InformationTheoryOptimization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#math and linear algebra stuff\n",
    "import numpy as np\n",
    "\n",
    "#Math and linear algebra stuff\n",
    "import scipy.stats as scs\n",
    "\n",
    "#plots\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams['figure.figsize'] = (15.0, 15.0)\n",
    "#mpl.rc('text', usetex = True)\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Information theory, statistics and optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many of the elements presented here, can also be found on the \"Book of statistical proof\" made available by its author online [here]() and that we hereby reproduce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#IFrame(\"doc/InformationTheroryOptimization/StatProofBook.pdf\", width=1200, height=800)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Some notation\n",
    "Let's talk about a set of N sample vectors $x_i, i=0,1,\\dots N-1$ where $x_i \\in \\mathbb{R}^P$, such that each $x_i$ is an output of a random process, that can be modeled using a probability density function: \n",
    "$$\n",
    "    P_{\\theta}(x) = P(x|\\theta)\n",
    "$$\n",
    "$\\theta \\in \\mathbb{R}^K$ being the pdf parameter vector.\n",
    "\n",
    "We can also define the empirical data distribution, that sums to one, using:\n",
    "$$\n",
    "    P_{D}(x) = \\frac{1}{N} \\sum_{i=0}^{N-1} \\delta(x-x_i)\n",
    "$$\n",
    "\n",
    "Where $\\delta(x)$ stands for the Dirac delta function. \n",
    "\n",
    "## Quantity of information\n",
    "\n",
    "### Information theory framework\n",
    "In the framework of information theory, a signal of interest can be modeled as a message produced by a transmitter, enventually modified by the channel, that should be retrieved by the receiver.\n",
    "The intrinsic complexity of the message, or the quantity of information it contains can be modeled using shannon entropy, defined itself as the expectation of the self information for symbols coming from a given class of message.\n",
    "\n",
    "### Self information\n",
    "Self information $I$ of a random event $\\omega$ with probability $P(\\omega)$ is defined as\n",
    "\n",
    "$$\n",
    "    I(\\omega) = log\\left(\\frac{1}{P(\\omega)}\\right) = -log(P(\\omega))\n",
    "$$\n",
    "\n",
    "We generally use the logarithm in base 2 so that self information can be defined in bits, and so do the entropy.\n",
    "Let's list some interesting properties of this metric:\n",
    "  - as $I$ is a monotically increasing function of $\\frac{1}{P(\\omega)}$, the realisation of the event that have a low probability gives us a large quantity of information.\n",
    "  - An event that is not random, ie for wich $P(\\omega)=1$ gives no informations.\n",
    "  - The simultanneous occurence of two independent events $\\omega_a$ and $\\omega_b$ with respective probability $P(\\omega_a)$ and $P(\\omega_b)$ bring us a total quantity of infomation equal to the sum of the information of the two events, due to the use of the logarithm, ie $$ log\\left(\\frac{1}{P(\\omega_a)P(\\omega_b)}\\right) = log\\left(\\frac{1}{P(\\omega_a)}\\right)+log\\left(\\frac{1}{P(\\omega_b)}\\right) = I(\\omega_a)+I(\\omega_b)$$.\n",
    "\n",
    "\n",
    "### Entropy\n",
    "Shannon entropy $H(x)$, is defined as the expectation of the self information for a random variable $H(x)=E[I(X)] = E[-log(P(x))]$ which reads in the discrete case:\n",
    "\n",
    "\\begin{align*}\n",
    "    H(x) = - \\sum_{i=0}^{N-1} P(x_i)log(P(x_i))\n",
    "\\end{align*}\n",
    "\n",
    "It is interesting to notice that $H(x)$ can be interpreted as the entopy rate of a data source or the average number of bits per symbol needed to encode a message whith a known symbol probability density function.\n",
    "\n",
    "This concept can obviously be extended to blocks or structured blocks of data instead of symbols.\n",
    "\n",
    "#### A small numerical illustration\n",
    "Let's say that we have a random bit generator, that can be tuned to generate the value $1$ with a probability $P_1$ varying from $0$ to $1$, the probability that the random bit generator output $0$ is given by $P_0 = 1-P_1$. This is a classic Bernoulli scheme.\n",
    "The entropy of this binary source is then\n",
    "\n",
    "\\begin{align}\n",
    "    & -P_1 log_2(P_1) - P_0 log_2(P_0) \\\\\n",
    "    =& -P_1 log_2(P_1) -  (1-P_1) log_2(1-P_1)\n",
    "\\end{align}\n",
    "\n",
    "Let see what does the entropy of this random bit generator, along the value of $P_1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Entropy in bits')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#P1 values:\n",
    "P1=np.linspace(0,1,101)\n",
    "\n",
    "#Handle the infinite value of log in 0, so that it returns 0\n",
    "def SafeLog2(v):\n",
    "    r=v.copy()\n",
    "    r[v!=0]=np.log2(v[v!=0])\n",
    "    return r\n",
    "\n",
    "#Entropy of a Bernouilli distribution with probability p\n",
    "def BernoulliEntropy( p ):\n",
    "    return -( p*SafeLog2(p)+(1-p)*SafeLog2(1-p) )\n",
    "\n",
    "#plot entropy functions of P1\n",
    "plt.plot(P1,BernoulliEntropy(P1))\n",
    "\n",
    "#Fancy stuff\n",
    "plt.title('Entropy of a Random bit generator')\n",
    "plt.xlabel('P1 value')\n",
    "plt.ylabel('Entropy in bits')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#In some cases later, we will need to compute the entropy of a dataset\n",
    "def GetEntropyFromQuantizedData(v, num_bins=100):\n",
    "    \"\"\"\n",
    "        We assume that v is a vector\n",
    "    \"\"\"\n",
    "    \n",
    "    #Data is divided in num_bins equally spaced bins, then the histogram is returned\n",
    "    hist,edges = np.histogram(v, bins=num_bins)\n",
    "    \n",
    "    #get the empirical distribution, use floating point division\n",
    "    p=np.double(hist)/np.sum(hist)\n",
    "\n",
    "    #scipy entropy simply compute -sum(p * log(p))\n",
    "    return p, -np.dot(p,SafeLog2(p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interesting property of entropy\n",
    "### Concavity of entropy\n",
    "This section is a reproduction of \"book of statistical proof\", in particular for [entropy](https://statproofbook.github.io/P/ent-conc.html) and [kl-divergence](https://statproofbook.github.io/P/kl-conv.html)\n",
    "#### Link between entropy and KL-divergence\n",
    "The entropy is concave in the space of probability mass function, more formally, this reads:\n",
    "\\begin{align*}\n",
    " H[\\lambda p_1 + (1-\\lambda) p_2] \\geq \\lambda H[p_1] + (1-\\lambda) p_2 H[p_2] \\tag{1.1}\n",
    "\\end{align*}\n",
    "where $p_1$ and $p_2$ are probability mass functions and $\\lambda \\in [0,1]$\n",
    "\n",
    "Proof: Let $X$ be a discrete random variable with possible outcomes $\\mathcal{X} := {x_i, i \\in 0,1,\\dots N-1}$ and let $u(x)$ be the probability mass function of a discrete uniform distribution on $X \\in \\mathcal{X}$, ie $u(x_i)=\\frac{1}{N}$. Then, the entropy of an arbitrary probability mass function $p(x)$ can be rewritten as\n",
    "\n",
    "\\begin{align*} \\tag{1.2}\n",
    "    H(X) &= - \\sum_{i=0}^{N-1} p(x_i)log(p(x_i)) \\\\\n",
    "    &= - \\sum_{i=0}^{N-1} p(x_i)log\\left(\\frac{p(x_i)}{u(x_i)} u(x_i)\\right) \\\\\n",
    "    &= - \\sum_{i=0}^{N-1} p(x_i)log\\left(\\frac{p(x_i)}{u(x_i)}\\right) - \\sum_{i=0}^{N-1} p(x_i)log(u(x_i)) \\\\\n",
    "    &= -KL[p\\|u] - \\sum_{i=0}^{N-1} p(x_i)log(u(x_i)) \\\\\n",
    "    &= -KL[p\\|u] - log \\left(\\frac{1}{N} \\right) \\sum_{i=0}^{N-1} p(x_i) \\\\\n",
    "    &= log(N) - KL[p\\|u] \\\\\n",
    "    log(N) - H(X) &= KL[p\\|u]\n",
    "\\end{align*}\n",
    "\n",
    "Where $KL[p\\|u]$ is the Kullback-Leibler divergence between $p$ and the discrete uniform distriution $u$ over $\\mathcal{X}$. We will explain KL-divergence more in detail later on this page."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Convexity of KL-divergence\n",
    "Note that the KL divergence is convex in the space of pairs of probability distributions $(p,q)$, ie:\n",
    "\\begin{align*}\\tag{2.1}\n",
    " KL[\\lambda p_1 + (1-\\lambda) p_2 \\| \\lambda q_1 + (1-\\lambda) q_2] \\leq \\lambda KL[p_1\\|q_1] + (1-\\lambda) KL[p_2\\|q_2]\n",
    "\\end{align*}\n",
    "\n",
    "We recall that KL-divergence between two distribution $(p,q)$ reads\n",
    "\\begin{align*}\n",
    "    KL[p\\|q] &= \\mathbb{E}_p[I[p]-[I[q]] \\\\\n",
    "    &= - \\sum_{i=0}^{N-1} p(x_i)log\\left(\\frac{p(x_i)}{q(x_i)}\\right)\n",
    "\\end{align*}\n",
    "Which, reads, when using expression (2.1):\n",
    "\\begin{align*}\\tag{2.2}\n",
    " &KL[\\lambda p_1 + (1-\\lambda) p_2 \\| \\lambda q_1 + (1-\\lambda) q_2] \\\\\n",
    "&= - \\sum_{i=0}^{N-1} (\\lambda p_1(x_i) + (1-\\lambda) p_2(x_i))log\\left(\\frac{\\lambda p_1(x_i) + (1-\\lambda) p_2(x_i)}{\\lambda q_1(x_i) + (1-\\lambda) q_2(x_i)}\\right) \\\\\n",
    "\\end{align*}\n",
    "Now we are going to use the log sum inequality to prove that:\n",
    "\\begin{align*}\\tag{2.3}\n",
    "    \\sum_{i=0}^{N-1} a_i log\\left(\\frac{a_i}{b_i}\\right) &\\geq \\left(\\sum_{i=0}^{N-1} a_i\\right) log\\left(\\frac{\\sum_{i=0}^{N-1}a_i}{\\sum_{i=0}^{N-1}b_i}\\right)\n",
    "\\end{align*}\n",
    "Where $a_i,b_i \\in [\\mathbb{R}^{+} \\times \\mathbb{R}^{+}]$, $a=\\sum_{i=0}^{N-1} a_i$, $b=\\sum_{i=0}^{N-1} b_i$.\n",
    "\n",
    "Now, let $f(x)=x log(x)$, we can write\n",
    "\\begin{align*}\n",
    "    & \\sum_{i=0}^{N-1} a_i log\\left(\\frac{a_i}{b_i}\\right) \\\\\n",
    "    =& \\sum_{i=0}^{N-1} b_i f\\left(\\frac{a_i}{b_i}\\right) \\\\\n",
    "    =& b \\sum_{i=0}^{N-1} \\frac{b_i}{b} f\\left(\\frac{a_i}{b_i}\\right) \\\\\n",
    "\\end{align*}\n",
    "Because $\\sum_{i=0}^{N-1}\\frac{b_i}{b} =1$ and $b_i \\geq 0$, we can reinterpret the sum $\\sum_{i=0}^{N-1} \\frac{b_i}{b}$ as an expectation over a finite discret distribution, an more easily recognize and apply the Jensen inequality for the convex function $f$\n",
    "\\begin{align*}\\tag{2.4}\n",
    "    b\\mathbb{E}_b \\left[ f\\left(\\frac{a_i}{b_i}\\right) \\right] &\\geq b f\\left(\\mathbb{E}_b \\left[ \\frac{a_i}{b_i}\\right]\\right) \\\\\n",
    "    b\\sum_{i=0}^{N-1} \\frac{b_i}{b} f\\left(\\frac{a_i}{b_i}\\right) &\\geq b f\\left(\\sum_{i=0}^{N-1}\\frac{b_i}{b} \\frac{a_i}{b_i}\\right) \\\\\n",
    "    &\\geq b f\\left(\\sum_{i=0}^{N-1}\\frac{a_i}{b} \\right) \\\\\n",
    "    &\\geq b f\\left(\\frac{a}{b}\\right) \\\\\n",
    "    &\\geq b \\frac{a}{b} log\\left(\\frac{a}{b}\\right) \\\\\n",
    "    &\\geq a log\\left(\\frac{a}{b}\\right) \\\\\n",
    "\\end{align*}\n",
    "\n",
    "You can notice that the last line of (2.4) is equivalent to the equation (2.3) we just have proved, we can now get back to our original problem, ie proving convexity of KL-divergence. Lets restart from (2.2):\n",
    "\n",
    "\\begin{align*}\n",
    " &KL[\\lambda p_1 + (1-\\lambda) p_2 \\| \\lambda q_1 + (1-\\lambda) q_2] \\\\\n",
    "&= - \\sum_{i=0}^{N-1} (\\lambda p_1(x_i) + (1-\\lambda) p_2(x_i))log\\left(\\frac{\\lambda p_1(x_i) + (1-\\lambda) p_2(x_i)}{\\lambda q_1(x_i) + (1-\\lambda) q_2(x_i)}\\right) \\\\\n",
    "&\\leq - \\sum_{i=0}^{N-1} \\lambda p_1(x_i)log\\left(\\frac{\\lambda p_1(x_i)}{\\lambda q_1(x_i)}\\right) + (1-\\lambda)p_2(x_i))log\\left(\\frac{(1-\\lambda) p_2(x_i)}{(1-\\lambda) q_2(x_i)}\\right) \\qquad \\text{thanks to (2.3)} \\\\\n",
    "&= \\lambda \\left[-\\sum_{i=0}^{N-1} p_1(x_i)log\\left(\\frac{p_1(x_i)}{q_1(x_i)}\\right) \\right] +(1-\\lambda) \\left[-\\sum_{i=0}^{N-1}p_2(x_i))log\\left(\\frac{ p_2(x_i)}{q_2(x_i)}\\right)\\right] \\\\\n",
    "&= \\lambda KL[p_1 \\| q_1] + (1-\\lambda)KL[p_2 \\| q_2]\n",
    "\\end{align*}\n",
    "\n",
    "KL-divergence is indeed convex in the space of pairs of distributions with matching support. Note that the support constraint is important, this will be reminded later on in the section dedicated to KL-divergennce."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Using convexity of KL-divergence to prove entropy concavity\n",
    "\n",
    "Lets take a special case of equation (2.1) where $(q_1,q_2)=(u,u)$ a pair of uniform discrete distributions:\n",
    "\\begin{align*} \\tag{2.5}\n",
    " KL[\\lambda p_1 + (1-\\lambda) p_2 \\| \\lambda u + (1-\\lambda) u] &\\leq \\lambda KL[p_1\\|u] + (1-\\lambda) KL[p_2\\|u] \\\\\n",
    " KL[\\lambda p_1 + (1-\\lambda) p_2 \\| u] &\\leq \\lambda KL[p_1\\|u] + (1-\\lambda) KL[p_2\\|u]\n",
    "\\end{align*}\n",
    "\n",
    "Lets now replace $KL[p\\|u]$ from equation (2.5) with the expression obtained in (1.2), ie $KL[p\\|u]=log(N)-H[p]$ :\n",
    "\\begin{align*}\n",
    " KL[\\lambda p_1 + (1-\\lambda) p_2 \\| u] &\\leq \\lambda KL[p_1\\|u] + (1-\\lambda) KL[p_2\\|u] \\\\\n",
    " log(N)-H[\\lambda p_1 + (1-\\lambda) p_2] &\\leq \\lambda (log(N)-H[p_1]) + (1-\\lambda)(log(N)-H[p_2]) \\\\\n",
    " log(N)-H[\\lambda p_1 + (1-\\lambda) p_2] &\\leq log(N)(\\lambda+(1-\\lambda)) -\\lambda H[p_1] + (\\lambda-1)H[p_2]) \\\\\n",
    " log(N)-H[\\lambda p_1 + (1-\\lambda) p_2] &\\leq log(N) - (\\lambda H[p_1] + (1-\\lambda)H[p_2]) \\\\\n",
    " H[\\lambda p_1 + (1-\\lambda) p_2] &\\geq \\lambda H[p_1] + (1-\\lambda)H[p_2]\n",
    "\\end{align*}\n",
    "Which is equivalent to equation (1.1), ie the concavity of entropy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conditional Entropy\n",
    "The concept of entropy also extends to conditional probability of events, in this case, $H(x|y)$ can be interpreted as the amount of information needed to describe the outcome of a random process x, given the value of the random process y and reads:\n",
    "\n",
    "\\begin{align}\n",
    "    H(X|Y)  &= \\sum_{j=1}^{K} p(y_j) H(x|y=y_j) \\\\\n",
    "            &= \\sum_{j=1}^{K} p(y_j) \\sum_{i=1}^{N} -p(x_i|y_j) log(p(x_i|y_j)) \\\\\n",
    "            &= -\\sum_{j=1}^{K} \\sum_{i=1}^{N} p(x_i,y_j) log(p(x_i|y_j)) \\\\\n",
    "            &= -\\sum_{j\\in J,i\\in I} p(x_i,y_j) log(p(x_i|y_j)) \\\\\n",
    "            &= -\\sum_{j\\in J,i\\in I} p(x_i,y_j) log\\left(\\frac{p(x_i,y_j)}{p(y_j)}\\right) \\\\\n",
    "            &=  \\sum_{j\\in J,i\\in I} p(x_i,y_j) log\\left(\\frac{p(y_j)}{p(x_i,y_j)}\\right)\n",
    "\\end{align}\n",
    "\n",
    "~~It is interesting to notice that this expression of conditional entropy fall back to entropy in the case the $y_j$ form a finite or countable partition of the sample space.\n",
    "I.E as entropy is simply defined as expectation of quantity of information, one should be able to derive conditional entropy formula from law of total expectation ie, assuming a new random variable X = I[z] = :\n",
    "begin{align}\n",
    "    \\mathbb{E}(X) = \\sum _{i}{P(A_{i})\\mathbb{E}(X | A_{i})}\n",
    "end{align}~~\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Chain rule\n",
    "If a random process output can be described using two random variables $X$ and $Y$, its entropy can be considered as the joint entropy $H(X,Y)$, which in the binary case, is the minimum number of bits needed to describe one output.\n",
    "If we know in advance the value of $Y$, we have gained $H(Y)$ bits of information, so we now only need $H(X,Y)-H(Y)$ to describe the output, that is somehow more deterministic.\n",
    "\n",
    "This is called the chaine rule and reads:\n",
    "$$\n",
    "    H(X|Y) = H(X,Y)-H(Y)\n",
    "$$\n",
    "\n",
    "The proof is quite straightforward:\n",
    "\n",
    "\\begin{align}\n",
    "    H(X|Y)  &= \\sum_{j\\in J,i\\in I} p(x_i,y_j) log\\left(\\frac{p(y_j)}{p(x_i,y_j)}\\right) \\\\\n",
    "            &= -\\sum_{j\\in J,i\\in I} p(x_i,y_j) log(p(x_i,y_j)) + \\sum_{j\\in J,i\\in I} p(x_i,y_j) log(p(y_j)) \\\\\n",
    "            &= H(X,Y) + \\underbrace{\\sum_{j\\in J,i\\in I} p(x_i,y_j) log(p(y_j))}_{\\text{ marginalization of }x_i}\\\\\n",
    "            &= H(X,Y) + \\sum_{j\\in J} p(y_j) log(p(y_j)) \\\\\n",
    "            &= H(X,Y)-H(Y)\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayes' rule\n",
    "The famous Bayes theorem links conditional probability of two random variables, for instance $x$ and $y$:\n",
    "\\begin{align*}\n",
    "    p(X|Y) = \\frac{p(Y|X)p(X)}{p(Y)}\n",
    "\\end{align*}\n",
    "Following the chain rule, and the fact that $H(x,y)=H(y,x)$ we can easly extends the Bayes rule for conditional entropy:\n",
    "\\begin{align*}\n",
    "    H(X|Y)  &= H(X,Y)-H(Y) \\\\\n",
    "            &= H(Y,X)-H(Y) \\\\\n",
    "            &= H(Y|X)+H(X)-H(Y)\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conditional entropy for Markov chain\n",
    "\n",
    "### Introduction\n",
    "It is very common in engineering to try to find dependency between data, so that we can exploit some knowledges or intuitions over relationships between them. In some cases, we can measure the validity of this model by measuring the relative quantity of informations given by a random variable when the outcome of some other random process in known, using the following tools:\n",
    "\n",
    "### Markov source\n",
    "A common way to give probabilistic interpretation of signals, or messages, is to account for the probability of occurence of a symbol given the 1, 2, ..., k previous symbols in the signal. This model is known as the order-k Markov source.\n",
    "In the general framework, for an alphabet with n symbols $s_0, s_1, \\dots, s_{n-1}$ we can study the probability of occurence of symbol $j$, right after symbol $i$ as $p(x_{t+1}=s_j|x_{t}=s_i)$ where $t$ is a placeholder for the discrete time index of the occurence of the symbol generated by the source. This definition extends to $x_{t+2}, x_{t+3}, \\dots x_{t+k}$.\n",
    "\n",
    "However here, we will first focus on the order-1 markov process. In this framework, we simplify the notation, and use $p(x_j|x_i)$ as the probability of symbol $s_j$ to occur, knowing that the previous symbol was $s_i$. Hence $x_j$ can be considered as the current symbol, and $x_i$ is the preceding symbol.\n",
    "\n",
    "One can eventually build a $n \\times n$ matrix $P$ out of the $p(x_j|x_i)$:\n",
    "\\begin{align*}\n",
    "    P = \\begin{pmatrix}\n",
    "    p(x_0|x_0)   & p(x_0|x_1) & \\dots  & p(x_0|x_{n-1}) \\\\\n",
    "    p(x_1|x_0)   & p(x_1|x_1) & \\dots  & p(x_1|x_{n-1}) \\\\\n",
    "    \\vdots   & \\vdots & \\vdots & \\vdots   \\\\\n",
    "    p(x_{n-1}|x_0) & p(x_{n-1}|x_1) & \\dots  & p(x_{n-1}|x_{n-1}) \\\\\n",
    "    \\end{pmatrix}\n",
    "\\end{align*}\n",
    "\n",
    "This matrix can define a discrete-time dynamical system where an $n$-column vector $v$ defines the current distribution (actual distribution or probability distribution) and $Pv$ defines the probability distribution after one iteration of the dynamical system."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conditional entropy for order-1 random Markov process: example\n",
    "\n",
    "This source model can actually be deterministic in case each symbol is automatically always followed by the same symbol (but they don't have to be the same), i.e when all $p(x_j|x_i)$ are either equal to 0 or 1, while suming up to one column-wise. \n",
    "But of course, the source model can be probabilistic, in this case the concept of relative quantity of information generalizes as follow for a order-1 markov process:\n",
    "\\begin{align*}\n",
    "    H_{rel}(x) = -\\sum_i p(x_i) \\sum_j p(x_j|x_i)log(p(x_j|x_i))\n",
    "\\end{align*}\n",
    "Where $j$ is the current symbol, and $i$ is the preceding symbol.\n",
    "\n",
    "### Build conditional entropy from chain rule\n",
    "\n",
    "It is interesting to build the conditional entropy in the case of markov chain starting with the basic definition of entropy:\n",
    "\n",
    "\\begin{align*}\n",
    "    H(x) = - \\sum_{i=0}^{N-1} P(x_i)log(P(x_i))\n",
    "\\end{align*}\n",
    "\n",
    "Where $P(x_i)$ is simply the probability of occurence of symbol $x_i$ (we should write $s_i$) independently of its discrete time point of occurence.\n",
    "In the context of order 1 markov model, we have a way to express the probability of each symbol $x_j$ outcome as a conditional probability on the previous symbol $x_i$: $p(x_j,x_i) = p(x_i)p(x_j|x_i)$. This can be also simply interpreted as the chain rule. Hence, the entropy has to be integrated on the discrete event set, which can be done with a double sum:\n",
    "\n",
    "\\begin{align*}\n",
    "    H(x_i,x_j) &= -\\sum_{i,j} p(x_j,x_i)log(p(x_j,x_i)) \\\\\n",
    "         &= -\\sum_{i} \\sum_{j} p(x_j,x_i)log(p(x_j,x_i))\n",
    "\\end{align*}\n",
    "\n",
    "We can now use the chain rule, and express the joint probability $p(x_j,x_i) = p(x_i)p(x_j|x_i)$:\n",
    "\n",
    "\\begin{align*}\n",
    "    H(x_i,x_j) &= -\\sum_{i} \\sum_{j} p(x_j,x_i)log(p(x_j,x_i)) \\\\\n",
    "    &= -\\sum_{i} \\sum_{j} p(x_i)p(x_j|x_i)log(p(x_i)p(x_j|x_i)) \\\\\n",
    "    &= -\\sum_{i} p(x_i) \\sum_{j} p(x_j|x_i)log(p(x_j|x_i)) - \\sum_{i} p(x_i)log(p(x_i)) \\underbrace{\\sum_{j}p(x_j|x_i)}_{\\text{amounts to 1}} \\\\\n",
    "    &= H(x_j|x_i)+H(x_i)\n",
    "\\end{align*}\n",
    "\n",
    "We have simply recovered the chain rule for entropy. However, in the case of markov chains, we are often more interested in the relative quantity of information, ie how much insight about the next symbol one has when given one symbol than the actual symbol-wise entropy $H(y)$. We denote $H_{cond} = H(x|y)$ this information and call it conditional entropy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generalization: understand the order-k markov process\n",
    "\n",
    "Now, in order to extend this definition to order-k markov source, one simply needs to compose the conditional entropy over all dependency (from one symbole to the next) from the generic discrete time index $q$ to index $q-k$.\n",
    "For the sake of comprehension, we will use here double variable indexing for both time point $x_q$, and symbol value at this time point $x_{q,i}$\n",
    "We then have the following expressions:\n",
    "\n",
    "* for k=1:\n",
    "we start from\n",
    "\\begin{align*}\n",
    "    H(X) &= H(x_q, x_{q-1}) \\\\\n",
    "    &= H(x_q|x_{q-1})+H(x_{q-1})\n",
    "\\end{align*}\n",
    "and derive\n",
    "\\begin{align*}\n",
    "    H_{cond}(x) &= H(x_q|x_{q-1}) \\\\\n",
    "    &= -\\sum_{i} p(x_{q-1}=s_i) \\sum_{j}p(x_{q}=s_j|x_{q-1}=s_i)log_2(p(x_{q}=s_j,x_{q-1}=s_i))\n",
    "\\end{align*}\n",
    "\n",
    "* for k=2:\n",
    "we start from\n",
    "\\begin{align*}\n",
    "    H(X) &= H(x_q,x_{q-1},x_{q-2}) \\\\\n",
    "    &= H(x_q|x_{q-1},x_{q-2}) + H(x_{q-1},x_{q-2}) \\\\\n",
    "    &= H(x_q|x_{q-1},x_{q-2}) + H(x_{q-1}|x_{q-2}) + H(x_{q-2})\n",
    "\\end{align*}\n",
    "and derive\n",
    "\\begin{align*}\n",
    "    H_{cond}(X) &= H(x_q|x_{q-1},x_{q-2}) \\\\\n",
    "    &= -\\sum_{i,j} p(x_{q-1}=s_j,x_{q-2}=s_i) \\sum_{k} p(x_{q}=s_k) log(p(x_q=s_k|x_{q-1}=s_j,x_{q-2}=s_i)) \\\\\n",
    "    &= -\\sum_i p(x_{q-2}=s_i) \\sum_j p(x_{q-1}=s_j|x_{q-2}=s_i) \\sum_k p(x_{q}=s_k|x_{q-2}=s_i,x_{q-1}=s_j) log(p(x_{q}=s_k|x_{q-2}=s_i,x_{q-1}=s_j)) \\\\\n",
    "\\end{align*}\n",
    "\n",
    "\n",
    "Similarly, we can define an arbitrarily complex order k markov process where the probability of symbol $x_{n-2}$ depends on the $k$ previous symbols:\n",
    "\\begin{align*}\n",
    " p(x_n|x_{n-1},x_{n-2},\\dots,x_{n-k})\n",
    "\\end{align*}\n",
    "\n",
    "This model needs $n^k$ parameters to describe each possible combination of precursor. The exponential complexity of those types of model usually prevents them to be used to predict long time range dependencies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#This code compute the entropy of a markov chain whose matrix is given in parameter\n",
    "def GetEntropyFromMarkovRandomProcess( markov, prob ):\n",
    "    \"\"\"\n",
    "        We assume that markov is a 2D square matrix that\n",
    "        stands for a random markov chain.\n",
    "        For the record, the jth column of the matrix should sum to 1\n",
    "        and M(i,j) is the probability that an element in the state\n",
    "        j, will move to the state i, ie p(i|j)\n",
    "        \n",
    "        We assume that prob is the probability of each state in the\n",
    "        same order as in the markov matrix\n",
    "    \"\"\"\n",
    "    \n",
    "    entropy = 0\n",
    "    #for each state\n",
    "    for i in range(markov.shape[0]):\n",
    "        Pji = markov[i,:]/np.sum(markov[i,:])\n",
    "        Sent = np.dot(Pji,SafeLog2(Pji))\n",
    "        entropy += prob[i]*Sent\n",
    "\n",
    "    return -entropy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### A small numerical illustration\n",
    "\n",
    "Let's say that we have a 1 dimensional signal from $\\mathbb{Z}^N$, and we want to model the occurence of every new symbol in this signal as a first order random markov process.\n",
    "This model allows us to study the entropy of the signal in another framework, let's see how entropy values compares in the basic and markov models.\n",
    "\n",
    "A very interesting basic introduction to markov chain can be found here: http://www.ams.org/samplings/feature-column/fcarc-pagerank\n",
    "It should help to understand the link between graphs, probability and random linear algebra."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Symbol wise model entropy is  1.0\n",
      "Sum of empirical distribution is 1.0\n",
      "First order markov model entropy is -0.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Markov matrix, first order markov model entropy is -0.0')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#First: generate a binary sinusoid like signal, of amplitude -1 or 1\n",
    "nbPeriod = 10\n",
    "s=np.round(np.cos(np.linspace(0,nbPeriod*2*np.pi,nbPeriod*2+1)))\n",
    "#drop the last element for pefectly flat histogram (no repetition)\n",
    "s=s[0:s.size-1]\n",
    "\n",
    "#Plot signal of interest\n",
    "plt.figure()\n",
    "plt.plot(s)\n",
    "plt.title('sinusoid')\n",
    "\n",
    "#compute histogram and symbol-wise entropy of this signal\n",
    "p,entropy=GetEntropyFromQuantizedData(s,2)\n",
    "print( \"Symbol wise model entropy is \",entropy)    \n",
    "\n",
    "#Now use the first order markov model, by first computing the markov chain matrix\n",
    "hist,edges = np.histogram(s,bins=2)\n",
    "\n",
    "#plot the histogram of values in the signal\n",
    "plt.figure()\n",
    "plt.bar(edges[:-1], hist, width = 1)\n",
    "plt.xlim(min(edges), max(edges))\n",
    "plt.title('histogram, symbol-wise entropy is '+str(entropy))\n",
    "print(\"Sum of empirical distribution is \"+str(np.sum(p)))\n",
    "\n",
    "#Define markov matrix\n",
    "markov=np.zeros((hist.size,hist.size))\n",
    "\n",
    "#loop over current elements\n",
    "for i in range(hist.size):\n",
    "    #index in s where you can find previous element\n",
    "    if( i < hist.size-1 ):\n",
    "        curMask = (s>=edges[i]) * (s<edges[i+1])\n",
    "    else: #last range has both sides included, see numpy doc\n",
    "        curMask = (s>=edges[i]) * (s<=edges[i+1])\n",
    "    \n",
    "    #Now we shift the idx mask toward the right in order\n",
    "    #to get the mask of the current element\n",
    "    nextMask = np.roll(curMask, 1)\n",
    "    n = s[nextMask]\n",
    "    \n",
    "    #Check if the current state is present\n",
    "    if nextMask.any():\n",
    "        #Get the histogram of the next elements\n",
    "        for j in range(hist.size):\n",
    "            #index in s where you can find previous element\n",
    "            if( j < hist.size-1 ):\n",
    "                jMask = (n>=edges[j]) * (n<edges[j+1])\n",
    "            else: #last range has both sides included, see numpy doc\n",
    "                jMask = (n>=edges[j]) * (n<=edges[j+1])\n",
    "\n",
    "            #Now fill the ith column, jth line of the markov matrix\n",
    "            markov[j,i] = np.count_nonzero(jMask)\n",
    "\n",
    "        #When the ith column of markow matrix is full, we can normalize\n",
    "        #the weight so that they sum to 1\n",
    "        sum_weight = np.sum(markov[:,i])\n",
    "        if sum_weight > 0 :\n",
    "            markov[:,i] /= sum_weight\n",
    "        else:\n",
    "            raise ValueError('Definition of state based on floating range is wrong')\n",
    "    else:\n",
    "        #if current state is not present, we assume\n",
    "        #equiprobable next state, to avoid dangling nodes\n",
    "        markov[:,i] =  1/hist.size\n",
    "\n",
    "#Now compute the first order markov model entropy\n",
    "Mentropy = GetEntropyFromMarkovRandomProcess(markov,p)\n",
    "print(\"First order markov model entropy is \"+str(Mentropy))\n",
    "\n",
    "#Print markov matrix for fun\n",
    "plt.figure()\n",
    "heatmap = plt.pcolor(markov, cmap=plt.cm.autumn)\n",
    "plt.colorbar(heatmap)\n",
    "plt.axis('off')\n",
    "plt.title('Markov matrix, first order markov model entropy is '+str(Mentropy))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The previous numerical case was interesting because, our bit generator is perfectly balanced: there is as much -1 as 1's but it is not random, it is perfectly causal.\n",
    "The symbol wise entropy definition gives us an entropy of 1 bit, but the first order markov based model give us an entropy of 0, because the same input always generate the same next output, there is no information in this framework."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rate entropy\n",
    "\n",
    "In the mathematical theory of probability, the entropy rate or source information rate of a stochastic process is, informally, the time density of the average information in a stochastic process. For stochastic processes with a countable index, the entropy rate $H(X)$ is the limit of the joint entropy of $n$ members of the process $X_{k}$ divided by $n$, as $n$ tends to infinity:\n",
    "\n",
    "$H(X)=\\lim _{n\\to \\infty }{\\frac {1}{n}}H(X_{1},X_{2},\\dots X_{n})$ when the limit exists.\n",
    "\n",
    "### Strongly stationary process and asymptotic behaviour of source entropy\n",
    "\n",
    "In mathematics and statistics, a stationary process or strictly/strongly stationary process is a stochastic process whose unconditional joint probability distribution does not change when shifted in time.\n",
    "Let's write the conditional entropy of the latest symbol given all previous symbols:\n",
    "\n",
    "\\begin{align*}\n",
    " H'(X)=\\lim _{n\\to \\infty }H(X_{n}|X_{n-1},X_{n-2},\\dots X_{1})\n",
    "\\end{align*}\n",
    "\n",
    "For strongly stationary stochastic processes, $H(X)=H'(X)$. The entropy rate can be thought of as a general property of stochastic sources; this is the asymptotic equipartition property.\n",
    "\n",
    "The entropy rate may be used to estimate the complexity of stochastic processes. It is used in diverse applications ranging from characterizing the complexity of languages, blind source separation, through to optimizing quantizers and data compression algorithms. For example, a maximum entropy rate criterion may be used for feature selection in machine learning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generalization to entropy rate of a markov chain\n",
    "Most of the sources here are coming from wikipedia (https://en.wikipedia.org/wiki/Markov_chain)\n",
    "\n",
    "Entropy rate, also called Kolmogorov entropy or measure-theoretic entropy can be computed for a dynamical system as a markov chain.\n",
    "\n",
    "### Introduction\n",
    "Lets recall the definition of a probability space $ (X,{\\mathfrak {M}},\\mu )$, that is used extensively in the world of applied mathematics:\n",
    "A probability space consists of three parts\n",
    "* A sample space, $X$, which is the set of all possible outcomes.\n",
    "* A set of events ${\\mathfrak {M}}$, where each event is a set containing zero or more outcomes.\n",
    "* $\\mu$, the assignment of probabilities to the events; that is, a function from events to probabilities.\n",
    "\n",
    "Lets define $ (X,{\\mathfrak {M}},\\mu )$ a probability space and $f:X\\to X$ a measurable function, that stands for the evolution function applied to a discrete-time dynamic system on the phase space.\n",
    "\n",
    "$f$ is assumed to preserve the measure, i.e $\\forall M\\in {\\mathfrak {M}},\\mu (f^{-1}(M))=\\mu (M)$.\n",
    "\n",
    "Starting from an initial state $x$, one can define the sequence of its iterates as $ x,f(x),\\dots ,f^{n}(x),\\dots $\n",
    "The set $\\{f^{n}(x):n\\geq 0\\}$ of all the states the system takes is called the \"orbit\"\n",
    "\n",
    "Given a finite partition $\\alpha$ of $X$, made out of measurable sets $\\alpha =\\{A_{1},\\dots ,A_{p}\\}$ and an initial state $x$, the states $f^{n}(x): n\\geq 0$ taken by the system each fall into some subsets of the partition $\\alpha$ \n",
    "The sequence of those subsets give some information on the initial state $x$. The rate entropy stands for the expectation of the quantity of information given by each iteration.\n",
    "\n",
    "### Computation\n",
    "\n",
    "The entropy rate of a Markov chain with transition matrix $P$ and stationary distribution $\\pi$ is\n",
    "\\begin{align*}\n",
    "h\\left( Q \\right) = -\\sum_{i,j} \\pi_i P_{i,j} log \\left( P_{i,j} \\right)\n",
    "\\end{align*}\n",
    "\n",
    "As recalled on the ams website, the stationary distributions $\\pi$ of a random markov process $P$ can be found as the eigenvalues of its transition matrix.\n",
    "For a random markov process to possess a stationary state, it must be:\n",
    "* irreducible: A Markov chain is said to be irreducible if it is possible to get to any state from any state. ie. $P(X_{n_{ij}}=j\\mid X_{0}=i)=p_{ij}^{(n_{ij})}>0$\n",
    "* aperiodic: A state i has period k if any return to state i must occur in multiples of k time steps. ie. $k=\\gcd\\{n>0:P(X_{n}=i\\mid X_{0}=i)>0\\}$\n",
    "* positive recurrent. State i is recurrent (or persistent) if it is not transient. A state i is said to be transient if, given that we start in state i, there is a non-zero probability that we will never return to i\n",
    "\n",
    "To explicit the later condition, we will use some temporary definitions:\n",
    "* let $T_i$ be the first return time to state i (the \"hitting time\"): $T_{i}=\\inf\\{n\\geq 1:X_{n}=i\\}$\n",
    "* let the number $f_{ii}^{(n)}$ be the probability that we return to state i for the first time after n steps: $f_{ii}^{(n)}=P(T_{i}=n\\mid X_{0}=i)$\n",
    "* Therefore, state i is transient if: $P(T_{i}<\\infty \\mid X_{0}=i)=\\sum _{n=1}^{\\infty }f_{ii}^{(n)}<1$\n",
    "\n",
    "### Information-Theoretic Metric Learning\n",
    "It might be interesting to notice that in an ICML paper from 2007 called Information Theoretic Metric Learning, Kulis et al used the concept of maximum entropy rate in order to setup an objective (used in a log-det based bregman divergence) for mahalanobis distance learning. But this goes far beyond the point of this notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "### Cross Entropy\n",
    "The concept of cross entropy is useful to characterize the difference between two distributions. \n",
    "It gives the number of bits needed to encode one symbol from the distribution x, using a code that is optimal for the distribution y.\n",
    "\n",
    "It reads:\n",
    "$$\n",
    "    H_y(x) = -\\sum_{i \\in I} p(x_i) log( p(y_i) )\n",
    "$$\n",
    "\n",
    "Cross entropy is used A LOT in machine learning because it usually yield differentiable objective functions that have a real meaning in terms of information theory."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "### Mutual information\n",
    "This quantity gives an indication about the dependence between two random variables, it is more general than correlation coefficient, and not limited to real valued data. [Wikipedia](http://en.wikipedia.org/wiki/Mutual_infomation) gives the following interesting definition:\n",
    "Mutual information measures the information that X and Y share: it measures how much knowing one of these variables reduces uncertainty about the other. For instance, the mutual information of two independent variables is zero. At the opposite, if X is a deterministic function of Y and vice versa, the mutual information is equal to the entropy of X (or Y) which should be equal.\n",
    "\n",
    "The mutual information between two random variables $x$ and $y$ reads\n",
    "$$\n",
    "    I(x,y) = \\sum_{i=1}^{N} \\sum_{j=1}^{K} p(x_i,y_j) log\\left( \\frac{p(x_i,y_j)}{p(x_i)p(y_j)} \\right)\n",
    "$$\n",
    "\n",
    "We can link this expression to conditional entropy:\n",
    "\n",
    "\\begin{align}\n",
    "    I(x,y)  &= \\sum_{i=1}^{N} \\sum_{j=1}^{K} p(x_i,y_j) log\\left( \\frac{p(x_i,y_j)}{p(x_i)p(y_j)} \\right) \\\\\n",
    "            &= \\sum_{j\\in J,i\\in I} p(x_i,y_j) log\\left( \\frac{p(x_i,y_j)}{p(x_i)p(y_j)} \\right) \\\\\n",
    "            &= \\sum_{j\\in J,i\\in I} p(x_i,y_j) log\\left( \\frac{p(x_i,y_j)}{p(x_i)} \\right) - \\sum_{j\\in J,i\\in I} p(x_i,y_j) log(p(y_j))\n",
    "\\end{align}\n",
    "Using the fact that\n",
    "$$\n",
    "    p(x_i|y_j)p(y_j) = p(y_j|x_i)p(x_i) = p(x_i,y_j)\n",
    "$$\n",
    "we can rewrite the left side as\n",
    "\\begin{align}\n",
    "    & \\sum_{j\\in J,i\\in I} p(x_i,y_j) log\\left( \\frac{p(x_i,y_j)}{p(x_i)} \\right) \\\\\n",
    "    &= \\sum_{j\\in J,i\\in I} p(x_i)p(y_j|x_i) log(p(y_j|x_i)) \\\\\n",
    "    &= \\sum_{i\\in I} p(x_i) \\sum_{j\\in J} p(y_j|x_i) log(p(y_j|x_i)) \\\\\n",
    "    &= -\\sum_{i\\in I} p(x_i) H(y|x=x_i) \\\\\n",
    "    &= -H(y|x)\n",
    "\\end{align}\n",
    "and we can recognize a marginal probability in the right side, which can be rewritten as:\n",
    "\\begin{align}\n",
    "    & \\sum_{j\\in J} log(p(y_j)) \\sum_{i\\in I}p(x_i,y_j) \\\\\n",
    "    &= \\sum_{j\\in J} log(p(y_j))p(y_j) \\\\\n",
    "    &= -H(y) \\\\\n",
    "\\end{align}\n",
    "The two parts together give:\n",
    "$$\n",
    "    I(x,y) = -H(y|x) + H(y)\n",
    "$$\n",
    "Doing the same reasoning linearizing $p(x_i)$ out of the log in the denominator of the first expression of $ I(x,y)$ instead of $p(y_j)$ gives:\n",
    "$$\n",
    "    I(x,y) = -H(x|y) + H(x)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mutual information in gaussian case\n",
    "\n",
    "#### Introduction\n",
    "Thanks to the central-limit theorem, many different types of random process outcome can be modeled with normal distribution. More generally, in higher dimensions, multidimensional gaussian distributions can be a useful tool, see our EllipsoidEstimation notebook for more on that topic. It happens that, in some occasions, it can be interesting to get a quantitative overview of the actual dependency (intricacy?) between pairs of multidimensional gaussian, as distance between center of distribution, orientation, and decay rate can have significant impact, that is not trivial to evaluate. That's where mutual information can help, and it has a nice closed for expression when dealing with two gaussians:\n",
    "\n",
    "#### Closed form expression\n",
    "\\begin{align*}\n",
    "    I(X;Y)= \\frac{1}{2} log \\left( \\frac{|K_{X}||K_{Y}|}{|K_{XY}|} \\right)\n",
    "\\end{align*}\n",
    "\n",
    "Where:\n",
    "* $|K_{XY}|$ is the absolute value of the determinant of the covariance matrix of the set of variables from $X$ and $Y$\n",
    "* $|K_{X}|$ is the absolute value of the determinant of the covariance matrix of $X$ \n",
    "* $|K_{Y}|$ is the absolute value of the determinant of the covariance matrix of $Y$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mutual information in practice\n",
    "\n",
    "#### Introduction\n",
    "Mutual information is a very useful tool that is often under utilized in favor of correlation coefficient. However we recalled in another notebook (StatisticalTest) that uncorrelated does not mean independant, and that correlation implicitly implies a linear relationship between two dataset. Mutual information does not rely on such assumption, however it is by definition, tied to a discrete set of events.\n",
    "\n",
    "However, it is so useful that researcher have developed quantization scheme that allow to extend mutual information metric to be computed even on continuous variable, although this method also have some drawback\n",
    "\n",
    "#### References:\n",
    "See in particular work from\n",
    "* A. Kraskov, H. Stogbauer and P. Grassberger, “Estimating mutual information”. Phys. Rev. E 69, 2004.\n",
    "* B. C. Ross “Mutual Information between Discrete and Continuous Data Sets”. PLoS ONE 9(2), 2014.\n",
    "\n",
    "#### Short insight\n",
    "The quantization scheme is based on k-nearest neighbour algorithm\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Numerical application\n",
    "For the numerical implementation, we are going to rely on [scikit learn documentation](https://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.mutual_info_regression.html)\n",
    "More specifically, we have decided to reproduce the example that is presented [here](https://scikit-learn.org/stable/auto_examples/feature_selection/plot_f_test_vs_mi.html#sphx-glr-auto-examples-feature-selection-plot-f-test-vs-mi-py) from sklearn documentation, as it is a very good example of a case where non-linear dependencies are not catched by a more common statistical test.\n",
    "\n",
    "#### Reproduction of sklearn example:\n",
    "This example illustrates the differences between univariate [F-test statistics](https://en.wikipedia.org/wiki/F-test) and mutual information.\n",
    "We consider 3 features x_1, x_2, x_3 distributed uniformly over [0, 1], the target depends on them as follows:\n",
    "y = x_1 + sin(6 * pi * x_2) + 0.1 * N(0, 1), that is the third features is completely irrelevant.\n",
    "\n",
    "The code below plots the dependency of y against individual x_i and normalized values of univariate F-tests statistics and mutual information.\n",
    "\n",
    "As F-test captures only linear dependency, it rates x_1 as the most discriminative feature. On the other hand, mutual information can capture any kind of dependency between variables and it rates x_2 as the most discriminative feature, which probably agrees better with our intuitive perception for this example. Both methods correctly marks x_3 as irrelevant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.feature_selection import f_regression, mutual_info_regression\n",
    "\n",
    "# 3 features, 1000 samnples\n",
    "X = np.random.rand(1000, 3)\n",
    "# encoding the dependency\n",
    "y = X[:, 0] + np.sin(6 * np.pi * X[:, 1]) + 0.1 * np.random.randn(1000)\n",
    "\n",
    "# compute f-test\n",
    "f_test, _ = f_regression(X, y)\n",
    "f_test /= np.max(f_test)\n",
    "\n",
    "#compute mutual information\n",
    "mi = mutual_info_regression(X, y)\n",
    "mi /= np.max(mi)\n",
    "\n",
    "# Now show for each feature\n",
    "plt.figure(figsize=(15, 5))\n",
    "for i in range(3):\n",
    "    plt.subplot(1, 3, i + 1)\n",
    "    plt.scatter(X[:, i], y, edgecolor='black', s=20)\n",
    "    plt.xlabel(\"$x_{}$\".format(i + 1), fontsize=14)\n",
    "    if i == 0:\n",
    "        plt.ylabel(\"$y$\", fontsize=14)\n",
    "    plt.title(\"F-test={:.2f}, MI={:.2f}\".format(f_test[i], mi[i]),\n",
    "              fontsize=16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kullback Leibler divergence\n",
    "\n",
    "The Kullback Leibler divergence, also called the relative entropy or discrimination information, can be computed between two distributions, say $x$ and $y$ and writes $ D_{KL}(x\\|y) $.\n",
    "This metric represents the expectation of the difference of the number of bits needed to encode a symbol from the distribution x, in case either the encoding is optimal for the distribution x or for the distribution y.\n",
    "\n",
    "The general case reads:\n",
    "\n",
    "\\begin{align}\n",
    "    D_{KL}(x\\|y) &= \\mathbb{E}_x \\left[ log \\left( \\frac{x}{y} \\right) \\right]\n",
    "\\end{align}\n",
    "\n",
    "In the discrete case it reads:\n",
    "\n",
    "\\begin{align}\n",
    "    D_{KL}(x\\|y) &= \\sum_{i\\in I} p(x_i) log(p(x_i)) -\\sum_{i\\in I} p(x_i) log(p(y_i)) \\\\\n",
    "                 &= -H(x) + H_y(x)\n",
    "\\end{align}\n",
    "or equivalently\n",
    "$$\n",
    "    D_{KL}(x\\|y) = \\sum_{i\\in I} p(x_i) log\\left(\\frac{p(x_i)}{p(y_i)}\\right)\n",
    "$$\n",
    "\n",
    "For another super intuitive (but limited) introduction to KL-divergence and some of its basic properties, checkout [this short blog post](https://towardsdatascience.com/understanding-kl-divergence-intuitively-a4e876f9a532)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "# KL Divergence and maximum likelihood\n",
    "This chapter was inspired by [this article](http://www.hongliangjie.com/2012/07/12/maximum-likelihood-as-minimize-kl-divergence/)\n",
    "by Liangjie Hong\n",
    "\n",
    "## Definitions\n",
    "Let's consider $P(x_i|\\theta)$ a distribution used to generate (or sample) $N$ points $x_i, i=0,\\dots,N-1$\n",
    "\n",
    "We can define a general distribution model as:\n",
    "$$\n",
    "    P_\\theta(x) = P(x|\\theta)\n",
    "$$\n",
    "And, to handle data from real world, we will define the following empirical distribution (also called probability mass function):\n",
    "$$\n",
    "    P_D(x) = \\sum_{i=0}^{N-1} \\frac{1}{N} \\delta(x-x_i)\n",
    "$$\n",
    "\n",
    "## KL Divergence between model and data\n",
    "We can now express the Kullback Leibler divergence between the model distribution and the empirical one:\n",
    "\n",
    "\\begin{align}\n",
    "    D_{KL} \\left( P_D(x)||P_\\theta(x) \\right) &= \\int P_D(x) log(P_D(x)) dx -\\int P_D(x) log(P_\\theta(x)) dx \\\\\n",
    "    &= H(P_D(x)) - \\int P_D(x) log(P_\\theta(x)) dx\n",
    "\\end{align}\n",
    "\n",
    "As $H(P_D(x))$ is a constant term, relatd to the empirical distribution of real data, we will call it $\\epsilon$, and we may get rid of it later.\n",
    "Instead we will mainly consider, the $\\theta$, ie, the model related term:\n",
    "$$\n",
    "   D_{KL} \\left( P_D(x)||P_\\theta(x) \\right) = \\epsilon -\\langle P_D(x) , log(P_\\theta(x)) \\rangle_{L^2}^{2}\n",
    "$$\n",
    "\n",
    "Thanks to the definition of the empirical distribution, we can express this continuous expression as a discrete summation:\n",
    "\n",
    "\\begin{align}\n",
    "    \\langle P_D(x) , log(P_\\theta(x)) \\rangle_{L^2} &= \\int \\sum_{i=0}^{N-1} \\frac{1}{N} \\delta(x-x_i) log(P(x|\\theta)) dx \\\\\n",
    "    &= \\sum_{i=0}^{N-1} \\frac{1}{N} log(P(x_i|\\theta)) \\\\\n",
    "    &= \\frac{1}{N} \\sum_{i=0}^{N-1} log(P(x_i|\\theta))\n",
    "\\end{align}\n",
    "\n",
    "The last line amounts to the log-likelihood of the dataset. We can then conclude that maximizing the log-likelihood of a dataset, relatively to a set of distribution parameters $\\theta$ and a given dataset $x$ is equivalent to minimizing the Kullback Leibler divergence between the empirical distribution and the model distribution.\n",
    "\n",
    "## Practical KL Divergence between two data sets\n",
    "We are interested in computing the Kullback Leibler divergence between a model $X$ and a real dataset $Y$, indexed by $i$ where $i$ is the index of a specific event whose occurence probability is $X_i$ according to the model, and $Y_i$ in practice.\n",
    "\n",
    "As in the definition of the empirical distribution, our datasets must verify:\n",
    "$$\n",
    "    \\sum_{i=0}^{N-1} X_i = 1\n",
    "$$\n",
    "\n",
    "then the expression of the kl divergence is simply:\n",
    "$$\n",
    "    D_{KL}(Y\\|X) = \\sum_{i=0}^{N-1} log \\left( \\frac{Y_i}{X_i} \\right) Y_i\n",
    "$$\n",
    "\n",
    "Moreover there is an important condition that must be respected: \n",
    "$$\n",
    "    X_i = 0 \\implies Y_i = 0\n",
    "$$\n",
    "If so, if the event $k$ has no occurence, we have $X_k=Y_k=0$ and $log \\left( \\frac{y_k}{x_k} \\right) y_k$ has a limit in $0$ which is $0$. Otherwise, Kullback Leibler cannot be computed.\n",
    "\n",
    "The explanation is pretty straightforward: if an event, or a symbol from $Y$ has no occurence in $X$, it has no reason to be encoded using $X$ probability distribution, then the average number of bits needed to encode a symbol from $Y$ is a nonsense, as some symbols cannot be represented.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Wasserstein distance\n",
    "\n",
    "### Introduction\n",
    "This part of the notebook is inspired by [this wikipedia article](https://en.wikipedia.org/wiki/Wasserstein_metric). We also put more information about optimal transport and wassertein distance in the notebook called \"OptimalTransportWasserteinDistance\".\n",
    "\n",
    "### Definition\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hellinger distance\n",
    "\n",
    "### Introduction\n",
    "Elements from this notebook are coming from [this nice blog post by Djalil Chafai](http://djalil.chafai.net/blog/2020/01/22/about-the-hellinger-distance/).\n",
    "  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Maximizing the log-likelihood in practice\n",
    "\n",
    "### Presenting a \"hidden variable\" kind of problem\n",
    "\n",
    "We are now going to take a simple example, where we aim to fit a multidimensional noisy dataset, to the sum of independant random poisson processes.\n",
    "\n",
    "Here is how we formalize the problem:<br>\n",
    "\n",
    "- Let $\\lambda_k = [\\lambda_0, \\lambda_1,\\dots \\lambda_{P-1}]$ be the set of parameters of the P hidden Poisson random processes<br>\n",
    "- The $P$ hidden Poisson random process can be indirectly linked to $N$ observable values using a larger set of random variables $N_{nk}, n<N, k<P$ such that $N_{nk} \\sim Poisson\\{a_{nk}\\lambda_k\\}$<br>\n",
    "- Let $Y_{n} = \\sum_{k=0}^{P-1} N_{nk}$ be an observable state vector, defined using a sum of the P hidden poisson process, hence itself being a Poisson process defined as: $Y_{n} \\sim Poisson\\{ \\sum_{k=0}^{P-1}a_{nk}\\lambda_k \\}$<br>\n",
    "- Let $y_n$ be a realization of  $Y_{n}$, hence also of dimension N<br>\n",
    "- Let $A$ be the matrix of size $N\\times K$, that contains the $a_{nk}$, known in advance<br>\n",
    "\n",
    "Althoug this problem with hidden variables may seem weird at first glance, it has some simple instances:\n",
    "\n",
    "- $\\lambda_k$ can be the average number of cigarets the person $k$ smokes in one hour, among P different persons.<br>\n",
    "- $Y_{n}$ can be the total number of cigarets smoked in 24 hour in the room $n$, among N rooms.<br>\n",
    "- $a_{nk}$ is the amount of time in hour the person $k$ has spent in the room $n$ during the measure.<br>\n",
    "\n",
    "Another well known instance of this problem is the Emission Tomography Reconstruction Problem.\n",
    "\n",
    "Of course, in every case, our aim will be to retrieve all $\\lambda_k$ values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE for least square estimate is 23.642841704769737\n",
      "MSE for weighted least square estimate is 23.642841704769662\n"
     ]
    }
   ],
   "source": [
    "#We will instanciate the smoker problem:\n",
    "N=30 #Number of room\n",
    "P=50 #Number of people\n",
    "\n",
    "#generate the \\lambda_k, for 0<k<P-1, the mean number of cigaret smoked in one hour per each person\n",
    "#We consider those number uniformly distributed between 0 and 5\n",
    "LambdaK =  np.random.uniform(1e-2,5,P)\n",
    "\n",
    "#Now the occupancy matrix, for N rooms and P people:\n",
    "Ank = np.random.uniform(0,1,(N,P))\n",
    "\n",
    "#generate the number of cigarets smoked per each person, sequentially in each room\n",
    "\n",
    "#Here is the independent generation for each person\n",
    "#yn= np.zeros(N)\n",
    "#for room in range(N):\n",
    "#    yn[room] = np.sum(np.random.poisson(lam=Ank[room,:]*LambdaK, size=(1, P)))\n",
    "\n",
    "#We can exploit the fact that the sum of poisson distribution is a poisson distribution\n",
    "#This step can be though as applying a poisson noise\n",
    "yn=np.random.poisson(lam=np.dot(Ank,LambdaK))\n",
    "\n",
    "#Let's take a look at the pseudo inverse solution\n",
    "leastSquareSol = np.dot(np.linalg.pinv(Ank),yn)\n",
    "MSE = np.mean(np.square(leastSquareSol-LambdaK))\n",
    "print(\"MSE for least square estimate is \"+str(MSE))\n",
    "        \n",
    "#Let's take a look at the variance weighted pseudo inverse solution\n",
    "W = np.diag(1/np.sqrt(yn))\n",
    "WAnk = np.dot(W,Ank)\n",
    "Wyn = np.dot(W,yn)\n",
    "weightedleastSquareSol = np.dot(np.linalg.pinv(WAnk),Wyn)\n",
    "MSE = np.mean(np.square(weightedleastSquareSol-LambdaK))\n",
    "print(\"MSE for weighted least square estimate is \"+str(MSE))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "### Solving the problem\n",
    "\n",
    "Given a realization $y_n$ of $Y_{n}$, we can write the likelihood of this experience outcome as:\n",
    "$$\n",
    "L(y_n|Y_n) = \\prod_{n=0}^{N-1} \\frac{\\lambda_{Y_n}^{y_n}e^{-\\lambda_{Y_n}}}{y_n!}\n",
    "$$\n",
    "with \n",
    "- $y_n$ is known\n",
    "- $\\lambda_{Y_n} = \\sum_{k=0}^{P-1}a_{nk}\\lambda_k$\n",
    "\n",
    "The log-likelihood comes easily as:\n",
    "$$\n",
    "LL(y_n|Y_n) = \\sum_{n=0}^{N-1} y_n log(\\lambda_{Y_n}) - \\lambda_{Y_n} - \\epsilon\n",
    "$$\n",
    "\n",
    "Where $\\epsilon = log(y_n!)$ is a known constant\n",
    "\n",
    "As $\\lambda_{Y_n}$ is actually a linear function of $\\lambda_k$, we automatically think about computing the derivative, in order to test some gradient ascent in order to get the maximum log likelihood value:\n",
    "\n",
    "\\begin{align}\n",
    "    \\frac{\\partial LL(y_n|Y_n)}{\\partial \\lambda_k} &= \\sum_{n=0}^{N-1} \\frac{y_n a_{nk}}{\\sum_{i=0}^{P-1} a_{ni}\\lambda_i } - a_{nk}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Some words about concavity\n",
    "In order to show that $LL(y_n|Y_n)$ is a concave function, hence compatible with the gradient ascent method, we should be computing the second order partial derivative, and be able to prove that its matrix, the Hessian we call $H$ is negative definite. To do so, we can take the quadratic form $x^tHx$ and show that this form is negative for every $x$ and null only when $x=0$.\n",
    "\n",
    "Let's begin with the second derivative:\n",
    "\\begin{align}\n",
    "    \\frac{\\partial^2 LL(y_n|Y_n)}{\\partial \\lambda_j \\partial \\lambda_k} &= -\\sum_{n=0}^{N-1} \\frac{y_n a_{nk}a_{nj}}{\\left( \\sum_{i=0}^{P-1} a_{ni}\\lambda_i \\right)^2}\n",
    "\\end{align}\n",
    "\n",
    "The Hessian generated by these second order partial derivative is clearly symmetric (Schwartz theorem), and the corresponding quadratic form reads:\n",
    "\\begin{align}\n",
    "    \\sum_{j,k}^{j,k<P-1} x_j \\frac{\\partial^2 LL(y_n|Y_n)}{\\partial \\lambda_j \\partial \\lambda_k} x_k\n",
    "\\end{align}\n",
    "\n",
    "Reasoning over the rank of the matrix $A$ should allows us to derive negative definiteness of the previous quadratic form, but we won't do it here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Numerical tips\n",
    "For numerical applications, we will be extending the $Poisson$ distribution to $\\mathbb{R}$-valued data using the $Gamma$ function:\n",
    "\\begin{align}\n",
    " Poisson2 &: \\mathbb{R}^+ \\times \\mathbb{R}^+ \\rightarrow [0,1] \\\\\n",
    " Poisson2(x,\\lambda) &= \\frac{\\lambda^{x} e^{-\\lambda}}{\\Gamma(x+1)}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1754673697678507\n",
      "0.1754673697678507\n",
      "0.1754673697678507\n",
      "0.1799019386776792\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#first, define useful Poisson related function\n",
    "import scipy.special as scsp\n",
    "\n",
    "#Poisson distribution\n",
    "def Poisson(lambdaParam,k):\n",
    "    return (np.power(lambdaParam,k)*np.exp(-lambdaParam))/np.vectorize(np.math.factorial)(k)\n",
    "\n",
    "#Extend Poisson distribution to real cases\n",
    "def Poisson2(lambdaParam,x):\n",
    "    return (np.power(lambdaParam,x)*np.exp(-lambdaParam))/scsp.gamma(x+1)\n",
    "\n",
    "lambdaTest = 5\n",
    "intX = np.arange(0,2*lambdaTest,1) #integer case\n",
    "realX = np.arange(0,2*lambdaTest,0.1) # real case\n",
    "PoissonTest = Poisson(lambdaTest,intX) #integer case\n",
    "Poisson2Test = Poisson2(lambdaTest,realX) # real case\n",
    "\n",
    "#Check that curve match at integer points, and that\n",
    "#maximum likelihood is reached for x = 5\n",
    "plt.plot(intX,PoissonTest, label='Discrete')\n",
    "plt.plot(realX,Poisson2Test, label='Continuous')\n",
    "plt.title('Numerical trick to extend Poisson model to continuous variables')\n",
    "plt.legend()\n",
    "\n",
    "print(str(Poisson(lambdaTest,5)))\n",
    "print(str(np.max(PoissonTest)))\n",
    "print(str(Poisson2(lambdaTest,5)))\n",
    "print(str(np.max(Poisson2Test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#now defined likelihood related functions for the smoker problem\n",
    "\n",
    "#define likelihood of the given candidate solution\n",
    "def GetLikeliHoodForSmokerProblem( solution, yn, Ank ):\n",
    "    \"\"\"\n",
    "        Implementing the likelihood function for the smoker problem\n",
    "    \"\"\"\n",
    "    LambdaYn = np.dot(Ank,solution)\n",
    "    return np.prod(Poisson2(LambdaYn,yn))\n",
    "\n",
    "#define log likelihood of the given candidate solution\n",
    "def GetLogLikeliHoodForSmokerProblem( solution, yn, Ank ):\n",
    "    \"\"\"\n",
    "        Implementing the Log likelihood function for the smoker problem\n",
    "    \"\"\"\n",
    "    LambdaYn = np.dot(Ank,solution)\n",
    "    #return np.sum(yn*np.log(LambdaYn)-LambdaYn-np.vectorize(np.math.factorial)(yn))\n",
    "    return np.sum(yn*np.log(LambdaYn)-LambdaYn-np.log(scsp.gamma(yn+1)))\n",
    "\n",
    "#define Kullback Liebler Divergence of the given candidate solution\n",
    "def GetKullbackLieblerDivergenceForSmokerProblem( solution, yn, Ank ):\n",
    "    \"\"\"\n",
    "        Implementing the KL-Divergence function for the smoker problem\n",
    "    \"\"\"\n",
    "    LambdaYn = np.dot(Ank,solution)\n",
    "    return np.dot(np.log(yn/LambdaYn),yn)\n",
    "\n",
    "#define the gradient of the Log Likelihood\n",
    "def LLGrad( solution, yn, Ank ):\n",
    "    \"\"\"\n",
    "        Implementing the Log likelihood function for the smoker problem\n",
    "    \"\"\"\n",
    "    LambdaYn = np.dot(Ank,solution)\n",
    "    #print str(LambdaYn.shape)\n",
    "    num = Ank.T*yn\n",
    "    #print str(num.shape)\n",
    "    return np.sum((num/LambdaYn)-Ank.T,1)\n",
    "\n",
    "#Perform gradient Checking over a random point\n",
    "randomSol = np.random.uniform(1e-2,1e2,P)\n",
    "epsilon = 1e-4\n",
    "for dim in range(P):\n",
    "    mask = np.zeros(P)\n",
    "    mask[dim] = 1\n",
    "    numGradMinus = GetLogLikeliHoodForSmokerProblem(randomSol-epsilon*mask,yn, Ank )\n",
    "    numGradPlus = GetLogLikeliHoodForSmokerProblem(randomSol+epsilon*mask,yn, Ank )\n",
    "    numGrad = (numGradPlus-numGradMinus)/(2*epsilon)\n",
    "    #print str(numGrad*mask)\n",
    "    #print str(LLGrad(randomSol,yn, Ank)*mask)\n",
    "    assert( np.isclose(numGrad*mask,LLGrad(randomSol,yn, Ank)*mask).all() )\n",
    "\n",
    "\n",
    "#Check if the Log likelihood gradient is numerically close to zero near the maximum\n",
    "assert( np.isclose(LLGrad(LambdaK,np.dot(Ank,LambdaK),Ank),np.zeros(P)).all() )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE for maximum likelihood estimate is 11.59968011388382\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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tD5Mh6WvAPsBC4E7g4IiYl/cdDRwCdAOHR8QFS3w3JdXqqYKZmfVTJqdwH3AhaTC8lQqv4ZzKwLlMLwReFhFbALcBRwNI2hzYH3hpPuf7uXK7EvUkwcVHZmb9lenR/NmRvHFEXCZpRsO2PxdW/wm8OS/vB5yZ532+O0/ssy1wxUiuPRwXH5mZNTdooiDp+Ig4UtLvYGDbzYjYdymv/W7gl3l5HVIiUXd/3laJevGR0wQzs/6Gyimcnn9+fbQvKulTwGLgjBGceyhwKMD6668/wgDSDxcfmZn1N2iiEBGz889LR/OCkt5FqoDerTDF5wPAeoXD1s3bmsV1EnASwMyZM0f0VK/XKThNMDPrr6XDXEjakzS9574RURx46Dxgf0kTJW0IbAJcVVUcfa2PnCqYmRWVGuZiJCT9AtgFmCbpflKv6KOBicCFSg/mf0bEYRFxk6SzgJtJxUofiIjKBiZSb/FRVVcwMxubygxz8ZaI+NVw2xpFxNubbD55iOO/SJoPunK9Fc1OFMzM+ilTfHR0yW1jhvspmJk1N1ST1NcBewHrSDqhsGtlUhHP2OV+CmZmTQ1VfPQgMAvYF5hd2P4M8KEqg6paXz8FpwpmZkVDNUm9DrhO0s/zcetHxK0ti6xCbpJqZtZcmTqFPYFrgfMBJG0p6bwqg6qaXNFsZtZUmUThWNI4RPMAIuJaYMPKImqBmmdeMzNrqkyisCgiGudTGNNPU/dTMDNrrkzntZskHQB0SNoEOBy4vNqwqlYvPnKqYGZWVCan8EHSPAcvAD8nzcJ2ZIUxVa6v+MjMzIqGzCnkiW7+EBH/CXyqNSFVr6+i2cmCmVnRkDmFPP5Qj6RVWhRPS7hJqplZc2XqFJ4FbpB0IfBcfWNEHF5ZVBXz2EdmZs2VSRTOya9xQ55kx8ysqTJzNJ/WikDawUmCmVl/ZYbO3gT4MrA5MKm+PSI2qjCuSrn4yMysuTJNUn8C/IA0Mup/Aj8FflZlUFVT7yipThXMzIrKJAqTI+IiQBFxb0QcC7y+2rCq1TdKqpmZFZWpaH5BUg24XdL/Ag8AK1YbVrVc0Wxm1lyZnMIRwAqk4S1eCbwTOKjKoKrmfgpmZs2VaX30r7z4LHBwteG0hlx8ZGbWVJnWR79j4PPzKdKsbD+MiAVVBFYlVzSbmTVXpvjoLlIu4Uf59TRpSs6X5PWmJJ0iaa6kGwvbVpN0oaTb889V83ZJOkHSHZKul7T10tzUcFx8ZGbWXJlEYYeIOCAifpdf7wC2iYgPAEM9vE8lzdpWdBRwUURsAlyU1wFeB2ySX4eSmsBWxnM0m5k1VyZRWFHS+vWVvFxvfbRwsJMi4jLgiYbN+wH1HtKnAW8obP9pJP8Epkpaq0RsI9Lb+qinqiuYmY1NZZqkfgT4u6Q7SSUvGwLvlzSFvgd8WWtExEN5+WFgjby8DjCncNz9edtDVEC4otnMrJkyrY/+mIe62CxvurVQuXz8SC8cESFpiZ/Lkg4lFTGx/vrrD3P0YO/RG8OIzjczG68GLT6StGv++UZSD+aN82uvvG0kHqkXC+Wfc/P2B4D1Csetm7cNEBEnRcTMiJg5ffr0EQXRlyiM6HQzs3FrqJzCa4C/Avs02ReMbDjt80gd376Sf55b2P6/ks4EtgOeKhQzjTq5otnMrKlBE4WIOCb/HFGHNUm/AHYBpkm6HziGlBicJekQ4F7grfnwPwJ7AXcA86m4k1zNOQUzs6bKdF77EnBcRMzL66sCH4mITw91XkS8fZBduzU5NoAPDBvtKKlXNPc4UTAz66dMk9TX1RMEgIh4kvStfszqrVNw8ZGZWT9lEoUOSRPrK5ImAxOHOH6Z1zdKanvjMDNb1pTpp3AGcJGkn+T1g1ny/gnLlHrxkSsVzMz6K9NP4auSrgN2z5s+HxEXVBtWtXormtsbhpnZMqdMToGIOB84v+JYWqbeJLXH5UdmZv2UqVMYd3pHSW1rFGZmy57lMlHoHSXVqYKZWT/LZaJAb+sjpwpmZkWD1ilIuoEhSlgiYotKImqBepNUMzPrb6iK5r3zz3pP49PzzwOrC6c1XHxkZtbcUGMf3QsgaY+I2Kqw6yhJV9M3a9qYU88ouPjIzKy/MnUKkrRjYWWHkucts+R+CmZmTZXpp3AIcIqkVfL6PODdlUXUAi4+MjNrrkyP5tnAK+qJQkQ8VXlULeLiIzOz/oYtBpK0hqSTgTMj4ilJm+f5EMYstz4yM2uuTN3AqcAFwNp5/TbgyIriaYm+4iPnFMzMisokCtMi4iygByAiFgPdlUZVsb7WR20Nw8xsmVMmUXhO0urkxjqStgfGdL2CK5rNzJor0/row8B5wMaS/gFMB95caVQVk4e5MDNrqkyi8CTwGmBTUsnLrcCWFcZUufrQ2U4SzMz6K1N8dDawRkTcFBE3Aq8CTqk2rOpJuPzIzKxBmUThMOC3ktaUtBfwHWCvasOqnnBFs5lZozKd1/4l6XDgz8ACYPeIeHRpLirpQ8D/kEpwbiDN+7wWcCawOjAbeGdELFya6wwTA+ECJDOzfoYaOvt39C92X4HU6uhkSUTEviO5oKR1gMOBzSPieUlnAfuTch/fiogzJZ1IGl7jByO5Rhk1ufTIzKzRUDmFr1d83cmSFpESm4eAXYED8v7TgGOpMFEQcvGRmVmDoYbOvrS+LGkNYJu8elVEzB3pBSPiAUlfB+4DnicVS80G5uWOcQD3A+s0O1/SocChAOuvv/5IwwDh4iMzswZlxj56K3AV8BbgrcCVkkbcT0HSqsB+wIakoTOmAHuWPT8iToqImRExc/r06SMNg5pwm1QzswZl+il8CtimnjuQNB34C6mp6kjsDtxdr6yWdA6wIzBVUmfOLawLPDDC9y8lFR85VTAzKyrTJLXWUFz0eMnzBnMfsL2kFZR6ke0G3AxcTF9P6YOAc5fiGsOSK5rNzAYok1M4X9IFwC/y+tuAP430ghFxpaSzgauBxcA1wEnAH4AzJX0hbzt5pNcooya59MjMrEGZfgofk/QmUhEPwEkR8ZuluWhEHAMc07D5LmDbpXnfJZE6rzlZMDMrKpNTICJ+LenC+vGSVouIJyqNrGouPjIzG2DYREHSe4HPknoz95C+ZAewUbWhVavm6dfMzAYok1P4KPCyiHis6mBaSXLxkZlZozKtiO4E5lcdSKvVJBcfmZk1KJNTOBq4XNKVwAv1jRFxeGVRtYArms3MBiqTKPwQ+CtpNNOeasNpHckdms3MGpVJFLoi4sOVR9JicvGRmdkAZeoU/iTpUElrSVqt/qo8soqlidecKpiZFZXJKbw9/zy6sG3MN0n1MBdmZgOV6dG8YSsCabWaZ14zMxugzNDZb5G0Ul7+tKRzJG1VfWjV8hzNZmYDlalT+L+IeEbSTqRhr08GTqw2rOq5otnMbKAyiUJ3/vl60mB4fwAmVBdSa8gzr5mZDVAmUXhA0g9JQ2b/UdLEkuct01zRbGY2UJmH+1uBC4DXRsQ8YDXgY1UG1QpCbpJqZtagTOuj+cA5hfWHgIeqDKoVau7RbGY2wJgvBhopSW59ZGbWYNBEIdcdjFvu0WxmNtBQOYUrACSd3qJYWsoVzWZmAw1VpzBB0gHADpLe2LgzIs5pcs6YIfdoNjMbYKhE4TDgQGAqsE/DvqBQ+TwW1ZxTMDMbYNBEISL+Dvxd0qyIOHk0LyppKvBj4GWkBObdwK3AL4EZwD3AWyPiydG8br8YkCfZMTNrUKb10emSDpd0dn59UFLXUl7328D5EbEZ8ArgFuAo4KKI2AS4KK9XxnUKZmYDlUkUvg+8Mv/8PrA18IORXlDSKsDOpDGUiIiFuVPcfsBp+bDTgDeM9Bol43CNgplZgzLzKWwTEa8orP9V0nVLcc0NgUeBn0h6BTAbOAJYI3eMA3gYWKPZyZIOBQ4FWH/99UcchJukmpkNVGpAPEkb11ckbUTfIHkj0UnObUTEVsBzNBQVRXpaN31iR8RJETEzImZOnz59xEG4+MjMbKAyOYWPARdLuov0BXsD4OCluOb9wP0RcWVeP5uUKDwiaa2IeEjSWsDcpbjGsGouPjIzG6DM2EcXSdoE2DRvujUiXhjpBSPiYUlzJG0aEbcCuwE359dBwFfyz3NHeo0yJNz6yMysQZmcAjkRuH4Ur/tB4AxJE4C7SDmPGnCWpEOAe0mjs1Ym1SlUeQUzs7GnVKIw2iLiWmBmk127tSoGtz4yMxtoyIpmJeu1KphWShXNThbMzIqGTBRyK6A/tiiWlnLxkZnZQGWapF4taZvKI2mxmgfEMzMboEydwnbAgZLuJfUpyP2+YotKI6uYBD097Y7CzGzZUiZReG3lUbSBh842Mxto2OKjiLgXWA/YNS/PL3Pesk7g6TjNzBoM+3CXdAzwCeDovKkL+FmVQbWCxCADaZiZLb/KfOP/b2BfUn0CEfEgsFKVQbWCK5rNzAYqkygsLA5QJ2lKtSG1Rhrmot1RmJktW8okCmdJ+iEwVdJ7gL8AP6o2rOoJufOamVmDMgPifV3SHsDTwEuAz0TEhZVHVjHnFMzMBio79tENwGRSEdIN1YXTOp01z9FsZtaoTOuj/wGuAt4IvBn4p6R3Vx1Y1TpqYnG3EwUzs6Kyk+xsFRGPA0haHbgcOKXKwKrW4ZyCmdkAZSqaHweeKaw/k7eNaR01sdiVCmZm/QyaU5D04bx4B3ClpHNJdQr7MboT7rRFR61GjxMFM7N+hio+qndQuzO/6iqdJrNVOoRzCmZmDQZNFCLis60MpNU6ajW6nSiYmfUzbEWzpJnAp4ANiseP9aGzO2o4UTAza1Cm9dEZpBZINwDjZgaCjprodusjM7N+yiQKj0bEeZVH0mIdNTmnYGbWoEyicIykHwMXAS/UN0bEOUtzYUkdwCzggYjYW9KGwJnA6sBs4J0RsXBprjGUDjlRMDNrVKafwsHAlsCewD75tfcoXPsI4JbC+leBb0XEi4EngUNG4RqDcpNUM7OByuQUtomITUfzopLWBV4PfBH4sCQBuwIH5ENOA44FfjCa1y3qqLlJqplZozI5hcslbT7K1z0e+Dh9FderA/MiYnFevx9Yp9mJkg6VNEvSrEcffXTEAXTUaq5oNjNrUCZR2B64VtKtkq6XdIOkEfdolrQ3MDciZo/k/Ig4KSJmRsTM6dOnjzQMN0k1M2uiTPHRnqN8zR2BfSXtBUwCVga+TZrEpzPnFtYFHhjl6/ZT77wWEaTSKzMzK5NTiEFeIxIRR0fEuhExA9gf+GtEHAhcTBqaG+AgKh5OoyMnBM4smJn1KZNT+AMpERDpm/2GwK3AS0c5lk8AZ0r6AnANcPIov38/nR0pUejuCTpqzimYmUG56ThfXlyXtDXw/tG4eERcAlySl+8Cth2N9y2jpr5EwczMkjLFR/1ExNXAdhXE0lKdOXfgFkhmZn3KDIj34cJqDdgaeLCyiFqkVk8UPCWnmVmvMnUKKxWWF5PqGH5dTTitk6sUnFMwMysoU6cwLudV6OhIJWeLe8bNwK9mZkttqOk4f8LgTU8jIiodm6hqvU1SnSaYmfUaKqfw+ybb1gM+BHRUE07ruKLZzGygoabj7K03kLQR8ElgZ+ArVNyHoBVc0WxmNtCQTVIlbSbpZ8DvgL8Dm0fED6qc56BVnFMwMxtoqDqFXwGvBL5BKjLqBlaujxMUEU+0IsCq9OYUXKlgZtZrqDqFbUgVzR8FPpK31ceDCGCjCuOqXG9OwWmCmVmvoeoUZrQwjparD3PhJqlmZn2WeJiL8aKeU3CaYGbWZ7lNFOojozqnYGbWZ7lNFOoVzT1ufWRm1muo1kerDXXiWG99VC8+Wux+CmZmvYZqfTSbvsl1Go351ke98yk4p2Bm1muo1kcbtjKQVqvPvOYqBTOzPmWGzkbSqsAmpOk4AYiIy6oKqhXcJNXMbKAyk+z8D3AEsC5wLbA9cAWwa6WRVazTFc1mZgOUaX10BKl3870R8Z/AVsC8KoNqhQ5XNJuZDVAmUVgQEQsAJE2MiH8Dm1YbVvU6nFMwMxugTKJwv6SpwG+BCyWdC9w70gtKWk/SxZJulnSTpCPy9tUkXSjp9vxz1ZFeo4y+zmtOFMzM6oZNFCLivyNiXkQcC/wfaS6F/ZbimouBj0TE5qT6iQ9I2hw4CrgoIjYBLsrrlenoHRDPiYKZWd2wiYKk0+vLEXFpRJwHnDLSC0bEQxFxdV5+BrgFWIeU0JyWDzsNeMNIr1FGfTpOJwpmZn3KFB+9tLgiqYM0z8JSkzSDVHF9JbBGRDyUdz0MrDHIOYdKmiVp1qOPPjriazunYGY20KCJgqSjJT0DbCHpaUnP5PW5wLlLe2FJKwK/Bo6MiKeL+yIiSL2mB4iIkyJiZkTMnD59+oivX++8tsitj8zMeg2aKETElyNiJeBrEbFyRKyUX6tHxNFLc1FJXaQE4YyIOCdvfkTSWnn/WqTEpzKTuzoAWLCou8rLmJmNKWUqmo+WtK+kr+fX3ktzQaX5PE8GbomIbxZ2nQcclJcPYhRyI0OZVE8UFjtRMDOrK9Oj+cvAtsAZedMRknaIiE+O8Jo7Au8EbpB0bd72SeArwFmSDiE1eX3rCN+/lImdNSRYsNCJgplZXZmxj14PbBkRPQCSTgOuIT3Il1hE/J3mI68C7DaS9xwJSUzq7OB5Fx+ZmfUqO8nO1MLyKhXE0RaTJ3SwYJEHxDMzqyuTU/gycI2ki0nf8HcGlqqieVkxucs5BTOzomEThYj4haRLSIPiAXwiIh6uNKoWmdhVc6JgZlZQpkfzRbkX8nn59bCki1oRXNUmd3W4otnMrGCoOZonASsA0/LgdPXK4ZVJw1KMeZO7Otwk1cysYKjio/cCRwJrk+ZrricKTwPfrTas1pjU1cH8hYvbHYaZ2TJjqDmavw18W9IHI+I7LYypZSZ1dfD4cwvbHYaZ2TKjTI/mcZkgQGqS+oIrms3MepXtpzAuTXbrIzOzfpbrRGGS+ymYmfVTpvMaktYBNigeHxGXVRVUq0zu6vAoqWZmBWUGxPsq8DbgZqD+BA1gzCcKK0zoZMGiHhZ199DVsVxnmszMgHI5hTcAm0bECxXH0nIvWnkiAHOfeYF1pk5uczRmZu1X5uvxXUBX1YG0w5qrTALg4acWtDkSM7NlQ5mcwnzg2jy0RW9uISIOryyqFllzZScKZmZFZRKF8/Jr3OlNFJ52omBmBuVGST1N0mRg/Yi4tQUxtczUFbqY2Fnj4aeeb3coZmbLhDKjpO4DXAucn9e3lDQucg6S2Gj6itz04NPtDsXMbJlQpqL5WNIczfMAIuJaYKPKImqxV28yjVn3PMlzL3hgPDOzMonCooh4qmHbuJnDcrfNXsTC7h7OuPLedodiZtZ2ZRKFmyQdAHRI2kTSd4DLK46rZbbdcDV22+xFfPX8W/nFVfe1Oxwzs7Yqkyh8EHgpqTnqz4GnSPMsVELSnpJulXSHpKOquk7hepzw9q3Y8cXTOPqcG3jv6bOY69ZIZracUkSUO1BaISLmVxqM1AHcBuwB3A/8C3h7RNzc7PiZM2fGrFmzRuXai7t7+NHf7ub4v9zGhM4aH97jJRy43QZM6PTwF2Y2vkiaHREzm+0r0/poB0k3A//O66+Q9P1RjrFuW+COiLgrIhYCZwL7VXStfjo7arxvl405/8id2WLdVfjs725m929eynnXPUhPT7mE08xsrCvzNfhbwGuBxwEi4jpg54riWQeYU1i/nxbPB73htCn87JDtOPXgbVhhQgeH/+IaXnv8ZZw1aw4veD5nMxvnSpWNRMSchk1tezpKOlTSLEmzHn300aquwS6bvog/HP5qjn/blnTUxMfPvp6dj7uYEy66nQfnubObmY1PZYa5mCNpByAkdQFHALdUFM8DwHqF9XXztl4RcRJwEqQ6hYriAKCjJt6w1Trst+XaXHb7Y/z4b3fxzQtv41t/uY1XbzKdN261Dv+52YtYZfK4HC/QzJZDw1Y0S5oGfBvYHRDwZ+CIiHh81IOROkkVzbuREoN/AQdExE3Njh/Niuay5jwxn1/NmsPZs+/nwacW0NUhXrXxNF770jXYeZPprLfaCi2Nx8yWXRHB4p6guydY1N1Dd17u7gm6I1jcHfTkY3p6+o7tzss9Qxyz4bQpbLrmSiOKa6iK5jKJwqSIaFkbTUl7AccDHcApEfHFwY5tR6JQ19MTXHv/PC648WHOv+lh7n08Ncxab7XJ7LDRNLbbaDW2WHcqG02bQq2mtsRotqypPxwX9wSLu3tYmB+Ui7vrD7v6vr4H4+L6MYWHZXdPD4u6+6/3PXwL6939z1vc3TPgffpfr/+1FjVeu3BcY5zN3qvKNiqHvWZjjnrdZiM6d2kThTuAR4C/5dffm/Rwbot2JgpFEcEdc5/l8jsf5/I7H+OKOx/n6QVp2IwVJ3bysnVWZot1p/LiF63IxtNXZOPpU5i6woQ2R21jTU9PsKinh8Xd6WG1qDs/nLqDhd192xf31Pf35IdtDwsX9x3b/5i+B+XCxT2FY+rH9R2zaJD3X9RT319fb3iP7p7eY9rVkK+jJjpqorP+6qj1rhd/dg3Yntc76ttq6WdH/b36r/edW6Oro/967/4OUVPaXitcq6MmOlRYLrxSHNBRq/UeM23FCbwoj/S8pJYqUchvsD7wamBHYC9gXkRsOaJoRtGykig06u4Jbp/7DNff/xQ33P8U1z/wFLc8+DQLu/tGB1l9ygQ2nDaFtadOZq2pk1h7lcmsuUr6OX2liUxdoYtJXR1tvIvxJaL4kGp8uA58SNYfuH3bovcB2fugG7Atve+ixdHwMO17KBYf4M3OXdxd/wbd/yG+qEUP1PpDbEJHLT0IO2p05YdoV0d6aKYHZG3AMfV9XR3pAdjV2XduZ0d+z1r9mPrxtcKDuvCQzev1h2lnw/qwD/Leh3baJjm3XjRUolBmjuZ1SYnBq4FXADcBfx/VCMeZjprYbM2V2WzNlXnrzFRvvri7h/uffJ67HnuWO+c+x52PPsvdjz3HtXPmcf6NC/olGHUrTOhg1RUmsOqULlZdYQIrT+pihQkdTJnY2ftzclcHUyZ2MKmrI/+T9v3zdhX/GfM/XP1/o/4vUv9n6Vuv708L3ZGywj3RV9bZ028b/fdHKvcslpv2FQ80fOssPAT7vm3GkN9W6w/v4jfU3odxd995jd+Ku1vwRK0p9Xcp/r6LD9KuWt9Dsyvvn9Q18AHcVfgcO2s1ujqbn9uVz+msiQmdTR64hWO6ig/rwt9G8X3r31xt+Vam9dF9pArfL0XEYRXHM251dtSYMW0KM6ZNYdeGYsCenuCJ+Qt5aN4CHnzqeR5/diFPzl/Ik88t5In5C5k3fxFPPLeQB+c9z/yF3cxf2M1zLyxm8TjqVFd/0HU2PLyartdqTOissULvt1j1PYwL32r7HoqND+j++/t9++3sH0fjtYd64PuBauNBmURhK2An4IA8FtHtwKURcXKlkS1HajUxbcWJTFtxIi9fd5XS5y1c3MP8hYt5bmE3zy9c3FvMsTAXbyzu6V/WvKghN1IvOQyi/3rvduioQU195Z21QrlnrXcbA7Z11HK5aS4/7Sp8E+5fnODsvdmypMzMa9dJuhO4k1SE9A7gNYAThTab0FljQucEproVrJmNkjJ1CrOAiaThsv8G7BwRnnzAzGwcKlN89P6IuKq4QdKGEXF3RTGZmVmblBn76MQm284e7UDMzKz9Bs0pSNqMNLnOKpLeWNi1MjCyHhNmZrZMG6r4aFNgb2AqsE9h+zPAeyqMyczM2mTQRCEizgXOlfSqiLiihTGZmVmblKlTeFzSRZJuBJC0haRPVxyXmZm1QZlE4UfA0cAigIi4Hti/yqDMzKw9yjRJXSEirmrocbq4oniWyOzZsx+TNNI+E9OAx0YznjHA97x88D0vH5bmnjcYbEeZROExSRuTRj1A0puBh0YYyKiKiOkjPVfSrMFGCRyvfM/LB9/z8qGqey6TKHyANP3lZpIeAO4GDhztQMzMrP3KjH10F7C7pClALSKeqT4sMzNrh2ErmiWtLukE0rhHl0j6tqTVqw+tcie1O4A28D0vH3zPy4dK7rnMdJwXApcBP8ubDgR2iYjdqwjIzMzap0yicGNEvKxh2w0R8fJKIzMzs5Yr00/hz5L2l1TLr7cCF1QdWJUk7SnpVkl35ImDxgVJp0iaW+9omLetJulCSbfnn6vm7ZJ0Qv4dXC9p6/ZFPnKS1pN0saSbJd0k6Yi8fdzet6RJkq6SdF2+58/m7RtKujLf2y8lTcjbJ+b1O/L+GW29gRGS1CHpGkm/z+vj+n4BJN0j6QZJ1+ZpDKr/246Ipi/SGEdP5589pM5ri/Ly04Odt6y/gA7ShEEbAROA64DN2x3XKN3bzsDWwI2FbccBR+Xlo4Cv5uW9gD+RpmfeHriy3fGP8J7XArbOyysBtwGbj+f7zrGvmJe7gCvzvZwF7J+3nwi8Ly+/HzgxL+8P/LLd9zDC+/4w8HPg93l9XN9vjv8eYFrDtkr/ttt+0234Jb8KuKCwfjRwdLvjGsX7m9GQKNwKrJWX1wJuzcs/BN7e7Lix/ALOBfZYXu4bWAG4GtiO1JGpM2/v/Tsn5exflZc783Fqd+xLeJ/rAhcBuwK/zw++cXu/hftulihU+rddpvhovFkHmFNYvz9vG6/WiIh6Z8OHgTXy8rj7PeRigq1I35zH9X3nopRrgbnAhaTc77yIqI82ULyv3nvO+58CxloLwuOBj5NKKiDFP57vty5IRfizJR2at1X6t12m85qNExERkoZuWTBGSVoR+DVwZEQ8XRyWZTzed0R0A1tKmgr8BtisvRFVR9LewNyImC1plzaH02o7RcQDkl4EXCjp38WdVfxtL485hQeA9Qrr6+Zt49UjktYCyD/n5u3j5vcgqYuUIJwREefkzeP+vgEiYh5wMan4ZKqk+he94n313nPevwrweGsjXSo7AvtKugc4k1SE9G3G7/32iogH8s+5pMR/Wyr+2y6VKEjaSdLBeXm6pA2X9ELLkH8Bm+SWCxNIFVHntTmmKp0HHJSXDyKVude3/7/cYmF74KlClnTMUMoSnAzcEhHfLOwat/ed/wen5uXJpDqUW0iJw5vzYY33XP9dvBn4a+RC57EgIo6OiHUjYgbp//WvEXEg4/R+6yRNkbRSfRn4L+BGqv7bLlHRcQzwO+C2vL428I92V8AsZeXNXqRWKncCn2p3PKN4X78gDVa4iFSeeAipLPUi4HbgL8Bq+VgB38u/gxuAme2Of4T3vBOp3PV64Nr82ms83zewBXBNvucbgc/k7RsBVwF3AL8CJubtk/L6HXn/Ru2+h6W4913oa300ru833991+XVT/VlV9d92mc5r15Iq766OiK3ytusjYoshTzQzszGnTPHRwkgpR33o7CnVhmRmZu1SJlE4S9IPSZU67yFlV35UbVhmZtYOwxYfAUjag1TJIVIHkQurDszMzFqvTJ3ChsBDEbEgr08mdZ64p/rwzMyslcoUH/2Kvl6EAN15m5mZjTNlEoXOiFhYX8nLE6oLyWzJSApJ3yisf1TSsXn5VKV5xUf63l/LI5F+rWH7vsoj7Ep6g6TNR3qNJtfcUtJeza5lVrUyicKjkvatr0jajzTAlNmy4gXgjZKmVfDehwJbRMTHihsj4ryI+EpefQNpZNbSCj1xm9mS1Nei2bXMKlUmUTgM+KSk+yTNAT4BvLfasMyWyGLS1IQfGmT/7pJmSbotj6PTT+4B+jVJN+ax69+Wt58HrAjMrm8rnPMuSd+VtAOwL/C1POb9xvl1fh7E7G+SNsvnnCrpRElXAsdJ2lbSFUpzBFwuadPcy/5zwNvy+72tfq38HjMk/TWPl3+RpPUL731Cfp+76rkjSWtJuiy/142SXr30v24bz4YdEC8i7gS2VxpwjIh4tvKozJbc94DrJR3XZN8M0pgxGwMXS3pxveFE9kbSt/NXANOAf0m6LCL2lfRsRGw52EUj4vKcePw+Is4GkHQRcFhE3C5pO+D7pPF6II1Hs0NEdEtaGXh1RCyWtDvwpYh4k6TPkHqj/m9+v3cVLvkd4LSIOE3Su4ETSDkVSMMo70QaHO884GzgAFKLwS9K6iANtW02qGETBUkTgTeR/rE6lUefjIjPVRqZ2RKINDLqT4HDgecbdp8VET3A7ZLuIj00ry3s3wn4RaSRRx+RdCmwDSMYEyt/edoB+JX6RmqdWDjkV/k6kAZqO03SJqTOoV0lLvEqUiIGcDppwpW63+b7vFlSfTjlfwGnKA0a+NuIuHYJb8mWM2WKj84F9iNl0Z8rvMyWNceTxntq7HXf2O66ysHRaqRx/rcsvP6jsL/4v/N54OJIc6DvQxqzZ2m8UFgWQERcRpqR7wHgVEn/bymvYeNcmURh3Yh4W0QcFxHfqL8qj8xsCUXEE6QpGg9p2PUWpfnFNyYNMnZrw/6/kcrwOyRNJz1Er1qCSz9DmgqUiHgauFvSW6C3vuIVg5y3Cn1DG7+r2fs1cTlppFCAA3Psg5K0AfBIRPwI+DFpulazQZVJFC6X9PLKIzEbHd8g1QsU3Ud6yP+JVNa/oGH/b0gjjl4H/BX4eEQ8vATXPBP4WK4w3pj0sD5EUn10y/0GOe844MuSrqF/Ue7FwOb1iuaGcz4IHCzpeuCdwBHDxLYLcF2+xttI8xCYDapMj+abgRcDd5OypyJN+ONRUs3MxpkyicIGzbZHxL2VRGRmZm0zbPFRfvivB+yal+eXOc/MzMaeMjmFY4CZwKYR8RJJa5Oa1e3YigDNzKx1ynzj/29Sj83nACLiQQZvGWFmZmOYZ14zM7NennnNzMx6DVmnoNRPf13SsACeec3MbJwrU9F8Q0S485qZ2XKgTPHR1ZK2qTwSMzNruzI5hX8DmwD3kFoguUezmdk45R7NZmbWyz2azcysl3s0m5lZL/doNjOzXu7RbGZmvdyj2czMeg1apyBpYkS8kJf3wD2azczGvaEShasjYmtJp0fEO1scl5mZtUHnEPsmSDoA2EHSGxt3RsQ51YVlZmbtMFSicBhpAvKpwD4N+wJwomBmNs4MlSisFRHvk3RNRJzUsojMzKxtytQpXB0RW7c4LjMza4OhEoULScVE2wB/a9wfEftWG5qZmbXaUInCBGBr4HTgfxr3R8Sl1YZmZmatVmbso+kR8WiL4jEzszYaKqdwfEQcKel35CEuilx8ZGY2/gzV+uj0/PPrrQjEzMzab9jiI0hFSAAuRjIzG9+GHBBP0rGSHgNuBW6T9Kikz7QmNDMza7VBEwVJHwZ2BLaJiNUiYlVgO2BHSR9qVYBmZtY6Q1U0XwPsERGPNWyfDvw5IrZqQXxmZtZCQxUfdTUmCNBbr9BVXUhmZtYuQyUKC0e4z8zMxqihio+6yfMyN+4CJkWEcwtmZuNMqSapZma2fCgzR7OZmS0nnCiYmVkvJwpmZtbLiYKZmfVyomBmZr2cKJiZWa//D3v27UpG36ACAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Lets try to solve this using a simple gradient ascent method\n",
    "x=np.random.uniform(0,5,P) #initial guess\n",
    "niter = 500\n",
    "step = 1e-1\n",
    "pathLL = []\n",
    "pathKLD = []\n",
    "SumData = []\n",
    "\n",
    "for i in range(niter):\n",
    "    x = x + step * LLGrad(x,yn,Ank)\n",
    "    SumData.append(np.dot(Ank,x).sum()-yn.sum())\n",
    "    pathLL.append( GetLogLikeliHoodForSmokerProblem(x,yn,Ank) )\n",
    "    pathKLD.append( GetKullbackLieblerDivergenceForSmokerProblem( x, yn, Ank ) )\n",
    "    \n",
    "plt.figure()\n",
    "plt.title('Gradient ascent algorithm convergence')\n",
    "plt.xlabel('Nb of iterations')\n",
    "plt.ylabel('Log Likelihood')\n",
    "plt.plot(pathLL)\n",
    "\n",
    "plt.figure()\n",
    "plt.title('Gradient ascent algorithm convergence')\n",
    "plt.xlabel('Nb of iterations')\n",
    "plt.ylabel('Kullback Liebler divergence')\n",
    "plt.plot(pathKLD)\n",
    "\n",
    "plt.figure()\n",
    "plt.title('Gradient ascent Algorithm inconsistency')\n",
    "plt.xlabel('Nb of iterations')\n",
    "plt.ylabel('Difference between total Number of smoked cigaret in model vs data')\n",
    "plt.plot(SumData)\n",
    "\n",
    "#Let's take a look at the maximum likelihood solution\n",
    "MSE = np.mean(np.square(x-LambdaK))\n",
    "print(\"MSE for maximum likelihood estimate is \"+str(MSE))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### A bit of analysis\n",
    "Although the gradient ascent seen previously seems to provide interesting results, we should notice that equating the derivative to zero in order to find the minimum in a coordinate wise fashion is impossible (no analytical solution).\n",
    "It seems that we are stuck with ascent method, but one of the drawback of this method, is that it requires a gradient ascent step, which we have chosen manually in this case.<br>\n",
    "In practice, we could be using a linesearch algorithm in order to choose the right step at every iteration, bu this would need to evaluate the log likelihood multiple times per iteration, which can be costly for large problem sizes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "#### Expectation Maximization Algorithm\n",
    "\n",
    "##### Introduction\n",
    "\n",
    "##### Instance of the EM algorithm for our problem\n",
    "\n",
    "We will now suppose that the extended random variables $N_{nk} = a_{nk}\\lambda_k$, that actually only rely on the random variable $\\lambda_k$ and the determnistic matix $A$, can be directly observed, and yielded the observation $x_{nk}$, we can express the likelihood of the observation as:\n",
    "$$\n",
    "    L(x_{nk}|\\lambda_k) = \\prod_{n=0}^{N-1}\\prod_{k=0}^{P-1} \\frac{(a_{nk}\\lambda_k)^{x_{nk}}e^{-a_{nk}\\lambda_k}}{x_{nk}!}\n",
    "$$\n",
    "and log likelihood:\n",
    "$$\n",
    "     LL(x_{nk}|\\lambda_k) = \\sum_{n=0}^{N-1}\\sum_{k=0}^{P-1} x_{nk}log(a_{nk}\\lambda_k)-a_{nk}\\lambda_k-log(x_{nk}!)\n",
    "$$\n",
    "\n",
    "This log likelihood is not very useful as such, because we cannot observe directly the $x_{nk}$.\n",
    "What we can do however, is compute the conditional expectation of $N_{nk}$ given the current estimate of the solution $\\lambda_k$ and the observed values $y_n$ and later and replace the unobserved $x_{nk}$ by their expectation: <br>\n",
    "\n",
    "$$\n",
    "    \\mathbb{E}(N_{nk}|(y_n,\\lambda_k))\n",
    "$$\n",
    "\n",
    "This actually amounts to derive the expectation of a Poisson variable : $N_{nk}$  of known rate $a_{nk}\\lambda_k$, knowing the parameters of the PDF of $P-1$ other Poisson variables $N_{n0},\\dots,N_{nk-1},N_{nk+1},\\dots,N_{nP-1}$ where the outcome of the sum of all these variable is known : $y_n$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "#### Conditional probability, sum of Poisson distibutions and binomial law\n",
    "\n",
    "In order to derive the previous conditional expectation, we will need a more general result, that is less known that the additive property of Poisson variables:<br>\n",
    "\n",
    "Assuming $X$ and $Y$ are independant Poisson variables, the conditional distribution of $X = k$ given that $X + Y = n$ is binomial with parameters $k$, $n$ and $\\frac{\\lambda_X}{\\lambda_X+\\lambda_Y}$ :\n",
    "$$\n",
    "P( X = k | X+Y = n ) = Bin(k,n,\\frac{\\lambda_X}{\\lambda_X+\\lambda_Y})\n",
    "$$\n",
    "\n",
    "With, \n",
    "- $X \\sim Poisson\\{\\lambda_X\\}$<br>\n",
    "- $Y \\sim Poisson\\{\\lambda_Y\\}$<br>\n",
    "- $Bin(k,n,p) = \\binom{n}{k}p^k(1-p)^{n-k}$\n",
    "\n",
    "First, consider the random variable $X + Y = N$, we can write\n",
    "$$\n",
    "    P(X = x \\mid N = n) = \\frac{P((X = x) \\cap (N = n))}{P(N = n)}= \\frac{P((X = x) \\cap (Y = n-x))}{P(N = n)}.\n",
    "$$ \n",
    "\n",
    "\n",
    "We can derive the numerator easily using the Poisson distribution function expression and the fact that $X$ and $Y$ are independant so that $P((X = x) \\cap (Y = n-x)) = P(X = x)\\times P(Y = n-x)$<br>\n",
    "\n",
    "Let's take a look at the denominator:\n",
    "$$\n",
    "\\begin{align*}\n",
    "    P(N = n) &= \\sum_{x=0}^n P((X = x) \\cap (Y = n-x)) \\\\\n",
    "    &= \\sum_{x=0}^n e^{-\\lambda_X} \\frac{\\lambda_X^x}{x!} e^{-\\lambda_Y} \\frac{\\lambda_Y^{n-x}}{(n-x)!} \\\\\n",
    "    &= e^{-(\\lambda_X+\\lambda_Y)} \\sum_{x=0}^n \\frac{n!}{n!} \\frac{\\lambda_X^x \\lambda_Y^{n-x}}{x! (n-x)!} \\\\ \n",
    "    &= \\frac{e^{-(\\lambda_X+\\lambda_Y)}}{n!} \\sum_{x=0}^n \\binom{n}{x} \\lambda_X^x \\lambda_Y^{n-x} \\\\ \n",
    "    &= \\frac{e^{-(\\lambda_X + \\lambda_Y)}}{n!} (\\lambda_X + \\lambda_Y)^n\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "which proves that the sum of independent Poisson variables is Poisson with rate equal to the sum of the individual rates. Now let's get back to the conditional expression\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    P(X = x \\mid N = n) &= e^{-\\lambda_X} \\frac{\\lambda_X^x}{x!} e^{-\\lambda_Y} \\frac{\\lambda_Y^{n-x}}{(n-x)!} e^{\\lambda_X + \\lambda_Y} \\frac{n!}{(\\lambda_X + \\lambda_Y)^n}\\\\\n",
    "    &= \\frac{\\lambda_X^x}{x!} \\frac{\\lambda_Y^{n-x}}{(n-x)!} \\frac{n!}{(\\lambda_X + \\lambda_Y)^n}\\\\\n",
    "    &= \\frac{n!}{x!(n-x)!} \\frac{\\lambda_X^x \\lambda_Y^{n-x}}{(\\lambda_X + \\lambda_Y)^x(\\lambda_X + \\lambda_Y)^{n-x}}\\\\\n",
    "    &= \\binom{n}{x} \\left(\\frac{\\lambda_X}{\\lambda_X + \\lambda_Y}\\right)^x \\left(\\frac{\\lambda_Y}{\\lambda_X + \\lambda_Y}\\right)^{n-x}\\\\\n",
    "    &=  Bin(k,n,\\frac{\\lambda_X}{\\lambda_X+\\lambda_Y})\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Now that we have the proof that the conditional probability is a random variable with a binomial distribution of the form $Bin(k,n,p)$, we can easily derive its expectation $np$ which in ou case gives:\n",
    "\n",
    "$$\n",
    "\\mathbb{E}[X|X+Y] = \\frac{(X+Y)\\lambda_X}{\\lambda_X+\\lambda_Y}\n",
    "$$\n",
    "\n",
    "As, we proved how Poisson variables sums, we can easily extend this property to $P$ Poisson distributions:\n",
    "\n",
    "$$\n",
    "\\mathbb{E}\\left[X_k|\\sum_{i=0}^{P-1}X_i\\right] = \\frac{\\lambda_{X_k}\\sum_{i=0}^{P-1}X_i}{\\sum_{i=0}^{P-1}\\lambda_{X_i}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Deriving the E-step of the algorithm\n",
    "\n",
    "The theory behind the EM algorithm tell us that we should first evaluate the expectation of the current log likelihood of the complete dataspace given the current solution, and known data.\n",
    "This amounts for us, as stated earlier, as replacing the unobserved values of the complete dataspace, by their expectation:\n",
    "\n",
    "$$\n",
    "      \\mathbb{E}[LL(N_{nk}|(y_n,\\lambda_k^c))] = \\sum_{n=0}^{N-1}\\sum_{k=0}^{P-1} \\mathbb{E}[N_{nk}|(y_n,\\lambda_k^c)]log(a_{nk}\\lambda_k)-a_{nk}\\lambda_k-log(\\mathbb{E}[N_{nk}|(y_n,\\lambda_k^c)]!)\n",
    "$$\n",
    "\n",
    "We now know how to derive $E_{nk}$ the conditional expectation of the hidden variables $N_{nk}$, given the actual sum of their realization $y_n$, and the current estimate of their pdf parameter $\\lambda_k^c$:\n",
    "$$\n",
    "\\begin{align*}\n",
    "    \\mathbb{E}[N_{nk}|(y_n,\\lambda_k^c)] &= \\mathbb{E}\\left[N_{nk}|\\sum_{i=0}^{P-1} N_{ni}\\right]\\\\\n",
    "    E_{nk} &= \\frac{a_{nk}\\lambda_k^c y_n}{\\sum_{i=0}^{P-1} a_{ni}\\lambda_i^c}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "We now have the analytic expression of the expectation of the log likelihood of the current data. Let's now jump to the maximization part."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Deriving the M-step of the algorithm\n",
    "The second step of the algorithm is the maximization, its intent is simply to find how to update the main unknown so that the expectation function found at the E-step is maximized.\n",
    "\n",
    "In our case, this simply amount to solve:\n",
    "$$\n",
    "\\begin{align*}\n",
    "    &\\underset{\\lambda_k \\in \\mathbb{R}^{+}}{max} \\mathbb{E}[LL(N_{nk}|(y_n,\\lambda_k^c))] \\\\\n",
    "    \\iff &\\underset{\\lambda_k \\in \\mathbb{R}^{+}}{max} \\sum_{n=0}^{N-1}\\sum_{k=0}^{P-1} E_{nk}log(a_{nk}\\lambda_k)-a_{nk}\\lambda_k-\\epsilon\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "with $\\epsilon$ a constant equal to $log(E_{nk}!)$\n",
    "\n",
    "Fortunately, taking the partial derivative of this expression yield a simple result:\n",
    "\n",
    "$$\n",
    "    \\frac{\\partial \\mathbb{E}[LL(N_{nk}|(y_n,\\lambda_k^c))]}{\\partial \\lambda_j} = \\sum_{n=0}^{N-1} \\frac{E_{nj}}{\\lambda_j} - \\sum_{n=0}^{N-1} a_{nj}\n",
    "$$\n",
    "\n",
    "Equated to zero, this expression can be solved easily for updating each unknown $\\lambda_k^c$:\n",
    "\\begin{align*}\n",
    "    0 &= \\sum_{n=0}^{N-1} \\frac{E_{nj}}{\\lambda_j^{c+1}} - \\sum_{n=0}^{N-1} a_{nj} \\\\\n",
    "    (\\lambda_j^{c+1})^{-1} \\sum_{n=0}^{N-1} E_{nj} &= \\sum_{n=0}^{N-1} a_{nj}\\\\\n",
    "    \\lambda_j^{c+1} &= \\frac{\\sum_{n=0}^{N-1} E_{nj}}{\\sum_{n=0}^{N-1} a_{nj}} \\\\\n",
    "    \\lambda_j^{c+1} &= \\frac{\\lambda_j^c}{\\sum_{n=0}^{N-1} a_{nj}} \\sum_{n=0}^{N-1} \\frac{a_{nj}y_n}{\\sum_{i=0}^{P-1} a_{ni}\\lambda_i^c} \\\\\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE for maximum likelihood estimate is 10.964285341411871\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let's now implement this EM-Algorithm, and see how its solution compares to other algorithms\n",
    "x=np.random.uniform(1e-2,5,P) #initial guess\n",
    "niter = 500\n",
    "pathLL = []\n",
    "pathKLD = []\n",
    "SumData = []\n",
    "Asum = Ank.sum(0)\n",
    "\n",
    "for i in range(niter):\n",
    "    x = np.dot(Ank.T*yn,1/np.dot(Ank,x))*(x/Asum)\n",
    "    SumData.append(np.dot(Ank,x).sum()-yn.sum())\n",
    "    pathLL.append( GetLogLikeliHoodForSmokerProblem(x,yn,Ank) )\n",
    "    pathKLD.append( GetKullbackLieblerDivergenceForSmokerProblem( x, yn, Ank ) )\n",
    "    \n",
    "plt.figure()\n",
    "plt.title('Expectation Maximization algorithm convergence')\n",
    "plt.xlabel('Nb of iterations')\n",
    "plt.ylabel('Log Likelihood')\n",
    "plt.plot(pathLL)\n",
    "\n",
    "plt.figure()\n",
    "plt.title('Expectation Maximization algorithm convergence')\n",
    "plt.xlabel('Nb of iterations')\n",
    "plt.ylabel('Kullback Liebler divergence')\n",
    "plt.plot(pathKLD)\n",
    "\n",
    "plt.figure()\n",
    "plt.title('EM-Algorithm consistency')\n",
    "plt.xlabel('Nb of iterations')\n",
    "plt.ylabel('Difference between total Number of smoked cigaret in model vs data')\n",
    "plt.plot(SumData)\n",
    "\n",
    "\n",
    "#Let's take a look at the maximum likelihood solution\n",
    "MSE = np.mean(np.square(x-LambdaK))\n",
    "print(\"MSE for maximum likelihood estimate is \"+str(MSE))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "#### Some remark about this Expectation Maximization instance\n",
    "\n",
    "One of the nice property of the EM framework, in addition to the fact that it doesn't require any linesearch, is that it intrinsically handle the equality constraint with the sum of observed data:\n",
    "\n",
    "\\begin{align*}\n",
    "    \\sum_{i=0}^{N-1}\\sum_{j=0}^{P-1} a_{ij} \\lambda_j^{c+1} &= \\sum_{i=0}^{N-1}\\sum_{j=0}^{P-1} a_{ij} \\frac{\\lambda_j^c}{\\sum_{n=0}^{N-1} a_{nj}} \\underbrace{\\sum_{n=0}^{N-1} \\frac{a_{nj}y_n}{\\sum_{l=0}^{P-1} a_{nl}\\lambda_l^c}}_{\\text{no term in }i} \\\\\n",
    "    &= \\sum_{j=0}^{P-1} \\underbrace{\\sum_{n=0}^{N-1} \\frac{a_{nj}y_n}{\\sum_{l=0}^{P-1} a_{nl}\\lambda_l^c}}_{\\text{no term in }i} \\sum_{i=0}^{N-1} \\frac{a_{ij} \\lambda_j^c}{\\sum_{n=0}^{N-1} a_{nj}} \\\\\n",
    "    &= \\sum_{j=0}^{P-1} \\underbrace{\\sum_{n=0}^{N-1} \\frac{a_{nj}y_n}{\\sum_{l=0}^{P-1} a_{nl}\\lambda_l^c}}_{\\text{no term in }i} \\lambda_j^c \\frac{\\sum_{i=0}^{N-1}a_{ij}}{\\sum_{n=0}^{N-1} a_{nj}} \\\\\n",
    "    &= \\sum_{j=0}^{P-1} \\sum_{n=0}^{N-1} \\frac{a_{nj}y_n\\lambda_j^c}{\\sum_{l=0}^{P-1} a_{nl}\\lambda_l^c}  \\\\\n",
    "    &= \\sum_{n=0}^{N-1} y_n \\sum_{j=0}^{P-1} \\frac{ a_{nj}\\lambda_j^c}{\\underbrace{\\sum_{l=0}^{P-1} a_{nl}\\lambda_l^c}_{\\text{numerator has not term in }j}}  \\\\\n",
    "    &= \\sum_{n=0}^{N-1} y_n \\frac{ \\sum_{j=0}^{P-1} a_{nj} \\lambda_j^c}{\\sum_{l=0}^{P-1} a_{nl}\\lambda_l^c}  \\\\\n",
    "    &= \\sum_{n=0}^{N-1} y_n\n",
    "\\end{align*}\n",
    "\n",
    "The second nice property of this algorithm, is that, if initialized in the non negative orthant, multiplicative update makes it also intrinsically able to handle the inequality constraint linked to the appartenance of the solution to the non negative orthant:\n",
    "$$\n",
    "    \\lambda_k^c \\in \\mathbb{R}^{P-1^{+}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "## Bayesian statistics, MCMC, and the magical world of probabilistic programming\n",
    "\n",
    "### Introduction\n",
    "\n",
    "Although Bayesian statistics is not really a novel approach, the recent rise of probabilistic programming libraries, availability of a lot of data, and powerful computer to run markov chains, made the tedious task of running bayesian inference algorithms a lot easier.\n",
    "\n",
    "Let's recall some simple elements about the Bayes theorem that we have been using before:\n",
    "\n",
    "For two given random variables, $X$ and $Y$, we can write :\n",
    "\\begin{equation}\n",
    "    P(Y|X) = \\frac{P(X|Y)P(Y)}{P(X)}\n",
    "\\end{equation}\n",
    "\n",
    "We can use a slightly more formal version, that includes a model $\\mathcal{M}$ that we believe is the underlying model for the random variable $Y$\n",
    "\n",
    "\\begin{equation}\n",
    "    P(Y|X,\\mathcal{M}) = \\frac{P(X|Y, \\mathcal{M})P(Y|\\mathcal{M})}{P(X|\\mathcal{M})}\n",
    "\\end{equation}\n",
    "\n",
    "* Usually, $Y$ is the random variable that we would like to caracterize. It usually consist in a set of parameters for a given statistical model (mean and variance for a normal distribution for instance). We may be interested in knowing the parameters that satisfy an optimality condition, as seen previously, but we might also be interested in knowing the distribution of the model parameters (which is kind of meta, isn't it ?).\n",
    "\n",
    "* On the contrary $X$, called the evidence, is usually derived from a known dataset, for instance we have seen previously how to define an empirical distribution from a set of samples. $P(X)$ can indeed simply be a distribution extrapolated from an actual sampling of the physical process, that we try to model with $Y$. In this case $P(X)$ marginalizes $Y$ such that it mostly act as a constant used to normalize the result to make sure it is a probability.\n",
    "\n",
    "* We call $P(X|Y)$ the likelihood of $X$, given the model distribution for $Y$. This is exactly the likelihood we tried to maximize in the previous section, by finding the optimal model parameters $Y$. This was the most important term in the frequentist approach because that is the one we analyzed to \"tweak\" our model $Y$. However in Bayesian statistics, we will receive more samples from X along the experiment, so that we will update our posterior considering both the prior and the likelihood.\n",
    "\n",
    "* We call $P(Y|X)$ the posterior distribution of $Y$, given a known (usually empirical distribution of data) $X$. As opposite to the prior, it gives an idea of the probability of the model AFTER some data ($X$) has been seen.\n",
    "\n",
    "* We call $P(Y)$ the a-priori distribution for the variable $Y$. This one can be derived if we have a-priori knowledge on the model parameters $Y$, it may consist in apriori knowledge of some surrogate parameters that we integrate as a marginal distribution and scale. A prior usually allows us to compute the probability of a given set of parameters $\\theta \\in \\mathbb{R}^n$ that define the model for $Y$. A priori usually writes $M$ as \\begin{align*} \\theta&\\rightarrow P(Y=\\theta) \\\\ \\mathbb{R}^n&\\mapsto [0,1]\\end{align*}. A concrete example is for instance, the use of the framework of random markov field (or Gibbs random field) in a n-dimensional space like an image, were we can consider the pixels as a set of vertices of a graph, and only neighbouring pixels are connected by edges. The probability of a given graph $\\mathcal{G} = (\\mathcal{V}, \\mathcal{E})$ is given by $P(\\mathcal{G}) = \\alpha e^{-\\beta U(\\mathcal{G})}$ where $\\alpha$ and $\\beta$ are normalization factor, and $U(\\mathcal{G}) = \\sum_{c\\in C} V_c(\\mathcal(G))$ is a sum of clique potentials $V_c(\\mathcal(G))$ over all possible cliques $C$. A very common instance of Gibbs measure is the gaussian-like distribution where, we have, for each neighbouring pair of pixel $p_1-p_2$ (a clique): $V_{p_1-p_2}(\\mathcal{G}) = (\\mathcal{G}_{p_1}-\\mathcal{G}_{p_2})^2$\n",
    "When one has no apriori on $Y$, then the highest entropy hypothesis is implicitly used. More pragmatically, we write $P(\\theta=Y) \\sim Uniform(0,1)$\n",
    "Notice that, as long as we received new data, the prior distribution can be taken just as being the previous step posterior.\n",
    "\n",
    "* Usually $P(X)$ is the empirical distribution that correspond to a given set of outcomes (actual data). It represents the probability of the given outcome of the experiment regardless of the value of the underlying model $Y$. In general, it can also act as a normalization constant that is used to make sure that the posterior distribution integrates to 1.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Link with hypothesis testing for model parameter distribution estimation\n",
    "\n",
    "One possible interpretation of bayesian statistics for model building, is to consider it in the framework of hypothesis testing. In this framework, we assume that one can define a large set of values for $Y$, as exhaustive as possible, and initialize the prior as uniform probability.\n",
    "\n",
    "One can then draw a first sample from $P(X)$ and compute the posterior probability for all hypothesis. The set of posterior gives us then a new prior to use as $P(Y)$.\n",
    "We can then iterate by feeding the model the constant set of $Y$s, and computing the new posterior with the latest set of $X$ sample."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probabilistic programming in practice: a small example\n",
    "\n",
    "### Introduction\n",
    "\n",
    "Thanks to mkinet (https://github.com/mkinet), that kindly provided us with a base example related to coin toss, we are going to first take a look at a simple 1-dimensional example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "#Please don't forget to pip install --user --upgrade tfp-nightly\n",
    "import tensorflow_probability as tfp\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "\n",
    "tfd = tf.distributions\n",
    "tfe = tf.contrib.eager\n",
    "\n",
    "try:\n",
    "  tfe.enable_eager_execution()\n",
    "except ValueError:\n",
    "  pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class BiasedCoin():\n",
    "    def __init__(self, n_hyp=100, prior=tfp.distributions.Uniform(0.,1.)):\n",
    "        \"\"\"Class constructor\n",
    "        Args:\n",
    "            n_hyp : int\n",
    "                Number of hypotheses to consider in the range [0,1].\n",
    "            prior : Tensorflow distribution or custom function. Optional.\n",
    "                Distribution used to compute the prior probabilities of each hypotesis.\n",
    "                The object must have a prob method that accepts a tensor of values and\n",
    "                returns a tensor (not necessarily normalized) of probabilities. Default \n",
    "                Value is a uniform distribution.\n",
    "        \"\"\"\n",
    "        self.n_hyp = n_hyp\n",
    "        # note : tfd rely heavily on log_probs and logits and logits are \n",
    "        # undefined for p=1 and p=0. we exclude these two hyps.\n",
    "        self.hyps = tf.lin_space(start=0.01, stop=0.99, num=n_hyp)\n",
    "        self.prior = tf.to_double(prior.prob(self.hyps))\n",
    "        # normalize prior\n",
    "        self.prior = self.prior/sum(self.prior)\n",
    "        # Define the likelihood function\n",
    "        self.likelihood_fn = tfd.Bernoulli(probs = self.hyps)\n",
    "        # initially, set the posterior equal to the prior\n",
    "        self.posterior = self.prior\n",
    "\n",
    "    def likelihood(self, y):\n",
    "        \"\"\" Evaluate the likelihood for a given data point for all hypotheses.\n",
    "        Here we make use of tfp's broadcasting capabilities. Indeed, the like-\n",
    "        lihood function is defined jointly for all hypotheses and the result of\n",
    "        evaluating the likelihood of a toss is a tensor of shape n_hyp.\n",
    "        Note that we convert the probability to a double precision number, this\n",
    "        is to avoid underflow when making the problems. If we had even more data,\n",
    "        even double precision would lead to underflow. In that case, we would\n",
    "        need toc rely on log-probabilities or to rescaling techniques to avoid\n",
    "        numerical issues.\n",
    "        Args:\n",
    "            y : int\n",
    "                The data for which the likelihood need to be evaluated.\n",
    "        Returns:\n",
    "              : tf.Tensor\n",
    "                Tensor of probability under all the possible hypotheses.\n",
    "        \"\"\"\n",
    "        return tf.to_double(self.likelihood_fn.prob(y))\n",
    "\n",
    "    def update(self, data):\n",
    "        \"\"\"\n",
    "        Update the posterior distribution of the unknown parameter with data. \n",
    "        The operation is equivalent to applying Bayes theorem, followed by a\n",
    "        renormalization of the probability.\n",
    "        Args :\n",
    "            - data : list or array\n",
    "                list of outcomes for which the posterior need to be upadted\n",
    "            \n",
    "        \"\"\"\n",
    "        # Remember that the posterior is initially set equal to the prior. \n",
    "        for d in data:\n",
    "            self.posterior = self.likelihood(d)*self.posterior\n",
    "\n",
    "        # normalize the posterior\n",
    "        self.posterior = self.posterior/sum(self.posterior)\n",
    "\n",
    "    def plot_posterior(self, color='b'):\n",
    "        \"\"\"Plot the posterior distribution.\"\"\"\n",
    "        plt.plot(self.hyps.numpy(), self.posterior.numpy(),'-', color=color)\n",
    "        plt.title('Posterior probability for Bernouilli model with a selected set of parameters p')\n",
    "        plt.xlabel('Value of the tested model parameter p (all the sampled hypothesis)')\n",
    "        plt.ylabel('Posterior probability')\n",
    "        \n",
    "    def reset_coin(self):\n",
    "        \"\"\"\n",
    "        Method to 'reset' the coin, i.e. forget the data we have seen up to now.\n",
    "        \"\"\"\n",
    "        self.posterior = self.prior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have seen how we can define a simple statistical model and update it, let's now use it practically"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From <ipython-input-3-b481a973d870>:21: Bernoulli.__init__ (from tensorflow.python.ops.distributions.bernoulli) is deprecated and will be removed after 2019-01-01.\n",
      "Instructions for updating:\n",
      "The TensorFlow Distributions library has moved to TensorFlow Probability (https://github.com/tensorflow/probability). You should update all references to use `tfp.distributions` instead of `tf.distributions`.\n",
      "WARNING:tensorflow:From /home/gnthibault/.local/lib/python3.6/site-packages/tensorflow/python/ops/distributions/bernoulli.py:97: Distribution.__init__ (from tensorflow.python.ops.distributions.distribution) is deprecated and will be removed after 2019-01-01.\n",
      "Instructions for updating:\n",
      "The TensorFlow Distributions library has moved to TensorFlow Probability (https://github.com/tensorflow/probability). You should update all references to use `tfp.distributions` instead of `tf.distributions`.\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# lets instanciate our model, and use a uniform sampling of 100 hypothesis\n",
    "b = BiasedCoin(n_hyp=100)\n",
    "# lets plot the initial posterior probability (which should reflect the initial prior, as there are no actual data)\n",
    "b.plot_posterior()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1]\n"
     ]
    }
   ],
   "source": [
    "# Now we draw some actual data, that otherwise should be given as output of a real process\n",
    "nflips = 250\n",
    "phat= 0.7\n",
    "nheads = int(250*phat)\n",
    "data = nheads*[1]+(nflips-nheads)*[0]\n",
    "np.random.seed(324)\n",
    "np.random.shuffle(data)\n",
    "nb_sample=10\n",
    "sample_step=nflips//nb_sample\n",
    "cm = plt.get_cmap('gist_rainbow')\n",
    "colors = [cm(1.*i/(nb_sample+1)) for i in range(nb_sample+1)]\n",
    "\n",
    "print(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "b.reset_coin()\n",
    "# And let's see how the posterior evolve along the sample it is given\n",
    "for i, d in enumerate(data):\n",
    "    b.update([d])\n",
    "    if (i%sample_step==0) or (i==len(data)-1):\n",
    "        #plt.figure()\n",
    "        b.plot_posterior(color=colors[i//sample_step])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MCMC and the art of probabilistic sampling\n",
    "\n",
    "The previous example is nice... However in most real life problem, one is interested in finding parameters for complex models that might include thousands or even millions of parameters. It is of course numerically intractable to densely sample a high dimensional space, and assess $P(Y|X)$ for such a huge set of points.\n",
    "\n",
    "This is where MCMC (Monte Carlo Markov Chains) comes into play.\n",
    "\n",
    "Monte-carlo Markov chain method circumvent the dense sampling issue by constructing a markov chain that sample the space of parameters in such a way that only the region of the space where the product likelihood x prior is significant. If we run the chain for long enough, then the distribution of the values of the sample vector along that chain is a good approximation to the posterior."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First example: MCMC Metropolis-Hastings algorithm\n",
    "\n",
    "When given a \"simple\" low dimensional distribution, one has a good chance of being able to sample this distribution by starting from a uniform distribution and using [rejection sampling](https://en.wikipedia.org/wiki/Rejection_sampling) or some smart inverse transformation.\n",
    "\n",
    "However, when dimensionality is much higher, then it is usually a non trivial problem to drive samples according to an arbitrary multivariate probability density function.\n",
    "\n",
    "The Metropolis-Hastings algorithm describes a systematic strategy to design a random walk in the model parameter space, that would make the list of vector to converge towards the target distribution.\n",
    "Here is how [wikipedia describes the algorithm](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm):"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Metropolis–Hastings algorithm works by generating a sequence of sample values in such a way that, as more and more sample values are produced, the distribution of values more closely approximates the desired distribution $P(x)$. These sample values are produced iteratively, with the distribution of the next sample being dependent only on the current sample value (thus making the sequence of samples into a Markov chain). Specifically, at each iteration, the algorithm picks a candidate for the next sample value based on the current sample value. Then, with some probability, the candidate is either accepted (in which case the candidate value is used in the next iteration) or rejected (in which case the candidate value is discarded, and current value is reused in the next iteration)—the probability of acceptance is determined by comparing the values of the function $f(x)$ of the current and candidate sample values with respect to the desired distribution $P(x)$.\n",
    "\n",
    "For the purpose of illustration, the Metropolis algorithm, a special case of the Metropolis–Hastings algorithm where the proposal function is symmetric, is described below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Metropolis algorithm (symmetric proposal distribution)\n",
    "\n",
    "Let $f(x)$ be a function that is proportional to the desired probability distribution $P(x)$ (a.k.a. a target distribution).\n",
    "\n",
    "* Initialization: Choose an arbitrary point $x_{0}$ to be the first sample, and choose an arbitrary probability density $g(x|y)$ (sometimes written $Q(x|y)$ that suggests a candidate for the next sample value $x$, given the previous sample value $y$. For the Metropolis algorithm, $g$ must be symmetric; in other words, it must satisfy $g(x|y)=g(y|x)$. A usual choice is to let $g(x|y)$ be a Gaussian distribution centered at $y$, so that points closer to $y$ are more likely to be visited next—making the sequence of samples into a random walk. The function $g$ is referred to as the proposal density or jumping distribution.\n",
    "\n",
    "* For each iteration t:\n",
    "  * Generate : Generate a candidate $x'$ for the next sample by picking from the distribution $g(x'|x_{t})$.\n",
    "  * Calculate : Calculate the acceptance ratio $\\alpha =f(x')/f(x_{t})$, which will be used to decide whether to accept or reject the candidate. Because $f$ is proportional to the density of P, we have that $\\alpha =f(x')/f(x_{t})=P(x')/P(x_{t})$.\n",
    "  * Accept or Reject : Generate a uniform random number u on $[0,1]$.\n",
    "    * If $u\\leq \\alpha$ accept the candidate by setting $x_{t+1}=x'$,\n",
    "    * If $ u>\\alpha$ reject the candidate and set $x_{t+1}=x_{t}$, instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-18-a931a214aa38>, line 3)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-18-a931a214aa38>\"\u001b[0;36m, line \u001b[0;32m3\u001b[0m\n\u001b[0;31m    def __init__(self, prior=tfp.distributions.Uniform(0.,1.), jump_dist=tfp.distributions., data):\u001b[0m\n\u001b[0m                                                                                           ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "# Lets take our previous example with the coin toss, and now sample the parameter space\n",
    "class BiasedCoinMetropolis():\n",
    "    def __init__(self, prior=tfp.distributions.Uniform(0.,1.), jump_dist=tfp.distributions., data):\n",
    "        \"\"\"\n",
    "         Notice, that now, we assume that data are known from the beginning\n",
    "        \"\"\"\n",
    "        self.prior=prior\n",
    "        #self.initial_sample = tf.random_uniform(shape=[1], minval=0, maxval=1,\n",
    "        #                                        dtype=tf.float32,name='initial_sample')\n",
    "        self.initial_sample = np.random.uniform(0,1,(1))\n",
    "        self.all_samples = [self.initial_sample]\n",
    "        # note : tfd rely heavily on log_probs and logits and logits are \n",
    "        # undefined for p=1 and p=0. we exclude these two hyps.\n",
    "        #self.prior = tf.to_double(prior.prob(self.hyps))\n",
    "        # normalize prior\n",
    "        #self.prior = self.prior/sum(self.prior)\n",
    "        \n",
    "        \n",
    "        # Define the likelihood function\n",
    "        #self.likelihood_fn = tfd.Bernoulli(probs = self.hyps)\n",
    "        \n",
    "        # initially, set the posterior equal to the prior\n",
    "        #self.posterior = self.prior\n",
    "        \n",
    "        # set the data\n",
    "        self.y = data\n",
    "\n",
    "    def likelihood(self):\n",
    "        \"\"\" Evaluate the likelihood for a given data point for all hypotheses.\n",
    "        Here we make use of tfp's broadcasting capabilities. Indeed, the like-\n",
    "        lihood function is defined jointly for all hypotheses and the result of\n",
    "        evaluating the likelihood of a toss is a tensor of shape n_hyp.\n",
    "        Note that we convert the probability to a double precision number, this\n",
    "        is to avoid underflow when making the problems. If we had even more data,\n",
    "        even double precision would lead to underflow. In that case, we would\n",
    "        need toc rely on log-probabilities or to rescaling techniques to avoid\n",
    "        numerical issues.\n",
    "        Args:\n",
    "            y : int\n",
    "                The data for which the likelihood need to be evaluated.\n",
    "        Returns:\n",
    "              : tf.Tensor\n",
    "                Tensor of probability under all the possible hypotheses.\n",
    "        \"\"\"\n",
    "        return tf.to_double(self.likelihood_fn.prob(self.y))\n",
    "\n",
    "    def draw_new_sample(self, latest_sample):\n",
    "        \n",
    "    \n",
    "    def update(self):\n",
    "        \"\"\"\n",
    "        Update the posterior distribution of the unknown parameter with data. \n",
    "        The operation is equivalent to applying Bayes theorem, followed by a\n",
    "        renormalization of the probability.\n",
    "        Args :\n",
    "            - data : list or array\n",
    "                list of outcomes for which the posterior need to be upadted\n",
    "            \n",
    "        \"\"\"\n",
    "        # Draw a new sample with M-H method\n",
    "        new_sample = self.draw_new_sample(self.all_samples[-1])\n",
    "        \n",
    "        # Remember that the posterior is initially set equal to the prior. \n",
    "        for d in self.y:\n",
    "            self.posterior = self.likelihood(d)*self.posterior\n",
    "\n",
    "        # normalize the posterior\n",
    "        self.posterior = self.posterior/sum(self.posterior)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gibbs sampling for bayesian inference\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6fAq7ng90D/y9GyiYwnsJcVyREYdpNtmFiKqrq4GxP8mP1S7d60zUdN1nqNFGfKQ41JS6F4gBpcAq4Aml1Ota693DtG0C/h24FMhKPaCUcgCPAfcD7wHWAo8rpd4JRIHfDDRdpZTaMvD3a7XWh46x351A3sDf84COY7yOEHOOkv9pDqaU2rJ27dq1W7ZsmezrApP/kEr3umO1m6r+zdR9ht5vNJPZl3Xr1lFTU1MzZJ591lFK5dD/SXq+1rp54LXTgM3AMq11zyTcI5v+B/BpWut9A6/9FmjUWn99lPP+faBf16W8dhrwMpCrB35hSqn/Bf6mtb4tpd3QHAfr9V8BP9Ba7xrhnoOOK6VOB27VWl+llNoAZGqtfzKOH1+IOUumKsScprUe8etEprUOAm8Bq1Ne/i5w53BBg1Lqz0qprhG+/jzCbZYBCStoGPA6cOoxdHm4CFABR62UOKqRUk8C7wUeVEpdN/BamVJq40jHtdY7gQal1Av0j4D84hj6LMScJFMVQpy4ttEfODyhlLoIWAl8ZLiGWut/OIbrW6MaqbqB3GO41luAD/iqUupHwLvon67465B+rht6otb6/cO81gJ8e6TjA6/fegz9FGLOkxEHIU5cVuAA8D3gNq11bBKvHwQ8Q17zAOOeBhlY/fBh+pdOtgA3A48ARybYRyHEOEngMImsLaOH+xKz1wn8e9sGrFZKXUF/MuJDIzVUSj01UCRpuK+nRjhtH+BQSi1Nee0MYLjEyDFprd/QWq/VWhdqrS8FFgOvjHbOWAWgBtocVehJKbVIKdWmlNoy8FV8LH0WYi6SqQohTlyvA2XAD4EbtdbJkRpqrdeP9+Ja65BS6k/AvyqlPk3/qooPAecN135g5YQDsAN2pZQLiGut4wPH30F/MGIDPgeUA78aoxujFoAao9BTjdb6yjR/XCFOGBI4HK2ypqZmQp82165dO+KxdevWHfN1R5PudcdqN1X9m6n7jGa031NNTQ1wzIW7Ko+tR9NLa92rlNoJBLXWI40aTNTn6E8s9AHt9Acou6F/FAN4QWt950Dbf2Eg72DAJ4CNwO0D318DfBrIAF4A3qO17h3t5mMVgGL0Qk/nDyRHvgB8U5/oGbVCDJDlmAMGllxtAFbQv+789Sm61aqBP1+bouvLfWf2vucCMa31sSQATiullBOoAz6qtX55pvszlUZajqmU+gbwptb6v5VSXuARrfV7lVKZ9H+wCgMPAk9prTdNd7+FmI1kxGGA1roaqJ7q+1jFaaZ7nb/cd3rve5z4NvB/x3vQoJQqA/44zKErB1ZPjGbYQk8DIxm9A9f/E3AOIIGDEEjgIMQJRym1mv5ljG8AU1m2eVoMBAcXHOPpLwK3Ar+mv17D/wEopTxa68BAmwuBPRPtpxBzhayqEOIEo7XeobXO01pfqLX2z3R/ptpoBaBGKfS0VilVO/D6POD3M9B1IWYlyXEQQgghRNpkxEEIIYQQaZMchyGUUq8CxfRnmwsxXpVAm9b6ncMdlH9fYoJG/fclxHSQwOFoxXl5efNWrVo1b6Y7MtckEgkSiQR2ux273T7T3ZkSr732Gt3dQ7dnGGTO/vuyal+MVh9jvO2n4prHszT+fQkx5STHYYip2lZbQDKZJBwO43a7sdmmdpZsOu+Vaqxttefyv6/xbpmeTvupuObx7HjZtl3MbZLjIKaNzWYjJydnWh7k4XCYQCBAOBye8nsJIcSJRKYqxLSbjtEAt9s96E8hhBCTQ0YcxLSbjtGA6RzdEEKIE4n8X1VMO5fLBUA8HieZHHFDxmElk0mCweC4zxNCCDE5ZKpCTLtoNEooFCIUCuFwOMjJyUn7XGu0AhjXeWLqbd++fdLbT8U1hRATI4GDmHZut5vS0lLz9/GeeyznialXVVU16e2n4ppCiImRwEFMung8jt/vp6ioCIfj6H9iNpsNj8dzTNe2chdGYk1lAJLjIIQQU0ACBzHp/H4/TU1NAJSVlY37/NRVF9A/PeFyuYhGo2OuxAiHw7S2tgJjBxlicm3YsAGA6ur0dqdPp/1UXFMIMTFSAGqIuVygZ7qMNeIwlkAgQGtrK6WlpdhsNgKBADabjWQyicfjmdUjDlIASgpATSUpACVmgzk/4qCUUnqu/l9klnI4HGakYbQHuTWyYI0mWH+mrpiwRh1SRxxGM5FpECGEEGObk4GDUuoC4GSt9W+11lqCh5kz2tSBtULCWl5p/ZmTk0N5ebmZlrDOkWmH4581IjDWa/KfqxCz15wKHJRSNsANPND/rcrWWt8/EDzYtNay+H+ajbaCYuhowtA/LcNVmhxv9cmZ2rtCCCHmmjkVOAwEBkGl1K+BBHCeUipLa/2jsYIGpdQGYANwSnNz8zT0dm5KfUArpVBKkZubi9Z60OvQ/0nT7XYPej07O5tQKGRqNWRnZw+q3ZCdnY3WGp/PRzweN6+NRimVVv0HCS6mj9Z62HyE4UYfhBCzy1z9v2McWAD8GjhLKXW3Uuo7qt+wP7PWulprvQaoLS8vn86+zqjJrsQ4tJy01ppQKEQwGDSvW69ZwcTQ8tNZWVl4PB5cLhc9PT3E43FycnIGrbKIx+M4HI4Rcx5S7wH9oxsej2fUHAnZGEsIIcY2p0YcUjwG/D+t9bNKqVXAvwG/HMhzkMlT/v7pOjVwsNlsE/q0nUwmTY5C6kM+EAiQk5NjgoHU0YLUgk7JZJJIJEJWVpYZebDyI0pLS00iZerqCqWUCUBSEyiDwaBZmeHxeNJaminFpSZm9erVk95+Kq4phJiYuRo4RIBTlFKfAT4LfBc4Uyl1g9b6gZnt2tRLZ8h96AM9mUxOuJRzOBwmGAzi8XjMkLPL5SIYDOJ2u7Hb7YRCIWKxGL29veY+1lRDOBzG7/cTCARYvnw5LpeLrKws8zMFg0ET5KTeY2iS5bGSug8TU1tbO+ntp+KaQoiJmZOBg9a6SSl1GLgN+Get9eNKqXcBdTPRn+meO09nPj/107VVI8EacThWw31ij0ajxONxfD6fGYlwOp1EIhFaW1uJRqOUlJQA/e9TV1cXjY2NJJNJioqK8Pl8ZGdn4/F4zIiFNaqgtSYYDJrNslwu16Dpi4n+PGLmjJbrICsuhJhZczJwGPAg8JjW2voIUjNTqyqme2OmdIbch366th6yEwlwbDbboERFrbUJSHp6egiFQpSXl1NSUoLb7SYQCNDd3W362dzcjMfjIRwOY7fbaWlpIRqNUlRUZH6e1ITKeDxOfX29uUd2djbl5eXmoWP1RZIehRBi8szZwEFrfRg4bNVwmMmlmNM9dz7eIfeh+Q4wsQDHyjmIx+O0tbVRXFxMTk6OyYEAyM3NJZlM0tLSAkBxcTGRSISenh6cTqepOGklKgaDQRMcpAZiVj6EVVzK6XTS2tpKUVERNptt2J9LAompMRlVHoeem9omnRUXc71ypBCzwZz/v+ZsKPxkPcgn+pCa6AqIkc5PfRCPtfIgHamrE6yHdE5ODg6Hw+QphEIhoH8qo76+nmAwiNfrJRwOk0gkiEQitLe309TUZHIarOkJK7GyqKiIefPmUVZWZt5bn89HXV0dPp/vqJ/LyrdIXeEhhBBifObsiMNcNNyUh9b6qBoJiUTC7BVht9sHnZ+afJiRkQEMHhFJ/cQ2XO0Fy0jHtNaDCjsB9PT0kJOTM2jqIBAI4Ha7KS4uNjkPLS0t1NXVUVlZSWlpKfF4nIyMDLPSQilFKBSira0N6A8GsrKyaGtro7u7G5vNRlZWlsmlSE3MtNlsZjWHlS8xnfkPUidECDFXzPkRh7lkpFoEQ+sPWLtT+v3+o84PBAI0NjZy+PDhMe8XDAZpbm4mEAgMqokw3D211vT09JgpgezsbOx2O263m0gkQjKZNAWerGRHwIx+NDc3k0gkTIDQ1dWFUorMzEwz5WElQGZlZZGVlYXL5SISiRCPx8nNzaW0tJSysjIqKyvxeDwmMdPv95skSofDYYIYK+CZ7FoWwzlR64QIIeYeGXGY5YbOx6fmHqRuEgV/Hzmwkgm9Xq+Z77fb7SilWL58OdnZ2SxYsMBcxwoCUldWpI4ipA7pW6MGqaMKoVCIZDJJY2MjnZ2drFy5Eo/HY6YFsrKyBpWKtkYQQqEQvb29tLe3s3fvXpYuXUpVVRXFxcXYbDa6urqIRqPYbLZBSZR+v5/MzEzT16E1HaxAwHrPuru7cblceL3eYUdPpjt5VQghjmcSOMxyQx9qqYHE0FLMFrvdTmlpKa2trRw5coRQKMTJJ5+MUoqMjAwWL15MIpGgtbWVgoICU7QJMNezHtLFxcXA0UsbrdUNLS0tdHd3k5ubi81mIx6Pm4Chvr6e/Px8CgsLycnJQWtNW1ubWT4JsHDhQnp7e8nOzjajCdFolOLiYoLBoNmzwhq1SJ3mgP5pkOzsbILBICUlJUSjUZqbm4lEIixevJicnBxCodBRKz7g76MkQ4tWCSGEGJkEDjNsrAz/oSsyUoOF1GNDcw601rhcLvLy8lBKcfDgQRYsWEAsFsPtdpvpjFAoZEo8W31IDUp6e3vJyMjA6XQO+jRu7RfR3d1NZ2cn0L9SorKyErfbzYEDB+jp6TG5BgChUIju7m6ysrI4fPgwfr+fkpISsrKyKC4uxuPx0NraSldXF6eccgqRSIT8/HyTuwD9Uxp1dXUsXLjQJEU2NTXR0dHBaaedRklJCfF4nJaWFubPn09BQcGI9RxSd+4sLy+XFRZCCJEGCRxm2FjD5EOnJ4YWbrI+RVsbQ8XjcbPDZDgcNiMPzc3NJJNJ097r9eLz+SgvLyeZTB5VI8EqppRMJunt7SUSiQwqsBQOh4nFYjgcDpYtW0ZnZ6dZ/QCwaNEicnNzTX6CzWYzeQYNDQ3s2rWLlpYWzjzzTCoqKky+gsvlIpFI0NLSQjAYJJFIkJGRgcvlIhAIcOjQISKRCH19fdhsNkpKSgZNsUSjUdrb22lsbKSkpISCggKzMVYoFBo0VTHazp1i/B54YHxFWdNpPxXXFEJMjAQOMyzdGg9D8xlSWfP6OTk5BINBWlpaKCsrM6MIyWSSUChEYWGhCQY6OjqIxWI0NzebaQz4e0Jkdna2OTcnJ4f29naCwSCRSITS0lJzL2t6Iisry9ResMpOn3TSSTQ0NFBYWEgymaS7u5uuri5aWlro6emht7eXzs5OzjrrLHJzc+nq6sLn89HY2Ehrayt9fX3k5uaavmdlZVFYWEhRURFaazo7O3G5XNhsNjMtEQwGKSwsJBQKmWkTt9tNQ0MDdrsdl8tFSUmJ2bkzJydHlmVOkg0bNkx6+6m4phBiYiRwmCYjTUlYIwqpCX1Dk/eSyaTJDbAe/IBJMLRWPZSXl1NUVEQkEhlUACk7O5vKykqysrKIRCImRyA3N5fOzk7y8/PNdQOBAD6fz1zf4XCwaNEiysvLicVi+P1+s0LCKtpklYG2RgU6OzvNlIRVMtrtdpvXnU4na9as4e2336anp4eGhgZOPvlkM93S19dncg+sTa0ACgsLSSQSOBwOXn/9ddxuNxkZGYRCIRMA9PT04HA4WLx4sanXYK0k8Xg8FBQU4PP5TPAwUp4IyBbPQggxHAkcpslYUxLDPcCsegxOp9MkIBYVFRGNRk0Q0NzcTGtrKzabjeLiYvx+v5muAGhsbMThcLBgwQLa2tooKCgw9Q/C4TA+n4/6+vph+5ydnY3NZjNTIqlTHVZuhPV9VlYWra2tHDx4kCNHjgCwbNkyXC4X3d3dxONxEokEPp8Pr9dLWVkZsViMHTt28MILL9DR0cGCBQvIy8tj1apV7N+/n+7uburr68nOziYWi5nrlJWVmWWY1qqL3t5eAoGAqSJpTVuEQiEyMzOJxWKUlZXR09NjtupOXdpqrQ4ZLnAT6amurgbS/9SfTvupuKYQYmIkcJgmY01JDD2utaahoYHOzk5yc3PNFIFSimQyaT6RJ5NJEokE0B98hEIhIpEI0D9ScejQIXp6evD5fGRmZgL9W1Rbn+Zzc3Ox2+0m0HC73Xi9Xrq6uigtLcXpdJrERGsviHg8TnNzM/n5+XR2dlJYWIjNZqOlpQWn08mpp55KX18fS5cu5e233+bAgQN4PB4KCwuJxWL09PTQ0tJichOs3IxYLEY8HmehHkcPAAAgAElEQVT37t1kZmailMJutxMOh+ns7KSuro7c3FwyMzPJyMjg0KFDBINB8vPzyc3NRWtNe3s7CxcuxOPxcPLJJwP9K0VcLpd5zzo7O+ns7KS4uJh58+aZLbxHGnmQEtXpueGGG4D0H9rptJ+KawohJkYCh2ky1v4RVnEki7UU0eFwUFhYSGdnp3mo2u12+vr6gP6Hmt1uN8mBbrebtrY2YrGYGZno7OzE4XCQn59PQUGBeQj7fD5T26Grq4uDBw+Sm5vLypUrzfJK+PuyRcAswbTaBwIBKioqWLRoEdnZ2eTm5po+dHV1EY/HsdvtZrqhp6eHffv2UVBQQH5+Pl6vl87OTnJycmhpaeGNN97g4MGDaK1ZsmQJDoeD8vJy6uvrzYoQn8/HoUOHzNRJYWGhGdnIzMyktLSUrq4uADM94ff7ycvLw+l0kp2dTU9Pj+mr9XPB8CMPUudBCCH+TgKHWcSa47dKJVv1DZxOJ+Xl5TQ2NpqliNZqAusrMzOTaDRqRhna2trIz8/H6XSSl5fHggULzEN3z5497Nu3j7a2NrNSIpFIEI/HcbvdFBYWEo1GaWxsJBQKmREPKzDw+Xx0dHTQ19dHQUEBGRkZ5gGfmZlJfX09XV1dOBwOMjMzTU0Gv99PJBLB6XQSi8WIRCI0NDQQCoV44403iEQihEIhM93Q1dVFRkaGWZURi8Xo6urC7/fT2dlJV1cXBQUFZGZm0trais/nw+12U1BQQElJCcFgkKVLl5KTk4PP5yOZTLJs2TIqKipMhcvU9z11GWrqSo3p3qRMCCFmMwkcZpFgMEhra6vJJygpKcFms+FyuYjFYhQWFlJSUkJmZiaHDh0ySYmBQIDMzEyys7Pp6+sjPz+foqIiurq6OHDgAO3t7QQCAYqLi4nFYuTl5bFy5UqTNBiNRiktLaWoqIhFixYRi8XMvhHJZJL8/HxT5jkej5OZmUl+fj7RaBS3282hQ4fo7u7mrLPOor29nfr6enp7e8nJyaGvr4++vj6SySTRaJSKigr8fj/bt2+noKCAnp4eM5pi5SV4vV5CoRB5eXnE43EaGxvRWptKkvPnzycej6O1pre3l56eHvO61S+llKkRkZeXh9vtpqioyIwkWJUprYDBCiSs4MBKFIX+UQYZaRBCiH4SOMyQ0ebN3W43DofD1ECw2ttsNhYtWsTbb7+N3+835aMDgQAdHR3Y7Xays7MpLS3FZrNht9tZvHgxbrfbPNCt0YSysjIAsxtlIBBAa43T6TS1DwoLC83IQTwe56233qK8vJz8/HyTuLl48WIWLlxo8iCcTieJRML8XG1tbXR2dtLX14dSir6+Pg4cOMChQ4dIJBKUlZWZUZPe3l4zrWHtgmnVf7D2t9Ba09HRYaZwrCRNt9vN/PnzWbJkCfv376e8vJxEIkFbWxuJRMIs27QCGGukxapiaQVo1pSR1nrEwlFidJJcKsTcJoHDDBlu3txaImntu9Da2ko8HjerB6yaCtbIgpW/YE0VWJUee3t7icfjZprhjDPO4MiRIyilOHz4sFlOmUgkzHTDwoULqaurIxKJ0NHRgdfrBaC7u5tQKDRoRcKqVatoaGigpaUFgOXLl9Pb20s0GqW7u9skP5aWllJRUUF2djb79u0jmUzS0tJCQUEBJ598MrFYjNbWVjOSkZWVZWo39PX1UVhYSE9PD4WFhSxYsACPx0NDQwP79u0D+itVulwuCgoKCAQC+P1+k7dgt9sJBALs3buX0tJSk2wJmPeluLiY3t5eksmk2QxraI0HIYQQg0ngMEOGzpsnk0mzlDIcDhMMBunu7sbhcBAOh808f0FBAUopHA4HPp+Pffv2EYlEyMvLo7KykpaWFlN1UWtNIBAwyzHffPNNurq6yMvLw+v1UldXx1tvvUVXVxc9PT3YbDazgVRPTw99fX0Eg0FisRgFBQVmCefu3bvx+/2mIFNbWxsHDx7k4MGDeDweiouLaW9vJ5FImJLRVlDhcDgoKSnh1FNPpba2lmg0anbRtOoxNDU1EQgE6Onpoauri0gkYnIwMjIyTNDT1NSEw+HA6/WitSaRSODxeOjo6CAcDnPo0CEaGhpQSrF06VIz4mAVvwqFQhQXF5saENZ7P3RVhTg2qbupCiHmDgkcptBo0xFDCz9Zn3qt6otWZcXS0lJTdMna42HPnj0Eg0EWLFhgkhiVUrS0tNDX12cSBDs6OszyzY6ODiorK83QfmdnJ06nkwULFpiHs8fj4bzzzkMpxfbt2wkEAvT19RGJROjs7GT+/PmmP52dndhsNioqKigpKaG8vNwkQLpcLrN5lbWyIz8/n0OHDpkgZfny5SxYsICmpiby8/OJRCLs2bOHgwcPmlUh0L80Mj8/3zz4rSmFefPmoZTC4/GQl5dHa2sry5cvN0st6+rqaGtrY968eZSWllJSUmICGo/HQygUYseOHSxfvpwVK1aYEt3DVeYU6bEChXSnKtIJLMYbfEiwIsTUk8BhCqWzjM8q8WxVafR6vXR0dJhchHA4bPaSsJIMW1pa0Fqb7aRLSkpMiWVrJMBaLpmfn89bb71FZWUlK1asYPHixbz22mvU19eTkZFhVidA//4Se/bswev14vf7zf+Ek8kk9fX15Obmctppp+F2u+no6ODAgQPU19ebmgkej4dXXnnFFG3q7u7mzTffZPny5eTl5ZGZmUkymcTn85GRkcG+fft48803aWtrM3UkoP/Bc+qpp1JfX08oFCIUCpmiUllZWRQUFOD1elmxYgWFhYWDRhicTic+n4+DBw8SjUZZvny56X9PTw9tbW2mNLXP5zM1Laxckmg0OmjEITWws4I9qeUws0YLTCRwEGLqSeAwhYZbxjfcKIS1DNFa9tje3m6G5a0AweFwmD0pvF4vzc3N7Ny5k5KSEpNr4Pf7OXLkCPF4nMOHD5skRbfbTSKRICcnxzxAc3JyOHz4sMmdyM/PJxgMUldXZypFptZGyMjIoKOjg+7ubmw2GytWrDAbWzU2Npr9KKzNqjIzM00JaGsHSuu6ra2tPP/88/j9fvO+VFRUcMkll3DppZdy8cUXU1hYSF9fHzt27ODFF1+kpqaGrVu30t3dTWNjI7///e+58sorWbBgAZ2dnWZ7bWuEwypiBXDo0CHi8bjZOdPazbO0tJTy8nLC4TDFxcWDkiGtTbGSySStra1mmehY9TiEEGKuk8BhCg23D8XQUQi3201JSQlOp5NoNIrT6aS5uZnu7m6UUqbUcigU4qSTTgIwW04HAgFisRh1dXW84x3v4G9/+xvPPPOMuX/q1IfT6eS//uu/gP6HolW7QWtNXl4enZ2dLFmyxCQ2nnrqqVRUVNDa2sr8+fM5fPgwDQ0NvP322yxevJjKykq8Xi+HDx/G4XDQ2Nho8hLmzZtnhv6tqo9WaehgMMiePXvw+/0sWLCA2267jQsvvJDKysqj3r+MjAzOPvtszj77bG666SZsNht1dXVUV1dzzz338Kc//YnLLrvMvH8HDhygoqKC0tJSzjzzTJMz4nQ6aW9vZ8GCBRQXF5vgrbi4mL6+PmKx2KCdNltaWsyUjtfrNaMSsspidFVVVcfUvra2Nq02o40mWKMQ6VxTCDExEjgco7HKEFvBgmVonQDrT6tMNPRn+x84cIBwOGyCigMHDrB3714As8dCZmamWa7Y3t7OgQMHeP7559m5c+eEfqb8/HwuuugiEokE4XAYh8OBy+WioaGBjo4Oent7KSkpMZUXW1paTH2IlpYWXn75ZXJycrDb7ZSVlbFkyRLy8/M5ePAgvb29dHV1sWvXLhobG3G73Tz66KOsWrXK3H+sYWabzcayZcv4/ve/D8A999zDU089xfve9z6zCsQKAqLRKCeffDIdHR1mNUh7ezuVlZX09PSwZMkSbDYbzc3NhEIhs814Mplk586ddHV1sXr1aubPny9TE2nasWPHpLefimsKISZmTgYOSqlKwAvs1Fr3TsU9hstfSH3whcNhM0RfXFwMYIoWWQWerLnzZDJJLBYzNRVisRiLFy/G4/HwxhtvUFxcTDgcZuHChaYegrXtdDgc5oUXXiAYDJKbm8vtt99OeXk5AH19fdjtdtOnZDJpPmFbSzat5Ztbt27lmWee4X/+539YvXq1WdK4YsUKjhw5Yva5qKysJD8/H601xcXFpp5CLBYze2n4/X56enqIRCKmtLM1qnHgwAEAfv7zn7Ny5UqTBAmYPTeGE4vFTK0IgDvuuINwOEx1dTX/+7//y6WXXsoFF1xgpkOOHDlCd3c3LpfLFInav38/LS0tZGZmsnTpUlPRUill3ofi4mJKS0uBv2/ylSo1YLR+z7KHhRDiRDLnAgel1D8AdwLtQItS6tta632TfZ90Nq2yhrituf5QKGRWBqRWJgSoq6vj8OHDrFixAq/XS1FREW+//bapoJibm8vBgwfxer1mZ8iXXnqJ5557jkQiQVVVFb/5zW9YvHixuaY19TESaxoD+h+I3/ve97j99tupra2ltbWVSy+9lGuvvdYsgQwEAmRkZJCXl2d24zxw4IAJLKygxhqx6OjoIB6Ps3DhQgKBAA8//DBaazZu3Mjll19+VH9GG3Gw9uNIdc8999Db28uvf/1rnnnmGbMcs6ioyOyGefLJJ5tgwiqS5ff7UUrR1NTEkiVLyM3NNRtdhcNhFi1aRElJCTk5OaaGhlWlc+hIkuxhIYQ40cypwEEpdR7wA+AftdavKqV+BnwduD6NczcAG4BTmpubx7xXOptW5ebmmgQ7q7CTlWxXWFhIb28v4XCYpqYmDh8+THNzMytWrCA7O5uWlhazZbaVUAjQ3NxMNBpl06ZN7N69G4CbbrqJjRs3jhokpPPzfP3rX2fNmjVce+21HDlyhD/84Q8sWLCA7Oxsk8sQi8XQWptVEB0dHfh8PsrKysjLyzPLQRsbG4nFYqbvP/nJTwiFQnz84x/nlltuOeZ+Du3zz372M6LRKA8//DDPP/88Z511FgUFBbhcLrOHRWdnJ0opMjMzKSoqMkW0tNZma3ArAGxpacFms1FWVkY4HCYajZqRmczMTDwez6DtuGHY4NE+9AUhhJgr5lTgMOC7WutXB/7+beBBpVTmWFMWWutqoFoptaW8vHztZHTEWgVhLeGzPtUmk0na29vNp3RrW2mPx0MikeD1118nmUzS1NSEUgqfz0csFiORSPDyyy/zxhtv4PP5KC4u5oEHHmD9+vVj9iUajdLT00NRUdGoy9kuueQSXn75ZT7+8Y9TW1vLnXfeSVVVFZWVlWbPDKfTidvtNsmZVk6B0+nE4/HQ1dVFLBajr6+PpqYmnnjiCfx+P2eeeSb333//pJYkttvtPPjgg8RiMR599FF27NjB+vXrzRbb1rSJVcGysLCQ8vJys+V3W1sb4XDYlOu2WGW/XS6XqaPhcDiOWo45NHgcmG6RwEEIMWfNtcDhb8AuAKWUHcgETgI8QJtSqlBr3T5dnbEqQEJ/4mNpaSnZ2dnk5eURjUbp7e2loKDABAYej4fW1lZ6e3vJyMggEomQk5NDZmYmgUCAN954g7/+9a8kEgne9a538Zvf/Ib8/Hxzv5aWFjZv3kxjYyONjY0cOnSI5uZmmpqaaG/v/7HnzZvHueeey7nnnsuFF17IaaedNigPAmDhwoU8++yzfP3rX+f+++/npZde4sCBA1RWVnLSSSeZzbKsio6hUAi/309fX59JnszNzaW9vZ0XX3yRtrY25s+fzyOPPDIlBZYcDge/+93vWL9+PTU1NTz00EOcd955AJSUlHDKKaeQl5dHLBajo6PDjAB1d3dz4MABVq5cafbIKCsrM6NJ1lROSUlJ2rkMA+/lyMkaQghxnJtTgYPWOgFYiQMK6AI6tNZtSqmrgQuUUl/WWkemoz/WELa1bwRgcgPa2tpMQt7KlStNWemdO3cSCoUoLy+ns7PTFHeqra3lmWeeQWvNV77yFe644w7sdruZMqipqeGqq66io6Nj2L5Yn54bGxv54x//yB//+Eegf7+Hc845h/PPP59PfvKTVFRUAJCZmclPf/pTLr/8cv7lX/6Fbdu20draSm1tLatWrWLNmjVmI6hoNEpLS8ugqZmOjg7eeOMN6urqyMzMZNOmTWZjrbH09fXx+OOPc/bZZzNv3ry0znE6nVx++eXU1NRw+PBhuru7ze6YixcvJicnB5fLRUtLC7FYjObmZsLhsJlSys/PN4GBte+FtTvpMdRuOCEDh8985jMAPPjgg+NqP9E2E2kvhBi/ORU4pNJax4GgUuqwUuo7wHuB66YraEiVOrxt1QMoKioyFSEBs7eE0+mkqakJr9drkhBffPFFNm/eDMC//du/ceuttw66fnV1NTfffDPxeJzzzjuPc889l3nz5lFSUsJJJ51kykID7N27l5deeomtW7fy0ksvUV9fz+bNm9m8eTM/+tGPuOuuu7juuuvMtS+++GLe/e5388QTT7Bx40ZeffVVXn75ZXbt2sW5557L2WefjcvloqenB7/fT319PW+++Sbd3d3mGj/96U9Zs2bNoBUUo7n11lu57777yMrK4ktf+hI33XRTWvkbK1asAPoTFtvb280qjMOHD5Ofn28SR61y1MuXL2fJkiVkZWWZqQiXy0VbW5tJapWkx/RVV1cD6QcOVvuJtplIeyHE+M3ZwEH1T6RnABcO/Hmx1nr/VN9Xa22GtYPBIK2trWab60AggM1mIysrC5/PR3d3t9mjYv/+/UQi/TGN0+mkqKiIefPm8bOf/Yynn34agO985zv88z//M+FwGOj/ZP75z3+ehx56CIAbbriBr371q2bqoampyZRXtqZMMjIyuOiii7jooovIz8+npaWFbdu2sWnTJp577jk++9nP8tvf/pY77riD1atXm5/r3e9+N+9617t44oknuOOOO9i9ezebN2+mtraWoqIiDh06NKhsdHFxMe9973u58sored/73mc2lcrIyBjxvYtGo9TU1HDfffdhs9mIRCLceeed/PKXv+SWW27hmmuuGXaqIJFI4HA4WL58uXlfVqxYYZa+NjY20tXVRVlZGVprlFLYbDYz3eJyucjPzzfvVSwWM7uSWoGeEEKIfnM2cND9a/tiSql/A7ZNR9CglCIUCg1aZmlxu93E43G6urro6uqiu7vbPGztdjs+nw+lFEeOHKGzs5N9+/axZcsW/vKXv6CU4j/+4z+4/vq/Lw7x+/184hOf4MUXXyQzM5O77rqLj3zkI4PuGY/HR01EtDap+tCHPsQHP/hBHnvsMW677Tb+7//+j/Xr13P77bdzww03mEBEKcUHPvAB3ve+9/H000/zr//6r+zZs8dMj1RVVXHppZfy/ve/n6qqqqMeuE6nc9TAobOzky996UsAfOMb3+D888/n1ltv5bXXXuNLX/oSv/vd77jrrrs466yzBp1nLdWsqKigsLCQ9vZ2Ojs7ycvLM4HBggULKCgoIDs7m1gsRl5eHi6Xy6yqaG5upqurC4/HQyQSIZlMmu3ErbwHMbrxVmu02o9WcTKdNhNpL4QYvzkbOKT4tZ7GnW+G1newyhTbbDbC4TB79uwhPz8fu91OKBTi4MGDKKXIzs6mt7cXv99PKBTi2WefZffu3dhsNu6//36uuuoqc49du3bxsY99jIaGBkpKSnjwwQd55zvfOaF+K6X48Ic/zAUXXMC3v/1tHnvsMb72ta+xadMm7r33XvNp3vqZrrjiCj784Q/z5JNPEggEuOSSSygtLaWvr29QfYjxuOWWW2hsbOTMM8/kpptuwuFw8Nxzz/HQQw+xceNGtm/fzsUXX8xHP/pR7rjjjqNyJpRSrF69ms2bN9PS0oLb7aa9vd3s71FXV2e2zy4oKKC4uNgECjt37qS0tJQVK1ZQVlZmNuPq6ekxm4lN8P0d13Lf49GaNWuOqf1o/3mm02Yi7YUQ4zfnP0ZNZ9AAf6/vkJpUZ31atba71loTCARwOp0kEgkyMjLo7e3FbreTl5fHvn372L17NxkZGfzhD3/g4x//uLn+k08+ySWXXEJDQwOrV69m06ZNEw4aUhUVFXHvvfdSXV1NWVkZr7zyCueffz733nvvUW3tdjsf+MAHuPrqq021xWP16KOP8sgjj+B2u7n//vtN8GGz2bj66qvZunUrX/3qV8nMzOSRRx7hyiuvJJlMHnUda3rlzTffNOfbbDbi8Tg7d+5k+/bt7Nq1i6amJvbu3UtTUxONjY10d3ebh421bLWystIU8RruXuOhta7WWq8Baq3KnkIIcTya84HDdEgtH536WiAQMDUagsEg2dnZzJs3z4w+aK05+eSTSSQS+P1+2tvb2bZtG1u3bsXpdLJp06ZB0w87d+7kE5/4BMFgkI9+9KM8/fTTaa9UGK9LLrmEbdu2ce211xKLxfj617/Oww8/PCX36ujo4KabbgJg48aNLFmy5Kg22dnZfOtb32L79u04nU5ef/11Ghsbj2p35plnAtDe3o7dbuf888/n3HPPpbu7m/3793PkyBGzVNXn89HZ2UlhYSFVVVWccsop7N+/n23btnH48GGzK2kwGDR5JUIIcaKTwGESWPtWpD5crL0qWltb8fv9BAIBent7KSwspLS0lPz8fAKBAHl5eWb4PJFIsGvXLgBuvvlm3v/+95vrRSIRrr/+emKxGNdddx0///nPB+3dMBW8Xi/33nsvP/jBDwD4whe+wOuvvz7p9/nmN7+Jz+fjvPPO49Of/vSobRctWkReXh7AsCstLrzwQpRShMNh+vr6yMnJQWtNS0sLWmsWLVrEqlWrqKqqYvXq1aZC5KJFi/B6vaY6ZGFhIdA/SmRV/LQCwImOPgghxPFMAodJ4Ha7hy1DXFxcTHZ2NgUFBXg8HrKysujt7cVms9HX10d7ezvt7e04HA7KysrweDw0Nzfjdrv54he/OOge3/rWt9izZw9Lly7le9/73rirL/r9frZv3572kshUGzZs4JprriESiXDVVVeZYlKT4fnnn+dXv/oVTqeTe+65J62fy6qJkVrp0WKNHsRiMfbt28fevXvx+Xzmd1RSUsKSJUtYuHAhiUTCbLzV2tpKTk4Op556KqeccorJabCmOoLBoAkAZfRBCHEik8BhEqTmMqRugmTN08diMfMgCgaD7N69m4KCAlasWMHKlStZtmwZXq/XTAV8+tOfpqioyFz/mWee4b777sPhcPCLX/xixI21hmpvb+cPf/gDn/rUp7j44ou5/vrrueyyy/j9738/aOnkWJRS3H333VRVVXHo0CGuv/564vF42uePJBqN8vnPfx6Ar33tayxbtmzMc6wNtJRSI74P7373uwFobGwkHA4TiUSw2Wz09vZSX19PIpEgkUjQ3d1NIpHA6/WSlZVlArqenh6zUiQejxMIBHC73RQVFR0VIAohxInmRFhVMalSt1Uebstln89nHqrWA8blcpkh7m3btvG3v/2NJUuWcPrpp5uNoOrr69mxYwcZGRl88YtfNFtMt7W1ccMNNwDwpS99ifnz59PW1mbu+dxzz5Gbm2u+7+rq4pVXXuFvf/sbe/bsMa87HA5yc3NpbW3lu9/9Lvfeey9XXnkl69evH7YMdCKROCpL/mc/+xmXXXYZNTU1fPOb3+SOO+446ryhW3kPPZY6onDXXXexf/9+li1bxhe/+MVRpwCsxMXU0Qbr/bf2BLFcfPHFfO973+PIkSNmD42cnBxTdtpaFmoVenK73bjdbjo6OohGo+Tl5ZnAze/309LSQkVFBV6vVwpCCSFOeBI4jJOVzwBHb3AUDodNUSHoDxisja06OjpMwGGtrNi9ezfxeJzMzEyefPJJtNZcc801zJ8/H+h/IN544420tbVx1llnmQBiOIlEgl/84hds2bLFPGRtNhvLly/njDPOYOXKlTidTnbv3s2zzz5LY2Mjv/zlL9m0aRMf+tCHuOyyy8b8JF1RUcF9993HP/7jP/KjH/2I1atXc8UVVxzT+/jWW2/xwx/+EIAf//jHZsOvsYw2TWE599xzycrKMjUzEokES5cuxev10tjYiM/nY/ny5SxevBibzcaBAwc4cOAAsViMwsJCs/9HMBikoKCAZDKJy+WSYlBj2L59O5D+skyr/UTbTKS9EGL8JHAYp6F1GoYes+bC29racDgclJaW4na7aW5uZt++fTidTtauXUt7e7sp9tTZ2cnzzz+PzWbjy1/+srneL37xCx5//HFyc3P54Q9/OOon+R//+MfU1tZit9tZtWoVZ599NolEgsrKykFtTz/9dE477TTeeustXnzxRfbt28dvf/tb/vSnP3HjjTdy0UUXjfrzn3POOXzzm99k48aN3HDDDSxbtozTTz99XO9hJBLhn/7pn+jr6+NTn/oU559/ftrnWtNAo33yd7lcXHDBBWzevJmmpiYKCgrMHhWxWAyv10s0GiUUClFRUcE555xDR0cH8+fPp6enh1gsRkNDA5mZmXi9XjweD4FAwOyOKYY33qJL6bSfimsKISZGPj6N09DaDEO53W4WLVrE4sWLB+UpZGVlUVxcjNaaaDRqNogKhUI8/vjj9PX1ccUVV7B06VKgPy/iG9/4BtC/RNEahRjOY489Rm1tLdnZ2Xz729/m5ptv5oILLiAzM3PY9kopVqxYwfe//302btzIypUrCYVC3H333ezdu3fM9+CTn/wkV199NeFwmFtuuWXM9kP95S9/4Y033gDgc5/7XNrnvfbaa2zYsAHArKwYyTnnnANgkk+tLcArKiqoqKigq6uLXbt2sW3bNkKhELm5uSSTSbKyskxtDStnxeVyjZrbMNxyXCGEmKskcJhE1jbaTqeT8vJyM0IQCATw+XxorWlra+PFF19k69at5hPskSNHALj22mvNtV544QW6urpYsWIFH/zgB0e8Z3d3N0888QQAX/7yl48aYRiNUop3vvOdfPe73+UDH/gAyWSSu+++20y1jHbeD6w2s1sAACAASURBVH7wAzIzM3n++ecZbyXECy+8kEWLFgFw0UUX8ZWvfIVDhw6N2L6rq4tbb72Viy66iO3bt1NWVsZtt9026j2s/A6Px8P8+fM57bTTWLVqFfn5+XR3d/PWW2+ZuhmvvvoqoVAIt9uN1+vlpJNOoqCgwOxdEY1GRw0Wh1uOeyLasGGDCewmq/1UXFMIMTESOEyi4ZZlwt8DipycHBYtWsQZZ5xBRUUFWmuzJNDtdg+aJrCCgX/4h38Y9Z5//vOf6e3tpaqqyuwOeSyuu+46Fi1aRHNzM//5n/85Zvu8vDze8573oLXmv//7v8d1r6KiIl5++WUuv/xyIpEIDzzwAO94xzu48cYbByV0JpNJfve733HmmWfy61//GpvNxhe+8AVqa2u55JJLRrx+Mplky5YtAMyfP5/Ozk6Tb6K1Zv/+/bS2tuL1es223Xa7ndbWVpxOJ3a7nezsbHJycsjJySEWi9HU1DTiSpKRfu8nmgcffDDtnTHTbT8V1xRCTIwEDpMkdbWFtXJAa00oFKKgoACv10ssFkMpRTQapaGhgc7OTv76178C/UsIrdUNWmsTOFx22WUj3vPtt9/mxRdfRCnFxz72sQn1PyMjg5tvvpmMjAw2b97Myy+/POY5VmLkpk2bxn2/7OxsfvOb3/Dyyy+bvj/88MOcf/75XH311Tz66KOsX7+eL3zhC7S3t3PuueeydetW7rzzTjwez6jX3rVrF36/H4/HwwUXXEBpaSm5ubn09vaagk7WjpoLFiwgNzeXV199lW3bttHQ0GCuY40wvPXWW9TV1eH3+8f9cwohxFwjyZGTJHW1hZXxb71ms9nwer1mP4pt27bR0dFBb28vb7/9NtAfOFhD3Xv27KG+vp6ioiJOO+00duzYMeww+caNG0kmkyxfvpy6ujrq6uoGHW9tbR30CX4on8931GsXXnghzz33HD/5yU9YtWrVoDwNi/WJfO3atbjdbrZu3cqTTz7JRRddRCwWGzGJ08rtSFVZWcm9997LLbfcwk9/+lMeeughnnrqKZ566ikASkpKuP3223nve99r3sOhEonEoCWlzz33HIBJinQ4HDQ2NlJUVER+fj5Lly4lkUjQ3NyMw+GgoKCAQCBgdte0lnf6/X6cTif5+fk4HI5B70VqoJj6uxdCiLlOAodxGK2GgzVMbZWBTiQSdHV1mToBVrGhjIwMKisrCYVC7Nu3z+y3sH79elMw6umnnwbg0ksvJTMzE5fLdVSi486dO3nhhRew2+2cccYZww6jb9++3Xw6t6ZFUneuHG7Z3FlnncXBgwc5ePAgd999N/8/e28e5dZVJ+p+W3NpLJVUUqnmcjw7JCaOAyROQkICCRDgQZqbZmoeDQ6XoYFLVnjN0AxNGpLbTa8mjCFNOrcvdMOLAzSBsLgv4MyYOI4TO8HxUB6qXJNr0DyVpP3+UJ2NSpZqsKtsV3l/a2mV6pytfbakrbN/+zf+0z/9U02hxW63Y7fbue222/jKV77C7bffztNPP01DQ0PNVNAAHo+nblnt9evX8+1vf5svfvGLfOc73+GnP/0pb37zm/n85z+P1+sll8vVdfYslUrT3pdhprBarezbt4/GxkaEECoLpJSSzs5OXC4XHR0d5PN55ccA5ciNZDLJ0NAQLS0tdHR0TPvO6+XrON9NFRqN5vxAmyrmwUxOcCaTaVpSoqGhIXbt2sWRI0fo7+8nkUgwPDzMiRMnSCQStLS0qMyGGzduVLZ2QO22K2tVVCKl5Fvf+hYAq1atmjGnAZQXwsOHD3PgwAFVs6EeQgje/OY309DQwDPPPMMDDzwwY98f//jHWbt2Lb29vSovw+lgaBheeukl7rrrrlnNEtVMTk7y2GOPAfDKV76SVatW0dbWhtvtVmYJk8mE1+vliiuuYPXq1fh8PsLhMD6fjyNHjtDb24vD4aC1tZVQKHSSY6RRW8RisSiBYibnSY1Go1lO6DvdPKjnBGeE4xWLRRKJBIlEglKphNVqpVQqqToVbrebVCrF8ePHaWpqUtELlQLCxMQEzzzzDDabTaVOrua5555j9+7deL1e1q5dO+OYY7EYfX19SsU/MTHB0NDQjK9xu93cdNNNAHzve9+bUQ1v1JgA+Od//uezrrJ/9NFHSSaT+P1+Nm/eTFtbG21tbbS2tuJyuXA6nYyNjRGLxTh+/DiJRAKr1UpHRwdWq5WmpiYaGhpU/ZBKTYaBEX0RCoW0sKDRaM475mWqEELcIqX8z8UazLmOsbOsxtBEJJNJEokEAM3NzbS1tTE+Ps7Q0BAmk4ljx44pjcXhw4eV5uKiiy5SfZ04cQIpJR0dHXWTDf3xj38EyhEXM9WMKBaLKj11IBDA5XJx7NgxotGoyo5Yj7Vr17J69Wr279/P0aNHZ0zy9JrXvIaWlhaGhobU+z8bSCn58pe/DMC6des4duyYqnTZ3d2N2+1meHiYoaEhBgYGCIVCXHzxxUQiEfL5vMrn4PF4ZjQ71JsH5xPzLbJWi0suuWRB2pxOe41GM3/m6+Pwv4QQW4GPSSlfWowBLUWMRcZms6mF3O12s3r1al566aWTVOChUIhMJqN2583NzaqvuaRU3r17N1BWxT/zzDN128XjcYrFoqrUKYTA7/czMTFR0zGymra2Nvbv38/g4OCs2SEN7clsZpPF5MEHH+Tpp5+mubmZjo4OlTsDyjUnfD6f+vzb2tpob2+nu7sbk8mE1WplfHxchV6mUim6urpUMTBtilh4nn322QVpczrtNRrN/JnvnXATYAWeE0L8oxDi/N52TWHsQI1d6+joKOl0mmg0SjweZ+/evfT395PL5ZBS4nA4GBwcVEJCpeAwMTEBUFcjkM/nefHFFwG4+OKL645paGhIVZFsaWlRO8RgMKgyVvb29s74viKRCAADAwOzfgbGezlbDoLZbJbPfOYzQDmtdjabJZFIIKUkGo1isViYmJhASsmaNWvo6elh7dq1DAwMcPz4cfr7+ymVSthsNrLZLIODg/T19TE4OEhvb69Kda2ZjpSy7kOj0SxP5qVxkFLuAa4UQvwVcCfwl0KI26SU/7Eoo1tiOBwOVanSWIQsFgv5fB6TycS6deuQUjI+Po7dblcah2AwSDqdxmQyqSyMjY2Nahff29urFv79+/eTz+dpa2tjcHCQ4eHhk7Iulkol9uzZo8YUi8VOGmc6neZXv/oVl19+eU21c09Pj4qO2L9/P4cPH1bn7HY7PT096v98Pq+cBfP5fN1iVblcbkYV90yLzUxhnoVCge985zscOXKEUCjEhRdeSDweRwhBR0cHTU1NRKNR+vv7SaVS5PN5+vr6ePHFF3G73eqzttvtNDc3K61JKBRiZGSEVCql00kvEU51fmk0mrlzSuGYUsr7hRA/B/4B+PcK88WLCzq6U0QIsQZoAnYCJSllcTGvZ4RpOhwOlW0Qyv4Kfr9fOVX29/ezb98+MpkMmUxGLaTBYJBMJoPJZFI+AuFwWIV2+nw+tYgbOQouvvhi9brqXf7Ro0eV0GFcqxZGyGFHR8dJ54rFospEmUgkTqqVUWmSMAQFI7lSvXBMIUTdcMzZsFgsNR0VoawR+frXvw7A9ddfTzQaRUqJ1WolkUhQLBZV8TGfz0exWOTIkSNMTk7S2dlJe3s7/f39NDY2YrFYVNSF8bwyWkZTn8rEZwvVfr59ajSaxeeU8zhIKWPAR4UQ9wL/i7L54m7gS1LKs+YhJ4R4O2WB5vjUY6cQ4t+klIvm7l/pHGlEURiLp+FsNzQ0xJ49e8hkMqqYEpSTFFXupMfGxoCyM2MtDDPFhg0bap7PZDLTsh/Oxssvv0wkEqm5KLe0tADMWovibJspvvSlL5FMJmlubsbhcKhcEuPj42QyGbxeL36/HyEEXV1dtLS0sHr1al5++WXWrl1LU1OTKneeTCZJpVJKC1QqlfD5fOe9M+S5jiFY1BI0FsKRU6PR/Jl5b6OEEFYhxGVCiL8RQvwY2AZsoCyEfBTYJ4SoX5VpERFCWIH/Bvy1lPJ1wC+ADuB2IcT8EgLMQmVFREOjEAwGVejl+Pi4CsscGBhgYGCAbDaL1+tFSql26ZX+DfBnwaGpqemka0opeemlsk/qhRdeWHNcvb29lEolQqHQrO/B5/ORy+XqChqG4DAyMkKxWF9pY5hczobg8MADD3D//fer9NEjIyNkMhmGhobo6+tjfHyciYkJhBD09PSwcuVK5ejY2tqqhAOn00k2m+XYsWMMDw8zPj6uwy41Go2mBvMNx3wKeCVgA0rA88AvgSeAJ4Ek8EXgASHE30gpv7eww50TXmDV1Hh+BowCbwLeJYT4vqyj85wyt2wF1syl2mNlmmFjwRRCKBW+kZ44FosxMTFBY2MjGzduJJ/PK/8Ho59KDB+JerkWjN1TvYXcWODmEhZpRAzU25EZfdTL2Gjwwx/+EGDWyIuFpFQq8fd///fccccdQDmk1XD8NBwZI5EIl156KZ2dnQghppmR/H4/2WxWhcm6XC7C4TDd3d2k0+maqbY1Go1GM39TRRL4GuVF+Q9SylSNNp8WQgwDnwXOqOAgpZwUQnwD+LgQ4pCU8nEhxBNAG/BG4PszvPYe4B4hxPZIJHL1bNeqTDNsRFAkk0mCwSDZbJaGhgaam5uxWCykUilaW1sZGhpidHSUjo4OUqkUZrOZvr6+aT4Ir3rVqwDYsWPHSdcUQnDRRRfx9NNPs3v3bt7whjec1GbVqlVK3T4buVwOv9+vSlxX88ILLwBls0g9x8TDhw9z3333IYRQUQ2LTTKZ5AMf+AA///nPMZlMbNy4kXXr1uHz+bBYLLhcLtra2nA6naxevZqenh4mJiYYGxsjGo0q/wWbzaZMRiaTCYfDQT6fV1EoqVRKfa9a66DRaDRl5htV8fo5Nn0M+Pr8h7MgPA6sAd4rhBBSyseAHwshPghcDOxeiItUJgFyOp0kk0kKhYLywg8EAkxMTJBOpxkdHSWZTE7L9zAyMoLb7SYWi3Ho0CG1eK9fvx5gWhRDJRs3bpxRcLBYLLziFa9g165d5PP5Gd+DxWJh48aNdRdEQ3CoTFBVzR133EGhUOBd73oX69evn9GkcSrk83kOHTrESy+9xKFDh3j55Zd58skn6e3txefzcfHFF9Pd3Y3f76etrY1oNKrSe5vNZiYmJtixYwdtbW1YrVZ8Ph/Nzc2qboUh2AGMj4+r6Akjy6TxvabTae3noNFoNCxekavngbcuUt8zIqXMCiF+BEjgb4UQa4EcEAZmt0GcAiaTiVAopGoYpFIpldbYEByam5tpbGykpaWF5557joGBAVX8av/+/bS0tGA2mwkEAgghGBwcJJlMYrVaOXHihFrcjZoWu3btUrUuatXO6OjoUJU369HZ2Uk8Hq+ZJtrn87Fr1y7VV2XCKJvNRj6fJx6P8+CDD2KxWLjttttUWGY9X4disUg6nebhhx/m5z//OTt27MBsNk8r5GWz2XA4HJhMJo4cOcLhw4drCiNut5srrrgCp9NJJBKhpaUFp9OJy+Walh9jYmKC3t5eTCYT1113HY2Njaq+RCQSweFwkEwmicfj5PN5vF4vDoeDVCqFw+E41QJWtdUzGo1GswxYFMFBSpmh7PtwVpBSTgghfgC8BNwKZIH3SCmHF/pahpMkoHakhhp8fHycbDZLOp2moaGBfD7PxMQEfX197N+/Xy1GBw8e5MYbb8RkMqmFcGBggGg0SldXF+vWrVNhjBs2bODuu+9meHgYh8PBq171qrqFoH7605+q6ps9PT0EAgH27t1LNpslFApxww031H1fDoeDvr4+rFYrN9100zQ/Byklbrebp556ilKpxObNm1XNDKNGRyXj4+P88pe/ZNu2bTzyyCM1S2PXQwiB1+slHA5jt9tVCmmXy0WxWEQIobI9FotFenp6sFqtTE5OkkqlCIVCHDt2jIaGBhKJBNlsFqfTqcwUhtZhfHycZDLJypUrsVgsJ0XJzNVMMSXknJeCw/e/X9cSeMrtF6NPjUZzeizbstpSyjzweyHEY+V/5aJk8Emn0wwPnyyPWCwWwuEwxWJRJYIaGBjA4/HQ1NREW1ub0grs379/2ms7OjoYGBigr6+Prq6uaeeEEGzevJmHHnpoxnTTUFa39/T0cPjwYY4cOcLAwAC5XA6Hw0FnZ+eMr+3v70dKyYUXXljXOfLpp58G4NWvfnXN8zt27OCLX/wi27dvV6m4hRAEAgFaW1uVL4FRZdLlcnH8+HFGR0dxOBw0NTXh8Xjo6uqiWCxy9OhRfD4fr3jFK5iYmCAWi+FyuWhoaGBsbGyaxiAWi9HQ0ECxWMTr9TI+Ps5LL72E2+1WeRlcLpcS9jo7O8lms8rBEsrCkyFozJUpX5BFzRtyrrJ169YFb78YfWo0mtNj2QoOBouV/Kky6VM4HFbHDSGiMnFQqVRi3759TE5OEo/HWb9+Pe3t7USjUbZv386BAwem9d3R0cGOHTvo6+ureW1DcHj66adnTDsN5eyHRgplY6e/atWqus6OBkaI5qZNm+q2+cMf/gDUFhwymQxvf/vbGR4eRghBKBTioosuYsOGDQwNDdHU1EQ4HCYej+PxeGhtbSUcDrNr1y6OHj2Ky+UiGo0yNjZGU1MT6XSasbExXC4XdrudyclJxsbG6OzsJJFI4HK5aGxsVN+LxWIhm80SiURobGzEZDLR1NSE1WrF5XIxPj6u0oM3NDTg8/nUZ2UIMUYkxilwXgoOGo3m/GDZCw6LRWU4pmEqqExLbOxSk8mk0ioYmQz37t2Lw+FQ2oTdu3czOTmpdvYXXHABUHZO/Mu//MuTrn3ZZZdhs9nYuXMnTqdzxsUdyoKIlFJpPmbbQcfjceXfcPnll9dsMzY2xlNPPYXJZKrZ5itf+QrDw8N4PB7e9a53YTabVcVKI2tmIBDAbrfT0tJCe3s7Q0NDjI2N4fP5MJvNNDU1IaVkw4YNTE5O4nQ6VfTE008/TS6XU/4Mdrsdv9/P0NAQ8Xgcs9mMx+PhwgsvxOPxsH//fiYnJ+nu7lZahUKhoJwkC4UCo6Oj05wjF5L5hvsuRe655x5g7rv+ubRfjD41Gs3poePLThEj6VPlIiyEwOPx4Ha7SafTFItFVUbbMA94vV5SqRT9/f1Eo1Gam5tJJpOqVDbAVVddBcD27dtrXtvv9/M//sf/AODJJ59kdHR0xrEaGRMjkchJCaeqkVKyfft2Jicnuf7669m8eXPNdg8++CCTk5Nce+21J/X53HPP8Y1vfAMhBG9605toa2vDZrMxOjrK5OQkxWKRwcFBnnrqKfbu3cvY2BjPP/88f/jDH8jlcthsNoLBIFJKnE4nhUKBtWvXcs0113DRRRepbJxGXoZIJEIwGMTtdtPd3c3q1atxOBwqysXA0Cbk83kymQyjo6McO3ZM+TEYCbzqCVaVSb/mi5TyHinlpcCzRvGw5catt97KrbfeuqDtF6NPjUZzemiNwyliODKm02nlpW9g5HXI5XLk83mam5vp7u5GSqnCC81mM42Njaxbt44TJ07wyCOPcOWVVwJl1b/dbueFF15QmSSreetb38oLL7zAr3/9ax566CHe9a531a0RMR/27dtHf38/DQ0NfPazn63b7ic/+QkAt9xyy7TjhUKBW2+9lWKxyObNm7nyyiuJRCL09vZitVpV1c+hoSFVG6Krq4ujR4/idDrxeDxEIhEmJyeVQ+OLL76o0kgnEgnS6TQrV65kYmJCCV+BQIBisUggEMDr9VIqlRgbGyOZTJJIJAgGg/j9fkwmk8qxEYvFGBkZUf4UZrN5Rk1DpZZJh2ZqNJrzFS041KBYLFIqlWb1pK9eSIyklEb8fz6fJ5fL0d3drdIZHz9+XBVscjqdbNmyhccee4xHHnmEz33uc0DZsfKyyy7j8ccf5/e//z2BQKCmT8LWrVt58sknmZiY4Fe/+hVXXXXVtCyQhUJhxnLQ4+PjJ72fJ554AoCrr74aq9V6UmVNKPtxPPXUUzQ0NPDGN75xWrjk3Xffza5du3C5XLz5zW9WaZ0tFguxWAwppYoUaW1tZXx8nKamJk6cOKH8F4aGhnC73bS3t+P3+5mcnKRQKBCNRrHZbDidThU9kc1mKRaL2O12MpkMx44dY+3atYRCIVpaWvjjH/+oBCGr1YrD4UAIob7bYDCoQjlno1ZopuFTUS08ajQazXJFCw41MPINzLSrLJVKlEol3G43Tqdz2gJiOAMePnyYfD7PsWPHVE6GCy64gI6ODpUHIRaLYbVa2bVrF+l0WtWoeN3rXsfjjz/Ok08+yWc+85m6lSG//OUv89nPfpYjR45w44038ta3/jl9Rnd3N62trXXfQ2VVTCklX/7yl5mcnOSyyy7jox/9qPK1qOahhx4CylqPSjPFoUOH+Id/+AcAbrjhBtrb27FarZRKJVKpFC+//DJut5vOzk56enpYs2YNR48eJRaLMTAwgJSS7u5uVWV0bGyMyclJtbAbkRmpVEo5NkopCYVCmM1mFZoZjUYpFAoEg0G6urpUZk4jMiMcDlMqlZRTZktLi1r0q7/HSiqTfhntaoXjajQazXJGb5FqYDabZ92BptNpksmkcq6rrJBpOOx1dHTgcDjI5XKMjY1RLBaZnJzE5XKxYsUKhBD09fURCASUb4HBa1/7WgB+//vfzziO1tZWPvnJTwLwgx/8gD/96U+n9J63b9/OH//4R5xOJx/72Mfq1q+QUrJt2zaAaY6bUko+8pGPkMlkWLNmDevXr8dqtXL8+HFisRjFYpFMJoPD4QDKWpXDhw/T2Niosm3abDaEEDgcDvVcCEEkEiEcDrNy5Uqg/Nk3NjaycuVKVq1aRTAYxGq10t7ezubNm2lvb1d+H36/H4/Hw4oVKwgGgxQKBYaHhzGZTLS1tU0TGoy+Db+Umah2jj1blUE1Go3mTKMFhxqYzeZZ1c7VzpFGtsNSqaQWnnw+T2NjI3a7nUgkorIitrW1qQqNxWJRZYP8P//n/6j+L730UtxuN/v3769b8Mrgqquu4m1vexuFQoGvfOUr/O53v1PVN2dDSsmePXtU4pwPfehDMxZ42rt3LwcOHCAYDHL99der4/fffz+/+93vCAQCbNmyBZPJxMjICPv27SORSNDS0kJnZyddXV34fD6OHz/OyMgIzzzzjEq/3dXVhcPhUP4fK1asoLu7G4/HQ1tbG5FIhLVr1xIOh2lra6O1tRWn00kikeDgwYOMjY3h8XhobGxU78FwZDR8KYyU05X5HGb6XuthtDMcNLWZQqPRnC/ou90pYqitjQUjm80qvwgjCVGhUCCTyWCz2ZRqW0rJ2NgYQ0NDRKNRnE4nl156KVB2ODRqVFitVq6+ulxrywgxm4m//uu/ZsOGDUxMTHDXXXfxvve9j9///vdEo9Ga7ePxOA888ABbt27lM5/5DPF4nI0bN/L619cvR2JUpAR45zvfqTJE7t+/n0996lNA2TfC5/MxPj6O1+ulpaVFpXnu7Oykra2NXC6H1WolGo0ipcRqtbJ69Wp1LpvNEovFVB0Jw0fC5/MRi8UIBAIkEgkmJiZUiKnxXcRiMZUZc3R0lEQigc/nw+12q2qgFoulrkal+nutx1zbaTQazXJD+zgsEIafg/E8nU5z4sQJEokE0WiUcDiM1Wqlv7+fY8eOYTKZVLjh6tWrec1rXsPTTz/Nhz/8YR5++GFMJhN/93d/x29+8xvuv/9+3vKWtygBoxZWq5Wvfe1rPPLII/ziF7/gyJEjPPbYYzzxxBNccsklXHvttfT09LBv3z4ef/xxnn/+eeXU2NTUxPXXX8/NN99cd0EFuO+++3j88ccJBAIq4iKTyXDLLbeQTCbp6uqivb2d8fFx8vk8J06cwO/34/V62bhxIxMTEwghVOpnh8PBkSNHCAQCdHZ20tTURH9/P/F4nKGhIbq6urDZbORyOaSUjI+Pc+LECWw2G5OTkySTSTZs2IDValUhn0a9kFwuNy2xEzDNJ0Wz8NSpWH9a7RejT41Gc3powWGBMHwd4vG4CtUMh8M0NDSomgiZTAan00l3dzcWi4Vdu3aRzWYJBAJ84AMf4ODBg2zfvp17772XrVu3snHjRj796U9z1113cfvtt/PrX/9a+QjUwmazceONN3LDDTewZ88e7rvvPl5++WV27tzJzp07p7UVQnDZZZdxww03sHnz5lkzSR44cICvfvWrANx1110qW+anPvUp9uzZg9frZcuWLVitVkKhEJlMhnw+z8GDB+ns7GT//v14PB4lQEkpicViHD9+HCklra2tFAoFQqEQVquViYkJ2tvb6ezsJBaLkc/n6e/v58SJE3R3d3PBBReQz+dVWuhSqYTP58Pj8TA4OEgsFqOlpUWNc2RkhEKhQGNj44zCkUaj0WhmRgsOC0hluJ6RrrhUKpHJZIjFYiQSCSYnJ1WI4ejoqKrC2NzczGWXXcavfvUr/vZv/5bXv/71dHd387nPfY5t27Zx8OBBvvnNb3L77bfPOg4hBBdddBHvfOc7cTgcPProozzxxBMEAgGSySRXXHEFl19++YzlsiuZnJzk4x//ONlslne+853ceOONQDnj5b/+679it9t5y1veonwD/H4/DQ0NpFIpvF4vLpeLkZERxsfHMZvNJBIJhBCqvoRRUdRqtWI2m1mxYoXSFExMTGC1Wkkmk4RCIRWO6fP5lFnDEAjgzwJcNptVz1OpFIVCoW7WTB1SqdFoNHNHCw4LSGW4HpTDBk+cOEGhUMDj8WA2mzly5Aijo6M0NTXR0NCA3+8nn8/T19fH+vXreeGFF+jr6+MTn/gEv/rVr3C73Xzve9/j9a9/Pd/97ne55ZZbptWneOUrX0lDQ0PN8TQ2NuL3+3n7299OLpejWCwqJ04ol86uR+VifMcdd/D888/T0dHBN7/5TVUt8s477wTK9TCMyBEpJR6Ph2AwqHw7HA4HR48epa2tDSklxELO2AAAIABJREFUQgiSySTNzc0Eg0FCoRCrVq1iZGSEgYEBBgcH2bhxIzabTYVzulwuVffC8FVwuVzKLDE+Pk5LS4sKac1kMjQ1NSnBrLKcdjU6sdPCYKQ+f/bZZxes/WL0qdFoTg8tOCwihrnCSFMcDofx+/1MTEzgcrkYHR1VCZL+9Kc/kU6nueGGG/jP//xPfvOb3/Dkk09yxRVX8KpXvYoPf/jDfPe73+UjH/kI27dvP6l09WzUq3A5Gz/96U/52te+BsC9996Lz+dDSsm+ffvYtm0bNpuN7u5u3G63uoYQApvNRiQSoaGhgYGBATo7O9m4cSOBQIAnnnhCmXF8Ph8Wi4VSqaSEG7PZrN6fzWbD5/OpIlVSSlUbxChulcvllF+JYSqy2+0cP34cu91OY2PjjAJBZWRMMpnUmodTxKhvspDtF6NPjUZzeui74yJiRFhURhZMTk4q577Ozk42bNigKjkGAgGuuuoq1q9fD5STOxn83d/9HV1dXbzwwgt84xvfWPSxSyn59re/zfvf/36KxSKf+9znVA0NgDvvvBMppfJD8Pv9NDc34/f7icfjHDhwALvdrhI0tba20tbWxrFjx1QOjO7ubkwmE4FAQKWBXrVqFRs2bFC+CUYeDKMU96pVq4hEImQyGVKpFCaTiRUrVigziVFzwmKxYLVasVgsOBwO4vE48Xh8xjoTc83hoNFoNOczWnA4AxjOkn19fQwMDDAwMKDSPf/pT3/i4MGDqt3ExIQKaXzkkUe47777gLIK/e677wbgq1/9Ku973/s4fvz4oow3lUrxiU98gttuuw0pJXfccQef//zn1fkf//jH/Pu//ztms5krr7yS1tZWLBYLiUQCgIaGBsxmM9lslo6ODrq6unjlK19JNpulqamJ5uZmOjs76e3t5cSJE2SzWTKZDG63G7/fj5SSgYEB4vE42WwWu93OsWPHiMViyhwUiUQIhUKkUinlowB/rmppFK4ySmUPDw8zPDxcUyjQyZw0Go1m7mjB4QyRTCZVPoILLrhAFVVyOp20tLTQ1dWFlJKDBw8yOTmpHBc/8pGP8MwzzwBwzTXX8I//+I84nU5+9rOfsWnTJu699945J3uaCy+++CKvf/3refDBB3E6nfzwhz9UlTgB/uM//oMPfehDSCnZvHkzoVBImRuMCBLjf8OfYcWKFUqwEELwile8Ar/fj9/vp729nVKpRDQaZXR0FKvVit1uV34UTqcTi8VCPB5nYmICmF6FNJPJkEwmiUajjIyMIKVkdHSUoaEhstksQghlMgqHwzWFAp3MSaPRaOaOvkOeQYyU1DabjUAgQFtbG11dXaxdu5ZIJEKxWKRQKOB0Otm0aRMXX3wx+Xyed7/73QwODgLlssE7d+7kpptuIpVKceedd3LDDTfwhz/84bTGJqXk/vvv541vfCOHDh1izZo1PPnkk9PSSv/kJz/hgx/8IFJKtmzZwl/91V+pxdjpdBIIBPB4POTzeSKRiDJPZDIZlRyrubmZxsZGMpkMAwMD7N+/n4mJCUwmkzJLdHZ2qjLZ6XSa5uZmVq9ezfr161UxMSOtt8vlwu12Y7FYKBQKpNNpgsEgra2tKnukYTIyhJHq8tg6mZNGo9HMHe0cuYhUhvk5nU6CwaAq4OTxeMhkMrS1tSknv2KxyODgoGp7/fXX84lPfIKDBw/y7ne/m4cffhi73U5HRwc//vGP+e1vf8unPvUpXn75ZW6++Wbe8Y538PnPf35a4anZyOfz7Nq1i3vvvVcVr3rPe97DF7/4Rdrb21W7Bx54gA984AOUSiVe9apX8YY3vIFCocDk5CQrVqxQyZXi8bjKn2AymRgfH1dCQzgcxuVykclkKBQKDAwMqHNdXV3TFnKXy6XONTQ0qM8LyqaF8fFx5ftgMpkIBoOq6JRxrXpUR1HocMza6HwXGo2mFlpwWECqF6DKBQrKu2OPx6N2vVBeJC0WC7lcjmg0SjabJZvN0traSi6XY+vWrdx5550888wzfPKTn+Rb3/qWuqFfd911/Nd//Rf/9m//xne+8x22bdvGtm3b2LBhA694xStobW1l8+bNrFmzRkU8FItF9u3bx44dO3j22WfZsWOHWpBdLhd33XUXb3vb25icnFRj/NnPfsb73/9+SqUSV155Je9+97tJJBIMDQ1RKBTUQm+z2dR7SiaTFAoFwuEw+XyefD5POp3G5XKpMNSNGzcyOTlJd3c3LpeLVCql6kcYZg7DtGB8lsaYcrmc8nkwEmxVJuAyfB1qfTfV5bF1OObC8KEPfWjB2y9knzMJQjrjpEYzd7TgsADUK7FcGeaXTqdVGGEymVRVNMPhMIVCgePHjxOPx8nn87hcLvr7+5X9/i/+4i+4//77+d//+39z6aWX8rGPfUxde82aNdx1113ceuutfOMb32Dbtm28+OKLvPjii6qN2Wxm/fr1tLW1sWPHDuUrYLBu3TquvfZaPvrRj6oKlFJKstksX/rSl/iXf/kXSqUSl112Gddeey2Tk5MqH0QymaS3t5dAIMCKFSswmUyMjo6q959Op2lpaWF0dFTV7nC73bS0tChHRGOXb/TpcDhOuskbn6XxGQcCAaCci8JIClXZtvr16XSaaDSqEklVlsfWqahnZq6L6lxqqsy3/WL0qdFoTg8tOCwAxo7V7XZP88o3bOfJZJJ4PI7FYiEYDGIymSgUCiQSCeLxOKlUiubmZqxWK/l8nlQqRbFYxOv1YrPZkFJy5ZVX8tvf/pZPf/rTbNiwgWuuuWbaGC644AK+/e1v8/Wvf53nn3+e5557jp07d/L888+zb98+9uzZw549ewDo6urimmuuUY+WlpaT3tNvfvMb/uZv/oajR49iMplYs2YNmzZt4tChQ4yNjREOh2lsbMRkMpFIJAgEAioVtBFdkU6nVeXL6l1+dbIsgPHxcSXU9PT0TFv8hRC4XC6klNM0NhMTE0QiESV81NMYOJ1OpQVJp9OqXTKZZHh4WJlWNMuPmQQfbY7RaObPshQchBBCnqbucT5278pFsVZbp9NJPB4nFovhdDrxeDxqRz8xMUEqlSISiRAOh+nv78dut3PixAkaGxsZHR2loaGB6667jlwux6OPPsqNN97IW9/6VrZu3cqWLVum1ZnweDxs2bKFLVu2qCqUqVSKPXv20N/fz6ZNm+jp6QGoOdZMJsNtt93GD37wA6CcffLKK68kFAoRDocJhUKYzWa6u7vxer2MjIyoMEujHHYulyOfz5PL5bDb7cTjcXK5XM3FufJzDgaDJBIJ8vk8yWRSfU7GeSHENAGi8vM1+jFqV1R/FyaTiVAopPrSLDxGtkYje+NCtF+MPjUazemxLAUHQACnJTjMx+5da/dc67wRCQDlnU4oFJpmszfs/YlEglKppOowGOGNt912GyaTiccee0z5M6xcuZKtW7fy3ve+V6nvq3G5XLz61a+e9T3v3buX97znPbz00kvYbDa2bNnCO97xDqxWK6Ojo/T09JDP51UEgs1mo6uri+PHj+Pz+chkMni9XhoaGkgkEuRyObVQZzIZGhoaTopeqPycXS4X4XCY4eHhuucrPz+PxwOUd5RGESsjCyWc/L3V+p6M8Whh4vQxqrfOVWafS/vF6FOj0Zwey05wEEK8DnifEOIA8KKU8mdzfN1WYCuwxohsAE55QanWWNRboIyFLJVK0dfXR3t7OxaLRdW4EEIwMjJCPp9ncnKSm2++mQsvvJDHHnuMffv2cfDgQW6//Xa+8IUvcPPNN/O2t72NK664QoUizoaR92Dbtm3cfvvtZLNZ3G43N910kzKpjI+PEwqFVDXKjo4OisUiExMTFItFlbgpHA6TTqdJJBIUCgXsdjs2m01VykylUtPMBJWfr/G3+nNyOp0UCgXi8TgOh+OkKp6G0JDP57HZbASDQaVxmAuzCX0ajUajmc6yEhyEEG8E/idwN2AH3iGE2Cel/NNsr5VS3gPcI4TYHolErj7dBaVaY1HL09+wrzc3NzM8PMyxY8dUHodYLIbL5aK9vZ1kMsnExAQ2m42RkRFaW1t53etex7p16xgYGODAgQMMDQ3xox/9iB/96EcANDU1sWrVKtasWaMeLS0tHD16lAMHDrB//34OHjzIgQMHpjlLdnd3c8sttyCE4LnnnuOll15S4ZClUgkhBBaLRe3spZREIhHWrVtHoVCgVCqp8y6XC4vFgt1uVwu04YxYz/xjmCIq/0+n0/T29gIQiUQqv7NpQkMoFNKCgEaj0Swyy0ZwEEIEgf8b+Bsp5SNCiDBwOdACzCo4LCTz9dQ3mUyqEqXVaiUSiZBOp7Hb7axYsYLh4WH279/PkSNHcDqdhEIhNm3axGOPPUZbWxvr1q2jubmZPXv2cOjQIQ4cOMD4+Dg7duxgx44ds17fbDbj8/nYtGkTb3zjG2lubiaXy5FKpVixYgWpVIpkMomUks7OTqxW6zSNSDqdVpqKxsZGVaXSEHj6+vpoa2vDZrOpctdGxEVlJEq1YGXgdDpP+izrCQ0ajUajWVyWjeAgpRwVQtwNvCSEMEkph4UQB4HXAL8/k2MxFk0jU6FBtQd35c7YbDbjcDgYGxvD5/Ph9/tVdIXhDBiNRmltbeWKK65geHiY1atXs3v3bmw2G4cPH+aiiy7iTW96E6VSiT179hCPx+nr62NwcJBEIkE2myUUCtHY2Eg4HFZRG8PDw9jtdiKRCGNjY6RSKVW0ykhMlUgkaG1tZe3atYyPj3PgwAFsNhsejwchBMPDw3g8HlwuF0IIlcI5lUphNpvJ5XI0NTWRz+enVbKsjESp5+Hu9XpZuXLltDapVIpCoaCFBo1GoznDLAvBwYiikFI+Zvw/dSoD+KeO3QQkpJTbF3s8c/WPqExa5Ha7Wb16NfF4fJpvwN69e7HZbMRiMSYnJ8lkMgwNDZFOp5FScumll7J37176+/vp7e3F7XbT29vLyMgIa9asUYmkHA6Hyq5oVLU0ynofPnwYs9msnAtTqRRCCOWnYTabWblyJRdccAGxWEz5MEgp8Xg8WK1WSqUSmUxmmtbAZDLR09ODyWRSoaaG0OBwONRnNNuiX8v8MFskSzU6O6RGo9EsDMtCcJBSSiGEWUpZnDrkA6LAQcAvhLge+ALwl/X6WEjmY2evTGwUCoVoaWlR4YWFQgGr1Uo8Hqe9vR2z2YzJZKK3t1c5JRYKBdavX69CGI0EUmazGY/HowpEGWGKhrlgbGyMlpYWWltb6enpYe/evUgpaWpqUv4Uk5OTSshYuXIlfr+fAwcO0NTUpIQcj8dDe3s7Pp9PCQOVWCwWenp6lLBgRD80Njaeli/CfH0ZdHZIjUajWRiWheAwZZooTj3/CvAC8ACQBO6b+v8DUspDZ2+UM1MpQMTjcY4dO4bf7ycUCqkQx/b2dnK5HIcOld9GNBpVDouXX345g4OD+P1+9u3bh9VqJZPJKBPI6OgoNpuNlStXksvl6O3tJZFIYLfb8fv9tLW1EY/H8Xq9xGIxkskk4XAYs9mshIujR49SKpVwOBzKbGCEUBqpsmv5KVQmwjK0Gmc6/PF0o2Q0s7Nz584Fb78YfWo0mtNjyQsOU0JDaer5XcBlwFemTpeAGPBuKeXBszTEGamuZ3HkyBEmJiYYHBzEarXi8Xjw+/1YLBYGBgYQQtDT00M0GlWVJ8fHx8lms3R0dBCJRAgEAtjtdiYnJzGZTPj9fuVv4PV6VernyclJRkdHEUKoVM82m41isUh7ezsdHR14PB7sdjt9fX3KibKrq0vlWzAiJCojJqpDJg3ma15YSHS0xeIz36RLc2m/GH1qNJrTY0kLDlVCwz8CG4DrpJQFACnlr4UQG6WUQ2dznDNhmCWMR0NDA4VCgVgsRjQaJZPJEAgECIfDHDt2bFqpaZPJxNq1aykWi4yMjGAymQgEAmSzWTo7Ozlx4gSBQIBVq1YRjUYZHR1lbGwMv9/PmjVrcDgceL1erFYr0WiUWCzG4cOHsVqtCCEIBoM0NTWp6Agjj0M2m8VisSjhwcjNkEwmZ1ygz+fFuzpPiEaj0SxVlrTgUCE0/BOwDrhJSlkQQpjLp2XpXBYaDIc9KOd0cLvdtLW1YbFY8Pl8+Hw+BgYGyGQyDA4OqkXcYrEQCoVU5sR0Os3Bgwdxu92YzWacTid2ux273a5qYFgsFoQQDA4OkslkWL9+varKaSROGh4eJhKJUCqV8Hq9ZDIZ4vE4TqdT+VAY1zM0DR6Ph0KhoMbf0NAw43s9X50Tq/OEnO3xLAZbt24F5l5oai7tF6NPjUZzeixpwQFACNEJrAHeYggNFU6S5zT1QhKN8tJOp5MLL7yQw4cPk8/n8fv9CCGIxWJKeBgfH1fRFm1tbQSDQaV9KBbLH0NjYyNjY2NYrVZ1jaNHj+JwOMhkMiQSCZqammhqalJOmolEgsHBQYrFIpFIhGAwiM1mU0LG+Pg4hUIBr9dLOp1W5bXrmSm0c+Lyx6hvMtdFey7tF6NPjUZzeix5wUFKeUwIcVONyIpznmqHPWNHXn3c5XKpHb6hSTCbzRw+fJhUKkVjYyMrV67E7Xar0tSrV6/GarWq/A9SSrq7u1m/fj19fX0899xz5HI5/H4/pVJJ5UMAyOfzSutx6NAhUqkUDQ0N+Hw+UqmUygdhjNcwnzgcDpLJZE2twkzOiee7NkKj0WiWEktecICyTWLq75IRGmC6zT8ej6vyzh6PR4UuOhwOSqUSHo+HfD5PX18fjY2NKinTxMSESup0+PBh1a/H42HVqlWkUimamppUZU6Hw0EgEODiiy/GYrHg9/uZmJggHA5jtVqJxWIMDQ3R09ODy+Uil8sxODhIKpXC5/Ophb3aX6GyfLjxf733Wo3WRmg0Gs3SYVkIDsuR0dFRBgYGaGlpobGxkVKpxP79+4lGozidTpqbm1W0RTAYxOl0kkwmaWhoIJPJ0N/fTyAQoLW1lVKpRGtrKyaTiVgshhCCNWvW0NXVxdGjR1VaaJvNRiKRQAjB6Ogol1xyCc3NzSpro0G9kMZTDXnUoZIajUazdNCCwzlCdVVIo7plMBjEZDIhpaSlpQVAmRROnDjB8PAwwWCQlpYWwuEwuVxOhWD6fD7cbjfxeBy/368EA5PJRDab5ejRo/j9flwuF3a7XV0zl8sRDAbJ5/N4vV4sFgv5fJ59+/bh9/tVOulqTjVq4nyOttBoNJqlhhYczhGEECods9PpxGw2Kz+ChoYGTCYTkUhEaR+Gh4cZGRlhbGyMoaEh3G432WyWffv2sXLlShwOhwrZNHwjjh8/zsDAAKFQiFgshs1mw+VyqVTSuVyOQqFAa2urctY0zAhGbYi5Jm/SfgsajUazPNGCwzmAschWV4qstP27XC5VmrtUKimfhImJCVVgKpfLkc/nSSQS2Gw2Dh48iMvlwuv1UiqVOH78OMlkkvb2dlavXk02m50mXGSzWYrFIs3NzZjNZiXMQFnz4fF4CAaDdYtRVaL9Fs4/LrnkkgVvvxh91mK2OT3lRqXRaNCCwzlBvbDMStt/5Y3NbDbj9XoBaG9vZ3x8XIVR5vN5Wltb6e/vp6+vD4fDQVdXF8FgkMbGRpqamujp6VH1IgxtQCgUUkKLURMDyjdUY+E3TCVzQfstnH88++yzC95+MfrUaDSnhxYczgHqpWI2fB5qqfxLpRIAK1eupFQqkc1mVaZHh8OBxWJRpgiLxcLIyAjZbJaVK1eSz+dVBIcRSmn0H4/H5+xzMJM5QvstLA3moj1azsymSTjfPx+NphZacDgHOJVQxWQyqRZ/i8VCNptVlTEBWltblT9ENBoFyhoDo7R2rf7nqyXQ5giNRqM5/9CCwzlOdS2LWo6GtRZ8o3KllFI5NzY3N5PNZnE6nUQiERwOh9IYGBqMuQoAxnjcbrc2RywDFsKGb+zO59rXXNovRp8ajeb00ILDOY7huFhtQqgM3zSEhFoYlS/T6TRjY2OqncvlIpVKqcJUhlAyk2mk8ng6nSaZTOL1emdsp9FoNJrlhRYclgC1NAqGEFG5s5JSqkW70jYbCoUwmUw0NTWpCpepVAqHwwGgKl5Whl9CfdOI4cBZPSbQ5guNRqNZ7mjBYQkwV0fD6vBNA7PZTDgcBsBqtZJKpU5a3I2/c/VzqDcmHU2h0Wg0yxstOCwxqk0BlZqFeuGb1cy0uNcTCKozW9ZDR1NoNBrN8kYboZcYhlahMjLCwFi0Z/MtmGu7Wq+BstnCcKbUaDQazfmF1jgsMWYzBSy2c6L2YdBoNJrzGy04LDFqmQIqhYXFXti1D4OmHt///vcXvP1i9KnRnGmEEHcAVwHDwPuklOmKc2bgfwGtwGFgq5SyUO/4GR98DbTgsAyYaxKnhdBGaB8GTT22bt264O0Xo89TYSafIZ0zQlOJEGK7lPK1Ff9fCFwgpbxSCPFh4APAtype8n8BvVLKdwshbgfeDvx0huNnHe3jsAxwOp0qRHIm/4WZ/CM0Go1mLgghjgghrjvb41hCXAk8PPX8YWBL1fkLgN1Tz3dNtZ/p+FlnWQoOQojGqb/nRaL5uTo7VgoYGs1Cc88993DPPfcsaPvF6HM+SCnrPjTnPkKIJiHEz4QQKSHEUSHEu06lvRDCLoT416ljCSHEc0KIG+c4DD8Qm3oeA5qqzr8EXDv1/Lqp9jMdP+ssO8FBCHEp0C+EeLWcx69bCLFVCLET2DQ4OLh4AzyLnEo0hWZpI4SY8bGQ3Hrrrdx6660L2n4x+tScV3wbyANh4N3Ad4UQG06hvQXoA64GfMAXgJ8KIboBhBCdQojtQojtwEbjuRCiE5iYeg1Tf8errvkQkBVC/A5wUfaDmOn4WWc5riAewAzcLYSoVgnVRUp5j5TyUuDZSCSyaIPTaDSa5YIQYt3UAhkVQrwohHhLxblLpnbmCSHE/yuE+IkQ4qsV5y1CiC9MmT7GhBDvEkLcLoT43AKNzQW8A/iClDIppXwC+C/gvfNtL6VMSSm/JKU8IqUsSSkfouywuAlASnlMSvnaKd+G3cZzKeUx4AngDVOXeQPwZOV1ZZlPSymvBcaAX8x0/FxgOQoOT1CWBn8A3C+EWCmECJ3lMWk0Z5WZVO5a7a45FYQQVuCXwG+BEPBx4EdCiDVCCBvwM+DfKKvm/4Oys18lX6W8g78YeD/l+/b7gW/Wud5DUwJKrcdDNV6yGihKKfdXHHseqKdxmHN7IUR4qv2LdfpSSCn3AEeFEI9TFhx+ONVHixDiy1N/twshHgHyUsrHKs6fdPxcYFlFVUyFr7go24U+SFm18yjQOOXZemQ+5guNRqOZjfM44uLVgBv4upSyBPxuagH/S+B3lNeXb07dcx8UQvzReKEQwgt8ElgvpYwJIXYAa4HPSSkTtS4mpXzzPMfn5s++BQYxylrpU24/JTD9CLhfSrmvxjhfW+PY39Y4NgR8cerfWq8ZqnX8XGBZCQ6UtTtRIcQvKNuSdlE2W4wDdi00aJYj54kPsObcoxXomxIaDI4CbVPnjlfdc/sqnl8L7JdS9k79b6O8SN+9gONLAt6qY16gpmAyl/ZCCBPw75T9ID62MMNceiwbU4UQwlQxgU3AjylrG/4b8FnKKjQdTqDRaBaEuZh+zpRj6lliAOiYWkwNOoHjwCDQVhXZ1lHxvHXq9QZbKQsa9RZ1hBAPCyGSdR4P13jJfsAihFhVcexi6psXZmw/9V7+lbLj5DuklJP1xlpj7HcIIR4XQjxQvQ4JIcxCiB8JIX4vhPihEMIy0/FzgXNmIKdDpdAghPg88AKwF3hASvno1PGHKrN1zcDK3bt389rXvnbRxrtUKBaLmM3msz2MJcXu3bsBVs7QZOWjjz66KAvH1VdfXffcmZzP873WXNovRp9nm9OYAzPNrzPJDiAF3C6E+CfgCuAmYDPQCxSBjwkhvgu8CbgM2D712n7K0QcRysLGewG3EMImpczXupiUcq7hj0b7lBDiQeArQogPAhuBtwKXn2L77wLrgOuklJm5jkMswwRQYqlr76uEhruA11C2C0kpZUkIYZZSFoUQYi6mCiHEc0AzcHCRhrxx6u/uGVud/euapx7FqceZuu5Ccbau+xrKjkzVdtGtlHdV6yirOZ+v8dqzNeazee3z8T2fzrVXAieklK9c4PHMGSHEEeCDUsr/T5RDFb9D+f0cp+yj8LOpdpcC91Ie88OU7yfPSSn/fsp58l7gLZRNye8A7gIapJRzjoabw1ibKDsjXk85MuH/kVL+uOL8w8DjUsp/mKm9EKILOALkgMq0z7dKKX80yxj+O5CWUt4/1c+dUspbKs5/Bjgopdwmyom13iql/Hi946f3iSwMS1rjUCU0/CNl79drpwQFM4CUsjj1d04S0mL/IEU5zremA42+7vK5bjVSynuAGTMTna0xn81rn4/v+Wxf+3SRUnZXPH+RcmRErXY7+bOAxJQD5C+nzuWB91W95PpFGOs48LYZzt9Y9X/N9lLKo8Cpqoj8lE03UD8B1A3ANk5OAFXr+FlnSfs4VAgN/wSsB26SUk4aWoazOzqNRqM5fxFCXD0VUmgRQvwVcBHwm7M9rsVg6n0+UePRwjJMALWkNQ5QztgFrAHeIqcqimmhQaPRaM46ayjb5N3AIeBmKeWyTMs7FTpZ08QihHgC+FvgfuokgAI+PdX2S5RDWesePxdY8j4OUPZ2lVJKLTRoNBqN5lxDCPE1yoLFCOWy2qkpbcR/p+x0+Z+UfckeqfC3aKl1/FxgWQgOGo1Go9FozgxL2sdBo9FoNBrNmWXJ+zgsNGcgHFOzvJkxXE7PL81pUnd+6bmlOU3mHOqrBYeTafb5fG0bN25sO9sDOZ8pFosqAZWRhGopJKTavXs3sVh1uvtpnHfzq9Z3eaaue67Pl/kyy/xalnPr0UcfBWZOcDbf9ovR51JnDvcuhfZxqEIIsf3qq6++evv27Wd7KOc1pVKJdDqN0+nEZDKRTCaJx+N4vV6y9IP9AAAgAElEQVTcbvfZHl5dXvva1/Loo48+Wi8+/3ycX9Xf5ZlgqcyX+TLT/Fquc8vIsDnXtWou7Rejz6XObPeuSpa9xmGuGSM15xYmk2naDd/pdE77q1k6VH+XZwI9XzSaxWNZOkcKIbYIId4L5VjYqkIrmiWIsficqR2rZmmj54tGs3gsK43DVJU2J/D98r/CJaX83pTwUFk9U3MGOBsqas3SQc8PjWZpsqwEhynBICmEuJ9y0ozLhRANUsp/Ph+FhrN9Y06n08TjcYBlZWfWLAwLOT/O9lzXaM4nlpXgUEGBcqnW+4EPCiG+Qbmq2WcpO4SeJERUVC9cMzi4PLKinu2FW9uZ/8xynF+ny0LOj7M91zWLx86dOxe8/WL0eT6xXAWHXwB/IaV8RAixEfh74L4pJ8majpJG9UIhxPZIJLIsYm4qb8z1dmSLuVM7G05x5yrLcX6dLnOZHzPNz8pzWkhdvmzatGnB2y9Gn+cTy1WnlwHWCCE+BHwY+DrQKYS49ewO68xS6SBm7MjS6fS0NtXHS6USyWSSUum8s+xoFpCFmkf15m31Oe0MqdGcOZalxkFKOSCE6AO+AHxUSvlLIcQ1nAcZ1ert0OrtyKqPa5WvZiGY7zya77yd7Zxm+bB161YA7rnnngVrvxh9nk8sS8Fhih8Av5BSPjv1/6PnioPkYpoH6t2w66mFdb4EzWIw33k033mrnSHPH37wgx8Ac1+059J+Mfo8n1i2vzgpZZ+U8lkjh8O5IjTAzOrX08XpdOL1eud8w65WKVeqfLXZQnOqVC74c5lD8523s/2G9NzVaBaPZSs4GJyLWSPne5OcD3O19Ro3ViM172w25HOR010c9OKy+Mx1DplMJpxOJ+l0uu73Ufl9Vf+Gqr/Lc33uahaHylx/QoiaD83ps+wFh3ORxXTkmutiWKkariXElEolSqUSbrf7nDVbnO7ioBeXhaPevJtJSJ7vYj+TM2T1axdTONcsbWYSLjRzYzn7OJwXGAoVKaXarSWTSQBcLlfdH0OlDbqWAJNOp0kmk3i93jkJOGfa5rwQgo325zg9KpV5xsJdKBTIZrMEg0EsFktNHwXjdZXCq8vlmvX7qDxfrUisfm2t62q/iPOL6jmiBYOFQ/96lgnGTbhUKmEymXA4HDO2n03rYezYHA4HyWSSQqEwoybjTO3eK00syWQSk8l0youADuFbOIz5kk6nGRgYYHR0dM6vcTqdFItFRkZGcDgcdb8PIYQyZxSLRVKplFochBCzfpdaw3R+I6VUj+pjmvmhNQ5LhNl2S5W23lKpRDabxel0kkgkAOa9QBqLquEDUSk01PJyn+vu/XR3fcbN3+12a1X0OYQQApfLpRb+YDBYs53x/TscDjVHhRCMjo4yMDAAQEtLS83XGEJD9Xx0uVx1x6WTRC19LrnkkgV/zXz7PJUxLGe04LBEqBeuViwWGR0dJRgM4nK5kFJOczQbHh4GTlbdzraAV97ggWk3+lrMNUvk6eaJMLJgGmPSquczx1yEPrPZTDgcrtuH8f3H43FSqRThcBiPx6MEDeNv5bWSySTDw8OEw2E1Z2rNx1rjq55v8/kNLBWWezrzZ599dvZG83zNfPs8lTEsZ5bur+U8o56zl7FTM1TDxs7PUOuGw2HC4fBJr0un00SjUUZGRpSWotpRLRqNMjo6itPpxGKxLIhav9b7mE90g2GaSCaTjI6OatXzGaSeql9KOc1sYBybj7OkIXCYzeYZr2XMb7PZfJIPTzKZZHBwUPn4zHS9ma5RzbkefSOlvEdKeSnwbCQSOdvD0ZwHaI3DWWQ+O57qHX2hUGB0dJTGxkaAaarh6pt2rb4dDge5XE6NAZi2MzN2eoVCgXQ6vWBZJGtpJuppIWbLJjibFkQzP+ZqDqslhFY6OQLTtARer1f1XzkvDYE2lUopk4XRrtrx1dCiGU7A1aaOesykCZur6UJnU9VopqMFh7PI6dyQKm3C1arhZDJJb2/vtB1SS0sLLS0takHIZrNYrVYmJyex2Wxks9mTbtTBYJDR0dGajpYLqeady4JUL5ugvpEvHHMR4GbzbzFMZzabTQkKlfVShoeHSSQSmEwmVqxYQTabPUnoqBXR43a7KZVKjIyMUCgUsFgsan4bZjmn00kkEpmzIDlX85r2jTi7GILhfJwYhRAztp9vn6cyhuWMFhzOIvVuSNWLcvVklVLicDhoaWmp64Rmt9sxmUw0NDQwOjpKIpE4KbW0zWbDZDIxPj6udnjpdJqGhgagLJwY4XWVDmhSSnUDh1OvRVAZOup2u0/6sVeH39XbWc72Y9ZhWHPD8B8xHsbnVh2xU73LN8wH8GeBtqWlBY/HQywWA8rCbUNDA4FAgEQigdVqneZsa8w5KWXNsEtjzuXzeWw2G8FgUGkcamk8av1mgJPmW+V7qGY2gUmjOV/RgsMZoN7uvN6Ox/AvSCaThEKhk25q8XicI0eO0N3djRBCRU64XC5MJhMulwu/30+hUMDr9eL1eonH4wwODlIoFJicnGTFihU0NzeTyWSU2rdUKqkFIp1Oq5u0cSOvzBVh7PrmmyK4cvGpdN6s/KyMz8Xw0zDs0KFQCIul9pSdrwpbczKG/0g0GlWft/EdAGp+QP1IhqamJlKplFrYh4aGyGQyuN1uPB6P0jAYJjajP2Oum0ymaWGXxrXrCQ2V43M4HCQSiWmaNmOuGfN7cHCQTCZDd3c3Fotl2nyp1pxV/w6XsgOlRrOQaMHhDDAfk4Sx2zOZTMq/oPomnUwmGRkZUUl2hoeHKZVK+Hw+mpublZnBcHwEOHbsGLFYDJ/PRyAQAFBCRnWUQj3BoDIUsrGxcV5milqLj+G8aTA4OMjY2BiBQIC2tjacTicjIyMMDAyobIGhUKimEFYdpldvd6yZmWrfFsMBsTpixxDUGhoapn0P+fz/z96Zx8dZ1/v+/cw+ySzJZN/TNS1doK1tWcomIIhlu4Igy1XUA5x6EC4e1FuPXDgqHPSoLIIHehXpRRFkEbWC7KWlZS3dl6TZJ5lkZpJMZt/n/pHz+zJJky5QltZ8Xq++2ibPzDzJPPP8vr/v97MkMZvNDA4OUlpaSnl5+ajrUHW6zGYzALFYDLfbTTAYZNGiRVRXVwOjPzMwwulRRYPf7yeZTI4qrNW1Mjw8TCwWA9hHrllRUUFhYSGRSEQ8QMaTGecrigwGw2Hn+UxiEkc6JguHjwHjjSTGdiHU/8fOhcfb0dtsNsrLy7HZbFgsFqxWK6FQiKGhIQoKCigsLMTr9dLX10dhYSF2u12KAqfTiclkkt2ZgrqRKqMnZSKlihK1O8tfAA62aMj/WfNvyjqdbhRxzm63y98WiwWv1ytjkvLyckpLSycswsYSJvMLlMkb/sFjbHGWj/yRRCgUEvKj3W4HRqTBqqs0PDwsioZIJEI0GsVut2Oz2WhsbJTrJ51OMzQ0JMZRyp/DZDIRi8VwuVwkk0kcDof4iqjxRyQSIZvNUllZSTQaJZ1OY7fbpRgNh8P09fXR398vnyebzSZKIfU5GEuwzb/GJvpdTGIS/8iYLBw+BhyMkmA8YyO1MI+VuQFSOMTjcWKxGJFIhGQySVVVFbFYTIoCpZFPp9MUFhbKOGNwcFDaumoxMBgMeL1eMpkMDoeDbDZLJBKR+bPqQKjC4mA18WN3j8qgaizhsbKyUr6mFoJMJkNhYSFFRUVSYI1nMz1ee3uiwmsS+4d6b8fame+ve5PNZmlvb8fj8VBSUsLw8DBlZWU4HA7ZtcdiMdLpNL29vdjtdhoaGjAYDFRVVdHV1cXAwAAdHR1Mnz59VIFgtVrlM5JOp0cVvKr4VO9zfgfEbrej0+mk06YKj8LCQgwGg1z3Y2Wd6rlMJpN09ibHFJOYxPuYLBw+IYztQuT/nR9pnX+zzuVy9PX10dfXJzdIl8tFYWEhZrOZWCwmhMiKigqZU8fjcbxeL93d3cyaNUvGAKoICIVCRCIR8UWw2WxUVVVhs9lkPh2Px0kmk6MW7rGOfmPnwfndBTU+OBAhFEbm3vkLQj4JLp9tn//6wCjCpiqSxnuNI93w50A4XD/nRPkn8L4TqepchcNhuUbyzyGZTGI0GmV339raSmtrKzabjUQiQVFREaWlpVJgKImmyWQiEolQVVUlXYxgMEgsFiMej5PJZISAabFY0DQNi8WCz+ejtLQUvV5PLpeTDpYaaeSf93gy0HwyZF9fH729vWSz2X2K+Y/rPZjEJD6NmCwcPiGM3bHn/1/JzsbOcaPRqOy2dDodQ0NDwlBPpVKUlJRI0FA0GpUboyom4vE4vb29GAwGGhoaAGRR1+v1tLe3Y7FYcLlccl7Krc/hcMjCrG6EfX19hEIhKTLG+j7ka/nHku7yb6b5Mju1oBiNRnQ6HXq9XooGJQtVhYIy/FEtcMXLyB/D5LPn/1H0+IfKqTlQp0gVisFgUKS7MFJExGIxenp68Pl8ozgrZWVlmEwmurq6sNvtVFdXywhJSSZzuRyDg4NMnz6dnp4eTCaTFJ+qMA0EAnI+6rpobGyUc1dqIbvdvo9E2e/3s3fvXtLpNBaLhXQ6LQ6rkUiEQCAgP19+10/93pRiyWKxHPJ1849yrX0ceOCBB+TfB8tXyn/MB/n+hz3+aMdk4fApgLp5qy6CasmmUin5v+oq5M9w29vbyeVy6PV6kU0ODw+TTCax2+2EQiGRt+n1eoqKivB6vQSDQSG6KU19Mpmkv7+fxsZGbDYbHo9HFvmKigoMBgMlJSXEYjHZgYZCIWk/e71emUfny+gU1MKjZt8FBQX4/X5cLheDg4PCmNfpdJjNZgwGA1arVcysxs7T1Q7U5/NJl0HNwSey2j5Y+euRjkPxHchf4PJHPZqmYbVaRzmJ9vf3y/sdjUapqKiguLiYwcFBaemnUilSqRQ2m42hoSGGhoaEp6L4N6pLsHXrVjRN45133iGZTDI4OEggEKC+vp6qqiqy2Sxms1kUGEpirDwdWltbSSQSlJWVEYlEcDgc+Hw+HA4HoVAIk8mE3W7H6/WyZ88eIWSWlZXJz6V4QMpxUfGGVPFSUVFBLpc7JAXRob4Hk9g/rrnmmsP+mEN9zg9yDkczJguHTwHyb97qZp3fplc77XzuQllZGWVlZfT29hIOh6mtrRXPh56eHiGeeb1eCgoKZHFub2/H6XQyd+5cstksRqORWCzGwMCAjDTsdrvYTft8PlpbW5kyZQolJSUy3lDjDBgtD1U3eXi/na0WIpvNRiQSAd7X+0ciEemYVFdXo2madEjGW8Tz2+eqo2IymYTUCSM7RBW4lK+w2J/89WjaHR6ssRGMXuDG+iGo3Z3H48FqtVJWVobFYmFgYEAKt/7+fvr6+kilUmiaht1uJ5PJjHIm1ev17N69G7vdTn9/Py6Xi9raWpxOJ7FYjGg0SiqVIplMkk6n6ezsFNKsz+eTn0ddx6qzBCNFnzIpU0VzT08P0WgUk8kkYzan04nVaqW0tJRYLCZjD6vVKqRcn89HRUUF8Xh8n27EoV4Xh/IeTOLQMWnE9MlisnD4FEC1QtPpNJFIhGAwKDsctRtWskmllkin02SzWVpaWgiFQjLbTSQS9Pf3U15eLkVBMBhk79696PV64UF4PB7pHCjy2tSpUykoKCAQCDA8PExRUREmk4lcLic3dbVTUzfvwsJCGV+M1fnnExZV8VNRUSE/r1JK9PT0oNfr8fv9lJWV7cNNUAoMRVZT/hSqcFHdi6GhIdn5KkmegipgDsVK+WjE2O5KvlIi3wAql8uRyWTo7++XgszpdDI0NCSFrdVqZXBwELfbzdSpU6mvr2dgYEAKWdXxUt2znp4empubqaurA5CxWDQapa+vj0AgQDabJZlM4vP5mDNnDsFgkJ07d1JcXIzRaJRMlmOOOQYYUXIMDQ1hMpnIZDL09fVRUVHB8PAwwWAQp9NJaWkpZWVlGAwG6aSEw2Hp4LlcLjo7O6VzpYrj4eFhIpHIqC5HPqfmaOpSfZrx4IMPAge/6z+Y4z+K5/xHwmTh8DFiPAmmiq3u6+sDRtQSapbb2dlJMpkkkUgwdepU2TUrvXpRURFOp5NEIkFBQQF9fX1YLBaZQ6tRh16vJxQKicxN3ThtNpuMIAYHB9Hr9QwMDLBnzx4ymQxTp06loaGBdDpNcXGx7AIjkQher5fCwkLZoZWUlAjBLd8wSvEg1IjB4XBIa7u6upp0Oo3ZbCaRSJBOpxkeHsbn82G1Wqmurkav1zM4OCgMe9VuVtwPFYpUXl4uM2+FgoICsSbeX0ch35DqSFwIDnZBy+eSqNGWIhLC+/NjJcEdGBggEAhQVFQkBV++syQgqpdMJkMgEMDtdguBd2BgAKvVSm1trRBeLRYLdrtdCtwZM2ZQXFxMf3+/KIBaWlqora3FYDDg9/vp7+8nl8tRWlrK0NAQ4XCYaDRKJpMhHo9TVFQk47VgMMiePXswmUzSRauvrycejxOJRMTnxGKxyOjE5/MRCARGuVmWl5fvU1COVQcdTV2qTzOuvfZa4OAX7YM5/qN4zn8kTBYOHyPGk2Aq735FHOvq6qK4uJhIJIJeryeVSmG1WuVG39TUhNlsFiKjw+EQG1+9Xk9fXx+apmE0GqmpqcHpdKLT6aQIgfetpI877jjRuGcyGTwej5ALDQYDOp2O7u5uCgoK8Pl8IoksKyvD6XTidrsxGo3A+1JNpbxQP4/iQSiehNVqle5DaWmpjBzMZjMFBQW0tbXx1ltvUV5ezoIFC2hsbJTjVEEUiUSEm6H4HpqmUVlZicPh2Mc9Mt+46GDfmyMJB7ugKe6MwWCQXT6MzjpJp9P4fD7MZjNGoxGXy0V9fT0Gg4GBgQG2bNlCSUkJlZWVDA8PEw6HqampwWq1otfrqampobi4mHA4jNvtRtM06f6YTCZmzJhBbW0tw8PDWCwWIVcODg5SWFjIwMAA0WiUPXv2iPTSaDRSVFREcXExLpdLLNe9Xi+pVIr+/n48Hg9Lly4lGAxSUlJCJBLBYrHIZ8npdI5ylVTXcX9/PwaDAaPRiNFoxOfzSSdNFbuqoBqvMzVWXXSkFZ2TmMQHwWTh8DEivxWspIkVFRWUlZUBCOFQzW89Hg9VVVXY7Xba29vp6emhuLgYu90uu67p06fj9/sZGBigq6tLdu7d3d0YjUYMBgOZTAa9Xk80GiWRSJBKpejt7SWRSMjjmpqaSKfTOJ1OqqqqyOVy0pZW7eNgMMjg4CCNjY0MDw+zZ88eiouLaWhoEB8J5UYZiUSkI5HvC6AsrtWi1tnZyY4dOwBobGwkFApJbLJadAoLC7HZbBLcZbVaZRFRPAdgFLEvf9wx3rx57M3+SB5XjHfu+QQ/tZjlH6d4H2OzTsLhMD6fj6qqKsxmMw6Hg0wmQ0dHBz09PWzcuBGz2cw555wjfiA2m00W6/zFtqioiEgkQmtrK4AUc0otpAqCPXv2EAwGR/k+qOugtrYWs9mMXq+no6OD5uZm4UNEIhG5LtLpNNOmTaOyspJUKoXRaMRms5FKpdi7dy9dXV2Ul5cTCoVE1ePxeOjq6qKwsFBGZKobkY/8ayW/M6WuKcX1yE8CHfu4sfLhyQJjEkcyJguHjxFq1KDatkrmCCMt33zvAq/XCyApg21tbezcuROz2SyW0Uo339bWxqZNmwiFQtTU1GCz2ejo6BCjHb/fT3NzM8FgUG5+qVQKp9NJMBgkEonIDs1oNFJZWUk8Hkev11NVVcW0adNwOp2yszObzaMWb51Oh9/vx+/3U15eLoVDKBSiurqayspKNE0TdYTVaiUWi2E2m+np6SGdTkt3xW63M2XKFEKhkHRb1KzdaDSKkY9OpyMej8v8HRjFr8jHeK18Nb7I95040joNCmPPXUlhx3Ye8o9ThltjSWb50t3h4WGxj969ezd6vZ6SkhIpJJYuXUpFRYWMBfr7+ykpKSGZTBKPx3E4HLLAq7HV1KlTSaVSeDweEomEFC9q1FVQUCDcB1VoAvT09IgMs6qqCp1Oh9FopKCggJqaGjRNo7u7G4/HQ0FBASUlJRQVFYn3h5IDz5s3j1AoJJ8NdR2r4jQajY4KdRsb6Abjd3TGOr7CxCZvYx87iUkcaZgsHD4ijLe7UNLI/K6DaqX39/cTDAaFdKbki4ODg2iaRiqVwuFwiPa9srISl8vFzp07efHFF0mlUmICpbwXMpkM7777LuFwmK6uLjRNo6SkBKvVisFgwO12ixpBtWiVz4Nq2+r1embOnIlOpxPiZnt7O8lkkjlz5pDL5URHr2bUqoPS2dnJ0NAQOp2OkpISwuEwmUyGcDhMLBYjk8mQSqWkDa2IbL29vbjdboaHh8VcqL+/X3akwKjiS/3c+SmL2WxWWPORSGSUn4Riy0+UQ3Ck7Qzzz3dsWz2/8zBRAqRSuihr71gshtFoFFKsTqcjFovhdDopLy8nl8sRCoXYu3cvVquVgYEBtm/fjsfjobq6Gp1OR21tLeFwWDw1VLFps9moqKggkUgwNDREV1eXKBtCoRBdXV2SSxEMBunq6gIQH5GBgQFyuRxOp1OuDyW/bGlpYcqUKVRWVkpRHA6HsVqtJJNJ/H4/XV1dGI1Gent7aWpqYurUqdI9O/bYY3E4HJjNZhmfDQwMiFRYXVuASIWVWsjpdO5zLe3P5G0SkziSMVk4fETY3+5COeopnwS1MCrnRGX0FIlE6OnpkZus3W6XBd/r9TJlyhR6e3sJBALY7XacTifJZFJasDt27GDPnj0MDg6SSqUAhHTY0NCAy+XC4XCQSCRobW3F5XJRUFCA2WwmGo3idrtl0S8tLaWrq4v+/n62bNkijHyXyyVch8LCQlE0KA1+MpmUc3K73bhcLlnoiouLmT17NiaTiZ6eHrm5DwwMkE6n6enpwWw2U1xcDCAsfUWSUxkdmUxGFhDFpQBGdSPUjlDZB6tW83g5BBN5G3xai4ixMkp4P1dCFXv538tHKBRi27ZtAMybN0+Kqb6+Pmw2G8XFxVitVo4//nhisRiJREJMmex2u8hj/X6/qGPS6bTwSpTc1ufzYbPZ6OzslNGCyWSit7cXv98vBlGK46DyUXw+n7x3sViM9vZ28R/p6ekhl8vJOC+TyYiBmJIpq+tDKYQCgQBms5nCwkKcTicAgUAAj8dDUVERM2bMkEITkMJYeZPE4/F9pMJj8z3GOlDmHzfZaZjE0YCjsnDQNG06UARsy+VyiU/iHCbaXYxn7gTInFWNJWKxGFVVVVRVVREKhST1TxlAxWIxmpubMRqNokN/+umnaW5uHqUsUKioqKCiooKtW7eK7a/ZbKaqqkqMlYaHh5k3b57IHhXXoLe3l5aWFhKJhNzA1YKuZJHJZBKLxUJHRwfDw8P4/X50Oh01NTUykx4cHMTlcmE0GiV0y2g0igOkUoqUlJSwZMkSmTUHAgG6u7sJh8M0NTWhaZro7BUjPpvNYrFYKC0txeVySe6FIlUq4yJ4X/uv8j72994dCe3l/O6CGjkpPsF412F+9kQ4HJYCLd/Oe2yxNHXqVAoLC3nrrbfYu3evjBhUkVlaWkomk0HTNPr6+sRHRDl3plIpuY4NBoMYNg0NDREMBslkMqJqUAu84hx4PB5RZjgcDuEwFBUV4ff7aW9vx+Fw4Pf7KSwspK6uDrvdztDQEJlMBpPJxNSpU6VwSSaTlJWVodfr6e/vJ5VKiZzT4/EAIwRik8mEwWBAr9eLz4NS9YwtwvKLgvHGRJOYxNGEo65w0DRtOXA7MAD0aZr2f3K5XPPHfR4T7S7yb/JqZ6XIgiaTie7ubvx+P+FwWAiHat7r9Xppb2+nqqpKuhADAwNs3LiRjo4O0bgXFBSwcOFCPvOZz7BkyRKWLFlCXV2dzIH/9Kc/8dRTT7FhwwY6Ojro6OjAZDIxe/ZsZs6cicfjQdM06urqsFqtEousdoHKYjqdTpNIJEgmk9hsNrZt20ZPT4/I9hSXQrXLq6urcblcUlQkk0neeOMNMenp7+8Xktu0adOIRCJs27aNPXv24Ha7MRgMHHfccTLKUWoTu91OKpUaFaak9PdK1TE8PIzRaKSqqkpInxNFJR+M2+SnAfk72/zuwoGixVUxpHxDGhsbKS4upqCgQHgKOp2O4uJiuru7aWtro7KyktmzZ0sxF4lE6O3tpby8HIvFwpw5c8RnwWw2k8vlMJvNZLNZ8f9Q5l4FBQXs2bOHHTt24PV6iUajaJqGpmkYDAZxQ1VSYmUgpYoXxdVxuVxisx4IBOjr62NwcJAZM2ZQV1eH0WiUMVZ3dzf19fUUFBRIRyQSiTA0NASMFFNFRUUyCvT7/cyfPx+j0SiFuKZp0jVT4W9KypqPT/M1cyTiUM2eDub4j+I5/5FwVBUOmqadCPwn8OVcLveepmn3A98DvnYQj70GuAZoUruOww1lnwzITk6RBX0+H16vV9L7jEYjra2taJomXgc1NTUMDQ3R398vu/ANGzbIc5500kn86Ec/4vjjj8dgMMhimo+6ujquv/56rr/+ejwejxQRa9euZcuWLXi9XmbNmsWyZcuor6/H5/NRU1ODXq9n27ZtMuft6uoiGAxSWVkJjPgrKMfAyspKKSiCwaCMPdT5eL1ejEYjiUSC7u5u6aIocqbD4aCjo4PCwkLC4TB2u51Zs2aRTqdlXq3keyUlJQQCAUnSLCoqorq6mqKiInEhLCgowOl0iqxQWVqrG/vHYezzUVxfY0cU+UXp2GjxfCMuFVQWCATo7Oykrq5OLJ6Vf4N6fkVSHRwc5IUXXqCoqIi5c+eSyWTw+XxEIhHC4TCtra2ye4f3s1SUX8Pw8DCDg4PymA+CPXv2yL9Vd+ncc8+loaFhVHFaV1dHWVmZKDiGh4fp7e0VDo3qCAwPDxONRsXnpLOzE5fLRX9/P0NDQySTSYqLi8WYrLm5GY/Hg8ViEd+Q8YzFxm4ajjTOzCQmcSAcVYXDf+M/crnce//97/8DrBnJDfwAACAASURBVNI0zXygkUUul3sQeFDTtFerqqpO/ShObGyGQjqdpr+/X4hcg4ODZDIZ6S4okhogs2CXy8Xbb7/Nu+++KzfgefPmcdttt7F8+fKDDoEBqK6uZsWKFaxYsYJ3332Xb33rW7z11lt4PB76+vo466yzMBqNZDIZrFareEMo22Fl/uPz+YhGo9TV1VFfXy9SUTULX7x4scg+Q6EQM2fOpK2tjbq6OhoaGtA0jVmzZgmHYc+ePfh8PmCksFKSvJ6eHnH0a2lpQafT0djYKJbZmUyG+vp6KisrhZinVB9WqxWTySQ3b7XQKIynzjicTPiP4voau7PNl6EqUyZVLKj3I5FISP6DsiiPxWIEAgEMBoOMrJQVNMD8+fNxu920traKtbgaufX29orRU3l5uRQL4XCY7du309bWJrt6BZvNxuLFi1m6dCmLFy9m2rRpQhJOJBIyGsjlcgQCAVpbW9m7dy8tLS20tbXR2tpKPB7H7XbzyCOPcNppp4k/iPIuUSmaKszKbrezfft2MUGDEc8Kl8vF/Pnz6ezslEV92rRptLW1odfrCQQCDA0Nye/HYDCIsgcOzgTqSBh3TWISh4KjrXB4E9gOoGmaHjADDYAD8GmaVpLL5QY+rpMZzytAme0oa2e14KVSKfHiHxwcJBaLoWmazHWDwSCtra08+uijciNuamrilltu4eKLL/7QO5lFixaxbt06Vq9ezcqVK9m1axfNzc00NTVx3nnnMX36dCwWC8cccwwej4f58+dLQaEUIUajkdLSUok5TiQSEsQ1e/Zs9uzZQzgc5p133sHtdtPc3CxtX6fTKbvkkpIS2traxE44GAyOSmJUEsDy8nIJybJYLLJodXd3i1mW0+mkqKhIbvwqjKuvr4+2tjYKCgqYPn26SAEVjgQmfP7OdrxWqvp9Kr6DGmGobovJZMLv92MwGITQqro/qjOguCtlZWXkcjmRaiqSYTabJZPJyPsXiUTYuHGjECBhJFfl3HPP5fjjj2fp0qXMmDFDFu+xUPyFfJx22mnAyEKveBA9PT3ceuut/L//9/949tlnqaqqks6JKs6VX4RSdkQiETRNY/r06aIuUp2xuro6UeooQuXevXuJx+OS/aK6aQMDA5Lbkt/FmaircKBraLIjsX8sWrQIgHffffewHT/RMfvbeC1cuPCgz+Fox1FVOORyuQygLPQ0IAAM5nI5n6ZpVwDLNE27KZfLxSZ8kg+J/JtAfuxzeXm5MLITiQSZTIZsNovL5aKmpgadTkdra6uE+CjyVzweR9M0pk6dypNPPsnQ0BC1tbXceuutXHrppaNY8/kIBoMyQ+7s7KSrq4tAIMCCBQtYtmwZxxxzzD5GNwBf/OIXOfPMM/nxj3/Mb37zG3bu3InP5+Nzn/scixcvxuPx4Pf7yWQyIlObMWMGwWBQxgM2m01iurPZrKQqWq1WCR8qLS2lqqqKnp4eIU8CYkesnkdZaisSnkr3LC4uZsqUKQSDQex2OwUFBTQ1NVFaWiq7zPwcDhUQphYQ1TpX3hr5ZLcDmUcdKVBdFYvFIlJgxYfQNI1kMimFgMPhoLe3V4o1nU5HT0+PpFtarVbJJVH5EzqdToqQxx57jHfeeUe6FHq9nrPPPpsrrrhCOlcKHo9nXIUHIKTJ8RCNRuV7TqeTn//859TX1/PjH/9YZMSDg4MUFRWh1+ulI2axWERtU1RUJKMNZYi2fft2ISanUikp5mGkkKmvr5ewLsW9gNGFGUzsI6I6QWpUqTgn/2hx7x8UmzZtOuzHH+pzftDHHK04qgqHfORyuTQQ1jStW9O0O4DPAV/9KIsG2Nf+VxnYqNGEYvernY3RaBRTJSUR0+v1xONx7HY7mqZhsVj49a9/TXd3N+Xl5bz44otMmTJFXk+50v3Xf/0XTz75pPgnjIdnnnkGAJfLxcknn8ypp57KKaecIu1igOLiYu68806uu+46brzxRtavX8/vfvc7mpubufbaawmHw8TjcWKxmJgCGY1G2dENDg6K6kItOl6vF4fDQXl5OVu2bJEALJPJJETMaDRKTU0N27dvx2KxMHfuXJmLqx1xIpGgvLwcs9nMjh07MBgMTJ06FaPRSH9/v3RvYrGYBHMpN8LGxkYJNVJSPEWYm8iB8kjBeOcaj8dJp9P4/X7xBVGLXmFhIVarlYqKCulEOBwOhoeHZXxRUlIiY6hkMilcgP7+fnw+H+FwmKGhIdatWydZIjNnzuSqq65i+fLlNDQ0THiu+9tZj0c4nOhx3/72t5k2bRorVqygq6uLZ555hjPPPJPp06dLtyQej6PT6eRrvb29Yjjl8XiIx+MymqirqxM76vLycrmmFf9GhWWp4kCRPwEhOPf394/KAFEYTzYLn+6u1j8K9kd+PJLuAx8XjtrCQRt5t43Ayf/99xm5XK7lo37dsTeBqVOnyv/9fj/xeJz29nbZvRUUFNDb20symaSmpoZkMkkoFMLv99PW1kZRURHr16/n7bffxmq18vTTT0vRoOD1elmxYgWvvPKKfM1qtVJXV8eUKVNoaGigoaGBgoIC3nzzTdatW0dPTw/PPPOMFBK1tbXcfPPN/M//+T/lgzJv3jxefPFF7rvvPm6++Wbefvtt4vE4l112GYlEQmKLYWQX6XK5CIVCtLe3U19fL9HFu3btIpFIiCmVyiloaGgQrf7u3btFTuh2u8lms7z55pu0trZis9mor68nl8vhcDiYMWOG+AE4HA7KysrweDx0d3eTTqepqamhvr5eRhsqz8NgMEh2gVJWqAyQozG8SHW91MJmMBgkQXTq1KniC6J8RAwGA5WVlVJoqPCyjo4O6Vwocu7g4CDd3d00NzczPDzMMcccwz333MPxxx+PpmlSSHwcuPDCC6mrq+PKK6+kv7+f5557jpNPPpmioiIxnVKE2/b2duLxuPBrVNcAED8JNW5TUJ4W06dPl46YQjQalZ9VcZU6OjrIZrOS3qqQf29Qqg41njjSr7VJ/GPhqC0cciMlZFLTtB8Cb38cRQPs29rOb7uWlZURCoUwmUyEQiEsFgtFRUX4fD5JkQwEApIP0NzcTFdXF++++y6aprF69Wo+85nPjHq9119/nX/+538WGd1Pf/pTjj/+eMrLy6WNn48rr7ySXC5He3s7GzZsYO3ataxbtw63280NN9zA+vXruffee6W1rGka//Iv/8KMGTO44oor2LZtG/39/ZxxxhnSBo5EIjJeCIVC7NmzR9QSimCoui1KVmm1WvF4PKKQCIVCFBUViQGVSlrs7e1l2bJlsjNWs3FlDTx16lQ6Ojpwu90Eg0HJ1WhsbKSuro5YLEZBQYEYbSmlQDabpbi4WAyhYN/woiMFE83I842JFDl07969khiqrJ+z2SzDw8Ni4z1nzhwCgYCMuTZt2kQ8Hmf69Omi8mlubmbHjh3kcjkuuOACHnzwwUNe/KLRKJs2bSISiVBTU0N1dfU+KqCDxaJFi1i/fj0XXXQR27dvZ8OGDcycOZP6+npgpLjeuXMngHQgdDqdeKVEo1Hhd6i0VkXSTaVS1NbWypjO5XJRVFQkRF2r1SqcD/W8qvDI98zIJ6/mjxgni4ZJHGk4aguHPDyc+5SIcJUKQPkPKL8Bl8slC2g8Hqe8vJzi4mJsNhstLSP1zn/+539y/vnny3PlcjnuvvtuVq5cSSaT4cQTT+SBBx6gurr6gOehOBNNTU1cffXVZLNZ/vjHP3LTTTfxxz/+Eb/fz+rVq0fd0M4++2xee+01LrzwQjo7O3nhhRdYvny5MN+VLXFFRQUnnHCCaN9VnkRBQQGZTEZ2W8FgkOeff54ZM2YAIyMdFedcW1srqZ4qVhtGyG5VVVW89tprdHd3C4mtrq6OgYEBMQRSWQ2lpaWSQ9HX1yczcqfTKTNudW5qR63X6yecv39aMdGMXBUUqrhra2ujv79fFBXd3d10dHRQV1fHzJkzpQALh8PU1taOGqulUimGh4dxOp1s3bqV7du3A/CDH/yA73znOwdF6otEIrz11lu8+OKLvPPOO2zevFnkmwoqhrumpoaamhoaGho49thjOe644yYkVCrU19fz6quvctVVV/Hss8/yxhtv4PV6Wbp0qciBVfZJIBCguLiYtrY26fIVFxdjNBql+A+FQtTW1mIymdDr9WKKprwklNGV4tEoObAaZ4x9bybHE5M4WnDUFw6flqJBQd1oYIQIGIvFqK+vl+LhjTfeEIe9TZs2EQwGOffcc/mXf/kXeY5IJMJ1113H448/DsANN9zAypUrP/BuTafTcemllzJ37lwuvPBCXnnlFb785S/zzDPPjFqIjjnmGNauXcuyZctwu928/PLLNDQ0EAqFaGpqGjXTVl4TKoirtraW4uJiIVS2t7eTSCREiaFavH6/n6amJgoLC+V4lT6oWPLKxthgMOD3+4VIGo1GheTW29tLQUEB1dXVdHZ2SlHicrkoLy+XUZDBYJBOELwfMZ3JZPB6vRQUFIib4lh80mz4/MIAxncpVYZQik8zZcoUSktLKSgooK6uDhjhtAwMDFBcXIzH46G3t5d0Ok1ZWRmlpaVMnz5ditpt27bx3nsjauf77ruPr371q/s9x3g8zn333cfzzz/Pe++9NyosSqfTMW/ePMrKyiSfJBwO09LSIgVzPurq6li4cCELFixgwYIFki2RD7vdzpNPPsndd9/NbbfdJi6sTU1N1NbWShx3YWEhQ0ND+P1+iY6vr68XKecxxxyDy+ViaGhIosYVkVmpfiKRCJWVleJUqbpX+R4h47l6KgJpfiDWRO/tpNJiEp9GHPWFwyeB8T706muqla6UAoWFhRgMBpLJJLFYjLKyMrGF3rFjB2azmZ/+9Kfy3Hv37uVLX/oSO3bswGazcc8993DBBRcclvOeM2cOa9as4fzzz2f9+vWcd955PPPMM6NuzlVVVfzpT3/i9NNPp6uri7Vr1zJnzhx8Pp+wxhW5s6GhAY/HI+6RasFX3A71f4vFIlbCylBIkUrV6EK5D6rfnfKLUFbU8Xic2tpasSiuqakRTwAltVRW1aobEQqFSKfTlJSUyI1fQRUWarY9Xjv5k2bDH+j18xet8XwrotGozOVV90uZbvX09IhKwel0UlJSwnPPPcff//53crkct9122wGLBrfbzVe+8hUpNHQ6HQsWLGDhwoWceuqpLFmyREiqCr29vcJz6enpoaWlhc2bN7Nt2za6u7vp7u4WXo7RaORf//Vfuemmm0YREfV6PTfddBNf+MIXuPbaa9m4cSMej4epU6fymc98hsLCQux2+6hxgYpw93g8EoKmCt8pU6Ywb948sVePxWIykgiFQhI6p7hB43WsVHdLFXHq9zHRdXMo19bHYV73SeKf/umfDvvxh/qcH/QxRysmC4fDgLGFQn6aY/5uQbXFU6kU8Xgcr9dLQ0OD5FOoGX0mk+Hll18G4OabbxaCZVdXF6eddho+n4+ZM2fy+OOP70PA+rCYOXMma9as4bzzzmPDhg184Qtf4C9/+QtFRUVyzNy5c3nsscc477zzePXVVyVjQllBm0wmZs6cicFgYPHixVIguN1uBgYG0Ov1ssNTXZeBgQHMZjM+n49169ZJK3nhwoXiiqicEN1ut7D+lQqgvLycGTNmsHfvXtrb29Hr9VRWVrJjxw7JYEin02iaJh2EhoYGBgcHcTgcsvCombTL5WLq1KkS86zeu/z385NuN499/YkKVrVgeb1erFYrTqcTj8fDrl27SCaTpFIpent7gZFFr7GxUaSrfr+fdDpNS0sLr776KslkkhUrVrBy5UqR0I6HdevWsWLFCgYGBqivr+f2229n2bJlOBwOBgYGJlwM7XY79fX1zJ49e9TX0+k0W7ZskULivffeY9OmTdxxxx28+uqrPPDAAzQ1NY16TFNTEy+99BL33Xcft9xyi3QJKioqMBqNWK1WXC6XFO8q20R1GJQjaVVVFUajEa/XSyQSkU6MClnr6+uT90BFazscDjRNkwJAfc1isRzUdZNf9I137eXj4zCv+yTx4IMPHvbjD/U5P+hjjlZMFg4fEPk36YnmmOFwGL/fj9VqpaqqCofDQTabxWg0ivlTVVWVtPO7u7tJJpO89dZb+Hw+6uvrufnmmwkEAqRSKS655BJ8Ph/Lli3j4YcfFje8iWbyu3fv3i/nIX+HnQ+dTsf999/P9ddfz1tvvcXZZ5/NU089JSmVmUyGM888k3vuuYdvfvObvPfee5SWljJnzhyqqqrQ6XQSZlReXs706dMlotjr9Yocbv78+ZKf4ff7cbvd7NixQ1q5ABs3bqS0tJRZs2bJmEE5C6rI5KKiIux2u+QtqPAtr9dLUVER06ZNw+VyEQgEJKugvb1d4r/zX0+9bw6HQxwo+/r6iEQi8h7m/54+iU7DeOmLqtuj4sPtdjvRaBSPx8Pg4CAmkwmdTieuhx6Ph1AohE6no7OzU9JMVby5zWajt7cXu93O1q1befbZZ4nFYlx44YXceeedElo1Frlcjvvuu4/bb7+dbDbLCSecwI9+9COcTid+vx+/38+2bdvEqnwsOjs7mTZt2rjfC4VCnHbaaWIItXHjRlauXMnGjRs56aST+MUvfsHy5cv3edxVV13F0qVL+d73vseGDRvEsGzx4sXiodLb20s8HpcFXnEvSkpKRA3U29srYzCXyyWE03yPEa/XK9d8vg14vtRXBX/tT+anrq3JwKxJfBoxWTh8QIyNXs7/O9+O1mw2Y7fbJTq6qqpK0vj0er3cSLu6uiQjYPPmzcAIIVK19L/3ve+xefNm6uvr+fWvf72PWuJgkMvlDlqTXFNTI2OLzZs3c9FFF/HnP/951ML5T//0T2SzWW699Vb8fj9r166lvb2dz372s7JTCofDbNu2jXQ6TUdHBwMDAxLqpWkaW7Zs4c0338Tn84nMbcqUKVx++eU0Nzfz97//Hb/fz/r164H3d8TwvllUNpultbUVt9tNcXExCxYswGKxiCugTqfD6/WSTqelMzI8PEwoFBJOg+JAqERGNYtWOQvJZFKO/ahxoPn2/siQoVBIEhwV90HxONTPHovFmDJlCiUlJWzdulXUMMcccww2m42ioiJ2795NX18fbrebjRs3EovFmDt3Lr/+9a8n9FkIh8PccMMNrFmzBoCvf/3rXHPNNRMe/2Fxwgkn8OSTT3LLLbewdu1avvGNb3DllVdy22237VNMT506lRdffJFf/epXfP/736ejo0Mi5pVfhTIiMxgMwglRXYhIJMLMmTPl96ziu4uKisTaXHFoHA4HVqt1H0WFGo1MlHExHj7prtanAcqtUbk9Ho7jD/U51WMO5fijGZOFwwdE/gda7Q4UDzPfqKa4uJjy8nLa29vZu3cvXq+X4uJiibNW6Y9Go5GGhgYee+wxhoaGOPPMM7nwwgsBeOSRR/j973+PxWLhoYcekp3/gTA4OMjmzZvZvn0727dvx+v1smDBAj772c9yyimnHPDxdXV1rFmzhuXLl7NlyxauuuoqHn/88VEkzGuvvZbLL7+c+++/n1/84hd0dXXx29/+lvr6epYvX86ePXsIBALi5KeMorZs2cJzzz0n9sCapnHOOedw3XXXcfbZZ8tik0wmee211/jzn//MmjVr6O7uZseOHXR1dXH66adTWloqfIRUKkVxcTEnn3wyVqtVPAq2bNnCzJkzhdOgxiXt7e3ASKFSWFgoCwQgsdEVFRVYrVZJ2xwPY0OyPiwOhbuQ3+lSc3e/308sFhO2f/5IIRKJ4PP5KCkpERmtXq8X2WZfXx8dHR0iS9y2bRvt7e0UFBSwevVqCTkbi71793L11VfT0tKC3W7nO9/5Dp///OcPy+9jf3C5XNx77708+uij/PznP+eRRx7hzTff5L/+67+YM2fOqGN1Oh3f/OY3mTZtGhdffDG7du2itLSUiy++GJvNhtFoRK/Xk0qlpAtlNptxOp0MDQ1RUVEhybRqbKbT6TCZTHR2dmI2m2X0AaMll0q6rMy2FN/kQF2ESY8HRIJ+sDz3gzn+UJ9TPeZTxrX/xDBZOHxAHOgDnV9YqPFEeXm5pEJWVlaKiZHKaggEArz77rtYLBbuvfdeyaq45ZZbAPjZz37GvHnzJnzNbDbLrl27WL9+PevXr6e5ed808XfeeYd33nmHX/3qV/yP//E/uOSSS6ipqZnwOaurq3nqqac455xzeO211/jhD3/IbbfdNuoYu93Od7/7Xf75n/+ZX/7yl9x11110dXWxevVqPve5zzF9+nT6+/vZunUru3fvFuIjjBRWX/3qV7n22muFy5EPk8nEmWeeyemnn84999zDli1buOOOO3jqqafYuHEjF1xwATabjRkzZohdt9pNlpWVEQwGGRgYIJvNUllZKTbY6o8it8GI54bNZpN0RIvFIqZIKu9hPIx1C/2wONAuM7+NrQov1Q1R3RjlnaHizQcGBoSQ6/f7RcGzZ88eIenabDb6+vro7+8nHo9jMBjYsmULAD//+c+ZNWvWuOfj9Xq55JJL8Hg8NDU18Zvf/Ga//IfDDU3TuPzyyznrrLO47rrraG5uZvny5Tz00EMy1sjHOeecw4MPPsjXvvY11q9fz+zZs4nFYtKRi0ajFBcX09fXRywWw2w2k0qlyGQy4g6pPBuSySRbt24lk8kwc+ZMKazU9WWz2eR9VGZT6v3LNyCbVE9M4kjCZOFwGDGR2Yvf78fr9crNQqfTMTg4yNDQkCxuOp2Ov/71rwBcffXVTJ8+HYC//OUvxONxli5dyiWXXDLha2ezWf73//7fvPrqq/I1s9nMokWLWLBgAXPmzKG0tJT169fz7LPP0tLSwsMPP8zq1atZtmwZX/rSlzjppJPGHWU0Njbyu9/9jrPPPpv777+fz3/+83zuc5/b5ziHw8F3v/tdrr/+ei699FJefPFFXnnlFWG1K8ycOZMLL7yQhQsX8vnPf15urAeq5jVN47jjjuN3v/sd55xzDmvXruW1117jyiuvxGQyYbfb8fl8pNNpuru7xXegpKREFsylS5cSCATk/WloaBCTKng/7jyRSIziPhxskXg4cLC7zIKCAsrKykSto7I5ysrKhHSqRi7KHbG/v18kkQ6Hg4qKCqLRqPAgqqurCYVChMNh2traCAQCLFmyhKuuumrcc8hmsxLRvmTJEh599FEKCwvZtWvXYfldHAqOOeYYnnvuOb73ve/x+OOPs2LFCtauXStclnxcfvnlbNy4kVWrVrFx40bmzZsnPBHl96DGDpqmCXl3165dOJ1OMpkMZrMZr9eL3+8X+bDKZInFYsKVUZ8ptYlQUMoW9bV/9M7CJI4cTBYOhwH5UkvVglShNoqhPzw8LAY8TqdTTGRUiFUgEBBTnWuuuUaeW3k1XHTRRfs9hyeeeIJXX32VwsJCzjnnHE4++eRRfACF8847j+XLl7N7927+/ve/8/zzz7Nu3TrWrVvHxRdfzPe///1xn3/RokXceOON/OxnP+P6669n06ZNE5IynU4nd999N8cee6xkZhQWFnLxxRdz9dVXc+KJJ34o/3eDwcD//b//lwULFggPYt68eZSUlHDcccfhcDjYvXs3gUAAi8XC1KlTaWtrE1+GE088UdwAjUajcDHUDlE5CNpstv12GhQ+qXZyvicIIIZNBQUF2O12WcBUIau8MFTYWE1NDfF4nF27djEwMCC8B5Xn8NJLLwEj46iJ3q9f/epXrF27FpfLxapVqw7ZPEuFRKkden6HSL0fh/KcBQUF3HXXXXg8HtatW8e3v/1tHn744XGPvemmmyTIbebMmRiNRkwmE9FolFQqxXHHHceMGTNkxFVaWsqOHTtIJBI0NjZSWVkpI7WKigqSyaR0WlTnQcmQ1Xug0+kIBoPSYVD+Lf/IHIZJHHk4pMJB07TKXC7X91GdzJGKsZIr5Y7Y29tLX18flZWVYktrNBplTqpGEeFwmJ07dxIOhznxxBOZO3cuAENDQ7zwwgvodLpx2eIK7e3t/PKXvwRGnPxOP/10YERVMR40TWP27NmcfPLJ3HTTTfzpT3/iwQcf5IknnmDWrFl88YtfHPdx3/nOd3juuefYsWMH3//+97nrrrsmPKempiZ+/vOfs2bNGr74xS9yySWXHNZ2bGNjI3feeSff/OY32b17t0jqGhsb6enpwe/3o2kajY2NlJWVyc159uzZ6HQ6sRUeGhqSrAGlRFDR0/kSvQNJ4j4p5Esxs9ms7HRVDLki46lMhXA4TCAQoLe3l+rqaqqrq6ULEQqFKCwsxOFwsHXrVrxeLyUlJRMWrZs3b+aOO+4A4O677z4k8qjb7ebvf/87L7300oSBbDBSJJ5//vlcccUVB/3cOp2Ou+66i9NPP53nn3+eRx99lC996Uv7HDdlyhQuvfRSfv/737N3716OP/54SXNVn+m33nqLwcFBrFYrZrOZnp4eUaDY7XZ6e3vFPl7xRNLpNJFIRDpZ+TyHse9XMpmc7DRM4ojDoXYcWjVNuxe4M5fLjfq0a5pmAvQfdfrkpxH5rWq1MwuFQnR0dMi8uLa2Vhwi4/E4vb29aJqG0WjEbDazdetWAL72ta/JruWJJ54glUqxZMkSUqkUPT09+7z2u+++y913300ikWDJkiVYrVbeeOMNALq7u9m2bduE5604BbNnz+ayyy7j4Ycf5o477iAejzN37txxY7dvvfVWvvzlL3P//fdzzjnn7EOyVFHGMNI5ye+exGKxUfHKYzHWfjgfyWRyn53nV77yFZ544gleeeUVduzYwbx584jFYkJeU7Ppbdu2MTw8TElJCVarVXa5KuJbZWOUlJTIbD+fBPhJGz3tD6rbkU6n5fejFq78XXw2m8XpdFJRUSHdF5PJRC6XY8aMGZhMJsLhMJ2dnRQUFMho6bLLLiOVSu3z3oTDYb7xjW+QTqf50pe+xIwZM+jo6JDvb968eZ8uRSKRYMuWLbz22mu43W75bF264wAAIABJREFUusFgEGKnkimqf4dCIZ566inWrFnDsmXLuOiiiya0nh5Lhrzxxhv593//d77//e9TW1srBXU+VqxYwe9//3t2797NGWecIeOJXC4nCaAq7bKiooKFCxeSSCSEVDpnzhyGhoYoLS2V81a8E4V8noMakWUymVGunzDpFjmJIweHWjicCtwCtGma9jPgF7lcLvLf3/ss8BdGkij/oTBWVaFQUlIizoexWEyijDs6Oujt7SUajeL3+9m5cydutxuXy8XFF18s7c+nnnoKgHPPPXfCdu2zzz6L2+2mpKSEyy67bNRNtb29fb8+Dvlt7pNOOonu7m5efvllVq1axb/927+JrC8fxx57LNdddx2//OUvuf7663njjTdGSUM1TZtQfmcwGPYrzdsfxyGXy4372AceeIBFixbR09PDpk2bMJvNdHd3i6lTPlu+qKhoVKS5z+cTqWxXVxfpdFrkefk3bsWGH6+Q+iQw3gKjYs4BUZMMDw8zNDQkoUzFxcW43W7MZjNVVVUUFhYSj8cxmUxYLBa2b9+Oz+cjmUzS0tKCpml8/etfH3eh/rd/+zfcbjdNTU3cfPPN+1wr4XBYTMPcbjfr16/n3XffJR6PAyOuj7NmzeLYY4+lurpaiowdO3aMIsl6vV5ef/11uru7eemll9i0aRMXXnghJ5544j6L61jFxwUXXMDGjRt54YUX+PGPf8wZZ5yxzzU0d+5cli9fzl//+lc2btzI4sWLicVi4t2g1+ul4I9Go2Iz3dzcjN/vp6qqCq/XS3d3t4SK5XcWgsGgdK7yOVBqPKO8I+DTXaBOYhL5ONTCYRiI//e//x24QdO0VkAPzAU2HcZzOyIwVlqlboA2m426ujrxxne73SQSCfr7++Wmk0wm6evrEyLZVVddJYuTz+fjlVdewWAwcNZZZ4372ps2beKVV15B0zS+8pWvTCiVO1hcfPHFdHd309LSwgMPPMDnP//5cReNa665hvXr17N582ZWrlzJvffe+6Fe98Ogvr6eO++8kxUrVrB582ZqamooLCzEaDQKj6ShoQGj0UgqlaKzs5MpU6ZgtVolB8NsNstCqySZjY2N0h0Z7yb/SUItMPl+AEpFohYmZSOtFkqLxYLP58PtdsuCu2nTJmw2G8FgUObwZrNZrtUzzjhjnwh3gD/+8Y88+uijWCwW7rzzznELTIXNmzfzm9/8RorCxsZGysvLOfHEE/f7OIXy8nIuuugiurq6WLduHQMDAzz00EM8//zzXHLJJftVGWmaxsqVK3nvvffYsmUL9957LzfeeOM+x91444389a9/Zdu2bSKbLC4uxmKxYLVaZXyjjMoCgQCxWExi25ubm6VLpZJH4/E4paWlMrpQRNuJvF/g01egflKYiE9zsLyod95557Acczgec7TiUPthDwNLgLuBm4CfAjZgESPdho9euP0xQRUE+Szo8aBMgtRcVCGdTovvvbo59Pf3E4vFSKVS2O124UL09Y3QRr7+9a/L4//85z+TyWQ444wzRtk955/fypUryeVynHXWWZIy+WFgMBi49tprKSoqYu/evaxatWrc44xGIw888AAmk4mHHnpIDKs+KXzlK1/h7LPPZmhoiG3btmEymQgGg2KGlMlkSCQSeL1ecVL0+/3SDld21PF4nOHhYfr6+sSMazxZ3ceFia5BFbwFIwtRNBrdhyiZSCTIZDKS/9HZ2UkqlSIYDJJIJGhtbZU0TNVadzgclJeXy8jh6quv3uecQqEQ//qv/wqMcF7Gk9Aq+Hw+Vq9eTS6X4/jjj2flypV8+9vfFifRQ0F9fT0XXXQR3/jGN3C5XPT09HDXXXexdu3a/T7O6XRy6623AvDjH/9YvDvysXDhQs4880zC4TCtra1kMhkMBgOpVApN0yQ9MxaLCScmFosRCoUoLS2lrq6OU045hfLyclwul/hnqKRbFRevCgKlahkbcpVfoE7ig2PRokUHNGo6mGPGe8wkRnCohcNxwIpcLndrLpe7K5fL/QSYD3wL+AKwr0bvCIXa1Y21Ix6LgoICKioqqKioGLWwKKMiRXo0GAy4XC5ghCRVUlLCCSecIO3LuXPnijMdILLKiUiR69ato62tjaKiIs4777wP+dO+D4fDIeFFjzzyiLg5jsWcOXO48sorAXjuuecO2+t/EGiaxg9/+ENgZDwzNDREKBQiGo1KMJIq7lTIVTabFVOuzs5OcrkcpaWlNDU1iboA3g8nUjP4jxMTXYNqNJZPxs0vcHQ6HdlsFk3TKC4ulsVIdbm8Xi+NjY1UVVWRyWTo6Oigvb0dv99PNpvF7/djMpk444wz9jmnNWvWEAwGWbJkyYQkWoWnnnqKVCrFokWLuPzyyz90roqmaZxwwgncfvvtEuz22GOP4fP59vu4E088kS984QukUil+9rOfjXuMSp/1+XxiVuZwOER1U1dXx9KlSzn//PM57rjjxNZbOaGmUimy2ayMyWKxGPF4nGAwSDqdJhgM4vV6ZUQ23n1FFYSTCosR5HK5Cf9M4pPFod4JPUB5/hdyuVw2l8v9EvguIx2IowIH+yHW6XQ4HI5Rem0YcV2cM2cO9fX1RCIRzGaz3OyHhobIZDLs3LmTPXv2ALB48WJ5bC6X47XXXgPg1FPHz6xZvXo1MGK7ezBx2vF4nLa2NjKZzAGPnT17NrW1tQwMDIh98Hg488wzAXjllVcO+JwfNebPn4/VaiUYDLJ3717ZFUajUXw+H9lsVgyeNE2TXbwaP1RWVlJeXk4ikRA7YWWe9EndzA/02qqA0Ol0oqbQ6XQUFhZSVVVFdXU1sViMvr4+gsEguVxOFkSlMGlsbMRut8v3VNjV7NmzxyWyPvHEE8AIaXJ/reOWlha2b9+OxWLhoosu+lDy27EwGo2cf/75fOYznyGRSPDb3/72gJ3Br3/96+j1ev7whz+MInEqnHXWWbhcLpHmKvKs6hbkcjmsVivhcJjNmzcTCASw2WzMnDmTKVOmUFlZidfrpaWlhZ07d9LR0cHu3bvp6Oigra2NnTt3Mjw8LFLf8d7T/PdzEu9jLMn6cBx/qM+pHjOJERzqFfoQ8B+api0d53vdwL5OK0coDvQhnqiNnMvliEQiGAwGpk+fTm1tLRUVFRgMBkmOnD59Ona7HaPRKEFB+YXD7t276e/vp7KyctwRRHt7O+vWrcNsNo963ETwer384Q9/YM2aNTz55JMHdDnUNE2Kgt/+9rcTVvinnHIKer2eN954g507dx7wPA4GXq+Xn/zkJ5x99tn86Ec/OmhHRoPBwMKFC4ERt8mamhpKS0txOBxEIhF6e3ula7Br1y76+/sxGAw0NTVJeJYKG+vo6GBwcFBGAJ/UzfxQXlu1wZPJJMPDwwSDQUwmE4WFhVRUVFBTU4PD4WDWrFkUFxeTyWRE7TNv3jxmzpxJKpWS3buSBOfD6/Xy6quvYjAY9hvlnkql+Nvf/gaMuDSOjc4+XLjyyiux2+3s3r17lPHZeKirq+OSSy4hnU6P23UwmUzSQens7CQUCpHNZoVg29XVxdatW9mzZw9dXV14vV55nN1uZ2hoSHgyJpMJq9VKbW2tcDpUeFhlZSV2u/2wFlJHO1atWjXh2PSDHn+oz6keM4kRHCo58j+A04DXNU17Hvgb0A64GFFb7OtxfJRiPAa0GjuorysDHtU6Vg5zSu+dTCbx+/3AiOudykl44YUXgBGlQzQapbW1ddSNRsW7nnLKKbjdbtra2sY9R6/XyzvvvENXV5cs/v39/TzyyCM0NDTsVz9fXV0tYUdPPvkk8+fPl+/p9XqKi4sxGAxcccUVrF69mm9961s8/fTTpNPpCZUTiog4FrlcjrfffptVq1bxl7/8RaR/r7/+OqtWreKGG27g0ksvHdcBEEYkoDqdjsWLF/P666+TSCRwuVy4XC5ZMI1Go1hf9/T0YLVaKS0tlR2les8UDyCfGQ8TS+U+TgmdatPmu5Oqr/v9fkKhEF6vl3A4zODg4CiSn16vR9M0iS5XQV6KyxEMBikvLxe+ypw5cxgcHBz1M/3ud78jk8nw2c9+llwuJ4ZlY7FmzRr8fj92ux29Xs+6detGfd/v99PS0jLuYy0WC2+99da436uurmbDhg2jvrZ48WJefvllHnvsMRYsWDChl4TRaORrX/sajz/+OI8++ihXX301tbW1ACLd/eIXv8iqVavwer2ceuqpOJ1OLBYLvb29co1VV1cza9YsbDYbZrOZ9vZ2SkpKxHBLJYtGIhHpcEWjUUlWnSwYJnE04JAKh1wul9Y07Rzgm8C1wD153x4GLj6M5/apxnisaE3TRjGjlQGPzWbD6XQSDodxu91kMhmGhobo6elhYGCAwsJC5s+fLyMHdXM85ZRTMBqNEt8LIwWLcvS77LLL+POf/zxuUmY2m2XDhg0ymtDr9ZhMJiHNtbW1YbFYmDdv3rgLnopQ/u1vf8vf/vY3li1bJt/L5XJSANx222387W9/44033uDpp58eJScdC5PJNKr9HY1G+eMf/8iqVavEx0Kn03Huuedy3nnn8fDDD/PGG29wyy238OCDD/KDH/yASy+9dJ/n1+v16PV6lixZAkBXVxeZTEaklwaDQQiBfr+fSCRCLpcTVYLBYGDGjBkkk0lMJhNut5uysrJRv5eJpHIft4RuvAj3cDgsRaDyIQgEAvT19ZFKpUaFeHV1dUkSZHt7OzqdDo/HIyZYyl9BjX7yf9fKEv3iiy8eRdDMx9DQkMiIlY2zIgMqbNiwAYPBIN/L5XLodDr0ej1ms1n4JWORyWT2KR5nzJhBV1cXe/fu5Te/+Q233377uNdzJpNh1qxZXHDBBTz99NM8+OCD/OQnPwGQzsIpp5xCQ0MDnZ2d7N69m/nz5zMwMCBEWvWZrqmpwe/3Mzw8zIwZM7DZbNJRNBgMQqb0+XzE43H6+vqorq6Wzkt+8Tc5lpjEkYhDvmpzuVw6l8vdncvljgGqgJOBk4CaXC730uE+wU8rJmoj5zOjLRaLyOUqKiokZe/tt9+mo6OD9957DxhJXVM36FwuJzu0k08+eZ/Xfe6554hGoxx77LGSZzEW8Xicl19+WYoGZaWrdpxq8d65cyevvPLKqNCpfFxwwQUYjUZef/31cc2nAIqKioSY+IMf/GC/XYx8/P73v2fWrFlcf/31bN26lZKSEv7X//pfbNmyhUcffZTLL7+c5557jj/84Q/Mnj0bt9vNtddey4knnsizzz477vhEjW1UkqHRaGTv3r1s2LCBDRs20NzcjMvlYt68eRgMBgYGBkSCqQiVKhUzHP7/7J13fFvlvf/fR1uWLFmyZFle8oqzSQJJIIGyElahFAqFAr2lNC1QbqG09McoDYWWkbaMDspltIXbci+U0VB6SymroUADISEEMhwncRw73pIta1n7/P4wz4NsywvCKv68XnlBomPpSD46z/f5fj8jMmzBG4tv8GFzIMQ1NVKyl0gkiEaj+P1+UqmUjGwXqhGNRkMgEGBwcJDu7m46Ozvp6ekhGo1SVFQ0rOUOjJI5trS08MYbb1BQUJA3p0Tgv//7vxkcHMTlclFaWjrmcZlMRpp1JZNJ4vE40WiUgYEBGWWeSCQmRYQ7/PDDMZvNbN++XRY3Y+Gyyy5Dq9XyyCOPSH6RgEaj4bLLLgOgqakJg8GAzWbD5XJRUFAgjZu6u7sJBALEYjHC4TDJZJLm5mY2b95Md3e35JkMDAxIq+p0Oi2/j2ORXier5JrGND5qvK9yV1XVblVVX1FVdb2qquPLDz5ByGQy7/nLazAYGBwcxGAwyCIiEonQ2dkpHSFFZ0HI4HJ5Ctu3bycQCOD1eqmrqxv1/H/+858B+MIXvjDmuT/zzDNS4ikKBdEizXWrFB4Tzz33XF7SZHFxMStWrEBVVZ544okx3/PZZ5/NEUccQSAQGJO1notnnnmGiy++mGAwyOLFi7nnnnvYsWMH119/PVVVVfI4RVE46aSTeOWVV/jFL35BZWUl27dv56yzzuLKK68c9bw+nw+Px0M8HpfxyEajcRi/RLgstrW1EY1GcblcmM1m9uzZQzAYJBAI0NPTQ0tLi1QZ5Pp0jCwUP2wOxEjJXq4/gliohYukz+fD5/MBEAwGpRGZQFFRkTTAKi0tJZlMkk6nKS4uHrXoi+suN5RsJFpaWnjuueckd2QsiKJBKD+Ec6R4TCgQWltbaWlpmZDQazKZpIPp73//+3GL17q6Os477zyy2Sx33HHHqMfPP/98HA6H5LgUFhZis9moqamhoqJCjh/NZjMajYZEIkFfXx9arVZ6OIgiA5DyaxGGBWMXm5NVck1jGh81pnS3UxTlhXH+PKcoyuOKonxfUZTJm9Z/DCHsYN8L+vr6GBgYkP72VquV3t5eNm3axD/+8Q8cDgdHHnkkxx9/vLxZ5ro7CnJadXV13nmoaCUvW7Ys7+sHAgHpHWEwGMYcG2i1Wk488URpNTzW+12+fPmw180HRVG45pprAEbNoPMh97WeeuopzjnnnHFNb7RaLWeffTZvvPGGDOHKp+RQFIVFixYBsHnzZkKhEFqtlpkzZzJr1ixsNhvhcBin04nP58PhcGAwGPD7/UQiETKZjDSOqq6ulp2Hzs5OWTwIfBS7QzFeEfJL0fIWcl+v10t9fT0Oh4OqqirmzZuHTqeTYwvhiJhMJqVc0GQy4XQ6KSgokL/jGTNmjLr2tm3bBpDXtllgz549ABx22GHjdmDEZ6bVaqW/gVhsCwsLcblcshgTfggTobq6mpqaGpLJ5LAk1nwQMtN8Mk6r1cqxxx4LIH0uRMGfSqVk52BwcJDi4mLKysqkW+TAwAAmk4l4PE4mk8HhcOD1eqmsrKSsrAyXywW8azs9sticlmNO45OCqW6TFGAmQwRJH2B6579HA7OBGmA1sFVRlDkH7Cw/ZIgb2nuBaNGaTCYZ05tMJslkMrIVa7fbGRgYkK+RuygJs6eRC5WA2GGOtcMVbO+KiooJiVi5M+zxbKJzX3cszJ49GxhSfEx07Oc+9znJ2r/55pvHPTYXJpOJ888/H2DMXaUownbt2kVXVxeNjY00NzcTCARIp9NyERAqih07dpDJZKioqGDhwoWSS2Kz2caVuX4Uu0NRJMTjcVns5Y4uNBqNlPvZbDbpFClspY1GI+l0WvoMpNNp9Hq9JLqK9yJIg7kQMs18jwkIz4/Jcj0EYVNAdMPEgiueZ7wMk1yI78R4eSjwbhE0luukKGxElyAWi0muQjKZRKPRUFxcjMfjkV2IaDRKMBikr6+PgoICioqK8Pl8Uj3l8XjQarVSdZXvOzItx8yPgw8+WCqmDtTxU31O8TPTGMJUr9DbGbKcPkRV1TpVVZerqloHLHnn328AZgC9wE0H9Ew/RGi12vf85dVqtdhsNiKRCHv37pWZFB6Ph5KSEoxGI6+99hpbtmyRN1ohyYR3CW8TLUhjFQWicBhLgTAS4iY51vsV/z5RMeBwOCgqKiIajU5oyKPVarn99tvRarX8/Oc/lyqSyUAUVv39/XnPqby8HBhabESB1tTUJK2WtVot6XQaq9XKnDlzqK2tldHN7e3tcgEWsFqtwxYxgY9idyheU8hMR2YeCGg0Gvr7++nu7iYajUpVTyKRIJVKyRk8DO26W1tbaW5ultdhvuJAcFzE55sP4hwmskwWv7eJCltRxIlibyIITspEviYi+C1XKZTveWw2m1RTADISW4yCLBYLvb299Pf3y26J+O4Lm+loNCo3DWIjka+DNY2xsWnTJjZt2nRAj5/qc4qfmcYQpirHvBG4XlXVzbn/qKrqJkVRbgBuVFV1vqIoPwNuPVAnOVUoijKTIYnoRiCrqurErkcHAOKGKIxiBKtfo9HQ09MjjXrS6TSKosjFKNc2WNykYrGYnEe3t7fLfxcLfWtrK1qtlkAgIPkMqqpK3oRIRxxvPtzS0iJvkvv37x92w9Xr9bS0tMgiIBqNSuMco9GY12rY5/MRDAbZsWNHXsa9iKYGWLhwIVdeeSW33HILF110ES+88MKYbHrxswJiztzb2yvVAkLlkTvnr6urw+fzsX//fsxmM7W1tZSWlsqFU6gtAoGAbNsL8ySz2TyqMBF//6hY8aLFDe8WmGJskU6nGRgYkGTcyspK+blks1nJvenq6pImUEIuGAgE0Ov1cuEvLS0llUrh9/ul9bK4fgWpFBglqRTFhYjwDgaDed+H+BzT6fSoUY9er6evrw94t2CIxWL09fVhtVrZvXv3mJ+P+L6MTKeEoWtWKEeE5LSmpkaSY4WrK7zbORG+C4AcWwkFj9vtljyHdDrN7t27ZTS5eH+i+BcjrWny4zT+XTDVwqEB8I/xWC8gaP57gPxxjh8wFEX5AnAz0P7On42KojygqurknITeI3JJdBaLBbfbLRdJUTjU19eTTqfp6uqira1NPh6NRrFYLCiKIm9g8XhcPl5eXj4qbMrn80lCVm5uQSaTwWw2U1ZWNmGGRH19vdTM19fXDyscHA4HPp9PFiUmk0kS7SB/O7quro4tW7bQ2tqaVxFSWFg4bDd6zTXXsH79etatW8e3vvUt1q5dO+bIRFEU+Xk4HA7JyHe73VJOB0NGP4BMLJw5cyYOh4NYLEZzczM7d+4clqyYTqdJJBI0NDRgMpkoKSkZdg6xWEzaVJeUlKAoykeWYphvhy6inEUGh/CusFgs1NfXk81mGRgYkIt5IpEgFothNptRFAWDwUBFRQV79uyRHYeqqip0Oh1FRUXodDrpA+L1euWcHhh2PcC7nQZheJYvYwXg9ddfB4a4RCML21QqJa9nkWIqCiBVVUe9Zi7ECKKurm6UvbWqqrjdbnp7e+ns7MRisUg1UyaTGfb9Egu76A5UV1fT1dVFZ2enJNv29vZKpZQgQ4vRhSDjio1AbmdIxJuPvG6mI7U//hivQ/Zps8Ge6hXaAnx9jMcufOdxABcQeG+n9N6hKIoeOBtYparqCuDPQCVwpaIoo7fAw3/2QkVRNgKHTESuyodYLEZnZyfNzc2yPVxYWEhhYaFsTWYyGYLBoLx5iRtU7qgit5jIh/HavGKnlrt7mgiTHVVMZpckuhBjGVKNhFar5be//S1ut5t//vOfk1JkwFDhAPl5DoLjEI/Hh3VjiouL6e3tZd++fTQ1NUkim91ux2g0EgqFcDqd+P3+YYuZ0ObnJhwWFBRgtVrlQjAZvN/rKxcjd64FBQUUFhZSVFSE2WzG7/fT2NhIZ2cnb7/9Nh0dHbz++uvs2rWLwcFBBgYGpPdBW1sbW7ZsGdZxGDmOEJ2E8SLaYfKjislCFLKZTGZSN2bBhRiP49DY2AgMGa6NVaSK5xHfMWHiJor0goICST5WVZW2tjYMBoP00BDEU9FFFJwp4RvicrlGfX+nFRVjQ1GUKRlnTeb4qT7nNIZjqh2HHwEPKoryFvA40MNQdsUZDMVqn/vOcSuB1w7USU4RNoZ4Fq8AaxnqkJwMnKsoyj3qGHcgVVXvBe5VFGWd1+vNHxAxDgQrPBqNkk6niUajMuZatDdVVWXfvn0y7EbsWnPb8EajEY1GI6VxY81rxyscxMI6EQQzX+xax3udydy4q6urgXfZ9ZNBaWkpv/nNb/j85z/PmjVrOPLIIznssMPG/ZnxCgcxnxc7vEQigcVikdJMt9vNjBkzpKtiRUUFb775JvF4nKamJjm6yXUgHGn2JT6vUCgkCW0T4f1eX7kY2fHQaDR4PB6sVivd3d1S0iu6C3PnzsXj8UhXzHA4LGfvosAVpD2AWbNmDXs9UehMVDiIFv9Uky/HgqIosiMwmYyVyXAcxLU5lgdK7vPY7XYMBgPhcBiDwSD9PjweD4FAgP3796OqKuFwWEab79ixA6PRiMPhIJlMkkwmZYEpCmqr1SpN20SnQRRb04qKjx/EPVL8fy4+rcXHVJ0jH1IUxc8QCfL7gB5IMcQlOF5V1efeOfS7wIfCKxhxfilFUW4HLlUUZY+qqi8pivIyUA58Frjng3hd8eW3Wq1ytyEWrlgsJvXbbrcbq9UqzZjEDFcs+IDkPogb/MgiQNxIU6nUqPGFuKjb2tomvMkD7NixA3h3Xp4PYoGaaBfZ39/PnXfeCTDlbIKVK1fy3e9+l9tvv50rr7ySdevWjVnIhEIhGY2c75zEZ5LJZAgEAnIHGA6HSafTNDQ00NPTg8/no7y8nHQ6TWlpKaFQiPr6ekKh0LB2vFAyjLQLzi0mctvMHzRGxnyL1zYYDDLZsaGhgXA4TEdHBx0dHZhMJsrKyujp6UFRFJYuXUoqlaKjo4OBgQHa2tpkkWUymUbxU0RnY6LdsCiUhQLj/ULITyeDcDgscyLG+z20tbUBo8csAslkUnYlRM5HIpEgnU5jNpvlGEJYd5eWllJWVobVaqWlpYXdu3dTV1dHWVkZAwMDbN++Ha/Xi06nG8bxERBFoOhGTGManwS8F+fIZ1VVXQ6YgVLArKrq4TlFA6qqxlVVnZyG6sDjJeAZ4D8URTlSVdWMqqr/C5QBCz6IFxRffo1Gg9frpaSkRN58k8mknCW3tbVJK+T58+dLi+SRN9rxdtS5fIaRmDt3LmazmYGBAd54440Jz1twIMR55IMgo+UzoxKIRCKcddZZNDY20tDQwHXXXTfha4/ENddcQ1lZGW+99RaPPPLIqMdVVeWxxx5j8eLFtLe3M2PGjLwBX2JHKWb4VquVrq4uent7iUaj7N69m507d7Jjxw7a2towmUyYTCaKiooIBoNyxix2kkKBMfKGL55bo9F8qG3mkTHf4rXb2tpk6qrX66W0tJTS0lJmz56NVqvF6XRSUVEhd+42m02S+zwej/wc4vG4XFwFDj/8cGDIo2OsmHVA2pKvW7fugBAABwcHUVUVvV4/oVKiqalJnuvIgjoXgtiZWxzm4tlnnyUQCGC1WonH4/T397Nv3z6y2SyVlZUsXbqUkpISOc5IJpPU19fj9XqlvNW51/2XAAAgAElEQVTtduN2u9HpdJJcKoo9UWQI5Fp3T48qpvFJwXsucd+J0+5RVfVjRRFWVTUO/A+wBbjmndny+YCHoVjwAw7x5RcSLa1WK3dfGo2GSCQi0xgBaRBTVVUliZO5WnXBUcjtRAiI3bxgiOfCZDKxZMkSaWo0EbLZLA0NDeNK7ARzPl9KJwzdOM8//3w2btxIZWUlf/zjH8dVR4yFgoICfvCDHwBw4403DnM4bGpq4uyzz+ZrX/saXV1dLF68mP/93//N2yYU7WARJlZVVcXSpUuZM2cOVqtVkkctFgvhcJh4PI7L5SKVStHf309zc7P0SOju7qa7u3vCm3muNPOdrs/4RgLvAyNloOLvlZWVVFRU4Ha76e7upq2tjVQqRSKRoL+/H7/fL/0fmpubaWtrI5lMSn+BVColn3Nk7LTX62XWrFnEYrExA6hgaMTh9Xrp6+ub1PWXD5lMhnA4jN/vl6qMiTo52WxWXqcnnnjiuMeKwmGsa/Shhx4ChsZumUxG5nikUimcTqd0Wm1paZEjyO7ubjZt2kQsFqOsrIzKykoGBweprKykvLyciooKac5VWlo67LoVoy7xZyq8mWlM46PCVDkOKIriBa4AjmJI8hgA1gG3q6radUDP7j1CVdV+RVHuA7YzFMYVB76squpondYBgPjyC722kAuGQiGi0ahUSDidTkwmEzt27CCdTtPU1CTNY9ra2uR8XrDRu7u7SSQSdHZ2yjammB/v3r1bzl9zyZUwRFJsamqa8AZUUFCA1+vNm0Oh1+vp7OyUbduioiJJNNTr9XLneemll0op5R//+EeKiorG1N3HYrFxZ4Knnnoqv/71r9m2bRu/+tWvWLVqFT//+c+5++67SaVSOBwOVq9ezXnnnSftfmFoJi0+F7HzdDqdmM1mGSFtt9vR6/UMDg4yd+5c7Ha7lNQNDg6i1Wrp7++Xs2zBWRFSx1gsNuZIJ5fn8E4BeGCG/CMgZq3iPHL/ns1mKSkpkbwFoYgQNtqBQEAqAoQyRPBpMpkMiqJIq+V9+/aRTqcJhUKy2D3ssMNobGzkxRdfZMGCocbdyM4EwCGHHML//d//0dLSkleSOxFG5qaIMCwhL85HLBXFncfjweFwjHk9DwwMSJ+TXHmmUDokk0mZdbFkyRLi8Th2u51sNktdXR0WiwW/34/dbqehoYEFCxbgcrloa2vD7/dTXFxMTU0NHR0d0tcBhooVu91OSUmJ/L3BUNdqpJpiKryZaUzjo8KUCgdFURoYGgU4GCIf7mZoXPFt4CuKonxGVdX8ebkfMlRVTQL/UBTln0N/PbCdkXzyKVEswHAvB9E2z2QyWK1WysvL5UJVWFhINBqlv79f7upFGzUSiWA2m/H5fJIp7vF42LlzJxaLhdraWg466KC8nII5c+awdu1aVFWlvr6empoaYOgm9sYbb6AoCl/84hfH5EIUFBTgcDgIhULYbDYOP/zwYQShwsJC+vr6ePTRRzEYDDz55JMsWLCAVCo1Jh9CjGzGgl6v55ZbbuHUU0/l5ptv5o477pALyZe//GVuvvnmvC3mTCYjFzjBfzAajYTDYYLBIC6XC61WS3V1NfF4nKKiIlwuF/F4XBLfmpubh82Z/X7/MB8O4QQ6kWTund/T2P38AwxxTiK5MZvNYjabpXWz8F+Ix+OoqorVapXqiqKiImbMmIHD4aCnp0deY11dXej1ekpKSuTnevTRR/PAAw+wfft2uQDOnTt31Pl4PB6eeuop+vr6OOyww/IWW11dXdjtdnp6ekYRaXU6HcXFxdjtdux2+yiJcD7L6/vvvx8YSu0UjqQjIQpPUSzU1NTIkaDwudixYwfxeFzyWbLZLNFolLKyMpLJJDqdjvLychYvXozNZiOdTpNKpSgrK6Ovr4+5c+fK61PIMEVku3CKFURUcR3lEl3zJe5OYxofR0y14/ATIAQcqqpqi/hHRVF8DPEKfgLkT1/6iHAgzZ9yi4V8Wn6z2SxbjaqqUlBQQDqdJhAIyLm0iNhub28fZgKVu5MSbdSpjipyUVVVRVVVFfv27ZPdiZKSEql1r62tnZBAKboNM2fOzNspEFHYCxYsYOHCheM+12RxzDHHcPzxx/PMM88wODjIggULuP3221mwYMGkbqhiISoqKiKdTktiY39/P16vl4qKCrlQJhIJenp6KCgokMTBgw46SJr6iGwCsfACE/o3vPM5vW9+T77CNHfBEb8PcR3mpnmKjoPf76eoqIjOzk5CoRB+v1+SB4PBIMFgkP3798vrVXQI8u3YFy9eDAy5542n9nG5XCxevJgNGzawZcsWmXWSD263G5vNRkdHB2azWfJMRnowjIeBgQEaGxvRarWcdNJJEx4/3qhCXM+FhYUYjUaKiopk6JpGoyEYDFJRUSHzM0R3MRwOU1xcTCqVIh6PS9dWkQ0CQ+TN7u5u6emQr1jI7TRMxddBUZQLGZLDz3y/Ut+PI+65Z2qc9skc/0E856cJUy0cjgEuzi0aAFRV3acoyvXAXQfovD6WmGh3IHanguSUzWax2WzU1taSzWYlUVKw2YXzIQwnSAqOw3jkyIkKBxjaoZlMJnbu3Mn27dvZvn07MFR8COnkeMgtHPJBkCtF6/pA4e677waGEhkvuOACtFrtuKS8XIjCwePxyFGFUA6UlZWhKIo0RBIdncLCQgYGBjAajVJup9FoqKysHGbc82HuCPMVprn/JiKeRaCZIIG2tLRQXFxMNBqVIy6/309XVxfZbJbq6mppECXcSXU6HSUlJVRWVrJhw4a8gWYej4fq6mpaWlrYsWPHmDkPMMQz2LBhA5s2bWLZsmVjjqcURcFkMg1zIZ3MdZ2LDRs2kM1mOeiggyb0L0kkEoTDYbRabd4unSgcTCaTJD2mUimCwSA2m41kMkkwGERRFOx2O7Nnz8bv9+NyuTAYDFJGLbpkub8/g8EguSaiYzOyWMjFVEzGDqTU9+OICy+88IAf/0E856cJUyVHGoDwGI+F33n83xa5xLSxAmnMZjM2mw2n0ynblV6vV94cOzo6GBwcpL+/H6PRKG8KW7dulc8hPARGWvrmPvbSSy9NStteVVUlxxQwJOecN2/ehLuYRCLBk08+CeRvSQO8+OKLwIEPfxGs9K9//etjmvTkw8svv8z+/fslSVHM6wU3o7Ozk97eXnbv3o2qqjidTklIq6ysxOFwkM1mZcZDMpmUYVciXOrDCiHKl4Ux8t9EQSBCmGBop6rT6aSPgHDcXLRoEdXV1QQCASnbdLvdOBwOEokEmUxGum6+/fbbeX07hL/GAw88MO65H3bYYZjNZrq6uiaVlvpesXHjRp57bkjMdeihh054/Nq1a4Ehg6uRxUw2m+Xpp58Ghooy4a0iuBDJZJJ4PC5zP8RYURCdc/NA0um0LCRMJhOKouDz+aioqJDmT/nSMXMxnZQ5jY8zpnoHfJMhj4RhP6cMfQsveefxf1tMJb0uHo9Le+lc73xh7CS4CWLn/5e//EUqK8Qc97nnnhuVDHjSSSfhdrvZvn07f/rTnyZ13nV1dcydO5clS5ZwyCGHTOpm9Pe//5329nZmzZolY4hz0d3dzfPPP49Op+Pkk0+e1Hl8kEin01x66aXA0PvNdfez2Wwyc6ClpYVwOCxtuTUaDQ6Hg3nz5jFr1izZgfB4PKOUCwfqJp7JZCYkrua71nKJkdFoFKfTSVlZGSaTic7OTgoKCmhoaKCmpgaDwUB5eTlGo5Hi4mLq6uooKiqir6+PSCRCYWEhFouFoqIiYrEYra2tZDIZLBYL+/bty2tXfumll6LT6fjDH/7A5s2bRz0uYDAY5DXz9NNPT8kQbDLIZDI8/fTT/PGPfySbzbJixYoxVT8CPT09MpL9e9/73qjH//73v7Nz505sNhvLli2jpKSEUCiE3W7H6/XKUUMqlWLGjBlSzioyY4T9tCg829rahkWCi2NGFsJj5VdMJ2W+i3vvvZd77733gB7/QTznpwlTvSp/xJAr5A5FUX6kKMo33wm32gYcx5Ax1KcOokAQqgphJ63T6ejo6OC1114jHA5TUVGB0+mkuroaq9VKVVUVtbW12O12AoGA3MHX1dUxe/ZsgsEgL7/88rDXslgsfPe73wWG5m6TSdlTFIWysjKKioomZc60d+9eXn/9dXQ6HT/60Y/yWvg++uijZDIZjj/++DE18R8m7rrrLrZu3UphYSFLliyRfAafz8fMmTNZuHChDH9yuVw4nU5isRh79+6lsbERnU6HxWLBZDLh8XhkK18QJg/kTTyTybwvvb5oYws5peAb6HQ6PB6P3E3b7XbMZjOJRAK/3y/jnRsaGigrK0On05HJZCgtLcXn85FKpaSj4uOPPz7qdRsaGrj44otRVZWrrrpq3OKnvr6eo446imw2y8MPPzxm4NVU4ff7ueuuu3j++edRFIVTTz2VE088cVy1TjabZc2aNYTDYU488UTOPvvsUcf84he/AIY8TTQajQx5CwQClJaWks1mKSoqYuHChVRUVGC1WlFVFZPJNCxcTEiy9Xq97EKM57r6Hj1AJt+G+zfARRddxEUXXXRAj/8gnvPThCndCVVVfRo4haGxxLXAr4EfABHgFFVVnzngZ/gJgN/vp6OjY5h2XXjSCzlZLBYjlUpJEpherycWi1FTU8Ps2bMBhnUQxC7+r3/966jXO+qoozj66KOJxWK8+uqrBzRgJR6P89RTTwFw8cUXj7mTE3r3c889N+/jHya6urq4/vrrgSEZXXFxMV6vl4aGBrkTtNlsFBcXy9jst956i927d9PV1UU0GpUmUG63G41GIwtAUZgdyGRDkV3wXpGblSGUEmKElc1mGRwcJBKJSCIuQDAYpK+vj+rqaubMmUNNTQ27du1iy5YtdHR0kEwmicVisnD405/+lPe6uuKKK/B6vWzevJm//e1v457nypUrmTFjBrFYjN/+9rfvy1FSZELccccdtLa2UlRUxEUXXZQ3TG0k1q5dy6ZNm3A6ndx6662jioxt27bxwgsvSFmruDb0ej2hUIh//etfkmQrNgexWExKMquqqshms/T29jI4OIjNZqOoqEjKR8cr7sX1aDAYJnV9vTOe/FQVDtP4+GHKPg7vFA9PK4pSwJAss19V1U+13ZnYcbtcrmGJeLFYDJfLJdvLWq2WWCyGzWZjx44dNDc3YzQaqays5NVXX+XJJ5/krrvuQq/X8/nPf55bb72Vv/71r3zve98btev/6U9/yooVK2hra8NoNEp3v1xYrVY5t86HXO6DwG233UYoFKKhoYGrrroqL3t++/btvPnmm9jtdj73uc8NO0aEAcHQzT7XGttoNI7LWRjvsdznHYnVq1cTDocpKyvD5/PR2tpKZWUlXq+XeDwud4DFxcUy8VNkNQDD5s25ngG5OJCJmFqt9j11L8SCN1ZWRnd3txyxCHtjkf7Z399PNBplcHAQvV5Pa2urdI3UarVs27aN/fv3U15ejslkYvfu3TQ3N3PQQQcNOwej0cgtt9zCV7/6Ve6//37OP//8vNkoS5YswWazUV9fz7XXXktzczP33nsvF110EaeccsqYpmPt7e2jJJXhcJj777+ft99+G4DjjjuOq6++epRPhCAd5qKlpYW77hribP/qV7/KGwf/u9/9DhjK4kilUrKDYLFYaG9vJxAI0NDQgMPhYNeuXTQ0NLBw4ULS6bTMQRGfJSDNxYQZmcfjyauIgXczVfr6+uQ1N9719c535EO385/GNHLxfpwjY6qqtn+aiwaxC9VoNJSWlqLVauUcWjDGdTqdlGkKP/09e/bg9/tpbW1l7969WCwW7HY7/f39vPDCC8DQjbe0tJTW1laZKZGL0tJSrr76amBo/jaZkcVE2LBhA3//+9/R6/VcccUVYy7Uoo19xhlnjOnZ4Pf7OeaYY3C5XPzkJz8Z0xTq/eKf//wnDz/8MCaTiRNPPBGtViudOjdv3szGjRvZuHEjW7Zsoaenh127dkmW/KxZs1i+fDkej4dsNisli7nKhVxFhc1mw2QyHbDOw3tFvrwKcU7ZbFZ6UMRiMQKBAJ2dnTKzwuFwyEVMURSOOeYY5s2bRygUIhgM0t/fL4tNQY4didNPP52jjz6aYDDIT3/603HP1Wq18tOf/pTjjz+eVCrFnXfeyVNPPTXp62Hr1q384Ac/YOPGjZhMJm644QZuuummSZlLZTIZrrjiCgYHBzn11FM5/fTTRx3T2dnJI488gqIozJs3D7PZzOzZsyktLZWGUjabTUp6u7q6pIV5NpuVowmDwSALg0wmw/bt22Vhl2sNHolEiEajspsjriuXyzUVHs104TCNjxQTFg6KomQVRclM8k/6wzjpjwsmmk8KrXdPTw/9/f04HA4KCwtxOp1SwiXa44sWLQLgscceA4Z22GJcIZjjI3HeeefR0NBAMBickOk+EcLhMHfccQcAX/3qV6V+fSQymYwcqXz5y1/Oe0xzczNHHnkkL7/8MrFYjGuvvZZDDjlkFF/j/SKVSnHZZZcBMH/+fHQ6neSawJAPhnD01Gq16HQ6OSIym8243W5SqRSdnZ2SwCqikcW4oru7W7oNivyCDzNTIN+IJF9ehXA/FB4UougzGo3MnDmThoYGMpkMiUSCQCCAVqulsLBQdnIE/2bOnDnSk2OswkFRFH72s5+h0+l46KGH8hIpc2E0Grn00kv5zne+g8FgYOvWrdx+++20trYOOy6TyeD3+1m/fj2PPPIIP/vZz/jpT38qzdF+8IMf8NnPfnbSiYT33XcfGzdupKSkhB/+8Id5j7nnnntIpVKUlJQwMDBAX18f+/fvl4VUSUkJS5YsYdGiRXi9XjweDzNmzKC4uJhIJCLzTNrb2+no6KCnp4fGxkYCgQBOp5N58+bJAi9fJoXoGOl0umky5DQ+MZjMqOJHwIEbov8bYSJdf0FBAW63W9oWazQafD6flHOWlZXhcrlkkM+6det4/PHHueGGGygrK+OUU07ht7/9LY8++ijf/OY3Zf6FgEajYdWqVVx77bU8++yzOBwOzj333ClHvfb29rJmzRoCgQBz5szhC18Y28PrgQceoKuri+rq6rzmPs888wwXXHABfX19FBYWMn/+fLZt28aOHTs4/vjjufzyy7nhhhsmTNucCJlMhlWrVrF9+3asVit1dXWoqorRaMRoNNLd3Y2qqtjtdoxGI/F4nIqKCiKRCD09PZSUlNDU1ISqqsO8AwQ3JRaL4Xa7icVicveeG3b1Ycnk8o1IxGuL7ofgZ4h/F6MyAeFB0NXVRV9fH8lkkv7+frRaLYFAgGw2i8PhkAtiTU0Nzz//PI2NjTz++OOcccYZo85r5syZfP3rX+fuu+9m1apV/OY3v5HF71g49thjqa2t5Yc//CGdnZ3cdtttOJ1O6UnR3d09SmKs0Wg4/fTTOeWUUybt5QFDUs1bb70VgJ/85CfSxj0XjY2NcozhdDpJJBJYrVZZOFqtVumE2t7ezt69e1EUhXg8TktLC62trWSzWRYtWiR9Q0SB4PP5mDVr1rARo8ViQVXVUb+faUzjk4YJCwdVVa//EM7jE4mJPOUVRUGn00ljIfH3eDxOV1cXiqKgqipmsxmPx0NdXR179uzhyiuv5MEHH+SEE05g/vz5vP322/ziF7+Qo4lclJeXc8kll3DnnXfyyCOPsGHDBi655BJJchsLqqqyefNmnnzySdavX082m6W4uJirrrpKRnePxMaNG7nhhiHhzE033TSsQMlms9x8883ceOONqKpKeXm5NOVZsmQJr7zyCps3b+aOO+7g2Wef5YEHHhg1P58sMpkMF1xwAQ8//DBWq5VTTz0Vv9+P0WjE6/VitVplHoPdbieRSEiehWgt9/b2Eo/HMRgMlJaWykVpYGBA7u6FjDM3MvvDzhEYy2hMuF2m02mKioqGWTsLfo0YY+zbt0+aWZWVlUmyn8FgIJVK0djYKLtfsViM/fv3U1FRQV9fH9/61reYPXs2c+bMGXVul19+OW+//TavvPIKZ599NmvWrBm36ISh8KivfOUrvPnmm2zYsIFwODzMIbWoqIja2loqKyupqqqirq5uQmOnkWhububiiy8mlUpxwQUXcOyxx0pXTYFQKMQ555xDJBKhoaFBeno4nU5UVcXtduPxeHA6nQSDQXp7e7FarVRUVODxeGSmSTqdJhwOS45DNpsllUrJomEktyFXUjuNaXxSMWVy5DQmh9wMAWEQYzAYpOY+Fouh1+vR6/UyEOcLX/iCLAC++tWvsnLlSu666y6OPPJI7r33Xk477TRmzZo16rVWrFiB3W7nl7/8JS0tLVx55ZUUFhbi8/k49NBDZTIkIJUY69atk+15rVbLUUcdxQUXXDCm3a/f7+fCCy8klUqxatUqzjzzTPlYX18f559/Ps888wyKonDooYdSX19PPB6XjPOlS5eyaNEiHn30UbZu3cry5ctZvXo1J510EtXV1RPOrCORCC0tLTQ2NvLYY4/xl7/8BavVysknn0x1dTX9/f3Y7XbmzJmDwWDAarViNBqJRqPy52HIEEsEPUWjUekaKTIeEomEdPwcz9nvw8J4zoJiJDFy9yo4Hh6PR441RB6D2Wxm2bJlbNy4kVgsJlUZQhGwf/9+dDodbrebOXPmsH37ds4991zWrVs3atduNpv57//+b1avXs1DDz3Ed77zHdavX8+PfvSjcd+T0WiUXYSOjg76+vpwOByUlpYSCATGzJuYCCJ6/brrriMWi7Fs2TLp3TDyuAsvvJCdO3dSVFQkicW1tbUYjUY6OztxOBxYLBYGBweJRqM4HA6MRiMul4toNEpXVxcajUYqLdra2jCbzcN8MsTnHwwGiUQilJSUTLkbKCAsqD+NmKpqbDLHfxDP+WnCdOHwAUHcvN1uN8XFxXKmHo1GSSQSaDQa7HY7kUgEi8XCwMAATqeTgw46iNdee42rr76a119/nUMPPZTzzjuPBx98kGuuuYbHH3887xx08eLF3H333Tz44INs3LiR7u5utm7dytatW1EUhZqaGtxuN5s3b5bEtOLiYk4++WROOumkcaOwM5kMl1xyCZ2dnSxZsmTYzXjz5s2cffbZ7Nu3j+LiYr74xS/idrvx+/3YbDb0er0MBKqoqGDlypW88sordHZ2snr1alavXg0M2WNXVVXh8/moqqqSqZ07d+6kqalpVBKj1Wrl9NNPl0x6q9Uq/QqEAVIymZR+BwaDgUQiIQsJg8Eg37OQI+p0Okwm07Bwq48rRmYcjLyxCbJnQUEBPp9PfjYFBQV4PB5CoZCMhi4rK5O7YhEPX1paSklJCbfccgvNzc1ceOGFPPzww6M+ExFMtmDBAn74wx/yyCOP8Oabb7Jq1aq8XYqRP+vz+fD5fO/784hEIvz4xz+WvAwRlJbPg+S2227jySefxGazsXTpUiwWC0ajkdmzZ+N2u3nxxRdxOp0oikJ/fz8DAwNEo1EMBgMGgwGfz4fb7SYUClFRUYFGo5HKiurqaqmmAqTCZaKE1YkgRlaTcYudxjQ+aEwXDgcIYkdgMpmG5Rv09vbKOGORXqjRaCgvL6ewsJBgMCjJekajkZUrV9Lc3Mxbb73Fv/71L5YtW8Zll13G3//+dzZt2sTvf/97vvSlL8nXHRlVfe6553LOOefQ2dnJX//6V9rb22lubpZ/YMhgavny5cOklCNVGaqqygLj1ltv5aWXXqK4uJg777xTvt99+/Zx3HHHSSnkF7/4RbxeL4FAQC5Coq3rdrtRFEUuXv39/TQ1NdHT00MoFKK/v5/+/n62bNmS9/M1GAzSoMlisbBo0SLq6uoYHBzE5XLJFnEqlaKvr4/du3djtVpl0WAwGMhkMjKTQuzi3W63vJkLd0m/3/++ORgfNEZ2IkYWDoWFhYTDYQYHByksLKS3t1fO5wUJUMRRp9NpOarSarU4HA4URcHlcvGlL32JP/zhDzz99NOsWbOGq666Sr5GLufgC1/4AnPmzOHb3/42TU1NrF69mq997WscffTRo849Ho+PqQISiaVTeWzbtm3cdNNNdHV1UVBQwHXXXcdpp50m3y8MmbRlMhn+9a9/Sc8P0Rmz2+309vYSCATweDySh6TVarFarYTDYdxuNzqdDrvdjsfjkZ+ZRqPB6/Vit9tl+mVhYSGDg4NyPOFyud73NSUKxalYsH+c8V47L9P4eGC6cDhAyJVbCamc3W4nmUySSqUkQ99kMqHX69HpdNTV1UmG9dtvv004HEav11NRUUFvby/33XcfRx55JLNmzeK2227jK1/5Crfddhvnnnuu1IyvXLlyzBvS0UcfLbsa69evZ+/evRx77LGS/zBeCz6VSuF2u/mf//kffvWrX6HRaPjDH/7A/PnzJZnzP//zPwmHw9TV1fGNb3yDeDxOMBhEVVXpxOhwOOjt7ZVtXWFQBHDkkUcSDofZt28fHo+H4uJiWlpaAGQMNAzp8+vq6mhpaWHfvn0UFhai1+tpamoim82i1WpZsmQJ7e3tZDIZBgcHaW5uxul0UlRUhNfrZc6cOXL2D0MLbSgUIpvNSvdFjUYjmfK5LHiBqSQWftgQfJmenh6SyaT0IRCEznQ6jdvtxmQy0dXVRWFhocxTqKqqIpPJEAgEaG9vZ/369XR1dUlS6fLly3nqqadYs2YNXq+Xb37zmyiKMmo3X1ZWxvr16/nOd77DQw89xN13300gEOCWW24ZttMWi3U+iMU7HwYGBoY9lslk+NWvfsWtt95KJpNh4cKF/O53v8trWpbJZEin03zzm98km80yb948XC4XkUhEencAeL1ezGYzqqoSDodRVZWlS5cSDAZxOBzSxlwYuwlzMY1GQ3d397CgOxji1IiNhPAUmQxGXmsf9cjso8QhhxwCDCWzHqjjP4jn/DRhunA4QMhlusfjcenuJ7oQPT09xONxucMTem+Xy8Vrr71GKpUiEAiQTCaZP38+b775Jo899qQzkwkAACAASURBVBi33XYbFouF0047TcZNX3755fzhD38Y02dhJKxWK8cdd9yU39MTTzwhbVbXrFkzbPd4zz338Pzzz1NcXMyXvvQl/H4/qqqSyWQoKCigpKSEgoICent7GRgYIBwOM2/ePCoqKkgkEvT29lJcXCyTKB0OB1qtlpqaGpxOJ263m2QyKXfFer2eaDSK0WikoKBAZn4oioLRaJSdh2g0SlVVFXq9nurqahKJxDASpqIoFBYWSpvwtrY2uVhNVAwcSBOoqWCigkU8Lsh6uXHgRUVFxONxBgcH8Xg8RCIREokEkUhEKjJ0Oh3d3d3SgTISiQyLeZ87dy7JZJJnn32Wb3/722zatIlf//rXeXeNVquVe++9l0WLFnHdddfx6KOPsnnzZn784x9zxBFHTPqaHQ/pdJo333yTW265RYZoXXzxxdx0002SBJsPV155Jc3NzdhsNubOnYvBYMDj8VBWVkZjYyPd3d10dXXJdFFRLPj9fjKZDMlkUhYWucqLkSRhQBJThS21+Kwni4/qWvuwMRnuwBtvvDGl55zM8R/Ec36aMF04vEfk2xGI3UQ+hntJSYm0Cc5ms7JIWL9+PVu2bMHpdFJeXs7AwAA2m43Zs2ezfft2fvzjH7NmzRoUReH2229n6dKl/N///R8nnHACd999d16Z2fuFqqrcf//93HjjjWSzWa655hq+9a1vycf37NkjW9bLli2TZlZifq7X6yXbXGQkqKpKIpHAYrFQW1uLRqOhp6dHJgd6vV7eeust6bUgHBB7enoYHBwkk8lQW1tLMpmksLCQeDxOKpWioKAAnU4nF8tEIoHZbObwww9ny5YthEIh6eXgdrulgiUUCkkSZVVV1bhyxtzfZe5/PyyIRUS0xkcWEOJxq9VKUVERBoNBjoRE0ZprZCUcQ/v6+mSYU1dXFzabjZkzZ0qCrDCScjgcHH300cTjcTZu3Mjvf/97du3axSOPPJLXNVJRFM466yyWLl3KhRdeSFNTE+eccw5ut5vTTjuNI488kkMPPXTS7ep0Os22bdtYt24db7/9Nq+99pocdbjdbn7xi19wzDHHjFk0qKrKz3/+c+677z70er18bUFaFgZsAwMDbNq0CZ/PJ+PXLRYLJSUlaDQaamtricVi9PT0yKJBWHsLD4ZcUzjBaxBFxFQ6Dh/VtTaNaUwG04XDe0S+HcFI6ZWqqnR1dREOh/F6vRQWFg7jPcBQ21ZwHmw2G6+++iodHR0ceuih7Nq1i7vuuov58+fz5S9/GZ/Px+OPP87XvvY1NmzYwPLly/ne977HxRdffMBa55FIhCuuuIK//OUvwFCS4A9+8AP5uJC4RSIRampqOProo6XPvgiPEsTEqqoqEomElKDZbDYGBgYoLy8nlUrR1NREe3u7JMnp9Xq0Wi3pdJru7m76+vpobW0lFothNBrJZrNUV1ej0WgIBoNUV1czODiI0Wiko6OD+vp6jEYj5eXlkq2fTCbp7e1Fp9NJ3wx4tzjweDzDRhLixi/eQ+4i/VG1i8XiIQiPMHwXOnKREYWCkP7mmkOFQiF0Oh0Gg4GqqipUVUVRFEpKSnC5XBiNRmKxGJWVlYRCIRk17vf7mTVrFjabjS1btrB+/XpOOOEEnnjiCcrKyvKe98yZM/nb3/7GL3/5S/7yl7/Q3NzMfffdx3333UdtbS2f//zn+dznPkdlZSWDg4P09PSwe/duUqkUvb299PT00NTUxOuvvz6K21BdXc3KlSu57LLLcLvdY352qVSKyy+/nN///vfA0HhMFKChUIi+vj4ymQwej0d2sZqamnA4HMTjcUm2XbRokfR0EKZuooCorq4epm4RCiqRkJnr8jlZfJpHE9P4+GO6cHiPGHmzzmazo4qESCRCV1fXsJ8bHBwkmUzKzAC73c6iRYtIJBK0trbS398PDM2LV6xYwdNPP823v/1tGhoaWLp0KUcccQSvvfYaV111FQ899BA33ngjzz33HHfcccf7Zqc3NTXx9a9/nd27d2OxWLjnnntG6fJ//OMfs2nTJqxWK+eee650U6yurpZjCq/XS1dXl0wUFP+fyWTQ6XQEAgFgKNtDOO9lMhkKCwvJZDIYDAYGBwcJhULYbDa8Xq9MIRQkR7Gzdjqd6PV6gsEgwWCQqqoqNBqNdEFMpVLSrbOiooLdu3djt9ux2+3U1taSzWZpbm7GYrFQXl5OJBKho6ODaDQqDbc+6hu4WERyOw4jH8+N2xYyTZPJJAtZQUC1WCxyMXO5XCiKQiQSQa/Xk0ql2Llzp3RwdDgcMuiptbUVt9uNw+Fgzpw5RCIRtm/fzsqVK/nzn/88ZhhaQUEBV199NVdddRVbtmzhscce409/+hPNzc3ccccd0q10Ivh8Pg4++GBWrFjBsmXLxixWchEMBvmP//gP1q1bh8lk4thjj+Xwww8nFAqxfft2VFWloKBAFripVIqOjg6MRiM2mw2r1YrL5aKurk5ep4JsKszBROCVgPAJEceLAg7Im1UxjWl8EjFdOLxHjNwRxGIxyWLPhfBoKCgokDN6nU5HT08P7e3t6HQ60uk0TqdTxvk6nU6y2Syf+cxn6Onp4Y033uDcc8/ln//8J2VlZTgcDu69915OPfVULr30Ul599VVWrFjB6tWr+cpXvjLlG5OqqjzxxBP8v//3/4jFYsycOZP/+q//4rDDDht23Isvvshtt92GRqPhrLPOorS0lM7OTumGFwgEiMfj0kDK7/czd+5cOZYIh8OYzWY5Zqiursbr9VJaWkppaamUTIqujGgni51vSUkJlZWV+P1+tFotCxYsIBAIoCgK7e3tGI1GKaEzm814vV78fr9cAPbv3y/5JzAUQ93f3y9HSaK1D0NOgqLj8HHBeLvQXN8QMXYRXbG+vj527dpFT08PRx99NJWVlXJx1Gq17N27l0gkQl9fH83NzfLzrqqqwuPx0NTURGtrK+FwWFojH3/88axbt47W1lZWrlzJ2rVrOfjgg8c8d0VRWLhwIQsXLuQb3/gGW7du5c9//jNNTU3s3btXmi6JkV1JSYn8fS9ZsoSysrJR5Mjx0NLSwplnnsnOnTspKSnhlFNOwWAwSGKv3W4nFArhdDrx+Xz09PQQjUaprq6muLiYuXPnyu5TPB7HaDTKUZjFYkGn08kMi4KCgmHXVe7vS6gxcrtF0wZQ0/ikY7pwOEAQbe9cl0Gr1Up5ebnUcnd2dsqbhslkkumNQnVgsVgoKytDVVW6u7uxWCx8/vOfl8FY55xzDn/729/k4vbZz36Wmpoabr75Zp588kmuueYabrnlFi655BIOOeQQ6R+RD9FolBdffJF//OMfrFu3TkYen3766dxyyy3o9fphmvFAIMCqVatQVZUzzjiDY445ho6ODumIuWDBAsrLy1FVVSoWBHNesPPFjk3sZIPBoJwvB4NBGfglbsgiRyGRSOByuSgvL5cW1kIVIDo9wrRnxowZaDQa+vr6iEajaDQaTCYTfr+fcDiM0+mUJlBi9gwMG0eUlJR8bNUTYyF3dCaKBkF8FCFKg4ODpNNp+QeGIsmbm5uJxWI4HA4qKiqIRqMoikJ9fT0ej2cYJ6Snp4fKykq6u7s566yzePLJJ2ltbeWzn/0s119/PWeffba0uB5LOpjNZlm+fDnLly+X4W82m03KdYUsNhepVEoqlMaC4HE8/vjjXH311fj9foqLiznuuOOora1l//797Ny5k6qqKsrLy6mqqpIySqPRiM/nw2QyyUJFFEvhcBiHwyHt48WoTBBO8xkzCWmm1WpFq9VOW01P498K04XDFDEWwz039jkej0u2de4OUbjQWSwWvF6vZL2L3XIqlZJ+9t3d3VIWeNZZZ/HrX/+aN954gyuuuIL7779fdhXmz5/PI488wuOPP851111He3s7a9asAYYMdhYuXMihhx7KsmXL8Pl8vPjiizzzzDP861//GnYTLikpYfXq1XzjG9+QO31BNlNVlcsvv5yOjg5qamo488wzKSkpIZVKsWvXLvR6PUajkbKyMjQaDS+88AIdHR1kMhlmzZqFqqqUlpaSyWRQVVXyIFRVlXa+ogAQhdXAwADxeBxFUXA6nTgcDhk85HQ65Uw8kUhIFUdxcTE6nY49e/bQ2NhIXV0dbrebsrIy4vE4JSUlGAwGGhsbmTVr1rAdfDqdlhkWn0RGe+7oLPf8hYfA3Llz0Wq19Pf3k0gkSCaTmEwmzGYzdXV1ANK9MRwOk0qlKC8vx2w2y/FbZ2enVA2JkdPBBx+MTqejubmZ733ve1x//fWcd955rFq1aszRmTAGywcxlsoHj8cjuUH58MILL/D9739fhm6VlJSwcuVKCgoKZAGg0WjIZDL4fD4ZfJZIJJgxYwZtbW309PSwf/9+ORITih3RNRAdQiF7Fe6S8C5vRihcBCFy5L3g4yzr/TjiG9/4xgE//oN4zk8TpguHKWK8RSUfEzr3JiFm6uJm0dfXR1NTk3SfE26LwgOhv79ftlMvvPBC7rrrLh588EFmzJjB97///WEjiTPOOIPTTjuNhx9+mFdffZVXX32VrVu38vrrr/P6669L4yYBjUbDYYcdxgknnMCJJ57IwoULx7yJ/eY3v+GJJ57AZrNx1FFH0dfXR2VlJWVlZdTX18sdW2trK3q9Xo5cRBEgDHMSiYRsNwu2end3t2TIi39zu93U1NTI9nt5eTmhUEi23YPBoAxnUlWVgw8+mOLiYsrKyggEAvT19TE4OIiiKBQUFNDR0YHZbJbR5T09PbjdbgwGg4w+FgtCbsfok7I7zDUfE/8FZKclnU5jMpkkAVAsgqLl7na7SSQStLe309XVRTAYRFEUea0qikIwGJQFhdPpJBQKYTQaCYfDLF26FLfbzb59++jq6uKee+7hnnvu4YgjjuCiiy7itNNOG1cm+X6xefNmrr32WhlJb7FYqK+vlyqlRCIhZaqiWBQ8m0QiQUdHB4cddpj8HDKZjOzC1NTUyK6CIGja7XYKCwuJRqMyFAveLdqCwaB8nXzX0CexMP0oce+99x7w4w/0c040Hv53s6yeLhymiPEWlZEz6Gw2OyyIqLCwEBi6iCKRCMFgkN27d9PW1kZFRQWpVIq9e/dKeZzFYkGr1aIoCocccgjnnHMOv/3tb/nhD3/I008/zd133z0szEqr1XLeeedx3nnnAUPs+jfffJPXXnuNV199lZaWFpYuXcoJJ5zAscceO+G8uLe3l9tuu00S2GpqaggEAnR0dODz+eRcV7SzCwsL5XxcmOUIwuPBBx9MJBJh//79FBYWYjKZqKiowOVyySjjhoYGbDab9B1wuVxyZ6rT6aiurqa8vJzGxkYURSGVSmGz2RgcHMRisZBIJNDr9cyaNYu6ujoaGhokQS0Wi5FMJjGbzcydOxefz4dGo5E/U1RUJHeMQgXySSGxjTQfg6HFMxqNyva+1WrFbDZLomhfXx8Gg4FAIIDVapVcHLvdTnd3N7t27ZLuoZWVlSQSCbq7u8lms9Kq2mQy4XA4SKfTzJkzh7lz5xIMBtm6dSsdHR28/PLLvPzyyxQXF3PmmWdy5plnsmzZsgP2voPBIN///vf53e9+Bwwt6PPnz+eII46gv79fmjKJjlgikUCn09HS0iKDwYRdtN/vR1EUwuEwvb29uFwuSXQUo0bh3yC+x7nukAK5FtNj2ZZ/0grTaUxjJKYLhyliKjKp3CAiIeMSu5JIJCIDoFKpFA6Hg71799LY2Citmmtqakin0/j9fmDIiOczn/kMTU1NrF+/nsWLF/Pd736Xa665Jm9712azsWLFClasWDGl99jb28sdd9zB3XffLR31KioqmDFjBl6vlxkzZtDR0cG+ffsIhUKoqorNZpOWxalUipkzZ8oFrbOzU6ZQDg4OSv8EQWwUvgMmk4ny8nL27t1LS0sLTU1NJBIJ5s2bh9FolP+tr6/HZrMRCARku1mQLY1G4zBCmriBl5SUyN231+uVBFW9Xi/P55NSKIyE4GqMVF0INYVopeeSJkUbXRAALRaLnOFns1mi0SiZTIZgMCjdOWfMmCGNvmKxmBw3ia6EoijY7XZWrFiBVqtlw4YN7Ny5k3A4LLsQdrudY489lpNPPpnjjjtuXCklDC3OXV1ddHV1sX//fgKBgPz7s88+S0dHh8yP+MxnPoPJZJJR6S6Xi/nz5xOLxfB6vbS0tBAKhWS42bJlyxgcHKS3t5doNMq2bduAoXGJ1+uV37+NGzfKTpkgMUN+kqOQtuZ2rkZiWmo5NQi3RuHeeCCOP1DPOVEn4ZN6T5kI/5aFg6Ioivox6A2NNXfO/ff6+nq6u7vR6XSEQiH0ej1lZWUYjUYsFos06bFYLMRiMRYuXEh5eTk7duxgy5Yt/OQnP+FPf/oTd955J0cdddT7Ot/e3l5+/vOf81//9V+yYCgqKmL27NnU1dVJ8yS9Xk8ymZTpniJkSahEnE4nBQUFFBQUsGfPHpkhIdwizWazTGMsLCykuLhYSgMNBgMVFRVSUx8Oh6Xkbdu2bXKh7+rqkgWZyCSIxWIUFxfLDIXe3l46Ozsl0S/3hi46EIlEYsJkzo87xM42EolIkiEg5+qCJCoWutxCAxhmAx6NRmUsdHFxscwUgSGzpcrKSvbt20c8HieZTA4bYYichmw2S01NDclkkvLycjo7O2lvbycQCDAwMMDatWtZu3YtiqKwZMkSGhoaCIfDksMSiUQIhUKS5zIenE4ny5Ytk2Mor9dLd3e3JIBqtVrJJ7Lb7VJaWVxcLN+D4OvU1tbKPBSHw4HVaqWtrU2Ovcxm87CMCvG5ie9zrtzyk9Sx+rhj8eLFwOTb/ZM5/oN4zk8T/i0LB0ABPvLfcO7OIteSOnc3ImbNBoOBkpIS2U5vaWlh165dFBcXYzQaZfCQXq+noKCA5cuXM2PGDJ5//nl27drFCSecwFe/+lVuvvlmnE7npM8xnU7zxhtvsHbtWu655x5ZMNTW1lJeXo7D4aCwsJCSkhKMRiN9fX1yMa+pqaGiooKKigpMJhOFhYXSYjebzUqugTBe2rt3r3z/PT09cgcsOiPic+rp6ZHW0lqtlkAgQGtrK1arVZLWLBYLLpdLFgGis5BMJtm1a5cM2xLM+nw8AOEXIQyixHN9ErX2I9vfuWZkXq932O5XURRpBpXrESFGGYIPID5vk8lEOBwmGAxSVFQkHRczmQzbt2+XXSfReTAajSSTSVkA+nw+mR8SCAQwGAw0NTURiUTYsGEDGzZsGPN9abVaGQBXVFQki53KykqKi4sxGAw0NDRI7w0Y6hgEg0HMZvOwcxJFaX19vbRBT6fTUmXR398vyZB2u51sNksymaS0tBSNRkM0GqWzs5N4PC5Jp0Kdks1mZZS5GGVMkyCn8e+Kf7vCQVGUFcBXFEXZBWxTVXXtJH/uQuBCYGauT/+BQi7jWtgHx2Ix+vv7GRwcxGQyEQgEcDqdWCwWOjs7pYtfJpNh27Zt9Pf3U1NTQ19fH/F4HLPZzKpVq/jHP/7B22+/zQMPPMADDzzA4Ycfzvz585k9ezYHH3wws2fPlqOMdDrNli1beOmll3jppZd45ZVXhiUVNjQ0yCAs4XApsjWE86Ow4q2srMTr9coZsbCaFjdKq9VKOp0mmUxKPoTYlQq1BEBrayuzZs1Cp9PJm7HwhBAkyd7eXrlgiS5BVVWVvJGLjoNwHNTpdASDQWn2BIziAQjvBhjdFTrQWvsP+voSu1yBkR2ukYVQ7ixejCyE70A4HJYJmi6XC6/X+//bO/PwuLLqwP+OVCWppHKpJJUslSwvUntvt3FDN6GBppsAYW2SwPAlwLBm0pAFmExmkjADYRnIQgKTDIEEmISQSchCMmQhJIFkAgluYLoJbhps92LZblvWvu/rnT9endvP1SWpZFWppNL5fZ8+SVVPde+rOrr33LMyMjLCQw89RFNTk4+90XTdQ4cOUV9f7xs6TUxM+BiU9vZ2L0MqA3feeSdnz571BdOccywvL1NdXU1HR4fvTaLyo4XDOjo6ePDBBxkdHaW9vd13AF1aWqKxsdFbnObn5zl8+DBzc3O0trb6fh0tLS0+Zbi2ttYrFxrrAfjy5E1NTQwNDTE9PU1lZaXP5tCMFJVTtTyoTIWxIEijXCkrxUFEXgL8GvBRoBp4pYicd86dW+tvnXOfBD4pIl9Jp9Mbs/nzROliXZDVhx62NGj8AwR9ARYWFnxhmkQiQSwW49ChQ1y9epWBgQGuXr1KU1OT72g4MzPD5cuXOXnyJPF4nK6uLiYnJzl9+jSnT5/2c6msrOTo0aO0trZy//33+8VMqauro6mpidbWVu666y4mJyd91sL4+Dg1NTVekdFyzCdPnvSbulJTU+ObAV2+fNl3EtQNprGxkd27dwPBojo8PEx3d7fvoTA3N+ej2rVmQCKR4NKlSz41s6enh2g06pUPDQAUEcbHx2lqaqKjo8NX7hwfH/cnwEQicV0TMhG5zk0RViIKbXEotHxlk0sxgOstXOFTb9gXX1VVxfDwsD9tDw4Ocu7cOaampjh06JAPjFxcXCQej9Pa2sri4iJnz54lEonQ0NBAKpWit7eX4eFh37BNa5L09/f78t+jo6OcP3/edz9NJBLe4jY+Pu7dVeqO0voRR44c4dFHH/VKc39/P5OTk77g1+LiIocPH6ahoYGFhQWqqqqorKwkmUz6aq1jY2O+kJhWbp2fn+exxx7DOed7UmgQqBYbq62t9SnFmpJZU1Pj30/tV6GWHf0sLAjSKFfKRnEQkRTwJuDtzrl/EpEW4JlAK7Cm4lBopqen6evr83UbwhaH8EISj8dpamqir6/Pt+vVxbSyspLHH3+cZDJJNBpleXmZRx55hKGhIZqammhubva+246ODm677TZvgh0cHOTq1av09fUxPj7O9773PR/8lUgkSCaTJJNJ9u7dSzKZ9IudnvDUXKuBZNqqec+ePdTU1HDixAluuukmuru7SafTdHd3MzY25u8dYN++fQC+6NPY2JhXmDQ1U0+Jra2tvtxvMpmkr6/Pb/6Tk5NeUdDKfa2trVy5coXR0VGi0SidnZ2+jXZVVZXP3Ve/+p49e570GWk7Zd1Usz+j7WxeDjdhWunUW1FR4eNN9DNZXl72qbRzc3NUVVX5qpNNTU1Eo1FisZiXme7ubqamprh48SILCwuk0+nrOsCqwtfW1uZdXNpwrLOzk+HhYd+jZGFhwVsr1CWnpb9TqZTP+mhra2NmZsZb3R555BHfX+PYsWPMzMyQTCa5evUq0WjUjzs8PIxzjoWFBW699VYv11rwShXLK1euMD8/75Up59x1HTFVodZ4HpWX7M6fFgRplCtlozg45wZF5KPAWRGpcM71ichjwB3AP2/2fDRNMRzpnt3lUEsra3VHbUut6Yo9PT0MDAz41DmNQL927RqpVIqzZ89SXV1NY2OjD1pMpVIcOnSI8fFxBgcH+cY3vgHgMzk6Ojpoa2tjZGSE5eVlGhoaqKmpoa6ujr6+Pqqrq4lGoxw/ftz3i2htbfVR85oZEYvFGB4e9q4I7TypJ3rNYdfTpbbSTiQSvoyvBicuLS0xNjZGJBJh37593hetJ9WpqSkaGxs5evQovb29vvywWiaSySTpdNpbDzS98Pjx4/T39/tTt54Ww2bl7E213MzL4UDIsNzpZqfVJPVxgKWlJZaWlohGo76uSCqVIhKJ+ODTixcvMj09zdzcHP39/YyNjVFbW+szayKRCEtLS969deDAAR9HoTI2NjZGT08Pe/fu9ZY2DYhNJBK0trZ6pfLUqVNcuHDBy4ZWDh0aGmJpaYmhoSHS6bSvPnrt2jXS6TRHjhyht7fXW+QWFha8/CUSCbq6unyjr5mZGebm5tizZ4+vKKll0tVtovENGlx75coVXxl1LXmxmAejXCgLxUGzKJxz/6K/Z56aARoyj90DTDjnvrIZc6qoqHhStH6uLoeK+u1ramqIRqNcunTJxwFMT08zNjZGMpmko6ODU6dOMTAwgHOOhoYGHxGvft3z589z9epV9u7d60/td999N1NTU4yMjPiNfnh4mEQi4QMfAebn50kkEj6+YmJiwisBjY2NxGIxlpaW/AlOT33Dw8M+GG1mZoZEIsHw8DBzc3PU1NTQ1tbmNya1HKRSKRKJBEtLSz5aXdGF/Nq1a74MtRbR6uvr8+2cOzo6mJubo6KigkuXLhGLxbwfe3BwkN27d/v4B90As/sK5Pq5XMzLakkJB0KGlSNVWtW1Fo/HOXLkiD9dNzQ08NBDDzE1NcXy8jKNjY3s2rXLVx1Vd1Q4CHN4eNhnLWgBr9bWVl+bpL6+nnQ6zTe/+U2mpqaYnZ2lvr7eW98uXLhAfX29r27Z1tbG1NQUc3Nz9Pb2Mj09TV1dHbFYjJmZGVpbW7njjjsQEU6fPk1zczOVlZWMjY0Ri8XYvXs3lZWV7Nmzx9f80BiP6upqYrGYb8cO+CZWgFdw1XI1PT3t03v7+/sBruuMuRrlppQaO5eyUBycc05EKp1z2lyhHhgFHgMaROQFwLuBV5dqjmH0xKGn85qaGq9k1NXVMTY25qPaNSpcF2pt0Ts5OUl7ezvxeJyHHnroOsVDzaxtbW0kk0lfifLAgQM8/PDDxGIxH4SpgWMzMzO+RfDw8DC9vb045+jo6KC6uppUKkUsFmNhYcEvnmpJUZN3uJkXBOWONX5BI/S1ZbaaiHfv3s3c3Jw3YQ8MDHjXji78qVTKnwDVDaLlfvU90vRNeKJiovbf0LiKcKqckst8v9UX9bVOrtnPZytD2bEcdXV13hpRXV3N0NAQ9fX1JJNJbyFLJpO+gZa6m+LxOMlkkkQi4RVETf1U19Pi4qI39Wu/jN27dxOLxbjjjjtIJpO0t7czPT2NiHDo0CEqKyt9UzSNRdDNXy0aExMTdHd3e0VA0x/379/PzTffTFdXF7Ozs3z3u9/1dSggKMMeiUSuq7EyNzfHNmX3cgAAIABJREFUxMSE7y2haLDowMAAgI+B0NTh9fY0KZZSWuzA21LzwAMPFPz6YrzmTqIsFIeMa2Ip8/P7ge8Afw5MAp/O/P5m59yF0s3y+hOHbl76PR6P45zzG7hGow8ODvoGRJrmODY2xsjIiFcI9NQ0Njbmq+dpvwntOFhRUcGZM2eYmJigubmZ0dFRAL9YTkxM+PTGqqoquru7fWVJ3fC1Ln97e7svogR4X7ae2CKRiLc+JBIJ7w+uqKjwp8tUKsXc3JwPVNP0zXDBLM3AmJqa8rUc1NytDZx0w9CNb2Jigt7eXmpra2ltbb3OBw34mIbtlm4ZZq2T61rPh5UjzWiYmZmhurqavr4+uru7/Wbd3NzMzTffDODThbu7u3HO+awFzW7QUtUNDQ1UVFRw8OBBxsfHqays9LETN910Ez09PVy+fJn6+nra29t9w6iFhQV/8td+JupCicVi3lLQ3t7OhQsXGBoa8lVKwwGNWltB44s0xkavU8VjYWGByspKL5OqCITTKsNNz1TRVyUhuxdNNtkKXLGU0mIH3paafIs0ref6YrzmTmLbKw4ZpWE58/OHgKcD7888vQyMAa91zj1Woil6Vsu1B3xMgXbV1Kp/eppPp9M+40J9y3qiOnjwoO+0mU6nOXbsGEtLS7S0tNDQ0MB9991HT0+Pr1LZ39/PyMiIL/azb98+v+HoaaqpqYldu3b56o16UovH48TjcW8tye4OGHbJqIVEr9Of9ToNwlNrgfrRwyZ29cEvLi7y+OOP+9oXmgLonPMBk1pVUEtUqzKilENr47VOrtnPr6ZIaIBoT08PFRUVjIyMcP78ed8w7NixY97yoG3GOzo6fN+QSCTCwMAA586d8wrjwYMHqaqq8k2zenp6uHTpEiMjI+zatYt9+/ZRXV3trW7awlzdYtPT0wwNDfkiYpo2qRu11ltoa2vj1KlT3H777TzwwAO+qqVaqHQOe/bs8anPWiq7rq7Od2utqKjwrpVcaZVqlZmamlqX/JhrwihXtrXikKU0/DpwM/B859wigHPuiyJyyjnXW8p5KtknjuyFqKamhsnJSV/4SDdYLQF89epVv2guLy/T3d3N448/7pWKXbt2cf/993PmzBnfxyESiXDlyhWmpqZ8MZ89e/awuLjogyBPnDgBBP7crq4u31K7oaHBu1A0/UxTNeGJgMuxsTFmZmbo7Oy8rh+HRuurO0QrG87Pz/uSxxq7MDk56YvuzM3NeReEjh2NRv3r7d69m0gkwvz8PAMDA96E3NraSjwe92WF1UKhp9ZipltuJmudXLOfX03R0PdBLQ719fUcP37cp8YODQ2RSqW8Aqevr89p11NVOkSE+fl56uvrfQdNrcmg7rTm5mZmZ2d5+OGHfaCjbuSalquVU5eWlujt7WVhYYETJ074QlNLS0vs3buXw4cPMz8/T1dXFz09PcTjcQ4fPswznvEMxsbGiMfjXL161RcV27NnDx0dHVRUVHh3xcDAgK8FkiutMtf7mI/8lFu8TKm49957gfwbU+VzfTFecyexrRWHkNLwYeAYcI9zblFEKoOn3fJWURpy+aWzFxY98WgMQU1Nje83EIvFfBZGdXU1LS0t3HnnnQwODrJ//35SqRTxeNz7+lXZGB4eZmxsjMnJSV/cR60Y6tvVRk/nzp2jt7eXxsZGIpEIly9f5pZbbvEuiZqaGkZHR71bIhxToZs64HP3Z2dnWVpa8kqHWiA0dU27UcITufB635OTk96nrjELExMT3lQc7j2hlgx1jeipVU3LGviXa8PdCZHuayka8Xiczs5O4In4kKqqKubn530GQW9v8G908OBBn02hXTMbGxv934eLmw0NDfl21pWVld51MDExwfz8PG1tbb7KozaZ6u7uZnR0FOcczc3NPltDU4cXFhbo7+/3rzM2Nsb58+d9C/p0Ok19fb1P0R0dHaWyspK2tjZaW1t963cteqZyE663spIcrNfVsB3iZbYDn/rUp4D8N+18ri/Ga+4ktrXiACAi+4AjwMtVaQgFSW4Zcpkts33NYRP/6Oior3UwNDREc3MzBw4c8EGC8XjcxwpoJkNtba23FGgQ4/T0NLFYjFtuuYWLFy9y4cIF+vv7OXnyJKOjo76qoy724VO9lnbW3hPT09Mkk0kfCKeLrSoWWtSnt7fXp1fGYjGfxRAuDZ2rEZBu3tm1B1TZ0FoDGomvZX+zG3yF31f9+3CQ4Fqfy05DRLylSONJpqamSKfTPj5henqa6upqxsfHfZyBFvcSEW9Vqqqq8rU2NNCysrKS2tpa9u7dSzQaZXBw0McnqJK8f/9+lpaWOHDggE+zrK6uJhKJEI1GfUdZDW5sampiYWGBq1evcu7cOWZnZ7njjjs4efKkL98+OzvL1NSUd3UkEgmvwPT19QH4ltlqGVOlYScolMVmO1v1jNXZ9oqDc+5xEbknR2bFliIfs6X6UjW7oLKykt27d7N7927i8bgvgANPxA9oAR1VFPRk3dra6s3JGvB46tQpIpEIIyMjOOc4ePAgV69eZXZ2lkgkwu23305bW5tPn9OOlmrWVX/04uIiXV1dLC8v+z4UGm2uKZxzc3O+uZCmn2pAp75meKPWDV4tDeH3Sjd3zfrQ2IpsC81Ki/xqJz8zJ1+P1h8BfJYE4Os3qMWqpaXF+/mXl5c5e/YsEARQiggdHR2++JNmUqgL4Nq1azQ2NjI6Osr4+Dh79+6ls7OTxcVFHnvsMd+fQt0RIyMjPqPHOUcymWR+ft4XTFNlWfum6LixWIz6+nqqq6sZGRnx7rCamprr0lA1IDcsAxtVKE3xMMqZba84QOCTyHzfkkoDrM9sOTs765WBtrY23/gqvACNjY1x7tw5du3aRTQa9VkUBw4coLOzk2g0yv79+32u+dGjR5mamuKWW27h9OnTLCwsUFtby8mTJ4Fgoayvr0dEOHLkCMlkEsBXbtSUPDUR6zy1WI9uNmouBrzLQKPmNXUuXCwnvMCutFiH+yrMz8/7sbMtNJOTkz7e4UY/l52+4GdbHzRYt6Ghgfn5eSKRyHUWM635MTExwaOPPko0GqWlpYVEIuGtYwMDA0SjUWZnZ9m1a5fPqHHOUV1dzb59+0gkEnR3dzM4OEhbWxstLS1MTU0RiUQ4fvw4VVVV3m2hDcq0eJRmIZ04cYLZ2VkvC83Nzb4IW39//3VFvgYHB70VQputhT/vjSqUZsl6AusoWX6UheJQbuhGWVFRwfDwsI/0jsVi/gTY19fHwMCAr9an5YLT6bTf3Pv7+721QoPbxsfHedrTnkZPTw8dHR309fVRX1/vN+Vr1655JWJgYMCXkdZNAIKF8ODBg76SXthVEN54wveiwW5aTErJbsa0UpVDLdyU3WtCsyo0SLO2tnZDbbJtwX8i20c/V/1eVVXl3/uwSR9gYWGB5eVlH5uglUb1M1xYWCASifhCUlqYSV9XZUQzIerr630sTTqd9v8Pmj588eJFX5zp2LFjtLS0XNesSzMmVDnQ2BdFM5W0h4zKUKFSJ82SZZQzpjgUiHxOqvmeZjUdMtwkS6vkqW82FovR3NxMOp32AV1aahlgaGiI3t5eotEo0WjUdyJsaWnxKZkXL16kt7eXVCrFnj17SCQSpFIpAB94plUbwwusBiNOT0/7aPSV0tOyC+UAKxYn0vdE71HLU/f19dHc3OxrQWSPpWl6qlRtBFvwn1xvZGpqisnJSSYmJrh8+TJHjx71nU0nJyd97EtnZyft7e2+VoYWXdJCSppeOzAw4OW6paXFd6Kcm5ujsbHRx7Ro7E5VVRVTU1PXWTAaGhqYnZ3l0KFDPt5G5UazNmpqapiZmfGBtyp38XiclpYWH0uTSCTWVBjXa4mywEijnDHFoUBk96HItcCs5zSrgUUDAwO0tLT4IkdaCndyctIHiI2MjDA2NuYDFbXYTjqdprm5maqqKvr6+vwCqac5VQSccz5HP51OMzs7y6VLl6iurvanNc3SCHf91PtYKT0tvNjq/WYHPoYX2OzXzn7vlFzvnb7WRjf8nbbg5/rcVqo0qVkzWm9EZTyZTDI6OsqBAwd8lcWWlhb/eaTTaWpqaujt7aWrq8t3v6yqqvKv19/fTzQa9Y3K5ufnfdVTjbXQOJiJiQnfkVOzjrRfC+CvUbnLlqu6ujqmp6c5e/YsqVSKw4cPr6kwmiWqdDz1qU8t+PXFeM2dhCkOBSLsb19pgcn3NKunejXZa+qY1kFQtG6BFrSpqanxPunGxkZv1h8dHWVpacmf3LW638zMDPF4nOrqau/qSKVSXL58mfn5+etK8IZP/lryWuMe9PlsZSnXYpvLHRG+fnl52fct0L8Ll+de6b3baRt+ock+UWslU3giaFerdep3/bvR0VH/WTY3N1+nHGpczNTUFP39/b6PSWNjo3dvaObPrl27fDaEpvBq4GI6naaqqoqLFy/6uBsILGuqLIdrgihhd4l+X1pa8n03du/efd09r4RZokrHt771rYJfX4zXXI3VMky2YwyIKQ4FQhee1VL/8t3cdMPVTIrw6UlPfVpDYXh4mNraWu/a0KqOIuKD27T8svbEaGlp8UFumgGhikMkEmH//v3U1dX5bInse9AFWCPRs+MUdAPKtdiGK0KuVqhIx81OrbxRdnrQ41rkc6LWz05dE/pehpW66elpn87Z2tpKbW2tL2t94MABv1Gr7IR7tVRVVTE4OEgqlaKyspLGxkauXLniC4D19PTQ1dUFQHt7uy9yJiLe8qDzz3aDwRMWLbVetbe3+yyQtQj/f+dSkg1jJ2GKQ4HZyMlXA7S0TLO+jvrutWzu3NwcnZ2dDA8P+0ZOagXQhRSC8s2Dg4McPnzYZzponQStIhmJRHyPAF3oRcS7R5RcroBccQrZG1Cu92Kl09tGrQaqHIQ3Ml3cs+dlisT15Npks+NScqUuZmfFaI8R4EkKbCQS8XErWlMh3LOlr6/vusZkly9fpqenh+rqal8IbNeuXczPz9PT08OePXuIx+PefafzCgfNagZQOBMkO8B2PZjLwlgPq1kTtnOdC1McthDaYAcgnU77oD894euirRudBjLq93ANBOccjzzyCN3d3cRiMd+0Z3FxkYWFBX967Ozs9CWawwFk2UKdq+5CrudyKQWb1exHF/XsGIxc87IN4HqyP5Pw+wN4C5haGlQhUHlVd4S6ssJKYzidFvAuhWzC8qxZMirrOv7Jkyfp6emht7eXqqoq33FTm2CFmZycpKury7da1y6aOt8bwVwWm4+uRfma9PO5vhivuZMwxaEErHTaDRff0YUpXBRqenqa/fv3+0DGcMaCKhaDg4P+MY2H0K6AmpkQbkylC7xWz+vp6fFKxnrnD7mtBje6Sa/XKqDvWbhdedisnG//BiP3+6Pva/iacECi9gcBrrN8ZWfWLC4ucvHiRfbu3esbp+lrh10HsViMSCRCY2Ojd7lpFUpt4a5FzyC3MhBu914ILJbGMExxKAkrbaTZNRDCaI56uK1v+LXi8fh1/R9qa2tJpVLs27fPL6zZqYzailhNvOGgsrXmr0V2tL7Capv7jW7SK7kXcrki9P7C8RDZGRxhbANYnWxZydUdMiyvzjmvlOYKYtU4hOnpaR+roBa0aDRKVVXVdVkPGvQ7MzNDT0+PL11eV1dHZWWlb9cej8dJJBK+0mQ4RiIeD7rMqqIctqSFO9NuZ5OxYZQCUxxKwI1spLmyNurq6q57rbCrIcxqqYrhNMfwSW6tuajpeXBw8ElugWxudJNeyb2grojVUl9z/b2xMVZ6P7M34ZXcAPr5adv0aDRKf38/DQ0NtLW1ecuZcw4R8UG62nZby0QD/udwRdVwjITG6NTW1tLf3+/dJDq37FoVhmHkjykOJSDXRrrWqUfjHcKbpdZhyMVaQYrh2gn6erpwh0tCZ7NaJcdik+2KWC31FcyqsFGyZVJlMJuJiQl6enrYtWuX70OSi/DnF67lkEqlfOzO6Ogo09PTvnV6a2srgK/5oKhFIUw4RkLnroXMVCHWx8NKkFkcDGN9mOKwzcgniA1WPh1mxw1ohHuu9LVcaD0H7UcAxQsuzFZ+1tP10igc4Voi+jlkMzMzA/Ck0s5h9PMLV2xUxQCut2RpddL1EFY0co27klvLMIz1YYrDNifXZh8OBszOO8+uuRD+vtUW07UUma0233IlnO0Ttk6F5ayzsxPIzy20WjpurnbrG6FQFUWN3Ji1ZmdiisM2Z7U0SXjyqT27yNJ6N95iLcS5MihMMdgaZGf75LIEraex2Gqfa6E+81zlzo3tySc+8YmCX1+M19xJmOJQJqyW4hn+vtEKeMWuwQBWV2EroXIVNvVvNOh0M4pvmTxtLsWsb3DvvfcW/PpivOZOwkrmlQmTk5P09PQ8KaUyl38XnlhYw1kVpaS2tnbFwkBG6cglJ9kytVpzsnxfs9CYPBnbBW1Bn+trq2IWh23KRk9tWy1V0dwSW5N85GS1030uOd0M2TN5Kh8++clPAvmf+vO5vhivuZMwxWGbkivdcj2xB7awGvmQj5yspgjkUipM9oz18Ja3vAXIf9PO5/pivOZ62c59LExx2KZs9YwIY+ewmuxtNcuWYRgbx2IctikrxS7cKOv1UxvlSyFlodByamwuq/nft/qp2CgeZfnfLCLJzHeT7DzZasGSRukwWTCMrcFWVdrKTnEQkduAqyLyDLeOHCERuVdEHgCe1tPTU7wJblEsCr24bCf5MlnYWeSzOTnnVv0ydhZlpzgAu4BK4KMi8ux8/8g590nn3G3At9LpdNEmt1Uxk3Jx2U7yZbJQfmzVk6uRm3yUtLXcSMX8zMsxOPJrwLuBceAzIvJCYNw515/n3x88c+YMd999d7HmtyGWlpaorKws9TSMFThz5gzAwVUu2dLyVShMTovDGvJ18Ktf/eoNbwx33XXXis9tBXld7xzyub4Yr7kdWEVGVlu7nvj7cjIziUglgcXhs8B/AG4HPg4kgRPApbXcFyLybaAZeKxI0zyV+X7mBv62MvO1lPnarHE3wk4b9w5g3jm3K9eTa8hXqeZc6LHXI6flcs+bNfZBYMA5d6s+ICL3AvcCx4B5QHeFUtxXmFK+v2FsHtez0jyeJFsrUW6KQ4VzbllE3gL8CzAJ3A8sAC9wzp0v6QQBEfkKgHPubhvXxi3U326U7fh+2dib/9o2D5sHlJGrQpWGzK8VBFaHeuBHgH3AH4nInc45CxU3DMMwjBukLBSHsNIgIu8CvgN8F/hz59xXM49/wZQGwzAMw9gY295VkaU0fIjAx3w34DJui0rn3JKIyHrSMw3DMAzDeDLbOt8qS2n4deAW4Pudc0tkAoQyP2NKg2EYhmFsnG1vcQAQkQ8TRBS/3Dm3qFaGUs/LMAzDMMqNbW1xABCRfcARTGkwDMMwjKJTLhYHcc657ag07ITYCxGpc85NlXoem8VOu1/jxtgJ//vG1qMQcrftLQ7wRPzCdlMaMtRvxiAickpEjonIsc0YLzTu84F3ikhsk8d9uog8S0S+b5PHveH7LWVzts0eU0SOiMgdIhLNFG7bzLEPishtIlK9meNmxn62iLwOgnWrWO/7Vmj0V+omg6WUsax5lEzeQnMoqNyVheKwXRGRlwL/ICIJESnaZyEiLwb+BvhJ4HMi8qZijZVj3F8Fvuycm9mMMTPjvhD4a+ClwB+LyE+LSHwTxr3h+5UbbM5WQDZtkReRVwB/BXwA+F3gp0QksUljvwz4P8CvAb8vIoc3adyKjAx+gkCxfCv4Rbyg//tbQJb8VEo2cAllLGseJZG30PhFkTtTHEqEiLwIeBfwLufceKh4VSHHkIzQvA34Kefc2whKcf83FaBiISJHgM8DH3HOfVVEdovIARE5UcQxJaPVvxp4u3PuvwKvAH4QeGsxrR4FuN8bas5WCETkecCnReRdIvLDRR4rSlCU7cecc88jWNz3Aj9X7IVdRJ4J/DrwBufcc4ER4BeKOabinFt2zk0CnyHYyJ4pIj+jzxV4uJLJkrKZMpVj7JLJWNY8SiZvSrHkzhSHTSazue0B/hT4Xefcl0WkTUR+SEReJCL7CzWWC5gEHgASIhJ1zn0D+FHg50XkDYUaKwcTwG8B35f5B/osgaL0TyLyE8UYMHO/c8A54KSIxJ1zZ4D/CLwEeHMxxs2w0fvV5myfImjOdlBEdhdtthlE5CXA/wS+TnAPr5Tiu7MSwKHMz58HvgBUAa/ZBPP2rzjnvp35+T1A4yabkBcJNrHPAE8XkY+IyC9n1oVCrcclkSWlRDKVTSllLEyp5U0prNyt1WfdvorzRbCp3Ac8P/P9Y8BXCUzdNxd4rJ8EPg0kQo89m0Ch6CjiPe4Ffomg8c7bMo/dBgwBzyjiuC8Gfht4ChDJPPY04ALwlK12vwSnwyTwRaCNwELSDUwBHWSCmIsw3xTwOeB5md9bCBTa5xbrPcqM8wICV9Kdoft/DfCHxbrX0DiJ0M/twLeB5sxjTcW878wYNwG/kPn5Z4Fp4GMFvsdNl6VSy9RWkbGtJm/FkjuzOGwyqt055z4A/C2BJvxZ59xPAW8ADgM3F2gsLYL1caAW+B0Rqc9YHr5GUJq74D7Q0LhXCLqTvtw591EREefcA8Afs/7unusZ9+8IGpy9AziRsTx8C/h7Cuh3FZF2EanS3zdwv845N0pgUq0H/o1goRkGql3mv73QOOcGgY8CD0pQTK2PoGvnHcUYL8S/Al8CXiciz3HOLTnnPkuw0T2lWINmxhnP/CrAKDDsnBsQkdcCHyimOyvDDHBERH4ceCvwK8A+CRrzFYKSyFJo8FLJVDYlkbEwW0TelILKXVn0qtjqZDYQzfxYzvxDLTvnPigiX3LO3Z957pKInAdu2KyY8bU3ElgTlslsWM65HxGRPwF+A/iGiESAuwhMWBtGRA4SnHS+65yb1cedc1dFpDfzsxOR1wB3Ah8q0Lj3AJ3Oud/MvL6+t/9FghLkbwFmReQK8EMEQUqFGPeFwHuB1wJdkkkFXu/9Somas6lMOuf+RX/PPDUDNGQeuweYcM59pZBjO+dmReSPCJTWd4rIUWCO4HTaU8ixVpnDIjApIldE5JeBHwDe6IocxOucu5aRxXcTxB39jYg8l9xt1tdFqWQpNH7JZCqbrSBjWfMpibyFxi+s3G2WqWQnfwEVWb9L9mOZx18PPAQcusFxXgGcB/4J+APg7YTcE5lr3kzgJvkcBXKJAC8jsF78M8Hp+kT2fRP4F19F0HysUOP+AEFP+RdkPV4Z+vm5BJaHjwHHCzzuJeA3V7hmzfvNen/eBbwc+N/AD4YebyiiXIbfp2Tm+48CP0Fg6v1/wE1FHL8q8/n8CfD7wK3FGivH2JIZ/wLw+I3+z93g2HuBp+WSgw28ZkllaavI1FaSsax5lEzeQnMomNxt+hu4076A5xEEpLwL+OEVrokSNOY6d6ObauY1/hR4Vub3VxKcrj8A1Oe4vrpA9/dMAmXl1szvHwd+b4Vr7wAOFHDcPuDpmd/rgf1AHZm4hqzrn/TYDY77fAIt/ebMe/4l4Dnrvd+shf5DBKbVSn1cF2CKF98QHv/9wL/L/PwyghPiN8kogMX+Ct/3Zn8Bb7zR/7kCjF2Qz7bUsrTCPEoqUznmVjIZy5pHyeQtNIcNy4HFOBSRfKOLnXMLLjDdPdc5970NDLlSJPGrM/N5uog8NfP8/AbGyWbVyGERuV1EfsA593Xn3KUCjTkELABpEWkC/pIgIPLTwOtC4740c32hYioqgddnPqc64GEyMSlqmhWR7xOR5690v1Li5mzy5I6yzyF4/yBwb40Br3XOfbfQY+fCBS6egqcj58lnNvg/d8MU4rMttSytMI+Sy1Q2JZaxMCWTN6UQcmCKQ5EQkRTwJoJ6Ar9DYCqLAq1Z1z0v4/PCOdd7o+M55xaAjwCvyPgxlwnSss4Az8kE4TwLuJa5vlCLyDcJCpwgQXW2aoKTfyLzWDtwlMCVUTCccw8TFHj6H8CDBP7clxEEQL5QgpTXDoLgsILdr3PuH5xz92UWylGCANf3iMgtzjknQQ55J7Di4hBaYD8MHAfucc4tyCaUTF9ho3m+C3ywOOe+CJxyzm3Y574dKOZmuhmUUpYUk6n82e7yppRFr4qtiog8BzhLEEm7LCIfBKacc78UuqaewBd4uQDj1RAUeDoJ/KF7IkjpKwTFUC5sdIw1xo8ANcBfOeeeJyL/HrgVeK9zbqJIYx4nsNR8LPTY3wPvyCgXRUdE3k9giv3VzOe8Zi14CZqzfRz4IVeC5mySo6Mswbq2FU5lxjootSyF5mEytUOwrIoicAPRxWOFGNetHEncTJCeWFRc7sjhNxVLaciMeZZAOQNARF5JcL8FeU/z5EHgZwhiSpbzOVU45x4XkXsyVorNVhqso2wZUUpZUkymdhZmcSgS4X8cEUk650ZF5EcJFIfHgA8Cry6GFUCC2gLPIpOKSBD5/+3V/6og4wqBO+Zc5vvznHOPFnvc0NhvAv4z8KrN9iOKyJ8BP1fAGI6iosqtLfBGoTCZ2jmY4lAEsnx+7we+45z7cwkannyOwN//Y8UOFCqVqVBE3gjcv5mbd0ZxuAvodc6d38xxy8VvaRiGkQ+mOBSYHNHFTycTKJTJsvg94NnlHChkm6lhGEb5YopDAckRXXwzQZTzYuia1o1kTxiGYRhGKTHFoQhYdLFhGIZRrlhWRYGx6GLDMAyjnDGLQxGw6GLDMAyjXDHFwTAMwzCMvLGS04ZhGIZh5I0pDoZhGIZh5I0pDoZhGIZh5I0pDoZhGIZh5I0pDoZhGIZh5I0pDoZhGIZh5I0pDoZhGIZh5I0pDoZhGIZh5I0pDoZhGIZh5I0pDoZhGIZh5I0pDoZhGIZh5I0pDoZhGIZh5I0pDoZhGIZh5I0pDoZhGIZh5I0pDoZhGIZh5I0pDoZhGIZh5I0pDoZhlBQR+bKIfD3H47eIyIKIvKbww01kAAAEVUlEQVQU8zK2FiLyXhFxpZ6HYYqDkQcicjCzgL8v6/HfFpEJEbmtVHMzyoKvAU8VkWp9QEQE+Dhwn3PusyWbmWEYT8IUB2NNnHOPAf8L+BkRSQGIyC8CbwZ+2Dn3QCnnZ2x7TgNVwK2hx14PPAP46ZLMyDCMFTHFwciX9wGVwM+LyI8B7wFe55z7x9JOyygDvgEsESgKiEgS+BDwW865h0o5MWNrIyIvEpGvi8iMiIyJyF+KyJEc171aRM6LyKyIPCQiLxeRr4jIV7Kui4rIu0SkK/OaXxeRIyJym4hMi0jbpt3cFiZS6gkY2wPnXK+I/AbwswRy83bn3J+VeFpGGeCcmxSRB8koDsAHgWUC5dQwciIiLwL+Fvi/wI8AceD9wNdE5JRzrjtz3QuAPwL+mmD9SgG/AdQAj4ReLwr8HXASeCfQR+Au+0Dm2o85565tys1tcUxxMNbDo0A18DXn3MdKPRmjrDgNvFxEngq8FXiDc268xHMytjYfALqAFzvnFgEyQbaPECgI/ylz3fuAswRuVZe57iHgW4QUB+Ange8Hnu2cuy9z3e3AOwAB3ljk+9k2mKvCyAsR+X7gE8DXgWeJyFNKPCWjvPgasB/4A+C0c+4PSzwfYwsjInXAU4E/VaUBwDl3kUAJvStzXSVwG/AXqjRkrvs34GLWy74V+JIqDRlGgXrgI865oWLcy3bEFAdjTTKnwL8kCJC8G3gc+KVSzskoO05nvh/FAiKNtWkgsAL05HiuF2jM/JwCokB/juv69AcRaSWQvS9mXVMFDAMf2eB8ywpTHIxVEZGDBH6/LwFvc87NE5j+XiIizynp5IxyYhKYJwiI/E6pJ2NseUYAB7TmeK4VUOvAILAA7M5xXUvo54OZ794KkbFWvB644Jyb2OiEywlTHIwVyWjhXwLOAa91zi1nnvoD4DzwK6Wam1F2/CLByc4CIo01cc5NEcQovCqzwQMgIvuBZwJfzVy3BDwAvDJTG0SvexrQEXpJXdsaQ4/9BHCcIJvMCGHBkcaKOOd6gc4cjy8BxzZ/RkY5ISK1wFOAOwkC0F7lnBsr7ayMbcS7CbIqviAiHyfIqngfMAZ8OHTdewgOQJ8XkU8SuC/eS+DSUIXhwczf/aKIjAHtBCnBfwHcIyIvBv7ZOTdb7JvaDpjFwTCMUvF84D7g7cA7nHOfL/F8jG2Ec+7vgZcCSeDPgN8hsI4+O5w26Zz7MvBagsPO54GfJ8i66CVQFtSC8SpgJvNa7wR+nCBg8kHgC5jlwSOhQFPDMAzDKHtEpB14DPigc+6/l3o+2w1THAzDMIyyRURiBFkR/0gQLNkJ/BxBcOTNzrlcmRnGKliMg2EYhlHOLBFkWvwW0ARMAf9KEFNjSsMNYBYHwzAMwzDyxoIjDcMwDMPIG1McDMMwDMPIG1McDMMwDMPIG1McDMMwDMPIG1McDMMwDMPIG1McDMMwDMPIG1McDMMwDMPIm/8PfMLXldJeuc8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 547.2x547.2 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#pip install corner\n",
    "import corner\n",
    "# Set up the parameters of the problem.\n",
    "ndim, nsamples = 3, 50000\n",
    "\n",
    "# Generate some fake data.\n",
    "np.random.seed(42)\n",
    "data1 = np.random.randn(ndim * 4 * nsamples // 5).reshape([4 * nsamples // 5, ndim])\n",
    "data2 = (4*np.random.rand(ndim)[None, :] + np.random.randn(ndim * nsamples // 5).reshape([nsamples // 5, ndim]))\n",
    "data = np.vstack([data1, data2])\n",
    "\n",
    "# Plot it.\n",
    "figure = corner.corner(data, labels=[r\"$x$\", r\"$y$\", r\"$\\log \\alpha$\", r\"$\\Gamma \\, [\\mathrm{parsec}]$\"],\n",
    "                       quantiles=[0.16, 0.40, 0.60, 0.84],\n",
    "                       show_titles=True, title_kwargs={\"fontsize\": 12})\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}