg\nKSkJIMlaG5ReeIH0MS1njEkwxjTJu3R63te18r4/whgz6YDn9wAmAXcCXxtjquY9KgTjJyASMlu3\nQnLy/qn7uXNVlIpI8JUqBaNGuan9WbPc1P7Chb5TiYREIGtMmwILgXRcH9ORQAbwUN73TwVqHfD8\nPkAs8Bzw0wGPpwOLLOLBihVug9P777tR0mefdccNiogUlU6dXEFaqZI7PWrSpGPfIxLhCr3G1Fo7\nm6MUtNba3od8fVEAuUTCx9tvw7XXQvXqbvdsfLzvRCISLerWhTlz3EzN9dfDV1+5KX59MJZiyke7\nKJHIkJMDgwa5NV7t26soleOyZMkSatasyZIlS3xHkUhTujS89BKMG+d+vPBCyMz0nUqkSKgwFTmS\nzZvhkkvg8cfhiSfczvsKWhYtgdPJT3Lc+vRxo6c//QRJSa61lEgxo8JU5FCLFrkjAhcvho8/hrvv\nVrsWOW7VqlVj6NChVKtWzXcUiWTnnQfp6XD22dCunet/qtOipBhRYSpyoKlTXf/Ak092f/m3bes7\nkYjIwapUgbQ017bujjvcaXO7dvlOJRIUKkxFAHJzYfBg1zT/iivgiy+gVq1j3yci4kNsLDz5JLzy\nCrz2Glx0Efz8s+9UIsdNhanIH3+486mHD4cRI9xf8mXL+k4lxUxWVhZTp04lS+egSzBdcw18/jms\nXeuWIC1Y4DuRyHFRYSrRbdUqaN4cPv0Upk93p61oPakUgTVr1tCtWzfWrFnjO4oUN3/5iytIa9SA\nVq3ch2uRCKXCVKLX7NnuL/Rdu1xvwMsv951IirGEhAS2bNlCQkKC7yhSHFWv7v5O69YNevZ0re5y\nc32nEik0FaYSnSZNgosvhiZN1J9UQiI2NpYKFSoQGxvrO4oUV6VLw8SJrsXdY49B9+6wY4fvVCKF\nosJUoktuLjzwgDtB5brrYMYMqFjRdyoRkeAwxrW4e+st+OADaNNGm6IkoqgwleixYwf8/e/w6KNu\nN+u4cVCypO9UIiLB16mT6y6SmQnnnw86cUwihApTiQ4bN7p2Ku+9B//9L9x1lzY5SUgtX76c5s2b\ns3z5ct9RJFokJrr185Uquf7MH37oO5HIMakwleLvu+/ciMG6dW4EoXNn34kkCpUuXZrGjRtTunRp\n31EkmtSs6f7ea9PGbfAcM8Z3IpGjUmEqxdvnn7uRgrg4t8kpKcl3IolSderUYfz48dSpU8d3FIk2\n5cvDtGnwz39C//6uLZ527EuYKuE7gEiRefNN13y6VSu3EaBCBd+JRET8iI2F0aOhdm2480748Ud4\n+WU44QTfyUQOohFTKX6shVGjXKuUbt3czlQVpSIikJICb7zh1tp37Ai//+47kchBVJhK8ZKT4/7i\nvfNO12D6lVegVCnfqUTYunUr8+bNY+vWrb6jSLTr2hU+/hgWLXIzSj/+6DuRyJ9UmErxsWOHGyV9\n9lkYOxaGD9fOewkbK1asoEWLFqxYscJ3FBFXkH75JfzxhzuW+ZtvfCcSAVSYSnHx++/QoYObtp82\nDfr1851I5CDx8fEsXbqUeJ0yJuEiPh7mzYNTToHWrd3ufRHPVJhK5Pv5Z9cKZelS+OQTuOIK34lE\nDlOmTBkaN25MmTJlfEcR2a9aNfjsM9fztH17ePdd34kkyqkwlci2apVrB7Vpk/u037y570QiIpGl\nQgU323Tppa7P88SJvhNJFFNhKpFr0SJXlMbGurVSjRv7TiQiEplKl3Yt9m64AXr3hqee8p1IopQK\nU4lMn38OF17oTjWZMwfq1vWdSOSoVq9eTdeuXVm9erXvKCJHFhsLL7wA998Pd98N997r2u+JhJAa\n7Evkefdd15+0RQt4+2048UTfiUSOKScnh+zsbHJycnxHEcmfMTBsGFSpAnfcAZs3u2K1hMoFCY1C\nj5gaY1oZY6YbY9YbY3KNMcfcaWKMaWOMSTfG7DTGrDDGXBdYXIl6qaluDdSll7o1USpKJULUr1+f\ntLQ06tev7zuKyLHdfjtMngyTJkGPHrB7t+9EEiUCmcovBywCbgGOOcZvjKkLvAd8AiQAzwDjjTEX\nB/DeEs3Gj4eePd3jjTd0lJ6ISFHq1Qv+8x945x246irXK1qkiBW6MLXWzrDWPmitfQcoSPfym4HV\n1tp7rLXLrbXPAf8BUgr73hLFnn4a+vSBm2+GCRM0rSQiEgqdOsF778Gnn8Jll7mG/CJFKBSbn5oB\nMw+5lgaor48cm7VuvVNKCtxzD/z73xCjPXsSeXbv3k1mZia7NSUqkebiiyEtDRYscL1Os7J8J5Ji\nLBTDTqcCGw+5thGoYIw5wVq7q6AvtH07fP99ULNJOLOW6s8O5NRJT/DTLcP4udsgWKgjRiUyLVu2\nlF69kpgyJZ34+ETfcUQKp1wryo75lHq3dmB3s4tY+dxH7K10iu9UEkING0LZskX/PmE9H5qSkkJc\nXNyfX2/ZAp9/ngwk+wslIWHI5Vluoz9juIPRPDPmDhjjO5XI8agHzKBXr3q+g4gEqCmNmc3MLe0o\ndXFrOvIJP1HDdygJkeHDU5k/P/Wga1u2bAn6+xh7HD3KjDG5QCdr7fSjPGc2kG6tHXDAteuB0dba\nivnckwikp6enk5i4f2RBI6ZRIjeX2o/24+S3x7Pu/nH82vkm34lERCTPCet+oH6/v5JbshQ/vDCL\nPafW8h1JQuBII6YZGRkkJSUBJFlrM4LxPqEYMZ0HdDzkWvu864VStqw7zleKsZwct8np7YkwYQJ1\nrruOOr4ziYjIfon1IWE2XHQRZ996IcyaBXX0N7UERyB9TMsZYxKMMU3yLp2e93WtvO+PMMZMOuCW\n5/Oe87gxpoEx5hagCzDquNNL8ZKT447DmzTJ9c+7Tu1uRUTC0mmnwezZ7r8vvBDWrPGbR4qNQLY3\nNwUWAum4PqYjgQzgobzvnwr8Oa5vrV0LXAa0w/U/TQFutNYeulNfotnevXDttfDqq/Daa65XqUgx\nkpmZyYABA8jMzPQdRSQ46tRxxWnJkq44XbXKdyIpBgLpYzrbWhtjrY095HFD3vd7W2vbHnLP59ba\nJGttGWttfWvt5GD9BKQY2LPHFaJvvgmvvw7du/tOJBJ02dnZpKWlkZ2d7TuKSPDUqgWffQZlyrji\n9IcffCeSCKeGkOLXnj3uuLtp01xh2qWL70QiRaJRo0Z8++23NGrUyHcUkeCqUcMVpxUquOJ0+XLf\niSSCqTAVf/budSOl77zjjr3r3Nl3IhERCUS1am4TVKVKcNFFGjmVgKkwFT/27oVrrnEjpVOnwhVX\n+E4kIiLHo2pV+OQTiItzxanWnEoAVJhK6OXkQO/eriB9/XW48krfiUREJBiqVoVPP4Vy5Vxxqt36\nUkgqTCXB4xAgAAAgAElEQVS0cnPhxhvdzvvXXoOrr/adSCQkMjIyMMaQkRGUHtQi4ataNVeclioF\nbdvCunW+E0kEUWEqoZObC337uh6lkydDt26+E4mETO3atXnxxRepXbu27ygiRa9GDbfm1Bg3cqo2\naVJAKkwlNHJz4eab4eWXYeJEtxNfJIpUrlyZm266icqVK/uOIhIatWq54jQnxxWn69f7TiQRQIWp\nFD1rISUFxo2Dl15ym55ERKT4q1PHFae7dkG7dvDLL74TSZhTYSpFb/Bg+Ne/YMwYt+lJRESix2mn\nud36WVnQoYP7USQfKkylaI0YAcOHw5NPuql8kSi1ceNGRo0axcaNG31HEQm9+vVh5ky3EerSS+GP\nP3wnkjClwlSKzrPPwqBBMGQI3HWX7zQiXm3YsIGhQ4eyYcMG31FE/DjrLPjoI/juO9e7escO34kk\nDKkwlaLx8svwz3/CnXe6wlQkyjVp0oTs7GyaNGniO4qIP0lJ8P778L//uXaBu3f7TiRhRoWpBN8b\nb0CfPvCPf7gpfGN8JxIRkXBxwQXuKOpPPnHHUu/d6zuRhBEVphJc770HvXq5dlBjxqgoFRGRw7Vr\n507/mzbNHbqSm+s7kYQJFaYSPF98AV27wuWXw4QJEKPfXiIiko8rrth/4Mqdd7rWghL1VDlIcCxa\n5ArS5s0hNRVKlPCdSCSsLFmyhJo1a7JkyRLfUUTCR3IyPPccPP206+IiUU/Vgxy/lSvhkktcO5C3\n34bSpX0nEgk7OvlJJB833wybN8P998PJJ7v9CRK1VJjK8fnpJ7j4YjjpJPjwQ6hQwXcikbBUrVo1\nhg4d6juGSHh64AFXnN58M1SsCN26+U4knqgwlcD99ps7xWPvXpg9G6pU8Z1IREQikTEwejT8+qvb\nQHvSSdC+ve9U4oHWmEpgtm1za0o3bHANk2vX9p1IREQiWUyM2zjbvj107gzz5/tOJB6oMJXC27PH\n7b5fssRN38fH+04kEvaysrKYOnUqWTonXCR/JUvCm29CYiJcdhksW+Y7kYSYClMpHGuhb1935vFb\nb8F55/lOJBIR1qxZQ7du3VizZo3vKCLhrWxZePddqF7dbaz96SffiSSEVJhK4TzwAEyc6B4XX+w7\njUjESEhIYMuWLSQkJPiOIhL+9m2ozc2Fjh1hyxbfiSREAipMjTH9jTFrjDE7jDHzjTFHHTYzxvQ0\nxiwyxmwzxvxkjHnJGFMpsMjizZgx8Oij7pjRHj18pxGJKLGxsVSoUIHY2FjfUUQiQ82akJYGP/4I\nnTrBrl2+E0kIFLowNcZ0B0YCQ4BzgcVAmjHmiM35jDEtgUnAi0AjoAvwF2BcgJnFh7fegltvhTvu\ncCd0iIiIFLVGjWD6dLcR6tprdXRpFAhkxDQFeMFa+4q19nugH7AduCGf5zcD1lhrn7PW/p+1di7w\nAq44lUjwxRduhLRbNxg50rX1EBERCYULLoDXXoP//AcGDNDRpcVcoQpTY0xJIAn4ZN81a60FZgLN\n87ltHlDLGNMx7zWqAl2B9wMJLCH27bfuPOMWLWDSJNfOQ0QKbfny5TRv3pzly5f7jiISeTp3dkeX\nPvMMPPWU7zRShArbYL8yEAtsPOT6RqDBkW6w1s41xvQC3jDGlM57z+nArYV8bwm19evdjsjatWHa\nNDjhBN+JRCJW6dKlady4MaV1ZK9IYPr1c/8u3XMP1KihvQ7FVJGf/GSMaQQ8AwwFPgKqAU/hpvNv\nKur3lwD98YdroA/wwQcQF+c3j0iEq1OnDuPHj/cdQySyPfyw2wzVu7fbHNW6te9EEmSFLUw3AzlA\n1UOuVwV+zueegcCX1tpReV8vNcbcAnxhjLnfWnvo6OufUlJSiDukIEpOTiY5ObmQsaVQ9u5160lX\nr4Y5c9wnUxEREd+MgXHj9u/UnzsXGjb0nSoqpKamkpqaetC1LUXQxsvYQi4iNsbMB76y1t6e97UB\n1gH/stY+eYTn/wfYba3tccC15sAcoIa19rCC1hiTCKSnp6eTmJhYqHxynKx10yUvv+x6yLVr5zuR\niIjIwX7/3W2K2r4d5s2DqoeOl0koZGRkkJSUBJBkrc0IxmsGspNlFNDHGHOtMaYh8DxQFpgIYIwZ\nYYyZdMDz3wWuNsb0M8acltc+6hlccZvfKKv48sQT7tPouHEqSkWCaOvWrcybN4+tW7f6jiIS+U46\nCd5/H3bscBt0t2/3nUiCpNCFqbX2TeAu4GFgIXAO0MFauynvKacCtQ54/iRgANAfWAK8ASwDrj6u\n5BJ8r78OAwfC4MFu/Y6IBM2KFSto0aIFK1as8B1FpHioU8cVp99+Cz17Qk6O70QSBIWeyg8FTeV7\n8MUXboS0e3fXFkq9SkWCaseOHaxevZrTTz+dMmXK+I4jUny89x5ceSXcdhs8/bTvNFElXKbypbj5\n4Qe3iLxlSxg/XkWpSBEoU6YMjRs3VlEqEmyXXw7PPut6nD77rO80cpyKvF2UhLnffnN/qKtUgf/+\nF0qV8p1IRESkcG65BVatcsdm16sHHTv6TiQBUmEazfbsgS5dYPNm+OorqFjRdyIREZHAPPGEmwHs\n3t21kTrrLN+JJACayo9W1rpPmHPmuFOd6tXznUikWFu9ejVdu3Zl9erVvqOIFE+xsfDaa3D66W4m\ncGO+bdIljKkwjVajRrn1pOPG6eQMkRDIyckhOzubHO0cFik65cvDu+/Crl1u78TOnb4TSSGpMI1G\n06fD3Xe71lDXX+87jUhUqF+/PmlpadSvX993FJHirVYteOcdWLQIbrjBzRBKxFBhGm0WLYIePdwn\nyeHDfacREREJvr/8BV55BVJT4eGHfaeRQlBhGk02bIC//Q0aNIDJkyFGv/wiIlJMde0Kw4bB0KHu\nABmJCKpMosXOndC5M+Tmuqn8cuV8JxKJKrt37yYzM5Pdu3f7jiISPQYNgl693GmGCxb4TiMFoMI0\nGlgLffu6afy334YaNXwnEok6S5cupVatWixdutR3FJHoYQy8+CKcc45bwrZhg+9EcgwqTKPByJFu\n6v7ll+G883ynEYlK9erVY8aMGdRTazaR0Cpd2g3KWOtmDrVTP6ypMC3uPvgA7rnH7cDv0cN3GpGo\nVaFCBTp06ECFChV8RxGJPtWqueJ08WI3g6id+mFLhWlx9v33kJwMl13mFoCLiIhEq/POg5decjOI\nI0f6TiP50JGkxVVWFlxxBdSsCa++6k7EEBERiWY9esDSpW4msVEjuPRS34nkEBoxLY727nVnBf/6\nq9uBr6lDEe8yMzMZMGAAmZmZvqOIRLdhw9yRpcnJsGyZ7zRyCBWmxdG998Knn8LUqXDGGb7TiAiQ\nnZ1NWloa2dnZvqOIRLeYGJgyxZ0QdeWV8PvvvhPJAVSYFjevvQajRrlH27a+04hInkaNGvHtt9/S\nqFEj31FEpEIFd2zppk2uz2luru9EkkeFaXGycCHceCNcey3cdpvvNCIiIuHrjDPckaUffABDhvhO\nI3lUmBYXmze7/myNG8Pzz7umwiIiIpK/Sy6BRx91606nTfOdRlBhWjzs2+y0fbv7g1WmjO9EIiIi\nkeHee6FLFzfb+N13vtNEPRWmxcG998Ls2W6zU61avtOIyBFkZGRgjCEjI8N3FBE5kDEwYQLUreuO\nLdVmKK9UmEa6Azc7XXih7zQiko/atWvz4osvUrt2bd9RRORQ5cu7GUdthvJOhWkkW7gQbrpJm51E\nIkDlypW56aabqFy5su8oInIk9ert3ww1dKjvNFFLhWmk+u03uOoqd3KFNjuJiIgcv0sugeHD4ZFH\n3AE1EnIBFabGmP7GmDXGmB3GmPnGmPOO8fxSxpjhxpi1xpidxpjVxpjrA0osboqhVy/Izob//leb\nnURERIJl4EC31vTaa2HlSt9pok6hC1NjTHdgJDAEOBdYDKQZY442PzUVuAjoDZwJJAPLC51WnEce\ngRkz3JRDnTq+04hIAWzcuJFRo0axceNG31FE5GiMgYkT4ZRT4OqrXccbCZlARkxTgBesta9Ya78H\n+gHbgRuO9GRjzCVAK+BSa+0sa+06a+1X1tp5AaeOZh9+CA89BA8/DO3b+04jIgW0YcMGhg4dyoYN\nG3xHEZFjiYuDt95yI6b/+AdY6ztR1ChUYWqMKQkkAZ/su2attcBMoHk+t/0NWADca4zJNMYsN8Y8\naYwpHWDm6LVmDfTsCZddBoMG+U4jIoXQpEkTsrOzadKkie8oIlIQZ50F48fDlCkwdqzvNFGjRCGf\nXxmIBQ6di9oINMjnntNxI6Y7gU55rzEWqATcWMj3j147drgGwBUrwuTJEKN9ayIiIkUqORnmzYM7\n7oDERGjWzHeiYq+whWkgYoBcoIe1diuAMWYAMNUYc4u1dld+N6akpBAXF3fQteTkZJKTk4syb3i6\n9VZ3IsX8+XDSSb7TiIiIRIennoL0dDc4lJHh1p5GodTUVFJTUw+6tmXLlqC/j7GFWDeRN5W/Hbja\nWjv9gOsTgThrbecj3DMRaGGtPfOAaw2Bb4EzrbWrjnBPIpCenp5OYmJiwX82xdX48dCnD0ya5HYJ\nioiISOisX+9GTBs3ho8+ghKhGNcLfxkZGSQlJQEkWWuDcqxdoeaDrbV7gHTgr/uuGWNM3tdz87nt\nS6C6MabsAdca4EZRMwuVNhotXOhGS/v1U1EqEsGWLFlCzZo1WbJkie8oIlJYNWrAG2+447/VfL9I\nBbJQcRTQxxhzbd7I5/NAWWAigDFmhDFm0gHPfw34FZhgjIk3xrQGngBeOto0vgBbtkDXrm4B9tNP\n+04jIsdBJz+JRLg2bVzz/eHDXYccKRKFHou21r6Z17P0YaAqsAjoYK3dlPeUU4FaBzx/mzHmYuBZ\n4GtckfoGMPg4sxdv1sINN8DmzfDxx3DCCb4TichxqFatGkM10iIS2e65B+bMcYfcLFoEtWod+x4p\nlIAWSVhrxwBj8vle7yNcWwF0COS9otYzz7geam+/Daed5juNiIiIxMS4/R6JidCtm5vaL1XKd6pi\nRT2HwtG8eXD33XDXXXDllb7TiIiIyD4nnwxvvul26g8c6DtNsaPCNNxs3uw+hf3lL/Doo77TiEiQ\nZGVlMXXqVLKysnxHEZHjdf75ro3U6NEwbZrvNMWKCtNwkpvrdt7v3Ol2/5Us6TuRiATJmjVr6Nat\nG2vWrPEdRUSC4bbb4Oqr4frrYdVhnS8lQCpMw8ljj8GMGfDqq1Czpu80IhJECQkJbNmyhYSEBN9R\nRCQYjIGXXnIN97t2dYNKctxUmIaLzz+HwYPhgQegfXvfaUQkyGJjY6lQoQKxsbG+o4hIsMTFwdSp\n7mTGAQN8pykWVJiGg82b3Xm8rVvDkCG+04iIiEhBNWniOumMHQv/+Y/vNBFPhalvublufcru3W4K\nX6MpIiIikaVvXzedf+ONoHXkx0WFqW+jR8P778Mrr0D16r7TiEgRWb58Oc2bN2f58uW+o4hIsBkD\nL77oWkn9/e9usEkCosLUp//9z/VAu+ce6NjRdxoRKUKlS5emcePGlC5d2ncUESkKcXGuo87ChTBo\nkO80EUuFqS+//w7du0PTpjBsmO80IlLE6tSpw/jx46lTp47vKCJSVM47Dx5/HEaOdLOhUmgqTH2w\nFvr0ccVpaqr6lYqIiBQXd9wBl18O110HmZm+00QcFaY+PP+827n38stQt67vNCIiIhIsxsDEiVCm\nDPToAXv3+k4UUVSYhto330BKCtx6K3Tu7DuNiITI1q1bmTdvHlu3bvUdRUSK2sknuxnRuXPh4Yd9\np4koKkxDaft2t1uvYUN48knfaUQkhFasWEGLFi1YsWKF7ygiEgoXXABDh8Lw4e4QHSkQFaahlJIC\na9e6T1HamSsSVeLj41m6dCnx8fG+o4hIqNx3H7RqBT17wm+/+U4TEVSYhspbb8G4ce50CP3DJBJ1\nypQpQ+PGjSlTpozvKCISKrGxMHkybNvmNj1b6ztR2FNhGgo//gg33QRdurgfRUREJDrUqgUvveQG\nqF580XeasKfCtKjl5ECvXnDiiW7E1BjfiURERCSUOneGfv1cK6nvvvOdJqypMC1qjz4Kc+bAq69C\nxYq+04iIJ6tXr6Zr166sXr3adxQR8WHkSDjtNLcJeudO32nClgrTovTll/DQQzB4sNudJyJRKycn\nh+zsbHJycnxHEREfypaF11+HFSvcUeRyRCpMi8rvv7tdeM2awQMP+E4jIp7Vr1+ftLQ06tev7zuK\niPhy9tnw1FPw7LPw3nu+04SlEr4DFFu33OKK09mzoYT+N8uRrVu3js2bN/uOISJBVrlyZWrXru07\nhoSj/v3ho4+gd29YsgROPdV3orCiiqkovPqq61Wamgp16vhOI2Fq3bp1xMfHs337dt9RRCTIypYt\ny7Jly1ScyuGMcbv0zz4bbrzRjZxqY/SfAipMjTH9gbuAU4HFwG3W2q8LcF9L4DNgibU2MZD3Dntr\n17rR0l693AJnkXxs3ryZ7du3M2XKFDVdFylGli1bRq9evdi8ebMKUzmyKlVgwgS49FIYM8aNogoQ\nQGFqjOkOjAT6Av8DUoA0Y8yZ1tp85ySNMXHAJGAmUDWwuGEuJweuvdbtvv/3v32nkQgRHx9PYmLx\n/JwmIiL56NjRFaR33QUXXQSNGvlOFBYC2fyUArxgrX3FWvs90A/YDtxwjPueB14F5gfwnpHhiSfc\nTvzJkyEuzncaERERCWdPPulaSPXsCbt2+U4TFgpVmBpjSgJJwCf7rllrLW4UtPlR7usNnAY8FFjM\nCLBgATz4IAwc6M7FFRERETmaMmXcvpRvv3U1hBR6xLQyEAtsPOT6Rtx608MYY+oDjwI9rbW5hU4Y\nCbZtc592EhJgyBDfaURERCRSnHsuDBvmRk8/+8x3Gu+KtI+pMSYGN30/xFq7at/lonxPL+66CzIz\n3aeeUqV8pxEREZFIcuedcOGFcM01kJXlO41Xhd38tBnI4fDNS1WBn4/w/BOBpkATY8xzeddiAGOM\n2Q20t9Z+lt+bpaSkEHfIWs3k5GSSk5MLGbsIvfcePP+8ezRo4DuNiIiIRJrYWHjlFddC6uabXbvJ\nMGshlZqaSmpq6kHXtmzZEvT3KVRhaq3dY4xJB/4KTAdXYeZ9/a8j3JINnHXItf7ARcDVwNqjvd/o\n0aPDe7fypk2uB9nll0Pfvr7TiIiISKSqVcsNciUnw5VXuh/DyJEGBjMyMkhKSgrq+wQylT8K6GOM\nudYY0xC3274sMBHAGDPCGDMJ3MYoa+13Bz6AX4Cd1tpl1todwflpeGAt/OMfkJsL48eH3ScbkeJg\n4sSJxMTEsG7dOt9RCuWLL77gyy+/9B1DRCLN3//uHrfc4pYIRqFCF6bW2jdxzfUfBhYC5wAdrLWb\n8p5yKlAraAnD1eTJMG0ajBsHVYtnW1aR4zVp0iRiYmL+fJQpU4YGDRpw22238csvvxzzfmMMJsI+\n9K1cuZL33nuPli1b+o4SkJEjR3LGGWdQpUoV31EYOHAg27Zt8x1DJLSeew7KloUbbnCDYFEmoM1P\n1tox1tq61toy1trm1toFB3yvt7W27VHufSjiT31atw5uu8010+/c2XcakbBmjGHYsGFMmTKF5557\njpYtWzJ27FhatGjBzp07j3rvtddey44dO0J2es7mzZu544476NSpEwDz58+nW7duVKtWjYoVKzJi\nxIhjvsagQYN44IEHijpqgXzyySe0adOmUPfceeedXHPNNSE7jexoGW+99VZSUlJCkkMkbFSqBC+/\nDB9/7E6FijIBHUka1XJz4frrXQP9fx1pWa2IHOqSSy75c734DTfcQKVKlRg9ejTvvPMO3bt3P+I9\n27dvp2zZspQKYqeLfa+Zn3fffZe0tDQuuOACBg8eTPny5XnllVf4448/6NKlCw888AD9+/enQoUK\nR7x/3rx5nHLKKZx44olByxyIqVOn8sEHH7B169aAlkEsXryYFi1aFEGy/QqSsWbNmpx55pm8/fbb\nf35YEIkKHTq46fy774aLL4Yzz/SdKGSKtF1UsfSvf8GsWTBxok53EglQ27ZtsdayZs0aAIYOHUpM\nTAzLli2jR48eVKpUiVatWv25FODQwmXhwoV07NiRuLg4TjzxRNq1a8dXX3110HPye82j6d27N7/+\n+isffPABOTk53HvvvZQuXZoqVarQvXt3qlevnm9RCjBmzBiuueaaAP+vBE/Xrl2ZMGECl19+eUD3\nz58/n+bN8z0zJSgKmrFPnz6MHj26SLOIhKUnnoCaNV0Lqb17facJGRWmhfHdd+5kpzvugLb5rlYQ\nkWNYuXIlACeffDLAn+tIu3btys6dOxkxYgR9+vQ56Hv7fPfdd7Ru3ZolS5YwcOBAHnzwQdauXUub\nNm34+uuv/3ze0V4zP1lZWWzevBljDA89tP+gut9++41p06bx5ptvHvX+OXPmBH2HaqitXbuWX375\npcgL04KKi4vjpJNOYunSpb6jiIRWuXKuhdSCBfDYY77ThIym8gtqzx63pvT00+HRR32nEYkoW7Zs\n4ddff2Xnzp3MmTOHRx55hLJlyx42WnbuuecyefLkP7+eNGnSYa91//33s3fvXr788kvq1KkDwDXX\nXEODBg245557mDVr1lFf82gWL14MwO23307JkiVZsmTJn1P5EyZMoGbNmvneu3LlSqpUqUKJEkf+\na3X9+vU8/PDD1KtXj23btpGZmUnnzp257LLLCpQtVObPn0/16tV54403yM3NZe7cuQwdOjRka06P\npHnz5nz44Yecddah3QdFirlmzWDQIHjoIejYESL8g29BqDAtqGHDYPFimD/fnW0rEmLbt8P33xft\nezRs6DaDBpO1lr/+9a9/fm2MoW7duqSmplKtWrWDrv/jH/846mvl5uby8ccf07lz5z+LUoBTTz2V\nHj16MH78eLZu3Ur58uUL/JoHysjIoFSpUvTt25ebb76Zt956i82bN1O3bl3atWtHly5d8r13/fr1\nnHLKKUf83qZNm2jTpg0TJ06kZcuWfPXVVzRv3pxu3boVOFuozJs3j5IlS9KtWzeqVq1K9erV6dev\nH7Nnz/aWKSEhgSlTpnh7fxGvBg+G9993U/rp6cW+BlFhWhALFsDw4fDgg1HxaUXC0/ffF/1vv/R0\nCPaZFsYYxowZQ/369SlRogRVq1alQT6npJ122mlHfa1Nmzaxfft2zjzCRoD4+Hhyc3P58ccfDxrd\nO9ZrHig9PZ3WrVsTFxfH2LFjGTt2LAsWLODaa68lOTmZ+vXrk5CQkG+2Q0+q2+fOO+/k3HPP/bOF\nVMWKFYmNjT3iBqPc3Fyuvvpqdu3aBbjC/kD7lihYaznppJMOO4nleM2fP58HHniAqnlt8MqXL8+8\nefO85qxUqRKrVq069hNFiqNSpVyLysREV4c8+aTvREVKhemx7NwJ110HTZrAfff5TiNRrGFDVzgW\n9XsUhfPOO69Ap7iVKYKRgMK85qeffsqgQYMOuta0aVOmTJlC06ZN+fTTT/MtTHNzc494/bfffuP1\n118/aMTvyy+/JCEh4c+R3QPFxMQwbdq0AmcOpt27d7N48WIuuOCCP699//33nHDCCYc9N5Q5K1as\nWCRHH4pEjMaN4ZFH3D6XTp0gQvskF4QK02MZMgRWrnQVQcmSvtNIFCtbNvijmZGmSpUqlC1bluXL\nlx/2vWXLlhETE0OtWoGd77Fw4UJ++eWXI7YlatSoEcBR15hWrlyZ33///bDr8+fPJycn56COAHPn\nzj1mhwAfVq5cSfny5Q8akf7ss8+8HxaQk5MT1LZhIhHpzjvdwT7XX++WFgZ73VWYUGF6NPPmwVNP\nuWl8LboX8S4mJob27dvzzjvvsG7duj8b72/cuJHU1FRatWp1xFHIgnj//fc577zzjljYfv755zRq\n1IjORzlQo1q1avz666+HXd+5cycnnnjiQetpv/zyS4YNG8bXX39NTk4OzZo1+/N7h06R56copvJ3\n7NhxUFGalZXFzJkzmTp16mHPDWXOrKyssDiJSsSr2FjXqnLfDO4zz/hOVCRUmOZn+3b3qeS88+Cu\nu3ynEYlYh649PF7Dhg1j5syZtGzZkltuuYXY2FjGjRvH7t27eeKJJwJ+3cmTJ1OzZk3q1KnDqFGj\n6NSpE3v27CEtLY0JEyaQlpaW7457gIYNG7Jx40Zyc3OJidnfie/888/HGMPevXspUaIEY8eOZe3a\ntcTHxzN9+vTDTjYK5hR5Tk7OEZcYTJo0icGDB7No0SIqVar05/X4+Hj27Nnz59e33347Xbt25dJL\nLz3sNYKVM7+MB9q8eTPVq1c/7vcSiXgNGsCIEZCSAlddBRde6DtR0KmPaX7uv98dPTppEhzlHyMR\nObpgn3XfqFEjvvjiC84++2wee+wxHnnkEU477TQ+++wzmjZtGtBrfvzxx5x//vk8++yz1K1bl549\ne1K9enU6d+7Mtm3bePvtt6lRo8ZRX8MYw/nnn/9ny6l9atSowciRI7n11lt56KGHaNiwIffffz+j\nR4+mYsWKRTJFPWPGDLp06cKgQYP48ccfadWq1UE9XHNzc9m1axfz588/6L6yZcty3333cdddd9Gv\nXz/q1avHhAkTgp6vIBkPtGDBgoB/bUWKnX/+E1q1gt69YetW32mCzgR7NCMYjDGJQHp6enqBNkwE\n3eefQ5s2bhp/wIDQv79EhYyMDJKSkvD2+1yCLi0tjc8//5zhw4f7jnJMf/zxB5988klEHPV58cUX\n8/zzz3PGGWf4jlIg+rMtRW7VKjjnHLc5e8wYbzH2/V4Hkqy1GcF4TY2YHmrrVvcppGVLuP1232lE\nJIJ06NCBb775hp07d/qOckyzZ8+OiFOq1q9fj7U2YopSkZA44wzXNmrsWJg503eaoFJheqh774Wf\nf4YJE9xCYxGRQhgyZMhBx5mGo7179/LNN98E3MEglJ599lkGDx7sO4ZI+OnXzx2PfsMNUIzaqakw\nPX7A8DwAABsvSURBVNCsWW5I/LHHoF4932lEJAI1bdqUpKSkw45GDSfr16/Pdz1nOFm8eDG7d+/m\nwmK4wUPkuMXEwMsvQ1YW3H237zRBo109+2zbBjfdBK1bQ//+vtOISAQ72tGl4eDA41zD2QcffMCT\nxfyUG5HjUqeOm9K/+Wbo1g3atfOd6LhpxHSfQYNgwwZ46SX3KURERLy67777iNWSKpGj69sXLrrI\nDa798YfvNMdNFRjAnDnw7LOukb6m8EVERCRSxMTA+PGwaVOxODpdhemOHXDjjdCsmesNJiIiIhJJ\nTj/d7Y957jmYPdt3muOiwvTBB+H//s8tINaUkYiIiESi/v1d4/0bb3SnV0ao6C5Mv/oKRo2Chx6C\nhg19pxEREREJTEyM2yezfr07vTJCRW9humuXa6SflAR33uk7jYiIiMjxqV/f7Zd55hmYO9d3moBE\nb2H68MOwcqWbwi+hrlkiIiJSDNx+O5x/vmu8v2OH7zSFFp2FaUYGPP44DB4MZ53lO42IiIhIcMTG\nukG3tWth6FDfaQotoMLUGNPfGLPGGLPDGDPfGHPeUZ7b2RjzkTHmF2PMFmPMXGNM+8AjH6c9e9zC\n4MaNYeBAbzFEREREikR8PAwZAiNHusG4CFLowtQY0x0YCQwBzgUWA2nGmMr53NIa+AjoCCQCs4B3\njTEJASU+XiNHwjffuAXCJUt6iSAiIiJSpO66C84+2w3G7dnjO02BBTJimgK8YK19xVr7PdAP2A7c\ncKQnW2tTrLVPWWvTrbWrrLX3Az8Afws4daBWrHDD2gMGQNOmIX97ERERkZAoWdI13v/mGzcoFyEK\nVZgaY0oCScAn+65Zay0wE2hewNcwwInAb4V57+OWmwt9+kDNmq49lMj/t3fn0VFV2eLHv7sCAjEh\nERMSspgUGUK7ZP4hTYM8ZBDsFngQEWRosENAG9FGAWlogpJGFPU5MSkCKr+A3Q2KLTxEQSIQ+GmA\n0NCgjQ8ajApJmBEIpM7vj1vJy1RJVaWmJPuzVi3JrXPP3eVJVXadewallFKqOitYeSg52eqcqwLc\n7TGNAkKAUyWOnwJiXazjaeBm4AM3r105y5ZBWpr139BQv15aKVU9rFy5EpvNxokTJwIdilu+/PJL\ndu7cGegwlFKBkJxsdcr97ndWJ12Q8+usfBEZCcwGEowxORWVf/LJJ3nggQeKPVJTU92/8Pffw7Rp\n1jiL3r3dP18p5ZFVq1Zhs9kKH/Xq1aN169ZMnjyZ06dPe/166enpzJ07lwsXLni9bgARwbrpU3Uc\nPXqUv//973Tv3j3QoXjkpZdeokWLFkRHRwc0jhkzZnD58uWAxqCUR0JD4a234Msvrc45D6WmppbK\nyZ588kkvBupgjHH5AdQGrgMPlDi+ElhfwbkPAZeA+1y4TkfAZGRkmEqz2435zW+MiY015syZyten\nlJdkZGQYr/2eB6mVK1cam81mUlJSzOrVq83y5cvNuHHjTEhIiGnRooW5cuWKV6+3cOFCY7PZzL//\n/W+v1lvAbreba9eu+aTusmRnZ5spU6aYQYMGGWOMSU9PNwkJCSY2NtZERkaaP//5zxXWkZCQYC5c\nuODrUJ26fPmymTNnjpk8ebLp0aOHGTNmjPnpp5/cqmPOnDmmR48ePorQUlGcJ0+eNImJiS7VVRPe\n26oK+t3vjAkPN+bkSa9VWfC7DnQ0buST5T3c6jE1xlwHMoB7C445xozeCzjdYkBERgDLgYeMMf/t\nzjUr7YMP4OOPYdEiuOUWv15aKWW57777GDlyJOPHj+edd97hiSee4NixY3z00UdevY6xvth63c+O\nfadFhJtuusnr9Trz8ccfs3nzZqKjo5k9ezbbt2/n3Xff5cCBA9x1113MmjWr3N7h9PR0GjZsSHh4\nuNdidtdzzz1HUlISr732GmlpaZw6dYrevXtz3Y1ZwpmZmfzyl7/0YZQVx9m4cWNatWrFhx9+6NM4\nlPKZF1+EsDB49FHw0WelN3hyK/9lIFFExohIG2AJEIrVa4qIzBeRVQWFHbfvVwFTga9EJMbxqF/p\n6CuSmwuTJ8PQoTBkiM8vp5RyTe/evTHGcOzYscJj+/btY8CAAURERBAeHk6fPn3Ys2dPsfMuXbrE\nE088wW233UbdunWJiYmhX79+7Nu3j7lz5zJt2jQAmjdvjs1mIyQkpNh40B9++IHx48cTGxtL3bp1\nufPOO1mxYkWxayQnJ2Oz2Th8+DAjR46kQYMG9OjRA3A+xtSV2Mur15lx48aRm5vLxo0byc/PZ/r0\n6dStW5fo6GiGDx9OXFwc9es7/yhdtGgRo0ePLvcavnTt2jXeeOMNli9fXnhs6tSpHD58mA0bNrhc\nz+7du+nWzaX5tR5xNc7ExEReeeUVn8WhlE9FRlqddB9/bHXaBSm39+I0xnzgWLP0WSAG2A/0N8Zk\nO4rEAk2KnJKINWHqTcejwCqcLDHlNU89Za3d9cYbPr2MUso9R48eBeDWW28F4NChQ/Ts2ZOIiAhm\nzJhBrVq1WLp0Kb169SItLY0uXaw9PJKSkli3bh2TJ08mPj6e3NxcduzYwZEjRxg6dCjffvsta9as\n4dVXXy2su2Bs4unTp+natSshISE8/vjjREVFsWnTJh555BEuXrzI448/DlA4hjQhIYFWrVoxf/78\nwp7YssaY/vOf/3Qp9vLqdebs2bPk5OQQFxfH3CKriZw5c4b169fzQQV/XHbs2FEq8fan/Px8oqKi\nio3NbNasGQDfffedS3UcP36c06dP+zQxdTXOiIgIIiMjOXjwIHfqroGqKho8GIYNszrt+vaFBg0C\nHVEpHm0Sb4xZBCxy8ty4Ej//hyfXqLStW2HlSmvAb6yrCwYopXzh/Pnz5ObmcvXqVXbs2MFzzz1H\naGgov/71rwGYNWsWN27cYOfOnYUJwejRo2ndujXTpk1j27ZtAGzcuJHExEReeOGFwrqfeuqpwn93\n7NiRNWvWMGjQIJo2bVoshpkzZ2KMYf/+/URGRgIwYcIERo4cSXJyMklJSdSpU6ewfIcOHXjvvfcq\nfG1//OMfXYrd3XrBuoUNMGXKFGrXrs0//vEP3n33XS5evMiKFSto3Lix03OPHj1KdHQ0tWqV/TGf\nlZXFs88+yx133MHly5f5/vvvGTJkCPfff79LsbkiNDS0WK84WIkmwG233eZSHbt37yYuLo61a9di\nt9vZtWsXycnJxMfHByTObt26sWnTJk1MVdX12mvWzlDTplnrnAYZjxLToHflCiQlQc+eMN63nbJK\n+c3PP8ORI769Rps2Xl9OzRjDvfcWDktHRGjevDmpqak0atQIu93Oli1bGDJkSGFiBxAbG8vIkSN5\n++23uXTpEmFhYURGRrJnzx5+/PFHGjVq5FYc69atY/jw4eTn55Obm1t4vF+/fqxdu5a9e/cW9sqJ\nCElJSRXW6U7s7tRbYO/evdx0001MmDCBSZMmsW7dOnJycmjevDl9+vRh2LBhTs/NysqiYcOGZT6X\nnZ1Nr169WLlyJd27d2fPnj1069aNBx980OXYPJWamkrr1q0ZPHiwS+XT09OpXbs2Dz74IDExMcTF\nxTFx4kS2b98ekDjbtWvH+++/79NrK+VTjRrBggUwcSKMGgW9egU6omKqZ2KakgInTljjKGx+XRFL\nKd85csRaLNmXMjKgY0evVikiLFq0iJYtW1KrVi1iYmJo3bp14fPZ2dn8/PPPtGrVqtS58fHx2O12\nTp48SXx8PC+88AK//e1vadKkCZ06dWLgwIGMGTOmwt637Oxszp07x7Jly1i6dGmZMZZcvsqVHj13\nYnen3gIZGRmFwwQWL17M4sWL+frrrxkzZgwjRoygZcuWtGtX9u7O2dnZRERElPnc1KlT6dChQ+ES\nUrfccgshISGlJhjZ7XaGDh3KtWvXgNKTywqGJxhjiIyMrHA5v8zMTD788EO2bNlCbRe3hN69ezez\nZs0iJiYGgLCwMNLT0wMWZ4MGDVwehqBU0EpMhPfeszrxMjOhbt1AR1So+iWmBw9a3wRmzbJ6f5Sq\nLtq0sRJHX1/DB7p06UJHLyS8CQkJ9OzZk/Xr1/Ppp5+ycOFCFixYwPr16+nfv7/T8+yORaVHjRrF\n2LFjyyxz1113Ffu5Xr16lY63LO7Uu3XrVmbOnFnsWOfOnXn//ffp3LkzW7dudZqY2p0spH3mzBnW\nrFlTrNdv586dtGvXrrBnt4DNZmP9+vUux1ueS5cuMWHCBNatW0dnF7eEzsvLIzMzk1/96leFx44c\nOVJsyIW/47zllls4f/68V66lVMDYbNaapu3bw/z5QbUjZvVKTO12mDAB7rgDZswIdDRKeVdoqNd7\nM4NBdHQ0oaGhfPPNN6WeO3z4MDabjSZN/nc+ZUxMDBMnTmTixInk5OTQoUMHUlJS6N+/v9PF76Oj\nowkPDyc/P5/eXtxkw93Y3bFv3z5Onz5d5i3vtm3bApQ7xjQqKopz586VOr57927y8/OLrQiwa9eu\nClcIqKxJkyaxcOHCwuscO3aswt7jo0ePEhYWVqxH+osvvvDpZgEVxZmfn+/VJcOUCpi2ba1caf58\nGD7c+jkIVK/EdOlSSE+3th4t8Y1aKRWcbDYb/fr146OPPuLEiROFk5ZOnTpFamoqPXr0ICwsDLvd\nzqVLl4otjxQVFUVcXFzhLdybb74ZgHPnzhWb/GSz2Rg6dCipqak888wz/OIXvygWQ05ODlFRUT6L\n3ROffPIJXbp0KTOxTUtLo23btgwpZxm8Ro0aFRtLW+Dq1auEh4cXG6O7c+dO5s2bx1dffUV+fj53\n3303UPoWuTMV3SJPSUlh7NixhcneiRMn2L59e4WJ6ZUrV4olpWfPnuWzzz7jL3/5S7Fy/ozz7Nmz\nAd+FSimvmTkT1q61OvXS0oJi+GP1SUyzsqzMf8IE8PE3f6WU61xZ9H7evHl89tlndO/enUcffZSQ\nkBCWLVtGXl5e4Qz8ixcv0rhxY4YNG1Z423nLli18/fXXvPzyywB06tQJYwwzZ87koYceonbt2jzw\nwAPUq1eP559/ni+++IKuXbuSmJhI27ZtOXPmDBkZGWzdupWcnAp3SfY4dk+89957NG7cmGbNmvHy\nyy8zePBgrl+/zubNm1mxYgWbN292OuMeoE2bNpw6dQq73Y6tyB+brl27IiLcuHGDWrVqsXjxYo4f\nP058fDwbNmwotsWgN26Rr127lm3btlGrVi0yHENRDh06xMSJEwFrbdg//elP7N+/nwYllq6Jj48v\nthD/lClTSEhIYODAgcXK+SPOAgXLdylVLdSta93S79XLWsXIjcmZPuOtLaS8+cCTLUn/8z+NiYnR\nbUdVlVETti0s2JLUlde4f/9+M2DAAFO/fn0TFhZm+vTpY/bs2VP4fF5enpk+fbrp0KGDiYiIMOHh\n4aZDhw5m6dKlxepJSUkxTZo0MbVq1Sq1PWl2draZPHmyadasmalTp46Ji4szffv2NcuXLy8sk5yc\nbGw2m8nNzXX6ekpueVpR7BXVW9Knn35qRo8ebQ4dOmR69uxp6tSpYxo2bGjuu+8+s3r16grPLzB8\n+HCzd+/eUseXL19ukpKSTHJystm6dauZN2+eSUxMLPX/srJyc3NNaGiosdlsxR4hISEmOzvbGGPM\nO++8Yxo2bGg++eSTMuv429/+ZqZOnWqSkpLM3Llzjd1u92qMrsZZYPbs2ebVV18tt76a8N5W1cz4\n8cZERBjzww9uneaLLUnFBOG2VCLSEcjIyMhwbcLEhg0waJDVHe2H5U6U8oa9e/fSqVMnXP49V8pN\nmzdvJi0tjZSUlECHUq6LFy/y+eefu7yEVCD17duXJUuW0KJFC6dl9L2tqpwzZ6zJr/fcAyWGypSn\n4Hcd6GSM2euNUAI/mKCyLl2C3/8eBg6EhIRAR6OUUkGjf//+HDhwgKtXrwY6lHJt37694I9bUMvK\nysIYU25SqlSV1KAB/Nd/wV//Chs3BjSUqp+YJidDTg68+SY4mZGrlFI11Zw5c4ptZxpsbty4wYED\nBzxevcCfXn/9dWbPnh3oMJTyjREjoE8feOwxa0OXAKnaiWlmppXhz5kDzZsHOhqllAo6nTt3plOn\nTqW2Rg0WWVlZJCYmBjqMCmVmZpKXl8c999wT6FCU8g0RWLQIfvwR5s0LWBhVd1a+3W5tp9WmDfzh\nD4GORimlglZ5W5cGWtGtXIPZxo0befHFFwMdhlK+1bKltYTUc8/Bww9DiaX1/KHq9pi+9Rbs3g1L\nloCLW9sppZRSnnjmmWcICQkJdBhK+d706XD77Vbnn5Md5Hypaiamp05Za5Y+8ggU2apOKaWUUkpV\nQp06sHgx7NgBq1b5/fJVMzGdOhVCQmDBgkBHopRSSilVvfTuDaNGwdNPWxPM/ajqJaaffw6rV8PC\nhXDrrYGORimllFKq+lm4EPLzYdo0v162aiWmV6/CpEnQsyeMHRvoaJRSSimlqqeYGHj+eVixAtLS\n/HbZqpWYLlgAx49bE550zVKllFJKKd9JTIS777YmQuXl+eWSVScxtdut2/hPPw3x8YGORimllFKq\nerPZrM7A7Gw4eNAvl6w665jabLBtG9y4EehIlPKqw4cPBzoEpZQX6XtaVSvt2sGJE1Cvnl8uV3US\nU7Bm4us6cqqaiIqKIjQ0lFGjRgU6FKWUl4WGhhIVFRXoMJTyDj8lpVDVElOlqpGmTZty+PBhcvy8\nFIcKjNzcXDZt2sSAAQO4VVcUqfaioqJo2rRpoMNQqsrRxFQFhdTUVEaMGBHoMPyuadOmNfKPV01s\n7/379/P2228zZswY2rdvH+hw/KomtndNpu2tKsOjyU8i8piIHBORKyKyW0S6VFC+l4hkiMhVEflW\nRHStJ1VMampqoENQflQT27t9+/ZcuHChxiWlUDPbuybT9laV4XZiKiLDgZeAOUAHIBPYLCJlDqYR\nkebA34HPgXbAq8DbItLXs5CVUkoppVR15EmP6ZPAUmPMu8aYI8BE4GdgvJPyk4D/McZMM8Z8Y4x5\nE/irox6llFJKKaUANxNTEakNdMLq/QTAGGOAz4BuTk672/F8UZvLKa+UUkoppWogdyc/RQEhwKkS\nx08BrZ2cE+ukfH0RqWOMuVbGOXVB14KrSc6fP8/evXsDHYbyk5rY3v/617+YPHkyr7/+Oi1btgx0\nOH5VE9u7JtP2rjmK5Gl1vVWnWB2eLhYWaQRkAd2MMXuKHF8A9DTGlOoFFZFvgHeMMQuKHBuANe40\ntKzEVERGAqvdeSFKKaWUUiogHjbG/F9vVORuj2kOkA/ElDgeA/zk5JyfnJS/4KS3FKxb/Q8Dx4Gr\nbsaolFJKKaV8ry7QHCtv8wq3ElNjzHURyQDuBTYAiIg4fn7NyWnpwIASx/o5jju7Ti7glcxbKaWU\nUkr5zC5vVubJrPyXgUQRGSMibYAlQCiwEkBE5ovIqiLllwC3i8gCEWktIo8Cwxz1KKWUUkopBXiw\n85Mx5gPHmqXPYt2S3w/0N8ZkO4rEAk2KlD8uIvcDrwCPA98DjxhjSs7UV0oppZRSNZhbk5+UUkop\npZTyFY+2JFVKKaWUUsrbNDFVSimllFJBISCJqYg8JiLHROSKiOwWkS4VlO8lIhkiclVEvhWRsf6K\nVVWeO+0tIkNE5FMROS0i50Vkl4j082e8qnLcfX8XOa+7iFwXEV2Zuwrx4PP8JhFJEZHjjs/0/xGR\n3/opXFVJHrT3wyKyX0Qui8gPIrJcRBr4K17lORHpISIbRCRLROwi8oAL51Q6X/N7Yioiw4GXgDlA\nByAT2OyYUFVW+eZYi/F/DrQDXgXeFpG+/ohXVY677Q30BD7FWmKsI7AN+FhE2vkhXFVJHrR3wXkR\nwCpKb1+sgpiH7f0X4D+AcUArYATwjY9DVV7gwd/v7ljv67eAtlgr8vwfYJlfAlaVdTPWBPdHgQon\nJHkrX/P75CcR2Q3sMcZMcfwswEngNWPMC2WUXwAMMMbcVeRYKhBhjBnop7CVh9xtbyd1HATWGGPm\n+S5S5Q2etrfjPf0tYAcGGWM6+iNeVTkefJ7fh7VG9e3GmHN+DVZVmgftPRWYaIxpWeTY74Fpxpim\nfgpbeYGI2IHBxpgN5ZTxSr7m1x5TEakNdMLKpgEwVmb8GVBqO1OHuyndi7K5nPIqSHjY3iXrECAc\nOOOLGJX3eNreIjIOuA2Y6+sYlfd42N6/Ab4GpovI9yLyjYi8KCJe22db+YaH7Z0ONBFrG3JEJAZI\nAD7xbbQqQLySr/n7Vn4UEAKcKnH8FNb6p2WJdVK+vojU8W54yss8ae+Snsa6nfCBF+NSvuF2e4tI\nS+DPWPss230bnvIyT97ftwM9gF8Ag4EpWLd33/RRjMp73G5vY8wuYBSwVkTygB+Bs8DvfRinChyv\n5Gs6K18FLREZCcwGEowxOYGOR3mXiNiA1cAcY8x3BYcDGJLyPRvWcI2RxpivjTH/DfwBGKsdDdWP\niLTFGmeYjDVnoD/W3ZGlAQxLBTm3d36qpBwgH2vHqKJigJ+cnPOTk/IXjDHXvBue8jJP2hsAEXkI\na4D8MGPMNt+Ep7zM3fYOBzoD7UWkoMfMhjWCIw/oZ4z5wkexqsrz5P39I5BljLlU5NhhrC8kjYHv\nyjxLBQNP2nsGsNMYU7AF+UGxtiX/UkT+aIwp2bumqjav5Gt+7TE1xlwHMoB7C445xhDeC+xyclp6\n0fIO/RzHVRDzsL0RkRHAcuAhR4+KqgI8aO8LwJ1Ae6wZnO2AJcARx7/3+DhkVQkevr93AnEiElrk\nWGusXtTvfRSq8gIP2zsUuFHimB1rhrfeHal+vJOvGWP8+gAeBH4GxgBtsLr0c4Fox/PzgVVFyjcH\nLgILsD7AHgXygD7+jl0ffmnvkY72nYj1TavgUT/Qr0Uf3m/vMs6fA+wN9OvQh2/aG2u8+L+BtUA8\n1vJw3wBLAv1a9OGT9h4LXHN8nt8GdAf+H7Ar0K9FHy61981YnQTtsb5QPOH4uYmT9vZKvubvW/kY\nYz5wrHn2LFbCsR/ob4zJdhSJBZoUKX9cRO4HXgEex/pW/YgxRtc7rALcbW8gEWuA/ZsUnxCxChjv\n+4hVZXjQ3qoK8+Dz/LJjTcPXga+wkpq1WGPJVZDzoL1XiUgY8BiwEDiHNat/hl8DV57qjLWWuHE8\nXnIcL/h77JN8ze/rmCqllFJKKVUWnZWvlFJKKaWCgiamSimllFIqKGhiqpRSSimlgoImpkoppZRS\nKihoYqqUUkoppYKCJqZKKaWUUiooaGKqlFJKKaWCgiamSimllFIqKGhiqpRSSimlgoImpkoppZRS\nKihoYqqUUkoppYLC/wd63+FGPbaNZgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110fc9080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.special import gammaln\n",
    "\n",
    "def log_beta_pdf(x, a, b):\n",
    "    return - gammaln(a) - gammaln(b) + gammaln(a+b) + np.log(x)*(a-1) + np.log(1-x)*(b-1) \n",
    "\n",
    "x = np.arange(0.01,1,0.01)\n",
    "\n",
    "a = 1\n",
    "b = 1\n",
    "c_0 = 1\n",
    "c_1 = 1\n",
    "N = c_0 + c_1\n",
    "\n",
    "pi_ML = c_1/N\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.plot(x, np.exp(log_beta_pdf(x, a, b)), 'b')\n",
    "plt.plot(x, np.exp(log_beta_pdf(x, a+c_1, b+c_0)), 'r')\n",
    "yl = plt.gca().get_ylim()\n",
    "plt.plot([pi_ML, pi_ML], yl , 'k:')\n",
    "plt.legend([\"Prior $\\cal B$ $(a={}, b={})$\".format(a,b), \"Posterior $\\cal B$ $(a={}, b={})$\".format(a+c_1, b+c_0)], loc=\"best\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Illustration: Learning from a sequence of coin flips"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/cemgil/anaconda/envs/py35/lib/python3.5/site-packages/ipykernel/__main__.py:11: RuntimeWarning: divide by zero encountered in log\n",
      "/Users/cemgil/anaconda/envs/py35/lib/python3.5/site-packages/ipykernel/__main__.py:11: RuntimeWarning: invalid value encountered in multiply\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ncQEAREdcAADR/QyN5jtOY0uJ9AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1107c4940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110e31828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1110e2be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAIABJREFUeJzt3Xt4XVWd//H3JpQmFMIUIhBpklqTB5MICSBiwihMGQyO\nA4jSQilykcIAikIUKzcJMojIUECw2idVqLTSGmAAR0lUQLmFW4OQU2pSOeFyJIQiIaeBtqec7t8f\n3/ZXLr2k7c5ZeyWf1/PsZ7XkJOe7wpN8utbae60gDENERESitIPrAkREZORRuIiISOQULiIiEjmF\ni4iIRE7hIiIikVO4iIhI5BQuIiISOYWLiIhEbsehvCgIgj2ABuBFYNVwFiQiIrGWD0wE2sIw/Oem\nXjSkcMGCZUEERYmIyMgwHfj1pj441HB5EWD+/PlUVlZGUNPWu+CCC7j++uudvLeISFy4/l24dOlS\nTj75ZFiXC5sy1HBZBVBZWcmBBx64fZVto912283Ze4uIxEWMfhdudolEC/oiIhI5hYuIeCOZTDJl\nyhSSyaTrUpxIJuHpp62NO4WLiHgjm82STqfJZrOuS3Eim4V337U27oa65uLctGnTXJcgIo5VVFTQ\n1tbmugxnKirgxhunUVHhupIt82bkonAREfHnd6E34SIiIv5QuIiINzKZDKlUikwm47oUJzIZSKWs\njTuFi4h4I5FIUFJSQiKRcF2KE4kElJRYG3cKFxHxRnl5Oa2trZSXl7suxYnycmhttTbuvLlbTESk\nsLCQhoYG12U4U1gIvnRfIxcREYmcwkVERCKncBERb6RSKRobG0mlUq5LcSKVgsZGa+NO4SIi3kin\n07S1tZFOp12X4kQ6DW1t1sadFvRFxBtVVVUsWbLEdRnOVFWBL93XyEVERCKncBERkcgpXEREJHIK\nFxHxRkdHB0EQ0NHR4boUJzo6IAisjTuFi4h4o7S0lObmZkpLS12X4kRpKTQ3Wxt3ultMRLxRVFTE\njBkzXJfhTFER+NJ9jVxERCRyChcREYmcwkVEvNHX18esWbPo6+tzXYoTfX0wa5a1cadwERFv9Pb2\n0tTURG9vr+tSnOjthaYma+NOC/oi4o3a2tpRu68YQG2tH/uKgUYuIiIyDBQuIiISOYWLiIhETuEi\nIt7o7OxkwoQJdHZ2ui7Fic5OmDDB2rhTuIiIN9Y/oV9UVOS6FCfWP6HvQ/d1t5iIeKO4uJimpibX\nZThTXGy3IvtAIxcREYmcwkVERCKncBERb/T399PS0kJ/f7/rUpzo74eWFmvjTuEiIt7o6elh6tSp\n9PT0uC7FiZ4emDrV2rjTgr6IeKOmpoaBgQHGjRvnuhQnampgYAB86L7CRUS8kZeXR2FhoesynMnL\nA1+6r2kxERGJnMJFREQip3AREW90dXVRV1dHV1eX61Kc6OqCujpr407hIiLeyM/Pp7q6mvz8fNel\nOJGfD9XV1sadFvRFxBtlZWXMnTvXdRnOlJWBL93XyEVERCKncBERkcgpXETEG4ODg7S3tzM4OOi6\nFCcGB6G93dq4U7iIiDe6u7upr6+nu7vbdSlOdHdDfb21cacFfRHxRmVlJYlEgkmTJrkuxYnKSkgk\nwIfuK1xExBsFBQVUV1e7LsOZggK7FdkHmhYTEZHIKVxERCRyChcR8UYymWTKlCkkk0nXpTiRTMKU\nKdbGncJFRLyRzWZJp9Nks1nXpTiRzUI6bW3caUFfRLxRUVFBW1ub6zKcqagAX7qvkYuIiERO4SIi\nIpFTuIiINzKZDKlUikwm47oUJzIZSKWsjTuFi4h4I5FIUFJSQiKRcF2KE4kElJRYG3cKFxHxRnl5\nOa2trZSXl7suxYnycmhttTbudLeYiHijsLCQhoYG12U4U1gIvnRfIxcREYmcwkVERCKncBERb6RS\nKRobG0mlUq5LcSKVgsZGa+NO4SIi3kin07S1tZFOp12X4kQ6bU/o+9B9LeiLiDeqqqpYsmSJ6zKc\nqaoCX7qvkYuIiERO4SIiIpFTuIiISOQULiLijY6ODoIgoKOjw3UpTnR0QBBYG3cKFxHxRmlpKc3N\nzZSWlrouxYnSUmhutjbudLeYiHijqKiIGTNmuC7DmaIi8KX7GrmIiEjkFC4iIhI5hYuIeKOvr49Z\ns2bR19fnuhQn+roHmHVhLz50X+EiIt7o7e2lqamJ3t5e16U40Xv+NTRdtwu9Patcl7JFWtAXEW/U\n1taO2n3FWLiQ2vuuJj2/Gj4z3XU1W6SRi4hI3L3yCpxzDpx4Ipx0kutqhkThIiISZ2vXwqmnwi67\nwOzZ9hSlBzQtJiISZzfcAA8+CPffD+PHu65myDRyERFvdHZ2MmHCBDo7O12Xkht//StcdJGdEDZ5\nMp2dMGEC+NB9hYuIeGP9E/pFRUWuSxl+77wD06bZIS4//CGw4Ql9H7qvaTER8UZxcTFNTU2uy8iN\nxkZ46SXbpXLsWACKi8GX7itcRETi5u67Yc4c+PnP4ROfcF3NNtG0mIhInKRScMYZcOyxcNZZrqvZ\nZgoXEfFGf38/LS0t9Pf3uy5leGSzcPLJUFAAv/jFh2477u+HlhZr407hIiLe6OnpYerUqfT09Lgu\nZXhcdRU8/DAsWAB77PGhD/f0wNSp1sad1lxExBs1NTUMDAwwbtw416VE7+GH4Yor4NJL4bDDNvqS\nmhoYGAAfuq9wERFv5OXlUVhY6LqM6L35JkyfDoceCpddtsmX5eWBL93XtJiIiEthCKefDm+/bdNh\nO46Mf/OPjF6IiPjqhhvg3nvtKilxXU1kNHIREW90dXVRV1dHV1eX61Ki8eSTMHOmPTB59NFbfHlX\nF9TVWRt3ChcR8UZ+fj7V1dXk5+e7LmX7vfWWbaF/wAFw9dVD+pT8fKiutjbuNC0mIt4oKytj7ty5\nrsvYfuvXWd58Ex54AHbaaUifVlYGvnRf4SIikmvXX29bvNx9N0yc6LqaYaFpMRGRXHr0Ufjud+E7\n37EtXkYohYuIeGNwcJD29nYGBwddl7Jtli+HE06wVfl12+hvjcFBaG+3Nu4ULiLije7uburr6+nu\n7nZdytbLZuGkkyCTgYULYcyYrf4S3d1QX29t3GnNRUS8UVlZSSKRYNKkSa5L2XqXX26L93/4A+yz\nzzZ9icpKSCTAh+4rXETEGwUFBVRXV7suY+v99re2KeXVV8MRR2zzlykosFuRfaBpMRGR4ZRMwle/\naov3M2e6riZnFC4iIsPlnXfgy1+Gj3wE5s370PksI5nCRUS8kUwmmTJlCslk0nUpWxaGdpLksmVw\n112w227b/SWTSZgyxdq405qLiHgjm82STqfJZrOuS9myG2+0XY4XLYL99ovkS2azkE5bG3cKFxHx\nRkVFBW1tba7L2LI//9kekrzwQjs6MiIVFeBD90HTYiIi0Xr5ZQuUww/fpgclRwqFi4hIVN55B770\nJTuHeOHCEXPw17ZQuIiINzKZDKlUikwm47qUDwtDOOMMO2zlnnugqCjyt8hkIJWyNu4ULiLijUQi\nQUlJCYlEwnUpH3bttTZamTcP9t9/WN4ikbDDKuPY/Q9SuIiIN8rLy2ltbaW8vNx1Ke/3+9/D974H\nl14Kxx8/bG9TXg6trdbG3eidEBQR7xQWFtLQ0OC6jPd7/nk7UfLoo+GKK4b1rQoLIW7d3xSNXERE\nttUbb1ioTJwI8+fDDvqVup5GLiIi2yKTsSmwdBruvx923dV1RbGimBURb6RSKRobG0mlUm4LCUP4\nxjfgscdsa5ccHVWcSkFjo7Vxp3AREW+k02na2tpIp9NuC5k1C5qbYc4c+Oxnc/a26bQ9oe+6+0Oh\naTER8UZVVRVLlixxW8Q999i2LjNnwumn5/Stq6rAdfeHSiMXEZGheuYZO6r4uONG9dYuQ6FwEREZ\nilTK7gyrqoLbbtOdYVug746IyJak0/DFL0JeHtx7L+y8s+uKYk/hIiLe6OjoIAgCOjo6cvema9bY\nLscvvmhP4hcX5+69P6Cjww6zzGX3t5UW9EXEG6WlpTQ3N1NaWpqbNwxD+PrX7TmW1laors7N+25C\naandpJar7m8PhYuIeKOoqIgZM2bk7g2vusp+m99yCxxxRO7edxOKiiCX3d8emhYTEdmYW2+Fyy6z\n/cJOO811Nd5RuIiIfFBbG5x5pl2XXea6Gi8pXETEG319fcyaNYu+vr7he5PFi23PsIYGmD3bVtBj\noq/PNgcYzu5HReEiIt7o7e2lqamJ3t7e4XmDZcvgC1+wZ1kWLYrdMcW9vdDUZG3cxes7JyKyGbW1\ntcO3r9hrr9loZffd4Xe/g3Hjhud9tkNtrR/7ioHCRUQEBgbgqKNg9Wp48EG7LUu2i8JFREa3lSvh\nmGPgpZfgoYegrMx1RSOCwkVERq81a+CEE+Cpp+CPf4T99nNd0YihBX0R8UZnZycTJkygs7Nz+7/Y\n2rXwta/Zk/d33QWHHrr9X3OYdXbChAnWxp1GLiLijfVP6Bdt75pIGML558OCBXD77bbe4oH1T+j7\nsCSkcBERbxQXF9PU1LT9X+jSS+Gmm+DnP7dpMU8UF9utyD7QtJiIjC5XX20Hff3P/8B//ZfrakYs\nhYuIjB433QQXXwyXXw7f/rbrakY0hYuIeKO/v5+Wlhb6+/u3/pObm+Gb34TGRgsXD/X3Q0uLtXGn\ncBERb/T09DB16lR6enq27hPnzbMpsHPPtemwGO0XtjV6euzcsq3tvgta0BcRb9TU1DAwMMC4rdma\nZeFCu+X4jDNsWszTYAGoqbHNBGK4M82HKFxExBt5eXkUFhYO/RPuuANOPtmuOXNgB78na/LyYGu6\n75Lf32kRkU254w448US71fiXv/Q+WHyj77aIjDx33mnBMnWqrbfk5bmuaNRRuIiIN7q6uqirq6Or\nq2vTL1ofLFOmwK9+FbszWbZHVxfU1VkbdwoXEfFGfn4+1dXV5Ofnb/wFixbZNNjxx8Ntt42oYAHI\nz4fqamvjbmR950VkRCsrK2Pu3Lkb/+D8+XDqqTB9Otxyy4icCisrg011P240chER/916K5xyCpx2\n2ogNFt8oXETEb7Nnw+mnw1ln2VP4CpZYULiIiDcGBwdpb29ncHDQ/sO118LXvw4XXAA/+9mIv914\ncBDa262Nu5H9f0JERpTu7m7q6+vp7uqyvee/+13bPv+667x+8n6ouruhvt7auNOCvoh4o7KyksRz\nzzFpzhz46U9t6/yLLnJdVs5UVkIiAZMmua5kyxQuIuKNgjFjqL7uOnt+ZfZsOOcc1yXlVEGB3Yrs\nA4WLiPhh1So46ST47W/teOJp01xXJJuhcBGR+BsYgGOPhSeegP/9X/jP/3RdkWyBFvRFJN56e+Gw\nw+DZZ0nOm8eUefNIJpOuq3IimbRdbXzovsJFROJr2TI49FBYvhwefpjsAQeQTqfJZrOuK3Mim4V0\n2tq407SYiMTTE0/Y9Ncee8CDD0JZGRVAW1ub68qcqagAX7qvkYuIxM///R/827/BvvvCY4/Zplri\nFYWLiMTLnDm2eH/UUfDHP8Luu7uuSLaBwkVE4mHtWpg5E84+27Z0aWmxBzveI5PJkEqlyGQyjop0\nK5OBVMrauFO4iIh7K1faAV/XXgs33AA/+clGN6BMJBKUlJSQSCQcFOleIgElJdbGnRb0RcSt11+H\nL30J/vpXuOsu+/MmlJeX09raSnl5eQ4LjI/ycmhttTbuFC4i4k4iYXeErV4Nf/kLHHzwZl9eWFhI\nQ0NDjoqLn8JC8KX7mhYTETd+/3vb4nf8eHjyyS0Gi/hF4SIiuRWGtkX+0Ufb7cYPP2wLCTKiKFxE\nJHdWrbKjiL/zHbsz7K67YJddhvzpqVSKxsZGUqnU8NUYY6kUNDZaG3cKFxHJjVdfhcMPh9/8xnY1\n/uEPt/pI4nQ6TVtbG+l0enhqjLl02p7Q96H7WtAXkeH32GPwla/YMcQPPbTN6ytVVVUsWbIk4uL8\nUVUFvnRfIxcRGV5z5tiIpbwcFi/Wwv0ooXARkeGxahXMmGFP3J91Ftx/P+y9t+uqJEc0LSYi0evp\ngeOPh+efh1tusUV8GVU0chGRaN13Hxx0EPT3Q3t7pMHS0dFBEAR0dHRE9jV90tEBQWBt3ClcRCQa\n774LF18M//Ef9nDk4sVQWxvpW5SWltLc3ExpaWmkX9cXpaXQ3Gxt3GlaTES236uvwrRp8Oij8KMf\nwYUX2p1hESsqKmLGjBmRf11fFBXZMpYPFC4isn3a2uCUU+yZlQcegM99znVFEgOaFhORbbNmjT1l\nf9RRcMABtquxgkXWUbiIyNbr6bEgmTULfvxj24Ryzz2H/W37+vqYNWsWfX19w/5ecdTXZ99yH7qv\ncBGRrTN/PtTU2G+4Rx4ZtvWVjent7aWpqYne3t6cvF/c9PZCU5O1cac1FxEZmoEBOPdc+PWv4atf\nhZtvtgNGcqi2tnbU7isGdvOdL91XuIjIlv35z3Dqqfbsyvz5MH2664ok5jQtJiKbtmqVbY8/eTJM\nnAjPPadgkSHRyEVENm7xYhutLFtmi/YXXLDVW+TL6KWRi4i8XyYDl18OhxwCO+0ETz9to5cYBEtn\nZycTJkygs7PTdSlOdHbChAnWxp1GLiKywTPPwNe+BokEXHopXHIJjBnjuqr/b/0T+kVFRa5LcWL9\nE/o+dF/hIiKwejVceaVt3VJdDY8/bptPxkxxcTFNTU2uy3CmuNhuRfaBwkVktHvsMTjzTFtb+f73\n4Xvfs+kwke2gNReR0Sqdhm98A/71X2HcOFvA//73FSwSCYWLyGgThnD33Tb9deutcP31du7Kfvu5\nrmyL+vv7aWlpob+/33UpTvT3Q0uLtXGncBEZTV56CY49Fo47zrZwWbIEvvWtWNwJNhQ9PT1MnTqV\nnp4e16U40dMDU6daG3dacxEZDTIZ2/Hwyith/Hi4804LmCBwXdlWqampYWBggHHjxrkuxYmaGtuF\nx4fuK1xERro//AHOOw9eeAG++U244grYdVfXVW2TvLw8CnO8n1mc5OXlfDu3baZpMZGRqqcHvvIV\naGiAvfe281ZmzfI2WMQvCheRkebtt+Gyy6Cy0p5XWbDANp785CddVyajiMJFZKRYuxZuuw323Reu\nvda2bOnqgpNO8m5tZVO6urqoq6ujq6vLdSlOdHVBXZ21cadwERkJHnoIPv1pO8u+vh6WLoX//m/Y\nZRfXlUUqPz+f6upq8vPzXZfiRH6+3UHuQ/e1oC/is6VL7Yn6e++Fgw+2kyEPPdR1VcOmrKyMuXPn\nui7DmbIy8KX7GrmI+OjVV+Gss2wd5bnnbF3l8cdHdLCIXzRyEfHJP/8J11wDN90EO+8M110H55wD\nY8e6rkzkfTRyEfFBOm0PQE6aBLNnw4UXQjIJ558/qoJlcHCQ9vZ2BgcHXZfixOCg7dTjQ/cVLiJx\nNjho2+B/7GNw1VVw+ukWKj/4Aey2m+vqcq67u5v6+nq6u7tdl+JEd7fdr+FD9zUtJhJHK1bYCOW6\n6+Ctt2xL/IsusmMIR7HKykoSiQSTJk1yXYoTlZV2jpsP3Ve4iMTJwAD89KcWKitW2KmQF11ktwkJ\nBQUFVFdXuy7DmYICuxXZBwoXkTh4/XW44QYLllWrbKQycyaUlLiuTGSbKFxEXEombb+vX/7SdiU8\n+2xobLTzbEU8pgV9EReefhpOPBEqKmDRInsQ8qWXbNsWBcsmJZNJpkyZQjKZdF2KE8kkTJlibdxp\n5CKSK9ks3HOPnfz4yCO2KnvzzXDqqfbMimxRNpslnU6TzWZdl+JENmt3pfvQfYWLyHDr77dpr5tv\nhhdfhM9+Fu66C445xpsTIOOioqKCtrY212U4U1EBvnRf4SIyXJ57zm4nvu02WLPGpsFaWuBTn3Jd\nmciwU7iIRGnVKjtCePZseOwxWz+ZOdP2Adt7b9fVieSMwkUkCs8/D83N8KtfwZtvwhFHwB132NTX\nmDGuqxsxMpkMr7/+OnvuuSc77bST63JyLpOxu9b33BPi3n3dLSayrVasgF/8wnYirq6G+fPhjDPs\nJKc//cmOGFawRCqRSFBSUkIikXBdihOJhD365EP3NXIR2Rpr19qRwfPm2chk5Ur4/OftduJjjx1V\nm0i6UF5eTmtrK+Xl5a5LcaK8HFpbrY07hYvIUCQSdmbKggXwyit2285FF9ltxHqKPmcKCwtpaGhw\nXYYzhYXgS/cVLiKb0tMDv/mNBUpnJ4wfb3d8nXIKHHLIiDmXXmQ4KFxE3uull2y6a9EieOop2ynw\nmGNsu/uGhvivoorEhBb0Rbq77cyUgw+GiRPhkktsa/uFC+3WnIUL4eijFSwxkEqlaGxsJJVKuS7F\niVTKtp7zofsKFxl91q6FJ56Aiy+GqirYd1875bGsDG6/HZYvtyfoTzgBdtnFdbXyHul0mra2NtLp\ntOtSnEin7Ql9H7qvaTEZHQYG7Pbg3/3Ortdfhz32sBHJ1VfDkUdqfy8PVFVVsWTJEtdlOFNVBb50\nX+EiI9Patbb9Slsb3HcfPPoovPuu/XSedpqFymc+AzvqR0BkOOgnS0aOl1+G+++3Ecqf/mSjk513\nhsmT4cYb4QtfsLPoRWTYKVzEX//4B/zlL3Y98AD8/e92e/ABB9iT8kceCfX1erBRxAGFi/ghDGHZ\nMjsH5eGH7XrhBftYVZU9JX/NNXD44bD77k5LleHT0dHBQQcdxOLFiznwwANdl5NzHR1w0EGweDHE\nvfsKF4mnwUE7rfHxx2134fZ2eOMNG5nsv79NcR12GHzuc7aLn4wKpaWlNDc3U1pa6roUJ0pLbX9U\nH7qvcBH3Vq2yJ+CfftquJ5+0XYbXrrVbgT/zGTjnHKirs2mu3XZzXbE4UlRUxIwZM1yX4UxREfjS\nfYWL5Nabb9pdXM8+C888Y9fzz9udXDvuCPvtZyFy/vm2xUplpU5rFPGQwkWGx4oV8Le/WXAkEnZz\nfmfnhkeLx4616a1DDoGzz7aJ5P33h/x8t3WLSCQULrLtslkLi2XL7AyT9dfSpbZz8Hof+5idd3Ly\nyVBTY1dFhZ4xka3W19fHggULmD59OnvttZfrcnKur8/2UZ0+HeLefW9+um+//XamTZvmuozRJ52G\nF1+0q6cHkkm7XnjBrkzGXjdmDHz847aVykkn2R1clZXwiU/Arru67IGMIL29vTQ1NTF58uRRGS69\nvXDJJbczefI0hUtUFC7DYMUKePVVe17kH/+wUUgqZQ8jvvKKtf39G14/dixMmmTXv/+7LbJXVNjJ\nRRMnaiQiw662tnbU7isGUFsLRx55O7W18f9dqN8GI8m771oYvPGGXcuX2/X663a99pqNq197zf4J\nNDj4/s/ffXfYZx+7z7G+3s4uKS21aa2JE20cvoP2OhWRLVO4xMWaNfD223atWPH+K522a2AA3nrL\n2v7+919vvmkf+6AddoCPfMSeBdlrL9v595BDYO+94aMf3XDts482bhSRyPgRLsuX2y/Ujo4PfywM\nN/7n9X/f3LV27YZ2/ZXNbrjWrrXRwPq/v/vuhmvNGrvW/zmTsWv16g3t6tX2DMf6duXKDe3KlRYk\n77xj7Zo1m/8ejBljz3f8y79saMePt1HF+PG2w+/6q6how7X77hptiEjODTVc8gGWLl06jKVsxp13\nMvDQQ3QcdJCb99+YHXf88DVmjLU77WTXmDG2TrH+7wUFFgpjx9ott++9Cgo2XDvvDOPGWbvLLvbn\nrT2o6p13bM3k5ZeHp/8iDixbtozzzjuPm266iYqKCtfl5NyyZdDWNsCiRR246v57cmCzzw0E4Qf/\ntb+xFwXBScCC7S9LRERGiOlhGP56Ux8carjsATQALwKrIitNRER8kw9MBNrCMPznpl40pHARERHZ\nGlrpFRGRyClcREQkcgoXERGJnBfhEgTB14Mg6AmCYGUQBI8HQXCw65pERGTTYh8uQRCcAFwHXA4c\nADwLtAVBUOS0MBGRCAVBcHYQBM8GQTCw7nosCIKjNvK6B4Ig+FoQBLsHQXBfEAT/CIJgVRAELwdB\ncFMQBLHYKTb2d4sFQfA48EQYht9a9/cAeAX4SRiGP3ZanIhIRIIg+CKQBZYBAXAacCFQG4bh0nWv\nGQ/0AhOAd4ETgKeA5UA5MBtYHIbhybmu/4NiHS5BEIwB3gG+Eobhve/577cCu4VheJyr2kREhlsQ\nBP8EvhOG4S3r/n4ycG4YhvWbeP15615flsMyNyru02JFQB7Q94H/3gfsnftyRESGXxAEOwRBcCKw\nM9D+ng8dA9yzic/5KPBl4M/DXuAQxD1cRERGjSAIPhkEwQpgNTbFdVwYhn9b97GdgKOAez/wOb8O\nguBtIAUMAGfmtuqNi3u4vIHNQX7wzLW9gNdyX46IyLD6G1ADfBr4GfCrIAg+se5jRwB969df3uN8\n7GanY4CPA9fnqNbNivWaC2xyQf9lbEH/WqfFiYgMoyAI/gj8PQzDc4IgmA2sDMPw25t5/aHAw0Bx\nGIYfXE7IKR/Oc5kF3BoEwWLgSeACbB7yVpdFiYjkwA7A2HV/PhqYvoXX5wHhez7HmdiHSxiGv1n3\nTMsPsOmwvwINYRgud1uZiEh0giD4IXAfNjOzKxYkhwGfD4LgIKAAeOQ9r/8C9jvxKWAQ+CTwY+CR\nMAydH+QU+2kxEZHRIAiCucBkoBhbmH8O+FEYhg8EQfADYGIYhqe85/WHA1cBldhI5RXgTuCaMAzT\nOS7/QxQuIiIxFwTBs8CVYRje4bqWoYr73WIiIqPauofJ78CmzLyhkYuIiEROIxcREYmcwkVERCKn\ncBERkcgpXEREJHIKFxERiZzCRUREIqdwERGRyClcREQkcgoXkSEIgqAuCIIngiD4pOtaRHygcBEZ\ngjAM24G7gYtc1yLiA23/IjJEQRAUA11ASRiGA67rEYkzjVxEhigMw17gQeCrrmsRiTuFi8jWuR2Y\n4boIkbhTuIgMURAE5dhpf3sGQfAp1/WIxFnsjzkWiYMgCD4NnA2cif3cnAk87bQokRjTgr7IFgRB\n8EXgXODLYRiuDoKgAju3vDgMw5VuqxOJJ02LiWxGEAQfB74LnBCG4WqAMAyXYQv7p2zuc0VGM41c\nREQkchrGW0AvAAAASklEQVS5iIhI5BQuIiISOYWLiIhETuEiIiKRU7iIiEjkFC4iIhI5hYuIiERO\n4SIiIpFTuIiISOQULiIiEjmFi4iIRE7hIiIikft/3lJywhVAPssAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111268b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nvJB9YNIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1112bdb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11155ea20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nERGR2ClcREQkdv8f2mgaPadeRmUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1114910f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1114857f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1115817f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110cfe358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11115add8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nOoWLiIiETuEiIiKhU7iIiEjo/g86fjkjb+OXoQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111637940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRUREQqdwERGR0P0/yfo1iVSXrz8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1114914e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1115599b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ncBEREd8pXERExHf/DxBnX4OJxd9CAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11154c6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11148c4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110e3f208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e2f9f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111a197f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d861550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d6951d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nvX3hI50AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d69a358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11159bba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAPYQAAD2EBqD+naQAAIABJREFUeJzt3Xt0lNW9//H3BsFEMKJGLG0SQJLmWsPFVhMRFS/xaKv1\nEnq09fSsHmq7aj2t8bRdPb2ctLX29Jz+0lpX9VdDvdVLK4L+FDFBJBUvqNSIzXBJ1AR1NGaBxIxR\nYGDy/P7YiSDkCZPkmXmeyXxea7G2K9/JzKbVfLIvz97GcRxERES8NM7vDoiIyNijcBEREc8pXERE\nxHMKFxER8ZzCRUREPKdwERERzylcRETEcwoXERHx3GHxvMgYcyxQBWwFdiWyQyIiEmgZwAyg0XGc\nd91eFFe4YIPlHg86JSIiY8OXgXvdivGGy1aAu+++m+LiYg/6NHzXXnstv/3tb335bBFJHfpZkVib\nN2/mK1/5CvTngpt4w2UXQHFxMXPnzh1dz0boqKOO8u2zRSR16GdF0gy5RKIFfRER8ZzCRURSRnt7\nO9XV1bS3t7vU4e9/t634S+EiIikjFosRiUSIxWIuddi717bir3jXXHx3+eWX+90FEfFZQUEBjY2N\nQ9Thxhsvp6AgiZ2SQaXMyEXhIiLx0M+KYEiZcBERkdShcBGRlBGNRgmHw0SjUZc6hMO2FX8pXEQk\nZYRCIXJzcwmFQi51yM21rfhL4SIiKSM/P5+Ghgby8/Nd6tDQYFvxV8rsFhMRycrKoqqqaog6DFGW\nJNLIRUREPKdwERERzylcRCRlhMNhampqCIfDLnWoqbGt+EvhIiIpIxKJ0NjYSCQScalDY6NtxV9a\n0BeRlFFSUsLGjRuHqMMQZUkijVxERMRzChcREfGcwkVERDyncBGRlNHc3IwxhubmZpc6GGNb8ZfC\nRURSRl5eHvX19eTl5bnUob7etuIv7RYTkZSRnZ3N4sWLh6jDEGVJIo1cRETEcwoXERHxnMJFRFJG\nV1cXdXV1dHV1udShrs624i+Fi4ikjM7OTmpra+ns7HSpQ22tbcVfWtAXkZQxe/Zs13PFbF3nigWF\nRi4iIuI5hYuIiHhO4SIiIp5TuIhIymhpaSEnJ4eWlpaPF954A26+mZarbiJn0g5avnS9Fl98pgV9\nEUkZA0/oZ2dn7/tiWxucfjps30721HIWH51J9mN/hjOWw2OPwfHH+9fhNKZwEZGUMW3aNGpra/d9\nob0dFi6EY46Bl19m2tSp1AL843Nw3nkwfz6sWgUzZ/rT4TSmaTERSU2vv26D5YgjYPVqmDp1X+3E\nE+GZZ8Bx4NRTIRz2r59pSuEiIqln7174/Odh3DhYswamTTv4NTNn2oCJRuGXv0x+H9OcwkVEUkZ3\ndzdLly6l+6abIBSCBx6AnJz96rB0qW0Bu97yve/Bn/5kRzqSNAoXEUkZHR0dLFq0iI4bboArroC5\ncw+ow6JFtv3I1VfDUUfBr36V3M6mOYWLiKSM8vJyen78Y8p7euD66wepQ0+PbT8yebIdvdx2m0Yv\nSaRwEZGUMX7HDrJuvJHxV1896A6w8eMhK8u2H/Otb9nRyw03JKejonARkRRy/fVgDPzoR8P7Po1e\nkk7hIiKpobMTbrkFfvADe5/xcF19tR3W3Hyz932TgyhcRCQ13H47rePGUfHQQ7S2tg76ktZWqKiw\n7UEmTYJLLoFly+zzL5JQChcRCb6+PliyhIwvfIHSE08kIyNj0JdlZEBpqW0Hdeml8Npr8I9/JK6v\nAuj4FxFJBU88AR0dTL/7bpZUVrq+bPp0WLJkiPdZuNAu7C9bdsCWMvGaRi4iEny33mqHJBUVo3uf\niRPhwgttuEhCKVxEJNi6uuChh+DrX7c7xUbrsstg0ybYsmX07yWuFC4iEmx33mkfXLnySnp7e1m3\nbh29vb2DvrS3F9ats62rc8+1W5M1ekkohYuIBJfjQH29HW0ccwxtbW1UVlbS1tY26Mvb2qCy0rau\nMjLgggsULgmmcBGR4Fq7Fl591U6JAcXFxYRCIYqLiwd9eXGxPc/SpbzPpZfCSy/Z+2AkIRQuIhJc\n998PubmwYAEAmZmZlJaWkpmZOejLMzPtur9LeZ9/+ic7gtHoJWEULiISTH19sHy5HWV4sZC/v8mT\n7drLihXevq98ROEiIsH07LPwzjt2vSURFi6E55+H3bsT8/5pTuEiIsG0bJm9YXK/Z1va29uprq6m\n3WWtpL0dqqvjXEpZsMAGy/r1HnVY9qdwEZHgcRwbLpdcYq8y7heLxYhEIsRisUG/LRaDSMS2h3Ti\nifYgy7VrPeq07E/hIiLBs349vPnmQVNiBQUFNDY2UlBQMOi3FRRAY6NtD2n8eJg/X+GSIAoXEQme\nBx6A446D005L7OcsWADPPAN79yb2c9KQwkVEgsVxbLhcfPEgV0p6bMEC+zj/Sy8l9nPSkMJFRIJl\nwwbo6LBbkA8QjUYJh8NEo9FBvzUahXDYtnGZN88+FKOpMc8pXEQkWJYvh6OPhjPPPKgUCoXIzc0l\nFAoN+q2hkH3m0qV8sIkT7W40hYvnFC4iEiyPPmqfoJ8w4aBSfn4+DQ0N5OfnD/qt+fnQ0GDbuC1Y\nAE89ZR/aFM8oXEQkODo77frH+ecPWs7KyqKqqoqsrCyXOlRV2TZuCxZAdzds3DiCDosbhYuIBEdD\ngz3qpaoqeZ958sl2lKSpMU8pXEQkOFautD/ss7OT95lHHAGf/azCxWMKFxEJhj17YNUq1ykxgHA4\nTE1NDeFw2KUONTW2HZaBdRfxjMJFRILh2Wft2S1DhEskEqGxsZFIJOJSt0/ou5Tdfe5zdr3n7beH\n+Y3i5jC/OyAiAtgpseOPhzlzXF9SUlLCxiEW3ktKRrguP2+ebV98ET75yRG8gRxIIxcRCYaVK+0W\n5HE+/FjKzbXrPM3Nyf/sMUrhIiL+e/NN++TjEFNiCWUMzJ1rRy7iCYWLiPjvscfsOWLnnONfH+bN\nU7h4SOEiIv5buRIqK2HKlCFf1tzcjDGGZpfpq+ZmOwgZ0ezWvHl2Qf+dd0bwzXIghYuI+GvPHliz\nJq4HJ/Py8qivrycvL8+lDvX1th22uXNtq3UXTyhcRMRf69fD++/HNSWWnZ3N4sWLyXZ5yDI7GxYv\nHuEzmDNm2AMzFS6eULiIiL8ef9xOhw1sB/aLFvU9pXAREX+tXg0LFyb+YrB4aFHfMwoXEfHP++/D\nc8/FvUusq6uLuro6urq6XOpQV2fbEZk3z26L3rZthG8gAxQuIuKfJ5+099effXZcL+/s7KS2tpbO\nzk6XOtTW2nZEtKjvGR3/IiL+efxxmD4dZs2K6+WzZ892PVfM1kdwrtj+Zs2Co46yU2PJPPZ/DNLI\nRUT8s3q1nRIzxu+eWAOL+hq5jJrCRUT88dZbsGlT3FNiSaMdY55QuIiIP554wrZnneVvPw40bx5s\n3Qrvvut3T1KawkVE/PH44/Z4/WE88djS0kJOTg4tLS0udcjJse2IzZ69781kxBQuIpJ8jrNvvWUY\nEvqE/oD8fJg4cYQXw8gA7RYTkeTbvNkeEDnMKbFp06ZRW1s7RN1uRR6VCROgqMheASAjppGLiCTf\nmjX2h/ipp/rdk8GVlSlcRknhIiLJ19QEp5wCkyb53ZPBDYSL4/jdk5SlcBGR5Orrs+GycOGwv7W7\nu5ulS5fS3d3tUoelS207KmVl8N579n4XGRGFi4gk18sv25/+Z5457G/t6Ohg0aJFdHR0uNRh0SLb\njkpZmW01NTZiWtAXkeRaswYyMuy02DCVl5fT09PDJJfptPJy6OnxYLZt+nT7JqGQjoEZIYWLiCRX\nUxPMnw+HHz7sbx0/fjxZWVlD1GGIcvzGjYPSUo1cRkHTYiKSPHv22JOQR7DeknTaMTYqChcRSZ4X\nX4Te3hGttyRdWZl9kLKvz++epCSFi4gkz5o1cOSRcNJJI/r21tZWKioqaG1tdalDRYVtR62sDHbu\n9GB3QHpSuIhI8qxZAwsWwGEjW+7NyMigtLSUjIwMl7pdKnEpD492jI2KwkVEkmP3bnjmmVGtt0yf\nPp0lS5Ywffp0lzosWWLbUfvEJ+CYYxQuI6RwEZHkeO452LUrNdZbwF4cpkX9EVO4iEhyNDXB0Ufb\nh1FShcJlxBQuIpIcTU1w+un2GZIR6u3tZd26dfT29rrUYd0623qirAy2bIFo1KM3TB8KFxFJvJ07\n7bTYKKfE2traqKyspK2tzaUOlZW29URZGezdC6+84tEbpg+Fi4gk3rPP2t/+RxkuxcXFhEIhiouL\nXep2FsulPHwDO8Z0K+Ww6fgXEUm8piZ7PWRp6ajeJjMzk9Ih3iMzc9Qf8XFHH213jW3Z4uGbpgeN\nXEQk8Zqa4IwzRrXe4puiIntzpgxLCv4/LSIppbcXXnghdbYgH6ioSCOXEVC4iEhiPfOMXRT3IFza\n29uprq6mvb3dpQ7V1bb1THGx3SEQi3n4pmOfwkVEEqupya5bFBWN+q1isRiRSISYyw/6WAwiEY9z\noKjIPvz5+usevunYpwV9EUmsgfUWY0b9VgUFBTQ2Ng5RhyHKIzOw9WzLFjjhBI/ffOzSyEVEEicS\nscfsp+p6C8CnPmVvpdSi/rAoXEQkcZ56ys5RpXK4jBsHhYVa1B8mhYuIJE5Tk/3NPz/fk7eLRqOE\nw2GiLsexRKMQDifgtJbiYoXLMClcRCRxmprgrLM8WW8BCIVC5ObmEnI5TDIUgtzcBJw1qWddhk3h\nIiKJsWMHvPSSp1Ni+fn5NDQ0kO8yEsrPh4YGzwZK+xQVwbvvwvbtHr/x2KVwEZHEePJJcBxPwyUr\nK4uqqiqysrJc6lBVZVtP7b9jTOKicBGRxFizBmbN8uhaSJ/l59uFfU2NxU3hIiKJsWbNqK40DpTD\nD7fPuGjkEjeFi4h4r6sLNm3yfAtyOBympqaGcDjsUoeaGtt6rrhYI5dhULiIiPeammzrcbhEIhEa\nGxuJRCIudfuEvkt5dHSA5bDo+BcR8d6aNVBSYs8U81BJSQkbN24cog5DlEenqAi2brW3amZmJuhD\nxg6NXETEe2NpvWVAcbHd/ebZHcpjm8JFRLz1xhvw2mtjL1wKC22rqbG4KFxExFtNTfaJ/NNP97sn\n3jrmGJg6VYv6cVK4iIi31qyB8nL7w9hjzc3NGGNobm52qdtccymPnhb146ZwERHvOA6sXg1nn52Q\nt8/Ly6O+vp68vDyXOtTX2zYhCguhtTVBbz62KFxExDtbtsDbbycsXLKzs1m8eDHZ2dkudVi82LYJ\nUVhoF/T7+hL0AWOHwkVEvPPEEzBxIsyf73dPEqOwED78EN56y++eBJ7CRUS8s3o1VFTYmxvHooEd\nY5oaOySFi4h4Y+9eu1MsQVNiAF1dXdTV1dHV1eVSh7o62ybEzJkwYYLCJQ4KFxHxxt//bs9dSWC4\ndHZ2UltbS2dnp0sdamttmxCHHWZPela4HJKOfxERb6xebS9SOemkhH3E7NmzXc8Vs/UEnSu2P+0Y\ni4tGLiLijdWr7UGVh43x31kVLnFRuIjI6H3wAaxbl9ApscAoLLRH3Ozc6XdPAk3hIiKj9/TTEI3C\nWWf53ZPEKyy0D4u+8orfPQk0hYuIjN7q1fDJT9rjURKopaWFnJwcWlpaXOqQk2PbhNF25LgoXERk\n9AaOfDEmoR/j+xP6Ax9yzDEKl0MY4ytvIpJwXV2wYQNcd13CP2ratGnU1tYOUbdbkRNOi/qHpJGL\niIzOqlW2Pfdcf/uRTAqXQ1K4iMjoNDbCnDn2rpN0MRAujuN3TwJL4SIiI9fXZ0cuVVVJ+bju7m6W\nLl1Kd3e3Sx2WLrVtQhUW2qc1E3bOTOpTuIjIyG3YANu2JS1cOjo6WLRoER0dHS51WLTItgmlHWOH\npAV9ERm5xkaYPBkqK5PyceXl5fT09DDJ5dTl8nLo6UnCocyzZsG4cTZcxtp1zh5RuIjIyDU0wMKF\n9g6XJBg/fjxZWVlD1O3xZgl3+OH2hGSNXFxpWkxERiYSgWefTdqUWOBox9iQFC4iMjJNTfYOl3QN\nl6IihcsQFC4iMjKNjXbtYdaspH1ka2srFRUVtLr8UG9ttRdhJuVnfmGh3Tmwe3cSPiz1KFxEZPgc\nx663JHnUkpGRQWlpKRkZGS51KC21bcIVFUEsBq+9loQPSz1a0BeR4Xv1Vftbe5LDZfr06SxZsmSI\nOgxR9tb+25FLSpL0oalDIxcRGb4VK+yOqXQ4Yt/N1KkwZQps2eJ3TwJJ4SIiw7dihb11MuEPlASY\nMXZqTOEyKIWLiAxPTw+sXQuf/3zSP7q3t5d169bR29vrUrcXYrqUvaftyK4ULiIyPI8/brcgX3BB\n0j+6ra2NyspK2traXOr2sACXsvcGRi46wPIgChcRGZ4VK6CsDGbMSPpHFxcXEwqFKC4udqlDKGTb\npCgstCM5HWB5EIWLiMQvFoOVK32ZEgPIzMyktLSUzMxMl7rdiuxS9t7Atc6aGjuIwkVE4rd+vT0F\n2adwCZxZs+yBZlrUP4jCRUTit2KFvT/+lFP87kkwTJwIJ5ygcBmEwkVE4rdiBZx/vv1t3Qft7e1U\nV1fT3t7uUofqatsmjc4YG5TCRUTi8+ab8PLLvk6JxWIxIpEIsVjMpW4Pa3YpJ0ZhoUYug9DxLyIS\nn0cesSMWH09BLigooLGxcYi6PU8zqYqKYOtW2LkziTsJgk8jFxGJz4MP2ovBpkzxuyfBUlRkn3N5\n9VW/exIoChcRObQdO+z9LZdc4ndPgmfgAEtNjX2MwkVEDu2RR6CvDy66yNduRKNRwuEw0WjUpQ7h\nsG2TJjsbjj1W4XIAhYuIHNry5fZclWnTfO1GKBQiNzeXUCjkUofcXNsmlc4YO4jCRUSG1ttrV8kD\nMCWWn59PQ0MD+fn5LnV7h5lLOXF0OvJBFC4iMrTHHrNX+V58sd89ISsri6qqKrKyslzqdjObSzlx\nBp510QGWH1G4iMjQli+HOXNg5ky/exJcRUV2hBcO+92TwFC4iIi7XbvsU/kBmBILtIFrjjdt8rcf\nAaJwERF3TzxhfyMPSLiEw2FqamoIu4wQwmGoqfFhADFjhn2AcuPGJH9wcClcRMTdAw/Apz+dxAtS\nhhaJRGhsbCQSibjU7d4Dl3LijB9vp8Y0cvmIjn8RkcHt2mXXW777XXtffACUlJSwcYjRQUmJj4OH\n0lKNXPajkYuIDG7lSjsEuPxyv3uSGkpL7chFO8YAhYuIuLn3Xpg7d99tizK0khIbxm+95XdPAkHh\nIiIH6+mxu8Q0aolfaaltNTUGKFxEZDAPPWQP6Prnf/a7Jx/T3NyMMYbm5maXul0ecikn1syZdseY\nFvUBhYuIDObee2HBAsjJ8bsnH5OXl0d9fT15eXkudaivt23SjRtnd9Vp5AJot5iIHKirC1avhltu\n8bsnB8nOzmbx4sVD1GGIcuL5ul0tWDRyEZGPu/9++1v4pZf63ZPUox1jH1G4iMjH3XOPPf3x2GP9\n7knqKS3VjrF+ChcR2WfTJnj+efjXf/W7J4Pq6uqirq6Orq4ulzrU1dnWFwNnjGlqTOEiIvv505/s\nwsWFF/rdk0F1dnZSW1tLZ2enSx1qa23rC+0Y+4gW9EXEikbhrrvgyith4kS/ezOo2bNnu54rZus+\nnCu2P+0Y+4hGLiJiPfwwbN8O//ZvfvcktWnHGKBwEZEBS5bAKafse9JcRkY7xgCFi4gAvPEGrFrl\n80MiY4R2jAEKFxEBuOMOOOIIWLTI754MqaWlhZycHFpaWlzq9lABl3JyaMcYoHARkVgMbrsNvvQl\nOPJIv3szpIEn9LOzs13qdvDlUk6OmTPt/44bNvjYCf9pt5hIunv0UXj9dbjqKr97ckjTpk2jtrZ2\niLrdiuyrceOgvBxeesnnjvhLIxeRdHfjjXDyyfaPeGPOHIWL3x0QER/94x+wZo29yli8M2cOvPIK\n9Pb63RPfKFxE0tnvfw+f+lTKHFLZ3d3N0qVL6e7udqnD0qW29dWcOXYr8ssv+9wR/yhcRNLVtm1w\n991w9dUwYYLfvYlLR0cHixYtoqOjw6VuN7y5lJOnpMT+b5rGU2Na0BdJV7feaq9tTIGF/AHl5eX0\n9PQwadIkl7q9odmlnDwTJ0JZmcJFRNJMNAo332zPEUuho/XHjx9PVlbWEHUYopxcab6or2kxkXT0\nl7/A22/Dv/+73z0Zu+bMgVDIBnkaUriIpJtYDK6/Hi66yE7dSGLMmQN79qTt8fsKF5F089e/2m2y\nP/mJ3z0ZttbWVioqKmhtbXWpQ0WFbX1XXm7XtNJ0akzhIpJOBkYtF1wA8+b53Zthy8jIoLS0lIyM\nDJe6PTfSpZxckydDQUHahosW9EXSybJlsHkz3H673z0ZkenTp7NkyZIh6vbmgMBI40V9jVxE0kVf\nH/ziF1BVpaNekmXOHHuAZV+f3z1JOoWLSLp48EG7e+mnP/W7J+ljzhx7BMxrr/ndk6RTuIikg2gU\nfvhDOPdcqKz0uzcj1tvby7p16+h1ObOrtxfWrQvQkV5z5tg2DafGFC4i6eCWW+xvz7/5jd89GZW2\ntjYqKytpa2tzqdvsdCkn33HH2dvLXnzR754knRb0Rca6HTvgZz+zt2h95jN+92ZUiouLCYVCnHDC\nCS51O/PnUvZHZSU8/bTfvUg6jVxExrqf/xz27rVtisvMzKS0tJTMzEyXut2K7FL2x2mnwfr1sHOn\n3z1JKoWLyFjW1gZ/+AP853/C8cf73Zv0dNpp9kn955/3uydJpXARGascB6691t7XosvA/FNWBkcd\nBU895XdPkkrhIjJW/eUvsHIl/O53AXlkffTa29uprq6mvb3dpQ7V1bYNjPHj4dRTFS4iMgZs22ZP\nPF60CL74Rb9745lYLEYkEiEWi7nUIRKxbaAsWGD3SO/d63dPkka7xUTGou98xz4VftNNfvfEUwUF\nBTQ2Ng5RhyHK/jntNPvwzYYNcNJJfvcmKTRyERlrHnkE7rsPbrwRpk71uzcCNlAyMtJqakzhIjKW\nbN8O3/wmnH8+fPnLfvdGBkycaM9zW7vW754kjcJFZKzo64OvfMVue731VnuXyBgTjUYJh8NEXW53\njEYhHA7o5Y+nnWYfpnQcv3uSFAoXkbHihhtg1Sq45x67/XgMCoVC5ObmEgqFXOqQm2vbwFmwwI4s\nt2zxuydJoXARGQvWrIH/+i974vE55/jdm4TJz8+noaGB/Px8lzo0NNg2cCoq7LbkNFl3UbiIpLpw\nGK64As48MyWvLh6OrKwsqqqqyMrKcqnb62pcyv6aPNmekpwm6y4KF5FU1t0N550Hhx9up8PGj/e7\nRzKUs8+2e6XT4HkXhYtIqtq1yz4g2dlpf2Dp7LDgu+wyu+7yt7/53ZOEU7iIpKJYDK68El54wT7X\nUlTkd4+SIhwOU1NTQzgcdqlDTY1tA2nuXJg5E5Yu9bsnCadwEUk1e/fau1mWL7cPS6bwzZLDFYlE\naGxsJBKJuNTtIM6l7D9j7OFny5eP+akxhYtIKolG4fLL4c9/hrvuGlPnhsWjpKSEjRs3UlJS4lKH\njRttG1jV1XZq7Mkn/e5JQilcRFLFhx/CRRfBww/DsmV6Aj9VzZsHM2aM+akxhYtIKgiH7VbjtWvh\n0UdtyEhqSpOpMYWLSND97W92Ibiz0/7z2Wf73SMZrepqey3CGJ4aU7iIBFUsBv/7vzZMPvMZePFF\n+Oxn/e6Vr5qbmzHG0Nzc7FK3AwOXcnCcdNKYnxpTuIgE0ebN9qDD738frrvOboE67ji/e+W7vLw8\n6uvrycvLc6lDfb1tA21gamzZMti50+/eJITCRSRIdu2CX/4SZs+Gd9+151D9+tdwmO71A8jOzmbx\n4sVkZ2e71O0ubZdysFx1Fbz33pi70G2AwkUkCGIxuP12+PSn7QGU115rby2cP9/vnkmi5OfDN74B\nv/oV7Njhd288p3AR8dPu3fZ5lRNPhK99DU45xT6o8d//DZmZfvdOEu0nP7E7xm64we+eeE7hIuKH\nt9+Gn/0Mpk+Hr37VLhK88ALcfz8UFvrdu8Dq6uqirq6Orq4ulzrU1dk2JRx/PPzHf9ipsddf97s3\nnkqZcLnvvvv87oLI6OzYAUuWwFlnQU4O/M//wMUXw6ZN8Nhjab8TLB6dnZ3U1tbS2dnpUocf/eg+\nXMrBdN11MGWKvYtnDFG4iCRKNArr1tkRSmWl3e31jW/YnUJLlsBbb8Ett0Bxsd89TRmzZ88mEokw\ne/Zslzqcc859uJSDafJku8725z/bByvHCG1BEfHCrl32+tqWFrsQ/9xz9rmU3bvtzVXnnAN//CNc\ncAFMm+Z3byVorrrKPlB52WXw+9/Dt7/td49GTeEiciixmJ3S2r7drpW89ZZtt26F9nZ47TU7Xx6L\n2dfPmAEnn2yfY6iosE/XT5jg599Agu6ww+wJ17m5cM019t+nX/8axqXM5NJBUiNctm2Dnp4UeOxW\nDuI4h/76ga9xnH1fG+yfHQf6+g5uY7F9bSxmd+HEYrBnj/3nPXvsVFU0akcUu3bZB9h27bKHQvb2\nwgcfwPvv23/f3nvP/unuPriPRx9tF+FnzYJLL4WCAigrg9LSgN6xK4E3bhz85jf236vvfhfuuAPO\nOAMWLrT39UyYYP8ccYQ9sSHg4g2XDIDNmzcnsCtDWLaMnrVraZ43z5/Pl7HjsMPsnwkT7NXAEyfa\nNiPD/kd7xBF2C/CMGXDkkXY+fMoUGyZTptin87Kz3bcJv/pqUv866eaVV17hmmuu4aabbqKgoGCQ\nOjQ29vDXvzYzSDk1zJ8Pd95pDyldvx4efHDfqBjg2GNh1SrfurdfDmQM9TrjuP1muf+LjLkCuGf0\n3RIRkTHiy47j3OtWjDdcjgWqgK3ALs+6JiIiqSYDmAE0Oo7zrtuL4goXERGR4UjdrQgiIhJYChcR\nEfGcwkVERDyXEuFijLnaGNNhjNlpjHnOGKNDmEREAizw4WKM+RLwf4D/AuYALwONxphUuA5IROJk\njDnNGPOwMeYtY0yfMebCA+pTjTF39Nc/MMasNMbku7xXuzFmoTHmdGPMQ8aYt40xvcaYl/ofrdj/\ntacaY57vxf2aAAAENUlEQVQ2xmw3xnxojNlsjPluIv+u6SDw4QJcC/zRcZy7HMfZAnwT+BD4mr/d\nEhGPTQI2AN8CBtvG+v+wW2C/AMwG3gBWG2M+9kSrMeZEYArwJFCJ/YX0EuAzwO3AXcaY8/f7lg+A\nm4DTgCLgF8D1xpjFXv3F0lGgtyIbYyZgg+RSx3Ee3u/rdwBHOY5zsV99E5HEMcb0AV8c+O/eGFMA\ntAIl/b9kYowxwDvADx3HuW2/7/1x/+uuOPidwRizAnjHcRzX8DDGLAN6Hcf5qld/p3QT9JFLNjAe\nOPDqny7gE8nvjoj45HDsaGb3wBcc+5vxbuDAu6AvxI5y3BwFuN4rbIyZA1QAfxthX4Xgh4uICMAW\n4E3gV8aYKcaYicaYHwA5wEd3GBhjPomd/npssDcxxiwCTgJuG6T2pjFmF/AC8AfHcW73/q+RPoIe\nLtuBGHD8AV8/HjscFpE04DjOXuBi4NPYUUcvcDqwEujb76UXAk87jhM58D2MMWdiQ2XxwNTaAeYD\n87Drutf2byaSEQp0uDiOswd4EThr4Gv986xnAc/61S8RST7HcV5yHGcudlprmuM452Onztv3e9mF\nwMMHfq8x5vT+r3/HcZxBD+F1HOd1x3E2Oo7zJ+C3QK3Hf4W0Euhw6VcHfN0Y8y/GmCLg/wJHAHf4\n2isR8YXjOO87jvNu/yL/ScBDAMaYScCZHLDeYow5A1gBfK8/OOIxHrvOIyMU+MvCHMe5v/+Zlp9j\np8M2AFWO42zzt2ci4qX+cMgHTP+XTjDGlAM7HMd50xhzGbANuwX5ROB3wHLHcZ7of/15QKvjOG/s\n955nAo/0v/ZBY8zAFHvUcZzu/td8q/89B6bKTgeu6/8eGaFAb0UWkfTRP3XVxMHPuNzpOM7XjDHX\nAN8DpgKdwJ3A9f3rMRhj7gK2Oo7z0/3e83bgXwb5uCcdx1nY/5pvA9/APkOzF3gNuNVxnFs9/Oul\nHYWLiKQ8Y8zAIwvnOY7zd7/7I6mx5iIicijHAHUKluDQyEVERDynkYuIiHhO4SIiIp5TuIiIiOcU\nLiIi4jmFi4iIeE7hIiIinlO4iIiI5xQuIiLiOYWLSByMMRXGmOeNMWV+90UkFShcROLgOM467NHu\nP/S7LyKpQMe/iMTJGDMNaAVyHcfp8bs/IkGmkYtInBzH6cQeCX+l330RCTqFi8jw3Acs9rsTIkGn\ncBGJkzEmHygDphpjTvK7PyJBFvhrjkWCwBjzOeCbwNex/918HdDdISIutKAvcgjGmAuAbwGXOI6z\n2xhTAKwHpjmOs9Pf3okEk6bFRIZgjJkFfB/4kuM4uwEcx3kFu7A/2N3sIoJGLiIikgAauYiIiOcU\nLiIi4jmFi4iIeE7hIiIinlO4iIiI5xQuIiLiOYWLiIh4TuEiIiKeU7iIiIjnFC4iIuI5hYuIiHhO\n4SIiIp77/67M81MvdmyZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110e4d278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAElCAYAAAAoZK9zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110c74e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.special import gammaln\n",
    "import numpy as np\n",
    "import scipy.special as sps\n",
    "\n",
    "#savefigs = \n",
    "\n",
    "def log_beta_pdf(x, a, b):\n",
    "    \n",
    "    y = - gammaln(a) - gammaln(b) + gammaln(a+b) + np.log(x)*(a-1) + np.log(1-x)*(b-1) \n",
    "    idx = np.where(x == 0)\n",
    "    if a==1:\n",
    "        y[idx] = - gammaln(a) - gammaln(b) + gammaln(a+b)\n",
    "    elif a<1:\n",
    "        y[idx] = np.Inf\n",
    "    else:\n",
    "        y[idx] = - np.Inf\n",
    "    \n",
    "    idx = np.where(x == 1)\n",
    "    if b==1:\n",
    "        y[idx] = - gammaln(a) - gammaln(b) + gammaln(a+b)\n",
    "    elif b<1:\n",
    "        y[idx] = np.Inf\n",
    "    else:\n",
    "        y[idx] = - np.Inf\n",
    "    return y\n",
    "\n",
    "a = 1\n",
    "b = 1\n",
    "\n",
    "xx = [1,1,1,1,1,0,1,1, 1,0,1,0,1,1,1,1,0, 1,1,1,1,1,1,1]\n",
    "\n",
    "p = np.arange(0.0,1.01,0.01)\n",
    "\n",
    "c = [0,0]\n",
    "N = 0\n",
    "plt.figure(figsize=(5,3))\n",
    "plt.plot(p, np.exp(log_beta_pdf(p, a+c[1], b+c[0])), 'r')\n",
    "plt.xticks([0,1])\n",
    "plt.yticks([])\n",
    "plt.xlim([-0.1,1.1])\n",
    "plt.ylim([0,6])\n",
    "pi_ML =  (a+c[1])/(a+b+N)\n",
    "yl = plt.gca().get_ylim()\n",
    "plt.plot([pi_ML, pi_ML], yl , 'k:')\n",
    "\n",
    "plt.xlabel('$\\lambda$')\n",
    "#plt.savefig('/Users/cemgil/Dropbox/tex/cam/talks/cmpe547/beta{n}.eps'.format(n=N), bbox_inches='tight')\n",
    "plt.show()\n",
    "\n",
    "for x in xx:\n",
    "    c[x] += 1\n",
    "    N += 1\n",
    "    plt.figure(figsize=(5,3))\n",
    "    plt.plot(p, np.exp(log_beta_pdf(p, a+c[1], b+c[0])), 'r')\n",
    "\n",
    "    \n",
    "    pi_ML =  (a+c[1])/(a+b+N)\n",
    "    pi_mode = (a+c[1]-1)/float(a+b+N-2)\n",
    "    tmp = str(int(a+c[1]-1))+'/'+str(a+b+N-2)\n",
    "    plt.xticks([0,pi_mode],('0',tmp))\n",
    "    #plt.xticks([0,pi_mode])\n",
    "    plt.yticks([])\n",
    "    plt.xlim([-0.1,1.1])\n",
    "    plt.ylim([0,6])\n",
    "    \n",
    "    yl = plt.gca().get_ylim()\n",
    "    plt.plot([pi_ML, pi_ML], yl , 'k:')\n",
    "    plt.plot([pi_mode, pi_mode], yl , 'b:')\n",
    "    \n",
    "    plt.xlabel('$\\lambda$')\n",
    "    #plt.savefig('/Users/cemgil/Dropbox/tex/cam/talks/cmpe547/beta{n}.eps'.format(n=N), bbox_inches='tight')\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Finding if a Coin is Fair or Fake \n",
    "\n",
    "We consider the folowing problem: Given a sequence of coin tosses $X = \\{x^{(n)}\\}_{n=1\\dots N}$, determine if the coin is fair or fake.\n",
    "\n",
    "This can be cast as a model selection problem:\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\pi_1|m & \\sim & \\left\\{ \\begin{array}{cc} \\delta(\\pi_1 - 0.5) & m = 0\\\\ \\mathcal{B}(\\pi; a, b) & m = 1 \\end{array} \\right.\n",
    "\\end{eqnarray}\n",
    "For $n = 1\\dots N$\n",
    "\\begin{eqnarray}\n",
    "x^{(n)}| \\pi_1 & \\sim & \\mathcal{BE}(x; \\pi_1)\n",
    "\\end{eqnarray}\n",
    "\n",
    "This model defines the following:\n",
    "- The indicator $m$, that denotes if the coin is fake,\n",
    "- What a fake coin is: a fake coin is one that has an arbitrary probability $\\pi_1$ between $0$ and $1$. \n",
    "- What a fair coin is: a fair coin has $\\pi_1 = 0.5$\n",
    "\n",
    "We need to calculate the marginal likelihoods for $m=0$ and $m=1$\n",
    "\\begin{eqnarray}\n",
    "p(X| m) & = & \\int d\\pi_1 p(X | \\pi_1) p(\\pi_1|m)\n",
    "\\end{eqnarray}\n",
    "\n",
    "###### Not Fake\n",
    "\\begin{eqnarray}\n",
    "p(X| m) & = & \\int d\\pi_1 p(X| \\pi_1) \\delta(\\pi_1 - 0.5) \\\\\n",
    "& = & \\prod_{n=1}^N \\left(\\frac{1}{2}\\right)^{x^{(n)}} \\left(\\frac{1}{2}\\right)^{1-x^{(n)}} = \\frac{1}{2^N}\n",
    "\\end{eqnarray}\n",
    "\n",
    "###### Fake\n",
    "\n",
    "\\begin{eqnarray}\n",
    "p(X| m) & = & \\int d\\pi_1 p(\\pi_1; a, b) \\prod_{n=1}^{N} p(x^{(n)}| \\pi_1)  \\\\\n",
    "& = &  \\int d\\pi_1 \\left(\\prod_{n=1}^N \\left(1-\\pi_1\\right)^{1-x^{(n)}} \\pi_1^{x^{(n)}} \\right) \\mathcal{B}(\\pi; a, b) \\\\\n",
    "& = & \\frac{\\Gamma(a + b)}{\\Gamma(a)\\Gamma(b)} \\int d\\pi_1 \\left(1-\\pi_1\\right)^{c_0+a-1} \\pi_1^{c_1+b-1} \\\\\n",
    "& = & \\frac{\\Gamma(a + b)}{\\Gamma(a)\\Gamma(b)} \\frac{\\Gamma(c_0+a)\\Gamma(c_1+b)}{\\Gamma(c_0 + c_1 +a + b)}\n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The log-odds is the ratio of marginal likelihoods\n",
    "\n",
    "$$\n",
    "l(X) = \\log\\left( \\frac{p(X|m = \\text{Fair})}{p(X|m = \\text{Fake})} \\right)\n",
    "$$\n",
    "\n",
    "If $l(X)>0$, we may conclude that the coin is fair and biased when $l<0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "log_odds =  -0.826678573184\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.special as sps\n",
    "\n",
    "def log_odds(c_0, c_1, a, b):\n",
    "    # Total number of tosses\n",
    "    N = c_0 + c_1\n",
    "    \n",
    "    M_fair = N*np.log(0.5)\n",
    "    M_fake = sps.gammaln(a+b) - sps.gammaln(a) - sps.gammaln(b) +  sps.gammaln(c_0+a) + sps.gammaln(c_1+b) - sps.gammaln(N+a + b) \n",
    "    return M_fair - M_fake\n",
    "\n",
    "# Number of Zeros observed\n",
    "c_0 = 6\n",
    "# Number of Ones\n",
    "c_1 = 1\n",
    "\n",
    "# Prior\n",
    "a = 1\n",
    "b = 1\n",
    "\n",
    "\n",
    "print('log_odds = ', log_odds(c_0, c_1, a, b) )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYsAAAETCAYAAADH1SqlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEM9vuvkVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1085784a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 1\n",
    "b = 1\n",
    "N = 10\n",
    "\n",
    "l = np.zeros(N+1)\n",
    "\n",
    "for c in range(0,N+1):\n",
    "    l[c] = log_odds(N-c, c, a, b)\n",
    "\n",
    "plt.plot(range(0,N+1), l, 'o')\n",
    "plt.plot(range(0,N+1), np.zeros(N+1), 'k:')\n",
    "ax = plt.gca()\n",
    "ax.set_xlabel('Number of ones $c_1$')\n",
    "ax.set_ylabel('log-odds $l(X)$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize the region where we would decide that the coin is fake by plotting the points where the log-odds is negative."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAERCAYAAABowZDXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107bee748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 1\n",
    "b = 1\n",
    "\n",
    "for N in range(1, 25):\n",
    "\n",
    "    l = np.zeros(N+1)\n",
    "\n",
    "    for c in range(0,N+1):\n",
    "        l[c] = log_odds(N-c, c, a, b)\n",
    "    \n",
    "    \n",
    "    idx = np.where( np.array(l)<0 )\n",
    "    p = np.arange(0,N+1)/N\n",
    "    plt.plot(N*np.ones_like(p), p, '.k',markersize=4)    \n",
    "    plt.plot(N*np.ones_like(p[idx]), p[idx], '.r',markersize=20)\n",
    "    \n",
    "\n",
    "ax = plt.gca()\n",
    "ax.set_ylim((0,1))\n",
    "ax.set_xlabel('$N$')\n",
    "ax.set_ylabel('$c_1/N$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Estimation of a Categorical distribution\n",
    "\n",
    "## Maximum Likelihood Estimation\n",
    "\n",
    "We observe a dataset $\\{x^{(n)}\\}_{n=1\\dots N}$. The model for a single observation is a categorical distribution with parameter $\\pi = (\\pi_1, \\dots, \\pi_S)$ where \n",
    "\n",
    "\\begin{eqnarray}\n",
    "x^{(n)} & \\sim & p(x|\\pi) = \\prod_{s=1}^{S} \\pi_s^{\\ind{s = x^{(n)}}}\n",
    "\\end{eqnarray}\n",
    "where $\\sum_s \\pi_s  = 1$.\n",
    "\n",
    "The loglikelihood of the entire dataset is\n",
    "\n",
    "\\begin{eqnarray}\n",
    "{\\cal L}(\\pi_1,\\dots,\\pi_S) & = & \\sum_{n=1}^N\\sum_{s=1}^S \\ind{s = x^{(n)}} \\log \\pi_s\n",
    "\\end{eqnarray}\n",
    "This is a constrained optimisation problem.\n",
    "Form the Lagrangian\n",
    "\\begin{eqnarray}\n",
    "\\Lambda(\\pi, \\lambda) & = & \\sum_{n=1}^N\\sum_{s'=1}^S \\ind{s' = x^{(n)}} \\log \\pi_{s'}  + \\lambda \\left( 1 - \\sum_{s'} \\pi_{s'} \\right ) \\\\\n",
    "\\frac{\\partial \\Lambda(\\pi, \\lambda)}{\\partial \\pi_s} & = & \\sum_{n=1}^N \\ind{s = x^{(n)}} \\frac{1}{\\pi_s} - \\lambda = 0 \\\\\n",
    "\\pi_s & = & \\frac{\\sum_{n=1}^N \\ind{s = x^{(n)}}}{\\lambda}\n",
    "\\end{eqnarray}\n",
    "\n",
    "We solve for $\\lambda$\n",
    "\\begin{eqnarray}\n",
    "1 & = & \\sum_s \\pi_s = \\frac{\\sum_{s=1}^S \\sum_{n=1}^N \\ind{s = x^{(n)}}}{\\lambda} \\\\\n",
    "\\lambda & = & \\sum_{s=1}^S \\sum_{n=1}^N \\ind{s = x^{(n)}} =  \\sum_{n=1}^N 1 = N\n",
    "\\end{eqnarray}\n",
    "\n",
    "Hence\n",
    "\\begin{eqnarray}\n",
    "\\pi_s & = & \\frac{\\sum_{n=1}^N \\ind{s = x^{(n)}}}{N}\n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Maximum A-Posteriori Estimation\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Full Bayesian Inference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualizing the Dirichlet [http://blog.bogatron.net/blog/2014/02/02/visualizing-dirichlet-distributions/]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.tri as tri\n",
    "from functools import reduce\n",
    "from scipy.special import gammaln\n",
    "\n",
    "corners = np.array([[0, 0], [1, 0], [0.5, 0.75**0.5]])\n",
    "triangle = tri.Triangulation(corners[:, 0], corners[:, 1])\n",
    "\n",
    "refiner = tri.UniformTriRefiner(triangle)\n",
    "trimesh = refiner.refine_triangulation(subdiv=4)\n",
    "\n",
    "\n",
    "# Mid-points of triangle sides opposite of each corner\n",
    "midpoints = [(corners[(i + 1) % 3] + corners[(i + 2) % 3]) / 2.0 \\\n",
    "             for i in range(3)]\n",
    "\n",
    "def xy2bc(xy, tol=1.e-3):\n",
    "    '''Converts 2D Cartesian coordinates to barycentric.'''\n",
    "    s = [(corners[i] - midpoints[i]).dot(xy - midpoints[i]) / 0.75 \\\n",
    "         for i in range(3)]\n",
    "    return np.clip(s, tol, 1.0 - tol)\n",
    "\n",
    "class Dirichlet(object):\n",
    "    def __init__(self, alpha):\n",
    "        self._alpha = np.array(alpha)\n",
    "        self._coef = gammaln(np.sum(self._alpha)) - np.sum(gammaln(self._alpha))\n",
    "    def log_pdf(self, x):\n",
    "        return self._coef + np.sum(np.log(x)*(self._alpha - 1)) \n",
    "    def pdf(self, x):\n",
    "        '''Returns pdf value for `x`.'''\n",
    "        return np.exp(self.log_pdf(x))\n",
    "        \n",
    "def draw_pdf_contours(dist, nlevels=200, subdiv=8, **kwargs):\n",
    "\n",
    "    refiner = tri.UniformTriRefiner(triangle)\n",
    "    trimesh = refiner.refine_triangulation(subdiv=subdiv)\n",
    "    pvals = [dist.pdf(xy2bc(xy)) for xy in zip(trimesh.x, trimesh.y)]\n",
    "\n",
    "    plt.tricontourf(trimesh, pvals, nlevels, **kwargs)\n",
    "    plt.axis('equal')\n",
    "    plt.xlim(0, 1)\n",
    "    plt.ylim(0, 0.75**0.5)\n",
    "    plt.axis('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW8AAAD7CAYAAAClvBX1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAA2CeAMANAjiDQDQIIg3AECD/D+hbGG8uW0OHQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11047b6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_pdf_contours(Dirichlet([1, 3, 1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW8AAAD7CAYAAAClvBX1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f5ce978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_pdf_contours(Dirichlet([1.99, 3.99, 10.99]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 6-faced die with repeated labels\n",
    "\n",
    "Consider a die where the numbers on each face are labeled, possibly with repetitions, from the set $1\\dots 6$. \n",
    "A 'normal' die has labels $1,2,3,4,5,6$ but we allow other labelings, for example as $1,1,3,5,5,5$ or $1,1,1,1,1,6$.\n",
    "\n",
    "Can we construct a method to find how the die has been labeled from a sequence of outcomes?  \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Does my data have a single cluster or are there two clusters?\n",
    "\n",
    "We observe a dataset of $N$ points and want to decide if there are one or two clusters. For example, the below dataset, when visualized seems to suggest two clusters; however the separation is not very clear; perhaps a single component might have been also sufficient. How can we derive a procedure that leads to a resonable answer in this ambigious situation?\n",
    "\n",
    "<img src=\"clusters.png\" width='180' align='center'>\n",
    "\n",
    "One principled approach is based on Bayesian model selection. Our approach will be describing two alternative generative models for data. Each generative model will reflect our assumption what it means to have clusters. In other words, we should describe two different procedures: how to generate a dataset with a single cluster, or a datset that has two clusters. Once we have a description of each generative procedure, we may hope to convert our qualitative question (how many clusters?) into a well defined computational procedure. \n",
    "\n",
    "Each generative procedure will be a different probability model and we will compute the marginal posterior distribution conditioned on an observed dataset.\n",
    "\n",
    "The single cluster model will have a single cluster center, denoed as $\\mu$. Once $\\mu$ is generated, each observation is generated by a Gaussian distribution with variance $R$, centered around $\\mu$.\n",
    "\n",
    "Model $M =1$: Single Cluster\n",
    "\\begin{eqnarray}\n",
    "\\mu & \\sim & {\\mathcal N}(\\mu; 0, P) \\\\\n",
    "x_i | \\mu & \\sim & {\\mathcal N}(x; \\mu, R)\n",
    "\\end{eqnarray}\n",
    "\n",
    "The parameter $P$ denotes a natural range for the mean, $R$ denotes the variance of data, the amount of spread around the mean. To start simple, we will assume that these parameters are known; we will able to relax this assumption later easily.\n",
    "\n",
    "Below, we show an example where each data point is a scalar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1QAAAB8CAYAAABudvGbAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1118e2b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Parameters\n",
    "P = 100\n",
    "R = 10\n",
    "\n",
    "# Number of datapoints\n",
    "N = 5\n",
    "\n",
    "mu = np.random.normal(0, np.sqrt(P))\n",
    "x  = np.random.normal(mu, np.sqrt(R), size=(N))\n",
    "\n",
    "plt.figure(figsize=(10,1))\n",
    "plt.plot(mu, 0, 'r.')\n",
    "plt.plot(x, np.zeros_like(x), 'x')\n",
    "ax = plt.gca()\n",
    "ax.set_xlim(3*np.sqrt(P)*np.array([-1,1]))\n",
    "ax.set_ylim([-0.1,0.1])\n",
    "ax.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model $M = 2$: Two Clusters\n",
    "\\begin{eqnarray}\n",
    "\\mu_0 & \\sim & {\\mathcal{N}}(\\mu; 0, P) \\\\\n",
    "\\mu_1 & \\sim & {\\mathcal{N}}(\\mu; 0, P) \\\\\n",
    "c_i & \\sim & {\\mathcal{BE}}(r; 0.5) \\\\\n",
    "x_i | \\mu_0, \\mu_1, c_i & \\sim & {\\mathcal N}(x; \\mu_0, R)^{1-c_i} {\\mathcal N}(x; \\mu_1, R)^{c_i}\n",
    "\\end{eqnarray}\n",
    "\n",
    "The parameter $P$ denotes a natural range for both means, $R$ denotes the variance of data in each cluster. The variables $r_i$ are the indicators that show the assignment of each datapoint to one of the clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1QAAAB8CAYAAABudvGbAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11109cac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Parameters\n",
    "P = 100\n",
    "R = 2\n",
    "\n",
    "# Number of datapoints\n",
    "N = 10\n",
    "\n",
    "# Number of clusters\n",
    "M = 2\n",
    "\n",
    "mu = np.random.normal(0, np.sqrt(P), size=(M))\n",
    "c = np.random.binomial(1, 0.5, size=N)\n",
    "x = np.zeros(N)\n",
    "for i in range(N):\n",
    "    x[i]  = np.random.normal(mu[c[i]], np.sqrt(R))\n",
    "\n",
    "plt.figure(figsize=(10,1))\n",
    "#plt.plot(mu, np.zeros_like(mu), 'r.')\n",
    "plt.plot(x, np.zeros_like(x), 'x')\n",
    "ax = plt.gca()\n",
    "ax.set_xlim(3*np.sqrt(P)*np.array([-1,1]))\n",
    "ax.set_ylim([-0.1,0.1])\n",
    "ax.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Extension\n",
    "We dont know the component variances\n",
    "\n",
    "\n",
    "#### Combining into a single model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.array([1.1, 0.9, 0.95, 3.2, 3.3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Capture\n",
    "\n",
    "Recapture"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Change point\n",
    "Coin switch\n",
    "\n",
    "Coal Mining Data\n",
    " Single Change Point\n",
    " Multiple Change Point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{\n",
      "  \"key\": \"5fe2a052-2599-465d-96fa-793a58b02ea2\",\n",
      "  \"transport\": \"tcp\",\n",
      "  \"signature_scheme\": \"hmac-sha256\",\n",
      "  \"shell_port\": 65197,\n",
      "  \"stdin_port\": 65199,\n",
      "  \"ip\": \"127.0.0.1\",\n",
      "  \"hb_port\": 65201,\n",
      "  \"control_port\": 65200,\n",
      "  \"iopub_port\": 65198\n",
      "}\n",
      "\n",
      "Paste the above JSON into a file, and connect with:\n",
      "    $> ipython <app> --existing <file>\n",
      "or, if you are local, you can connect with just:\n",
      "    $> ipython <app> --existing kernel-457030b1-3d25-4222-9094-06fb4bbdbefe.json \n",
      "or even just:\n",
      "    $> ipython <app> --existing \n",
      "if this is the most recent IPython session you have started.\n"
     ]
    }
   ],
   "source": [
    "%connect_info"
   ]
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}