2- Metamodeling of univariate black-box functions using Meijer G-functions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Symbolic Metamodeling of Univariate Functions using Meijer $G$-functions\n",
    "\n",
    "In this notebook, we carry out the first experiment (Section 5.1) in our paper *\"Demystifying Black-box Models with Symbolic Metamodels\"* submitted to **NeurIPS 2019** by *Ahmed M. Alaa and Mihaela van der Schaar*. In this experiment, we demonstrate the first use case of symbolic metamodeling using synthetic data, where we show how can we learn symbolic expressions for unobserved black-box functions for which we have only query access."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Can we learn complex symbolic expressions?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start off with four synthetic experiments with the aim of evaluating the richness of symbolic expressions discovered by our metamodeling algorithm. In each experiment, we apply our Meijer $G$-function-based symbolic metamodeling on a ground-truth univariate function $f(x)$ to fit a metamodel $g(x) \\approx f(x)$, and compare the resulting mathematical expression for $g(x)$ with that obtained by Symbolic regression [1-3], which we implement using the [**gplearn library** ](https://gplearn.readthedocs.io/en/stable/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the following four expressions for the underlying univariate functions:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| **Function** | **Notation** | **Expression**   |\n",
    "|------|------|------|\n",
    "|   Exponential function  | $f_1(x)$ | $e^{-3x}$ |\n",
    "|   Rational function  | $f_2(x)$| $\\frac{x}{(x+1)^2}$ |\n",
    "|   Sinusoid function  | $f_3(x)$| $\\sin(x)$ |\n",
    "|   Bessel function  | $f_4(x)$| $J_0\\left(10\\sqrt{x}\\right)$ |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the functions $f_1(x)$, $f_2(x)$, $f_3(x)$ and $f_4(x)$ have very different functional forms and are of varying levels of complexity. To run the experiments, we first import the univariate functions above from the **benchmarks.univariate_functions** module in **pysymbolic** as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pysymbolic.benchmarks.univariate_functions import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we create a list of the univariate functions $f_1(x)$, $f_2(x)$, $f_3(x)$ and $f_4(x)$ as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "True_functions  = [('Exponential function exp(-3x)', exponential_function), ('Rational function x/(x+1)^2', rational_function), \n",
    "                   ('Sinusoid function sin(x)', sinusoidal_function), ('Bessel function J_0(10*sqrt(x))', bessel_function)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before running the experimens, let us visualize the four functions in the range $x \\in [0,1]$ to see how different they are, and the extent to which their complexity vary from one function to another."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABJUAAADHCAYAAACgPWIxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nqakkIiIiIiIiIiJD9t/4adWdm/8hNgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1440x180 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "get_ipython().magic('matplotlib inline')\n",
    "\n",
    "x_points = np.linspace(0,1,100)\n",
    "\n",
    "fig, axs = plt.subplots(1, 4, figsize=(20,2.5))\n",
    "\n",
    "axs[0].plot(x_points, True_functions[0][1](x_points), linewidth=4)\n",
    "axs[0].set_title('$f_1(x)$')\n",
    "axs[1].plot(x_points, True_functions[1][1](x_points), linewidth=4)\n",
    "axs[1].set_title('$f_2(x)$')\n",
    "axs[2].plot(x_points, True_functions[2][1](x_points), linewidth=4)\n",
    "axs[2].set_title('$f_3(x)$')\n",
    "axs[3].plot(x_points, True_functions[3][1](x_points), linewidth=4)\n",
    "axs[3].set_title('$f_4(x)$')\n",
    "\n",
    "for ax in axs.flat:\n",
    "    ax.set(xlabel='$x$', ylabel='$f(x)$')\n",
    "\n",
    "for ax in axs.flat:\n",
    "    ax.label_outer()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the Bessel function is the most complex. So will our symbolic metamodeling algorithm be able top recover the underlying mathematical expression describing these function and recognizing their varying levels of complexity?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running the experiments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we set up the experiment by first setting the number of evaluation points (npoints=100) that we will input to both the symbolic metamodeling and the symbolic regression models, and creating an empty list of learned symbolic expressions and $R^2$ scores."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "npoints             = 100\n",
    "xrange              = [0.01, 1]\n",
    "\n",
    "symbolic_metamodels = []\n",
    "symbolic_regssion   = []\n",
    "\n",
    "sym_metamodel_R2    = []\n",
    "sym_regression_R2   = []"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before running the experiments, we first import the **algorithms.symbolic_expressions** from **pysymbolic**. This module contains two functions **get_symbolic_model** and **symbolic_regressor**, which recovers univariate metamodels and symbolic regression models respectively. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from mpmath import *\n",
    "from sympy import *\n",
    "\n",
    "from pysymbolic.algorithms.symbolic_expressions import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we run the experiments by feeding in each function in **true_function** to both the functions **get_symbolic_model** and **symbolic_regressor**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for true_function in True_functions:\n",
    "    \n",
    "    print('Now working on the ' + true_function[0])\n",
    "    print('--------------------------------------------------------')\n",
    "    print('--------------------------------------------------------')\n",
    "    \n",
    "    symbolic_model, _mod_R2 = get_symbolic_model(true_function[1], npoints, xrange)\n",
    "    \n",
    "    symbolic_metamodels.append(symbolic_model)\n",
    "    sym_metamodel_R2.append(_mod_R2)\n",
    "    \n",
    "    symbolic_reg, _reg_R2   = symbolic_regressor(true_function[1], npoints, xrange)\n",
    "    \n",
    "    symbolic_regssion.append(symbolic_reg)\n",
    "    sym_regression_R2.append(_reg_R2) \n",
    "    \n",
    "    print('--------------------------------------------------------')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results and discussion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us check the symbolic expressions retrieved by both symbolic metamodeling and symbolic regression. In order to enable printing in LaTex format, we first invoke the \"init_print\" command of sympy as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "init_printing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us start with the first function $f_1(x) = e^{-3x}$, and see what the corresponding symbolic metamodel stroed in **symbolic_metamodels[0]**..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAU4AAAAwBAMAAACMIo5fAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nEEie/Dq1L/YXO/5TmX8Cz3SidJNBuP4AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\frac{0.999994662735281 e^{- 2.99999776052408 x}}{x^{4.85820397608223 \\cdot 10^{-6}}}$$"
      ],
      "text/plain": [
       "                   -4.85820397608223e-6  -2.99999776052408⋅x\n",
       "0.999994662735281⋅x                    ⋅ℯ                   "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "symbolic_metamodels[0].expression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, this is almost exactly equal to $e^{-3x}$! This means that the metamodeling algorithm was able to recover the true expression for $f_1(x)$ based on 100 evaluation samples only. To check the corresponding values of the poles and zeros recovered by the gradient descent algorithm used to optimize the metamodel, we can inspect the attributes of the **MeijerG** object **symbolic_metamodels[0]** as follows:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([array([], dtype=float64), array([], dtype=float64)],\n",
       " [array([-4.85820398e-06]), array([], dtype=float64)],\n",
       " 2.999997760524081)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "symbolic_metamodels[0].a_p, symbolic_metamodels[0].b_q, symbolic_metamodels[0]._const"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us check the expression learned by symbolic regression (whcih is stored in **symbolic_regssion[0]**)... "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAUBAMAAAA6im/5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\left(x - 0.966\\right) \\left(x - 0.941\\right)$$"
      ],
      "text/plain": [
       "(x - 0.966)⋅(x - 0.941)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "symbolic_regssion[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, the symbolic regression algorithm retreived an approximation of $f_1(x) = e^{-3x}$, but failed to capture the exponential functional form of $f_1(x)$. This is because the symbolic regression search algorithm starts with predefined forms (mostly polynomials), and hence is less flexible than our Meijer $G$-function parameterization."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**What if we want to restrict our metamodels to polynomials only?** In this case, we can use the *approximate_expression* method to recover a Taylor approximation of the learned symbolic expression as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from copy import deepcopy\n",
    "\n",
    "polynomial_metamodel_of_f1 = deepcopy(symbolic_metamodels[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkEAAAAVBAMAAACzqidWAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$1.00409204011538 x^{2} - 1.67348361984597 x + 0.808848770361795$$"
      ],
      "text/plain": [
       "                  2                                         \n",
       "1.00409204011538⋅x  - 1.67348361984597⋅x + 0.808848770361795"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polynomial_metamodel_of_f1.approximation_order = 2\n",
    "\n",
    "polynomial_metamodel_of_f1.approx_expression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the second order Taylor approximation of our metamodel appears to be very closed to the symbolic regression model!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But what about the other functions? Let us check $f_2(x) = \\frac{x}{(x+1)^2}$ and see what the metamodel was for that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGoAAAA4BAMAAADnSXBYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVO8Qq5l2zWbdiTIi\nu0T8UsK3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAACmUlEQVRIDe1VPYgTQRT+Nnv52SSYaGfjRQQt\nbFIcZ5locSgiBBQVq0XvLNIYQQh2QayusRAPQdFtotgFQe3MNoLN6YFaiimsziKRUwQV43szO5vN\nTjZmrxAEXzHzve97HzPz9meAKWGeW+1MkcOSsU8w6aJ5NyxF5wuntoR4DXgYXaUpKel6C8yXNTGS\n8FxfgH4xskgTpMv8Si5bEyMJ6cp/B7pOZJEmeC5aK75rezsEdWM+djfwHrgRv/P0lM9oZ44muBuV\nBqyieTC6KKwkj3w7CqsK88FyJ6z9z//FDgy3E3/roO13MT4DtamsO9dQePbZcnM/Z69WlVYv/0vh\nOLMhf7HTLc+EXK/7VZbtQwbPxzIveXKMQcYxqoDNEG0xqiG3odDYvJszqwfa10eGmRqPfqQnPwfh\nqnSwF8i2qHgTn3wLgdPBZISFq+viNlE3gdzlnW9GIvIRrZGuMtaodgVIDIeDgCvL+/UuyQANtdZ+\nIl8HBYETRUBdkmS3VYFw0bn42Votxaq5y82QlwmBkEv2EMkNVa1m+j1PdO0C1supGj8vpEo0iFhc\nflW3CYk/ur7Wi/tLeOyi3eat7FAdM53MmtUghi6QiWsxrSL3w0PZcnbLcCm5woS+FrN++K+7ibQ8\n4i3WpCvbbF490GxWiSiMfisDIP+Zi0QUbDHFWosu7M7MLv8zNsqXkCqT7wR7/3Auv4f94ge8ZMP5\nGVyZEhdRLFxcPNti0KcFxSXJSeDdEKk36O9GohfUR28UfVYrT49LLW0HaxgnHRr8MF0f4sJc457M\nKtyAsciVxtJA0km3vOx6gPXgYZ3ymILrgTt6ySGd8pgu5CPNOHqJUdM5ZvKDR3CEtC7G0LAnlHup\nubRZl104OblgVvY34VbTMbaxDzQAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\frac{1.0}{x \\left(1 + \\frac{1.0}{x}\\right)^{2}}$$"
      ],
      "text/plain": [
       "    1.0     \n",
       "────────────\n",
       "           2\n",
       "  ⎛    1.0⎞ \n",
       "x⋅⎜1 + ───⎟ \n",
       "  ⎝     x ⎠ "
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "symbolic_metamodels[1].expression()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For $f_2(x)$, the metamodeling algorithm nailed it! It exactly recovered the true symbolic expression. For the symbolic regression model for $f_2(x)$, we have the following expression:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALMAAAAvBAMAAABanub4AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nULkt/0nW+wV2E7NObtG6IezEAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\frac{0.672 x}{x \\left(x + 0.872\\right) + 0.75}$$"
      ],
      "text/plain": [
       "      0.672⋅x       \n",
       "────────────────────\n",
       "x⋅(x + 0.872) + 0.75"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "symbolic_regssion[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the symbolic regression algorithm also did a good job in finding the true mathematical expression for $f_2(x)$, though it recovered a less accurate expression than that of the metamodel. Now let us examine the results third function $f_3(x) = \\sin(x)$..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA3IAAAAzCAMAAADl5cqHAAAAOVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACXHtMAAAAEnRSTlMAVO8Q\nq5l2zWbdMrsiiUTz+737EACXAAAACXBIWXMAAA7EAAAOxAGVKw4bAAARNUlEQVR4Ae1diZaDOK6F\nsIQQ4L3h/z92tFi6MiFVqSw9hIZzKghblmUjYVu+UEVxHB/sgXH6oPC9i+531MCq3lFjttyUsdmy\ndlvX7bR1Bf+i33T+C/fB+2QPjMej7cmek2K7crmiO3zuFWN4rGx5qh5jPLhWe2BfLldcx9VWHonv\n64HqdGchVzVjN/pCpffJp1JV245NKjmOrTEaGQoPTXO9LuSc26rom5JbAU4wDuM4XiX3h3aiIDP9\npF9hWhVOhcKoNsiBguAMjFHBnblcdfqt43+4J0fWIz1wdV8q8vHuTF1fXYYk43I1YUpJqZrvTnUm\nz2tkPgIShWVFPs7m11r6NNOhj1PnBOPAwsu5sxrt/Jx+QcGH9Sug4Ip+RabgzlyOrMD6+zh/pAfK\nOU0rq7qpjeaaOun5MU3t25O5nFKl+MPAueKzV8l2MhSuRf4p3cck5zzWrTozOMHYzuzK84XV8ONp\n/YKCD+tXuIJr+hWZgruz0MsxtXSr+wRxwSBHlhRWdVcJqiSPHLpzcrlEjXJZkVdMsw2EgQyFT+I5\n9SxTS5ODgA04wTjxXLeabxbyT+kXtIKqqLVAtdS9pl/hCoIzMGYK7s7lStzRT1jcv11mF7s3M+lZ\nrG6SAacYC3O5RE3zldxzpLHuCpMDGQqfxY+Ty5kct+gCnBnj6sTyKf2Cgo/rB5e7q5/PfNH+vRhT\nfAzvpU3baQeWaKRTNOlqluFvmlvK6AZzOafqee7Y44r53I+tBlKczApLYy/ieCjddW3D494NpzLy\nKvJ2evOUfkHBx/Ur6qTgXf2g4P5crouzHbl9x8/beqD3sAaLjCY9aHSj51NFbqejHKhinOczDXQ0\n/2PH4zAXyFhYdJ1EGkrzEDlw3UtOZSyG8dKESa7IeE6/oNUf9CtMwTv6RQX353KVPGdTp3/JqY/L\nkHQxNle3Il0XUeiarZXGCI0cdESxnaVzX/dDJwxW0kRYibIZdSjw+pLIh7upyewldzkZ5cTluBJ1\nOVBlPV1mWnNVszwSG9rcAznoECmFRZeLzCRRWhKvtMpbciojZ4+3mxfP6Be0+qt+BSl4Xz9XMOtC\nadgX/bRhKQ+1z9F+kbxdqm9qBNvsYqQgQ51aojEJiq0PdLsa8qqGfbCjiVZFhJ0niqOzpXpJI6xE\nS7ncZVYF+YWKfLxrTlhUUaFo0mFGVfIMUFwOVMcF25kcTQOLHQ9ZTobCoksjNxalJbFoaB254FRG\nzT7dbNE/pR+0ArWotVjXjxVccEb9iqTg/6m63/nbe+wr6t/GFX7M2C5dwuUoDiAXvMHVa0uqkQcG\ndhieaTX07O9masuVW09Oaeep7GVu5SWNsBI6MWOeVJ+JfLhj+nzvK5p0imuUc1nx4CQuB6o4ya3q\nKbhykedIx5JAatCBCosq+igNpfXZI5t1GWd65g4i/JpKozVP6Re0eli/9HBkBdf0KzIF/x8K7oUa\ncrv4hmatuZwsXOiHnK1il4ub/DLKNTST6skP7TwJMxmylXSCZFCJQeLu7HfmclEkV/TrsXiaZSat\nO220ki5rPuZT3YKq+BlBR90VtUysZJQD6YWZqeQxbhhQujiJmzbcDZEzMRY6V/3F5bwg5IIK+gUF\nH9YvKOjVoCE0nMtkOin41RNLvj8rRz77WWHYXNKKy7GOOqHsS3G5uWx16UaD3UmCd5dZtmqrdJ4a\nZ0glXYSUqNTleCBJ9QWRXN3vB6Lmwpu5nO4BK6qEcn0rXCkd5XhE7sX8ZFEIMhZWKFba+dbSuoCQ\nQSdwOqPWdbmZ3TylX1DwYf0KKLimX+qMpOAXu9zE86JiODMWaNadUzUaXmZ/13HH5S4ccKc9LnY5\nWZdP0rL2LOmE95gFX5XOA41fnQZaCi1JhZXQEjyo6dRQ6wsiH+wu+JEUSCadNqEvHISUhwFnzkmT\nRE0crSw6VrymiWcC5oFE4eFCgEmsbkWOAKY6dVvnBKMEjUoJmyVdWANfa/5Rv6Dgo/opoksVXNGv\nCArSw0iV+8bfUR7+Td+3VVPxDbVjTLMYu/ZzAtg6/JYQqGMt6wBnoeWSw28BUA3ZXri/1FScDnJ7\nAHGBX4VwQF4jJ2T6qKNJ7n/6WhrtTXFDK1mpyLQwhU+o5pJX5Hbm0mn15y+0OcFT0ZL+2jCxzERC\nnfY6z1eaGl5Py9hvig0k1qY+zWeaKZJf87OvqMa2rXn4pWMkGZLlVE+9lWDNY9M4n5EonB6h+tg0\nOUMz1il+65yBcWroDui8+nIxU3havwIKOuW1FqHa0E4o6JyRMSh4x+VgJDAc2BWozIQMfg1LhVWC\noltza+gxG0YLLfQ+5r9DxbZJ/UtTEB3XLV/WCWRhNxEs3ccF7vRE9jKkKY9xiyiB3xbOSIItG2md\njq60XAa+Vp92ArCtIByQ18BpysrZvYyv7KITVThiohNLNqm0TOUwBIOn6Ke0c8E7B5V4lJakbCfI\nF3mIa1v1yVSFMK+sfA06dWV/Cke/9MGQtxmyXDxDN6OYKWKjnJmUpruRwHBgLaCisa2BrmGVoGhO\ncWvoITuArl0LU3Zxvur8igIDucuxZSxBrVxUIbI62Wb4ra6OayoM7gC/BSOykVY0emvpAQ98LQ0i\nvFTi4DeEA/IaObO2mJdJYrqYaPiceool0DFTnF92kOdJpm4cIRpk5taWdpag4MALpVTSCC/Bj/9J\nSqUqkshMFeZJmP2i04HD8y2i6AlbJCReukXFTCdxOZhUSnZcNAwHdgUqmtAa6BpWCSrYIqoN2TDa\nYKqmbXamZz9PY8jkJpnYeGaa/2SLZ2ZUqC1wp/owT9PQxA34bQFGKpyyQ5reWn7vaxW/GoRDu8Dp\n2jKh7z8MDGGwi/5clqUm0DqOHYmnhvSg4OVbxwP4mX2eboadR0rjiaSXNMJK8CNKX0RL71uYSK41\nHKM8NyhBNsZCRhdXzCF9SyTPCrZ92CiX26cbCQwH1gIqGNsq6BpWCYogbNwjC0OXTpLXFgPo2rVY\n70KyPxZLA0BvrUiMujeSN4mq1O1ZzST4baUr/FbtKHEDfhsAtCQ2ZXvhVNPEN3iBrxX8ahSOdiw5\nVcrQXOaaBPU8x7ULGeJ1UdpdZ57pdrQYIq8ihKIuQGmC3vJut51pUcc7cPrqFpc0EVZioogmu6lV\n4SJVDf9VLYmzpOrisdgjiFmboRdz4c3oBUXMWHP7NCMJhgNrARWMDeHjVauUCsU+g0hKjNVKtmqm\nrxuaFtA2o6qaDU6e+r5kVgbzpcxiEkQ2wAN0tye9DWmaOPw2MJJUzc7TKFmmaVqp4WsTfjUIN8ir\n8pHGPGhRmKYepnbc4ENZQCHDiu2ON2F4a9JxfrwH7ricAbeD4YhMtyu1G62HE++DrmGVSmUizdBZ\nEBgTKhymmtknh4TSTFTrv/nVKqJsNnFFRATcqY60Z40fOHeC39JsTobmhPvT7DyNBk7YpS2ADGAb\nhBvkNekpnAyt6CiCrwCHmxb84wkGx6SKJwE8aiTXwZiikOxF/+Oq7a3CdZdzIwmGwy03u4qUJN4H\nXcMqE5WJdEMP5mtG6+hsCj8H+5x4aTKIO9y7GTr1DbKJkQsw7i/iTnl/q0wrF+M2+G3GaKNcLEzy\nDLPAegBfm/CrUTjlY7NQOGXhRY+qjcTXDI7JLRkp9F/LW9kAY3I6LRzv7b5o9vH7UA8YxtIsLhQS\nI8kNB3YFSoztLugaVulUFIlqPZs1CKhw1iLa5yCvfci7U0HXnLzIgwSyKdchstncsKOo+Zit5QC/\nzRjXJ5atLEul7hX8ahBOLIzJDZw851Wwvab+j3/5MZb29HS1IGFp6jbeifDjcDnvihcIw1hm9qny\n1Eii4cCuQCVU9T1QOKwSVBCJapHNtQMVLvBxSjH7rE9UvMtWaapu+L11uQCR1bUm4t3pAx5JE92l\nk12sjDFlZ2kF3te0dxoy/CppxMIDJpdSjJPIDe1yRTim3MqKNzuWLndMLKVTXvxZnVjmRqKGQ/XA\nWkBZ4j3QNawSFKucGzolWDaMNtfC7FONnkXcPy7ybIY7k+k41DbDxbKIs0ZplNvGWkZORICqxXmy\ntMp1MXxtjl9NwnVlmczVOXlUSVCN+w35R3PSZ0uweKDa81HuCJ+844asulxmJFSLWiWsBZShvgP8\n+o5Vwj5F7czQKcWzAbrOtHD7tG3anxq/Fj5hfoEIAncqmDibTmWjnLwQA0YqmrKztF5frCTnka14\nBuICYAvhuk+vzyTnpPh7yysj+j7jVo6Ey8T37Eix3OXSfspWFP5SPVZdDkYCwwl25XYTjG0ddE1P\ncpXFz/REBZFuySEbRgston2eNHDyY2xdZSQvCUBX3Txw3GlLUNtKEBh08xJ3gN8WzojsLK1MTQK+\nNuBXITxgcp2Tv8pzJZdbC8X/jyzJ4JiXGCPJXS4h6d6vYIAQivB4bThC1AogYA6ITXhZAApBhQ/O\nshy1YCJ+Er6azaVfPBYup/YJIwmG4wBvtxuyGE8M8OtoqWaV9Lw0l4NIUj0ZesgG6Nq1yOxT1nzV\nz5sEXNUS1Erdm6C2jjtl+GpC2oI7wG/BiGykUevT+2br+FUIB+TVOau6bau2kca+eAffVDwhOmtS\nsUbv5i5XJlT1m6p0MQFCKGnhGjhCspEEmgUQUJ7K+j1ahxECUAiKJmq0Nr35ru3PwsMnZF3TdxDq\ncjApjUTCSNxw3FoilBqJZNG3oHBYZaRcZHALN1/afnBUuGmR22fbtL9YavXI5PMdnbcjGY7LzNuU\nu9ynYM0BQijVh2vHEQIdCCBgAMQGZKKYNCNnkXbnu7Y/CqfFPHu0rpPyXnntyka516Rsq/SnLGNb\nrXyrNgbHXApdfPzaZipLthevA4RQJOEaOELKsCmRo5ICIBYwwjUqx8va915/Fk77zWlb58XWLYvv\n0eWwAbBs7XF9pwcMjplnA4yZ0j+ElQkQQqkI18ARUsaNywEQCxjhGkX7MeKmi+/a/iw8fEI275VX\nr/bockcs+1WruFe+iaGVe0zPpgNMqBIyHCEnucsZHJG2mtL3aNPHRzjaquHqnMpgDf49WgcprgvP\nslWlt/zu0eUOkMRbTGNFyCc/y5vtB1LdfA0cIStjLudwRAog6PdomWAOxsuuUREba2Db34TndbP0\nNx17dDndI3hTBx1iQg8IKidcv5MMEEIRy9fAEXKSuZxkCxzRAbHkbY6XXaEiNtbAtr8Jz+uWOt/z\ns0OXGwyo8p4eOqSEHvjcx9MChFDq02vHEXJa5nIMBAQglnIBI7ylwsTSwbb68j6V052PG+H4cKzo\n876f/7xP1FYkfcOLlFvpq7/q8bHFXIAQik7pGjhCSk1eASBgAMRqQ/AP7xaUY2MD2DZ8I3ZNeJ6t\n8t/yu8NRDq/JvKWHDiGhB6YPbYYHCKHUZte6tZYPRA4EjIBY1THBCOliQTkKMYBtA0iRCiR/duG2\nrfd+xM3+XO4b/w2IGsw3/H7mX4kFCKF0gl8DRwivEMiJjEHp42z8hXjACNeotBW++K7tz8IJosj4\n1/wfn7zjFu3P5bJJ+Tu66JAReuAjMUvgBhPgcA1H6AORAwGLAIgFjHCNohdVGPC1/K4tvgy7IpyG\nOYq0fOCfz+/P5T63wg+W9+8lTzrIvLUDAm5Q4pbhGjhCgBINCEjw5Ox7tPgy7Q1177u2BlJcEx4w\njG9t7e5c7vjHxW+1jxth6a26m/Qj4dEe2J3LnT/wFH60M/8VfEcHv3ib9+Zy9oLHi91yFL/bA/o/\ns+5mHxm/9cDOXK66/e+1v/XAkf/HHshf6Plj4YP9zr8B+dqOkVecvlb7L1G88bdnvkThbam5r1HO\n/r3atvp4d9rw19yP49ke2JXLTfiu5LP9cZR7pAdSEP4R1oNn2QN7crlKX+BfNvG4PnpgSz2w02n5\nfwHPmcs+YWFLWgAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$1.40918010723952 x^{1.12463885223916} {{}_{2}F_{1}\\left(\\begin{matrix} 1.0448660245023, 1.0448660245023 \\\\ 2.26158999046156 \\end{matrix}\\middle| {1.59222607791735 x e^{i \\pi}} \\right)}$$"
      ],
      "text/plain": [
       "                  1.12463885223916  ┌─  ⎛1.0448660245023, 1.0448660245023 │   \n",
       "1.40918010723952⋅x                ⋅ ├─  ⎜                                 │ 1.\n",
       "                                   2╵ 1 ⎝        2.26158999046156         │   \n",
       "\n",
       "                  ⅈ⋅π⎞\n",
       "59222607791735⋅x⋅ℯ   ⎟\n",
       "                     ⎠"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "symbolic_metamodels[2].expression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALUAAAAWBAMAAAB09cDaAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nvSWjYOZoAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$- 0.17 x^{2} + x + 0.016$$"
      ],
      "text/plain": [
       "        2            \n",
       "- 0.17⋅x  + x + 0.016"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "symbolic_regssion[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, both algorithms came up with approximations of the sinusoid function in the range $[0,1]$. This is because in the range $[0,1]$ we see no full cycles of sinusoid, and hence it is indistiguishable from, say, a linear approximation. The confluent hypergeometric function $_2 F_1$ in the metamodel is very close to 0, and hence the metamodel can be though of as a linear approximation for the sinusoidal function. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we look at the most tricky of the four functions: $f_4(x) = J_0\\left(10\\sqrt{x}\\right)$. This one is diffcult because it already displays a lot of fluctuations in the range $[0,1]$, and has an unusual functional form. So what symbolic expressions did the two algorithms learn for $f_4(x)$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8MAAAAmBAMAAAASOlSpAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVO8Qq5l2zWbdiTIi\nu0T8UsK3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAM/klEQVR4Ae1afWxb1RX/OS/+dmxDYQgxlkAR\nID4flBal02aPltIBWrOVMAgrNaRJUUBqEFOFGGxWJVhXmBoYK/ujW80gGQpFzRgMDTHFKqpAbBBL\nHZsQoHp0ILGJJiUFymjj/c657zn2SyjSalsgcqR73333nHvO8e/cr3cSYI4ah8DGxplSSxc12N6c\nuUB/gzGIN9rg0fw+31D2aIZ/Psa+ZTfIj6BrZ43b+AI8j499kSbk7IBaZ8/eX/tey1UZzLqtz//z\nnM+/i5/pYXP6M0VqLRCbrLXGCn0FaW/qsRHl8nt4wQK+FRAYygFDV9laItx7+/qAyKqVCA2t1Cee\nkWEtUklT5aVt7d80Is9pkpFGQIRUkAMiPUtMe/gmY931QIwKU4yBzMi8BeygByzRK17MAj3TuuvU\nGs3XSbFXra8X8QceeFC6l3p5tXv3yfQJjViF6FUDwIpSqQB2bcJx8Gf9BSn4cawtlPOlsR2X4V58\nQ59Pf1tcaLVZSVPklaxP0GZaTq0jjYAISZEB12CVtoPFnWrd9UANClOMCbO5VDosHkiJlw5Q63NV\n+uvx8sN6KJ1Np+9t+CIB5YwKlPWhxRLiljz64WOIv7PvPRvs+g0Stj8XmpASSFuZcBGT2IrR/BsI\n6hMncpi1Q/1iU+QXdnZ2JjGB6q1aRxoBEZIiY7uwWQetwSK17nogBpUpxoTZvG/fbvFASvwktUfL\ndaXYofqpj2VKSo6F14GFfm0HM3Uz2i0h9p8XTWuIk/ga0D3JtdiUZHdBirRSIziFIRkrfq/4lD41\nxIGUQn4iHHlx8gproMpXHakC86hUSlLHYpUOOsWxXvZAjXIVizFh+uArigdS4sUq1fV68Vf/gpqa\naa76CdZAETeE1UCoraZ2KpRF50mIrW2vEkz5ZVYO7IoeQjgLXDgiJfGVHpun06/IbbXbD3foU8P0\nezfEjjw5WNjDQRVkRorAvU7J6ljrbB20v3elWp/2QIzqlbbVFiawGOKBlPjVvDK8k8YLXAjVVioM\nHn2zKXP0Oj5NwwvVjGU2ljTrT4lNTXOsLl5oPJXhrrefTkKrhY89Dvzp0uHhXLA7+l1yh/tGoJ3K\njg0/kXQURiwJMTZ8nDchbubdxpqMTiKcQWA9r0nrMdYRH+BJsYViWxA6f6s+NUy5cohVXhTNIDNS\nFN7slIyOXZuRvls+wLvGuuuBGMXaDKstMWViiXogXsSKoQIemcR1f1y4gAKBFR/9gI+a01h5+ijM\n1O+Fe1Hf9WL1aUBbyvbCrZg78Ec7XCclGLPTWez2zVdeMGlthacyvPNL/wW0uhXteWzmXE83lUo5\n4OKivx/aqexd8B107NynIY7kjp1vQvxngF1cYDKVzUadSmKKa/F0XoM7MOw7lZOAHvM8DeVTtqVN\nR97RWfUwI0XgZqeYEGOV9HXvR6Io1qc9EKPcqGnEEiaiBYgHUoDoodgFAxZuMedXor/KVK1eNqsi\ngVth5psX7g40J9n9a0BbyvbCrZgb+BGW3yTkOcVMp6kvAy66StcbNgC/81aGd8eyPCAV9/VIPzjD\nmxF89BZqeBUtBdOpMuuS+Ji9JCujIW6Hdb8J8aB28ZgkuIjul8LWQZ6oBPhucbE9yaeGeBFSdpSX\nKz2LRb6aTn6TZJuRonCvU4q6ijHKczlRnEIiK9anPRCjGFUjwpT5JB5IabatKbRk+FW3S02N5/RR\n6+paUaiQKtZ88WDuyyLG2RU4F6albA/cirkDP250Q+yXmTFN5upVmpCedSwBE+K/yZHoqQwvLZJS\ntaTlwycHPM4gk+KHyp1peX+raH0kT+4MnZ0fZIGXgRtMiO8wXXLxvXAkdlBKMIspvRfHc/Hn+Mmc\n5HNEwnR85+prRAmbelGW9gya/UbNw3YsK4NuZ/zEuuuBGFSmGBEmgjmIB1Ka8swQpL6OWOFfamdH\ncYa5WnRwcZIEboWZbQ/ckYIuxxfvgmkpO1cNt2Ju4Efsp26I20VzJT37RN55bWXDCfEBYDzpqTwh\nTqQRl7UQzxgbLW18MZ1ptkjljRoE7WU7mOeJ52sj40wWdvXw8zWcD82XEi/4+gMdvjSeOeZk+040\n2/LEsRTEmC01myI/O8nI2G4VECEV5ICt2GBL+z2cALHueiAGlSlGhImmLMQDKRGbS/qECL/Yn1Rj\nP5nd5NH2fqAKBG6FmW8euOOH7UgWyN0F03LEquBWzJ0QR4JuiB/z+laIDzhd3LicEFt0YLy7usoY\n3vJ7rgOkSnUg/iFHtnCr3sgbbuJHQ9c7nSoDtOdg9V75zhDw8wPJJ/NWV18+du2BjCxH7Yp0rUR0\n6NG8FNw9aGOQ5fxSCQuHtutz17ZlPIz3fIvi0hT5Slrcy33LEEdyNxcBt8iAZ/uu1PcQ+8W664Ea\nFKYYEya4DagH4sVwF3fQ7Zx8YZ1bzlbkWqrVU6BTuBXrDI8zL9wrDjJWofxdzBWx5YpVwa2YG/hx\nnxtiPYoXrXmlLwMHoX5z3aW9VNYNcYxXqtHt1VXOhHg3PyUh1VgOUUqAfrTYvI2nbudnpelUGbz0\nSyY48LPMQxSqB8W34qV66K3WqdO4uqsWb9ZB1cJVrFjnuK154Y6UbuNlGgyxtFyxKrgVcwO/lXFD\nHMhyvuRCW8L9ZYT0U1UMJjLlEHNGjW6vrpwQM6Cy6lsGxjo0xNaEDMVrSE3CP9/pNDKR8/AIdthf\nVYHaVzuTFjeUelPkE2junNAMEQKnuMltzaIz4z2d5Hay3pL5fuq5jZqD16y3pMUHX7Xh68qJy7Hp\nEAvM7OPXWyXmORz37vtF3nUYYmkpm9tiFdyKuah7DRFIiPexHWbhaTPpy5cRujjPPqFEzg2xZ9Po\npvXxjLOJwy/3Kv8hZ6MO9MtQrM4nBhCacndvlcGpti0e1okuuecmu06qK9QGJzBLBtxNbksmXDLe\n5SS3y5DM93gprUzJeotQJN/cjzW8KZD0Sq9wuzuwB/NMKI11830jBFBbjlg13Iq5qFudP0lCHDiD\n7V4WSwPuImQtERmhRIcbYjn6W+W6VVlpiOlkZEor3qx8vG7J1xi/tnYUw/0IHdROZeOvwJ4kYM4c\nY6C2Nd1rACUKclDzVqQXermfS3GT23LR9zPj7Sa5NbUuWW8p//yDYUrWW4TCeX6lT5nrY7S8ig3W\n1O+BuynPebAYDLG2HLFquBVzhX8vPwkKeH5dERigLrMluwgtfD6nfVUhfhPYbHsqDXFTP/yTWrUU\nEOIvT6UBzp3VdnMbV7F2KhslW0Ic5T5XJ5KLQP2Juxe/uk/hwnCy35oBd5Pb5uvbX3CT3JwHJuvN\nAbprMsiFeFHc9BfCxdhUzCQDKjZqKMwU8MCdYtfy45YufX+ZthyxargVc4X/gqVLV5xGVxmUHAdy\nzx8BXIS2lUzYGS0ynY+mDcD35Vu8slKen+u2X6tQG5jNwmiHZF/wEJgq9Ldpp7JxLrAtPy8wgW41\nWfvqLHpbe61ejTtG+NcoyZ1zBVZkwJk20OQ2V7FJs5skN18MQ5hvswhTs96ai/fJ314SSfZa5Ru1\ngZldHri5dvEGu8+VVcyWsj1wK+YGfn74FTiP6KTNQT57HQL2TITGsibEqX6Ek0wNeCoNcawDG/Ja\n4X71upXx3YXQOcDluDCpnYa9Eb4P4/tbJmLUWhdaC6v80VQXA6p0G2ex5s4l231zOQPuJrclxJrx\nNkluvmnWWzPfr+DnytSstwqFM9wPRrOi2KwwWVEK80zM47chlKHgYZiWisEDt2Ju4AePFLmzbRLt\n48k9eBEzEeJ3sf+Sj5YjnIY1tIZ/hqiulIddj3JqarW49woq25mk4q5LOXUinXzXTmXHO1cVrWXd\nPbxV1ocCV9dNddnh2GWly2UVn66ruCID7ia3dRUz4+0kuYmCZr33auZbRnKD1rH6HAROhpyXwGlS\nKaQK80zM8VSX/BniidJy01IxL9yKuQP/ngNZfkLbvxDFF/UuuiaLmQiNF4U7R14EeBYzdy5b7F6n\nFCWDPiXJbQ0xr8dOkltS7MoQ5hKkigzvfs16yx061MHXXok78A+pak+jD9PGp9Nm+9N5X2bOLDfq\ncnKbIZaMt5vkhsuQzPc5vDwLU7LeKvRv/Ac206lCv60PosEzjhjEOlmtz29poNZZMuDl5DYz4Zrx\nbjJJbk2xS9ZbyiMYVKZkvUUoeusxu/F3vK6utx4xFP/3r/MxhXEEevAIvC81a3BGBtxNbksmXDPe\nbpLbZUjmOzKYM0xmvUWIf9edwDs9ecUyldVHzas7j6TRSZseSWSOVzME+LfYxpPvUONtfnktMoPQ\neJJExhw1CgH+Q1HjiTeGOWocAmsbZ6ps6cZya67RAASaRhpgxGPiTM/73GtdEQg1/lx0/hJZ1581\np7wCgfUV7cY0d+YbY2fOioNAe6N3av6P8xw1FIHY1oaa4z9jZRtscM7cXxoMwTfF3v8AOr90U5of\nNsMAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$1.00001550756053 x^{4.81740336028214 \\cdot 10^{-6}} e^{- 0.000130688133267665 i \\pi} I_{0.000261376266535329}\\left(10.0008480756654 \\sqrt{x} e^{\\frac{i \\pi}{2}}\\right)$$"
      ],
      "text/plain": [
       "                                                                        ⎛     \n",
       "                                                                        ⎜     \n",
       "                  4.81740336028214e-6  -0.000130688133267665⋅ⅈ⋅π        ⎜     \n",
       "1.00001550756053⋅x                   ⋅ℯ                         ⋅besseli⎝0.000\n",
       "\n",
       "                                      ⅈ⋅π⎞\n",
       "                                      ───⎟\n",
       "                                       2 ⎟\n",
       "261376266535329, 10.0008480756654⋅√x⋅ℯ   ⎠"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "symbolic_metamodels[3].expression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIAAAAAUBAMAAAC35yitAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$- x \\left(x - 0.773\\right)$$"
      ],
      "text/plain": [
       "-x⋅(x - 0.773)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "symbolic_regssion[3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is an exciting result! The symbolic metamodel is very close to the ground truth: it corresponded to a Bessel function of the second kind $I_0(x)$ instead of a Bessel function of the first kind $J_0(x)$! Using the identity $J_0(ix) = I_0(x)$, we can see that our metamodel is in fact identical to the ground truth! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above \"qualitative\" comparisons show that symbolic metamodeling can recover richer and more complex expressions compared to symbolic regression. The quantitative comparison can be done by simply comparing the $R^2$ scores for the two algorithms on the four functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAzkAAAAUBAMAAABc5u5fAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAAdxOnOwSM12AAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left [ 0.9999999998861328, \\quad 0.9999999999997805, \\quad 0.9998123031773816, \\quad 0.9999999327069724\\right ]$$"
      ],
      "text/plain": [
       "[0.9999999998861328, 0.9999999999997805, 0.9998123031773816, 0.999999932706972\n",
       "4]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sym_metamodel_R2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAwUAAAAUBAMAAAAuKYzpAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n+m9zAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left [ 0.970924474901646, \\quad 0.981343377759323, \\quad 0.99859315772987, \\quad 0.116801130317559\\right ]$$"
      ],
      "text/plain": [
       "[0.970924474901646, 0.981343377759323, 0.99859315772987, 0.116801130317559]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sym_regression_R2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, to evaluate the numeric value of any metamodel for a given $x$, we can use the **evaluate** method of the **MeijerG** object. In the cell below, we evaluate all metamodels in the range $[0,1]$ and plot them along the true functions to see how accurate they are."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABJUAAADHCAYAAACgPWIxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzs3XmczdUbwPHPuXf2fTXGjLHvS4Ox\nJksq0UKllKJfSBSiLMkSEqm0KERCVAgpIluyZDeMfTeDGcbs+3pnzu+P0ZixZZu5szzv12ter/s9\n33O/92F4zr3PPd9zlNYaIYQQQgghhBBCCCHuhMHcAQghhBBCCCGEEEKI4keKSkIIIYQQQgghhBDi\njklRSQghhBBCCCGEEELcMSkqCSGEEEIIIYQQQog7JkUlIYQQQgghhBBCCHHHpKgkhBBCCCGEEEII\nIe6YFJWEEEIIIYQQQgghxB2TopIwC6WUp1JqvVIqVin1/U36TFJKDbrN6+1WStW5v1EKIUo6yUVC\niKJAcpEQoiiQXCTuhtJamzsGUQoppT4HbLTWb97kvCcQBFTVWqfexvVeALpqrZ+7v5EKIUoyyUVC\niKJAcpEQoiiQXCTuhsxUEubyCLDkFuf/B6y+nWR1xQqgrVLK+14DE0KUKpKLhBBFgeQiIURRILlI\n3DEpKolCpZSyUkrFA/WAlUqpQzfp2gHYfM1zP1FKLc9z/KlS6i+llKXWOg0IBB4rqNiFECWH5CIh\nRFEguUgIURRILhL3wsLcAYjSRWudoZRqDvyttfa6Rdd6wIlr2iYDZ5RS/kAz4HGgpdY688r5Y8AD\n9ztmIUTJI7lICFEUSC4SQhQFkovEvZCikjAHf+AAgFLKGVgP1Aaaaa0PX+njAiTmfZLWOlop9SUw\nH3AmJ1nF5+mSCMjUSiHE7cqbi5oDnwMZwEWgx5U3Q5KLhBAFLW8u8gKWA5lAFvCy1voSkouEEAUv\nNxf9Syn1EjBVa+15pUlykbiO3P4mzCFvwkoBngCWXtMnFnC8wXP3k1MhH6G1vnDNOUcg7j7GKYQo\n2fLmonPAw1rr1sBZoNOVdslFQoiCljcXRZHzgaw1OR/Qel1pl1wkhCho+YpKSikD0AXIm1skF4nr\nSFFJmMMDXElYWutMrXXkDfocBKrnbVBK1QNmAD8APW/wnFpcU10XQohbyJuLLuZZdNIEZF95LLlI\nCFHQ8uaiLK31v/nHEThy5bHkIiFEQcvNRVd0I+eL/+w8bZKLxHWkqCTM4dqEdSOrgdb/HiilfICV\nQF/gTaCeUqpNnvPWQCNybqUTQojbcV0uUkpVImcRyj+uNEkuEkIUtHy5SCnlr5TaBfQH9l1pllwk\nhChoublIKWUEXgAWX9NHcpG4jhSVRKFSSpUFXIHj/9F1PtBRKWWrlHIiJ4F9rrVeobVOAT4FPsrT\n/2lgk9b6YkHELYQoWW6Ui67kmh+A7lrrjCvNkouEEAXmRrlIax2ktW4KjAZGXGmWXCSEKDA3yEWv\nAL/kmTn5L8lF4jpKa23uGIRAKTUP+CzPQt0opSYCEVrrL2/j+buAXnmfL4QQt0spZQH8DkzRWm+8\n5pzkIiFEoVBKWWut0688bg+011q/c+VYcpEQolAopSYDDci59a058IPWeuCVc5KLRD5SVBJmp5Ra\nTc7CcOeAmVrreeaNSAhR2iilugNfAP++6Zmhtb52yrcQQhSoKztRTiZn57c0oOeV3d+EEMIslFJ7\ntdYB5o5DFF1SVBJCCCGEEEIIIYQQd0zWVBJCCCGEEEIIIYQQd0yKSkIIIYQQQgghhBDijklRSQgh\nhBBCCCGEEELcMSkqCSGEEEIIIYQQQog7ZmHuAO6Fh4eHrlixornDEELco8DAwCittae547hbkouE\nKBkkFwkhigLJRUKIouB2c1GxLipVrFiRvXv3mjsMIcQ9UkqdM3cM90JykRAlg+QiIURRILlICFEU\n3G4uKpTb35RSc5RSEUqpwzc5r5RSU5VSp5VSB5VSDQsjLiGEEEIIIYQQQghxdwprTaV5wOO3ON8B\nqHblpw8w436+eLopi7nbgknJMN3PywohhBBCCCGEuAdpmVmkm7LMHYYQ4i4Vyu1vWustSqmKt+jS\nCZivtdbATqWUi1LKW2t96R5fl3VHLzNx9THORacQl5LJ4Eer38slhRBCCHELWmuSM7JISjORlG4i\nOd1EcoaJ5PQsUjJMpGZkkZqZ85OWbiIrOZkkgxXpWZp0U3bOB4vkFLzOnUSnp6MyMlCZmWAyoTJN\nkJWJMmVBdhYqKwuTMrDK/1Gydc5ra8AjPpKHj20j2sGV9XVaUbecMz/2bmruvxohRCmntUYpZe4w\nioSpf51i9aFLXE5IIzYlk2ndGvJEfW9zhyWEuAtFZU0lH+BCnuPQK233VFT6add5Rv2Wc8dd9cgQ\nwqZv5mLjcZRzsb2Xy4piIDMzk9DQUNLS0swdisjDxsYGX19fLC0tzR2KEOI/aK1JSDMRnZROTHIG\n0ckZxCZnEJOcTlJsIpmRUZgioyEulkDvGkRnKhLTMklKN2GXlsL7f3+PY3oK9hmp2GemUTYjFbvM\nNOwy0rA1pWObmY51ViYANd79lXQLq9zXrhp1nunfv3lbcSZb2jC3Sqt8bVUvXeC91dMJ8q7OkkrN\nSUwvvTOVZTwsmmQ8LD0iEtNYeeASvweF8VbbqrSvU9bcIRUJEYlpHA9PBMA6M51L8almjkgUBhmT\niqZ7HZOKSlHpRiV7fcOOSvUh5xY5/Pz8bnnRp/3LMWPVQd5YNZOXg/4kw2jJpB/bMr5/h3sOWBRt\noaGhODo6UrFiRflGqIjQWhMdHU1oaCiVKlUydzj37E5ykRBFidaauJRMLsWnEZ6QSnh8OpcT0ohI\nTCMiIZ2IxHSiEtPosm4BrklxuKfE454SR/nUBOqnJOCWmpBbDPpXqz7fEeZ69RtmDXQ7sPa2Y7I2\nZeQrKmUYb/9NjVFn33bf0kjGw6KnpI2HIg+tYccOTF9OZV3Pd1kYls2201FkX/lU83tQWIktKt3p\n+yJvZ1t+m/8OFWIv4ZqWyCfNdwOVCzhKYW4yJhU992NMKipFpVCgfJ5jX+DijTpqrWcBswACAgJu\nWHj6l5ONJQM61qXerGMYdTa2pnQaTZ9M4FNNaVTB7X7FLoqgtLQ0SVZFjFIKd3d3IiMjzR3KfXEn\nuUiIwqS1JiY5g/MxKZyPSSE0JoW44FAyz5zFcOEctpcu4hEXgXdiFGUTo6iTGE2/TiPY51sr33Ve\n37kMp/Tk23pN57SkfMcpVjZkozDc+PuhfNIsrLA2ZVz3/CDv6qQbLTEZjZgMFmQajJiMFpiUkSyD\nkSyDgSxlJNN4/VuZyw5u/NDwCcKcytxW/CWZjIdFT0kbDwWQkUH24l9I/vRzHA/txwI4EwpbW3XP\n123DsQgS0jJxsil5M9Tu9H2Rl5MNrqkJuKblzFZKPxcKNC7QGIX5yZhU9NyPMamoFJVWAP2VUouA\npkD8va6n9K/nm1bkva6D+PTrgQB0OraZYV8tpsFnfTEY5B9zSSbJquiR34kQ909SuomzkUmciUwi\nODKZs1HJhEQncy4qhcR0E5P+nEqT0KO0T4jA5pqizbW8E6Oua4u0d7lpUSndaEGcrRPx1g7E2TqQ\nZTDmO29jZclHnQej7GzJtndAOziiHBzA0QGjg33Oj6MDFnZ22FhZ8KalARtLI1ZGA9aWBqyMBmL7\nP4a10YCl0YCtUWFpMGBhVFgYFMY8Pwal2KkUBgMoFErlTH9W6lUA+gFGY+nOPZJ7ix75nZQQUVFE\nT/kaq1kzcIyJxDHPqW5BfzL1wRfJzDPzMjMrmz3BMbSr5VX4sRYxZZ1sCHdwp0JcOADZF0LNHJEo\nLJL/ip57/Z0USlFJKbUQaAN4KKVCgQ8ASwCt9bfAaqAjcBpIAV67X69tNCieG9SNVesW88SJbQC8\nvPALlnbtyAtNK9yvlxEin+joaNq1awdAeHg4RqMRT09PAHbv3o2VldWtnn7btNZ07dqV48eP07t3\nbwYOHHhfrrtx40bs7Oxo1qwZANOmTcPFxYWXX375vlxfCHH70jKzOHk5kePhiQQHh5N64DDG48fw\nDD1LlegLPBAdyu4mz/KHf/5NVn3jI6gSc3tv0r2SYq5rmxvQCafsDDLcPTC5e6A8PTF6emJV1hN7\nV2dc7a1xtrXE2daSybaWONla4GRjiYONBZZGA7fe9FWUFjIeipIoaV8Q4eMmU/7PX3HPzF+0Tzda\n8lvtNswLeCq3oFTL24nO/uV42r8c3s6ytitAWWcbjjq65x4bL4WZMRpRWsiYVDAKa/e3l/7jvAbe\nKqjXb1bZnZFvDOeRoc9hnZXJA+GnWDHpK+IXTsbZtuRNPxXm5+7uTlBQEABjx47FwcGBIUOG5Ouj\ntUZrjcFguOvXCQsLIzAwkDNnztxTvNfauHEjHh4euQnrrbcK7L+nECKP2OQMDl+M53BYAhcPHsdi\n7x7czxynRkQwzSPP8UL85Rs+r1rU+evazruWhXM5j+NsHAhzKkOYcxnCnDyJdPUiraw32qc8Rl8f\n7Cv6Ms7NiTKO1pRxssbTwQYPx/bYWRWVCc2iuJLxUJQUWmsCA0/h0Ot/1Dy4g6rXnI+wd2VBg478\n1KAjMXbOeDvb0Nffh2ca+FCjrOONLlmqlXW2YaPD1aKSbUS47I4nCpyMSQWj1Lxb7PtqO7779Xn6\n//MzAG+t+55vf+3C8JdbmDkyUZAqvreqQK8f8vETd9T/9OnTdO7cmZYtW7Jr1y5+++03HnjgAeLi\n4gBYtGgRGzZsYPbs2Vy+fJl+/fpx/vx5DAYDU6dOzU0g/3rssce4ePEi/v7+TJ8+nWHDhvHNN9/g\n7+9PeHg4LVu25PTp08yePZs1a9aQmJjI2bNn6dKlC5MmTQJg1apVjB49mqysLLy8vJgxYwazZ8/G\naDQyb948pk+fzurVq/Hw8GDQoEHs27ePfv36kZqaSrVq1ZgzZw7Ozs60bNmSli1bsnHjRuLj45k7\ndy4tWsj/LyFuJjUji8MX4wkKieHkyQvsjNNciLm6+837G7+nz57lt3WtyjH5v+G1tTTy1+OvcPqZ\nV7CuXoUyvl74uNri42JLE1dbnG0t5Y17KSPjoYyH4u5EJKaxLDCMX/ZeICQykQ2h+Yv4h7yq8H3j\nzqyq2RILGxs61CvLcw19aVbZHaMstXFTDtYWxLheXffOMz6K2JRM3Ozvz0wRUbTJmFSyxqRSU1Qq\n72aHGj6c0IMb8E2IwC01Ae/PJ3G83U/ULOtk7vBEKXL06FHmzp3Lt99+i8l0822uBw4cyLBhw2jW\nrBkhISE8+eSTHD58OF+fFStW0KVLl9yK+60cOHCAffv2YWFhQfXq1RkwYAAGg4F+/fqxdetWKlSo\nQExMDG5ubvTu3Ts3QQGsXr069zqvvPIKs2bNomXLlrz//vt8+OGHfPbZZ0BOZX/37t2sWLGC8ePH\ns2bNmrv5KxKiRIpITGNPcCyHjp4jdes2PA4E8kDYcV64dJKjXpVZ8tKkfP2PeF2/C06mwUiwqw8n\nPfw461Ge+IpVya5eA/u6NZlc3pOK7vZU8rDH09FaikaiyJPxUBRVWdmanTuPsmHTIRYkOWH6d/s2\nZWBuQCfGrf+WddWaMSfgafb41qFpZXcmBZSnQ92y2FuXmo9X9yyj7NVdQ8smRXMpPlWKSsJsZEy6\ne6Uq6/VqX4fxT7/JxB/HAvDy/tWMmLqMyR/9T958i0JTpUoVGjf+790tNmzYwIkTJ3KPY2NjSU1N\nxdb27u7Ff+SRR3B0zJl+XbNmTc6fP8+lS5do27YtFSrkrC/m5nbrXRGjo6NJS0ujZcuWALz66qt0\n7351Z5Nnn30WgEaNGhESEnJXcQpRUkQkpLHjbDSHA0+Q9fcmKhzbR5MLR+gQee66XdHqhZ/GkJ1F\ndp4Frw96V2dLxQYc9apMRKWa6Dp1cG5Qlyq+7lT3cuQxD3usLO5+arYQ5ibjoShqIhLT2LBsEw7T\nv6b9vvXYl6nE3O5TIM/nhKV1H2ZzpYZkVahIl0a+TGlUHj93OzNGXXxp73K5j70So7mckEadcs5m\njEiUZjIm3b1SVVSysTTSZngftvzzO61C9mPU2bww/1OWPtOO5xv7mTs8UUrY29vnPjYYDOQsKZYj\nLS0t9/G/FeU7WTDOwsKC7Ozs664FYG1tnfvYaDRiMpnu+N71vLHeyL+v8e/1hShNktJN7DwTzT+n\no/jndBTpJ08zd8lYOt3GYtnpRku8kmKIdClDNS9H6vk4UadcHeze78Ir3k44yDff4iaUUn2APgB+\nfsXrvYyMh6Io0Fqz43QUu+f9ygOLZ9PtzN7cc/6XTtIo7BiBvrUBsDIaeKR+JV4IKM+DVT3k9rZ7\nZCzvm/vYOzGKI/HpZoxGlHYyJt29Uvcu9dE6ZXn/jfdpOuoljnhVYcyj/Qhfc4JH65TFxU6mW5Y0\nd3o/bWEzGAy4urpy6tQpqlSpwvLly3N3IHjkkUeYNm0agwcPBiAoKAh/f/9bXq9ixYoEBgbSsGFD\nli5d+p+v/+CDDzJo0CDOnTuXb2qlo6MjiYmJ1/X38PDA1taW7du306JFCxYsWEDr1q3v4k8uRPGn\nteZURBJ/H75I2Lot/J7tRrzRJve8paM7PgmR1z3PpAwcK1OJQJ9anKteH5o3x69hbab5uVLb2wkb\nS+N1zxHiZrTWs4BZAAEBATd9Vynj4a3JeFj6JKRl8uuuYMJmzefpvxYx6PL1C+oGeVdDoalaxoEX\nG5fn2Ya+cnvWfWRXwZdsFAY0HslxREQnmDskUUhkTLq14jYmlbqiklKKfq935KVTU9jvUQmtDJCc\nweQ1x5n0bH1zhydKocmTJ/P444/j5+dH7dq1SU/P+ZZm2rRp9OvXj7lz52IymWjbti3Tpk275bWG\nDh1K165dmTt3Lm3btv3P1/530bdOnTqhtaZcuXL8+eefdOrUieeff55ff/31utdcsGBB7iJwVatW\nZe7cuXf/hxeimMnMymZPcAxbdp8ibeUq/A/+Q9ezgbikJXHp2VGsr3Z1ocZMoyV7fGvT9MIhgsrV\nZLdfXaL8m+LYpiX1avnyhJ8rno7Wt3g1IUoXGQ9FYTgensCijUexmTeXV3Ytx/ea4n82ig3VmjKv\n2bOUfeIR3mtagUYVXGWpjALg6eFEtL0znslxGNAkX7gI1DV3WEIAMibdCfVfU6WKsoCAAL13797/\n7ngDX/91iinrT+ZrW9K3OY0r3vp+RVE8HDt2jFq1apk7DHEDN/rdKKUCtdYBZgrpnt1LLhJFX7op\ni60no9i25QCWK1fQ6sg/NL1wGMvsrHz9fvTvwKj2V7d2NRoUbe3TqFOvMgG1fGhUwRU7q1L3XU6x\nUhJzkYyHRZf8bgqPKSub9UcvM297CLuCYxi7/lv+t++PfH3SLKxYUu8R1j/2Em2efJDnGvribGdp\nlnhLYi66kfVHL/PlJ4tIsHEgwsGNprV9mN+zSSFEKMxF8l7RdS+f0Urtu9s+rSuzPCiMs5HJuW0j\nlx7gj0GtZeFTIYQo5TKzsvnndBSb/w7Cbvky2h3ewgcXj9+0/2UHN2JtnajsYc9D1TxoWc2TZpXd\ncLQxzwcSIYQQEJucwaI9F1iwI4SL8VfXMZnf8El67FuFAU2UnTM/NnqSS91eo/Oj/rxS2U1mJRWS\nsk42HClbNfc4PD7VjNEIIe5WqS0qWVsY+ahzPV76bieG7Cxe3fcHzx3eyOzay3mzYz1zhyeEEKKQ\naa3ZfyGO3/aH8cfBS8QkZ/Bq4EqGbZh1w/5B3tXYVK0pMW0fo+pjLelUw4sBsgOQEEKY3cnLiczd\nFkzwivW8svM3Uh/rB3ZXdxU76+7L3ICniSxXAcc3etOtZTXKONnc4oqiIJR1zv93Hh6fdpOeQoii\nrNQWlQCaV3Hn+YY+PDW8J61C9gOwfcKHnA6YQ9UyDmaOTgghRGEIj09j+a6znF26miVu+af9rq7R\nkjF/fYdRZ2NSBnb61WNL3YcwPfUUTVvWp081D7mlTQghioDsbM3mU5HM3XIGi7Vr6LtrKU1CjwJw\n0rMCUx98Kbdv00pueM+ZQY/aXlga5Q4Fc3G3t8LSqMjMylmOJSHNREqGScZVIYqZUv8/9v0najPt\np9a5RaWeO5fx3hcd+OSj/2GQbUKFEKJEMmVls/F4BFt+20Sl3xfxwuG/cU9N4GDPbzjhWTG3X6SD\nK981eYbIsn4Yn+1Mmxa1GVbJDQv5ECKEEEVCWmYWy/eHMW/zKepsXsXIXcuoEXU+X58e+/5g7kMv\n8GRARV5tUZGaZZ3MFK3Iy2BQlHG0ISYiFu/EKAw6m/D4NCp7ypf7QhQnpb6o5GpvRb0P3mFH0F80\nP38IC53Na3Mm8GOHlvRoVc3c4QkhhLiPLieksXjLSWJ++Jknd6xgQtixfOefO/QXEx/uBYCTjQUd\n63lTv/e3NK3sjlG+aBBCiCIjOimdBTvPsWTzcR7dsYrv91y/k1uGwYJ1DdqRPGAQW59/GBc7KzNF\nK27mkfAjjPtqIAC7ytclfMTzUlQSopgp9UUlgKcb+PL+m2NpMOolbEwZ1Ik4y/qxH3Fh6XTKu8n6\nGEIIUZxprdl3PpbfftuO76J5dA9ah2ta4nX9whw9iXJyp30dL55t6EubGp5YWxjNELEQQoibCY5K\nZvbWs/yx8zSvbl/GysCVuKUm5OuTZGXLXw91xmH4uzz+cAOZXVqEGcuVy33slRjN/gRZV0mI4kYy\nLKCUYmDfDkxr0z23rd+Wn/h66nKys7UZIxPFmVKK7t2v/psymUx4enry5JNP3vJ5QUFBrF69uqDD\nyyckJIS6devecx8hihJTVjYrD1xk4MgFRD72JGMHd+KNncvyFZQyDBb8UaMlI/t+xoY/ttP392nM\n7B5A+zplpaAkxH0i46G4H/afj6XvgkAenrKJn3adJznbwAsH1+UrKEXbObOySz+C9x6l04afafdo\nIykoFXFWFcrnPi6bFE14nBSVRMGSMen+k5lKV3g72+I9dgRBR7bgf+kU1lkmXp45jp8facYrLauY\nOzxRDNnb23P48GFSU1OxtbVl/fr1+Pj4/OfzgoKC2Lt3Lx07diyEKIUoeVIzsli85zyz/wkmNDaV\nBmGRPH5yR74+F5y9+KVRR1Jf6c7TjzbgCR9n2UJaiAIi46G4W1prNp2IZMbmMwSeiSTLcLXYbzJa\n8F2TZxm3YSahLl4cfrE39ca8w1PebmaMWNwpd28PEq1sccxIxcaUQXxoOFDV3GGJEkzGpPtPSvd5\nvNSiMj/3HUe6MafW9kD4KaLGfMiFmBQzRyaKqw4dOrBq1SoAFi5cyEsvXd15JDk5mZ49e9K4cWMa\nNGjA77//TkZGBmPGjGHx4sX4+/uzePFidu/eTYsWLWjQoAEtWrTgxIkTAMybN4/OnTvz1FNPUalS\nJb755hs+//xzGjRoQLNmzYiJiQFyEmCzZs2oX78+zzzzDLGxsQAEBgbywAMP0Lx5c6ZNm5YbV1ZW\nFkOHDqVx48bUr1+fmTNnFtZflxD3JCEtkxlrj9Dmo7WMXXmU0NhUAPb71GRfuRoAbKnYgJE9J/L3\nym28vmomo15rS31fFykoCVHAZDwUd8KUlc3vQWF0+GorH3+6hG5TRzB3ydjr+m1p+RQbx3yB84Vg\nHp8xAR8pKBU7Xs42XHZwzz3OOH/BjNGI0kLGpPtLikp5KKUYOKAT01tfnQ735uafmDplCVlyG1zx\nNnYsKHV7P336XP/8Pn3y9xk79rZe9sUXX2TRokWkpaVx8OBBmjZtmnvuo48+4uGHH2bPnj38/fff\nDB06lMzMTMaPH0/Xrl0JCgqia9eu1KxZky1btrB//37Gjx/P+++/n3uNw4cP8/PPP7N7925GjhyJ\nnZ0d+/fvp3nz5syfPx+AHj16MHnyZA4ePEi9evUYN24cAK+99hpTp05lx478Mzi+//57nJ2d2bNn\nD3v27OG7774jODj4zv6+hShE8amZfL3qIDM6D+SZLq14eNef1/UZ164PoyYsRK1by4TZ79HjoSo4\n2ViaIVohzEzGQxkPi7C0zCwW7DxH2ymbmPP5Yt6dNoy1c/rT+ehmWoXsp0HYcQBqezvx1Yv+rBvV\ngYfHDcLRwdbMkYu75e1sw0Unz6sN58/fvLMoeWRMKhFjUqHd/qaUehz4CjACs7XWH19z3g/4AXC5\n0uc9rXXh3rQI+Lra4TV+JEHHtuF/6SRhzp4cD41lzj/BvN6qcmGHI4q5+vXrExISwsKFC6+bKrlu\n3TpWrFjBZ599BkBaWhrnbzCQxsfH8+qrr3Lq1CmUUmRmZuaea9u2LY6Ojjg6OuLs7MxTTz0FQL16\n9Th48CDx8fHExcXRunVrAF599VWef/7569q7d+/On3/+mRvXwYMHWbp0ae7rnzp1iurVq9/nvx0h\n7k1yuon5fx8n/qtp9Ny6mDLJOd/wvLFrGb/Uf5QsgxErCwPPNfShV8vWVC0ju8kIYS4yHopbSUo3\n8fOuc3y35SyVjwYycftiHjoXdF2/V+KP8c6YHrSs6iEzTEsIHxdbNucpKlmFhZoxGlFayJh0fxVK\nUUkpZQSmAY8CocAepdQKrfXRPN1GAb9orWcopWoDq4GKhRHftV5qUZnh/Sew/9cFfNLqVVKtbDix\n9gStqntSo6yjOUISxdjTTz/NkCFD2LRpE9HR0bntWmuWLVtGjRo18vXftWtXvuPRo0fTtm1bli9f\nTkhICG3atMk9Z21tnfvYYDDkHhsMBkwm001j0lrf9M2Y1pqvv/6a9u3b52sPCQm55Z9TiMKSbspi\n0bazXPh8Or02LsA7KTrfebvMNGqmRPLQEw/Ss2VFyjjamClSIUReMh6Ka8WlZDBvewhz/wnmgaO7\nmLZjMU1Cj17XL6hRGxzGjuG5J9uaIUpRkLycbLjk4pV77BJ5kZQME3ZWsvSvKFgyJt0/hXX7WxPg\ntNb6rNY6A1gEdLqmjwacrjx2Bi4WUmzXUUrxbv+n+PKp/qRa5XwYycjK5u1F+0k3ZZkrLHEvxo4F\nrW/vZ9as658/a1b+Prc5tRKgZ8+ejBkzhnr16uVrb9++PV9//TVa59xauX//fgAcHR1JTLy6O1V8\nfHzu4nHz5s27oz+2s7Mzrq7V73O1AAAgAElEQVSubN26FYAFCxbQunVrXFxccHZ25p9//gHgp59+\nyhfXjBkzcqvtJ0+eJDk5+Y5eV4iCoLVmRVAYH772IS2fbcuoFV/mKyiFO7gxqcObLPllMz9/2oP3\nOtSUgpIQ15LxEJDx0NyiktKZvOY4LSf/zd/z/+CHWQOYv+SDfAWlLGVgf6uOhG7djf/ev6kqBaUS\nyWhQpHhfXSTZNyGSsCtrIopSQMYkoPiPSYVVVPIB8q66FnqlLa+xwCtKqVByZikNKJzQbszLyYYJ\nnfNvzXc8PJFP15wwU0SiuPL19eXtt9++rn306NFkZmZSv3596taty+jRo4Gc6ZJHjx7NXQRu2LBh\njBgxggcffJCsrDsvav7www8MHTqU+vXrExQUxJgxYwCYO3cub731Fs2bN8fW9upaBL1796Z27do0\nbNiQunXr8sYbb9yyol5aKaX6KKX2KqX2RkZGmjucEi/wXCzDhs6i3JOPMuHHcVSJCcs9F2nvwuT2\nfVm+ZDP9f/2StzrWw9lW1ksSoqiR8VBEJKQx4Y+jtJy8kRmbzpCUbiLDwhL/S6dy+2QaLNj/2HPE\n7jtEg82r8G3Z2IwRi8Jg8i2f+9gnPoLQOCkqiYInY9L9o/6twBXoiyj1PNBea937ynF3oInWekCe\nPu9ciWeKUqo58D1QV2udfc21+gB9APz8/BqdO3euQGN/e9F+fg/KmTT19NFNNL1wmPKLfqBVjTIF\n+rri3hw7doxatWqZOwxxAzf63SilArXWAWYK6Z4FBATovXv3mjuMEik8Po1Jfx7j96CLfLhuOt33\nX11qL8Hanu9bPI9h0ED+92hdKSSJe1YSc5GMh0VXafrdhMen8e3mMyzeGYwp00SmMX++/m7ZeFoF\n7+foky9SafIHuNSoYqZIi4aSmItuZcK0PxnVvyORdi4cKluViz8t5ZVmFQowQmEupSnvFTf38hmt\nsG5WDQXK5zn25frb23oBjwNorXcopWwADyAibyet9SxgFuQkrIIK+F/jO9Vl/5koBv88kWeObgLg\ng5FTqD1vPB4O1rd+shBCiLuSYcpmzrZgpv51ipSMnG9/vmj5Mp2ObsYmM50fGz3J5QHv0rtzYzwd\nJRcLIURRFB6fxoxNp/llVwjtD23ij+2LWVT/Mb5r+mxuH3d7Ky6P+5jMFlVpULH8La4mSiq7qpWo\n8c4y0i1zxvN+MlNJiGKlsIpKe4BqSqlKQBjwItDtmj7ngXbAPKVULcAGMPs9Jc62lnzWrREhv1z9\nRmXYiqmMm9qYj997DoNBdp4QQoj7aXdwDEsnz2ONjQ8pNld3bIuxc+btp4ZQrpk/vXo8QmVP2c1N\nCCGKotxi0s4QOh7cyKodi6kcm/N9cp/dv7KgYUec3Jx5o3UVujXxw9bKaOaIhTn5utnnFpQAQmVN\nJSGKlUIpKmmtTUqp/sBawAjM0VofUUqNB/ZqrVcA7wLfKaUGk7No9/90YdybdxuaVHJj5/iPOdPz\nGFViQrHPTKPH1PeY26QOvR6R6XtCCHE/xKdkMvXnf6j/+Tg+ObaZ+v4dGNX+rdzzNcs60uf1ATSv\n4m7GKIUQQtzM5YQ0ZmzKuc2t44GN/Ll9ERXjLuXrY5uVwRc1FG1fa4uNpRSTBPi42uY7DotNMVMk\nQoi7UWh7NWqtV5OzAHfetjF5Hh8FHiyseO7Um0/6894bH/LRJ69jnWWi7uUzBL43nH2//kBDP1dz\nhydu4FZbMgrzKCJ1YlEE/XnwIrvHfs7bf87EJS0JgG5Ba1hWtx1nq9ZjSPsadGvih1Fmhwpxx2Q8\nLHpK2ngYmZjOt5vPsHD7WTrcpJiUYONAyCu9qTFpFB085MsBcZXvtUUluf2tRJMxqei51zGp0IpK\nxZ2F0cDgYV35ImgP7/05HYBXA1cy8v2vqDzrfVzsrMwcocjLxsaG6Oho3N3dJWkVEVproqOjsbGR\nLd7FVdFJ6Xzx/QYe+3I0H4Tsz3duRe1WNGjlz+yXWuIua9gJcVdkPCx6StJ4GJucwcwtZ/lhewht\nDm1m9eYfri8m2ToS0v11ak4cRX13+SJWXM/b2Ra31HhqXg7GJyGCMGcvMkwPY2VRWBuVi8IiY1LR\ncz/GJCkq3QEfF1safDKKNWf28/jJHQAMX/IpE+s/wMQhnWV9pSLE19eX0NBQZKv3osXGxgZfX19z\nhyGKiLWHL7F71KcM//NbHDOufit53tmLaV2H8Nx7Pelcyc2MEQpR/Ml4WDQV9/EwIS2T2VuDmfNP\nMEnpOVtaV4gLz1dQSrB1JLh7H2pNGkV9NxdzhSqKASsLA89eCGTU8s8B+LVOWy7Fv00Fd3szRybu\nNxmTiqZ7HZOkqHSH2tf15pNxn1O7b2f84i/jlJFC9ylDmFW/Gn0fr2vu8MQVlpaWVKpUydxhCCFu\nIDEtk88XbOHBySMYfWZPbns2irlNOpM6agzjO9TD2kLW2hDiXsl4KO6nlAwT87aHMHPTGeLTTPnO\nzW/4BK/v/hUL9JVi0kgecJOZSeL2mHyv7vznEx9BaGyqFJVKIBmTSiaZU3gXBnVpwld9PiLdmFOT\nqxNxFtfh77LtdJSZIxNCiKJt3/lY+o76if5vP8sjeQpKZ9x8GDZ4Oi1//4H+T/lLQUkIIYqQdFMW\nP2wPofXHGzn05fcsmt6XGpEh+frYu7uw44s5WJ8PwX/mZ1hLQUncAUPFq4UGn4QIwmQHOCGKDZmp\ndBesLAwMHvESnx0NYuSqb4iyc+a32q05sXA/fwxoSTkX2/++iBBClCLZ2ZoZm8/w+fqTYHDjrJsv\n7mFHAZgb0InUcR8yqX0dLI3yXYcQQhQVWdma5fvD+GLdCWoGbmbe1p+oE3EWgLf/+Zk3n3kfN3sr\n+rauTPdmFbG1ki8ExN2xrVIx97F3YjQXoxLMF4wQ4o5IUeku+bra8dCU0UxOSmR57baEO3lAcgZ9\nfwzklzeayxapQghxRVRSOoMXB7H11JXZnAYjg54awpylY/n+ubfpMboXdX2czRukEMWUUqoP0AfA\nz8/PzNGIkkJrzdojl5my9jhld29l2tYf8b90Ml+fViFBjGzswUtPNsLBWj5SiHtT1suFCHtXyiTH\nYtTZJJ05B9Qxd1hCiNsgI8A9aFWjDEGjRxK+/uogezA0npHLD/PZ8/VlRXshRKkXeC6G2R/OZat7\nDciTE8Ocy7Bw1krGP1lHivBC3AOt9SxgFkBAQEDJ2qdemMWOM9FMXnMcy+3/MGHLApqGHsl3PsXS\nmkOdXqHmlPG87lfOTFGKksbX1ZYwpzKUSY4FICskxLwBCSFumxSV7lH/tlU5GBrHhmMRuW3bNgUx\nv4wNr7apYcbIhBDCfLTWzN98EjVkCDMC/2Bim9eY1fQ5AFztLPm0ywM8UtvLzFEKIYT415GL8Xyy\n5gQxm7czZOsCWgfvy3c+3WjJvo4vUvWLD2lapYKZohQlla+LLSecy9Dg0gkAjOfPmzkiIcTtksUr\n7pHBoPi8qz+VPXN2J2h2/iCr5g3EZtDbbD0Z8R/PFkKIkictM4uxMzdQ9+XO9Aj8A4Dhm38gIPQI\njSu6svrth6SgJIQQRcSFmBQGLdrPk1//w+aTkYzaODtfQSnTYGT7o88Tvf8IzVfMx1MKSqIA+Lja\nEupcJvfY8dIFMrOyzRiREOJ2SVHpPnCysWRW9wAaxwTz46JRuKcm0PXAWra9/QFnI5PMHZ4QQhSa\nS/GpjBo+mzeHvkiji8dz29dWa0bzZ9qy8PVmeDvLZgZCCGFuMckZjF95lHZTNvNb0EX0lZsnP2vV\nHYAsZWB7yycI3bGPFut+oVy9amaMVpR0dlYWRJe9ui5c+dhLsgOcEMWEFJXuk6plHOg7qAsra7fO\nbRu6dhbfvj+duJQMM0YmhBCFI+hCHDN6jeWjqf3xSooBcj6UfPro6xiXLeXd5xpjIbu7CSGEWaVl\nZjF902meHbMM548nkJ2R/33qnvJ1+blzX46v30aLrX9QqUl9M0UqShtTxUq5jyvEXuJcTIoZoxFC\n3C5ZU+k+ale7LN99/g37//csDS6dwKizGTV/HB/6+PLRqBexspAPU0KIkumPoFBC33qX8dt/yW2L\ntXFkYo8P6DvhDap4OpgxOiGEEFnZml/3hTJrxT46bfiZ1Xt/xy4znUuO7izyfxyAmmUdGf54TdrU\n6CgbzohCZ6henWOeFTnn6s1hryqUiU4GPM0dlhDiP0hR6T7r/Wgtxo75mjLDXsYnMRKnjBQGfvkO\nE329+aBXGxmghRAlitaa79YdxeftN+h7Yltu+wkPP+YO+4oxA57A0cbSjBEKIYTYcjKSz34Lotmf\nC1mycwkuaVeXZ3h720J2tuhI/yfq8UwDH4wGea8qzMOlRmU69Pwm97hnlMxUEqI4kKLSfaaU4v3e\nDzMy9FPGftoPh4xUysdfpvOYvnzrvYR+T8gUYiFEyWDKymbMiiO0Ht6H9qd25rZvrBzAgU9mMPGZ\nRhjkw4kQQpjN8fAEPl55GK9fFzHzn5/xTorOd/6EVyXODB7JmsGPYmMlHwvE3VNK9QH6APj5+f1H\n7xur4GGf7/hcdPI9xyWEKHgyehQAawsj7494ifFhF5n0wyiMOhv/SyeJGPwGyzwX8VwT2TVDCFG8\npWVmMWDhftYfvcyRZs/TKng/tqZ05gc8hd20rxkseU4IIcwmIiGNKWtPELdoCaM2/UDVmNB858+7\nlCXw9XdoO2YANRxszBSlKEm01rOAWQABAQH6bq5R0d0u33GIFJWEKBakqFRA3Oyt6DN5AJMjwnh/\n9TQAHju1kx/7vcWWn+fQqkaZ/7iCEEIUTfGpmfT+YQ97QmIBOFCuBm8/NYQqKVE8NG0CLap4mDlC\nIYQonVIyTHy3JZiZm08za8EIWp47kO98pL0Lf3ftR/OPhvFMWRczRSnEjVVwyz9T6UJMKlnZWm7J\nFKKIk6JSAapaxoFHvhnPd93CeX3nMgBirR2Y+GMgC/s054HyMpgLIYqXyMR0es7axqHI/Nv8Hmny\nMENfa0w1L0czRSaEEKVXdrZm+f4wPl17gvCENAAOeFfPLSolWtmy+vFXqP3pB7xQ3cecoQpxU852\nltRLjeChoE1UiL3EWXcfwhPa4ONia+7QhBC3UGjbkSmlHldKnVBKnVZKvXeTPi8opY4qpY4opX4u\nrNgKUpNKbpSb8RW/1W7NmEfeYEqr7qRkZvPavD2cjUz67wsIIUQRERaXyqfvfMW0D7tRMSYst72G\nlyPL+rWQgpIQQpjB7uAYXvjiL95dciC3oAQws+lzhDu4sfShLgRu3MsLv82knhSURBHXMCuOYVvm\n0/XQeh4+s5dzUXILnBBFXaEUlZRSRmAa0AGoDbyklKp9TZ9qwAjgQa11HWBQYcRWGJ7w9yHm2znM\nb/RUbltMcgbdv9/NxbjUWzxTCFFUKaX6KKX2KqX2RkZGmjucAnc+OoWpAz9jwpyR+MVf5sfFoyib\nEEXjiq780rc5ZZ1lTQ4hhChM56NTGPzdZna+/CazRz2Db/zlfOct3N34a+U2Ov29mDYP1pYdiEWx\nYKxWJfdxhdiLhETLDnBCFHWFNVOpCXBaa31Wa50BLAI6XdPndWCa1joWQGsdUUixFYqeD1Wmb+sq\n+doiohMYN/5HopPSzRSVEOJuaa1naa0DtNYBnp6e5g6nQAVHJTNzwMdM+GkcVtmm3PaHyjswv2dT\nnG0tzRidEEKULolpmXyy8hBzXh7KyEGdGLhjMS5pSby7ZQEAVkYDb7SuzKahbXi5TU0sjYV2Y4IQ\n98yxRlUyDUYAyibFEHYxyswRCSH+S2GtqeQDXMhzHAo0vaZPdQCl1DbACIzVWq8pnPAKx/DHaxCd\nlM6SwFBsMtP4dvkkGoceYYw2MWZib/lgJoQockKikpndfxLjf5mEUWcDcNa1HN+P/Y6P3nwcKwv5\nsCKEEIUhK1uzZM959nw1lzfXzqZKntuQAapGX6BzDVfe7eRPeTe7m1xFiKKtQhknQp3LUCn2EgCp\nx08BDc0blBDilgqrqHSj+bbXbjVpAVQD2gC+wFalVF2tdVy+CynVB+gD4Ofnd/8jLUBKKSY9W4/E\nNBNPTBxMm+BAAD6YMZRx1taMG9cDB2tZO10IUTSci05m9oCPGZenoHTazZcFH81h3OvtsJBvv4UQ\nolDsDo7h52+W8tKSr3nxwuF850KdPPmlUx8eGjuILyvL7puieKvgbsc5l3K5RSV9+rSZIxJC/JfC\n+kQQCpTPc+wLXLxBn9+11pla62DgBDlFpnyK+y0nFkYDX73kz5ZubxFl5wyAU3oyI6cO5oOPFpGS\nYfqPKwghRMELjU1h5tufMXbxRCyuFJROuvvx08c/MKbPI1JQEkKIQhAam8Koqau4+OSzfPn5GzTN\nU1BKsLbn6/a92btmO4PmfUhjKSiJEqCCuz0hrt65x7bngtH62rkIQoii5I4/FSil7K8svH0n9gDV\nlFKVlFJWwIvAimv6/Aa0vfIaHuTcDnf2TuMrDqwtjIwb/hwfD/6KOBsHANxSExgxpT8fTPyF1Iws\nM0cohCjNIhLSmDpkKmMXTsgtKJ1yL8/Pk+YyuldbjAZZ7FUIIQpSakYWX6w/Sbspm+ny8WA6H92c\ney7TYGR+wNP8uGADvVbMoHPzqhgkL4sSwt3einCPq7sU+kSHEZko688KUZT9Z1FJKWVQSnVTSq1S\nSkUAx4FLSqkjSqlPr+zadktaaxPQH1gLHAN+0VofUUqNV0o9faXbWiBaKXUU+BsYqrWOvts/WFFn\nZ2XBB6O68WH/z0m0sgXAIyWeYZ++xeiPl0hhSQhhFrHJGYwdt4Dx8z/IXZT7jJsPP06cw+hebeWD\nixBCFCCtNSsPXKTdlE189dcp0k3ZTHmoe+75tdWaMenTpbRbv4g3n2+GnZUsmyBKFqUUaRUr5x5X\nirnImchkM0YkhPgvtzMS/Q1sAEYAh7XO+dpaKeVGzsyij5VSy7XWP97qIlrr1cDqa9rG5HmsgXeu\n/JQKjjaWjBn3P8aaTIyb/i4OGal4psQxfHI/RmdnMW5EV+xljSUhRCFJTjfx2rw9HDF48leVxjxx\nYhsXnL2YO/Y7xvVuJzOUhBCiAB27lMBPXyziR1UO1NV8u7VSQ2Y1foYzzdvSZfDLjKnoZsYohSh4\nhtq1ch9Xiz7PmsgkmldxN2NEQohbuZ2KxSNa68xrG7XWMcAyYJlSSrYtu0vOdpaMmtCLD7I1474d\nkltYGvHJm4wxZTFudDdZvFsIUeAyTNn0+2kfQRfiwGjJwKeHEbZpHme7dOfDN9tLQUkIIQpIXEoG\nP8xZQ70vJzDhzB7inxrKytqtc897OFjhPO1LJjUqL7NFRangVqsaaRZW2Jgy8EyOI+x0KDSrYO6w\nhBA38Z/Vin8LSkqpL4HB+gYrpd2o6CRun6u9FSMn9maMgnEzhuCYkYp7agJdFnzGy2Ur80PPJrjY\nWZk7TCFECaW1Zviyg2w5GZnblmUwsrH3UOa91gRLWZRbCCHuu6xszbL1B8kcO5Y3d6/EMjtn6YPh\nm+exrlozsqxteO3BigxoVw0nG/n+VpQeVcs5M6vxMyRb23LK3Y/sBPmoKURRdidTYJKAFUqpF7XW\nyUqpx4APtNYPFlBspYqbvRVjJvbmA6ORsdPeJcrOmQFPDyMqNJ4XZ+1kfq8mlHG0MXeYQogS6Kvl\n+1ALfoK67XLb6vo48V2PAGws73RfBiGEEP9l7+kIdo+YxEt/fI9rWmJuezaKbRX8aVfJiXe7NqOK\np4MZoxTCPKqWcaBvq6triXnFye7Y5qK1JiHNRGxyBglpmWRmabK1xtrCgL21Ba52VrjaWaKUzKIs\nzW67qKS1HqWU6gZsUkqlA8nAewUWWSnkYmfFBxN68oGlJbsSFFH2rgAcD0/khW93sKBXU8q72Zk5\nSiFESfLzttM0GNKHQcH7qHP5LBMe7kUFDwfmvdYER/lmXAgh7quIhDSWfTKPh2dO4s2o8/nO7Sxf\nl9nPDuClNzoxvZaXmSIUwvwquNtjYVCYsnNukLmckE5CWqbM2CtgGaZsgi7EceBcDJcCD6GPHcP2\nXDAesRG4pibglJ6MZZaJGc2eZ0eF+rnPszIaaJsQjLe7A/b161Czijf+5V3wdbWVYlMpcdtFJaVU\nO+B1copJ3kAvrfWJggqstHK2teTDcT3oNW8PF4NjcttDolPoP/FXPhnSiRplHc0YoRCipNhyIgJD\n//60Dt4HQK+9v7O3TnPeG9YfDwdrM0cnhBAlR2ZWNr8u2YzH2JH0O7Ej37nzzl589ujr1OjXg2mt\nKmNtITNERelmaTRQ0cOe0xFJuW2nI5Jo6OdqxqhKpvjUTNYeusSRddtw3PQXTc7so+ulkzil33zH\nvWV1H853nJGVTa/fptEk9CjZKE55lGeHd3WOV2+Ibvcw9ZvVoW2NMrKcSwl2J7e/jQRGa63/UUrV\nAxYrpd7RWm8soNhKLQdrC+a91oR+PwWy6UTOGiePndzBtN8/ZsqR12k7bQJNK8sOCEKIu3fyciK7\nBoxiaNDa3LZvHurGGx++QQV3ezNGJoQQJcvOs9GM+f0wPeZ/Srs8BaUkK1umNX+B8Nf6MqLzA3g7\n25oxSiGKlqqeDrlFJYssE6cvS1HpftFas+NsNAt2nOOvYxFkmkxsmzGQcolRt/V8i+zs69qqRIcC\nYEBTI+o8NaLOw6ENsOwTTrr7sbB6U8Jat6d2p0foWN9bCkwlzJ3c/vZwnseHlFIdyNn9rUVBBFba\n2VoZmdU9gCFLDhC2agNfr/gEy+ws3lvzLbNeiSJmxpd0eMDH3GEKIYqhmOQM5gz/ionrZ+e2La/T\nlurTP8O/vIsZIxNCiJLjckIaE1cf4/egiwB8/tArPH1sC07pySyt245lXd7i7e6taCZfFApxnWpl\n7Hnyo4+pFRlC+bhwvmq2AxqXN3dYxVpWtuaPA2F8v/YIB/OuU6UMrKjVir67f81tirZ14miZygS7\n+XDZrSzpbu5kO7ugrayI96lCHQcnktNNRCVlkJGcyl7f2lSNDqVi7EWMOn/RqXr0earvOA87lnDu\n27K80mUUfm2a0bWxHw9V9ZBdLUuA/ywqKaXUTXZ8u3Tllrib9hH3xsrCwJdd/fkkK4XDf1eh0cXj\nAPTZsZTfukUyZ+oMXnu4ptyrKoS4bZlZ2Uz85BfGLpyIgZy0vdu3NrFfTeOZut5mjk4IIYq/zKxs\n/pi7ks+Pp3HB4upC2zF2zgx/fACxHt60f+0pFjSrgIXsrinEDVX1cqRWZAhVYnJmwKQcOgrPBZg5\nquJJa82fhy6x7ct5vPDnPP7n7ss7T76br89vddrimxDJvlpN0G3a4NewNnV8XOjgYY+Hg9UtP28m\npZsIGdyWw5FJLA8OJ3Hbbpz27abJ2SAahx3FxpSR27dMUixnHb04fCic1YfCKe9my6vNK/J8QHmc\nbWXNrOLqdmYqbVRK/Qr8rrXOXVFQKWUFNFdKvQr8DcwrmBBLN4NBMfzlFsx0W0zM23149PQuADof\n3czO115g0qRvGfZic3lTIoS4LZ/+tJ2BXw3BISMVgAvOXqwbP52RD9c0c2RCiLuhlOoD9AHw8/Mz\nczQicO9JLg94l047V5H6QHvef7x/vvN23V5kfIeaeDrKunVC3ErVMg6c8iifW1QyHD9m5oiKp8Nh\n8SyYtpxnF3zGR6FHAKh7+Qxft3iRYLecu14qutvxWLvHqDyhB094O97xhAUHawvq+jhT18cZ/H3g\nmUakm/qw/3wc0w+eJ37lauru3kT7k9vZVCWAFKurt/peiEll8bw1xI0LJPv1PrzSvj7lXORW4OLm\ndopKp4AsYLlSyhuIA2wAI7AO+EJrHVRwIQqlFH071mep20J+erM/L+9fDUCzC4fxHNiVkRe+ZNSg\nTrJTkxDiln7ZcZZWY/rjF38ZgGRLG74a+BkTuz8kMx6FKKa01rOAWQABAQEya9xMImKT2PLuRzyy\n8BsapeWsA/PigbX85P84R8pWpZa3ExM616FRBTczRypE8VDF04FN7uWBnHXI3M6fITUjC1srWcj+\ndqRmZDH990DKThrLpP1rcmenA2QaLah/+TS1WjeiR/OKNK3kdt/fB1pbGGlW2T3n9t7ODTgb+Tbz\n94Tw986TkJG/b8+9v/PSwXUkbF3EwoYdiXj9Tf7XWXY9L05up6jUQmvdRynVG/ADPIFUrXVcwYYm\nrtWlWSW2LJzLlLfe592/vgegSkwYI8a9xrgLH/L2h33kP58Q4oYOXIgj7t33eOHcgdy2D7uOYMSw\n57GykJmOQghxN7KyNetmLqXSuPfocvlsvnObKjci28mJcU/X4eWmfjKrXIg7YGNpJMav8r81JapG\nXeBMZFLObBhxS/vPx/LLBzN4e+kUyiZd3U0802Dkp4ZPcL7PQAY/04yKHoW3MUtlTwf6d6zLWx3q\nsPdcLAt3neePg5ewS4rjmaObAHDKSOGNnUtJCVzJzzM7Et53AD2faSYzl4qB2ykqrVVK7QC8gB7A\nAeBIgUYlbqpVjTJ4LvicUe94M2rpJ9iYMnBJS2LSt0P4KOwCj00ZQYsqHuYOUwhRhMQkZ9Dvx0Aq\nl6/P8/9n776jorjaOI5/h16lCCiCCDZs2HvHEnuviS2WWKJGE3vU2FvU2EuMXRNLbDH23juCBDsi\nIqiIIE06zPsHvqtEY0mEpTyfcziHuXd29scCs7vP3rnX8wBWcVEsrvUF3WcNJbeZXIIhhBD/ho/H\nbZ4OGEKTywfTtPtb2jO5/ldYdWzLernUTYh/LblYCc33RZ4F4P1UikrvkpyisuKgD2bjxjDj6t40\nfccKVuRIn1H06t2YwnZm/3CE9KcoCpWcrankbM33zYqz5bQvPwYMpsupLZpLHU0S4+lzaSfRXgdY\nt6oVMYOH8lWLcrJiXCb23o9MVFUdBnQh9RI4F2A88JeiKNcVRdmSzvnEWxS3z8U3P49l3JBFPDVN\nXVpTNyWFB/rmdFt1iWSRZk4AACAASURBVHXn/JF504UQACkpKkO3ePEoIo4zLuVo8eV8fq7clvzz\nZ1IiXy5txxNCiCwnIjKWP/uMxqlGeeq9VlCK1TPkx9rdGfz9OgbMGcLcjmWkoCTEf2BapiTJSurb\nVefnj/H1f6LlRJnX8xcJfDf3T+p1b0631wpKISaWjOs8Dvb8yfQx7bVaUPo7GzNDBjYpycits7i0\n9zTjuk3khp2Lpt8sIZaBZzfTu+dnLG83hJVHbxKflKzFxOKffMhIJVRV9VMUpYGqqnf+36YoihlQ\nKt2SiXeyy2XElOm9merkSOfp37CvWE2OF6oEKSoTdl/nWmA409u4YaQv1x0LkZMtOe7LqTshmu1A\nizwEj5tCv/KyLK8QQnwMVVXZcTWI83N+Yc7mWWn69rrWYF6jvnRuX5Od1Z3lUjchPoGiLnnws3ag\nSOhDdFCJvuwFbSpoO1amc+NRJH03XCHkaRJ9dV69vd9ftDpXx85kdKdqmBl+0Nt+rTDS1+Xzqs4k\nVRrPH1d78tvitXTdt5pizx4AYB0byegDyzl16yINB8zl+6bFaFQyr8wHmol88DPe6wWll9vRqqpe\n+PSRxIcyNtBl6uAmnF6zi2VV2qfp23E1iM7zjxMQGqOldEIIbTt37xkr9qZdR6FiASvGNJWV3oQQ\n4mP4Po2i84oLDPv9GtucKnEhf+rnqvesHejacQr7f1jIxskd6VOroBSUhPhESubLxQ27gpptAx9v\nuRrjb47fekr75ecIfB5LvL4h/dqO5ZG5DVNbDsFg53bGdq+VqQtKr9PT1aFdJScmrB7Htd3HmdBx\nDA8t8mj6fyvbmICwGPpvvEqXlRe5ExylxbTidVnjL0z8I0VR+LpJKQo72fDd1mtExycBYBsdxpKl\nw9h4tC3l506kYcm8Wk4qhMhIodHxHBg9h0MHVjK41UiuOJbE2tSARV+UQ1/e8AghxAeJjU1g7Y7z\n/HTjBYnJL9/MKgrjGw6goe9FjjTpwvh25ahVxFa7QYXIhlxszNhpXxBungTAOeAOT6PiyZPLSMvJ\nMocN5+4z4c8bpLxWZwu0yMN3U7ey4MtqWfZx0tfVoVM1F+IqTmHd8a5EzplPGf+/OFC0umafc/dC\nabLgNL3L52Fw89KyCrqWyTuLbOKzknnZNbAGhWxN0U1JZtHuH3GICmHUwZ9JbNuO2VsukpCUou2Y\nQogMoKoqsxfvYeTuhdhHh7L5tzHUu3eZ+Z3KYm8hK2gIIcSHuLLtEP5FS1NvaHfUhMQ0fQ/sXTD6\nYRx/Dq8vBSUh0omujkJ08dKabbvoUK4/itBiosxBVVWW/HkNp67taXftcJq+rlWdWP91nSxbUHqd\nkb4u/T4rQe+dizk7+xd0//ahaPV7Hnz1ZQNmdx3HH56BMopNizKsqKQoSmNFUW4riuKrKMrod+zX\nXlEUVVGUihmVLbsobGfGroE1aONiilFSvKa96Z1zdOrXijHfr5bL4YT4RBRF6asoyhVFUa6EhIS8\n/wYZaO2JO3yxYDRmCbEABFjmpXSXFtQuKm98hBDifYIfPOFEw46U79CY4oG3cX0WQM8ruzX9dYra\ncvjb2nxTvwiGejJ3pRDpSbdaFbp0mkq5wb/Sp/0EbjyK1HYkrUpJUflx83mq9u9MnftXmX5wMdUe\nXENHgUktSzK1tRsGetlr3Ii1qQGTWpXiwJBa1CqSusq5QVIikw4vx/ZFOJO3/0ieVk0YPXUL95+9\n0HLanClD/uIURdEFlgBNgBLA54qilHjLfubAN8DFjMiVHZkb6TO7fz2ubviDDeWba9qdIoKZMXcA\nv3f+hj+uPtRiQiGyB1VVV6iqWlFV1Yq2tpmnWHPzcSSJ34+j9BNfABJ09FjadwoDW5TTcjIhhMjc\nkpNTODFxAbolS1D3yO/okPqpd7yuPgoqeXIZsqxLedb2rESB3KZaTitEzlCocD7OOpfluYkFANdz\ncFEpJUVl+obTtBjalQqPbgGgn5JMhae+rOhWkR7VnbUbMJ0VyWPO+l6VWd61ApWTwzBOfDWIoupD\nH6ZM7Mb+1r1Zuu8vuUIng2VUGbMy4Kuqqp+qqgnAZqDVW/abAvwIxGVQrmxJURR61S9OiR3rGPv5\neCINTAAwSEli2JFVWLVrxcRlh4iMS3zPkYQQWUlcYjJrpq2hz4Xtmrb5DXoxZGRnmUdJCCHe4fZp\nT7xLVqXupKHYvHiuaT/pUp7GfZaQ+N0wjnxXhyZu9rLikBAZqIR9rjTbNx7nzKLS/wtK7Ub0oMTT\n+5r2mY37U3fVHBqUyPOOW2cfiqLQuFRefpnVg63rD7KySjuSlNTXuAYpSXx9dgtNujZi3KD5XPEP\n03LanCOj3mU4AK8Pjwl82aahKEo5IL+qqnsyKFO2V6GANcN/GceMqRvxsi+qaa/t78mQ79ozq880\nLvqFajGhEOJTWrT9MkPWT9N8un7KuRzFZ44nv7WJlpMJIUTmFB35guNdBuPsXoVyty9r2p+YWfN1\nq9HM/XY+i8Z3ZEKLkjIRrBBaUCxvLnReq+M+CI0hKod9MK6qKj/+do52I3pQPMQfgBQUJrYZTqvV\ns6jobK3dgFpgbKDLkDYVcP9zLWPHr+OKQ3FNn8vzx/z48zD8W3Rk6vrTMpAiA2RUUeltH+loZtJS\nFEUHmAcMe++BMvE8JpmRlakB04e3xnvzHpZX70jKy1+FVVwU036dxOQpvzJlzw3iEpO1nFQI8V+c\nvxdKoanf4xCVel58bmTO0ZEzaVHOUcvJhBAiczp0LZDHrqVx/20xhsmpbzqSFR1WV2hJ64G/UHVU\nP3YOrEkpBwstJxUi5zI20KWgrRmm8TFUCLzBZ3fOc/NxzlpKfsGuqzQe2StNQWlS2xF0Xf4Dxf82\nkiunKWRrxsyJXXj4xwGmtfiGSMNXlya39zlK/wEtGDNwHgevP9Fiyuwvo4pKgUD+17YdgUevbZsD\npYATiqL4A1WB3W+brDuzzmOSmSmKQvfaRaiz7RdGfT2PIPPUx22LW0Ou5ynEqjP3abrwNB4Pnr/n\nSEKIzCg6Pondk5bQ9vpxTducdt8xrKe7FlMJIUTm9Cg8lq/WX6HvpmvsK1hF034tbxFadf8Jj+8m\n8Mf3TelezRldHbnUTQhtq6kfzfX5Hdn+60hmHFjEjaBwbUfKMCsPXafK0J6UfXxH0zap7XC6LRtH\nYTtzLSbLPBRFoU0FJ77eNJsFi3axp1gtTZ9JYhzX9HPTb4MHAzZ68DRKZtlJDxlVVLoMFFEUxUVR\nFAOgM6BZRkNV1QhVVW1UVXVWVdUZuAC0VFX1SgblyxGK2+diyvxB/LZiN6srtGRq/T6aPr+QF7Rf\nfo4pf14nJiFJiymFEB9r3pbzfLd9nmZ7e0l3WkweTC65VEMIITSSU1RWn7lPw59OcvhGMABLq3XA\nO29hJjTox+BvljBs9Ocs+aJ8tliOW4jswr5UUaIMjAHIHRvJQ++7Wk6UMbZfDsBx8FdUC/hL0zat\n2SC6LB0vBaW3sDI1YPxXDbDes4MxPacTZG7LTzW7EGiZF4D9Pk9oMPckWy8/RFXV9xxNfIwMKSqp\nqpoEDAIOAjeBraqqXlcUZbKiKC0zIoNIZaSvy4jOVSm2ZRW58tik6TOPjaZFvzZM/Wo6p+/KpYVC\nZAVn7j5j9fVwllXtQJyeAU/MrPEdO5WqBXNrO5oQQmQad856caVsbVZvPMaLhFeX/MfrGdDuy3kY\nfTeEg8Pq4V7MTosphRBv45bfCp+8hTXbKRfOazFNxjhx+ymjdvqkmSvop/q9aL5sCkXzSEHpXaoX\nsmHCzyP5fd1+NlRunaYvMi6J85PmM2rKZgJCY7SUMPvRy6g7UlV1H7Dvb20//MO+dTMiU05WvZAN\nB4bWYvq+m2y6lDqH+rhjKyn7+C5l109g/4WDTBjyA4O718XGzFDLaYUQb/MiPonRO7xRFR1WV2rF\niYIVKKUfz6x2Vd5/YyGEyAFiXsRyYfB4qm1YTNGkeKZGx/Jlh4nwcgW3ck6WzGjrRrG8OXteEiEy\nszL5LVnnUEwzYsfhphfhMQlYmhhoOVn6uPEokoG/XiUpRWVl5bY8NbOm1LMHVP15FmXyW2o7XpZg\npK/L0DYV+KxKEUbv8MY7MAKAQs8eMvPAQjgAPx/tjOkPY+lRtyh6skryfyKPXg5mbqTPjLal2di7\nCiX0E6jr56Hpa3LnHMO/bcPKDkP57ew9klNkiKAQmc2cQ7cJfB6r2b5v40iPUV0xNtDVYiohhMgc\nPLYdIqiIG/XWzMU4KR6AWv6elAy+h7mhHlNal2J7/+pSUBIikzM11CO4VAXNdvlHt/AMyJ7zKgVH\nxtF73eU0Iyr/LFmXfMvnU72QzTtuKd6mRL5c7BhQnXHNimOkr8PUw0sxTE7CMDmJb05tpGbnRowe\n8QvXH0VoO2qWJkUlQc0iNvw+rgVrftnDltKfadrNE2IZfWA5Zdp+xugRK7j2MHuevIXIijwePGft\n2ftp2r6s7kyFAjlvWVkhhHhdyJMwjjXrRtmOTSjy+J6m/bpdQVp3m4tTg5ocGVaHblULoCMTcQuR\nJRjUqKb5vmTwPa75BmsxTfqISUhi4o/bCQ1Nu7rd+GYlaF46n5ZSZX16ujr0qVWQQ0PrsKvXKDzt\nXTV9rs8C+HHeAK607MZP2z1kRfR/SYpKAkj9BGDU59Up+udmRgxcgK/1q2XISz71Y/ZP/bndrAOT\nVx4jJCpei0mFEInJKWyZtY6tG0dR6Fnq5auOVsaMaOT6nlsKIUT2paoqJ5f8SnzxktTbtxFdNQWA\nWD1DptftSf/Byxg6+nOWda0gE3ELkcUUK1UQP6vUwophchLPz17QcqJPS1VVpi87yOR5g9iwZRyW\nsZFA6geGvWq6aDld9uCU24SZP3yB784DzGzcnxf6qc8DOqj08PiTTj2bMLHvLM7cfablpFmPFJVE\nGuWcrJi+YBAnthxkft3uxOq9mk+p419HGDqwBQu7fs/PJ+8RnySVXCG0YfXRm/TfPJtKQTfYt3Yw\nje6cY2bb0pgYZNg0eUIIkak8uPuQUzWaU2dQVxzDn2jazxQoQ5Pei0keNpwDI+pRv3geLaYUQvxb\n5QtY4elQTLNt6nE5W03PsWyvN51nDME2JpwqgddZtW0y9VxtGd+8hLajZSuKotChijO9ts5j5o+/\nc8Ll1WWVDlEhzFw7lvAWbZiw/DCh0TKQ4kNJUUm8QV9Xhz4NStBx53Kmzf6dQ0WqavpyJcTwTDFg\nxv5bNPzpFHu8H8mSjEJkoIDQGBKnTKfg80cAxOsakK+xOzWLyHX2QoicJzE5hSXHfZkwYT11zr9a\nDybcyIxhTb9l+tCFLBzXnvHNS2BqKIV3IbIq59wm3HIppdkuGXCDO8FR77hF1nHQ5zFOwwdRKjj1\nct1EHV02tR7Awi/KoyuX6KYLO3MjpgxtTtKfe5jQcQyhxq/m1mt++wxNp39Hvbkn2XwpgJRsVLxM\nL1JUEv8on6UxU4e2wHjvbkZ/9SP3rB256FiS/a41AAgIi2HQb560WXqOC36hWk4rRPanqipLl++h\n77mtmrbFDXsxuEttLaYSQgjt8HoYTotFZ5h98DYnnMqyrVR9AP4sVotm/X+m6MiB7B5ck9KOslqS\nEOlNUZS+iqJcURTlSkhISHocn4SKlTXb5YNucTXg+Se/n4zm+zSKG0PG0vz2GU3bzGaDGDKlD2ZS\nCE93DUrmZfi6Sfzy815+d2sAQAoKM+r2JCI2kdE7/qLDz+e5+ThSy0kzN/lLFe9Vq4gtVZcNY8MX\nrdj45xXNMrz/l+foPsIXjmBM9yF07dmYkvkstJRUiOztoM8Tmv8yHYOUJAA87V0pOmEE1qbZc0ld\nIYR4mxdxifzy20kW3I3n9cHSU+r1YZ9rDRKbNGVTazeccptoL6QQOYyqqiuAFQAVK1ZMl6EdeapX\n5L6VPXdtCnA1XzFC/Z7RpUqB9LirDBEZl8iKccuZcXydpm1j+WY0mDee/NZy/soo5kb6jO5WE886\nWxk5ax02Pp545Xs1T6nHg+e0XHCSPuXz8HXLcpgb6WsxbeYkRSXxQfR1dehVtyhtKjkz/8gdfr0Y\nQFKKim5KMiNPrqdQWCANx19kx+Z6bO49hB5f1KGwnbm2YwuRbcQkJHF2xjKmPLgGQLKiw6be3zOr\nYn4tJxNCiIxz4ehldPv3p/MTf1b3XkqkkZmmTye3Nc17fEWbcg4oilwyIkR2U9YlN+59f9FsFwjM\nuqNHUlJUZizZx/cbJmsWFbjoWBJ1/jyqFcqt5XQ5UzknK0ot/IbVZ+5jdOQOcYkpmr72XofotXgj\nsxv3pdz3g2hdzlGeZ14jl7+Jj2JlasCkVqU49G1tGpXMQ5WAvygUFgiArppCB58jjB/WhguNOzFh\nyX7uhURrObEQ2cOKvdcY+OcSzfaGCs3pM6iNPKEJIXKE0MhYtvUchVuT2lTyvUre6DDGHF+t6W9T\nzoEj39WhbXl5oS9EdlU2vyX6uq/+vx+ExvAwLEaLif69Xw5fp8vsYVjGpb5XemJmzYEfFtC1ZmEt\nJ8vZ9HV16FenEIe/rUOD4nYAWMVEMPLkOmxfhDN5+484tmzMiLHr8AmK0HLazENGKol/paCtGT93\nq4hH7YKMcslHs82LqO3vCYBBShJdPfcTP+QwW1c3Yt2XX9OlQy1c88rIJSH+Df9nLzD5cSZ5o8MA\nCDG15NnwMRTNI/9TmV1iYiKBgYHExcVpO4p4jZGREY6OjujryxD2zE5VVQ7vPoPNkK9p/8BH056s\n6BBpZIajpRHT2pamTlFbLaYUQmQEEwM9yjlZcel+mKbtrO8zOld20mKqj3fW9xmWI4dpJuZO0NFj\nzlfTmfplXSmKZxL5rU1Y2aMSh64/YevSHcTrvXq9UCnoBhVm9GLLvs1sHzyKAR2rYWdupMW02idF\nJfGfVChgTfnpX3KiRzNGLd1Cu53LqRx4AwDD5CS6Xd1LotcBtq+sz/ou/Wjf2Z1yTlZaTi1E1rJi\n1UEmXtql2V7SpC/DW1fUYiLxoQIDAzE3N8fZ2VleKGYSqqoSGhpKYGAgLi4u2o4j3iHwWRSnBo6n\n7Y5lGCUlaNrv5s7PyGZDqdixMYcaFsXEQF7OCpFT1Cps86qopKqcvROcpYpKTyLiGLPmDCse3da0\nzWnSn6Hju2Gkr6vFZOJtPiuZl1rz+rGiQRVMfpxBj0t/YJCShA4qn187SNTXp1ix6XNMhn/Ll/WK\nY2yQM3+Hcvmb+M8URcG9mB0z5g8idO9hxvSbg0e+Ypp+/ZRkOnsfwmn7r7RZeo5OP5/n+K2nqKos\nzyjE+5y6E4LB4YOaybk98hWj7JjBsiJIFhEXF0fu3LmloJSJKIpC7ty5s83osfRecUkbklNUdvx2\nhJByVfhi6wJNQSlJ0WFhtU58N3o1E6f2YmyzElJQEiKHqVHEhsoPfZi5fyFnlvcm79aNWWbJ98Tk\nFAZvukpAsj5tus1lZ4m67CzpTo2543G0kom5MytjA12GtKlAwz/XMXHqJo4XrKDpM0+IZdjR1bTo\nVJ/p3X5g68UHJCWnvONo2ZMUlcQno6Oj0KR0PqYt/Y7H+44wpt8cLjqWBCBeV49VFVsBcPF+GD3X\nXuazeafYfPEBcYnJ2owtRKaVmJzClD03WFuxJW26zuFqPle2dB1Oq3IO2o4mPoIUlDKf7PQ7UVV1\nhaqqFVVVrWhrm/UvAbsTHMWqz4fRrHtTygXe1LTfsHOhXa8F6E6byo5v61Emv6UWUwohtKW0gwXl\nQ/3p7H0Ix8inlLt9hZtPssaE3bMP3uay/3MAYg2M+Lb5MB7OWUQdVzstJxMfwtnGlOlj2sO+fYzp\nPRNfa0dNn2PkU6ZsnY7XhNk0WXCaAz6Pc9QACikqiU9OR0eheRkHpi39jvADRxg9ZDFT6n3FU/O0\nKxnE375L2eZ1mNvuO+b/4UVwZPb41FiIT2XzpQDuPk2dwNHToRhtu86h6+B22eoNsUhfoaGhlC1b\nlrJly5I3b14cHBw02wkJCe8/wAdSVZWOHTtSunRpFi5c+MmOe+zYMS5cuKDZXrJkCb/++usnO77I\nPBKSUph/5A7NFp7GLyIRw+REABJ1dJlX4wum/rCWeTO+ZKB7YfR15eWrEDmVnq4OsbXrararB3hz\n7naw9gJ9oEPXn7DilF+atlpFbRn0WQktJRL/lrurHZN/HsHZHUeZ0XQgoca5AAg2s2ZnCXfuPo2m\n/8artFx8NsdcnSNjhkW60dFRaFQyL5/N+5qzvqH4nfDl3L1QTX9Pj90Ue/aAsX8uJPzwaraWaURg\n5x40a1mdyi7W8sZZ5GiRcYnMO3I3TVv7ivkp7SifzosPlzt3bry8vACYOHEiZmZmDB8+PM0+qqqi\nqio6Ov/+jXpQUBAeHh7cu3fvP+X9u2PHjmFjY0PVqlUBGDhw4Cc9vsgcPAOeM2q7N3eCU4vom8s0\nounts1jHRjKh9TDa9WzGxkr50dGR1wVCCChYpzLBZtbkiQ7DMi6ah8fOgXtRbcf6RwGhMVwaOZUO\nqh6/l24IgL2FEfM7lZXzWhalr6tDjzpFiag8j5V7umM6fy6+lvmINXg1YfdfQRFMn72N/Za6NP6q\nNe6udtn2/a0UlUS6UxSFmkVsqFnEhr8CI1hx2o9DXg9pcvusZh/LuGj6XtxOysUdHFtckXHu7XDt\n3p5WFZ2wMJbVeUTOs+rAXySEhYNh6jX2xvq6jGzkquVU4t9yHr03XY/vP7PZR+3v6+tL69atqVmz\nJhcvXmTXrl2UKVOG8PBwADZv3syRI0dYuXIlwcHBDBgwgICAAHR0dFi4cKGmyPN/n332GY8ePaJs\n2bIsXbqUkSNHsnjxYsqWLcuTJ0+oWbMmvr6+rFy5kgMHDhAVFYWfnx/t27dnxowZAOzdu5fx48eT\nnJxMnjx5WLZsGStXrkRXV5e1a9eydOlS9u3bh42NDUOHDuXq1asMGDCA2NhYihQpwurVq7GwsKBm\nzZrUrFmTY8eOERERwZo1a6hevfqneaDFJxWTkMTq1YfYfcWfOzYFXnUoCt+0HEHVMi4saVeWvBY5\ne1UdIURaNYrYcqZAGdpdPw6A5ZkTxCVmzomu45OSWThtAzMOLEc/JZnKD68zsfHXLP6iOrnNDLUd\nT/xHFsb6DOtQmaCGa5l3+A7K1UBeH5g06uRaGty7zJntyxjT7Euqf9WBpm726GWzEbfZ66cRmZ6b\nowWLPi/H0dENWL9qP7Ma9eOBZV5Nvw4qDe5dZtrK0dRrXp01TXozafkhLt0PyxFDB0XWkZ6T4waF\nx2Iwdw7HV/Sli+c+dFOS6VenIHa55I2V+HRu3LhB79698fT0xMHhn+fp+uabbxg5ciRXrlxh69at\n9OnT5419du/ejaurK15eXu8t4Fy7do1t27bh7e3Nxo0befToEU+ePGHAgAHs3LmTa9eusXnzZgoV\nKkSfPn0YMWLEW4/btWtX5s6di7e3N66urkyZMkXTp6oqly5dYvbs2UyePPkjHxmREc7cCmZl22/o\nM7gNC3bPRv/l5W4ANmYGTO9Tl2U9q0hBSQjxhkK2pviUqKzZrnf7PKfuZM6FCn7adJ6hq8ajn5I6\nh2yR0AcMa1yMCgVkNezsxMHSmDkdynBoaG2alEp9b+v2+C4N7l0GoOaDa8xc+i1OTesxqcck1p3y\nJTo+SZuRP6kMKyopitJYUZTbiqL4Kooy+i393ymKckNRFG9FUY4qilLgbccR2YOjlQkjO1Zm0B+L\nOb3nLON6TuOkS/m0+0Q+ZejJDYz9ugnf/vgH9eaeZMlxXx5HxGoptRCvpOfkuCs3n6HXhR3YxoQz\n7dBSOgVcpm/tgp/0PoQoVKgQlSpVeu9+R44coX///pQtW5bWrVvz/PlzYmP//Xm4QYMGmJubY2xs\nTLFixQgICOD8+fO4u7tToEDqU7+1tfU7jxEaGkpcXBw1a9YEoEePHpw6dUrT37ZtWwAqVKiAv7//\nv84qPr2ImERmLt6DQcN6fLN3GUZJCRQP8WfQuS0AtK/gyJHv6tDUzT7bXiYghPhvFEXBoGULEnVS\nRyaVfXyHCye8tJzqTX96BlJl4rc4RqYWvCIMTdkybDY96xV7zy1FVlUkjznLulZgz+CalCrtwvaS\n7iQpr0ouZR/fYcqvk6nbqhZLWg7ixy0X8X/2QouJP40MufxNURRdYAnQEAgELiuKsltV1Ruv7eYJ\nVFRVNUZRlAHAj0CnjMgntMfUUI+uNQqiVh/DuXt9GbfrNAW2baSd9xGsY1NXcvDJW4ggCzt49oLZ\nB28z59BtahewpGVFJxq72WMqS6uLbOT2kygK//wTxknxAFy3K0jpob1l2WzxyZmammq+19HRSTMa\nNC7u1cIJ/x/1Y2Bg8MHH1tPTIyUl5Y1jARgavhrur6urS1JSEqqqflQB4X0jV/9/H/8/vsgcDngH\n4T12Jt8c/AWTxHhN+w07Fzwr1mN9r8rULpr1V7ATQqS/OtVcOe9Umtr+ngAY/PkHCf0+w0Avc1yI\n4xcSje/wH/jW74qmbWanUYz+uqkUzHOAUg4WzBjWCp/OdZm89STF1i+j3V9HMExOfU1SIPwJow79\nTPSJ9fxRog4rWnWhZrv6NCieJ9P8DX+MjHqXUhnwVVXVD0BRlM1AK0BTVFJV9fhr+18AumZQNpEJ\nKIpCjcI21BjehuC+TfjtjC8h6zfT6Pyf7CleK82+qgolN62g9LjjrHCrR0Tr9tRoWInaRW0w1Mt8\n11IL8THWrzvIpGuHNNsbWg9gWmUZuJnVfeycRxlNR0cHKysr7t69S6FChdi5cyf/H4HXoEEDlixZ\nwrfffguAl5cXZcuWfefxnJ2d8fDwoHz58mzbtu2991+jRg2GDh3KgwcPKFCgAGFhYVhbW2Nubk5U\nVNQb+9vY2GBsbMy5c+eoXr06GzZsoE6dOv/iJxcZ4WlUHAtWHaHp/LGMfOCtaU9SdFharSORw0ax\npFkp+ZBICPHBmYMXCQAAIABJREFUKjtbM8utlqao5H7jDOfuPaOuq52Wk0FsQjJLJ65m1vF1mraV\nVdrxxbRvZK7YHKaUgwWlvm3Jva71mP3HJazXrOCLq3uxjEtdmMIsIZYuXgfYmpzE13FWWJsa0LJM\nPtqWd8DNwSLLFCAz6tnbAXj42nYgUOUd+/cG9qdrIpFp5cllxKCmpUhuPIXTd78h4vJD9G8Gk5j8\n8pNpVaXN9eMUCX3ItyfWwYl1XM3nyjw3dxLatKVW3TLUKGSTJau8Ime77B9GtTUL0FNTR3icLVCa\neoO7oCsrg4gMMGvWLBo3boyTkxMlSpQgPj51JMmSJUsYMGAAa9asISkpCXd3d5YsWfLOY40YMYJO\nnTqxZs0a3N3d33vf/5+Yu1WrVqiqSr58+di/fz+tWrWiQ4cO7Nix44373LBhg2ai7sKFC7NmzZp/\n/8OLdKGqKts9AvGZMo/RB5ZjnvDqssnbNk4s6DqWPt92oLyTzC0ihPg4ero6qK1ak/LnInRQqfTw\nOtPPXNd6UUlVVWauOcaodRPQffl67rJDCYzmzMTN0UKr2YT2FLI1Y1yfejztVJ31x28StXItHc7t\nomhoAAC/lm0CQNiLBNae82ftOX9aRPlRuEkdGlV0xjWPeaYuMCkZMfmxoigdgEaqqvZ5ud0NqKyq\n6uC37NsVGATUUVU1/i39fYG+AE5OThUePHiQrtlF5hD2IoHdXkFsvxpE6M27HF75NaaJcW/sl4LC\nZccSHC9Vi4SWbahWpwy1ithkytUgxCuKonioqlpR2zn+rYoVK6pXrlx5/47voKoqo79fy6yZvTRt\nI0f+wqyZvTP1k4h4t5s3b1K8eHFtxxBv8bbfjZyLPp3A5zGM3e5N11lDaeh7UdOerOjwS9V2xH8/\nnv6NS8gIYyHeQs5FH+bE7acYN6xPlYc+eOQrxo+th/Drwr5aXVlr8zk/XDq3ospDHwCemViwcNZm\nJg1sJK/nhEZcYjJ7rj3Cc+MfOF44yaw6PeC1vw/L2EiuLOpKrL4hRwtXxqtcHYxbNqNm+YJUdLbK\nsOfODz0XZdRIpUAg/2vbjsCjv++kKEoDYCz/UFCC1MlxgRWQesL69FFFZmRtasCXNVz4soYLd4PL\nsOKzMkRs2kbtK4ep5e+pWVFBB5UqgdepEngdDizH094V988nU6ZsIT4rmQd3VzusTD98XhAhMsrp\nu89ovPXVSIx9RavTrl8beQEihMhSUlJUNlx4wKwDt4hJSKaCrbOmqORnlY9lPcfTe8QXFMubS8tJ\nhRBZXfVCNnze9GsCdU0INrcB4LxfKLWKaGdutmsPw4kcPlpTUEpBYVa3H5j4VQN5PSfSMNLXpX3F\n/LSvOIjrj7rx5PJDdnoGERmXOudSozvn0VNTME+IpfWNk7S+cZKETdO5nL8EiwpXIrJWXRzrVKFq\nYVuK2+dCX4uFVMi4otJloIiiKC5AENAZ+OL1HRRFKQf8DDRWVfVpBuUSWVCRPOZ827o8KS3LceXB\ncGaf9iFl+w7crx2naoCPZqgpQO6YcB7rmfD4+hMOXH+CjgLV7E2oVTIf7iXzUTSPmZzkhdapqsre\n5duY5ecBpH6Sf6rbN8wsmFvLyYQQ4sPdC4lm1DZvrjx4rmlbVKMz9fyu4OFUiuSp05hRv7hWRxEI\nIbIPAz0dCtSrhsfVIE3bpksBWikqhUbHM2CjBw4uFWjjfRjbF+EsqtuNfpO/kvnixDuVzGfBpFYW\njGlanGO3nrLTM4iUG/rct7LH5fljzX4GKUnUeOBNjQfecHQVz43MuZy/JBtK1OJh0zaUdrTEzcGC\n4va5cM5tkqHPtRnyF66qapKiKIOAg4AusFpV1euKokwGrqiquhuYDZgBv798kx+gqmrLjMgnsiYd\nHYXKLtZUdqlNUpeanPcLZeZpH9i1i9rep6gW4M2BotXTDCVMUaHI7s10HvUbp1zKs6VUNXQbN6JC\n5eJUL5ybXEYyeZ7IeEdvPqXljuWa7T9K1OGLLxtpMZEQQny4pOQUVpz2w3vpBgJtCkIuG01foq4+\nM8etZGrnSjjbmL7jKEII8fE6VMjPjteKSoeuB/M0Kg47c6MMy5CUnMLgTZ48iojjUf5SNOuxgO6e\ne3H5aRqF7cwzLIfI2oz0dWnqZk9TN3si2pfh0PUhrN17EpujB6h35wIln/ql2d8qLorP7l4gKJct\nv/uFccEvTNPX4MFVnIwVVFdXTFwLkzevNfksjLAzNyJPLkNymxl+0jlbM6xsqqrqPmDf39p+eO37\nBhmVRWQ/ero61CpiS60i7iT1qMOl+2HMuXCbUzceQ0rafev7XsIyLpqWN0/R8uYp+H0Wf+UpxMaC\nFXhSpRY2DepSrWQ+yua31PpQQpH9qarK2m3nWBR8H0hdDelKj8G0dbTUcjIhhHi/G48imbjxLB03\nzGW5z1FOOZeje8fJoCiYGeoxpmkxPq/khI4sOCCESAdVC1pT0NYUv5AXAKhJSWy/5M+A+sUyLMO0\nfTc5dy9Us/3UPDfPv5/AoHKOGZZBZC8WJvp0qOREh0rdiB7zOafuhLDz3F9w8BBlbl6iasBf2MaE\nA+Dh8Obcnf1Ob6ZS0A3NdoipJY/MbXliZk2fzwYQksuGfUNqfbJL0WUsnsh29HR1qF7YhuqFbRil\nqvwVFMGh68EcuRmMb9BzCoQ/fuM2bsH3cAu+B+e3ErPEkMuOJVlQsByBjVtRrFIJqhbMTal8uWTI\nvvjkDt8I5kyMAbX6r6LXlT/IFRdNt671tR1LCCHeKT4pmSXHfPFas415exfgEBUCQG1/Tzp5HyKk\nUzemtSmFvYWxlpMKIbIzRVH4orITKzedprP3QTpdO8TyoIGkuE/MkGL27xfuc2D/Zcj16pK7yi7W\njG6ScUUtkb2ZGeppRjCpfRvi+zSafb7P8D99Bd0L5zmfv3TaG6gqriH+aZpsX4Rj+yK1CDWqyTek\nqKlzFn8qUlQS2ZqiKJR2tKS0oyXDG7kS+DyG423O43vkHLmOH6bmPQ8qBN7QLOEOYJIYT537V6lz\n/ypt8xZj17PUQpKpgS4VnK2p6mRBxUK2lHa0kFXlxH+iqioLjt4FINrQhIU1PqeZmz197GUCWyFE\n5uUZ8Jwffr1Ih98Xs95zb5q+fW7u1B7Vl6Z1SsqchUKIDNGuvCOxYw8x+OwmAD47u4vTvoOoUzR9\n51a67B9G1JBh7PM+wtetR3O+QBnyWRix5IvycrWDSBeKolAkjzlF8phDDRdUtT3dw2K5FhjOX0ER\n3HwciV/AM7a71adgWBAuYUHkiwzRvNdN1NHlubE5ujoKuU0NP1kuKSqJHMXRyoRu1V2gugtxYzpz\n6X4Yc6/6EXPwMEW8zlHjgZdmQrQX+kZ42xfR3PZFQjI3r95hyYC+eOYrxnKnkjwvVxmzWtVwc3Wg\nvJMVdrky7vptkfUdu/WU648i07R9U7/IP+wtxL+jKApdu3Zlw4YNACQlJWFvb0+VKlXYs2fPP97O\ny8uLR48e0bRp04yKir+/P82bN8fHx+c/7SPSR2xCMnMP3ebalr0s2jMP59dG/oYZ52LHV2NpPW0I\nNmaf7oWqEEK8j5WpAc86dSP5zGZ01RRqPPBm1Jrd1J7eK92K234h0RwcPJFxl3YCsGHLeLr0mMP4\nwb2wNZdzoMgYiqLglNsEp9wmtCiTT9P+fGRD/J694NKzFwQ9iyTK9wHJQUEkhYRiYWqIkZ5u1pxT\nSYjMxkhfl9pFbald1BY6V+FxRCxn7j5j/XlvdI8dRTf8OUm6af9FKgVexzwhltr+ntT294RTG0la\nqMMtOxcO5CuGf2E3UqpWwbGiG2WcrCiVzwJjAxnNJN6kqiqLD91M09akVF5c88qEjuLTMjU1xcfH\nh9jYWIyNjTl8+DAODg7vvZ2XlxdXrlzJ0KKSyLwu+IUyfvMV2v2xgi2XdqKDquk7WawaKct/pk8d\nNy0mFELkZK1aVGHf4hq0uHUagCZblnG6Z8vU1/mfWNiLBJaPXsyMvUs0bUcLV6bLNx0o5WDxye9P\niI9lZWpABVMDKhSwSm1oVELTNwVITE55+w3/JSkqCfGSvYUxHSrmh4r5UQc15V5INA73QrnoF8YF\nv1BCXyRQMvjeG7fTU1MoFXyPUsH3wHMv/A7hRmbsKlGXzo0GUMTODDcHC9wcLSiZz4Li9uaYGMi/\nXk536u4zBi8cQaSRKYurdcLXxonB9WSUkkgfTZo0Ye/evbRv355Nmzbx+eefc/p06gvvFy9eMHjw\nYP766y+SkpKYOHEiTZo04YcffiA2NpYzZ84wZswYXFxcGDp0qKY4tWbNGlxdXVm7di27du0iOTkZ\nHx8fhg0bRkJCAhs2bMDQ0JB9+/ZhbW2Nl5cX/fv3JyYmhkKFCrF69WqsrKzw8PCgV69emJiYULNm\nTU3m5ORkRo8ezYkTJ4iPj2fgwIH069dPWw9hjhUVl8jM/bfYefo2OzcMw/VZgKYv0sCEfX1G0+TH\nUVh8wrkZhBDiY5V3suL3rgNpOv4sumoKde97MGr5NmrN7f9JRytFxycxbcJaJm2cjO7LS4qu5S3C\n3bnLZGJukWV86ssz5WJPId5CURQK25nTvZozS7qU58q4Bhz5rjYWP/3I5IV7mdxhNL+VacwtmwKk\n8OYTlWVcNPopSSSnqNx6EsXvHoH88Md1fh04hTV1uzCp+0Qmz/uD5cfvcvJOCE8j41BV9S1JRHa1\nf+0e6vldofWNk+xfM5i2DnqUyCdzKWV7EyeConzYV9++b96+b9+0+0yc+EF327lzZzZv3kxcXBze\n3t5UqVJF0zdt2jTq1avH5cuXOX78OCNGjCAxMZHJkyfTqVMnvLy86NSpE8WKFePUqVN4enoyefJk\nvv/+e80xfHx8+O2337h06RJjx47FxMQET09PqlWrxvr16wHo3r07s2bNwtvbGzc3NyZNmgRAz549\nWbhwIefPn0+TedWqVVhYWHD58mUuX77ML7/8wv379z/u8Rb/yYnbT2k07xS/XgwgxsCYa/ZFNX2X\nC5fn5qGzdF4yXgpKQohM4fMejdhVoo5mu+WO5Ry5+fSTHT8uMZlJM7YybslwzBJiAQjMZcuOSUsZ\n2LzMJ7sfIbIaGS4hxAf4f5GpsJ05VHOGwU15HBGLx4Pn7Lr+gNizF7D29qB00C3KPrqDVVwU1/IW\nfeM4LW+cou59DzgPbIBoA2Nu2xTgsJ0zDxwKk1C8BEblyuBUyJGiecwoksccC2P9DP95RfryeBBG\nrR2rNNv7XWvQo3WVd9xCiP+mdOnS+Pv7s2nTpjcuZzt06BC7d+9mzpw5AMTFxREQEPDGMSIiIujR\nowd3795FURQSExM1fe7u7pibm2Nubo6FhQUtWrQAwM3NDW9vbyIiIggPD6dOndQX+z169KBDhw5v\ntHfr1o39+/drcnl7e7Nt2zbN/d+9e5eiRd88t4pPKzwmgSl7brL9amCa9in1v6J80C1udfgS9/k/\nYGokz09CiMyjtKMlm3sMptWok+i9nFvp+xnLqbZyLGaG/+1tb1xiMhPm7mTY3MFYxUUBqXPJLRy2\ngKm96snCBCJHk6KSEP+SvYUxzUsb07x0Pvi8GnGJyVx/FMmOgOcEXfXhZrgKsa/dQFUpFeyb5hhm\nCbFUeHSLCo9ugRfwchGdx2a5GdF0KGdcymFnbkhhOzPNVyFbMwrampI3l5E8gWVRO347ypTb5zTb\n5zt+Rcv8llpMJHKCli1bMnz4cE6cOEFoaKimXVVVtm/fjqura5r9L168mGZ7/PjxuLu7s3PnTvz9\n/albt66mz9Dw1aSkOjo6mm0dHR2SkpL+MZOqqv94HlNVlUWLFtGoUaM07f7+/u/8OcV/c8DnMRO2\nX6PFyd/JVfozIo3MNH02DnaEXfCgeRE7LSYUQoh/1q1rfbb+9hlfeB0A4Lsd85hfrzbjerr/62O+\niE9iwozfGTlnIHYvngMQZWDMtEE/MWlUBwz05OIfkbNJUUmIT8RIX5cKBaxSJ0SrVRCAiJhEfB5F\n4B0YwfXAMJa2HozdvZuUCPajxFM/bGIi3nos++hQnhunTtj8NCqep1HxnPN9xokVfQk2z81xawcC\nbfMT41wIHdcimBcvilNeK5xtTHCyNsXGzEAKTpnUrSeRlNm0QjPJ7dFClWjRtbGWU4kMM3HiB1+y\n9lYrVqR+/Qu9evXCwsICNzc3Tpw4oWlv1KgRixYtYtGiRSiKgqenJ+XKlcPc3JyoqCjNfhEREZoJ\nvteuXftR921hYYGVlRWnT5+mVq1abNiwgTp16mBpaYmFhQVnzpyhZs2a/Prrr2lyLVu2jHr16qGv\nr8+dO3c+aIJx8e+ERMUzcfd17h09x6p98ykVfI+izwIY2XQoOgr0qVWQ7xoWxUhfFp8QQmRexe1z\n8cfIH3jc9zL20aHYxERQacb3HKu6k3rF83708Z5GxjFw1VmWvFZQitUzZGLv6Yyb0O0/j4ASIjuQ\n/wIh0pGFiT41CttQo7ANUAi6ViIqLpGbj6PY+yiChzf8SPLywuT2DQo/uY9ryAMKhwagn5zMvdxp\nJ/vLGxWKc/hjnMMfU+Vh2qW0kxUdgnLZ4m+VjwNW9jy2ceDUZ51wyGOBk7UJ+a1NyG9lQn5rYxws\nTWRFOi3asuM8318/rtk+3LInMwrl1mIikVM4OjoyZMiQN9rHjx/P0KFDKV26NKqq4uzszJ49e3B3\nd2fmzJmULVuWMWPGMHLkSHr06MFPP/1EvXr1Pvr+161bp5mou2DBgqxZswaANWvWaCbqfn1UUp8+\nffD396d8+fKoqoqtrS27du369w+AeCtVVfnD6xHTdnrxxbHfmHd+KwYpqaPLOv51hEu1mtFt9JeU\nkdGUQogsYmj7yvxwfBQ//jISANsXz/l63TlWDKpHaccPP5f5BEXw1forPI6IY2nVDkw8uoJoA2Mm\n9J3F6Ol9sZL55IQAQMnKkwNXrFhRvXLlirZjCPGfJaeoPAh9wZ3gKO4EhRN64w7nseT+sxckJqf+\nj9a878nGreM/6Hgx+oaU+HZb6kS+LxV+FsCQs5sItMhDuK09CY75UQoUwLCgCzb5bHCwNMLewhh7\nSyNsTA3R0cm4kU6Konioqloxw+7wE/vQc9Gj8Fj2NO5G34vbAbjkWILnB47SqOTHf3ImsoabN29S\nvHhxbccQb/G2301OORf935OIOMbu/IsnJ84xZ998iof4a/ridfW52Otbqi6aioGhzJ0kREbKaeei\n9OD1MJyrbb8kxNSSnyu3JUVHFwtjfX77qgol81m887ZJySn8fMqPBUfukvD/pddVlTEn1nCn5meM\nm9xTCkoiR/jQc5GMVBIiE9DVUShoa0ZBWzMal7KHRqlvdBKTU3gQGoPv02j8nhRmSs1yJN+8hfG9\nu+QLeUjBsECcwx7jEBWS5ngBFnnTFJQAXEMe0OLW6bfef4ShKY9y2fIoly1/mdtw074wJ2q3xt7C\niDwWRuTNZUSeXIbkyWWEnbkRdrkMsTM3xMxQTy6z+wi/HfGhr+d+zfYfDbswpXgeLSYSQuREqqqy\n5fJD5uzyovexDXx1aQd6L5fGBrjpXAqDdWuoXTvLvqcVQuRwZfNbcn72XJYduKVpi4hNpN2ycwxr\n6ErPGs7o/W1Z9ZQUlUM3gjm2fCs3olUS8hZ+1akonO03isVflCOXLFIgRBpSVBIiE9PX1dFM0E2p\nvNDAFWiGqqo8i07g/rMXnH32goCgUGJu3SHlri8mAfeJ0Hnz05P8EcH/eD8W8S+wCHmh+ZT6ZER5\nfi3diKDwVzONf3llN/U99/LUzBofU2uemlkRbpGbeBs7ku3yopM3D3oO+TDJa4eNhRE2ZoY4Whm/\n99OgnCIyLhF+XkGuhBgAfK0dKdX3iwwdESaEEA/DYhi9w5vkY8fZemAxBZ8/0vTF6hlyte8wqsyb\niJ6BvGkSQmRt/esUJCoukaUn7mnadKOjKdyzI1OqNMa0VQvyu9ijquB/25+EQ0dpdmIbPwbd4E5u\nJ1p8OZ94vdTX1L1rujCmSbE3ClFCCCkqCZElKYqCrbkhtuaGVHaxhkr5gbIAmoJT27AXPAyLJSAs\nhodhMQSbNmaqXR5MnwSSL/wpDpGpX/kin2GYnJjm+I/Mbd64zwLhjykUFkShsKB3ZktSdFhRpS1j\n63xJJWcrfu9f/ZP93FnZ1rO+dLmwU7O9qVYHRlTIr8VEQoic5taTSNosOUcx/+vs3PR9mj6fIuUw\n37CGGlXKaCmdEEJ8WoqiMKKRKwlJKaw8cx+AEafW4+7ngbufBwlbZvHcJBcqkDc6LM1ti4YGMPDc\nFtY26c3kViVTV3sWQryVFJWEyGZeLzhVKPB6TxmgE0nJKQRHxRP0PBav8Bj2hcUQEfCIxPsP4OFD\nDJ484nquN5847f72ZPtP9NQUYvVSlxO3MTN8z945Q0JSCisvBHGm8SD6XdpB4dCH5O7XS1ZRyiFU\nVZXLRDOZrDyf5N8pitIX6Avg5OT0zn2L2pnj5mDBpQRXTrhUoO59D6IMTfhr8PdUmTEaXT05Jwkh\nshdFURjbrDiuec1ZvOUc7XyOavoMUpLI85bXtwk6euwoVY9nn3fnUM/a8npWiPeQopIQOYyerg4O\nlsY4WBoD1i9bi6bZ50V8Ek8i4wiOiONJZOqXt9uPeDwMRA0KQjf4CUbPnmIdGYbti+fYvXiOzYtw\nbF88J1f8C0JNU1fWyM5Pwh/zRu7G40jC4xI5UagSJwpVIl9CFHtrF33nbUT2YGRkRGhoKLlz55bC\nUiahqiqhoaEYGRlpO8onoarqCmAFpE6O+659dXQUZrZzo8mC04xr9DWzrm7BedVSqpcqlCFZhRBC\nGxRFoUPF/NRxbcVPzjuw3Por9W6fxy341WVxiTq6XLMvynnnMoR+8SWft61O57zmWkwtRNYhRSUh\nxBtMDfUoZGtGIVuz11oLp9lHVVUiY5MIiY7jaVQ816MTCImK53lYJGpUPO4JUDJfrowNnoE+5o1c\n2fyWnB9dnw0XHrDunD8Nq5WSVUNyCEdHRwIDAwkJCXn/ziLDGBkZ4ejoqO0YWlHQ1oyxzYqjr1uS\n6kt7SrFTCJFj2JkbMWFgY170acCpOyHs9fEnJSoaNTkZI/s8lC/mQA9nK5mIW4iPlGFFJUVRGgML\nAF1gpaqqM//WbwisByoAoUAnVVX9MyqfEOLjKIqChYk+Fib6FLaTT3Lex8rUgG/qF6Fv7YLEJ6a8\n/wYiW9DX18fFxUXbMYRIo3s1Z21HEEIIrTE11KOJmz1N3Oy1HUWIbCFDpq9XFEUXWAI0AUoAnyuK\nUuJvu/UGnquqWhiYB8zKiGxCCJGRjPR1sTCRT8CEEEIIIYQQWV9GrYlYGfBVVdVPVdUEYDPQ6m/7\ntALWvfx+G1BfkTHZQgghhBBCCCGEEJlSRhWVHICHr20Hvmx76z6qqiYBEUDuDEknhBBCCCGEEEII\nIT5KRs2p9LYRR3+f2PZD9kmz4hIQrSjK7Q/MYAM8+8B9MwPJm76yWl7Iepk/Jm+B9AyS3jw8PJ4p\nivLgA3fPzr/HzCCr5YWslzk755VzUeaV1fJC1sssedOXnIveLqv9HiHrZZa86Ss75/2gc1FGFZUC\ngfyvbTsCj/5hn0BFUfQACyDs7wd6fcWlj6EoyhVVVSt+7O20RfKmr6yWF7Je5qyW979QVdX2Q/fN\nao+L5E1/WS2z5M285FyUuWS1zJI3fWW1vP9Fdj4XQdbLLHnTl+TNuMvfLgNFFEVxURTFAOgM7P7b\nPruBHi+/bw8cU1X1nct0CyGEEEIIIYQQQgjtyJCRSqqqJimKMgg4COgCq1VVva4oymTgiqqqu4FV\nwAZFUXxJHaHUOSOyCSGEEEIIIYQQQoiPl1GXv6Gq6j5g39/afnjt+zigQzpG+OhL5rRM8qavrJYX\nsl7mrJY3o2S1x0Xypr+sllnyZg9Z7XHJankh62WWvOkrq+XNKFnxcclqmSVv+srxeRW5wkwIIYQQ\nQgghhBBCfKyMmlNJCCGEEEIIIYQQQmQj2a6opChKY0VRbiuK4qsoyui39BsqirLlZf9FRVGcMz5l\nmjzvy/udoig3FEXxVhTlqKIoWl1i9H15X9uvvaIoqqIoWp0J/0PyKorS8eVjfF1RlN8yOuPfsrzv\n78FJUZTjiqJ4vvybaKqNnK/lWa0oylNFUXz+oV9RFGXhy5/HW1GU8hmdUVvkXJS+5FyUvuRclH3I\nuSh9ybko/WWl85Gci/6ZnIvSV1Y7F73MkqXOR3IuegdVVbPNF6mTgN8DCgIGwDWgxN/2+RpY/vL7\nzsCWTJ7XHTB5+f2AzJ735X7mwCngAlAxM+cFigCegNXLbbtMnncFMODl9yUAf23lfZmhNlAe8PmH\n/qbAfkABqgIXtZk3k/0u5VyUjnlf7ifnovTLK+eiLPAl5yLt5325n5yL0jdzpjkfybnoP/0e5VyU\njnlf7pcpzkUf8RhnmvORnIve/ZXdRipVBnxVVfVTVTUB2Az8r727CbWijOM4/v3HXUT0BkogKVSQ\nUNlCaNMqoTcp8G4LXAgSCNGqpYtEWwUVBO6ziMAiSII2gVZI4koQiiIqSIraVESRGD0tZqjj3PMy\nc73PzDPnfj8wMOfyoD/nzPkt/s59zmpjzSpwoj5/F3g4IqLHjJMW5k0pnU4p/Vm/PAds7znjpDbX\nF+AY8BLwV5/hpmiT9xngeErpF4CU0s89Z5zUJm8Cbq7PbwF+6DHfGimlT6i+rXGWVeCNVDkH3BoR\n2/pJNyi7KC+7KC+7aHnYRXnZRfmNqo/sopnsorzG1kUwvj6yi+ZYtqHS7cD3E68v1T+buial9Dfw\nG7Cll3Rrtck76SDVRHEoC/NGxG5gR0rpgz6DzdDm+u4EdkbE2Yg4FxF7e0u3Vpu8R4D9EXGJ6tsU\nn+sn2rp1vceXhV2Ul12Ul120POyivOyi/Jatj+yiil20scbWRTC+PrKL5li55jhlmTbNbn69XZs1\nfWmdJSLtDLaiAAADdklEQVT2Aw8AD2VNNN/cvBFxHfAqcKCvQAu0ub4rVI9W7qH6H4ZPI2JXSunX\nzNmmaZP3aeD1lNLLEfEg8Gad95/88dalpM9bn+yivOyivOyi5WEX5WUX5bdsfVTS561PdlFeY+si\nGF8f2UVzLNuTSpeAHROvt7P2sbP/1kTECtWjafMeDcupTV4i4hHgMLAvpXS5p2zTLMp7E7ALOBMR\n31H9fuapATeCa3s/vJ9SupJS+hb4kqq8htAm70HgJEBK6TPgemBrL+nWp9U9voTsorzsorzsouVh\nF+VlF+W3bH1kF1Xsoo01ti6C8fWRXTTPok2XxnRQTTO/Ae7k/w207museZarN4E7WXje3VSbgt09\nhuvbWH+GYTekbHN99wIn6vOtVI8Bbik474fAgfr8nvrDHwPfF3cwexO4J7l6E7jzQ2Yt7L20izLm\nbay3izY+r100gsMuGj5vY71dlCdzUX1kF637fbSLMuZtrB+0izpc42L6yC5a8HcNeTNlunhPAF/V\nH/LD9c+OUk2QoZoYvgN8DZwH7io870fAT8CF+jhVct7G2hIKa9H1DeAV4HPgIvBU4XnvBc7WRXYB\neGzgvG8DPwJXqCbeB4FDwKGJ63u8/vdcHPp+KOy9tIsy5m2stYs2Pq9dNJLDLho2b2OtXZQnczF9\nZBdd0/toF2XM21g7eBe1vMZF9ZFdNPuI+g+VJEmSJEmSWlu2PZUkSZIkSZLUA4dKkiRJkiRJ6syh\nkiRJkiRJkjpzqCRJkiRJkqTOHCpJkiRJkiSpM4dKkiRJkiRJ6syhkiRJkiRJkjpzqKQiRcTpiHi0\nPn8xIl4bOpOkzccuklQK+0hSCewiNa0MHUCa4QXgaETcBuwG9g2cR9LmZBdJKoV9JKkEdpGuEiml\noTNIU0XEx8CNwJ6U0u9D55G0OdlFkkphH0kqgV2kSf76m4oUEfcD24DLFpWkodhFkkphH0kqgV2k\nJodKKk5EbAPeAlaBPyLi8YEjSdqE7CJJpbCPJJXALtI0DpVUlIi4AXgPeD6l9AVwDDgyaChJm45d\nJKkU9pGkEthFmsU9lSRJkiRJktSZTypJkiRJkiSpM4dKkiRJkiRJ6syhkiRJkiRJkjpzqCRJkiRJ\nkqTOHCpJkiRJkiSpM4dKkiRJkiRJ6syhkiRJkiRJkjpzqCRJkiRJkqTO/gW3g4F9l6JDSQAAAABJ\nRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1440x180 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "get_ipython().magic('matplotlib inline')\n",
    "\n",
    "x_points = np.linspace(0,1,100)\n",
    "\n",
    "fig, axs = plt.subplots(1, 4, figsize=(20,2.5))\n",
    "\n",
    "axs[0].plot(x_points, True_functions[0][1](x_points), linewidth=4, label='True function')\n",
    "axs[0].plot(x_points, symbolic_metamodels[0].evaluate(x_points), color='red', linewidth=3, linestyle='--', label='Metamodel')\n",
    "axs[0].set_title('$f_1(x)$')\n",
    "axs[0].legend()\n",
    "\n",
    "axs[1].plot(x_points, True_functions[1][1](x_points), linewidth=4, label='True function')\n",
    "axs[1].plot(x_points, symbolic_metamodels[1].evaluate(x_points), color='red', linewidth=3, linestyle='--', label='Metamodel')\n",
    "axs[1].set_title('$f_2(x)$')\n",
    "axs[1].legend()\n",
    "\n",
    "axs[2].plot(x_points, True_functions[2][1](x_points), linewidth=4, label='True function')\n",
    "axs[2].plot(x_points, symbolic_metamodels[2].evaluate(x_points), color='red', linewidth=3, linestyle='--', label='Metamodel')\n",
    "axs[2].set_title('$f_3(x)$')\n",
    "axs[2].legend()\n",
    "\n",
    "axs[3].plot(x_points, True_functions[3][1](x_points), linewidth=4, label='True function')\n",
    "axs[3].plot(x_points, symbolic_metamodels[3].evaluate(x_points), color='red', linewidth=3, linestyle='--', label='Metamodel')\n",
    "axs[3].set_title('$f_4(x)$')\n",
    "axs[3].legend()\n",
    "\n",
    "for ax in axs.flat:\n",
    "    ax.set(xlabel='$x$', ylabel='$f(x)$')\n",
    "\n",
    "for ax in axs.flat:\n",
    "    ax.label_outer()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] Patryk Orzechowski, William La Cava, and Jason H Moore. Where are we now?: a large benchmark study of recent symbolic regression methods. *In Proceedings of the Genetic and Evolutionary Computation Conference*, pages 1183–1190. ACM, 2018.\n",
    "\n",
    "[2] Telmo Menezes and Camille Roth. Symbolic regression of generative network models. *Scientific reports*, 4:6284, 2014.\n",
    "\n",
    "[3] Ekaterina J Vladislavleva, Guido F Smits, and Dick Den Hertog. Order of nonlinearity as a com344 plexity measure for models generated by symbolic regression via pareto genetic programming. *IEEE Transactions on Evolutionary Computation*, 13(2):333–349, 2009.\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}