1-Generating-Random-Numbers.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# multidimensional arrays\n",
    "import numpy as np\n",
    "\n",
    "# inline plots\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# nicer figures\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams['axes.titlesize'] = 16\n",
    "mpl.rcParams['axes.labelsize'] = 14\n",
    "mpl.rcParams['legend.fontsize'] = 12\n",
    "mpl.rcParams['xtick.labelsize'] = 12\n",
    "mpl.rcParams['ytick.labelsize'] = 12\n",
    "mpl.rcParams['axes.spines.right'] = False\n",
    "mpl.rcParams['axes.spines.top'] = False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generating uniformly distributed random numbers\n",
    "We will use `numpy` to generate random numbers. To generate numbers uniformly distributed between 0 and 1, we can use the function `np.random.uniform()`. If you execute the cell below more than once, you will see how the output changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6335029204757673\n"
     ]
    }
   ],
   "source": [
    "x = np.random.uniform()\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To generate many random numbers at once, use the `size` keyword"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.9971163  0.24489731 0.59915671 0.62654878 0.36522264 0.85216915\n",
      " 0.54369438 0.46001866 0.69287015 0.52221977]\n"
     ]
    }
   ],
   "source": [
    "x_1d = np.random.uniform(size=10)\n",
    "print(x_1d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also generate a whole matrix of random uniform numbers at once!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.73888917 0.85229025 0.15193648]\n",
      " [0.52529906 0.63604803 0.3576822 ]\n",
      " [0.2526178  0.87488889 0.21631991]]\n"
     ]
    }
   ],
   "source": [
    "x_2d = np.random.uniform(size=(3, 3))\n",
    "print(x_2d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that `x_1d` and `x_2d` are a vector and a matrix. In python, elements of vectors and matrices are accessed with the `[]` synthax. Notice that indexes start at 0. For instance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array([4, 7, -3.1, 2, 5, 6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-3.1"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also select a subset of a vector with the `[start:stop]` synthax. For example, to get the 2nd and 3rd elements of our array, we could do"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.1,  2. ])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[2:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrices work the same way, but we use two indices instead of one. The first index corresponds to **rows** and the second index corresponds to **columns**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([\n",
    "    [1, 2, 3],\n",
    "    [4, 5, 6],\n",
    "    [7, 8, 9]\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 6])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[0:2, 2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you come from C, you might be used to operate on arrays iterating over them. In python, we can operate with arrays without iterating over them! For instance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([\n",
    "    [1, 2, 3],\n",
    "    [4, 5, 6],\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3, 4],\n",
       "       [5, 6, 7]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  4,  6],\n",
       "       [ 8, 10, 12]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 * A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,   8,  27],\n",
       "       [ 64, 125, 216]], dtype=int32)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A ** 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also make arithmetic operations between arrays. Python will \"guess\" what to do as long as the shapes of the last index(es) match."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([\n",
    "    [1, 2, 3],\n",
    "    [4, 5, 6],\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = np.array([0, 1, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 3, 5],\n",
       "       [4, 6, 8]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A + v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "Create a vector containing the numbers 9,...3, 2, 1. Then:\n",
    "\n",
    "+ Select the first element (9)\n",
    "+ Select the last element (1)\n",
    "+ Select the 2nd, 3rd and fourth elements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n",
      "1\n",
      "[8 7 6]\n"
     ]
    }
   ],
   "source": [
    "# write your answer here\n",
    "v = np.array([9, 8, 7, 6, 5, 4, 3, 2, 1])\n",
    "print(v[0])\n",
    "print(v[-1])\n",
    "print(v[1:4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "1. Create a random matrix A of 3 rows and 6 columns\n",
    "2. Add 1 to rows 0 and 2\n",
    "3. Substract 5 from columns 1 and 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# write your code here\n",
    "A = np.random.uniform(size=(3, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.38988898, 0.42422749, 0.80100872, 0.43949146, 0.70817969,\n",
       "        0.49790501],\n",
       "       [0.58233926, 0.67788476, 0.16004998, 0.91714633, 0.7909508 ,\n",
       "        0.0474873 ],\n",
       "       [0.77447688, 0.47606469, 0.90564162, 0.30240551, 0.38659841,\n",
       "        0.22811837]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.38988898, 1.42422749, 1.80100872, 1.43949146, 1.70817969,\n",
       "       1.49790501])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[0,0:7]+1 #A[0,:] = A[0,:]+1; A[0, :] += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.77447688, 1.47606469, 1.90564162, 1.30240551, 1.38659841,\n",
       "       1.22811837])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[2, 0:7]+1 #A[2,:] += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.57577251, -4.32211524, -4.52393531])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[0:4,1]-5 #A[:, [:] += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.56050854, -4.08285367, -4.69759449])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[0:4,3]-5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "How would you generate 1000 random numbers uniformely distributed between 5 and 20?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.random.uniform(low=5, high=20, size=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the density of a sample\n",
    "As a simple sanity check, we want to plot the density of the data we have generated. We will use the function `plt.hist()` to plot the estimated pdf of our randomly generated data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-34-2febd01fd35a>, line 11)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-34-2febd01fd35a>\"\u001b[1;36m, line \u001b[1;32m11\u001b[0m\n\u001b[1;33m    color=\"red\",\u001b[0m\n\u001b[1;37m    ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "fig, (ax,ax2) = plt.subplots(1, 2, figsize=(10, 5)) #(1,1 --> 1 riga e 1 colonna di plot (1 plot) : fig, (ax,ax2) = plt.subplots(1, 2, figsize=(10, 6))\n",
    "bins = np.linspace(0, 25, num=100)\n",
    "ax.hist(\n",
    "    data,\n",
    "    bins=bins,\n",
    "    density=True\n",
    ");\n",
    "\n",
    "ax2.plot(\n",
    "    x, x+2\n",
    "    color=\"red\",\n",
    "    lw=2\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make sure our estimation ressembles the actual probability density function of a uniform random variable, we will create a function that computes the pdf of a uniform random variable between $a$ and $b$ at an arbitrary point $x$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "What is the probability density function (pdf) of a uniform random variable between $a$ and $b$?\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\rho (x)= \\frac{1}{(b-a)}  \\;\\;  a<x<b$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "Write a function that gives the density of a uniform random variable between $a$ and $b$ at an arbitrary point $x$. Notice that you can define optional arguments by including them in the definition and giving them a default value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def uniform_pdf(x, a=0, b=1):\n",
    "    if x < a:\n",
    "        return 0\n",
    "    elif x > b: #else if\n",
    "        return 0\n",
    "    else:\n",
    "        return 1/(b-a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can add the expected pdf into the plot. The function `np.linspace(start, stop, num)` generates `num` equally spaced numbers between `start` and `stop`, both included."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(start=0, stop=25, num=1000)\n",
    "pdf_x = np.array([\n",
    "    uniform_pdf(t, a=5, b=20)\n",
    "    for t in x \n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1ac7a10d460>]"
      ]
     },
     "execution_count": 45,
     "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"
    }
   ],
   "source": [
    "# generate a figure with a single subplot, of some size\n",
    "fig, ax = plt.subplots(1, 1, figsize=(6, 4))\n",
    "\n",
    "\n",
    "# plot empirical estimation\n",
    "bins = np.linspace(0, 25, num=100)\n",
    "ax.hist(\n",
    "    data,\n",
    "    bins=bins,\n",
    "    density=True\n",
    ");\n",
    "\n",
    "# plot theoretical prediction\n",
    "ax.plot(\n",
    "    x, pdf_x,\n",
    "    color=\"red\",\n",
    "    lw=2\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adding labels and legend\n",
    "Axis labels and legends are the most important parts of a plot. Without them, we don't know what is what! So, let us add labels, a legend and a title to our plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "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": [
    "# generate a figure with a single subplot, of some size\n",
    "fig, ax = plt.subplots(1, 1, figsize=(6, 4))\n",
    "\n",
    "\n",
    "# plot empirical estimation\n",
    "bins = np.linspace(0, 25, num=100)\n",
    "ax.hist(\n",
    "    data,\n",
    "    bins=bins,\n",
    "    density=True,\n",
    "    label=\"Empirical\"\n",
    ");\n",
    "\n",
    "# plot theoretical prediction\n",
    "ax.plot(\n",
    "    x, pdf_x,\n",
    "    color=\"red\",\n",
    "    lw=2,\n",
    "    label=\"Theoretical\"\n",
    ")\n",
    "\n",
    "# add labels for axes\n",
    "ax.set_xlabel(r\"$x$\") # r per inserire LaTeX nella stringa\n",
    "ax.set_ylabel(r\"Density, $f(x)$\")\n",
    "\n",
    "# add legend\n",
    "ax.legend(loc=(0.95, 0.7), frameon=False)\n",
    "\n",
    "# add title\n",
    "ax.set_title(f\"The uniform distribution $U(a, b)$\\n$a$=5, $b$=20\"); # f permette di inserire stream con variabili"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "Verify that, if the sample size increases, our empirical estimation gets closer to the theoretical prediction. Do so for the following cases:\n",
    "+ $a=0, b=1$\n",
    "+ $a=-3, b=-1.2$\n",
    "+ $a=1800, b=1990$\n",
    "\n",
    "**Hint** Instead of copy-pasting the code to generate the figure many times, you could put the code inside a function `plot_comparison(N, a, b)`. The function will have 3 arguments: the sample size $N$ and the bounds $a, b$ of the uniform random variable. You can set a title that depends on the values of $a, b, N$ as follows\n",
    "\n",
    "```python\n",
    "ax.set_title(f\"The uniform distribution $U(a, b)$\\n$a$={a}, $b$={b}, $N$={N}\");\n",
    "```\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_comparison(N, a, b):\n",
    "    \n",
    "    # generate the random data\n",
    "    data = np.random.uniform(low=a, high=b, size=N)\n",
    "    \n",
    "    # compute the theoretical distribution\n",
    "    dx = (b - a) / 10\n",
    "    x = np.linspace(a - dx, b + dx, num=1000)\n",
    "    pdf_x = np.array([\n",
    "    uniform_pdf(t, a=a, b=b)\n",
    "    for t in x \n",
    "])\n",
    "    \n",
    "    # generate a figure with a single subplot, of some size\n",
    "    fig, ax = plt.subplots(1, 1, figsize=(6, 4))\n",
    "    \n",
    "    # plot empirical estimation\n",
    "  #  bins = np.linspace(a, b, num=N) se non metto nulla, ci pensa python\n",
    "    ax.hist(\n",
    "    data,\n",
    "   # bins=bins,\n",
    "    density=True,\n",
    "    label=\"Empirical\"\n",
    ")\n",
    "\n",
    "    # plot theoretical prediction\n",
    "    ax.plot(\n",
    "    x, pdf_x,\n",
    "    color=\"red\",\n",
    "    lw=2,\n",
    "    label=\"Theoretical\"\n",
    ")\n",
    "\n",
    "    # add labels for axes\n",
    "    ax.set_xlabel(r\"$x$\")\n",
    "    ax.set_ylabel(r\"Density, $f(x)$\")\n",
    "\n",
    "    # add legend\n",
    "    ax.legend(loc=(0.95, 0.7), frameon=False)\n",
    "\n",
    "    # add title\n",
    "    ax.set_title(f\"The uniform distribution $U(a, b)$\\n$a$={a}, $b$={b}, $N$={N}\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "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"
    },
    {
     "data": {
      "image/png": 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d07L3RxeMd2L288665VcCL5J6y+rXteIWUgv9R8BU4FDSqPCJ+SQNzX8fBb43M8MtaqsASfuRutvXioh/lh3PQIZavGbWWW5RWxVsBXx7CCW9oRavmXWQW9RmZmY9rNQWtaSDJE3Lps87t8nPXKM0dZ9HrJuZ2bBXdrJ7gvQQjO1IA3j6JWkyMNiJHMzMzIaMUhN1RFwEIGkS6VaYPkl6I/A1YC9effBEv7bffvu48sorBxummVnVqOwA7FVlt6iLOAE4nf5vWamNmN0PYNy4cf0VNTMz63lDYtR31uLeAjhloLIRcVZETIqISWPGjBmouJmZWU/r+UQtaQnSQyEOrj3W0czMrCp6PlGTptabBPxc0izgtmz5Y5K2LC8sMzOzziv1GnV2i9VIYAQwQtIywKK6lvPzwGq592sCt5Ie+Ti7W7GamZmVoewW9ZGkB/MfDnwq+/1ISeMkzZc0LpJZtRevJucn2/j8ZTMzs55U9u1ZU0izEzWyXB+fmYlvHTAzs4oou0VtZmZm/XCiNjMz62FO1GZmZj1sKD2ZzFq09uFTu7KfmSfu2JX9mJlViVvUZmZmPcyJ2szMrIc5UZuZmfUwJ2ozM7Me5kRtZmbWw5yozczMepgTtZmZWQ9zojYzM+thTtRmZmY9zInazMyshzlRm5mZ9TAnajMzsx7mRG1mZtbDnKjNzMx6mKe5tLbpxnSankrTzKrGLWozM7Me5kRtZmbWw0pN1JIOkjRN0kJJ5/ZTbm9Jt0uaK+kxSSdJcre9mdkwImmKpJ+WHUcjkiZLuqoN2wlJ6xb5TNkt6ieA44CzByj3BuAQYBXg3cA2wGEdjczMzNpK0vzc6xVJL+TeTy47vhpJa2cJdXGDMCLOi4gPlRFPqa3SiLgIQNIkYI1+yp2ee/u4pPOAD3Q4PDMza6OIWK72u6SZwOci4ne5ZVO6EYekkRGxqBv7aoeyW9Steh8wvdEKSftl3enTZs+e3eWwzMxskJaS9GNJ8yRNzxpyAEhaTdKFkmZLekjSF3Lrlpb0f5KeyF7/J2npbN37s8um/y1pFnCOpCUkHS7pAUnPSPqFpNHZ5q7Pfj6XtfY3l7SPpBtz+9tQ0tWS5kh6UtIR2fJNJd0s6TlJ/5D0PUlLDeYfZMglakmfASYBJzdaHxFnRcSkiJg0ZsyY7gZnZmaD9RHgZ8CKwKXA9wAkLQFcBtwFrE66BHqIpO2yz30F2AyYCEwANgWOzG33TcBoYC1gP+C/gF2BrYDVgGeBU7Oy78t+rhgRy0XEzfkAJS0P/A64MvvsusA12eqXgS+SLtVunsV5YEv/Epkhlagl7Qp8HdghIp4uORwzs94ntfKKwq/2uTEiLo+Il4GfkJIuwLuAMRFxTES8FBEPAt8HPpGtnwwcExFPRcRs4Ghgz9x2XwG+FhELI+IFYH/gKxHxWEQsBKYAuzc5UHknYFZEfDMiXoyIeRHxJ4CIuD0ibomIRRExEziTdDLQsiEzclrS9qQvZceIuKfseMzMrCNm5X7/J7BMljzXAlaT9Fxu/Qjghuz31YCHc+sezpbVzI6IF3Pv1wIulvRKbtnLwNgmYlwTeKDRCknrAd8i9fy+gZRnb29im30q+/askZKWIf1jj5C0TKOzGUlbA+cBu0XErd2O08xsyIpo5aXCr857FHgoIlbMvZaPiA9n658gJd+acdmyxf8SDba3Q932lomIxxuUbRTLm/tYdzrwV2B8RKwAHAEM6t+n7K7vI4EXgMOBT2W/HylpXHYBf1xW7ijgjcDluaH8V5QTspmZleBWYF42IGxZSSMkbSTpXdn6C0j5Y4ykVYCvAv3dk30GcLyktQCyz+2SrZtN6irvKxn/BlhV0iHZILblJb07W7c8MBeYL2l94IBWD7im1EQdEVMiQnWvKRHxSHYB/5Gs3AciYmS2rPbaoczYzcyse7Jr1juRBos9BDwN/IDUiIP0TI5pwN3APcAd2bK+fIc0WO0qSfOAW0jP6SAi/gkcD9yUjd7erC6WecC2wM6krvr7efWW4cOAPYB5pMu1P2/1mGsU0c4xAL1l0qRJMW3atLLDKF03JsvoFk/KYdYV3ejKtiaV3fVtZmZm/XCiNjMz62FD5vas4Wo4dUubmVn7uUVtZmbWw5yozczMepgTtZmZWQ9zojYzM+thTtRmZmY9zInazMyGnexR0309AhRJZ0g6apD7eL+kxwazjWb49iwzs2GuhdtACz2ycuaJOzb9JDNJM0kzVL2cW3xuRBxUZJ8DiYjlBli/fzv310lO1GZm1m07R8Tvytq5pBHZs8OHBHd9m5lZ6STtI+kmSd/OJsJ4UNJ7suWPSnpK0t658udm3ddXS5on6Q+1mbCy9SFp3VzZ0yVdLmkB8IFs2XG58rtIulPSXEkPSNo+W/5pSfdl+3hQ0ue7+M8CuEVtNqx148l3nijF2ujdpBmxVgaOBn4GXAasC2wFXCjpwoiYn5WfDOwI/Ak4CTgPeG8f294D+DBpBq6lSFMrAyBpU+DHwO7ANcCqpOkqAZ7KPvMg8D7gCkm3RcQdbTjeprhFbWZm3XZJ1mquvfbNlj8UEedk3dI/B9YEjomIhRFxFfASKWnXTI2I6yNiIfAVYHNJa/axz19HxE0R8UpEvFi37rPA2RFxdbb+8Yj4K0BETI2IByL5A3AVsGV7/hma40RtZmbdtmtErJh7fT9b/mSuzAsAEVG/LD9I7NHaL1krew6wWh/7fLSP5ZBOCB5otELSDpJukTRH0nOkVvkq/Wyr7ZyozcxsqFrcepa0HDAaeKKPsv2NZH8UeEv9QklLAxcCJwNjI2JF4HK6PF+3E7WZmQ1VH5b0XklLAccCt0REfy3nvvwQ+LSkbSQtIWl1SeuTrmUvDcwGFknaAfhQ26JvkhO1mZl122XZA0lqr4tb3M75wNdIXd6bkBsgVkRE3Ap8Gvg28DzwB2CtiJgHfAH4BfAsaUDapS3G2jKP+jYzG+ZaGJnfsa7diFi7n9Xn5sr9vT6OiFijrvzTfT24JCKU+32fBuv3qXt/MfC6E4aIOBU4tY99XAfUx9R2blGbmZn1sFITtaSDJE2TtFDSuQOU/aKkWdnN6GdnF/nNzMyGtbJb1E8AxwFn91dI0nbA4cA2wFrAm0k3w5uZWQVFxD4RcWTZcXRDqdeoI+IiAEmT6L+ff2/ghxExPSt/LOkJNId3PMhOOvZYLvrJeWVHMbT84biBy9hiFz3ybOd34u+kmPHj4ZxzYMSIsiOxIUIRhSZJ6UwQ6XmrazS64J+tvws4ISJ+nr1fhTRcfpWIeKau7H7AfgDjxo3b5OGHH+5k6IOz5JKwaFHZUZhZt915J0yYUHYU/enqfcLWv6Ey6ns50pD5mtrvywOvSdQRcRZwFsCkSZPKPwvpz8tp8pbdJp9EyPWiGRcduEXZIQwp/37aTR3fh7+TAvbeG+6/H155pexIbAgZKol6PrBC7n3t93klxNI+WW/G7au/DZyom7P55mVHMKTc8es5nd+Jv5PmjRqVfvZAT6YNHWUPJmvWdCDfTzQBeLK+29vMzGy4Kfv2rJGSlgFGACMkLSOpUSv/x8BnJW0gaUXgSHI3xg95bk2bVUOtrrtFbQUU7vrO7l9eDVgWmB0Rswex/yNJj3+r+RRwtKSzgb8AG0TEIxFxpaSTgN9n+72w7nNmbeM5nM2slzSVqCUtT0qinwQ2BZYkjQoMSY8DvwXOiojbiuw8IqYAU/pYnZ/KjIj4FvCtItvvaT6jNqset6itBQN2fUs6FJgJfAa4GtgFmAisB2xOSrQjgaslXSlpfIdiNTMzq5xmWtSbAVtFxL19rL8VOFvS/sBnga2A+9sU3/CVnVG/4tsVzarDLWprwYCJOiL+o/a7pDF9XZOOiIXAaW2MzczMrPKKDib7o6TtIuLBjkRTJdkZtR90Ukw3BnpZNXXjb+vXj89N95m6RW0FFL0963JSst44v1DS+yR1/hFIZmZmFVMoUUfEwcDJwLWSPiRpoqQrSbdNPdKJAIetWou65DDMrHui1oHmFrUVUPg+6og4WdII4DekW7QuAd5Rm9nKzMzM2qdQi1rSmpLOBI4BbgMWAlOdpFvga9RmFeRR31Zc0Rb1/cDdwE4RcbWkrYGLJK0eEce3P7xhzBXVzMyaUDRRT46IC2tvIuJaSVsBl2fJ+sD2hjf8he+jNquMcIvaWlB0MNmFDZbdBbwHeH+bYqoGV1Szygmfl1sLmnmE6DoDlYmIh4EtlKzZlsgqwhXXrIJ8om4FNNOivlnSDyX1OTu8pJWAT5BmvNqlXcENa66oZpXjS13WimauUa8PHAFMlfQKcDvwBPAisBKwAfA20jO/D4mI33Yo1mHKFdeGNk8L2gKfqFsBzbSoTyTNkLU68HngPmBFYB1gEfAj4J0RsYWTdAGuqGaV49sxrRXNtKg/A3w1Ip6StAewd0TM73BcleGKa1ZBPlG3ApppUT9KmuoSYFdg2Y5FUyWuqGaV42vU1opmu74vlHRH9v5z2SQcK3QwrspwxTWrIJ+oWwHNzEf9fUnXk0ZzTwT2Bo4GRkh6GLiz9oqISzsW6XDjilppnq6zmnw7prWiqQeeRMTfIuIk0iNE3wssD2wKHA88DmwL/LhTQQ5nrrhmFeQTdSug0CNEI+Ktube3Zy9rhSuqWeX4Upe1otAjRNtN0mhJF0taIOnhbFR5o3JLSzpD0pOS5ki6TNLq3Y63E1xxzSrIJ+pWQKmJGjgVeAkYC0wGTpe0YYNyBwObA+8AVgOeBU7pVpAd4YpqVj2+HdNaUFqiljQK2A04KiLmR8SNwKXAng2KrwP8NiKejIgXgZ8DjRL6kOP7qM0qyCfqVkCZLer1gEURMSO37C4aJ+Afkib9WE3SG0it7ysabVTSfpKmSZo2e/bstgfdNq6oZpXjWm+tKDNRLwfMrVv2PGlEeb37SQ9eeTz7zNuAYxptNCLOiohJETFpzJgxbQy3M1xxzSrIJ+pWQNsStaRxkopsbz5Q/9CUFYB5DcqeCiwNrAyMAi6ijxb1kOGKalY5vtRlrWhni3omcJekLZssPwMYKWl8btkEYHqDshOBcyNiTkQsJA0k21TSKoOItyd41LdZBflE3QpoZ6L+DKmle3IzhSNiQVb+GEmjJG1BevrZTxoUvw3YS9IbJS0JHAg8ERFPtyf0EriimlWOT8ytFW1L1BFxbkR8LSLeXeBjB5Im+XgKuAA4ICKmS9pSUn6GrsNI81/fD8wGPgx8tE2hl8tdYWbV4xN1K6DQk8naLSLmkGbkql9+A2mwWe39M6SR3sOHK6pZ5fiRwdaKQi1qSZdI2qngoDHrh9O1WQX5RN0KKJpwF5AeNvKYpBPqBoJZEa6oZpXja9TWikKJOiImA6sCxwIfBP4m6XpJe0lathMBDne+XcOsgnyibgUU7sKOiLkRcXpEbAq8nTSD1pnAPySdKelt7Q5yWHJFNasct6itFS1fa5a0Gul2qp2ARcCFwJrA3ZIOa094w58rrlkF+UTdCig6mGxJSbtLuhx4mDRi+yRg1Yj4bER8mDTRxpFtj3S4cUU1qxxf6rJWFL096x+AgPOBwyPi7gZlridNQ2lNcMU1qyCfqFsBRRP1d4BvRsQ/8wslCVgzIh6JiOdI01Jaf1xRzcysCUUT9RTSwLF/1i0fDTwEjGhDTJXidG02sLUPn1p2CO3lE3UroOhgsr76aZcjPeLTmuWKalY5vtRlrWiqRS3pu9mvAZwgKd+iHgFsCtzZ3tCqwRXXrIJ8om4FNNv1/fbsp4C3AS/l1r0E3EGTs2ZZxhXVrHJ8O6a1oqlEHREfAJB0DnBwRMztaFQV4oprVkE+UbcCCg0mi4hPdyqQynFFNascz55lrRgwUUu6FPhURMzNfu9TRHykbZFVhSuuWfX4RN0KaKZF/Qyv3kX0TAdjqRZXVLPK8aUua8WAiTrf3e2u7/ZzxTWrIJ+oWwFFn/W9gaS35t5vK+mnkv5Hkh92UoQrqlnl+HZMa0XRB56cDbwTQNKawK9JTyX7T+C49oZWDa64ZhXkE3UroGiiXp90zzTA7sCfshmz9gQ+2c7Ahj1XVLPKca23VhRN1CN49WEn2wCXZ78/AIxtV1BV4oprVkE+UbcCiibqe4EDJG1JStRXZstXB54uunNJoyVdLGmBpIcl7dFP2Y0lXS9pvqQnJR1cdH89xRXVrHJ8qctaUTRR/zewL3AdcEFE3JMt/whwawv7P5XUQh8LTAZOl7RhfSFJq5BOCs4EVgbWBa5qYX89x6O+zSrIJ+pWQNEnk10vaQywQkQ8m1vVaOrLfkkaBewGbBQR84Ebsweq7AkcXlf8UOC3EXFe9n4hcF+R/fUcV1SzCvKJuRVXtEVNRLxcl6SJiJkR8VTBTa0HLIqIGblldwGva1EDmwFzJP1R0lOSLpM0rtFGJe0naZqkabNnzy4YUve5K8ysgnyibgUUalEDSPo46fr0v1GX6As+QnQ5oH5yj+eB5RuUXQPYGNgWuAc4CbgA2KK+YEScBZwFMGnSpN6tDa6oZpXjE3NrRaFELel/gUOA3wNPMLhBy/OBFeqWrQDMa1D2BeDiiLgti+No4GlJb4yI5wcRQ+l8jdqsgnyibgUUbVHvBXwyIn7Vhn3PAEZKGh8R92fLJgDTG5S9m9eeFAz9v3JXVLPKca23VhS9Rr0EcGc7dhwRC4CLgGMkjZK0BbAL8JMGxc8BPippoqQlgaOAG4d6axo87Z1ZJflE3QoomqjPAj7Vxv0fCCwLPEW65nxAREyXtKWk+bVCEXEtcAQwNSu7LtDnPddDgiuqWeX4GrW1omjX94rAHpK2JXVH/yu/MiK+UGRjETEH2LXB8htIg83yy04HTi8W7lDgimtWOT5RtwKKJuoNeLXre/26df7LK8IV1axyPHjUWlH0gScf6FQgVeWuMLMK8om6FVD4gSfWJq6oZpXjWm+tKJyoJe0gaaqk+7I5qZH0OUnbtD+84c8V16yCfKJuBRRK1JImA78g3QO9NrBktmoE8OW2RjbcuaKaVY4vdVkriraovwzsGxFfBBbllt8CTGxXUFXiimtWQT5RtwKKJurxwM0Nljd6HKj1xxXVrHI86ttaUTRRP0Ga9are+4AHBh9O9bjimlWQT9StgFaeTPbd7HGfAGtK2ps0m9UwfBhJB7mimlWPL3VZC4reR32SpDcCVwPLkGbRWgicHBGndiC+4StL1H7Wt1kF+UTdCig8H3VEfEXS8aSnlC0B/CUi5g/wMTOzynN6tlY0naglLUsa9b0b8GbS39yDwC8lfTMiXuhMiMNUrUXta9RmlbH4Lg+3qK2AphK1pJHAtcDGwJWkWaxEalV/FdhB0lYRsajvrZiZGeBEbYU026LejzS15MYRMT2/QtJGpGvV++IBZc1bfI3aLWqzqnAPmrWi2VHfuwPH1ydpgIi4F/g68LF2BlYdrrhmleMWtRXQbKLekNT13ZffARsNPpwKcUU1qxzf5WGtaDZRrwTM7mf9bGDFQUdTQU7XZhXkE3UroNlEPYLXPtu73itZGWuWK6pZ5fgatbWi2cFkAn4qaWEf65duUzyV48FkZhXkE3UroNlE/aMmyvx4MIFUjiuqWeX4xNxa0VSijohPdzqQqnJXmFkF+UTdCig6KUdbSRot6WJJCyQ9LGmPAcovJek+SY91K8aOcUU1qxzXemtF4Wd9t9mpwEvAWGAiMFXSXY3u1858iTTCfPnuhNd5vl3DrIJ8om4FlNailjSK9NzwoyJifkTcCFwK7NlH+XWAT5EerjL0uaKaVY+vUVsLyuz6Xg9YFBEzcsvuIj1cpZFTgCOAfif/kLSfpGmSps2e3d+t373B16jNKsgn6lZAmYl6OWBu3bLnadCtLemjwIiIuHigjUbEWRExKSImjRkzpj2RdoIrqlnl+MTcWlHmNer5wAp1y1YA5uUXZF3kJwEf7lJcXeXbNcwqyCfqVkCZiXoGMFLS+Ii4P1s2AagfSDYeWBu4QSmpLQW8UdIsYLOImNmdcNvMFdWsctyitlaUlqgjYoGki4BjJH2ONOp7F+A9dUXvBdbMvX8P8D3S3Ni9fxHazKyeT9StgFLvowYOBJYFngIuAA6IiOmStpQ0HyAiFkXErNoLmAO8kr1/ubzQB8kV1axyfDumtaLU+6gjYg6wa4PlN5AGmzX6zHXAGh0NrIt8jdqsgnyibgWU3aKuLldUs8rxNWprhRN1yVxxzSrIJ+pWgBN1WVxRzSrHl7qsFU7UJXPFNasgn6hbAU7UZXFFNasc13prhRN1yVxxzSrIJ+pWgBN1WVxRzSrHl7qsFU7UJXPFNasgn6hbAU7UZXFFNasgn5hbcU7UJfN91GYV5BN1K8CJuiyuqGaV42d9WyucqEvmimtWQT5RtwKcqMviimpWOb7UZa1woi6dK65Z5fhE3Qpwoi6LK6pZ5fh2TGuFE3XJ3BVmVkE+UbcCnKjL4opqVjk+MbdWOFGXzKO+zSrIJ+pWgBN1WVxRzSrHJ+bWCifqkrkrzKyCfKJuBThRl8UV1axyfGJurSg1UUsaLeliSQskPSxpjz7KfUnSvZLmSXpI0pe6HWun+HYNswryiboVMLLk/Z8KvASMBSYCUyXdFRHT68oJ2Au4G3gLcJWkRyPiZ90Mtq1cUc0qxyfm1orSWtSSRgG7AUdFxPyIuBG4FNizvmxEnBQRd0TEooj4G/BrYIvuRtwZ7gozqyCfqFsBZXZ9rwcsiogZuWV3ARv29yFJArYE6lvdtfX7SZomadrs2bPbFmzbuaKamVkTykzUywFz65Y9Dyw/wOemkOI+p9HKiDgrIiZFxKQxY8YMOshO8+0aZhXkE3UroMxr1POBFeqWrQDM6+sDkg4iXaveMiIWdjC2znNFNascX+qyVpTZop4BjJQ0PrdsAn13aX8GOBzYJiIe60J8XeGKa1ZBPlG3AkpL1BGxALgIOEbSKElbALsAP6kvK2kycAKwbUQ82N1IO8QV1axyPOrbWlH2A08OBJYFngIuAA6IiOmStpQ0P1fuOGBl4DZJ87PXGSXE236uuGbV4xN1K6DU+6gjYg6wa4PlN5AGm9Xer9PFsLrDFdWsclzrrRVlt6grzxXXrIJ8om4FOFGXxRXVrHJ8jdpa4URdMldcswryiboV4ERdFldUs8rx7ZjWCifqkrnimlWQT9StACfqsriimlWOL3VZK5yoS+ZnfZtVkE/UrQAn6rK4oppVjmu9tcKJumS+Rm1WQT5RtwKcqMviimpWPb5GbS1woi5LlqjdojarIJ+oWwFO1GZmXeITc2uFE3VZai1qd4WZVcbiuzzcorYCnKjNzMx6mBN1WXxGbVY5i7u+Xf+tACdqMzOzHuZEXRZfozarnMX13S1qK8CJ2szMrIc5UZfF91GbVY6vUVsrnKjNzMx6WKmJWtJoSRdLWiDpYUl79FFOkr4h6Zns9Q1piF/cXXyNuuQ4zKxrFrej3aK2AkaWvP9TgZeAscBEYKqkuyJiel25/YBdgQmkv/WrgYeAM7oWqZmZWQlKS9SSRgG7ARtFxHzgRkmXAnsCh9cV3xv4ZkQ8ln32m8C+dCpRP/IIzJ7dkU0vdv/9gK9Rm1XJ4lHfjz8Ot9/e2Z2NGgXrr9/ZfVhXlNmiXg9YFBEzcsvuArZqUHbDbF2+3IYdi+wb34DTTuvY5vNeGeI9+GbWvMWJ+swz06uT3v1uuOWWzu7DukJR0rUSSVsCv4yIN+WW7QtMjoj315V9GdgwIv6avR8PzACWiLoDkLQfqasc4K3A3zp2EO2xCvB02UG0yXA5luFyHOBj6UVD4Tiejojtyw7CkjJb1POBFeqWrQDMa6LsCsD8+iQNEBFnAWe1K8hOkzQtIiaVHUc7DJdjGS7HAT6WXjRcjsO6p8xR3zOAkVnruGYCUD+QjGzZhCbKmZmZDSulJeqIWABcBBwjaZSkLYBdgJ80KP5j4FBJq0taDfh/wLldC9bMzKwkZT/w5EBgWeAp4ALggIiYLmlLSfNz5c4ELgPuAe4FpmbLhoMh003fhOFyLMPlOMDH0ouGy3FYl5Q2mMzMzMwGVnaL2szMzPrhRG1mZtbDnKg7bDg9z7zAsXxJ0r2S5kl6SNKXuh3rQJo9llz5pSTdJ+mxbsXYjCLHIWljSddLmi/pSUkHdzPWgRT4+1pa0hnZMcyRdJmk1bsdb18kHSRpmqSFks4doOwXJc2SNFfS2ZKW7lKYNoQ4UXde/nnmk4HTJTV6qlr+eebvAHYGPt+lGJvV7LEI2AtYCdgeOEjSJ7oWZXOaPZaaLwEdfq5sS5o6DkmrAFeSBmGuDKwLXNXFOJvR7HdyMLA5qZ6sBjwLnNKtIJvwBHAccHZ/hSRtR3pc8jbAWsCbgaM7Hp0NOR5M1kHZ88yfJT3PfEa27CfA4xFxeF3ZPwLnZg9sQdJngX0jYrMuh91QkWNp8Nnvkv7W/qvzkQ6s6LFIWge4HDgU+H5ErNHNePtS8O/rBGDNiNiz+5EOrOCxnA7Mi4gvZ+93BL4VEW/tctj9knQcsEZE7NPH+vOBmRFxRPZ+G+C8/NMazcAt6k7r63nmjVoJ3X2eeXFFjmWxrPt+S3rrATVFj+UU4AjghU4HVlCR49gMmCPpj5KeyrqLx3UlyuYUOZYfAltIWk3SG0it7yu6EGO7NarzYyWtXFI81qOcqDtrOWBu3bLngeX7KPt8Xbnleug6dZFjyZtC+js7pwMxtarpY5H0UWBERFzcjcAKKvKdrEGahe5gYBxpmtgLOhpdMUWO5X7gUeDx7DNvA47paHSd0ajOw8B1yirGibqzOvI885IUORYgDaohXaveMSIWdjC2opo6lqw79iTgC12Kq6gi38kLwMURcVtEvEi6FvoeSW/scIzNKnIspwJLk661jyI94XAotqgb1Xnop05ZNTlRd9Zwep55kWNB0mfIBsrU5hHvIc0ey3hgbeAGSbNICWHVbJTu2t0IdABFvpO7gfxJX6+cANYUOZaJpPEcc7ITwFOATbMBc0NJozr/ZEQ8U1I81qsiwq8OvoCfkboYRwFbkLq3NmxQbn/gPmB10kjW6cD+Zcff4rFMBmYBbys75sEcC2l2uTflXv9OGtH7JlJ3+JA4jqzc1qTBWhOBJYFvAzeUHX+Lx3IOcCHwxuxYjiANOiv9GHJ/N8sAXyfNXbAMMLJBue2zerIBsCJwLXBi2fH71Xuv0gMY7i9gNHAJsAB4BNgjW74lqWu7Vk6kbtY52eskslH5vfIqcCwPAf8ide3VXmeUHX8rx1L3mfcDj5Ude6vHARxAuq77LOnZ+WuWHX+Lf18rA+eR5gh4DrgR2LTs+HPxTSH1WORfU0hjA+YD43JlDwWeJF1rPwdYuuz4/eq9l2/PMjMz62G+Rm1mZtbDnKjNzMx6mBO1mZlZD3OiNjMz62FO1GZmZj3MidrMzKyHOVGbmZn1MCdqMzOzHuZEbWZm1sOcqM26RNLukhZKWiu37DuSHpA0tszYzKx3+RGiZl2SzS1+G/DniNhX0mHAl4EtIuL+cqMzs141suwAzKoiIkLSEcBUSQ+QZn3axknazPrjFrVZl0n6I7ApsHNEXFF2PGbW23yN2qyLJG0NTCBNa/pkyeGY2RDgFrVZl0iaAFwPfBHYEVguIrYrNyoz63VO1GZdkI30vhk4IyKOkbQRcDewdURcV2pwZtbTnKjNOkzSaOAm4PqI+Hxu+c+BcRGxeWnBmVnPc6I2MzPrYR5MZmZm1sOcqM3MzHqYE7WZmVkPc6I2MzPrYU7UZmZmPcyJ2szMrIc5UZuZmfUwJ2ozM7Me5kRtZmbWw/4/av+PCmFJlGcAAAAASUVORK5CYII=\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"
    },
    {
     "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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\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"
    },
    {
     "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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\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"
    },
    {
     "data": {
      "image/png": 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TZQdsXyk9aOfNFFrmEbFI0lRSkBevb7W3en8N9Hemnd9Bs+a0+x4+T+2ZgHVIo61vAHYiPbDjPuBh4G8DtI4983Qaqcv1kPx526oyAfyadC3+/aTLBwF8t1BuFdK93/flcrsB9+b6jmyi3Pp5Hcf0sw2Vcg8D55JG/e8LPEJqFY8YpP20Oek+853z9I389zu+xvIaKjuQ+yqvJ4DtamxbkFrkJwzW96pF35kBLefJ02BMba+Apzb+8dM/xodIg91uI12fvwa4eoCWH3WmG6vK7QLcCMwitdruIY20H1ZVbl3SIL05udxl1H5wTL/lSN2pQRrF39c27JHLbZKX+TLwNHAisMpg7adc31tIT7F7hdTTsn+d5ZUpOyD7itRCDWC1qvSRuQ4BfGIwv1cD/Z1pRTlPnlo9KaLZMS1mnUvSFNKlifUi4uV212co874y61weeGe9alvgew5aDfG+MutQbsmbmZl1KbfkzczMupSDvJmZWZfyffJ17LzzznH11Ve3uxpmZp1G7a6ALeWWfB3PPfdcu6tgZma2XBzkzczMupSDvJmZWZdykDczM+tSDvJmZmZdykHezMysSznIm5mZdSkHeTMzsy7lIG9mZtalHOTNzMy6lB9ra31a/0tTW76Omd/+YMvXYWbWixzkre0G40QCfDJhZr3H3fVmZmZdykHezMysSznIm5mZdSkHeTMzsy7lIG9mZtalHOTNzMy6lG+h61S33gr339/y1ex1z30tX8dgOWrnX7V8Hcd9+O0tX4eVd9Sl3fE9Pu7YT8JWW7W7GtZBFBHtrsOQNGnSpJg2bVq7q1HbSy/B2LGwaFG7a2Jmg2nlleH559PPoUvtroAt5ZZ8J5ozBxYtYv4KK3H5Jtu1uzZWsNc71213FayG837/WLursNz2vO86RrzyCrz66lAP8jaEOMh3sBdXXpWjdj6s3dWwgr38VL0h6ahBeqpiK33wzzczYoF776wcB/lO5EssNgj83oIhyse/leDR9WZmZl3KQb4TLTmT9/gWs14Ryse7W/JWgrvrzTrMYL21bzB007aYDUVtbclLGiPpUknzJT0qaa865STpeEnP5+l4SSrkT5R0p6SX88+JhbxjJP1d0rzC9JZB2LyWC7klb9Yrwj131oR2d9efCiwE1gD2Bk6TNL5GuSnAZGACsBmwK3AQgKQRwOXAucBo4Gzg8pxecWFEjCxMD7doewaHu+vMepePfyuhbUFe0irAHsDRETEvIm4BrgD2qVF8X+DEiHgiIp4ETgT2y3nbkS47nBQRCyLiFNLF6u1bvAlmZjZE5F7bc9tdj1ok7S3pmgFYTkh6a5l52nlNfiNgUUQ8UEi7F9i2RtnxOa9Ybnwhb3os++i+6Tn96vx5V0kvAE8D34+I02pVSNIUUq8B6647hB9qkjfV5/NDj68xW6v0+sA7SfMKH/8BWAAszp8PGvwa1SZpfeARYIWIWAQQET8Hft6O+rSzu34kMKcqbTawap2ys6vKjczX5avzqpdzEfA2YCxwIPBVSR+vVaGIODMiJkXEpLFjx5bZFjMza6HiJVfgMWDXQtqgBVBJHTVgvZ1Bfh4wqiptFDC3gbKjgHm59d7nciLijxHxVEQsjojfAScDew5A/dvOA+/Mekdvtt9LGyHpHElzJc2QNKmSIWktSRdLmiXpEUmHF/JWlHSSpKfydJKkFXPedpKekPSfkp4BfirpDZK+JOmhPBj8Iklj8uJuyj9fygO93y1pP0m3FNY3XtK1kl6Q9DdJR+X0rSTdJuklSU9L+n7V+LLS2hnkHwCGSxpXSJsAzKhRdkbOq1VuBrBZcbQ9aXBereVAOlY6Ozr2aHedmeHjv2+7ARcAq5HGeH0fQNIbgCtJl3rXBnYAjpD0gTzfl4F3ARNJ8WUr4CuF5b4ZGAOsR7qk+x+kweDbAmsBL5IGkgO8N/9cLfcy3FasoKRVgetIl5PXAt4KXJ+zFwOfBVYH3p3reWhTeyJrW5CPiPnAJcCxklaRtDWwO/CzGsXPAY6UtLaktYDPAWflvBtJO+bwfDZWeZj7DQCSdpc0Ot+GtxVwOGk0vpmZ9UVqZorS08C5JSKuiojFpFhSaRy+AxgbEcdGxMJ8h9UPgY/l/L2BYyPi2YiYBfw3yw4Cfw34Wh7c/QpwMPDlPBh8AXAMsGeDXfkfAp6JiBMj4tWImBsRvweIiDsj4vaIWBQRM4EzqD1OrWHtvrZwKPAT4FngeeCQiJghaRvgV/naC6QNfQtQeSn0j3IaEbFQ0uSc9m3gT8DkiFiYy34sr2NF4Ang+Ig4u9Ub1lJLBt51doeEmTWu1wfeNeiZwu8vAyvlwLsesJaklwr5w4Cb8+9rAY8W8h7NaRWzIuLVwuf1gEslvVZIW0y6Hbw/6wAP1cqQtBHwXWASaXDhcODOBpZZV1uDfES8QOryqE6/mTSgrvI5gC/mqdZy7ga2rJNXc5CdmZn1o7kTiqHY+ngceCQixtXJf4oUuCuXedfNaRXVO+Jx4ICIuLV6QZLWa6AuH6uTdxpwN/DxiJgr6QiWcwxZux+GY8shhuKhZGYt4Z675fIHYG4ePLeypGGSNpX0jpx/PvAVSWMlrQ58lfSAtXpOB75ZCeh5vt1z3ixS9369J6v+ElhT0hH5EvOqkt6Z81Yl3XU2T9LGwCHNbnCFg3wncnedWe/y8V9avkb/IdLAukeA50iXeP8xF/kGMI30jJX7gLtyWj0nkwb2XSNpLnA78M68rpeBbwK35lHy76qqy1xgJ9KTW58BHgTel7M/D+xFujvsh8CFzW5zhcJfmJomTZoU06ZNa3c1anvwQdhoIx4ZvSbvm/LDdtfGzAbBHf/7Cca+/BI8/TS8+c3trk5f3OUwhLgl34k88M6s91QOdzfMrAQHeTMzsy7lIN/B/MQ7s97hnjtrhoN8J3J3nVnv8vFvJTjIm5mZdSkH+U605Eze3XdmvcKX56wZDvJmZp3E3fVWgoO8mVkHcGi3ZjjId6Il98mbWc9xS77l8nvg6z2WFkmnSzp6OdexnaQnlmcZjWj3W+jMzGwIW/9LU8vOUuosZOa3P9jwYANJM0lveltcSD4rIg6rPUdzCm9ArZd/8ECur5Uc5DtRpSXvgThmPcP3yS+xa0Rc166VSxqWn4XfEdxdb2bWSdxd/zqS9pN0q6Tv5ZfCPCzpPTn9cUnPStq3UP6s3OV+raS5kn5bfEWspJD01kLZ0yRdJWk+8L6c9o1C+d0l3SNpjqSHJO2c0/eX9Ke8joclHTSIuwVwkDcz6wjuuevXO0lvkXsjcB5wAfAO4K3AJ4DvSyp2w+8NfB1YHbgH+Hkfy96L9Ga5VYFbihmStgLOAb4ArAa8F5iZs58lvf1uFLA/8D1JWzS3ec1xkO9EfkGNWe9yS/6y3FqvTAfm9Eci4qe5K/1CYB3g2IhYEBHXAAtJAb9iakTcFBELgC8D75a0Tp11Xh4Rt0bEaxHxalXep4CfRMS1Of/JiPgzQERMjYiHIvktcA2wzcDshsY4yJuZWSeZHBGrFabK+7b/VijzCkBEVKcVW/KPV36JiHnAC8Baddb5eJ10SCcTD9XKkLSLpNslvSDpJeBfST0Hg8ZBvhMtGXjX5nqY2aBxz92AW9Jqz934Y4Cn6pTtq/vkcWDD6kRJKwIXAycAa0TEasBVDPKjSh3kzcw6ibvrB8q/SvoXSSNI1+Zvj4i+Wuz1/BjYX9IOkt4gaW1JGwMjgBWBWcAiSbsA7x+w2jfIQd7MrAO4526JK/PDairTpU0u5zzga6Ru+i1Jg/NKi4g/kAfVAbOB3wLrRcRc4HDgIuBF0uC9K5qsa9N8n3wn8sA7s941yC35md/+YNlZWvaPKSLW7yP7rEK5v1bXIyL+qar8c/UeahOx9JQqIvarkb9f1edLgdedbETEqcCpddZxI1BdpwHnlryZmVmXcpDvRH7inVkP8vFu5bm73sysk3jg3XKr1QXfrdySNzPrAO65s2Y4yHcin8mb9S4f/1aCg7yZmVmXamuQlzRG0qWS5kt6VNJedcpJ0vGSns/T8dLSvitJEyXdKenl/HNijWWMyG8DeqKFmzQ4PPDOrOe4/W7NaHdL/lTSSwPWIL0R6DRJ42uUmwJMBiYAmwG7AgdBCt7A5cC5wGjgbODynF70BdKTh8zMOpe7662EtgV5SasAewBHR8S8iLiF9DSgfWoU3xc4MSKeiIgngROB/XLedqS7BE7Kbxs6hXSvyfaFdW1AeprRt1q0OWZmLeWeO2tG6SAvaUVJG0jaRNLY5Vj3RsCiiHigkHYvUKslPz7n1So3Hpgesczp7fSq5fwvcBT5zUT1SJoiaZqkabNmDeFGv594Z2ZmDWgoyEtaVdIhkm4iPZv3r8D9wDOSHpP0Q0nvKLnukcCcqrTZwKp1ys6uKjcyX5evzltmOZI+DAzLjx3sU0ScGRGTImLS2LHLc/5iZtYi7q63EvoN8pKOBGYCBwDXArsDE0kt8XcDx5C6y6+VdLWkcQ2uex4wqiptFDC3gbKjgHm59V53OfmSwHdILwnoHj7IzXqOe+6sGY088e5dwLYRcX+d/D8AP5F0MPApYFvgwQaW+wAwXNK4iKiUnwDMqFF2Rs77Q41yM4DPSVKhy34z0qC+ccD6wM15MP4I4B8lPQO8KyJmNlDPIcvX6Mx6kE/yrYR+g3xE/Hvld0ljI6LmxeqIWAD8oNEVR8R8SZcAx0r6NKl3YHfgPTWKnwMcKekq0p0knyNdZwe4EVgMHC7pdODAnH4D8BqwTmE57wG+D2yBR9qbWQfxq2atGWUH3v1O0lsGcP2HAisDzwLnA4dExAxJ20iaVyh3BnAlcB9pLMDUnEZELCTdXvdJ4CXSZYXJEbEwIhZFxDOVifTe4Nfy58UDuB2Da8nAOzMzs/rKvqDmKlKg/9eIuKuSKOm9wLciYusyC4uIF0gBujr9ZtKAusrnAL6Yp1rLuRvYsoH13cggvL/XzKxl3F1vJZRqyUfEZ4ATgBskvT8/ae5q4DfAY62ooNXgg9ys53jgnTWj9KtmI+IEScOAX5IeOnMZsFlE1BowZy3kgXdmPcgn+VZCqZa8pHUknQEcC9wBLACmOsCbmbWWT+qtGWVb8g+Snib3oYi4VtL2wCWS1o6Ibw589awmP/HOzMwaUDbI7x0RF1c+RMQNkrYFrsqB/tCBrZ6ZmS3D3fVWQtmBdxfXSLuXdP/5dgNUJ+uPD3KzHuSeOyuvkcfabtBfmYh4FNg6v/d9nf7K28DwwzHMepBP8q2ERlryt0n6saR31ysgaTTwMeCPpKfWmZnZAHJot2Y0ck1+Y9JrWqdKeg24E3gKeBUYDWwCvI30XPkjIuLXLaqrVSw5k3dT3szM6mukJf9t0pvm1gYOAv4ErAZsACwCzgY2j4itHeDNzFrM3fVWQiMt+QOAr0bEs5L2AvaNiHn9zWQt5IPcrOf4PnlrRiMt+cdJr5uF9Jz5lVtWGyvF98mb9SCf5FsJjXbXXyyp8kKaT0t6r6RRLayXmZkV+KTemtFvkI+IHwKbAheQRnrtC1wHvCjpYUmXSPqqpN1aW1VbovLEOx/zZmbWh4YehhMRf4mI75Aea/svwKrAVsA3gSeBnYBzWlVJMzPL3F1vJZR6rG1E/HPh4515MjOzFnPPnTWj1GNtbYjwC2rMepdb8laCg7yZmVmXcpDvREsG3rklb9Yr3HNnzXCQNzPrJO6utxIc5M3MOoB77qwZAxbkJa0ryScNg8ED78zMrAEDGZRnAvdK2mYAl2lmZkXurrcSBjLIHwBcApwwgMu0WnyQm5lZA0o9DKcvEXFW/vVrA7VM65sfjmHWg3ySbyX4GrqZWQfwwDtrRqkgL+kySR/yALs288A7MzNrQNlgPR+4EHhC0nGSxi3PyiWNkXSppPmSHpW0V51yknS8pOfzdLy09LRW0kRJd0p6Of+cWMj7bH5b3hxJT0n6nqQBu0xhZjao3F1vJZQK8hGxN7Am8HVgR+Avkm6S9ElJKzex/lOBhcAawN7AaZLG1yg3BZgMTAA2A3YFDgKQNAK4HDgXGA2cDVye0wGuALaIiFGkV+ZOAA5voq5Dhw9ys57jnjtrRulu94iYExGnRcRWwNtJb6I7A3ha0hmS3tbIciStAuwBHB0R8yLiFlJA3qdG8X2BEyPiiYh4EjgR2C/nbUcaQHhSRCyIiFNI773fPtf3oYh4qbJa4DXgrSU3e2jyNTqz3uOTfCuh6WvrktYCdgc+BCwCLgbWAaZL+nwDi9gIWBQRDxTS7gVqteTH57xa5cYD0yOW+eZPLy5H0l6S5gDPkVryZ9TZpimSpkmaNmvWrAY2wcxscHjgnTWj7MC7FSTtKekq4FFSF/p3gDUj4lMR8a+k1vlXGljcSGBOVdpsYNU6ZWdXlRuZr8tX571uORFxXu6u3wg4HfhbrQpFxJkRMSkiJo0dO7aBTWiTJQPvzMzM6is7AO1pUpf3ecCXImJ6jTI3AS82sKx5wKiqtFHA3AbKjgLmRURIang5EfGgpBnAD4B/a6COZmZDi7vrrYSy3fUnA+tExH8UA3we/b4uQES8FBEbNLCsB4DhVSP0JwAzapSdkfNqlZsBbFYcbU8anFdrOZBObDZsoH5Dlw9ys57jo96aUTbIH0PqHq82BnikzIIiYj7pMbjHSlpF0taka/w/q1H8HOBISWvnsQCfA87KeTcCi4HDJa0o6bCcfgOApE9LelP+fRPgv4Dry9R1qPI1OrMe5JN8K6FskK8XVUYCrzax/kOBlYFngfOBQyJihqRtcjd8xRnAlcB9wP3A1JxGRCwkjQ34JPAS6Rn6k3M6wNbAfZLmA1fl6agm6mpm1jY+qbdmNHRNXtIp+dcAjpP0ciF7GLAVcE/ZlUfEC6QAXZ1+M4Uegzxy/ot5qrWcu4Et6+TtX7ZeQ56feGdmZg1odODd2/NPAW8jPcCmYiFwF377nJlZ67m73kpoKMhHxPsAJP0U+ExEVN/6ZoPJB7lZz3HPnTWj1C10Xdn13cH8qlmzHuSTfCuh3yAv6QrgExExJ/9eV0TsNmA1MzOzJXxSb81opCX/PEtv0Xy+hXWxRnngnZmZNaDfIF/sond3vZlZm7m73koo++z6TST9c+HzTpLOlfRfkoYNfPWsJh/kZj3IPXdWXtmH4fwE2BxA0jqk97iPAf4f8I2BrZr1x931Zj3IJ/lWQtkgvzHpnniAPYHf5zfP7QN8fCArZmZmS/mk3ppRNsgPY+mDcHYgPSIW4CFgjYGqlPWjMvDOj7k0M7M+lA3y9wOHSNqGFOSvzulrA88NZMXMzKwGd9dbCWWD/H8CB5Le/HZ+RNyX03cD/jCA9bK++CA36zm+T96aUfaJdzdJGguMiogXC1lnAC/Xmc3MzMzaoFSQB4iIxcCLVWkzB6pCZmb2eksG3rknz0ooHeQlfZR0Pf5NVHX3+7G2g8QHuZmZNaBUkJf0P8ARwG+Ap1j6uFtrA4+uN+tBPsm3Esq25D8JfDwiftGKyliDfJCb9Ryf1Fszyo6ufwNwTwvqYU3wwzHMzKwvZYP8mcAnWlERMzOrzwPvrBllu+tXA/aStBMwHfh7MTMiDh+gellffJCbmVkDygb5TVjaXb9xVZ4jzyDzwzHMepBP8q2Esg/DeV+rKmIl+CA36zk+qbdmlL0mb0OIB96ZmVlfSgd5SbtImirpT/md8kj6tKQdBr56ZmYGHnhnzSkV5CXtDVwEPACsD6yQs4YBXxzQmll9PsjNzKwBZVvyXwQOjIjPAosK6bcDEweqUtYYPxzDrAf5JN9KKBvkxwG31UifB4xa/upYQ3yQm/Uen9RbE8oG+aeAjWqkvxd4aPmrY2U41JuZWV+aeeLdKZK2zp/XkbQv8B3gtLIrlzRG0qWS5kt6VNJedcpJ0vGSns/T8dLS01pJEyXdKenl/HNiIe8Lku6XNFfSI5K+ULaeZmbttuSk3j15VkLZ++S/I+kfgWuBlUhvo1sAnBARpzax/lOBhcAapGv6UyXdGxEzqspNASYDE0jf9WuBR4DTJY0ALgdOAn4AHARcLmlcRCwERHqxznRgQ+AaSY9HxAVN1Hdo8EFuZmYNKH0LXUR8GVgd2Ap4FzA2Io4uuxxJqwB7AEdHxLyIuAW4AtinRvF9gRMj4omIeBI4Edgv521HOlk5KSIWRMQppMC+fa7vdyLirohYFBF/IZ0QbF29gk7kgXdmPcgn+VZCw0Fe0sqSviZpOvAsqRX/Q+AISSs3se6NgEUR8UAh7V5gfI2y43NerXLjgekRy3zzp9daTu7i3wao7imo5E+RNE3StFmzZjW8IYPOB7lZz/FJvTWjoe56ScOBG4AtgKuBqaTW8ibAV4FdJG0bEYvqL+V1RgJzqtJmA6vWKTu7qtzIHLSr8/pazjGkE5uf1qpQRJxJGnfApEmTOiCS+qA3M7P6Gr0mPwV4K7BF9fVySZuSWvUHUm7wXa3b7kYBcxsoOwqYFxEhqaHlSDqMdG1+m4hYUKKeZmZt5yfeWTMa7a7fE/hmjQFxRMT9wLeAj5Rc9wPAcEnjCmkTqN2VPiPn1So3A9isONoe2Ky4HEkHAF8CdoiIJ0rWc+jxQW5mZg1oNMiPJ3XX13MdsGmZFUfEfOAS4FhJq+Tb8nYHflaj+DnAkZLWlrQW8DngrJx3I7AYOFzSirnFTqW++VG8xwE7RcTDZeo41PkanZmZ9aXRID8a6Gsk2ixgtSbWfyiwMmkg3/nAIRExQ9I2uRu+4gzgSuA+4H7SmIAzAPJtcpNJXfEvAQcAk3M6wDeANwJ3SJqXp9ObqOvQ4Za8Wc9Z8qpZH/9WQqPX5Iex7LPqq72Wy5QSES+QAnR1+s2kAXWVz0F6bn7Nl+BExN3AlnXyNihbLzMzs27QaJAXcK6kegPWVhyg+lgJPp836x0eeGfNaDTIn91AmXOWpyJWgg9yMzNrQENBPiL2b3VFrDwPvDMzs76UfqytDQFuyZv1HHfXWzMc5M3MzLqUg3wHCz/W1qxnLLk855a8leAg34l8kJuZWQMc5DuYQ72ZmfXFQb4TuSVv1rt8/FsJDvJmZmZdykG+g/k+ebPe4YF31gwH+U7kg9zMzBrgIN/BfAudmZn1xUG+E7klb9Zz/MQ7a4aDvJmZWZdykO9kHnhn1jOicri7JW8lOMh3Ih/kZmbWAAf5DuZQb2ZmfXGQNzPrAB54Z81wkO9EPsjNzKwBDvIdzE+8M+tBPsm3EhzkO5EPcrOe45N6a4aDfAfzE+/MzKwvDvJmZh1gSf+de/KsBAf5TuSD3MzMGuAg38HCvfVmZtYHB/lO5Ja8Wc/x++StGW0N8pLGSLpU0nxJj0raq045STpe0vN5Ol5aOtRU0kRJd0p6Of+cWMh7n6TfSJotaWbrt8rMzGxoaHdL/lRgIbAGsDdwmqTxNcpNASYDE4DNgF2BgwAkjQAuB84FRgNnA5fndID5wE+AL7RsK9rEo+vNeolb8lZe24K8pFWAPYCjI2JeRNwCXAHsU6P4vsCJEfFERDwJnAjsl/O2A4YDJ0XEgog4hXQ0bA8QEX+IiJ8BD7dyewaVD3IzM2tAO1vyGwGLIuKBQtq9QK2W/PicV6vceGB6xDKRb3qd5fRJ0hRJ0yRNmzVrVtnZB50fjmFmZn1pZ5AfCcypSpsNrFqn7OyqciPzdfnqvL6W06eIODMiJkXEpLFjx5adffC4JW/WczzwzprRziA/DxhVlTYKmNtA2VHAvNx6L7McMzOzntHOIP8AMFzSuELaBGBGjbIzcl6tcjOAzYqj7UmD82otp6v4fN6sd/iJd9aMtgX5iJgPXAIcK2kVSVsDuwM/q1H8HOBISWtLWgv4HHBWzrsRWAwcLmlFSYfl9BsAJL1B0krACumjViqMvO9MPsjNzKwB7b6F7lBgZeBZ4HzgkIiYIWkbSfMK5c4ArgTuA+4HpuY0ImIh6fa6TwIvAQcAk3M6wHuBV4CrgHXz79e0dKsGiwfemZlZH4a3c+UR8QIpQFen30waUFf5HMAX81RrOXcDW9bJuxG67IZyt+TNeo4H3lkz2t2SNzMzsxZxkO9gfuKdWe8IP/HOmuAg34l8kJuZWQMc5DuYW/JmZtYXB/lO5Ja8Wc/xffLWDAd5MzOzLuUg38HCvfVmPcO30FkzHOQ7kQ9yMzNrgIN8B/PAOzMz64uDfCdyS96s5/g+eWuGg7yZmVmXcpDvYOEX1Jj1Dg+8syY4yHciH+RmZtYAB/kO5lBvZmZ9cZDvRG7Jm/UcP/HOmuEgb2Zm1qUc5DuYB96Z9Q4f79YMB/lO5O46s97l499KcJA3MzPrUg7ynWjJmby778x6hZ94Z81wkDczM+tSDvIdzK+aNesdPt6tGQ7yncjddWa9y8e/leAgb2Zm1qUc5DtRPpP3++TNeocH3lkzHOTNzMy6lIN8B/MTsMx6h493a0Zbg7ykMZIulTRf0qOS9qpTTpKOl/R8no6Xln7jJU2UdKekl/PPiY3O25HcXWfWu3z8WwntbsmfCiwE1gD2Bk6TNL5GuSnAZGACsBmwK3AQgKQRwOXAucBo4Gzg8pze57xmZmbdbHi7VixpFWAPYNOImAfcIukKYB/gS1XF9wVOjIgn8rwnAgcCpwPbkbbjpIgI4BRJnwe2B67uZ96B9+CDMGdOSxa9xGOPAR54Z9ZLlrTfH3kE7ryztSsbPRre8pbWrsMGRduCPLARsCgiHiik3QtsW6Ps+JxXLDe+kDc9B/iK6Tn96n7mHXhHHAFXXdWyxRe91uFXHcyscaHc8fq1r6WplT76UbjggtauwwZFO4P8SKC6yTsbWLVO2dlV5Ubma+vVedXLqTtv1YkBkqaQuvcB5kn6S4Pb0h53/XJ17vrlc+2uxhCwOuD9kHhfLNVV++Ijyzd7uX1x4YVpas7VEbFzszPbwGpnkJ8HjKpKGwXMbaDsKGBeRISk/pZTd97qlUTEmcCZDW9Bm0maFhGT2l2PdvN+WMr7Yinvi6W8L3pXOwfePQAMlzSukDYBmFGj7IycV6vcDGCzqhHzm1Xl15vXzMysa7UtyEfEfOAS4FhJq0jaGtgd+FmN4ucAR0paW9JawOeAs3LejcBi4HBJK0o6LKff0MC8ZmZmXavdt9AdCqwMPAucDxwSETMkbZO74SvOAK4E7gPuB6bmNCJiIekWuU8CLwEHAJNzep/zdoGOubTQYt4PS3lfLOV9sZT3RY9SjUvTZmZm1gXa3ZI3MzOzFnGQNzMz61IO8kOApMMkTZO0QNJZVXn/LulPkuZK+qOkyVX5n5X0jKQ5kn4iacVC3vqSfpOf6f9nSTsOzhY1r9l9IWk/SYslzStM2xXyO2pf9LMfPi3pr3kbr84DSit5Tb/nYahajn1xjKS/V30n3lLI76h9kQcW/1jpPR9zJd0jaZdC/g75u/1y/q6vVzXvT/L/iWckHVm17LrzWmdzkB8angK+AfykmChpbdIz+Y8k3d//BeA8SW/K+R8gPQJ4B2A94C3AfxcWcT5wN/BG4MvALySNbemWLL+m9kV2W0SMLEw3FvI6bV/U2w/bAceR7kQZAzxC2raK5XnPw1DV7L4AuLDqO/FwnrcT98Vw4HHSU0H/EfgKcFE+gV2ddLfS0aR9MQ0oPs3mGGAc6f/E+4AvStoZoIF5rZNFhKchMpH+kZ1V+PxO4NmqMrOAd+ffzwOOK+TtADyTf98IWACsWsi/GTi43dvZon2xH3BLnWV17L6osR9OAE4tfF6L9FjzDfPn3wFTCvmfAm7Pv78feJI84DanPQbs3O7tbNG+OAY4t86yOnpfFOo8nfQOkCnA7wrpqwCvABvnz08B7y/kfx24IP/e57yeOntyS35omwb8SdJukobl7ukFpAMbaj+Xfw1Jb8x5D0fE3Kr81j23v7X62xcAm0t6TtIDko6WVHmiY7ftC9X4fdP8s9n3PHSqvvYFwK6SXpA0Q9IhhfSO3xeS1iCdwM6g6u8e6TkkDwHjJY0G1qTv70XNeVtZfxsc7XysrfUjIhZLOofUYl+J9Frej+SDEGo/lx/Sc/vrPdN/7dbVuHUa2Bc3kf65P0r653QhsAj4Ft21L64GLpB0OvAg8FVS6/Ufcv7yvOeh0/S3Ly4i3R/+N1JP0MWSXoqI8+nwfSFpBeDnwNkR8WdJI0k9W0WV7RlZ+FydR86vN691OLfkh7A8OOw7pNfpjiBdi/tRYYBQrefyQ3puf5l3Awx5/e2LiHg4Ih6JiNci4j7gWGDPPHvX7IuIuA74GnAxMDNPc4EncpG+3tXQNfsB+t8XEfHHiHgqIhZHxO+Ak+mC74SkN5CeDLoQqDzhs6/tmVf4XJ3X37zW4Rzkh7aJwE0RMS0HrzuA3wOVkeG1nsv/t4h4Pue9RdKqVfmd+tz+ifS9L6oFS7tvu2pfRMSpETEuItYgBbjhpKc5wvK956Hj9LMvXlecZb8THbcvcn1/DKwB7BERf89Zy/zdJa0CbAjMiIgXgafp+3tRc94WbYYNIgf5IUDScEkrAcOAYZJWyteT7wC2qbRWJW0ObMPS69DnAJ+StImk1Uijbc8CiIgHgHuAr+XlfZj0T+ziwdquZjS7LyTtkq9RImlj0kjhy6Ez90W9/ZB/bqpkXVJ39Mn5Hzks33sehqRm94Wk3SWNzvlbAYeTvxN06L4ATgPeBuwaEa8U0i8FNpW0R95XXyWNOfhzzj8H+EreHxsDB7L0e9HfvNbJ2j3yz9OSUcBRNR2T8w4D/krqOnsY+FzVvEeSrjnOAX4KrFjIW5/0z+wV4C/Aju3e1lbtC9JI678B83PescAKnbov6u0HYDXSic184BnSmINhhflEuqzxQp6+w7IjyDcH7sz74S5g83Zvawv3xfnA86Tu6D8Dh1ctt6P2Ben2twBezdtUmfbO+Tvm7Xwlf9fXL8y7IukWxDn5ODmyatl15/XU2ZOfXW9mZtal3F1vZmbWpRzkzczMupSDvJmZWZdykDczM+tSDvJmZmZdykHezMysSznIm5mZdSkHeTMzsy7lIG9mZtalHOTNOoCkPSUtkLReIe1kSQ9VntlvZlbNj7U16wD57WN3AHdHxIGSPg98Edg6Ih5sb+3MbKga3u4KmFn/IiIkHQVMlfQQcBSwgwO8mfXFLXmzDiLpd8BWpFeN/qrd9TGzoc3X5M06hKTtgQmk18n+rc3VMbMO4Ja8WQeQNAG4Cfgs8EFgZER8oL21MrOhzkHebIjLI+pvA06PiGMlbQpMB7aPiBvbWjkzG9Ic5M2GMEljgFuBmyLioEL6hcC6EfHutlXOzIY8B3kzM7Mu5YF3ZmZmXcpB3szMrEs5yJuZmXUpB3kzM7Mu5SBvZmbWpRzkzczMupSDvJmZWZdykDczM+tSDvJmZmZd6v8D2Os1sJxPMdQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot all comparison in a loop\n",
    "for (a, b) in [(0, 1), (-3, -1.2), (1800, 1990)]:\n",
    "    for N in [100, 300, 1000, 3000,10000]:\n",
    "        plot_comparison(N, a, b)\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generating random numbers with non-uniform distributions\n",
    "In many cases, we want to draw random numbers from non-uniform distributions. For instance, we might want to generate Gaussian, exponential or Poisson distributed random numbers. How can we do this in plain python?\n",
    "\n",
    "### Inverse transform sampling\n",
    "The most general way of generating random numbers under a given distribution is known as **inverse transform sampling**. You can read about the method [here](link), but the key theoretical foundation of the method is very simple:\n",
    "\n",
    "Given a continous random variable $X$ with cumulative distribution function $F$, the random variable $F(X)$ has a uniform distribution between 0 and 1. \n",
    "\n",
    "$$\n",
    "F(X) \\sim U(0, 1)\n",
    "$$\n",
    "\n",
    "Think about it for a second. Here $F(X)$ is not a function, but a random variable, because we apply a function, $F$, to a random variable, $X$, getting a new random variable, $Y \\equiv F(X)$. The statement is then simply that $Y$ is a uniform random variable, no matter what form $F$ takes.\n",
    "\n",
    "As a consequence, one can see that $X = F^{-1}(U)$, where $U$ is a uniform random variable between 0 and 1. This gives as a very simple way of drawing random numbers from an arbitrary continous random variable $X$:\n",
    "\n",
    "1. Generate a uniform random number, $u$\n",
    "2. Compute $x = F^{-1}(u)$\n",
    "\n",
    "where $F$ is the cumulative distribution function of $X$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "Consider the **exponential** distribution, with probability density function \n",
    "$$\n",
    "f(x) = \\lambda e^{-\\lambda x}\n",
    "$$\n",
    "and cumulative distribution function\n",
    "$$\n",
    "F(x) = 1 - e^{-\\lambda x}\n",
    "$$\n",
    "1. Write a function that generates exponentially-distributed random numbers, using the inverse transform sampling method. For simplicity, set $\\lambda = 1$.\n",
    "2. Generate 1000 exponentially-distributed random numbers with your function.\n",
    "3. Plot a histogram of your generated sample, together with the theoretical probability density function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def inv_cdf_expo(y):\n",
    "    x = -np.log(1-y)\n",
    "    return x\n",
    "\n",
    "def inverse_sampling(size, inv_cdf):\n",
    "    # generate uniform data of given_size\n",
    "    u = np.random.uniform(size=size)\n",
    "    # inverse transform it\n",
    "    x = inv_cdf(u)\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1667006e190>]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 8, num=200)\n",
    "pdf_x = np.exp(-x)\n",
    "data = inverse_sampling(size=10000, inv_cdf=inv_cdf_expo)\n",
    "\n",
    "fig, ax = plt.subplots(1, 1, figsize=(6, 6))\n",
    "ax.hist (data,bins=30,density=True,label=\"Empirical\")\n",
    "ax.plot(x,pdf_x,color=\"red\",lw=2,label=\"Theoretical\")\n",
    "#ax.set_yscale(\"log\")\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## In practical situations, do not reinvent the wheel!\n",
    "What we did so far is a good exercise to get comfortable with python, random number generation, histograms and probabilities.\n",
    "\n",
    "If you need to generate exponential random numbers as part of a larger project, however, it is better to use a function from a **well-tested**, **well-documented** library such as [numpy]() or [scipy](). For instance:\n",
    "\n",
    "```python\n",
    "import numpy as np\n",
    "x = np.random.normal(location=0, scale=1, size=1000)\n",
    "```\n",
    "\n",
    "That is the beauty of **open-source** languages like python: there is a community of developers that contribute their code to standardized libraries in an organized fashion. These libraries are less likely than yours to contain errors or bugs, because they are used by many people and such bugs are reported and fixed very quickly. For instance numpy's `np.random` submodel contains functions to generate random numbers from many distributions, see [the documentation for numpy.random](https://docs.scipy.org/doc/numpy/reference/routines.random.html#distributions)\n",
    "\n",
    "However, as you can see **not all** distributions are included in numpy. If you need to work with a less well-known distribution, you might need to implement that yourself. In such case, knowing the **inverse sampling** method will come in handy!\n",
    "\n"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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   "codemirror_mode": {
    "name": "ipython",
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   "file_extension": ".py",
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