{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lab 3: Global Optimization with Gaussian Processes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gaussian Process Summer School 2020" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The goal of this lab session is to illustrate the concepts seen during the tutorial in Gaussian processes for Global optimization. We will focus on two aspects of Bayesian Optimization (BO): (1) the choice of the model (2) the choice of the acquisition function.\n", "\n", "The technical material associated to the methods used in this lab can be found in the slides of the tutorial. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Getting started" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In addition to GPy, this lab uses GPyOpt (http://sheffieldml.github.io/GPy/), a satellite module of GPy useful to solve global optimization problems. Please be sure that it is correctly installed before starting by following the Getting Started page." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some of the options of GPyOpt depend on other external packages: DIRECT, cma, pyDOE. Please be sure that this are installed if you want to use all the options. With everything installed, you are ready to start. \n", "\n", "Now, just as in the previous lab, specify to include plots in the notebook and to import relevant libraries." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline \n", "import GPy\n", "import GPyOpt\n", "import numpy as np\n", "from numpy.random import seed\n", "seed(12345)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Remembering the basics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before starting with the lab, remember that (BO) is an heuristic for global optimization of black-box functions. Let $f: {\\mathcal X} \\to R$ be a 'well behaved' continuous function defined on a compact subset ${\\mathcal X} \\subseteq R^d$. Our goal is to solve the global optimization problem of finding\n", "$$ x_{M} = \\arg \\min_{x \\in {\\mathcal X}} f(x). $$\n", "\n", "We assume that $f$ is a *black-box* from which only perturbed evaluations of the type $y_i = f(x_i) + \\epsilon_i$, with $\\epsilon_i \\sim\\mathcal{N}(0,\\sigma^2)$, are available. The goal is to find $x_M$ by minimizing the number of evaluations of $f$. To do this, we need to determine two crucial bits:\n", "\n", "1. A **Gaussian process** that will capture the our beliefs on $f$. \n", "\n", "2. An **acquisition function** that based on the model will be useful to determine where to collect new evaluations of f. \n", "\n", "Remember that every time a new data point is collected the model is updated and the acquisition function optimized again. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Running example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We start with a one-dimensional example. Consider here the Forrester function \n", "\n", "$$f(x) =(6x-2)^2 \\sin(12x-4),$$ defined on the interval $[0, 1]$. \n", "\n", "The minimum of this function is located at $x_{min}=0.78$. We assume that the evaluations of $f$ to are perturbed by zero-mean Gaussian noise with standard deviation 0.25. The Forrester function is part of the benchmark of functions of GPyOpt. To create the true function, the perturbed version and the boundaries of the problem you need to run the following cell. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "f_true = GPyOpt.fmodels.experiments1d.forrester() # true function object\n", "f_sim = GPyOpt.fmodels.experiments1d.forrester(sd=.25) # noisy version\n", "bounds = f_true.bounds # problem constrains (implemented by default)\n", "f_objective = f_sim.f # objective function " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To plot the true $f$, simply write:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f_true.plot(bounds)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "f_objective contains the function that we are going to optimize. You can define your own objective but it should be able to map any numpy array of dimension $n\\times d$ (inputs) to a numpy array of dimension $n\\times 1$ (outputs). For instance:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0.92961609],\n", " [0.31637555],\n", " [0.18391881],\n", " [0.20456028],\n", " [0.56772503],\n", " [0.5955447 ],\n", " [0.96451452],\n", " [0.6531771 ]])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = 8\n", "x = np.random.rand(n).reshape(n,1)\n", "x" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 9.99379804],\n", " [ 0.30951655],\n", " [-0.53213703],\n", " [-0.92083089],\n", " [ 0.70757395],\n", " [ 0.04499155],\n", " [14.12247715],\n", " [-2.14113699]])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f_objective(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The bounds of the problem should be defined as a tuple containing the upper and lower limits of the box in which the optimization will be performed. In our example:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "bounds = [{'name': 'var_1', 'type': 'continuous', 'domain': (0,1)}] " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To use BO to solve this problem, we need to create a GPyOpt object in which we need to specify the following elements: \n", "* The function to optimize.\n", "* The box constrains of the problem.\n", "* The model, that is fixed by default to be a GP with a SE kernel.\n", "* The acquisition function (and its parameters)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We create an SE kernel as we do in GPy" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "k = GPy.kern.RBF(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now we have all the elements to start optimizing $f$. We create the optimization problem instance. Note that you don't need to specify the evaluation budget of. This is because at this stage we are not running the optimization, we are just initializing the different elements of the BO algorithm. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# Creation of the object that we will use to run BO.\n", "seed(1234)\n", "myBopt = GPyOpt.methods.BayesianOptimization(f = f_objective, # function to optimize \n", " domain = bounds, # box-constrains of the problem\n", " kernel = k, # kernel of the GP \n", " acquisition_type='EI') # acquisition = Expected improvement" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "?GPyOpt.methods.BayesianOptimization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At this point you can access to a number of elements in myBopt, including the GP model and the current dataset (initialized at 3 random locations by default)." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0.19151945],\n", " [0.62210877],\n", " [0.43772774],\n", " [0.78535858],\n", " [0.77997581]])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "myBopt.X" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[-0.95287634],\n", " [-1.19407487],\n", " [ 0.29000479],\n", " [-5.3506129 ],\n", " [-5.22815975]])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "myBopt.Y" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# Run the optimization (may take a few senconds)\n", "max_iter = 15 # evaluation budget\n", "myBopt.run_optimization(max_iter) # run optimization " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And that's it! You should have receive a message describing if the method converged (two equal x's are selected in consecutive steps of the optimization) or if the maximum number of iterations was reached. In one dimensional examples, you can visualize the model and the acquisition function (normalized between 0 and 1) as follows." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "myBopt.plot_acquisition()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can only make the previous plot if the dimension of the problem is 1 or 2. However, you can always how the optimization evolved by running:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "myBopt.plot_convergence()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first plot shows the distance between the last two collected observations at each iteration. This plot is useful to evaluate the convergence of the method. The second plot shows the best found value at each iteration. It is useful to compare different methods. The fastest the curve decreases the better the method. \n", "\n", "Noise variance of the GP is automatically bounded to avoid numerical problems. In case of having a problem where the evaluations of $f$ are exact you only need to include 'exact_feval=True' when creating the BO object as above. Now, to run the optimization for certain number of iterations you only need to write:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "

\n", "Model: GP regression
\n", "Objective: -2.215595518683344
\n", "Number of Parameters: 3
\n", "Number of Optimization Parameters: 3
\n", "Updates: True
\n", "

\n", "\n", "\n", "\n", "\n", "\n", "
GP_regression. value constraints priors
rbf.variance 2.2938619468750314 +ve
rbf.lengthscale 0.11088633298610727 +ve
Gaussian_noise.variance0.00266399824756187371e-09,1000000.0
" ], "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "myBopt.model.model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use Bayesian optimization to find the minimum of the function $f(x)= x^2 + 10 \\sin(x)$ in the interval [-10, 10]. \n", "\n", "(a) Define the bounds of the problem, the function and check that it admits a numpy array of observations as input." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[8.56492259],\n", " [3.15258865],\n", " [5.64364388],\n", " [6.70667823],\n", " [4.78655946],\n", " [5.46222156],\n", " [8.2777045 ],\n", " [2.81455086]])" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def g(x):\n", " return x**2 + 10*np.sin(x)\n", "\n", "bounds_g = [{'name': 'var_1', 'type': 'continuous', 'domain': (-10,10)}] \n", "\n", "x = np.random.rand(n).reshape(n,1)\n", "g(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(b) Create a GPyOpt object for global optimization using a Mattern52 kernel and adding a gitter of $0.1$ to the expected improvement acquisition (Hint: when creating the object use the option acquisition_par = 0.1). " ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "k_g = GPy.kern.Matern52(1)\n", "\n", "BO_g = GPyOpt.methods.BayesianOptimization(f = g, \n", " domain = bounds_g, \n", " kernel = k_g, \n", " acquisition='EI',\n", " acquisition_par = 0.1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(c) For stability reasons, constrain the noise of the model to be 10e-4. " ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "BO_g.model.noise_var = 0.0001" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(d) Run the optimization for 10 iterations. Make and comment the convergence plots. Has the method converged? " ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "BO_g.run_optimization(10)\n", "BO_g.plot_acquisition()\n", "BO_g.plot_convergence()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Acquisition functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this section we are going to have a look to different acquisition functions. In GPyOpt you can use the expected improvement ('EI') the maximum probability of improvement ('MPI') and the lower confidence bound. When using GPyOpt you can simply specify the acquisition that you want at the moment of creating the BO object. However, you can also load these acquisitions as separate objects." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "from GPyOpt.acquisitions import AcquisitionEI, AcquisitionLCB, AcquisitionMPI " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To access these acquisitions 'externally' we create a GP model using the objective function in Section 1 evaluated in 10 locations." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "seed(1234)\n", "n = 10\n", "X = np.random.rand(n).reshape(n,1)\n", "Y = f_objective(X)\n", "m = GPy.models.GPRegression(X,Y)\n", "m.optimize()\n", "m.plot([0,1])\n", "\n", "## Now we pass this model into a GPyOpt Gaussian process model\n", "\n", "from GPyOpt.models import GPModel\n", "model = GPModel(optimize_restarts=5,verbose=False)\n", "model.model = m" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define the bounds of the input space to be between zero and one." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "from GPyOpt import Design_space ## GPyOpt design space\n", "\n", "space = Design_space([{'name': 'var_1', 'type': 'continuous', 'domain': (0,1)}] )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's have a look to see what do we need to create an acquisition, for instance the Expected improvement and the Lower Confidence Bound." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "AcquisitionEI?" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "AcquisitionLCB?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we create thee objects, one for each acquisition. The gitter parameter, to balance exploration and exploitation, need to be specified." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "acq_EI = AcquisitionEI(model,space, jitter = 0)\n", "acq_LCB = AcquisitionLCB(model,space,exploration_weight = 2)\n", "acq_MPI = AcquisitionMPI(model,space,jitter = 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The objects acq_EI, acq_LCB, acq_MPI contain the acquisition functions and their gradients. By running the following piece of code you can visualize the three acquisitions. Note that we add a negative sign before each acquisition. This is because within GPyOpt these functions are minimized (instead of maximized) using gradient optimizers (like BFGS) to select new locations. In this plot, however, the larger is the value of the acquisition, the better is the point. " ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot the three acquisition functions (factor 0.1 added in in the LCB for visualization)\n", "X_grid = np.linspace(0,1,200)[:, None]\n", "plt.figure(figsize=(10,6))\n", "plt.title('Acquisition functions',size=25)\n", "plt.plot(X_grid, - 0.1*acq_LCB.acquisition_function(X_grid),label='LCB')\n", "plt.plot(X_grid, -acq_EI.acquisition_function(X_grid),label='EI')\n", "plt.plot(X_grid, -acq_MPI.acquisition_function(X_grid),label='MPI')\n", "plt.xlabel('x',size=15)\n", "plt.ylabel('a(x)',size=15)\n", "legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(a) According to the previous plot, what areas in the domain are worth exoloring and why? How can we interpret the previous plot in terms of the exploration/exploitation trade off of each one of the three acquisitions?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(b) Now make a plot comparing the shape of the LCB acquisition (of GP-UCB in the literature) with values different values of parameters. Use the values $[0,0.1,0.25,0.5,1,2,5]$. How does the decision about where to collect the sample change when we increase the value of the parameter?" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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cuuR3vqqqKsLDw889NhgM7N2795J2e/bsIT09ndDQUH7zm9+Qmmr+4dSSYNnY3NvW0N/Xx963/42jswtLv/SQrUMSQgghJoWh9jkrpS54PGPGDMrKyvDw8GDjxo187nOfw2g0mj22JFg2ppRi/p330NvVycFN7+AbFk768htsHZYQQghhOVeYabIWg8FARUXFuceVlZWEhoZe0MbL67Pzg1euXMlXv/pVGhsb8ff3N2tsWY+aAJRSLF57P9EZM9n2wjrKjx2xdUhCCCGE3Zs1axZGo5GSkhJ6enp47bXXWLVq1QVtamtrz8107du3D5PJhJ+fn9ljS4I1Qeh0em78xnfxCQ7l3ad/IcVIhRBCCDM5ODjwzDPPsGLFCpKTk7njjjtITU1l3bp1rFu3DoA33niDqVOnkp6ezmOPPcZrr712yTLiWKiJVIcpMzNTO3DggK3DsKlTtdX86/FvEBAZwx0/flLKNwghhLBL+fn5JCcn2zoMixnq81FK5WialjlUe5nBmmCmBIey7L5HqCo4zv4Nb9o6HCGEEEKMgSRYE1DywqUkzlvEp/95mdqiE7YORwghhBCjJAnWBKSU4toHvor7FF82Pfs7+vt6bR2SEEIIIUZBEqwJysXdg+UPPEpzdSUH3vuvrcMRQgghxChIgjWBRU/PJH72PLLffE3uKhRCCCHsiCRYE9ySex9EKcX2F9fbOhQhhBBCjJAkWBOcl38AWZ+/m+IDezl5aL+twxFCCCHsxn333UdgYCBTp04d8nVN03jssceIi4sjLS2NgwcPWmxsSbDswIwbVuETHMLuV15EM5lsHY4QQghhF770pS+xefPmYV/ftGkTRqMRo9HI+vXreeSRRyw2tiRYdkDv4MD8O+6hobyUgk932jocIYQQwi4sWrQIX1/fYV/fsGEDa9euRSnF3LlzaWlpoaamxiJjy2HPdiIxayH73nmTT17/Fwlz56N3cLR1SEJMWpqmUWMsoPpEAW5e3nj4+hEUE4+zm5utQxPCLv1y3y8paC6waJ9Jvkl8b/b3zOqjqqqK8PDwc48NBgNVVVWEhISYG54kWPZC6XQsXLOWt556gqNbPyRjxY22DkmIScdk6ufAu29zZOtmTtfVXvCaq6cX8+64h7RlK9Dp5QgrISaDoY4LtMQ5hCAJll2JypiJIXkq2W//m6nXXIeDo8xiCWEp3R0dvP/HX1Fy6ADhqWlk3XYX0Rkz6Wpv53RdDfveeYOtf3+O3A/f53Pf/RHegcG2DlkIu2HuTJO1GAwGKioqzj2urKwkNDTUIn3LHiw7opRi7uo1tJ9qJm/nNluHI8Sk0dpQz6s/+g5lRw5x7QNf5Y7/fZLUxctw8/bBNzSM6OmZ3PG/v2DVt35AW3MTr//0h7Q21ts6bCGEmVatWsVLL72EpmlkZ2fj7e1tkeVBkATL7kRMSycwOpYD776JydRv63CEsHu93V28/auf0naqidt+8DPSl68csp1Sivg587j9//s5XW1n+M9Pf0hbc9M4RyuEGI277rqLrKwsCgsLMRgM/P3vf2fdunWsW7cOgJUrVxITE0NcXBwPPvggzz33nMXGVkOtP9pKZmamduDAAVuHMeEV7tnFe7//JTd/6/skzJlv63CEsFuaprH5uafJ27Wd2x5/gqiMmSO6rvpEAW/834+YEhLK3T//LXoH2W0hxMXy8/NJTk62dRgWM9Tno5TK0TQtc6j2MoNlh+LnzMMnKIT9G94YcoOeEGJkjm79gLyd28i67a4RJ1cAoQlJ3PDVb1JfUszet1+3YoRCCHslCZYd0un0ZN58K7XFRiqOH7V1OELYpZa6Wrb94y9Epc8g67Y1o74+fs48kuYvZu/b/6aupNgKEQoh7JkkWHYqdfG1uHp6cfiD92wdihB2aefLz6N0OlY8/A2UbmzfCq+572FcPb3Y/NzT9PX2WjhCIYQ9kwTLTjk4OTF16XKKDmRzprnR1uEIYVcq845h3Psps2+5HQ9fvzH34+rhyfKHvkZjeSm5H75vwQiFEPZOEiw7lnbtDWiaxtGtH9g6FCHshmYyseOff8PDz5/Mm241u7/YmXOImJrOvg1v0NPVaYEIhRCTgSRYdswnKJio9Bkc3foB/X19tg5HCLuQv3sHdSeLWHjXvTg6u1ikz/l3fpGO0y0c2vSuRfoTQtg/SbDsXPrylbSdaqY4Z6+tQxFiwtNMJrLffp2AqBiS5y+2WL+hCUnEzJjF/nffpKu9zWL9CiHMU1FRwdKlS0lOTiY1NZU//OEPl7TRNI3HHnuMuLg40tLSOHjwoEXGlgTLzsXMyMTTP4DcDzfaOhQhJrySwzmcqq5k1s2rx7yxfTjz7riH7vZ2ct7fYNF+hRBj5+DgwG9/+1vy8/PJzs7m2WefJS8v74I2mzZtwmg0YjQaWb9+PY888ohFxpYEy87pdHrSrllB+bFcTtfXXvkCIa5iOe+/jYefPwlzF1i876DoWOLnzOPQpnfo7eqyeP9CiNELCQlhxowZAHh6epKcnExVVdUFbTZs2MDatWsHjqObO5eWlhZqamrMHlvKD08CKYuu4ZPX/0Xeru1k3XaXrcMRYkKqLz1J+bEjLPrCl61WeX3mys9h3Psp+Z/sIG3Z9VYZQwh7VPvkk3TnF1i0T+fkJIJ/8IMRty8tLeXQoUPMmTPnguerqqoIDw8/99hgMFBVVWX2mYQygzUJeAUEEp6aRt7ObVLZXYhh5Lz3No4urkxbtsJqY4QmJhMQGc3hze/J/0UhJpC2tjZuu+02fv/73+Pl5XXBa0P9X1VKmT2mzGBNEimLruGDP/+e6hMFhCVOnrOfhLCE9pZTFHy6k4zrbsTF3cNq4yilyFhxEx+t/xNVBccxJE+12lhC2JPRzDRZWm9vL7fddhtf+MIXWL169SWvGwwGKioqzj2urKwkNDTU7HFlBmuSSJgzDwdnZ/J2brV1KEJMOHm7tmPq7yf9upVWHyt5wWKc3d059IEUHhXC1jRN4/777yc5OZlvfetbQ7ZZtWoVL730EpqmkZ2djbe3t9nLgyAzWJOGk6sb8bPnUbhnF0vvfQgHJydbhyTEhKBpGnkfbyUkPhHfUIPVx3N0dmHq0us4tOkd2pqbzKoUL4QwzyeffMI///lPpk2bRkZGBgBPPvkk5eXlADz88MOsXLmSjRs3EhcXh5ubGy+88IJFxpYEaxJJXbSM/F3bKc7ZS2LWQluHI8SEUF96ksaKMpbd/9VxGzNj+Upy3nub4x9vZc6td4zbuEKICy1YsOCK+yGVUjz77LMWH1uWCCeR8KnT8JjiS8EnO20dihATRt7ObegdHEicN36/dPgEhxCWlELeru2y2V2Iq5QkWJOITqcnfs58Sg/nyJloQgD9fX3k795BzMzZuHp4juvYyQuW0FxVQX3pyXEdVwgxMUiCNckkzJ1PX28PJ3P22ToUIWyuNDeHztbTpC5eNu5jJ8xdgE6vJ3/3jnEfWwhhe5JgTTJhiSm4T/GlcM9uW4cihM3l7dqBq6cXUekzx31sV08vojJmUvjJx5hM/eM+vhDCtiTBmmSUTkf87HmyTCiuer093ZQc3E/8nHlWq9x+JckLltB2qpnKvGM2GV8IYTuSYE1CiVkLZJlQXPXKj+bS291F/Kwsm8UQO3M2ji6uskwoxFVIEqxJ6Owy4YnsT2wdihA2U7R/D06uboRPTbNZDI7OLsTPzsK491P6+3ptFocQV6uuri5mz55Neno6qamp/PjHP76kjaZpPPbYY8TFxZGWlsbBgwctMrYkWJPQ2WXCkkMHZJlQXJVM/f0UH9hLzIxZ6B0cbRpL/Jz5dHe0UyHLhEKMO2dnZ7Zt20Zubi6HDx9m8+bNZGdnX9Bm06ZNGI1GjEYj69ev55FHHrHI2JJgTVLxs+fR19tD2ZFDtg5FiHFXVZhH55lW4my4PHhWZFoGDs7OFO3PvnJjIYRFKaXw8Bg4f7S3t5fe3t5LDnLesGEDa9euRSnF3LlzaWlpoaamxuyxpZL7JBWWlIKzuzvFB/YRP3uercMRYlwV7c9G7+hIdMYMW4eCo5MzUWnTKc7Zy7L7Hr7km7sQV4Ndr5+gsaLNon36h3uw8I6EK7br7+9n5syZFBUV8eijjzJnzpwLXq+qqiI8PPzcY4PBQFVVldnnEcoM1iSld3AgOiOTk4f2yy3i4qqiaRpF+/cQOS0DJ1c3W4cDQGzmXNqaGqkvKbZ1KEJcdfR6PYcPH6ayspJ9+/Zx7NiFy/VDnbZgiV+EZAZrEovNnEPBJx9TYzxBWGKyrcMRYlw0lJXQ2lDP3NVrbB3KOTEzZqGUjqID2QTFxNk6HCHG3UhmmqzNx8eHJUuWsHnzZqZOnXrueYPBQEVFxbnHlZWVhIaGmj2ezGBNYtEZM9Hp9RTn7LV1KEKMm5LDOQBET8+0cSSfcfPyJiwpRfZhCTHOGhoaaGlpAaCzs5MtW7aQlJR0QZtVq1bx0ksvoWka2dnZeHt7m708CJJgTWrObu4YUqZRfEASLHH1KMs9SEBEFB5TfG0dygXiZs2lsbyU0/W1tg5FiKtGTU0NS5cuJS0tjVmzZrF8+XJuuukm1q1bx7p16wBYuXIlMTExxMXF8eCDD/Lcc89ZZGyzlwiVUuHAS0AwYALWa5r2B6WUL/BvIAooBe7QNO2UueOJ0YmdOYft//gLp2qqmBISZutwhLCqnq5OqgrzmbFyla1DuURs5lx2vPQ3ivbvZeaNt9g6HCGuCmlpaRw6dOnd9A8//PC5j5VSPPvssxYf2xIzWH3AtzVNSwbmAo8qpVKAx4GtmqbFA1sHH4txFjtzNoDMYomrQsXxo5j6+4hKt/3dgxfzCQrGN9RA6RHLFDEUQkxsZidYmqbVaJp2cPDjM0A+EAbcArw42OxF4HPmjiVGzzswCP+IKEoOH7B1KEJYXWnuQRycnAlLTLF1KEOKSp9BZd4x+np6bB2KEMLKLLoHSykVBUwH9gJBmqbVwEASBgQOc81DSqkDSqkDDQ0NlgxHDIrOmEllfp5UdReTXtmRQ4SnTMXBycnWoQwpMn06fT3dVBYct3UoQggrs1iCpZTyAN4E/p+maa0jvU7TtPWapmVqmpYZEBBgqXDEeaLSZ2Lq76Pi+BFbhyKE1Zyur+NUTRWRaRNvefCs8ORp6B0cKM2VZUIhJjuLJFhKKUcGkquXNU17a/DpOqVUyODrIUC9JcYSoxeWlIyjswslh3JsHYoQVnP2WKiJuP/qLEcXF8KSUuUIKyGuAmYnWGqg3OnfgXxN03533kvvAPcOfnwvsMHcscTY6B0ciZiWTsnhnCEr1goxGZTmHsTTLwDfMIOtQ7msyLTpNJaX0tbcZOtQhBBWZIkZrPnAF4FrlFKHB/+sBJ4CliuljMDywcfCRqLSZ9LaUMepmmpbhyKExWkmExV5R4mYlj7hz/o7O8NWKrNYQoyLqKgopk2bRkZGBpmZlxYg1jSNxx57jLi4ONLS0jh40DJL+GbXwdI0bTcw3He0Zeb2Lyzj3Df13Bx8Q6UelphcGivK6Go7Q3jKNFuHckUBkdG4eftQduQQU5dca+twhLgqbN++HX9//yFf27RpE0ajEaPRyN69e3nkkUfYu9f80kZSyf0q4RMUzJSQMEoPyz4sMflU5A0c3mpInnqFlranlCIqbTplRw6hmUy2DkeIq96GDRtYu3YtSinmzp1LS0sLNTU1Zvcrhz1fRaIyZnB064f09nTj6ORs63CEsJjK/KN4+gfgHRhk61BGJDJtOnm7ttNQXkpgVIytw7G47o52aouNBERE4ebtY+twxASw/R/rqS87adE+AyNjWPqlh67YTinFddddh1KKr3zlKzz00IXXVFVVER4efu6xwWCgqqrK7PMIJcG6ikSlz+DQpnepKsgjKm26rcMRwiI0TaMy/zjRE/juwYsZUgZm2irzjk6qBKu1oZ6DmzZwdNuH9HQO1N3zDgombdn1zFp124TfHycmp08++YTQ0FDq6+tZvnw5SUlJLFq06NzrQ938ZYl/q5JgXUUMyVPR6fWUH8uVBEtMGs1VFXS2nsZgB/uvzvLyD8Q7KJiKvKPMWDk5ziVsKCvhtR9/j76ebhLnLSIxayHN1ZWU5h5k1yv/oJvP2uwAACAASURBVKGshBUPf2PCFoEV1jWSmSZrCQ0NBSAwMJBbb72Vffv2XZBgGQwGKioqzj2urKw8d405ZA/WVcTJxZWQ+ETKj+baOhQhLKYyf3D/VcrE3391vvCUaVTmHZsU+7DONDXy1lNP4OTqypef/gsrv/ZtYmfOZtbNq7n9hz9jwZq1FHzyMa//7Ad0d3TYOlxxFWlvb+fMmTPnPv7www+ZOvXC7xWrVq3ipZdeQtM0srOz8fb2Nnt5ECTBuupETM2grqSIzrYztg5FCIuoyDuGxxRffILM/4Y4nsJT0+hqb6OhvNTWoZilu6Odt556gp7OTlY//gQ+QcEXvK6UYs6td3DzNx+n1niCbc//2UaRiqtRXV0dCxYsID09ndmzZ3PjjTdy/fXXs27dOtatWwfAypUriYmJIS4ujgcffJDnnnvOImPLEuFVJmJaOnveeIXK40eJnzPP1uEIYZaB/VfHCE+ZZnf7e87e8Vhx3L73YX38r+dprqpg9eM/ISAyeth2CXMXMPe2Mva88SrRM2aRNG/RsG2FsJSYmBhycy9dtXn44YfPfayU4tlnn7X42DKDdZUJiUvE0cWVsqOHbR2KEGZrqa2m/VSzXZRnuJiXfwA+QSFU5B21dShj1lRZzrFtH5Fx3Y1EpmVcsf3c1WsIiU9ky9+epbVRTk8Tk5skWFcZvYMDhuRUyo/JPixh/yoLjgP2Uf9qKIaUaVTl2+8+rF2vvoijiwtzVt85ovY6vZ6VX/sOpn4TH/7lT1aOTgjbuqoSLM2kUXq0kdqTpzlV207nmR5M/fb5jc0ckdMyOFVTRWtjg61DEcIs1YUFuLh72O3pBOGp0+x2H1ZlwXGKD+xl9i234+blPeLrfIJDmH/HFyg7ckh+0ROT2lW1B6u7s4/3nz1yyfNOLnpcvZzw8HHG/ewfb2e8/F3wCXLDK8AVvX7y5KIRU9MBKD+WK0d1CLtWYywgJD4RpbPP/5+f7cM6Ylf7sDRNY+fLL+AxxZcZK1eN+vr05SvJeX8Du159kbt//lu72z8nRk7TtEnx9R2qVtaVXFUJlqOLntu+N5Pu9j662nvp7uilq72P7vZe2k/30HG6m5ri07Sf7sbU99mbqXQKL38XpgS54RfmQVCMN0FRXrh52Wc9F//wSNy8fSTBEnatq72NpspyEucttHUoY+blH4B3UDCV+ceYeePnbB3OiNUYC6g5UcCy+x7B0dll1Nc7ODmRdftdfPiXP1J8YC9xs+ZaIUphay4uLjQ1NeHn52fXSZamaTQ1NeHiMrp/61dVgqXX6wiOvvJUtqZpdLX1crqxk5a6DlpqO2ip6+BUXQflx5sxmQaSLy9/F4KivQmN9yEixRcvf1drfwoWoXQ6DCnTqMg7Oml+uxBXn1pjIQCh8ck2jsQ8YQnJlOQetKv/i0e2foCjswspi5aOuY/UxcvY/86b7H7tJWJmzkKn01swQjERGAwGKisraWiw/+0oLi4uGAyGUV1zVSVYI6WUwtXTCVdPp0sSst6efhrKz1B3spW6ktNUnziFcX8dAFOC3YjJCCAuMxC/MI8J/c0yPHkqJ/bs4nR93SV1a4SwB9XGAlCK4LgEW4diltDEFPJ2baeltpopIRN/L1l3RweFe3aRPH8xTq5uY+5Hp9cz/857eO/3v+RE9idStmEScnR0JDp6+NIdk50kWKPk6KQnNM6H0LiBA0w1TaNlcGar9GgjBz8sJ2dzGVOC3UhZEEpSVggu7o42jvpShuRUYKAKtiRYwh5VnyjAPzwSZ7ex/5CfCMISB2bgqgrz7SLBKvhkB33d3UxbtsLsvhLmzMcnKISDm96RBEtMOva5M3QCUUoxJdid9GXh3PL/pvPlX85n8d2JOLk68MkbRfzje5+w/Z/5tNRNrOMh/AwRuHh6UZl3zNahCDFqmslEbdEJQuOTbB2K2fwMETi7u1NdmGfrUEbkyNYPCIiIIjjW/JlDpdMx/fqbqDlRQG3RCQtEJ8TEIQmWhbl6OjF1URi3fy+TO/+/WSRlBVO4t45Xnsjmg78do6V+YiRaSqfDkJRKZb79FjkUV6+mqgq6O9oJSbD/BEvpdIQmJFNVmG/rUK6o7mQR9SXFTFu2wmJbIFKXLMfJ1ZWDm9+1SH9CTBSSYFmRv8GTJV9IYu2T85h+XSSlR5t49Sd72fX6Cbrae20dHobkqZyur5N6WMLuVJ8oACB0EiRYAGGJKTRXVUz4M0KPf7wVB0cnkheMfXP7xZzd3Ehdci2Fn+6i7VSzxfoVwtYkwRoHbl5OZN0ayz0/nUtSVghHt1fyyhPZFOXUj6m2hqUYUgZq8FTlyzKhsC81xgJcPDztYs/SSIQO7sOqnsCzWJqmYdy/h6iMGbh4eFi07+krbsJk6if3o00W7VcIW5IEaxy5ezuz9J4kPv+DWXhMceGDvx5j07qjdLb12CSegMgonN3cqZAES9iZGmPhQIHRCXyn7mgEx8aj0+upmsD7sOpLimlraiRuVpbF+54SEkbM9EyObNlEf1+fxfsXwhYkwbKBgHBPbv/eTLJujaXseBOv/99+aopaxj0OnU5PWFIKlfnHx31sIcaqp7ODpqoKQuISbR2KxTg6uxAYHTuhN7oX7d+DUjpiZsyySv/TrllBx+kWSnNzrNK/EONNEiwb0el1zFgRye3fzUSnV7z9u0Pkbq0Y9yVDQ/JUTlVX0t5yalzHFWKs6kqKQdMIjo23dSgWFZaYQm2xkb5e2+/PHErR/mwMyam4enpZpf/o6Zm4eftwbPsWq/QvxHiTBMvGAiI8ueOHs4lO82f3f4zs+rfxXKX48XB2H5bMYgl7UVdsBCBokiVYoYnJ9Pf20lB60tahXOJUbTWNFWVWPdJG7+BA8sKlnDy4j47T4z+jL4SlSYI1ATi7OnD9Q1OZvjyCozsq2bTuKL09/eMydmBULI7OLlKuQdiN2mIjXgGBuHld+dgrexISP7DkWVNUaONILlW8PxuA2Ezrnhk4dcm1mPr7yd+9w6rjCDEeJMGaIJROMe+2OBbflUDp0Ubef/bIuCRZegcHQhOTpeCosBt1J4sIiomzdRgW5+nrj4evHzXGiZdgFR3IJiAyGu/AIKuO4x8eSXBcAsd2bLHpHdZCWIIkWBPM1MUGrv1SClUnTo1bkhWeMo3GijI6z7RafSwhzNHV1kZLXY1FqohPRCFxiRNuBquj9TTVhQVWXR4839Ql19JYXkrdyaJxGU8Ia5EEawJKnBN8Lsna+NwR+vtMVh0v7Oy5hAWyD0tMbLUnB/dfWXkGq6+nn9qS0xj311F+vIn6stZx+WUnJD6R03W1dLSetvpYI1V+LBdNMxGdkTku4yXOW4Te0ZH8XdvHZTwhrEUOe56gEucEY+rX2PZSPtv/WcCyLyVbreZPcGwCDo5OVOYdI94KNW6EsJRzG9ytkGBpJo3iQw0c3lJOfdkZtItuNnFw1hOT7k/inGDCU3yt8v/xbOmJGmMhsTNnW7z/sag4dgQnV7dxW5Z1cfcgOiOTwuzdLF57PzqdflzGFcLSJMGawJLnhdDe0sXed0rw8HVm7i2xVhnHwdGRkIQkKqXgqJjg6k4WMSUkFBd3y1YSL89rYvfrRk7VduAd6MqMFREERnjhHehKT1c/Ha3dlB9vpvhgPSf21RGePIXFdyfiHeBm0TiCYuJQOh21RRMnwSo/lkt46jR0+vFLdJLmL6Jo/x6q8o8Tnpo2buMKYUmSYE1wM2+I4kxzNzmbyvAJdCMpK8Qq4xiSU8l+8990d7Tj7OZulTGEMFdtsZGwpBSL9Wcyaex/r4QDm0qZEuTGdQ+kEjsjEJ3u0tmp2OmBLLozgeO7q8neUMyrP91H1q2xpC01WGw2y9HFBf+IKKonyEb31oZ6WupqmH79TeM6bsz0WTg6u1Dw6U5JsITdkj1YE5xSisV3JRCW6MOOVwppqLDOYbCG5GlomomqgolbSVpc3dpbTnGmqcFiS1U9XX28+8fDHNhYSlJWCJ//wSziM4OGTK7O0jvqSFtq4O4fzyU82ZfdrxvZ/R/jJcuJ5giJS6C26ASaybp7L0ei/FguABFT08d1XEcXF2Iz53Bi76dydI6wW5Jg2QGdXsd190/Fxd2RzX85Sle75Ss9hyQkotM7yDKhmLDqSgbuKrNEBfe+nn42/vkIVSdaWPrFJJatTcbRaeRLYB5TnFn58DTSrwnnyLZKPvz7cYvdjBISn0RPZwfN1VUW6c8c5cdycfP2wS88ctzHTpy3iK4zreeSPCHsjSRYdsLNy4nrH5pK26lutvwjz+I1YhydnAmOS5B6WGLCqisuAqUIjDZvL2J/n4nN649RdaKFZfcmkzI/dEz9KJ1i/ufjmLc6jqKcerb/s8Ai/y8/2+heYHZf5tA0jfJjuURMTbfJodpR6TNwdnOn8NOd4z62EJYgCZYdCY7xZv7tcZQdbeLYx5b/7daQnEpdSRG93V0W71sIc9WXnmRKSBhOLq5j7kPTNHb8q4CyY00suTuRxDnBZsWklGL6dRHMvjmawr217H+/1Kz+AHxDw3B2c7d5wdHmqgraW07ZbA+Ug6MjcbOzMO7bQ19Pj01iEMIckmDZmWlLDESk+PLpm0Wcqm23aN9hSSmY+vupLTph0X6FsIT60pMERkab1UfBnhoKsmvJvDGK1IVhFooMMldGkZQVzP73SijMrjGrL6XTERQbf67ml62cXZqLnDa++6/OlzR/MT2dHZQcPmCzGIQYK0mw7IxSimvWJqN30rHlhTz6+y23ETY0PhmUko3uYsLpamujtaHOrOXBpqo2dr56grDEKcy60bxE7WJKKZZ8IYmwRB+2v1xIc415v/wExcTRWF5GX6/l91uOVMXxo3gFBOEdaN4snzkiUtNw9fKm4NNdNotBiLGSBMsOufs4s+TuJOrLznDogzKL9evi4YF/eCRVhZJgiYmlvvQkAIFRMWO6vrennw/+egxHVweW35dy2TsFx0rvoGP5fak4Ouv56HnzNr0Hx8Rh6u+jsbzUcgGOgqZpVBXmYTCzJIZm0miuaed0Q8eY9qfp9HoS5i7gZM4+ero6zYpFiPEmdbDsVNzMQIpyAjmwsYy4mUH4BFmm4GFYYgr5u7djMvVLBWUxYTSUmZdgHdhYyqnaDlZ9IwN3b2dLhnYBd29nlt6TxKZ1R9n37kmybh1bSYmzpSjqThotctfkaJ2ur6PjdAuhicljur4ir5mDH5ZRX9pKT9fAEUNOrg4ERXky4/ooDIlTRtxX0ryF5H74PsU5+0iev3hM8QhhCzKDZccW3hmP3lHHjlcsc/cSDOzD6unspLHccjNjQpirvqQYjym+uHn7jPrapuo2Dn9YTlJWMOHJvlaI7kIxGQGkLAjl4IflVBtbxtSHV0AQLh6eNjvwuPpEPgChCaNLsLrae9n6Yh7v/PEwpxs6SZgdzLJ7k1l6TxLxs4I4VdfBhqcPsXn9Uc40j+xmmrDEFDx8/eRuQmF3ZAbLjrl7O5N1aywfv1JIYXatRaq8n62SXVVwfMyzBUJYWn3pyTHtv9I0jY9fKcTRVc+81eNzlh7Ags/HU5HXzMevFnLHD2eh14/ud1mlFEExcdTaKsEqzMfJ1RW/8IgRX3OmuYu3fpNDe0sPM66PZNaNUTg4fjYLngL09cRxeEs5OZvLqDrRws1fTycw0uuy/SqdjsSshRza/B5dbW24eFj2mCQhrEVmsOxc6oJQgmO8+eSNIosUIPXyD8TTL4BK2eguJoi+nh6aqioIiBx9wl+wp5aaotPMWx2Hq6eTFaIbmqOzngV3xNNc3c7R7ZVj6iMoJo6mijKblCioPpFPSHzSiLcJdLb18M4fDtPT0cfq/5lB1udiL0iuznJw0pO5Mpo7fzgbR2c9/336EFWFp67Yf9K8RZj6+zDu/3TUn4sQtiIJlp1TOsXiuxPo6ujlwMZSi/QZlpRCdcFxixczFbZVcjiHPW++yrYX/sKWv/+ZpspyW4c0Io0VZWgmE4HRo0uwenv6yd5QTHCMF8lWOsPzcqLT/YlI9WPfeyW0n+4e9fXBMfGY+vtpKC+xQnTD6+7ooLG8jNCEpBG17+nq470/5XKmuYsbH00jONr7itf4BLmx+jsz8Zjiwrt/yr1ikhUUG49PUAiFcjehsCOSYE0C/gZPUuaHcnR7pUVqY4UlptB2qpnWhjoLRCdsrau9jff/+Gve+sWP+fT1l8nbuY3jO7bw4ne+xkd/fYaO02PbJzRe6kuLAQiMGt0S4dHtlXSc7iHr1jiUFe4avBKlFAvvjKe/z8Snb45+qe/cRvfi8V0mrC06gaaZRrz/audrJ2ioaGPFA6mExo9887rHFGdWf3sGXv4ubF5/jNbG4e8SVEqRkLWA8mO5dLSeHvEYQtiSJFiTxJxVMeiddGP6Rn6xsORUAKmHNQnUl57kpf/5OoV7djHvji/wjX+9zdde+DcPPvs8GStu5Nj2j3jtx9+ls806h4hbQn1pCU6ubngHBo34mu6OXg5+UEZEqh+h8aPfGG8pPoFuTF8ewYl9ddSXtY7qWk//AFw9vc6dwTheqk/kg1KExCdesW3ZsSYKs2uZeX0k0ekBox7LxcORlY+koWkaG/98lJ6u4Q92TsxaiGYyUbRvz6jHEcIWJMGaJNy8nMhcGUXp0SbK85rM6svfEIGzm7skWHauo/U0//31z9A0E3f/7Ddk3XYXDo6OALh5eXPNl7/C5//3SVob6nnv6afo7xv+h5st1ZcWExgVM6rz8A5vqaC7o4+5t9j+Ro3p10Xi7O7A3ndOjuo6pRRBsfHUFY9vRffqE/nnvgdcTk9nHzteLmBKiDuZN0SNeTyfIDeueyCV5uo2tr00/B3RAZHRTAkJo3CP3E0o7IMkWJNI+tJwvPxd2PN2MZpp7PunlE5HaGKyFBy1YyZTPxv/9Bs6Wk5xy7d/SHBcwpDtDEmpLH/o65Qfy2X7i38d5yivzGTqp6GsZFR3tHa09nB4awVxMwMJiPC0YnQj4+zqwMwVUZQfb6baeOUN3ecLio6jsbKc3p7R7+EaC81kosZYOKLlwT1vF9PW0s01X0xC72jej5KIFD/m3BJD8cF6TuwbemuCUorEeQupOH6M9pbRvY9C2IIkWJOI3lHH7JtjaKxoo+hgvVl9hSWm0FRZTueZ0S1riIlhz39eoezIIa657+Fhk6uzUhcvI/Pm1eR++D7GfRPrLq3TdbX0dXcTMIozCI/uqKSvp5/ZN1v2OBxzTFsShru3E9n/PTmqm0eCYuPQTCYaSsdno3tTVQXdHe1XLDDaWNnGsZ1VpC8NJzjmypvaR2L6dZGExHqz87UTtJ0aukZWYtZCNM2Ece/E+ncqxFAkwZpk4mcF4Rvqzr53SzCZcU7h2XpYZwsOCvvRUFZC9tuvk7r4WqZds2JE1yy86178DBHseuXFCbVU2DB4VMxIE6yerj6O7qgkJj2AKcGXX+IaTw5OejJvjKam+DRlx0a+hB8U/VlF9/FQO7gcGRx7+aR837sncXJ1IPPGKIuNrdMprrk3GVO/ie3/HHqp0D88Ej9DBIV75G5CMfFJgjXJ6HSKOatiaKnroGBP7Zj7CY5NQO/gIPuw7NDOl1/Axc2dxWvvH/G+JZ1ez4K77uVUTRXHtn9k5QhHrrG8FKV0+BrCR9Q+/9Maujv6mH7dyAtkjpfk+SF4+rmQs6l0xLNYnn7+uHn7UHey2MrRDag7acTRxRXf0LBh29SXtVKS20jGteG4uDtadHyfQDfmrY6jPK+Z/E9rhmyTmLWQyoLjtDWbt9dUCGuTBGsSik73Jyjai/3vl9DX2z+mPhycnAiKiZcEy86UHs6hNPcgc1bfiavH6PYfxc6cTVhSCnveeIXerpEdY2JtDWWl+ISE4uh05fMDTf0mcrdUEBLrbbFlK0vS63VMXx5B7clWaopGVhpDKUVQdOy4zWDVFRcRFBOL0g3/o2HfeyU4uzmQfs3Ikt7RmroojJA4b/a8VTxk8eTEeQtB0ziRvdsq4wthKVdVgqWZTLTt3EnnkSP0VFTQf+bMpCymqdTALFbbqW4KhvktcCTCklKoLTaO2wZbYR6TqZ+PX34B78AgMlbcNOrrlVIs+sKXaW85xYH337ZChKPXWF5KQETUiNoWHaznTHMXGcsn3uzVWUnzQnD1dCRn88iLvAbFxtNUWUFvt3WT3v6+PurLThIUM/zh0rUnT1N2tInp10Xg5Gqdk9aUTrH4rkS6O/vI3nDpnZe+oQYCIqMp3CMJlpjYrqqzCE2trVQ89JULn3RwQO/jg97HGwefKeh9fXEMCcExNASH0FAcQ0JxDAvFYcrIC+hNBIakKQRFe5HzQRnJ80PRO4w+lw5LSmH/O29SV2TEkDLVClEKS8rftYPG8lJu/MZ3z5VjGK3QhGRiM+dy8P0NZN68ekQzR9bS09VJS10NqYuXjah97pYKfILciE7zt3JkY+fopCftmnD2bjhJY+UZ/A1XnmUMiolH00zUl5YQdoXN5+Zoqiynv7f3XIHToRz8oAwXd0emLTFYLQ4AvzAP0pYayN1WQfK8EIKiLjyvMDFrIbtfe4nWxga8/Edff0uI8XBVJVg6NzciX32F/pYW+ltO03/q1ODHLec+7i4qom3XLrTOC6sK6/38cI6PH/wTh3N8PC4pKeicbfcD6HKUUsy6MZr3nsmlcG8tKfNDR93H2Vu1qwrzJMGa4DRNY/87bxIQGU1i1kKz+ppxwyqKD2RjzP6ElEXXWCjC0WssLwPAfwQb3OvLWqkvO8OiNQk2qdo+GtMWh3HwgzIOflDOdfenXrF9UMxABfu6k0arJljnNrgPk2C1NnZSeqSRGSsicXKx/o+O2TdFY9xfx85XC7n9e5kXfF3PJlgn9uwi8+bVVo9FiLG4qhIs5eSE2/TpV2ynaRr9LS30VlfTV1NDT0Ul3UVGuo1FtLz5JlpHx0B/jo64pKXhNnMmbpkzcZ0+Hb2n7evunBWR6ktgpCc5m0pJmhuMTj+6WSxXTy/8DBFUFRy3UoTCUsqOHqapspzrv/rNURXkHEp46jSmhISR+9EmGydYpQAjWiI8trMKBycdCXOCrRuUBTi7OZK6MIzcLeXM/VwMXn6ul23vMcUPd58p1J20bkX3+pIinN3c8Qka+tzGYzurQClSFw2/AX44/a2t9FZV0dfUjFO4AUeDAaW//EHSTq4OzFsdy5Z/5HNifx2J531tfYJDCIqJo1ASLDGBXVUJ1kgppXCYMmVgWTD1wt8wNZOJ3upquvLz6Tx4iI6cHJr+/nea1q8HnQ7XjAw8li7Bc9m1OMfYtg6PUoqZN0Sxad1RTuyvI2nu6A+8DUtKofDTXZhM/eh0l/+GKGzn4Pv/xc3bh8R5i8zuSylF+vIb2PHS32goKxlVDSpLaigvxcnVFa+AwMu26+7oxbi/joRZQThbaV+QpaUtNZC7pZxjH1cxb/XwS3IwuNE9Js7qCVbtZTa49/X0k/dJNTHp/nj6uoyov/62Nk6/9RbNL79Mb9mFe86UszNumZn4rv0i7gsXDrupPmF2MLnbKsneUEzsjAAcHD/7HpSYtZCdL7/A6fpavAMnfmItrj5X1SZ3S1A6HU4GA17LlxP0ve8S/fq/Sdy/j4gXnsfvKw9h6uqk4be/4+TKlZxcvZqm51+gr6HBZvFGp/vjF+bOwQ/Kx1TdPSwple6OdpoqRr4pV4yvpqoKSg7nkHHdjWPee3WxlMXL0Ds6krtls0X6G4vG8lL8w6OuOCNXuLeWvh7TmGZWbMXT14WYjADydlfT23PlO32DYuJorqqkp2v4A5HN0dfbS0NZybAb3I0H6uhu7xvR3itN0zj12msULV5C3ZO/wMHXj8D/+R/C/vAHIl56kZD/+zlT1txJt9FIxVce5uRNN9O2+5Mh+1I6xbzVsbQ1d3Nke+UFryXMXQAgm93FhCUJlgXo3Nxwz8oi8BvfIOatt4jbvo2g7z+O0jtQ/6tfYVx6DZXf/CYd+/eP+12LSimmXxfJqZp2yo6Pvm5MWOJAwVEp1zBxHdr0DnpHR9KX32CxPl09PEnMWkj+rm1W+6F+OZqm0VBeQkBk1BXbHdtZTWCkJ4GRXpdtO9GkXWOgu6MP4zBHw5zvs43uozvPcKSaKsow9fcNmWBpmsaR7ZX4hroTmnD5g7P729qo/va3qX3iJ7impxP1n9eJevUV/O6/D68V1+E+ezY+t91G0Pe/T9zWLYT++tcAVDzwALU//Smmwe0X5zMk+RI51Y+cTWV0tX1WtsE7MIiQhCTyd+8w75MXwkokwbICx5AQfO+9l+j/vE7Mxo343nMP7Z/uoeyLaylds4YzW7agmcZeZX204jID8ZjizKEPRz8L5RUQiIevn5xLOEF1tbdx/ONtJC9Ygpv35X/4jVb68hvo6ezkhA1mCM40NdLd3o5/xOWXJ2uKT3Oqpt2uZq/OConzwS/MgyPbK674i9fZO/vqrbRMeHaD+1B3EDaUn6Gxoo1pSwyXnU3sa2yk9M41tH7wIQHf+hbhf/srrtOmDdteOTriffNNRL/1Jr733supV1+j5PN30FtVdUnbrNWx9Hb1cWBj6QXPpyxYSmN5KQ1l43OUkBCjIQmWlTnHRBP0+PeI/3gHwU88QX9TM5Vf+zolq2+jbdfucZnR0ut1pC8Lp9rYQm3J6VFdq5QiLDFFZrAmqMJPd9HX00368pUW7zskPgnvwCBO7B16+caaRrrBvWBPDY7OeuIzg6wflIUppUi7xkBTVTvVxssXHvWY4ovHFF9qrZRg1ZUU4eLugXfgpe9jQXYtegcd8ZnD74Xrb22l/IEH6a2qIuLvf8P/oQcvW6z0fDoXF4K+/zgRz/+dvoYGStfcRVdBwQVt/EI9SJ4XwtGPKznd8NksV0LWAnR6PXm7to/wMxVi/EiCNU50Li5MWXMnsZs3EfqrX2Jqa6PiwQcpv+8+uoutsk/4iAAAIABJREFUfwxGyoJQnFwdODyGWaywpBTONDXQ2mjeAdLC8o5/vAX/8MjL1i4aK6UU8XPmU3bkMF3tbRbv/3LOzkj4R0QO26avp5+inHpiZwTg6GyfN2AkzArC2d2Bozsqr9g20Iob3etOFhEYE3fJDFV/vwnj/jqi0/1xdht6f5+po4OKhx+hu7gYw5/+hPvcuWOKwT0ri8h//RN0Osru+SIdOTkXvD57VQw6vSL7v58tk7p5eRM9PZOC3TswmcZ2aoUQ1mKRBEsp9bxSql4pdey853yVUh8ppYyDf9tXpU4rUQ4OeK9aRczG9wn6wffpysvn5Odupf7p32PqtN5eFycXB6YuDqP4cMMFvwGORFjSwJ2UVflSrmEiaaqqoMZYSOriZWaXZhhOwtz5mPr7OJmzzyr9D6exogxP/wCc3YY/sLkkt5Hern4Sx3B37ETh4KQnaW4IJbmNdLT2XLZtYFQsp6qrLH6MUX9fH00VZQRGxVzyWvnxZrraei8okXA+TdOo+d8f03n4MGG//jUeCxeYFYtLQgJRr72Kg78/FV95mM7jn33Pcfd2JmN5BEU59dSe/GwmPnnBUtpONVNx7KhZYwthaZaawfoHcP1Fzz0ObNU0LR7YOvhYDNI5OeG7di2xG9/He+VKmv7yF0puXU3nUet9k0hbYkCnFEd3XLrH4XL8IyJxcnWVfVgTTN7HW1E6HckLl1ptjODYBDz9AsZ9mbCpshx/w+WPvCnIrsVjijNh8Zbde6aZTPTW1dN5+DBnduyg48ABuo1Gq/0ClLIgFFO/RkH25Y+1CoqORdNMNJRbdr9Rc3Ul/X19BA5RjqMwuwZXT0fCU32HvPb0fzfQ+t57BHz9a3hdv8Ii8TiGhBDxwvPovDypeOBBuk9+NmM1fXkErl5OfPpm0bntFbEzZ+Pk6kb+blkmFBOLRRIsTfv/2TvvgKjr/48/bsGxjn3sjWzBgXulppm5+lZqlvqt/JWabW2XDRtmyzS/lmappWnLrbn3xI0IyD42B8iGW5/fHyhKbARX9/gHvXt/3u8XH+Duda/xfAn7gYJ/PDwaWH7l38uBMW1x1t2G1N4e17mf4vnjMgyVlaQ8OgH1//6HoG/7cLeFjSl+XZVcPJSJplLX7OvEYgmuAcHGOqzbCINBT8z+3fh06oqFTfsFh6vThL1JOXuKqno6vNoDg0FPQWY69h4NpwfLiqpQxeQT2MO5TZTbDeXlFG3cRMbLLxPfvQcJAwaQMv5R0qdOI/XxiSSNHEVc9x6kPPY4ed8sQJPedEqvudi5WODib03MwcxGazKVPtURptzktu0kvJqOdfxHBKuyTEvKuXw6RDohqUekuCo5mewPP8S8Wzfsn366TW2SubjgtWwZSCSkPfkU2tzq8gQTuZTuI3zISiwi+awaqB5MH9CzL/HHDt82Q8qNGIH2rcFyEgQhC+DK13orJEUi0dMikShKJBJF5d1CvahbjUWvXviuX4fivvvIm/8NqqefQVdY2ObnhA90R1OpJ+5odouucwsMQa1KpbL05tbiGKmftHNnKC0sIPSee9v9rIAefdBrtSSdPtHuZwEU5WSj12qxd/NocM2lEzkIAgT2vDGBSX1pGeolS0gYfC+Zs2ZRdvwEVsPuw/m92Xh8txjvNb/i8cNSXL/4HPvJkxC0WtSLF5M4ZCiq6c9Sfur0DZ1/lZC+rhTlVpAZ33Cxu5W9I3JLK3JT2rZmMzclCYlMhp1rbY2rxFO56HWGeu+xoNWS+cpMxDIZrvM+a1KVvTWYeHvjueR79MXFpD87A8MV5ymkjwu2zuYc+SsRvb66Gzu0/yC0lRW3pCHDiJGGuOVF7oIgfC8IQqQgCJGOjv/uoZ0Sa2vcvvgc5w8/oPz4cVIefoTKmLaNGjn5KFB6WXF+b3qLhEfdgqr1sDLjL7apPUZax4X9u5FbWOLbpXu7n+UaEISFrR2Xjt6cNy91enUjhr1HwynC2KPZKL0V2Do3XKPVFMV/bydx6FDyvvgSeVgYniuW02H/PlznzMF2/HgsBwzALCICyz59sH7gAZQzZ+Kzdg3+u3dh/8zTVJw+TeqECWS+9jo6tbrVdgD4dVFiYiblwsHMBteIRCKUPn5troWVl5qMg4cX4n84SfHHc7B1NsfRs+74r4JffqEyJgbn999H5tx+Kury4GDc5n1GZXQ0WW++iSAIiCViej3ox+Wcci4eqk6rugWHYuvixvndf7ebLUaMtJT2dLByRCKRC8CVr8YWtGZi+8gjeP3yM4JeT8pjj1O6b1+b7V3dGu5BYXY5qth/ZnUbxtk/ALFEapxLeBug1VSRePI4HXr2aTPl9sYQicX4d+tF8pmT6DSNF2K3BVenBtg3UINVmF1GfnopAd1aJ82gLy4m49VXyXjhBWQuLniv+RXPJd9j0b17s6QFZM7OKF98Ef9dO7F/5hmKtmwh8f7hFG/d2ip7AGQmEgJ7OJN4OreWmOY/UXr7ok5LQa9rfoq/MQRBIC8lCUev2unB8mINWQmX8euqrNNAoc3NRb1gIRb9+mF139A2saMxrAYPRvnKyxRv2Ur+4sUAeIc74OJvzfGNSWgqdYhEIjoOGkpGbAz5Gap2t8mIkebQng7WBmDylX9PBta341l3HWbh4fj8thZTHx9U05+l8Lff2mxv/y5KzKxknN/T/DoSmakcJ18/Y6H7bUDKmZNoKysI7Nnvpp3p06krOk3VTanDy09PQ+GoxERe/xDkhJO5IKqO+rQUTXp6tRjm5i04zJiB96+rMYuIaJWdYnNzlC+9iO+G9Zj6+ZHx0stkf/wxQiud0OA+Lhh0ApeiGlZ2V/r4VXf9pbfN6KqywgIqSorrzJtMPpuHIIBf57r3OPfzzxE0GpzferPdulf/id1TT6EYOZK8bxZQeugQIpGI3g/5U1Gi5cyO6nsR0n8QYomE6D07bopNRow0RVvJNKwGjgCBIpEoXSQSPQV8CgwRiUSXgCFX/m+kBUgdHfFauQKL3r3Jfudd1N8vaZN9JTIxof3dSInO53Ju8wuX3YJCyU6IvylRDCMNE3fkIGZWCjxCG1bJbms8QjsikUpJOXeq3c/KT09rtP4q4WQuLn7WWNqatmjfivPRpIwbj66gAK/lP+E441lEbRABNPXxwWvlCuwmT6JwxUpSn3wSfUlJi/dx9LDC3t2S2CMNdxNelVJoqzRhbmrSlX1rO1iJp/OwdjTD3q12Crb8xAmKN2zE7qknMfH2bhMbmoNIJMLl/fcw9fcjc+YstFlZOPtY49dFyemdKsqKqrCwscWvaw8u7NuFXtdwFNCIkZtFW3URPioIgosgCDJBENwFQfhBEIR8QRAGC4LQ4crX5uejjNQgtrDAY9G3KEaMIO/LL8n79ts22TesvxtikYjoFkg2uAWGoNfp2k3s0EjTaKsqSTp5nA49etepmWlPTORmuAWFkHK2fR2spjoI8zNLKcgsw79ry9KD5adOkTp5MmK5HO/VqzCPjGwLc2sQyWQ4vfEGrvPmUXH2HKmTJ6PLb/nsz+BeLuSmlpCfWX8zia2LKzJTObnJbVPonpdypYPwughWZZmWjNhC/Lo41opQCYJAzrzPkbq44PDMM21yfksQm5vjNv8bhKoqMl58CUGjoecYXww6Ayc2VX8fHQffR0VxEYlRx266fUaM/JNbXuRupGlEMhmucz/FeswY1AsWkvfNNze8p4X1FcmGw82XbHANDAYwpglvIclnTqKtqiSw181LD17FK7wL6rQUSgta7jg0l8vZVzoIG6i/SqxJDza/IaYyNhbVM1ORKZV4/7oaU9+6gppthfXIEXgs+hZNUjKpj09Em9P0IOfr6dDNCbFYRNyR+rt8xWIJjl4+bdZJmJuajLXSqZaga8o5NQaDgO8/0oOle/ZSee4cjs9OR2xWf/q2KQRBIKUohT/i/+CbU9/w6fFPef/I+yw+u5ityVtJKkpqVKrC1NcHl48/ouLsWXLmfY6N0pyw/m7EHMqiIKsMr/BOWDk4cnbntlbZZ8RIWyK91QYYaR4iiQSXjz8CqQT1ov8htrDA/qmnbmjP8EHuXDqRQ9zRbDre497kenOFNXau7tWF7qMfvqGzjbSOuMMHMLe2wT047Kaf7R3RhQOrfiLl3GnC2kkeIj89FaBekVFBEEg4mYurvw0W1s1LD2pSUkh7agpiCws8l/2A9CZ0Klv264fnD0tRPf0MaU89hffPPyOxaZ4YqrnCBM8we+KOZdNzjC/ievSnlD6+XNi3G8FgaPa8v4bIS02uU3+VeDoPSztTlF7XugcFg4G8b75B5umJ9ejRLT5HXaFmdexq1l1aR25Fdb+TRCTBXGqOTCKjoPJagsNb4c1gz8E81OEhPBR1U8WKYcOomHyaguUrMO/cicjh9xJ7JIuj6xIZPi2ciCHDObh6OWpVKg6NaKkZMdLeGCNYdxAisRiX999HMfx+cud9fsOF784+1ii9FS2SbHALCiEjLgbBYLihs420HG1lJUmnTtCh+81ND17F0csHCxtbUs6cbHpxK8lPr+4As3Ov+8ZakFlGYXY5/l2bV9yuLy5G9cxUMBjwXPYDMlfXNrW1Mcy7dsX922/Rpqahmja9RSrwwb1cKC/WoLpYvw6e0scPbWUFhdmNK783hbayksKsjFodhJoKHaqYAvw61+4eLNm+narY2BbXrZVqSvno6EcM/X0oS84tIdg+mHd7vcuGMRs4PfE0hyccZt+4fRx/7Dh/jPqDt3q8hbOFM8svLGfEuhG8uu9V4gri6t6DmTMx69yZrLffQZyrosswL5LPqkmPKyR88H1ITUw5tXXDDd0fI0ZuFKODdYchkkhw/fRTLPr1I3v2e5Ts3HlD+4UPdG+RZINbUChVZWVt1sVkpPmknD2FTlNFQM8+t+R8kUiEV3hnUs+fabfBuo11ECaeqk4P+nZuOgolGAxkvvY6mowM3BcuaNe0YENY9OxRXZN15gwZL73c7OkMXh3tkVvIGix2V3r7AdxwmlCtSgVBwPG6Ave0mAL0OkOteyzo9eQtWIiJnx+KBx5o9v770/czZv0Y1savZbT/aDaM2cDCwQt5JOARfKx9ajlwZlIzAmwDGB80niVDl7D94e1MDp3M/oz9PLLxEeYcnUNR1bX5gyKZDLevv0Ikl5P+/At07GmPlb2cA2viMTW3JKT/QC7u30N5cVF9phkxclMwOlh3ICITE9y/mY+8YxgZM2dRcT666Ysa4KpkQ/S+5hW7uwVWC44a67BuPglRR5FbWN6S9OBVvCO6UFla0m6NDvmq1Abrr5LOqnHxs25WejD/u+8o3bMHp9dew7xr17Y2s9koht2H09tvUbp3L3nzm1c7KZGK8Y9UknJOXW99pIOHJ2KJ9IY7Ca+OyLl+BmHKeTWmFlKcfa1rHivZsRNNYmJ19KoZkVO9Qc+8E/N4dtezWJlY8cvwX5jdazbe1t7Nts3R3JGXu77M3w/9zYTgCfwW/xsj/xrJ1uRrWmMyJyfcvvgcTXIyeR++T5+H/SnILCN6fwZd7h+FTqvhnLEWy8gtxOhg3aGIzczw+PZbpHZ2qKZPQ5vVunSBRCYmuLcrKefUlBQ0PcfL2skZCxtb41zCm4xBryfp1Al8unS7JenBq3iFdwYg9WzbjIi5HoP+SgdhPQ5WsbqC/PRSfCKajl6VHT1K3jcLUIwaie3jj7W5nS3F7rHHsBk7lvzvv2+2GGlANyd0WkPNvL3rkUhl2Ht43nAnoVqVikxuhsKhOuVqMAikRufjFWaP+Mp8R0EQyF+2DJmnJ1ZDmxYVLdeW8+LeF1kRs4IJQRNYM2INYQ6t/0BgbWrN691fZ+2ItXhYefDq/ld548AblGiqZTAsevXC8fnnKd68GZsLO/AItuX4xmTMrZ3xjujCme2bjZINRm4ZRgfrDkbq4IDHd4sRKipRTZ2GoZXDeEP7uSIAMY2M6biKSCTCLTDEGMG6yWTExVBZWoJ/ZI9baoe5whoHT2/S20HR/3JONnqdrl4H66qj4RPh0Oge+pISMt94ExMvL1zef/+mCWE2hdPbb2HWuTOZb75FZVx8k+udfa2xspMTf7z+LkQnHz9ykxMb7bhrCnVaCg7unjWF8rkpxVSWavEOu3aPK06epPLcOez+O7nJ6FWxppgn/36S/en7eaP7G7zR4w1MJCattu96Au0CWX7/cqZHTGdL8hYe2fgIsQWxANg//X9Y3nMPuXPn0i3cgLZSz5G/EukyfDRlhQXEHNjTJjYYMdJSjA7WHY5phw64ffUVVfHxZL3zbqtecBUOZniF2RNzMLNmeGpjuAWHUpyXS7H63zuc+2aTGHUUiVSKd0SXW20K7sFhZMZdbLNxLVdprIMw+Wwedq4W2CjNG90j5+NP0OXk4Dr301ZLCbQHYhMT3OZ/jdjSgoyXXmqy6F0kFtGhmxOqiwVUlNQV9lV6+1JRUtxqyQxBEMhTpeLgea3LLuW8GpFYhEeIXc1j+T8sQ2Jri82DDza6X5m2jGk7pxFXGMfX93zNhOAJTRuhq4LE3bBjNqyZCN/1h/kRsLB79b/XToZ9n0H8dtBWIBVLmdZpGsuHLUdr0DJxy0S2JW9DJBbjOvdTZEolpR/MomNfRy4ezkIm98HJtwPH/lzT5r+rRow0B6ODdRdg2a8vji++SPHmzRQsX96qPcL6u1FerCH5TNNDa6/WYWUao1g3BUEQSIg6hmdYBCZmjTsYNwP34DC0VZVtXod1dQbhPzsIK0u1ZF66jG+nxtODJbt3U/TXX9g//X+tHn/TnsiUStzmzkWTnEzOJ00Ptgjo7oRgqJam+Cc3WuheXnSZypLiWjIGKefzcfGzRm5R3SVYlZRE6Z492E6Y0KizWqmr5Lndz3FBfYHP+3/OQM+BjR+eeRr+mAJzvWHlg3B0EeTFgoUS3LuDMqj631lnYc/HsOoR+MwXfn0MYjbQyT6MNSPWEGwfzKz9s5h/aj5YWeL2zXz0+fm47lqAwkHO3lVx9HhwPEW5OVzYt6tV98mIkRvBqIN1l2D/9P9RGX2e3HmfIw8JwaJ79xZd7xla3YUTvT+9yTZ4Ry8fZHIzMuJiCOoz4EbMNtIM8lWpFOVk023kQ7faFADcg0MBSL8YjWtAUJvtq05PQ+HoVKeDMOW8GkFoPD2oLy0le/Z7mAYF4Th9epvZ1NZY9O6N/VNPkr/0Byz69kHRSF2TvZsldq4WXDqRU0enztHbB0QicpIS8eva8rSxOu1KtNDTG4CSgkry00vp/R//mjUFP/6EyNQU28cajkYZBANvHnyTqOwoPun3CYO9Bjd8aMbJ6mhVygEwsYKI8RAwDLz7gUkDHxw0ZZB2FOK2QOxmiN0ECnccuk/hhwFf8/HZBSw9v5S4gjjm9p+L09tvkf3ubDpN7M5+lQ/qDE+c/QM49tcaQgcMQiJt/+HoRoxcxRjBuksQiUS4fPIJJp6eZL4yE11ByyYTicUiQvu5khF3mYKsssbXSiS4BgQZC91vEglXxn74dW2Z09xeWNjYYufqTvrF1nev1kd+ehoOHvXXX1namuLoaVXPVdWoFyxEp1bj8uEHiEzapu6nvXB8/nnkYWFkvfMu2py60anr6dDNiazEIorza6cUTeRm2Lq4tbqTUK1KAaiJYKVGV6cavcPtAdAXFVG0cSPWo0YitbOrdw+A7859x47UHbzc9WUe8G1AwqGiEDa9DEsGgzoehs6Bly/AiK8g4L6GnSsAEwvwHwwPfAEvXYBxv4C9L+x8D9nCSGYL9rzT7TWOZB5hwuYJXB7aDeuH/oN05ef4eug5s0NF6IAHKc7L5cJeYxTLyM3F6GDdRUgsLXH76kv0RUVkvvZ6i8VAg3u7IpaKuLC/ackGt8AQ8tJSqCyrf2aakbYjMeoozv4BWNrZ32pTanAPDiMjNqbN9LAMej2FmenY/WPIs06jJy0mH+9whwYL1ivj4in4+Wdsxo7FrOPNG4DdWkQmJrjO+wyhspLs995rtG4yoFv1zMWEqPrShL6tThGqVamYW9tgbl2tMJ9yXo3CQY6NU7WzU7RuHUJlJbYTGo5e7UzdyaIzixjlN4rJoZPrX5R2FBb1hpM/Qo9nYMYJ6P0cyK3rX98YYgkEj4DJG2HKbnAOh+1vMXbHPJaGTqWoqojHtz6O6un7MevcGfe/3sNULuLCISnO/oEc+X0VmorWNQIZMdIajA7WXYY8KAinN16n7MABCpYta9G15goT/DoriT2Shbaq8TdOt6AQEASy4mNvxFwjTVBakE924iX8I3vealNq4R4ShqaivGZY8I1yOScLvU5XZ7RJRvxldBoD3uH1pwcFQSD7gw+QWFmhfOnFNrHlZmDq44Pjiy9SumcPxZs2NbhO4WCGs6+i3m5CJx8/StR5VJQUt/h8dVpKTbRQrzWQEVeIV1i1EysYDBSuWo1Zp07Ig4PrvT6lKIU3D75JuEM47/Z6t67zKwhweCH89ABITWHKLrh/brMcK0EQUBWUc+BSHr8eT+N/exP5fn8iPxxMZuPZTM6lX6bYIRwmrYNJG0BiQteNr7IKF5Smtkzd9xynXhyCXGFKyMXlXM6pwNrlPkoLCzjyx68tvldGjLQWYw3WXYjN+PGUHT1G7tfzMe/RE7OOzdehCRvgxqUTOVw6kUNI34ZHi7j4ByISi8mIi8Gnc2RbmG2kHhJPXkkP3mJ5hn9yVew0/WI0Tr7+TaxumqsF7v+UaEg9r0ZqIsYtoP5ZfsWbNlFx8iQucz5s9ry/2wW7SRMp+ftvcuZ8hEXPng3OSezQzZkDa+LJzyjF3s2y5vGaQvfkJLzCOzX7XMFgQJ2eRvig+wDISqx2Yj2vdA+WHTmCJjUV1xnP1nu9Rq/h1f2vYiIx4Yt7vsBU8g/hV70WNjwPZ1dB0AgYs6hJx0qnN7A7NpftMTkcTlCTWdS4Jp9IBMHOCnr5OXLvkPX0yF6F+4F5rJRImeXfidmxXzJ9+nAGfrwTH/uTJEd3xSuiH6e2rCfsnnsbFLM1YqQtMTpYdyEikQiXD96n4swZMl9/HZ8/fkcslzfrWhc/a+zdLDi/L53gPi4NpmVkcjlOPn7GOqx2JiHqGDZOLrfdG4KVvQPWTs6kX4ym6wNjbng/9RWJBvvrUoSCIJASnY97kB1SWV0NJkNVFXlffY1pSDDW//nPDdtws7k6wD15zINkz/kI9/lf17vOv6uSg79d4tKJnNoOlk/1+J/clMQWOVhFuTnoqqqwvxItTIspQCwR4XrFiS1cvRqJnR1W991X7/XfnPqGiwUXmT9wPs4WzrWf1JTBb/+FS9vhnjdgwGvV3lADFJZp+PFQMmuiVOQUV2FjLqO3nz3TfO3p4GSFm40Z9pYmGIRqJyy7uJLU/HJis0o4mpTPyqOp/HAwGaVVJx4P+pmnihex4MJuvvDowKKyLVx+MpRR3/1CQU8v8rPDkZqcYteyxTzyzke3jUaakbsXY4rwLkVibY3LRx+hSUwk7+v5zb5OJBIR1t8NtaqUnJTGUw9uQSFkJ8Sj0xqVktsDTUU5quiz+EX2uC3fDNyDw0i/eKFNBn/np6tQODohu+6DQGF2OSX5lXiF1V97VrhqNdrMTJxmzaoRy7zTMPX1xWHaVEr+/pvS/fvrXWOuMME9yJb4Ezm16rXMrBRY2Tu2uNBdrap2Zh2vdBCmxRTg4meNiVyKNiuL0t17sHn4YcT1NAsczjjM8pjljAscxyDPQbWfrCqpll1I2FldwH7P6w06V+UaHQt3X6L/Z3tYsCeBUFdrlkyKJOqte1n0WFcm9vKmp689HnbmmJtIsTSVYmNuQpCzgvtCnXnh3g6sfron52YPZdFjXejsacPC0zpC459iscPbvJRXwDv5l1lrFcPah+0IOfENYg3IFf1QXTjHhb03NsPViJHmcGe+KhlpFpZ9+2Dz6HgKli+n7PjxZl8X0MMZmamkyfmEboGh6LQacpPbZy7dv53kM6fQ63S3Xf3VVdyCQqgsLaEgq3lzLBujvg7C1PPVnW31OVj6oiLUixdj0bcvFr163fD5txK7p57CxNeX7A8+bFCANKCbEyX5leQk1/7Qo/TxI6eFI3PUaSkA2Lt7UFZURX56aY246OU//wRBwGbs2DrXlWhKeOfwO/hZ+zEzcmbtJzVl8MtYSI+Ch3+EyCcbPH9/fB5DvtzP59vj6elnz98v9mfZf7sxJMQJqaRlb0lymYThHV34bmIkh98YxCtDAllR1Jnulz/GWRPJ4qxsdnjlsf6eckLP/A9NVQBmCm92/biY/AxVi84yYqSlGB2suxynWbOQeXiQ9cab6Esbl1+4iolcSmAPZxKicqksbTg65RpYXQCbfrHtx6YYqe4elFspau7z7YZrh2q7brTR4WoHYZ36q2g19m4WWNnVTW/nL1mCobgY5cxXbujs2wGxiQnOs2ejTU9Hvfi7etf4dnJEIhXXKXZXevtSmJWBprJxZfjrUatSq/XGzMxJv1gt5+IZYo9gMFD0519Y9OqJibtbneu+iPoCdYWaOX3nIJde9zPRVsDq8aA6Cg8thdD6U8alVTpe/f0sk5YdRy4T89vUXiyZFEmAU8PyGy3BwdKU5wZ34MBrA3lldE9eNcxgcfHzLMqs4GRYOeu7JRJ46TcMoiEgSNn09Vy0mqo2OduIkfowOlh3OWJzc1w//RRtVha5c5tWj75K2AA39DoDF480PETawsYW23bQQzICep2OpNMn8LvFw50bw87VDVMLC7Iuxd3QPoXZmXVmEFZV6MhKKMIrrG73oC4vj4KVP2M9aiTyoLYTOr2VWPTojvWYMeQvW0ZVUt2Un4mZFO+O9iScysVguJYmVPr4gSCQl5rS7LPUqtSaaGHaxQLMrGQ4uFtSfuwY2owMrB+qK2h7JPMIf1z6g8mhk2sPbzboq1XZkw/AmMUQVn8t3KWcEkYtPMjvJ9OZdo8fm5/vRzfvhvXhWKEBAAAgAElEQVS1bgRTqYSJvbzZO+seBjzwGC8avuA/aR0oD65kW+hhvFWHEJkMQZ2Wwp6fvr+heY5GjDSG0cH6F2DepTP2Tz3F5d9+p2Tv3mZdY+9miYu/NdH7MxAMDb8AeYaGk37xgnHWVxuTEXuBqrKyNu0eFAwC6XGF7Fh2gaUv72fxc3tZNH0Pv8w+StSWZIrVzY+CAIjEYlz8A8m8dGMRrPz0uh2EqpgCDAYBr45104P5S39A0OlwuI0V21uDctZMxKam5MydW+/z/pFOVBRryIwvrHnMyedqJ2Hz0vR6nY7CrAwcPLwQDAKqmAI8gu0QiUVc/v0PxNbWWN17b61ryrXlvH/kfbwV3kyPuO6eCwJse6NaXf3+uRAxrt4zN53LZPS3hyiu0PHLlJ68NiwIeT1NC22NXCbhv3182PbaCAxD5qPJm4qrj55tIZvwzElGYtqN87v+5qhRusFIO2F0sP4lODw3A9PAQLLefgddYWHTF1A9n7A4rwJVbMOq8J4dI9BWVpCTdKmtTG2U9Jho9q5Ywqq3XmHxMxPZ8f1CshLi7rpPoYlRx5DKTPAOb5vhzvmZpaz5+ATrvzpNyvl8fDo5Ej7Qnc5DPTFXmHBsQzIr3znC0fWJGJox8PsqLh2CUKtSb0jAscbBuq6DMO1CPqbmUpx9FLXW6tRqCteswXrECEy8amtm3elI7e1xmD6dsn37KT1woM7zXh3tkZpKuHSd6KilnT1mVopmF7pfzsnCoNdj7+6JOr2UihItniF26IuKKNmxA+sRIxCb1pZd+O7cd2SUZvBe7/dqpwaPLoLj30GvGdUiov9AEAS+3ZPAjFWnCXFRsPn5vvTyu/liuXKZhCn9fJn32otIglbjbufLzs5/4lakRWwSwuHffuHExnU33S4jdz9GmYZ/CWITE1znfkryw4+Q++lcXJuRLvTrrOSg1SWi92XgGVL/C6NHSLVydtr5s7gGtG+tUNSmv9i38gekMhOc/DrgFhRKzIE9nNu1DZ/OkYx88fVaXWh3KjXDnTtG3PD3IwgCFw9lcWBNPDK5hMGTg/HvqkRqUjuCUJxfQdTmFE5uTSXz0mWGPhWGpa1pA7tew7VDYLXgbEI8Xh2bLxVwPfmqtFodhIIgoLpYgHugLeJ/FD3nL/sRQaPBYdrUVp11u2P3+GNcXrOGnE8+xaJnT0Sya7PzZCYSfMIdSDydS/9HA5BIxIhEIpQ+fuQmN8/BKkivLuy2c/Oo+eDkHmxH0abfETQabB6unR5MKExgxYUVPOj/IF2dul57Iv5v+PstCB4FQz6sc45Ob+Cd9dGsPq5iTCdX5j4cjqn01qa6FXIZLwzvTE7f31m77heiZZ8TdHIQ2VZ+7P95KdoKDb0eeeS27Ng1cmfyr4pgGQQDhzIOEa2ORlWiokRTctdFPhpDHhSEw9P/R9H69Q22hF+PRCYmuLcrKefUlBTUL/xnZqXA0duXtAvn2trcGgSDgT3Ll7Bv5Q8E9OjD9B9WMf79uYx86XWmfreS/o89QcqZU/z20dtUlt75o3vUaSkU5+XccHpQEAQO/5nInp9jcfazZtzb3Qnq5VLHuQJQ2JsxaFIw9z4RQp6qlD8+i6K0sOkCYOcOgQA3VIdVkJmOvfu16NXlnHJKC6twD65do6PLz6dw9WoUIx7AxNu71efdzohMTFC+9hqapCQKV6+u87x/VyVVZTrSY69FoZU+fqhVqeh1TculXI0W2rm5kxFbiK2LBRbWphT9+RemIcG1lNsFQWDOsTmYy8x5set1KvnqS9V1V84d4cHv4B8SGVU6PdN/OcXq4ypmDPTnq3GdbrlzdT1OCjnPTXqKSVP2kzHoMhb6LCRSX478sYKVM2eh02hutYlG7hL+VRGsEk0JU3fW/uQrFUlRmCqwNrXGxtQGW1NbnCyccLZwxsXCpear0lyJWHTn+6P2U6dSvH07WbPfw3fjRiSWFo2uD+3nyqntqcQczKTHKN9613iGhnNm+2a0mipkJk1HPVrK4d9XcWrLerrcP4p7Jk2ppXlkam5Ot1EPYe3kzJZv5rH2/dd5ZPYnmFm2TWfSrSAx6hiIRPh1vTEHK2pLCmd2pBE2wI1+4wIQi5v+ZB7Ywxk7Fwv++vIUmxae4cGZXTE1a/hlQm5hib27J1mtrMMSDAYKMzPwDIuoeSwt5mpnW20Hq2D5CoTKShymTmvVWXcKlgPvwaJ3b/IWfoti5EiktrY1z3mF2mNiJiUhKgev0OqostLbF4Neh1qVVlOT1RD5GSoUjkokElMyL10muK8rVUlJVF64gNObb9RauylpEydzTvJur3exk1/5WVQWw68TQCKD8b/UGdRcodEz9eeT7IvP472RIfy3j08b3JH2wc/VkZkv/MKxe89y6Pu3MMsNJi/9IgsnT6b/5Ml0GTbsVpto5A7nX+VgmUvNWXn/Si5XXeZy1WWKqoooqiqq9f+0kjROZJ+gRFtS61ozqRneCm98rH3wtfbF18aXUPtQXCwaVju/HRGbmOA6Zw4pj04g78svcH733UbXKxzM8AqzJ+ZgJpHDvZFI6zqZnmERnNy8jqz42FpvlG1BXloKx9f9Rki/gQz879MNrgvo0QeT18z569P32fH9Aka+9MYd9XO5noSoY7j4B2BhY9v04gY4szON4xuTCerlTP9xAYia4VxdxdHTivuf7simhWfZuvgcI2d0QiJr+MOFS4dAEqKOIQhCi+95sToXnVZTa8hz+sUCFI5mKBzMah7Tl5ZR+OuvWA0diqnv7fum3RaIRCKc3nidpDEPol6woNbfqEQmxjfCgaQzau6ZYEAiE18bmZOS2CwHy87Ng+zkInRaA+6BthRtXAViMYr7769ZV6Yt48uTX9LRoSMPdbiSNhQEWDcN8hNh8gawqS2rUa7R8eRPJziWXMBnD4Uztlvtwd23Kz1CI+gxfxPbd6wh6aciyvSF7PnxWw7/vJZ7n3uCoB79brWJRu5Q/lUOlkwio5OyeXUiZdoyssuyySrLIrM0k+SiZJKLkjmde5otyVtq1tnL7eno2JEIxwg6OlR/rVUIehti1qkTdpMmUrB8BYrhwzGPbHyWYFh/NzZ/e46kM3l0iHSq87xbUCgisZi06HNt6mAZDHp2fLcAU3MLBkya0uR67/DO9Bn3OAdW/UT0nh10HDS0zWy5WZQUqMlJukTfRye3eo+0C/kc+iMBv86ODHw8qEXO1VU8QuwYNCmInT9d5OiGJPo81PC8QZcOQUTv2cHl7ExsXerqJzVGQUY6UJ2yAtDrDGTEXyawR+0RLEV//I6huBj7pxoWsLybMO3QAdvx4ylcvRqb8eORBwTUPOcf6UTs0WzSYvLxiXDE1tkFmdysug5rYMN7Ggx6CjPSqzt/YwsRicC1gzXpr2zEonfvWrMQl5xbgrpCzfyB869F7o8srO4YvO9j8O5ba+8KjZ4py6M4nlzA1+M6MbpTy34PbgeGDhkHQ8axfukXpO2KpUqbzeYvv2Cn5Ce8+nVm5LQZt9pEI3cY/yoHqyVYyCzws/HDz6buJ8JybTlJRUmcV5/nfN55zqvPs1e1FwC5RE6kcyR93frSz60fnorba4bcVRxfeIGSXbvJeuttfNava3RWoWeoPVb2ci7sz6jXwTI1N8fZrwNpF84CE9vMxjN/byYrIY7hz83EXNH4sNirdBv5H1LPnWL3T9/hFhSKneud9UKfdLJacd+/lfVXpYVV7PgxBjsXCwY/EVKnSLwlBPZ0ISuxiDM70/Dt5IiLX/0/A9crdViZ8bEtdrCuqmnbuVY7WDnJRWir9HhcV38laLXkL1+OeWQkZuHhrflW7kgcZjxL0aZN5HzyCZ7LltVEB92DbTG1kHIpKhefCEdEYjFKbx9ym1B0L86tjhbau3sSH1WIo5cCQ1w02owMHJ9/rmadqkTFipgVjPQdSbjjlfudegR2zIbgkdCztjxGpVbP0yujOJKUz5djI+5I5+p6Rk95BabAnwu+IuPIOar0ecTv3cbX+05gaW/Fw+++hY2Ty60208gdwJ1fVHQLMJeZE+YQxqNBj/Jxv4/Z+OBGDo4/yLeDv+U/Hf5DWnEanx7/lAf+eoAH/nyA+afmk1TUsnlh7Y3Y3ByXDz9Ak5qK+ttvG18rFhHaz5WM+MsUZNavBu8ZFkF2QjxV5a1v17+eytJSDv66Eu9OXQnqM6DZ14nEYoY9+zJSmQnbvv2yTebk3UwSoo5h4+xSK2XWXAx6AzuWXUCnNTDs6TBk9RSzt5TeD/ljZStn94qL6DT6etfYu3tiYmbeqkL3gsx0zKwUNQ606mJ1ZMUt0KZmTfG2begys7C7CdErrUGLqkRFTH4Mp3NPcyL7BDH5MaQVp1GubZvf7eYitbXFccYMyo8cpXTP3prHJRIxfp2VpJxT1/xMlN5+5KUmYzDU/zOCa86sQulKbkox7kG2FG3ciMjMrJb21ZdRXyIVS3mhywvVD5Tlw+9PgK0XjP621nxBnd7AjFWnOXBJzdyHwnmws3sb3oFby3+ee4nnVv3IvdNnYCZXIqChSJ3CD89PZ8FjT7Lpm/kY7rDXFyM3F2MEq42wNrWmv3t/+rv3ByCtOI2DGQfZn76fH6N/ZOn5pYTZhzHSbyT3+9yPrbz19TVthUWvXtg88jD5y37E6r5hmIWFNrg2pI8rxzclc35fOgMeDazzvFfHThz7ay2qC+fw73bjs/PO7dqGtrKC/hP+2+K6His7B+6ZNIVti74i9tA+gvs1kje5jbg63LnTsJGtqh87ua1aYuHeJ0KwdW68eaG5mMilDJwUxIavz3B0QxJ9H+5QZ41ILMbJ179VWmgFGek16UEA1cUCnHwUmJpXyxMIgkD+sh8x8fPDckDzHe3moDfoOa8+z8mck5zNO0tcQRzZ5dkYhIbfNJVmSrysvejo0JFOjp3o4tQFa9PmRVdbg+34cRSuWkXuvHlY9utbI9vgH6kk5mAmqdH5+HVRovT2RVtVyeXsrJpo4D+52kFYVWGFwZCLu58VJZ9sxWrQIMQW1b8vUdlR7EzbyYxOM3CycKquu9rwHJTnw5SdIL/2vRoMAq/+cY6dF3P4YHQoYyPvjJqrlhIxYCgRA4ZSXlLCmg9nU6oqQqPLJ+7QDi4dPoa5hS2D/+8J/Hs2Xmph5N+H0cFqJzwVnkxQTGBC8ATUFWq2JG1hY9JGPjn+CfNOzGOQ5yAmhkwkwjHilhZjK2fNonTffrLeeguf33+rpbtzPWZWJgR0cyL2SBY9Rvkit6i9zjUwGJncjJSzp27YwdLrtJzeugHPjp1w9Kpb0FxerCHlnJqc1GIsbUxROJjhFmCDpe21NGdIv4Gc3raR/auX49+9FzLT27suDiDl7JXhzq3oHizILCNqSwodujnVqV+6UTyC7Ajt58q53emE9HHFzqWu8+bk68/prRvQ67RIpPX/DtVHQYaq5velskxLbkoxXYd71zxffuIEVRcv4vzhB7W6R1uLIAiczTvLpqRN7EzdSX7llYHSCi8ilBGMtBqJm6Ub1qbWyCVyxGIx5dpySrWlZJdlk1acRlJREitiVrDMsAyJSEIXpy4M8hjEMJ9hOJjVHe1zI4hkMpSzZpI+/Vku//47to8+CoBbBxvMrGRcisqtdrBqFN0TG3SwCjJUWNjakZuiQSIVY5kVTWlREYqRI2ruzVcnv0JprmRy6JUawJM/Qtzm6rorl2v1lYIg8OHmGP48lcHLQwKY1Mu7Tb/v2xFzKyue+OxLAKL2b+f4T2vQlGsoLU1l/VfvI5U44eDhyaiZz2HleOs/QBu59RgdrJuAg5kDk0InMSl0EnEFcaxPXM+6hHVsT91OmH0YUzpOYaDnwFsiAyFRKHB+bzbp058lf+lSHKY13AIfPsiD2CPZXDyUReehtWvLJFIZnmHhJJ852apusuuJP3KQ0sIChj7zfK3Hy4qq2LMyltQL+SCAqbmUqnLdlfPFRAx2p8swb0zNpIjEYu6ZNIU1773OyU3r6PnQ+Fbbc7NIiDrWquHOgkFgz8+xyOQS+j5SN8LUFvQY5Uv8iRyOrktk+LS6dVDOfgHodTrUaak4+TZcEH895cVFVJQU16RDM+IKEQTwvK7+qvDnX5BYW2M9cuQN2a8z6NiSvIVfLv5CTH4MZlIz+rr1ZYjXEHq49LgmQ9BMKnWVXMi/wKGMQ+xR7WHuibl8HvU5/d3783DAw/R169tmf8+WAwdi3q0beQsWohg5EomlJWKJGL8uSmIPZ6GprJ7jKJFKyUlObDClnp+hwt7Ng/TYQpz9rCnbugKJrS2WffoAsDttN+fU53i/9/vVjTp5cbDtTfAbBD1qvy4s2J3Aj4dSeKKPN88Nat7P+24isv9QIvsPRafTsXb+bPJPqdDqLpOdks33MyYhEVvh4t+B4AG9cfbvgL27R4s+eBi5OzA6WDeZQLtAXrV7lRmdZrAxcSMrYlbw4t4X8bfxZ2rEVIZ6Db3pES2rQYNQDL8f9aL/YTVkCKb+9b9gOnpY4RZgw7m9KiIGu9cpoPaO6Epi1DEKszJbXVwuCAJRm9dh5+aBd8S1MTGZCZf5e0k0mnIdkcO98eusxN7NAr3WwOXccs7sVHHq7zRiDmUx7P/CcAu0xT04jA49enN8/e+EDRyCpd3NH9PRXAx6PcmnTuAX2aPFw50vHMggO6mIwZODMVeYtIt9ZlYmdLnPi2Prk8hMuIyrv02t5539qn9nshMvNdvBKsis3UGouliATC5BeWU8jjYzk5KdO7F/6slGmzAawyAY2J66nYWnF5JanIqftR/v9HyHEb4jMJeZN71BA8ilcro6daWrU1ee7/I8SUVJrLu0jg2JG9ij2oO/jT+TQyfzgO8DyMQ39sYqEolQvvYaKQ8/TP73S1C+/BIAHSKdiN6XQcp5NQHdnLH38GpwZI4gCOSnqwjqPZBLp0vpNsyd0p/2YPPQQ4hkMnQGHfNPz8fH2odRfqNAVwV/PAUyMxjzv1pioiuPpPDljnj+09mNdx4IuWPlUNoCqVTKhFc+AiAx4Qzb53+BIU+OViQiPf4c6fEnARBLpDh4euHk44fSx//KVz8kUuNb8N2Mscj9FmEuM2dc0DjWj1nP3H5zEQSBmftmMnHrRM7knrnp9ji99RZiCwuy3nobQd9woWz4IA9KC6pIOqOu89xVhyjl7KlW25F+MZrc5ES6PjC6JiWUcDKX9V+eRmYi4eHXI+kx0hcHd0tEIhFSEwkO7lbc+98Qxr7ZDTNLGRsXnCX5bB4A/R97Er1Oy/H1v7fapptBRuwFKstKWywuWlZUxZG/EnEPsiWwZ9umBv9JxGAPLKxNOPxHQp0JCApHJ+RWihbVYV2VaLg6g1B1sQC3AFskVxz3wtXVQ3ivpsVaSnxhPBO3TmTWvlnIxDK+GfgNf43+i7GBY2/IuaoPX2tfXo58mR2P7ODjvh8jEol459A7jPprFJuSNjVa19UczMJCUYwaScHy5WgzMwFw8bPGwsaUhCuzCZXefuSmJNU7naIkX422sgKxtPpDhk1+LEJVFdajqiOD6xPWk1yUzAudX0AqlsLuDyH7fHVRu9W136v1ZzJ4d8MF7g1WMvfh8GaJ1/5b8PPvxLQFK3l65SLcR/phZmWCHZ0wNR2MSNoJtUpDzP4D7PphEavefoXFTz/OtkVf10T9jdx9GB2sW4xULGW473D+GPUHH/T+gMzSTCZuncgre19BVaK6eXbY2+P01ptUnD1L4S+/NLjOO9wBhYOcs7vq2mbj5IytiyspZ0+22o5zO7cht7SqKUzPU5Ww66cYnHwUPPJmN+zdLBu81tHTiv/M7Iq9uyVbv4sm7lg2Nk7OhA4YzLld2ygtyG+1Xe1NQtQxJDIZXhGdW3TdsfVJ6LQGBjwa2O6RBJmJhO6jfMlJLib5Hw62SCTC2def7KSEZu9XkJmOVGaClYMjRXnlFKsra9TbDZWVXF67FqvBg5G5urbITo1ewzenvmHcxnGkl6Qzp88cfh/5OwM9B7b/PRLLGOk3kj9G/sHCQQuxkFnwxoE3GLtxLCeyT9zQ3soXq8fV5H79NQAisQj/LkpSL+RTVaHDycePypJiSvLz6lxbcKWDsKrCCqlMjMmhDcg8PZFHRFCpq2TR2UWEO4YzyHMQJO6Bwwsg8kkIGl6zx964XF5Ze5Zu3nYsnNAF2Q1IgNzNyGQyHn70NaYt+RW36d0o91iLufYsnqUuyOWTMLWego3zaOw9O5Jw4gh/fjKbla+/QMKJo0ZH6y7D+BdymyARS3iww4NsenAT0yKmcSDjAKPWjeLLk19Sqat/DmBboxgxAssBA8j96ms0qvqdO7FYRPhAD7KTishOKqrzvHdEV1QXzrdqnpe2spKEqKME9OyDzMSUylItWxefx9RCxrBnOmJqJsVQUUHR5s2opk4jtktXYjt3IS6yGynjxlPwyy9ItaWMfrETrh2s2b38IpmXCuk+ZiwGvZ4TG/9ssU03A0EQSIw6ilfHTpjIzZq+4Ap5aSVcPJJF+CAPbJzaNiLTEEE9nbFWmhG1NaXOm4GTbwfUaSloNU3PMITqN31bF1fEYgmqi9Wz9a7qXxVv3oy+qAjbxx9vkX1pxWk8vuVxlpxfwgO+D7B+9HpG+49GIr65s/BEIhEDPAawduRa5vabS7GmmCf/fpJZ+2aRU5bTqj1lrq7YTZ5M8YaNVERfAKq7CQ06geSzeSh9qkdZ1Tf4Of/KkOfLeWY4eZhRceQw1iNGIBKJWBW7itzyXF7q8hKiikL4ayo4BMDQj2quP5lawNSfTxLgZMXSyZHIZbfPbMHbFZFIxNABo3nlw8M4TnqU6J5/Uax/iw6JG5Dkm5Kf3Qs7r+eIHPV/aCsrWP/5HH6f8zZllwub3txIk9wOEj1GB+s2w1xmzvRO09n04CZG+I7gx+gfeWjDQ0RlR7X72SKRCOf3ZiMSi8l6990GP00F93HB1FzKqb9T6zznHdEFnaaKjNiYFp+fdPoEuqoqgnr3RxAEtv8QTXmRhvuf6Yi5woTSg4dIGDKUzFdmUhkbi82Y0dg++ijWY8ZgqKgg58M5JPQfQPHyZQz7v1AUjmZs+z4aicyGkH6DOLdj62354pWvSqUoN6dF6UFBEDiwNh4zSxmR13XdtTdiiZjOQzzJSyshI672vXTy80cwGMhLSW7WXgWZ6TUF7qqYAqzs5Fgrqx3MwtW/YtrBH/Pu3Zpt298pfzN201gySjP4ZuA3zOk7Bxu5TdMXtiNikZjhvsNZP2Y90yOms0e1hzHrx/DnpT9bFa2wf/r/kNjZkfvZZwiCgJOPAis7OQlRuTh6+oBIRG5KXcHR/Iw05JZWFOYYsKvKAEFAMXIERVVFLD2/lH5u/Yh06npNkuGhpTVzBuOyS3jixxM4K+Qsf7I7CrmxWLslSMQiHrx/LC88fxSzniPYev8hCoS5hFz4gcrULKIPWOHV6XnumTSVzPhYVrz6HKnnbn6ZyN3G7x+9zcav595SG4wO1m2K0lzJh30+ZOnQpegFPU/8/QRzjs6hTFu/0GdbIXNxQTlrFuVHjlL0Z/0RHxO5lI73uJN8Vk1BVm17PEI6IpFKST7Tcocw9tB+LGztcAsOJf54DqqLhfQd2wGlm5ycefNQTZmC1NYGz59+wn/3LpzffRenV2fh/PZb+G5Yj8+6v7AcNIi8r74i+/+eYMhoB3RaA1sXn6friIfQ63S3ZRTr0vEjIBLh27V7s69JPJVHVkIRPUb5NjqMuT0I7OmMmcKEU9vTaj3u7FfdwdicOiydRkNRbg52bu4Y9AbS4wrxCLZFJBJRceECldHR2Iwb36yUniAI/O/M/5i5byb+Nv416cDbCTOpGdM6TePPUX8SaBfI7MOzmbpzKlmlWS3aR2JpicOMZyk/fpzSPXsRiUT4RypRxRSg10mwc3Unpx5F92qJBhdEiDCP3oW8Y0dMfXz4IfoHSjWl1aKip5ZXj8K5d3aNJIOqoJyJPxxDLpOw8qkeOFq1/TD3fws2FqbMeOYjhvb5FVGEgqXDTuOW8D7eKVuIO5bLhcN2DHv2Q+SWVvzx8bvEHt5/q02+o1Gr0jBpZXNMW2F0sG5zerj04M9Rf/J48OOsjVvLg+sf5HDG4XY902bsI5h3707Op3PR5uTWuyZ8oDtSmZjTO2q/ycrkctxDOpJ06niLPqFXlZeRfCaKwJ590WkEDv+ZgNJbQUgvJzJeeYWCH5Zh8+h4vH/7DYuePerVRJIHBeH29Ve4zptHVWIil6c9zoB7rchLKyH2SAVBfQdwdscWKkqKW3ZD2pn4owdxCwzB0rZ5UgF6vYEj6xKxd7MguE/L6pPaAqlMQsQgd1QxBeSlXRuKbmlrj4WNLTnNqMMqzKqOoti5upObWoKmQof7lfTg5TVrEcnlNQXYjVGlr+L1A6+z6OwiRvmNYtl9y3CxvH3HmHgqPFl23zLe7PEmp3NP8+CGB1kbt7ZFfyu2jzyCia8vufPmIWi1dIh0wmAQSDqTh9Lbt04noSAI5KvSEEvtkUhFmJ3bj+KB4WSXZbPq4ipG+I4g0CCGbW+A7z3Q81kA8kqqmPjDMSq1elY+1QMPu5uThr6bEYlEDO/VmZGTtxEp7sqKCRou2W2h66kv0KnV7P0llwET38E1MJitC78g6dSN1e39W6ksLaW86HKDmnA3C6ODdQdgLjPnte6vsXL4SsykZjyz8xk+P/E5Wr22Xc4TicW4fPgBglZL9gcf1Pvib2ZlQnBvF+KPZVNaWLtGzL9bLwqzMmu6xJpDwomj6LVaAnv35+TWFMqLNPQb60/OBx9QsmMnTm+8jsvs2TXt+qWaUnal7uLnmJ/5MupLFp1ZxI7UHaSXpGM9ckS1aKqFOXwwjZCOZpzbk453xFB0VVWc+Xvzjd2gNiQ/Q4ValUpAz75NL77CxUNZFOdV0HO03y3r4grr74ZMLuH09mtpYpFIhJOvPws2DDYAACAASURBVNmJTUewrkk0eKC6WACiakFTfWkZxZs2oRg+HIlC0ege5dpyZuyawZbkLbzQ5QXm9JmDiaR9ZCraErFIzKNBj/LnqD8Jcwjjw6MfMm3nNNQVdTtz60Mkk6GcORNNcjKFv/2Gg4cl1o5mXIrKQenjR2m+mvLia/WR5UWXqSwrRVOpwF5eiljQoRg2jP+d/R8GwcCzHZ+ulmSQymHMYhCLKa7U8t8fj5NdXMmPT3Qj0NmqvW7HvxJ/J2smPbeU0KoppPXRsLpPKp2PfYxZeQ5/L40jfOg0HL182PDlx6gunLvV5t5x/FMC5lZhdLDuICIcI1g7ci3jA8ezPGY5k7dNbrdOQxMvLxyff57SXbso2bat3jWdhngiCHBmZ20b/CKrU10JUUebfV7c4f0oHJ0wU3hwZpeKoJ7OiDcu5/Jvv2H/zDPYTa5Wlr6Yf5F3D73LoN8G8eLeF5l7Yi4/X/yZxWcX8/Lelxn+13D+u+2/HBYl4bliORKFAqflr2BlLeHk3yV4d4rk9LaNaKtuTuNAU8QfPQgiEQE9ejdrvVaj58TmZFz8rPHqeOt0vUzNZYT2cyPhZC4lBdfupbNfAPkZKjSVFY1en5+uApEIWxdX0mMLcfSwQm4po3jTJgzl5diOG9vo9SWaEqbunMrx7OPM6TOHKR2n3HF6TO5W7iwZsoS3e7xNVE4UD214qNnRacuB92DevTvqBQsxlJbiH6kkI64Qa6UXQK0o1tUOwvJSS6wzz2DWtSsqeTnrEtYxLnAcbieWQdZZGLUAFC5UavVMWR5FXHYJ/3u8K129WibCaqR52Fua8vKzr2AnehU7n0rmjSkhPOozrCvS2fNzEpGjnsda6cym+Z9RXnT5Vpt7R1GYlQFgjGAZaRmmElPe6vkWX93zFSnFKYzdOJZtKfU7QDeK3aSJyDt2JPuDD9Hl1W39VjiYEdDdiej9GZQVXescs7JzwNmvA4knmudgVZSWkHr+DIG9+3FicwoSiZgwpxzy/7cY64cfwvHFF6jUVfL5ic8Zt2kc21K2MdxnOD8NWcr+QUs42elNjnWcya/hL/FKwAQySzN5bvdzTDozE9GiOcgs5QSd+4Hi/EpMLXtQUVJM9N6dbXafboT4o4dwCwxutgjq+T3plBdp6DnG75Y7FB0HuCEAMQczax5T+viBIDRZ6F6QmY7CQYlIJCM7uQi3QFsEQaBw7RpMg4KQh9dVi79KqaaUp7c/zfm883zW/zNG+/8/e+cZHlXVteH7zEx6mUx6b6TRWyA06b1KFxSRDi8iKKCioq/4gRVeioKICjaQ3gWV3gmEEiCEkAbpvU3qlPP9OIIiCQRISIC5r2uu6Mw+++wzTDLPWXutZw2oqkt67AiCwPCg4fza51dsTW2ZtG8Si84uum90WjIffRNdTg5Z36zCP9gJUQR1jmRjkv6PPKxbFYQymS1WMaex7tWLJeeWYKYwY6KyARxfCs1fgbp9bzdvPhOfzcJhjekU6Fht124ATI3kzJowDr3iPZrYlPDF8yU0OLsQZVkah9fdpN2IaZQWqvnjm2UGC4cHIDspAZlcgdKxer0B74dBYD2hdPXqysZ+G6ljU4fZh2fz4ckPKdVVrjy+sggKBa6ffIy+qIjkd94t9xe8RR9v9DqRc3vvrCj0a9GalOhrlfKeuhF+Hr1Oh4tfU6LPplEvxI68+e9jEhCA8/vvE50bzbBdw/gh4geGBgxhf8h8/psYR/Nv+6D6rgfC5nGY7ZhG/e2v88rvn7A7/gYLrBqRnH+TF0Jf5ersAVinXsan+BLxl42x9/Tn7M6t6O9hqPo4yEpKIPNmfKW3B0uLNJz7/Qae9e1w9X/06jixrIzCEyfIWbeOzG9WkbHsS/J276YsPr5SJc7W9mZ41bcj4ngyOp00/rZVwI3yHcVvkZ2ciJ2bOymxeei1Im4BNpRciaA04iqq4cMqFI/F2mKm7p9KZHYkizouood3jwe86tqJn8qPdX3WMSxgGKuvrOblPS+TkH/v6LRZ/fooB/Qn+4cfsBbysXW1IC5cjbWD450CK+kmMoUJcpk51uoEbjZ340DCAcYEvIBq10yw84MeC9Dq9Exff4F9V9P4b7/6DGjycN0YDDwYpkZy5kx4mUL5W/jYF/PFAA31w5agKCvkxJYcWg58kZizp7l88M+aXuoTQ3ZyomQB84BdMaoag8B6gnGzdGN1z9WMazCOTVGbGLN3DKmFqVV6DpM6dXB8czaFR4+S88vau15XOpgT1NqZK0eTUef8LfDqBEuWAzFhofc9R/yFMEytrEmKNkaQCzid+BFdXh6un31KeG4Eo/eORl2mZmWz2cwN34/Vz0Mg9hC0GIc4aBWJw//gwvMHCO+5keh2ixBdmtPvyp9siYmkqWDKu+nfcmJsMB5nVmMmKwVZM/Iz0rh26liVvU8PQ9Rf5/ev5Pbg+T9uUlqkpdUA30c6b/GlSyS9MZOoNm25OXYcqR/OI2PRIjK/+orkmbOI6dmLmK7dyP7xJ/RFRfecq0F7N4ryym4bj1qq7DCzsiajgpYtIPnT5CQnYevmTtK1HASZgKu/DbmbNyGYmGDdt2+5x2l0Gl4/9Drn08/z8XMf17pKwUfFVGHK3NZzWdRxETcKbjB011B2x947X9Bh+nTJmmHxYgJaOpEam4fK1euuLUKFkT02xYlYBjflf/GrsTO1Y9T101CYCYO/RSs3Y8b6C+wOT2FOryBGt/Gu5qs18E9MjeS8Pu4V5OrR2LiUsKFtAQ3PLqY4r5jUeB886jXi4JpvyM8ov+jIwJ1kJyXW+PYgPGsCS1MC33aDX4bBlklS1czhzyB0FVzaBDEHpFwEdQY8IeFYI5kRM5rPYHGnxcTmxTJ813DC0h7eSb08VCNHYtGhPemffUZJVNRdrwf38kbUi5zbG3/7OTt3T2ycXe6bhyXq9cRdCMO9bmMiT6bh61KGdt9OHF6bxnnrHCb+ORGVsQ0/WTWlzZbpUJCKvt9S/uh5iIkZQwnerqLdD5k8/2sq/bdp6LrPmYBLL9LXdDXX7EewIuYqYwpK+J/1SSJ6eVPnyloKcl2xUDlzZvumGg27R506jltQPaxs7e87tjCvlIsHEvAPdsTB8+ESjstu3iTx9deJHzqMwuPHserZA/fly/E7cpjA8+cICr+Iz5bNOM/7EIWLC2kLFhDdqTO5myv2bPJsYIeVrSmXj0g5D4Ig4FBOJds/yc/MQFtWiq2bB8lRuTh6WaFAS/6u3Vj16I7c6u7rE0WRuSfmcjzpOB+0/oCePj0f6j14Eujm1Y3N/TYToArg7aNv896x9yjSlC90/2k+6mklJbbLFK7kpCSRmybdbGUmJKDT2aBMDSettR/n0s8xRdUU82u/QZe5aJ0a8fqGi+z6S1xN6lDnsV2rgb+xMTfm5fEz8cjoRmRjLRFeqfhHrCUlOh+vpsMR9XqOr/+pppdZ69FpteSmpaB6yH64Vcmz1WlSWyKZ5xWkQPpVKM6GMnX5Y+UmYO0C1u6gdJPC6HZ+YO8PtnVum/DVFrp4dsGntw/TD05n/O/jmd1iNiOCRlRJno4gCLjOn0/sgOdJmvE6Phs3ILOwuP26tb0Zddu6cOVYMk26eWJtbyb587RozbnfdlBaVISJefnvV/qNOIrychFknui0ehwPrMC0USMS+zbn1X0T8LJ045vMfOwvfYu+6cusV03gq32ZJOZE4KI0pVOQI8FeKjxszZEJAmU6PVeS8zh3I5exUf1wE5vxtXo1lpqbLKgfzf+uWmFbEEOOZWMybvzOjYvn8G7S/JHfowclPT6WzJvxdB4zqVLjw/bcQKcVadnv4aJXudu2kfrhPADs/zMF27FjkVve3XbItF49TOvVQzVsGEXnzpOxaBEp776L+uhRXD78L3Kl8o7xMplAvedcOb09lpzUQlTOFjh6+3J+7050Wm25zWxvJV1bO7iSFp9Fk66eFPy5D31BATaDBpe7/uUXl7M7djfTmk5jcED5Y54mXCxd+L7H96wMX8nKiyu5kHGBT5/7lPr29e8aazdxArmbNlH09UJcGk2nMM8LBIGrRw/SpGdfivJyUJg1QJV/nKXKGDwVLgw68yv4tEcbMpU3Nlxk58Vk3jaIqxrH18GSNiM/wmndUFb1SGfe2nPY57fkwp+B1OvQi/D9O2jedyCO3o8WxX6ayUtPRa/T1YoI1rMlsMxs4OXtdz6nLYPinL8e2VLIPD8Z8pP+eiRD/HEIX/+PgwSw8QDnRuDWDFybgksTMK/ZahtfG1/W9lnLO8fe4ePQj7mSdYW5reZiqnh0szWFvT1uC7/g5thxpLz/Aa5ffH6HeAvu7cO106mc2BJDz4kNACkP6+zOLcScPUW99p3LnTf+ghRtS423wc0yD9Oka8jmLWH6kddxNFHx3c04VAUZxHX5mqnn3Ik4mUCwl4r3+tSla10nFOX0Q+sQ4ABAekEJP528wYgTLswu+p43xNP8X3dY8OtGwhrOwsjkJKE7NteIwIo4ehCZXEFgm/b3HZufWcyVo0nUbevywC1x9CUlpP7f/5G3aTPmLVrg+sXnGDk5VepY82ZN8fxhDVnffU/G0qWUXL6M5+rvMfbwuGNcvbaunNkVx5VjybQb4o+jty86jYac5ETsPb3vmvdWCbWm1Aq9LhO3QBtyP9uMkbt7uc7t26O38/XFrxnoN5AJDSc80PWXiyiCOh2yYyA7VrrhUmdIDuaaYtAUgagDBJAbgakSzFTSw9QGzO1A5Q12dcDCAaqp2EAhUzC1yVRCnEOYc2wOL/32ElObTmVM/TF3tP6RW1riMO1VUj+ch2e7HE7HKHCuU4+IIwfwaCAVC8gFJQofBRfLrvO52gIjhQna/iuYuekSOy4m81bPICYbxFWtoK2/A+eDP2fy5RdZ2FvGvHU/cDbkv+Rm1cXEfD/H1v3AoDkf1vQyay237IFq2qIBnjWBVR4KY7Bykh73oqwQsmIg6zpkRkNGpLSdGLnr7zEqH/BuCz4dwbcDWD7+ChwrYyuWdFrCyvCVLL+wnOjcaBZ3XFwl5osWrVrh8NprZCxejHlwc1QjRtx+zVJlQrMeXoTujCP5ei6u/ja4BgRh7eDE1WOHKhRYcRfOYu3gSVmpCc5hKzHr2Z3pGcvRaEv4KvkGNoIxPwYt54PfTHC0KmXFi83o2cC5UpE5RytTZnYP5KVWXszZ4ojb9Z/p5bSNH9qJ9Io4QpxDYxKuHCU1Ogpnv4BHfn8qi16n4+rRg/g2C8bcWnnf8aG74hBkAi16+zzQeXRqNQmTJ1N8Ngy7yZNwePVVhHIiSvdCkMuxnzgBi5CWJEyazI0XX8JzzWpMfP++gza3Nsa7kT1Rp1NpPbDO7bvr9PjY8gVWUiKmVtZkJuqRyQTsTAu5eeoU9q9Nu8tA9kL6Bf578r+EuIQwt/Xch4vIlhVBwinpRin5PKRckMTUPzFRgrkKjC3ByAwEOSBCaYEkwopzoSQXxH8l/xtbgZ2vFN2+dcPl0lgSZVVEsHMwm/ptYt7JeSw5t4STySeZ324+zhZ/V0jZDB1Kztq1iJuWIPN/AwvbxqRGr+XygT8AsCoqZKdPGvUUSrrHXaJsyE9M25XK71fSeLNnIFM6GsRVbWJyj+a8d/1Nmsnm81szPW2uruMqL+PTtCeRxzZx83I4ng0qrrR9lrntgWWIYD1BGFuASyPp8U+KcyShlXweEs/C1V1w/mfpNcd64NMBAnuCVzuQP563WybImNJ4CnVt6zLn6ByG7xrOFx2+oKVL5VuxVITdxAkUnT9H6oKPMfHzw7zF3xGHJt08iTiWzLGN1xn6djCCTKBuu46EbttIYW4OFjaqO+YqKVSTHBWJlUNbrGQFKAviWdXWkRv58XydpcZLZs4MiwVsP2vEsGB35vath9VD9EFzsjblu9HBrD/jxOWdMkx9dpB5fS+msjkUykIJ3bGZ/m/MeeT3prLcCD9PUV4u9Tp0ue/YrCQ1106n0rSrJ5aqyrcp0ebkkDBhIiWRkbgu/AJlnz6PsmTMGjfG88cfuDl2HDdeGoXnmtWYBvwtSoNaORN7PoOEK9l41ndDYWRMenxsucI6KykBW1d3kqJycPS2pmjXdhAEbAYOvGNcRlEGbxx6AxcLFxZ2WIiR7AH+7fNTpJufqzvhxgnQayTR5FgPAnuBU0NJFNn6gLWrJKruh14PpflSlDsnTrrhyo6Rfiacgcub/x5r5y+JLc/W4NMebH0fKdKlNFHyRYcv2Ba9jY9DP2bwjsG8G/IuvXx6IQgCgkKB09y53Hx5NE6N88lOdcbIxJQrRw4ACuzyk1jhncf/EtLRNp/I6BOOnIxN4/2+9Rjb7sGEu4HqRyGXMXXUSDYuO8belqdpe/0cyuLOpN/0wtLOnuPrf8Kzwec1vcxaSXZSIhYqW0zMLe4/uJp5tpLcqwMzldReot3r8MIv8GYsTDwEXf8Llk4Qthp+HAALA2HndCmRvpoc2P9NR4+OrO2zFpWpiol/TuTHKz8+clK3IJPh9tlnGHt4kPjqNMpu/G3PYGQsp9XzdaTWNKekBNu67ToiinqunTx611w3L11A1OspKXLF+dpe0vu1ZEfRSWYUlNJcIzCi9F32JJrw2eBGfDak8UOJq9vrFgReaOlJr9Hvokzvw/H2BXgk/o7MuDHXT5+4bUz3OLhy5ACmllb4Ng2+79hT22MxNlXQrKdXpefX5uRw8+XRlEZF4f7lskcWV7cwDQjA66cfEeRyEiZPRpv5t/O4ZwM7zKyMiDyZgkwux97Lm4wKrBqykxOxcXIl/UYBbgFK8rZvx6J1a4xc/o6yanQaZh6eiVqjZnGnxShNKhER0hRD+Ab4oT8sqgu/zZK2+FtNhhc3w9s3YcoxGPCV9Jx/V2mbrzLiCkAmk9IM7P3Av5s0R+/PYdQWeP0SzI6FlzZDp/ekXM3YQ7BrBixrBovqwZaJ0s1Xzt1N0iuDIAgM9B/Ixn4b8bb25q2jbzH94HQyiiSPOouWLbHu0wfXk6spUYOFbT0QRQS5LbnmsTSS6Qi2DmRobC/OxGfzv+GNDeKqFuNha45Hj/cYlSOwtKeeOpEbKCoQcfbrSHLUVVKir9X0Emsl2ckJtSJ6BQaBVfXI5FJOVrvX4eVt8GYcDPtJ2jK8tAl+GghfBMDumZB6qdqX46P0YW2ftXTy6MTnZz/nraNvVViRVFnkSiUeX68AQSBh0mR0uX+7DAe0cMLZ15oTm6Mpyi/Dzt0DR+86XD168K554i6EIVeYIpc74lxwibneZ2mjFRiRX8zw4reJE53YPLkNw1p43HXsw9LWz56hEz8iqLglRwJPYq11AWSEbn88TaBLiwqJOXOKoLbtkSvuLRiTo3OJD8+kWQ9PTC0qJy71RUUkTp5C2Y0beKz8GquOHatg1X9j4uOD+9cr0OXkkjj1VfSlkjWHXC4joIUzcZcyKVFrcPTyJT0u9i5BX1yQT3F+HnJjO0S9iL2QiSYpCeXzd5qFLgpbxPn088xrM48A1X22b/NTYP88SVRtmSBFlzq+DVNDYdpZ6P5/kpgyuTupv0qxsAO/rtBhNoxYBzOvwatnoc8i8AyB6P2wfSosaQSLG8K2qZIgzH+whs9e1l782OtHZjafyfGk4wzYNoBfrv6CVq/F8c03URUnEKC5SGGBtFUrk9lwyjuO13ILGZEzieisMla9HMzAprXjS8hAxQwJqcM1i5l42xRzxT0O++xLpMa6YmxmzrnfdtT08modoihKFjAGgfWMYGwO9frDkO9hdjS8sBbqdIZzP8HX7WBVF+m/ywqrbQkWRhYs6riI6c2mszduL6P2jLqvieH9MPb0xP2rL9EkJUkiSy2tX5AJdHqpLmWlWo78Klk61H2uI6kx1++IEol6PbHnziLIPXFKC+NoCxCMdHyUksqYohlkmfuyeXIbGrpXXS7LLeq7Kun9yjIc3WwxLdiF3Lg+Vw7vpzA3p8rP9W+unTyKVlNWYU7aLURR5NTWGMyVxjTqXDmBKWo0JM6YQfGlS7gu/AKL1q2rYsl3YVa/Pq6ffkLxxYuk/MOANrC1M3qtyPWzaTh4+1JSqKYg684OALcSUMtKrJEpBEzP7EUwN8eqa9fbY/bf3M/PV3/mpbov3duOIS8Jdr0uiZWji8CrLby8A167KAksh8Cqv/gHQRCkSFaLcTB0jfT7/59T0OszKV8rcpckCBcFwZctYfcsiNgBRdn3nVouk/NKg1fY3H8zDewb8EnoJwzfNZwzumgcZs/C9dgqHDQ6ZEZ1sNRYYe1WwGr1aJJkLmyc3IZOQQaH9icBQRB4ZfhwgtIbsfk5Ee+4bWi1clRuwUSdOlYpI+dnieL8PEoK1djWAosGMAisx4uRGQT1gSHfwcxI6PmJlES741X4IhD2vPXQ2wf3QxAExjccz/Kuy0ktTGX47uEcSTzySHOaN2+O66KFFF++TMKkSegLJZFl62pBiz4+xJxLJ+ZcOkFt2ktl48cO3T42LS6GorwcBLkvTpmn+alhLvNSU1lYOoYc++ZsnNwGT7vqs8Ko76ai3aC13GgWi12xBaJex+mt1RvFEkWRC7/vxt7TG+c6947K3LiURUpMHi36+GBkXDk34tSP/o/CI0dx/u8HWHfrVhVLrhDr7t1xmDGD/N27yd2wEQAHDyvs3C2JPJmCo7e09ZT+r5Y5txJQ8zPNcPKyovD337Du1hXZXzYeKeoU3j/+PvXs6vF689fLP3lxDux9B5Y2lW5Omr4E08KkLXrfDtJWXm1EEMCxLoRM+kc6wWHo9pFUlXxhLWwYBZ/5wsr2sOdtKcKVeV3K/yoHb6U3K7utZGGHhRSUFTDpz0nMVP1BxqdTCUjeiLW8DYKQimtBXaKderJ9alvqud67ibaB2oWfoyW6VnPpKpZxsF4aLiknyc/yQ6/Xc+GP32p6ebWK2xWEhgjWM465LbSaAlNPw9jfIag3nPlW+tLYPL7atg/bubXj176/4mLhwtT9U/k09FPKdGUPPZ91t264ffE5xefPkzB5Cjq15CvWrLsnDp5WHF53DZnCCq+GTbh8aB96vdSeJvac5PBuqTHnWEA0HXVFRBV245J9X9ZOCMHBqvIJ3Q9LywB3WvT6lhzr35Eb1eHiH7spvY9z+aOQFHmFjBtxNO3Z957VcHq9yMltMSgdJX+xypC7aRO5GzZgN2E8qmH3bpRcVdhNnIBFmzakffwxpTFSa5agVs6k3yhAbuwoOYz/o2ULSAnucoUROWkyHBQ56AsKsO7fHwCtXsubR95EJ+r4ov0XGMuN7zyhXgdnvoOlzeD0Cmg0VBJW/RZLuVRPGjI5uDaBtq9JuVtvxUt/CzrOkaoTw9ZIEa4vg+FTb/ihn2SOHLpK2m5MiwB1BoJeS3evbuwcuJO3m88iLjeGV3O/ZtLwRGLM55EeeIyMBv9lw6RWOFo/umWLgcfP2C6N0RT342hLEcf0/YiiElu3+oTv24O27OH/fj9t3K4gdKu6tJJHwSCwahpBAM9WMOgbmB4uia5re6Ttw58GSaXlVYyHlQe/9P6FEUEj+Pnqz4zcPZLY3Hv3jrsX1r164frppxSdO8eNESPRJCUhk8voMroumhIdv6+6TMMuPSnIzLjdOifq1CkEuSvO6Wc53Eyka4Yj22zH88v4EGzMje9zxqqja0gIZp26Y1MsoteXceyX9fc/6CE5v2cnphaW1G3X8Z7jroemkp1cSEh/X+Tl+Hz9m+JLl0md9xEWbVrjMGNGFa32/ggyGS6ffIzMzIykmbPQl5XhH+wEAsRfykPl4nZXont2UgIWtk6ADMtrx1A4OmLRqhUAqy6t4kLGBT5o/QEe1v/6A5kWAd91g91vSFGgiYelZHVV5ZP/az0KY+lvQce3YMxumJMIU05A/y+h4WAoyYezq6Xk/Z8HwYrW8IUffGQPH9pg8n8uvLjpNfZcC+eX5FRWZOTi5upDw87f8eHgFpgoarYvm4GHx9RIToNeM+hfBHuapGOfeZGSwroUF+SXW0D0rJKdnIDC2AQru/t3x3gcGARWbULpBj3mw+uXofNcSA2HNb2lKsSEM1V6KlOFKe+EvMOyzstIK0pj+K7hbIp6+NYxyn598Vz1DZrUVOKGDafo3Dns3CzpNCqI5Ou5pMbaYmXvwIW9O1HnZJOVGIdC4cUll1BGlZTytcWb/Di+NSqLxyeubjH2xXfJCbqGXO7Oxf07KSmswN3/EcjPzOD6mZM06NwdI5OKowg6jZ7TO+Nw8LTCr9n982S0OTkkTn8Nub0drgsXIjzm5qZGjo64LJhPaWQkGUuWYGFjgluADdfPpOHo5XPXFmHGjTiMTJ2QKwSMju/Aul9fBLmcy5mXWXlxJX18+9DLp9ffB+g0cOgTacssJx4GfQuv7L7bLuVpRK4Ap/rQbBT0/R9MOgzvJMMbV6X3YMhq6PU5dH4POrwN7WZQ2G4Oux2msazgVT61+pFek3+lb4dWNX0lBqqAPk08SVeMI66eFqe0/ehEd8ys7Igop4DoWSU7KRGVq9tdfno1Re1YhYE7MVNB+1kw4xL0WACpl+G7rlIPxZSLVXqqjh4d2dx/M00cm/DhyQ+ZfnA6aYVpDzWXRZs2eP+6Dpm5OTdeGkXa55/j18iGxl09uHwkBZeAdty8HM7pbZsAsFWXkNIwl+MlU1k8vid2ltW/LVgecpnA6DfXYyYrQhTL2DL/syo/R/i+PSBCk+73tky4fDSJgqwSWj9fB0F2b98kUacjeeZMdJlZuC9ZikKluuf46sKqUyeUQwaTveYHSiIi8A92Ii+9GHMbN/Iz0ij5a9u4KC8XdXYWWo0tdhYlyDUlKPsPoFhbzJyjc7A3s+edkHf+njg7Dlb3gkMfQ/3nYeoZaVuwmpzTnwhkMsm3y7sdNBgEIROh/Wz0Hd5mg3IMbU80Y05Sa+p3HsG6/3TE16GaKycNPDYEQaD3tmeMyQAAIABJREFUwDG0K7TmWEAcNvmxIAvg5uWLhmT3v8hOrh1Nnm9hEFi1GSMzaD0Vpl+ELu9DwmnpTn79KMi4u+nyw+Jo7sjKbiuZFTyLE8knGLD977LvB8WkTh18tm7BZsgQsr/7nrjnB1LfOAr3IBtuRjgjkyu4sHcHyKzItDiPc0krXhs/AXdVzfZ2tFUq8X+lD0Yyd1JiwslJerDS+XuhKSkhfN9e6gS3ROlYcceAkkINZ3fH4xaowr3u/cVSxpKlFJ44ifP7czFr2KDK1vswOM2ejVylImXu+/g2tkMmFygulCpAb20T3srHKlIrUaaEYxIUhGlgAIvDFhOfH8/8dvOxNv4rAfvyZvj6OelzPuR7GPytZINg4C5OxmTR/6tjvLkpHH9HS/ZMf44ZXQMwqsT2soEni+bedhTZ/4fIxjpck/ahE4NAFLl6/HBNL63G0ZSVkpeRbhBYBh4QE0t4bibMCJe2AmIOwPIQyVMn99HsFm4hE2SMrj+arQO20sShCZ+EfsLgHYM5cPPAA28byi0tcZn3IZ7ffwcyGalvziJo97s4WYsIcql03gRnSv1S6DryfwQ6W1XJNTwqnbsOx9ixGNCx7p33q2zec3t2UFyQT4v+925SHLojltIiDe2G+t+3JUzBvn1kffMNNkOHYjNkSJWt9WGRK5U4v/sOJVeuULx1PZ71bEmPlyKSt7YJ0/4SWDKZI1bXjqLs358L6RdYF7mOkUEjCXEJkbYE974Dm8aCUz3JGLTB09/c+WEIu5HN6O9DGbHqFNnqMhYPb8L6ia3xc6wdv08GqocB/YbQosSK856XMdfoMTF34+qRAzW9rBonNyUZRLHWWDSAQWA9WZgqodMcKaIVMkUq4V7WXPpCKqyaELGHlQcruq5gccfF6EU90w9O56XfXuL3+N8fOKJl0aYNvrt24v7lMkzsbAjaPQe7EitAjkyeR0i/1QT7OlTJuquKMZ+twEjmRHFJGkc3bXjk+YrVBZzZsRnf5i1xDahb4bjMxAIuH0miQQd37N3vva1TGhtH8ltvY9qwIU5z33vkNVYVVj17YtmhA+lLluLrb0pRgQJTSyXp8ZKwSo+PxcTcFoXcGGt1Ama9u/PBiQ9wtnBmerPp0mf4p4Fw6itoOQlG7wIbzxq+qtqFTi/yZ0QaI745xeAVJ7mUlMdbPYM4MKsjzzd1Q3afbWUDTz7+Tlbo7adwsakO55QT6MQAMm7Gk3Ej7v4HP8VkJ0s+i7WlghAMAuvJxMIeei6Aaeeg4VCpZH1JYzj0qeSr9YgIgkAXry5sHbCVD1p/QE5pDrMOz6L3lt4sO7+MyOzIyke1BIHkZh7sebs982bYcNpjAybGZtj2akDHZrUvUdnExJx6z7cBFJzbtAut9sG3Sf/JmR2bKS0uot0LL1c4RhRFjq6/jom5ES373bt1ib6wkMTXpiEYG+O+dAky48dfFFARgiDgNHcuaLWY/7EGhZEMYwsXMuL/sUUod8RGHYdV65Z8n7KV2LxY3m/9PuZ5yfBtF0gIhYErofdnUlWdAQDiMwtZsu867T87yIQfzxKXWch7fepy7K1OTOlYB1MjQ4Xgs0S/fsNoprMkzewUcqMABEH2zCe7ZydLuzkqF9caXsnfVHv3YUEQegJLADnwrSiKn1T3OZ8ZbDzg+a8kH50DH8GhBRD6jZQgHzwWFI+WNK6QKRgSMISBfgM5kniEtZFr+fbSt3wT/g0uFi40tG9Iffv6uFq6YmNig7nCnEJNIWqNmpv5N7mWfY3wzHCS1EkIQLC+lNZOMhSdX2J4375V8x5UA12Hj+X67ycpKkxh9WvTmbD8q4eaR52Tzfk9O6nbtgMOnt4VjosKTSP5ei4dXwy8Z0scURRJfvc9ymLj8Pz+uzt699UWjN3dsB03lqwVX+M+tjfx11WoM0MpysslNy0FhakvdslhFE1owXeXVtDXty/tNAL81AVkCnhlF3g8elPyJx1RFIlIyedgZDp/RqRxMTEPQYA2deyY27cuXes6oTDkWD2z+DlaIdhNJqzRQtpHxJBq5k3k8SO0f3HMfdMLnlaykxKxdnC8Z5X246ZaBZYgCHLgK6AbkAicEQRhhyiKEdV53mcOh0AY/jMkhsH+D2Hv23DyK8mwsPELkqHhIyCXyenk2YlOnp3ILsnmwM0DnEg+wZWsK/xx448Kj3OzdCPIyosJBcV0uBlOqCaYy83nM7tPi0daz+Ng1OIv+HbiNPKzUgk/vp9Gbbs88BxHflmNXqelzdAXKxxTmFfK0fVROPsqqdv23nde2avXULB3L46zZt72jqoutHotsXmxRGZHklOSQ15pHjpRh8pEhcpUhb/KH3+VP0ayuwWh/YQJ5G3ZiurCbmJMvdDrdFw9JiXhCgpH7NX7+Ng4ByuseNOmqbQtqPKCkRvA9tlsPpxTWEZUWgERKfmcic8mNC6HTLXU57Ghm5I5vYLo19gVV5tKNqY28NTTt99wfv1pKSYFxxGsOqDO3ktabDTOdfxremk1Qm2rIITqj2C1BKJFUYwFEAThV2AAYBBY1YF7cxi9A2IOSkJr+3/gxFLJUyuoT5WUt9ua2jIkYAhDAqTE6rzSPNKL0sktzaVYW4y5whxLY0tczJxRXtkKf36ARqvhndLxaBuOZGH/Jk/EHZaltRLvtk2IOXaIQ1/+RP2QDsgVlf91iTx+mKtHD9Jq8AhsnMuPNImiyKFfrqHV6On8ctA982cKT4eSvnAhVt27Yztu3ANfT2VQl6k5kHCAPXF7CEsLo1hbfPs1mSBDJsjuyMMzlZvSyKERPbx70M2rGypTqfJRZm6O48w3KJnzPop276EBLh/6EwCrUj0Fze05VxDBpx79UW2ZBK7N4MWNUneDe1BcpiMhp4hMdSnZhWVkqcvIUpeSU6ShRKOjVKunVCv9LNPqkcsEZIKAQiYgk935UyGTYWIkw1Qhx8RIholCholCjqmR9NNE8e/XpedMjf5+7Z/j5RX82+n0IqVaHeoSLRnqUjLVZWQWlJKpLiUlr4SotAKi0tS3xRSAm40Z7fzsaFPHno6BDgb3dQPlUsfRCqX5cM7UWYdX4fNoEIg+c+qZFFiiXk92ciLuQfVreil3UN0Cyw34Z5lbIhBSzeesEL1e5HhMJjZmxtiYG6E0N8LKRPFEfOE/EHU6gW9HuLoD9n8E61+Umsu2nQ71npcMDKsIpYkSpcm/GjKnXIQtQyDxDBl2LRicPJLAuo1YPrTxE5WE+/y0N1hx5ipFpSl8++pUJn29slLH5Weks+/b5bgEBNF68AsVjosKTSM+PJM2g/1QOVtUOE6TmkrS669j7OWFy4IFVf55TVYns/ryarZGb6VUV4qrhSsD/QbSwL4B9e3r42jmiIWRtL5CTSGZxZlEZkcSnhnO8aTjfHTqIz4+/THdvLoxruE4Am0Dse7bF8tffsE+P5UEwYjMm/EgWOCYeY2lTaNpb+lNryNfgm8nKfpq8ndif5lWT0RKPleS84hJLyQ6Q01Mupqk3OK71i4TQGlmhJmRHJO/xI+xQoaRXIYoiuj0IjpRRKsT0YsiWr2IXi+i0UnCp1SjlwSZrvxef5VFIRNuCzBBgBKNJPY0uopzFS2M5fg5WdEp0IEAJyv8nSwJdLbCRWmIUhmoHG17TWSr+iecDl2g0MadqNMnaPfCqJpe1mOnIDsLbWkptm7PVgSrvG+CO/7iCIIwEZgI4OlZvRVDBSVaRn0XesdzcpmAjZkktmzMjLC1MMbJ2hRna1Oclaa4KM1wsTHFXWX2ZLWaEASoNwAC+0D4r3B8CWweB/v+C8FjoOkosLy/U/gDkR4pmUJGbANze8JbfsrAYx6E+NqxbETTJ9KXZ+iiBaybNhd1TiIHVn9H5zH3jh5py8r47csvEEU9fabNQlaBs3puetHtrcHGXSquetGXlpL42nTEkhLcv1yG3LJiIfagZJdks+z8MrZd3wYC9PPtxyD/QTR2aFyhiLM0tsTS2BJvpTc9fXoiBotE5USxI2YHm69vZk/8Htq7t+eN5m/gMmsWDjOXkujugKhLRqZwRGcaQ6KjyJcRxxEC+8DQ1WgFIy7eyOHY9UyOx2RyMSGXUq0keMyM5Pg6WBDsrWK4gwfe9hbYWxpjb2mCnYUxNubGFUaPHgSdXqTsHxGw2xExTTnP/SXM/v5/6blbokovcjvydeunhbEce0sT7K1McPjrp4Wx/Om7uTPwWGnq7cAho04kWJ9FZtSHnORD5KQmo3KuPYnej4NbPQhVLs+WwEoE/vnt4Q4k/3OAKIrfAN8ABAcHP1yflkpiZixn4+TW5BZpyC0qI69YI/13cdlfz2lIyi3h3M1csgvvbKApE8BdZY63vQW+9hb42FtQ18Waui5WWJlWnJhc48gV0PQlaDwSovbCqeWwfx4c/BgCe0L9QRDQA4wf8otbr4Prf0LYaoj6XZqn/WxOOY/k5V+u0dDNmlUvBz+xVU729g54dKlL3H4t5/fuwN7Li0adu5Y7tig/jx0L55MUGUHvabNQOjqXO66sRMuery+BAN3G1qswqieKIqnvv09JeDhuy5Zi4utbJdek0+vYELWBZeeXUawpZljgMMY0GIOzRfnrvReCIBBoG8hs29lMajyJXyN/Zc2VNQzeMZgXgl5gYKAFF0tU6HTJGInW7AiK4s20HJz8e3O08af8tuMav19JI7uwDEGQ8o1GtfKiqaeKRu5K3GzMHkvUUy4TMDOWY2b8ZH5ODTy7NO8yi/1ZvfCKMScHiDlziuB+g2p6WY+V7KRbTZ6fLYF1BvAXBMEHSAJeAEZW8zkrxFgho4X3vfM8blGi0ZGeX0pKXjFJucXEZxURl1lIXKaasPhsCst0t8d625lT301JfVdrgr1saeSurH2CQiaDoN7SIyMKwtbA5U1wdScozMCrNfh0kJrNOgSBmU358+j1kJcASWcher8krgrTwdJJMkNt9R/OZckY++1pfB0sWDOmBRYm1V6sWq08P34634S+jFrtzJ8rF5N4NZyu46ZgbCpt5YiiSFpsNLuXfkZBViZ9Z7xFYOvnyp1LFEUO/HCVnJRC+k1vgrV9xdtB2d+vJm/7Duxfm4Z1t25Vci2JBYm8e+xdzqWfI8QlhHdavoOvTdUIN2tjayY2msjQgKF8ef5L1kWu43IjazodaUWuDCxK1di4FRNEK9rGvETyhQtYGMvpXNeJ7vWcaOdnXyO9KA0YeJJ5roEvx36vi6X6KrmWDkSePPHsCazkRIzNzLGwqZl2YRUhPGxz30qfQBB6A4uRbBq+F0VxfkVjg4ODxbNnz1breqoCURRJyy8lIiWPK0n5XEnO50pKHgnZUo6IsUJGEw8bQnxsaeljSwtv29onuECKPt04IYmsuCOQcfXv1yydwcJBElpyIygrkjy2cuJAUySNMbWBOp2h/kAI7AVyI8Ju5PDK96HYWRqzYXJrHK2ejgTdlLRUfn/tPXJNvdGVnEJuZISTrz+2ru4kRlwiNy0FUytrnp/1Hm5B9cqdQxRFTmyO5sK+BNoO8aNJ14q3xAsOHCBx6qtY9eiB2/8WVclW0vbo7Sw4vQCZIGNOyBz6+fZ79Hn1OqkJc0YkFKRAUTaU5AFwRZvPe3kX6LrLG43cA61pBEpX+LRsHO0DnRna3J1OQY6183fDgIEniJ2HjhL581sYa/qgLTnFlG9+wlxZwU3yU8jGj96lrKSYF+cveuznFgQhTBTF4PJeq/bQgiiKvwG/Vfd5HieCIOCslHK0Ogf93Vsut6iMM/E5hMZlERqXzfJDMSw7EI2JQkabOnZ0DnKkU5Bjjffdu41MDj7PSQ+AgjRIuQDpVyHzOhRlSV+WmmJp68/cDnw7SLYQTg3BtckdFhCnYrMYu+YMjlYmrJ3Q6qkRVwAuTs7IBwbg8msa6fYvYGObgKjP4vrp47gEBNGi/2D8WrbG3FpZ7vGiXuTwr1FcOZJEww5u98y7Kjp3jqTX38C0YUNcF8x/ZBFUqitlwekFbLm+hWCnYOa3m4+r5UPmaIii9BmJ3g+xhyDxLGj/lXxuZA4I1Bd1rNeW8G39BEwiGlPgZgSt/o9jrb1xVj49nw0DBmqabm3bcPFoGfaXjclGJCYslIadu9f0sh4b2UkJeDZoXNPLuIsne++mlmFjbky3ek50qyeJLnWplrPx2Ry6lsGByHQOXrsC268Q4GRJj/rO9GnkQqCTVe1JdLVyAqseUk7WA3IwMp0pv4ThrjJn7fiQp7K0fMTQWXwa2Z66YaakKLrg5m/NwLcbYWZ5722tshIth9deIyo0jWY9PGn1fJ0K/81Lr18nYfIUjFxd8Vj5NTLzRxPjyepkZhycwdXsq0xoOIGpTaYifxhftLxEOP8LhK+HbKn1Dc4Nofkr4FQfHOuC0h3MbEFhzJXkPObvvsqZmDQCjUoYPcaDV9qHGHKcDBioBkyN5LjVGYlw8SooLLl28vQzI7BKiwpR52TXqhY5tzAIrGrE0kRBx0BHOgY68kG/esRmFnIwMp39V9P56mA0yw5E4+doSd9GLvRt5Iqf47170NVW1p6+ydztlwlytuKHsS2xt3w0B/naikIuo/fINWws7kfn08lcF0ewYf4ZWg+sQ53mjsj/VSUpiiKx5zM4uuE6hXmlhAzwpXlPrwrFVUlUFDfHjUNmaornt6tQqB4tn+BixkVeO/AaGp2GZZ2X0dGj44NPkhIOJ5bBlS3SdqB3O2g3AwJ7Sy2b/kWWupTPfw9n/dkEbMyMmNO3ESNDPA3bgAYMVDM9e01k7cmOyHM7kxhxEb1eh+wRTaafBG4nuLsbBNYziyAI1HGwpI6DJeOf8yWjoJS9l1PYFZ7Ckv3XWbzvOvVcrBnUzI3+TVyfiO01nV7kiz+useJQDB0DHfhqZLMnPqH9fjQN8ONY0Ah2a3/lhSPJRDafwp/fl3JyWwz+wU5YqkwwMVOQdqOAxKvZ5KQWYeduSc9JDXD2KX/7EKD40iUSxk9AMDHBc/X3GLk9Wkf4PXF7eO/YeziaO/JVz6/wVT5gIntWjFRtGrENjC2l5sshkyTH9XIQRZGNYYks+O0q6hIt49r6MK2zP0rzWlxha8DAU4SLyhLRPxCL4ybkU0Jq9HVcA4JqelnVTlaSZLVpVwsjWNWe5P4gPClJ7lVNWn4Jv11KYdv5JC4m5iEToJ2/A4ObudG9nnOt3FbJUpcyY/0Fjl7PZERLTz4aUP+Z6Y2WV1jG8hWdyInP5ZV9IoXPDSXBvy+p8WpEvfT7pDCS4Rpgg09jB+q1dUF2j/em4NAhkt+YidzODs/V32Ps/vClxqIo8nX41yy/sJxmjs1Y3GnxbYf1SlGSBwcXQOgqUJhCm1eh1X8qrioFEnOKeHNTOCdisgj2UvHxoIb4O1k99DUYMGDg4QiLuErYR4so0KfQpPsguowbW9NLqnaO/LKasN3bmf7T5gp9B6uTGk1yN3B/nKxNGdPWhzFtfYhOV7PtfBJbzycx/VepjL1nAxcGNXOjla9dlZgqPiqnY7OYsf4CWYVlfDKoIcNbeNSePLLHgNLCmIatlnLQ9AW+MTJm4h+baZwcRp/lX6FTuVCi1qB0MENudG/BKWo0pC/6H9mrV2NSty4eX3+NkdPDm7+W6kr54MQH7I7dTf86/fmg9QcYyytpeyCKUrRqz9ugTpNyqzrOkfLyKjxEZPO5JD7ccQW9KDJ/YANGtPB8otz6DRh4mmhWN4ijzrEIaT5cP3nimRBYWUkJqFxca0Rc3Q+DwKpl+DlaMqtHIG90CyA0Pput55L47VIKm88l4qI0ZUATNwY1cyOgBiIE6lItn+2N5MeTN/C0NWfLlDY0cKt42+tppk/bZsScGcqBeltYaGfG7J3pxA0chP2kSdi+MhrZPcSVKIoUnjhBxsJFlEREoBo5Ase33kJm8vC5a1nFWcw4OIMLGReY3mw64xqMq7zoLc6BXW9IeVbOjWDEWnBrfs9DCku1zNlyiR0Xk2npbcvCYY3xsK0l1bEGDDyjCIKAfZs+5G9JprDgGiVqNaaWT2Zub2XJTkrAwat2Nok3bBE+AZRodPwZkcbW80kcjspApxep72rNoGbu9G/sioNV9SaV6/QiW88nseiPa6Tkl/BKG29m9wjE3PjZ1udRqfmcX9WbJW451BXdmRvmS/GBQxi5u2MzZAiWnTpiEhBwW+hokpMpPB1K3pYtFJ05g8LFBae33sK654NXbd6xjpwopu2fRnZJNgueW0A3rwcwJY0/DlsmgjpVili1nXHfXpXR6Wqm/BxGTIaaN7oFMKWjX62IrBowYADyikpZN34ahbpkuoyZQZOe5XeeeBrQlpWx9OUhhAwcStvhd/Zg3P9DBMZmCp4bFlCtazBsET7hmBrJ6dfYlX6NXclUl7LzYjJbzyfx0a4IFvx2lef87Xm+iRudAh2rNKm4TKtn75VUvjoQzbW0Ahq6KVk2sinNvSrnhv+0E+BszZ7GnzA3YhRvOyfzv8EBfPTiKrKXfknG4sVkLF6MzNwc4a/IlC4nBwCFkxNO772HzbChyIwfzbn8SOIRZh+ejaWRJWt6raG+XSW7yes0cOgTOLYIVN4w9g9wv3fUCuC3SynM3ngREyM5P44NoZ3/3ZWEBgwYqDmU5iZo3fLhpjFhO7c/1QIrJzUZUdTfZdEg6kXiwjPxbeJQQyuTMAisJwx7S5N/5GsVsOVcEtvOJzFj/QXkMoHmXio6BDjQyteWhm42GCseLPFcrxcJT8rj9yupbDybQKa6DF97C74a2YxeDZwN+TX/YkLPVnwQPok3s5fxiXAIqzpK5v26Fl1GJurDhymNug46LaJWh4lfHcxDWmHi74cge7SCAFEU+SniJxaGLSRQFciyzstwsqg4X+oOcuJh01hICoMmL0GvT8Hk3tsIGp2eT/dE8u2xOJp62rD8xWa4KCtu82PAgIGao8nwqZxb+At5WSmIev0j/72prWT/VUH4b4GVm15EaaEWZ9+aTWExCKwnGD9HK97sGcSs7oFcTMxl/9V09kem8/nv1wAwUcgIcrainquSOg4WuCjNcFaaYGokx0QhR6PTk1ukIbuwjKi0Aq6lFnAmPpuswjJkAnQOcmJUay+e87M3CKsKMDdW0HXgK2SsC+U/sjMsj9mOpbElb7V4C9XQodVyzmJtMQtOL2Bb9Da6enZlfrv5mBtVMv/p+p+webyU1D50jdTm6D7kl2iY8nMYx6OzeKWNN+/0rvvAwt2AAQOPj7bN23FJ9gsabQlnt++gxcDna3pJ1UJWYgIIAraud9rapMZK7boMAsvAIyOTCTT1VNHUU8WsHoFkF5YRGpfFmfgcIpLz+e1SCnnFmnvPIYC3nQXP+dvTKciR9v4Ohsa7laR7PScm+85k2o3/oFYU8ePVX9Dqtbzd8m0Usqr9FYvNi2XmoZnE5MYwufFkpjSegkyohNjR6+Hwp9LDqQEM/xFs7++NlZxbzJjVZ4jJUPP5kEYMDa59XjMGDBi4E0EQUDSyQLhgy4lN6wge0P+pjGJlJyWgdHDEyORO38jUmDxMzBWonGq28MYgsJ5CbC2M6dnAhZ4NXABpOym/WEtyXjFp+SWUavWUaHQYy2UozY1QmRvjY29hcNt+SARB4INBzXhl0Uw2Z7+D3NSa1dfWk6xO5vMOn2NhZPHI59CLejZe28jCsIWYyk1Z0XUFbd3aVu7gomwpkT36T2g8AvosAuP7/+G5mpLPmNVnUJdqWTOmpSHfyoCBJ4iBkz9g86QPUWuvcfnwYRp26lTTS6pyspMSym2RkxKbj7OvEqGGd14MAusZQBAElOZGKM2NqOtiXdPLeSpxtTFjVO8OvLZjMqsTP8cj8DnmJ5/gpd9eYkG7BdS1q/vQc9/Iv8GHJz/kTOoZWru0Zl7beThbOFfu4OQLsGEU5KdIwip4LFTCvuHo9Qym/HwOSxMFGye3NnxuDBh4wrBXWqN1TEDIsOXwD9/SoEOHpyqKpdfryE5JwrNR0zueLy3SkJNSSECLh/cUrCqennfbgIEa5sWWnhR6dmERLzH02lGWq0LILc1lxO4RLD23lBJtyQPNl16UzkcnP+L5bc9zNesqH7b5kJXdVlZOXIkinPkOvusm9RAcuxdajKuUuNoUlsiY1WdwV5mxdWobg7gyYOAJpd7I8ViKXpQW53H58IGaXk6Vkp+ejk6juatFTmpcPlDz+VdgiGAZMFBlyGQCnwxuSK8lfWhsk0eXsF/Z1nM+n2lTWHVpFZuiNjEscBjDAofhaF7+3ZVOryM0NZQdMTv488af6PQ6BgcMZlKjSTiYV7LkuLQAds6Ay5vArysM/AYs7O57mCiKLDsQzaI/o2jrZ8eKl5pjbWroJWjAwJNKx5BuXDP7DqHUmX2rvsTG0RGP+o1qellVQlYFFYSpMXkIAjh61/yNoUFgGTBQhfg6WDKnV10m7hzGYY883Pe+x/z+yxjUcxBrrqzhm/BvWBm+Em9rbxo5NMLBzAGZIKNYW0xUThSR2ZHkl+VjZWRF/zr9GVN/DB7WD5BYnnYFNoyG7BjoPBfavQGV2BbQ6PS8t/Uy688mMKiZG58MamSoFDRg4AlHEAQUrV2xOVyfPP0htn42j2FzF+DsV73mm4+D7AqaPKfG5mHnbomxac3Lm5pfgQEDTxkvt/Zmf2Q6feLHc9JHjvmOV2neZxHNOy/jZv5N/rjxBxczLnI86Tj5ZfmIoohCpsDPxo/u3t0JcQ6hk2cnTOQP4NAvihC2BvbOARMreHk7+LSv1KHqUi1TfznH4agMpnX2441uAc9Ub0kDBp5mBgx9n22HXsbIajxoNrH54w8Y8u5HOPn61fTSHomspATMlTZ3tALS60XS4vIJbFXJHNVqxiCwDBioYmQygS+GNqbH4jxeVE9nk78J8t1vQFE2ns/NZHzD8VV7wvxk2DENoveBTwcYtOqeTZr/SXp+CWPWnCEytYCPBzX6o/8uAAAgAElEQVRkREvPql2bAQMGahQHlYrsxmX4nI4k3W4ACsVuNsx7h4Fvf4B7UCU7P9RCspMS7opeZSer0ZTqakX+FRiS3A0YqBacrE35ZFAjzicX8ZHZ29BwGBz8P1j/EpTkVc1JdFo4/Q181UrqKdjrcxi1rdLi6npaAQOXnyAus5BvRwcbxJUBA08pIe3fJsNkKwrRHAePEVjYqNg8/33iL56r6aU9FKIokp2UWG7+FdSOBHcwCCwDBqqNng2cmdjelzWhyWz1eR96fgLXf4eVHaRo08MiihC9H1a2hz2zwa0pTDkOIRMrlW8FcDImi0ErTlCm07NhUms6BdZ8SbMBAwaqh3YtO5DWoBTPm3tIuamgzbA3Ubm4su2zeVwPPVHTy3tgCnNzKC0qvFtgxeZjZm2Mtb1pBUc+XgwCy4CBauTNHoG09LFlztbLRHq/CKN3SlYJPw+GdSOkpPTKotNAxA5Y1Ql+HgSl+TDsRylqZVen0tNsDktk9PehOFmbsmVKGxq41Y67PQMGDFQPCrkMT8/BXLc7hHlRKqE7kxn0zv/h6FOHnf/7hIgjT5aFQ0UJ7imxebj4KmtNDqlBYBkwUI0o5DK+HNkUpZkRY1efIU3VDP5zCrr+F2IPw4o2sKozhK6C/2/vvqOjqvP/jz8/M5NMyqT3kEIgCb0HCB0BQUClqCyiuLpuUfyu3dX9ntXvfn+7a/uuDXvHtSG4FlSQohQpAQIBQwsJ6SG9T/rM3N8fg4EISCCTTJa8H+fMOcnMvXPf935OMq+593M/n5Mp0HLGWFk2m31i5qNfw5q74Z9x9kFDGyrhmhfgj/tg4Lx2jW0FYLVpPL72KA+sPsioaD/+fcd4Iv2dO5WEEKJrTJ2xjOzhLfTNWEVtZQtHd1Rw/V/+TuTAwax7+VlSvv3K2SW2W+sQDRERrc/V1zRTU9rQbS4PgnRyF6LTBXu58c6to1n02i5ufXcvq/6QiNfE+2DELfDjJ5DyPqx90L6w0oObt/0yoKUJLA325108of8cGLQQ4maC/uL+dGsaW7j74xS2pJWyNDGax64ZiItevl8J0VPEhvkTZhzC/ujDhJemsG+dot/YUBY8/Fe+fuFpvn/3dRrNZhKvW9xtzgCdT0VBHq7u7pj8To/vd3qCZ+ePf/UTCVhCdIFB4T68evMofrNiL3d+sJ+3fp2Am2cAjFsGiXdCRSYUpdofjVWgdKB3hcA4++TMIYPAxf2Stp1VVsdv39tLTnk9f58/mJsTox28d0KI/wTxQ+/hM+tvmfDBp1QEDeWHVenMXTaUa+//MxteX87O1R/SYK7hilt+162n1flpDsIzg2BRZjU6vSIo2suJlbUlAUuILjI5PoinrhvKg58e5Dcr9vLmLQl4Gg32S3wBfe2PQfMdus3Nx0q495MD6BS8f/tYxvW98IjuQojL07TxYzm834cdA6rpl/U1mcwj80ApfYYHMeuOezB6mti/9kuazGZm3nEPekP3jAjlBfn0/tkchEWZ1QRFeWFw0TupqrN134gqxGXoulERPLtoGEmZ5Sx9ezfVDS2dsp3GFit/XXOY21bsJczHjS/vmijhSogeztvNhQDfX7FxDPQq+A5vfR0/fHKc5kYLSqdj6i2/ZcKimznyw2bWPPs4luZmZ5d8lqb6OuoqK9rcQWi12CjJqe1W/a9AApYQXW7BiAheXjKS1IJqFryyg7SiWoe+//7cSua9tIMVO7O5dXxvvrhrAlEB0pldCAFDJy9hrLLy/VAbsfvfxFzZRPI32YB9ap3E6xYz/Td3krlvD1899wRWS+d8CbxU5flnz0FYlmfG2mJrE7CKHn+c0uXLu7y+M0nAEsIJZg8J4/3bx1LbaGHey9tZnZyHpmkdes/q+hb+8kUq1726k+qGFt65NYG/XjsIt250ylwI4VyJsSF41Y/hy0SFd+0Jot0KOfBdHmX55tZlhs+ay4zfLiNz/17WvvgMNqvViRW3dXqIhtN3EP7UwT2srz1gaS0tVH/+BS0lJV1f4BkkYAnhJIl9Avjm7okMj/TloU9/5MY3kzhUcPGjvFfXt/DsxuNMfOp7Ptqdy63je7PpgSlM69++Ed2FED2HTqcwDfkdQw2NbBmmI2rLcoxuOrZ+dAzNdvpL3rAr5zBl6e0cT9rOhjde7PAXQEcpL8hDbzDgE3x6vsGizGpM/kY8fe3ztzYcOICtthbT5PbNx9pZumcPNiF6iGAvNz78bSIf7c7huU3pXPPSdmYODGHhyAim9gvCaDj32SerTSMps5zPUwpYl1pIXbOVqwaFcs+MOAaEdZ/blIUQ3c9V4xOw/BjGysQqph6sY5D+EPsyB3Bkx0kGTerVulzC1Qtobqhn16cf4xfWi7Hzb3Bi1XYVBXn4hfVCp7f/b9Q0jaLMakL7nr48aN72AxgMeI4f76wyAQlYQjidXqdYOq4380b04rUtJ1iVnM/6w8V4GQ0MCPMmNsREgKcrzVYbdU0WjhXWcqSwhvpmKyajgTlDwrh1Qm8GhXevDp5CiO4p0t+DatMNBBpfYfcoLxLXvUbYkjfY9fkJYoYF4eHt2rrsuOuXUFl4ku0fv4d/rwjiRo9zYuVQUZBPcMzpmStqyxsxVzYRHuvb+px52zY8Ro5EbzI5o8RWErCE6Ca83Vz401X9uf/KeLZnlLHhSDHpxbV882Mh1Q0tuBp0uBl0xIV4sSghktG9/Zk+IFj6WAkhLlr8hPkEbX6ZFaMbSUzRMbDqOzY3TWDnZxnMuHVg63JKKWbecTdVxYWsffGfLPnbPwmKjnFKzS3NTVSXFNN/4tTW5wpPTfAcFmv/gtlSVERTWhrBDz3ojBLbkIAlRDdj0OuY2i+YqWdMwKxpWrcfXVkI8Z9j9pAIXvlqMjb/naSOD2Ho1x8z9OHZHNhVRP9xYUT082td1sXVyLwH/8IHj9zDN8v/j5ueeA4XV2OX11xRkI+m2QiMPD1Y8smMKlzdDfiH289WmX/4AQDPSZO6vL6fk07uQvwHkHAlhHAkd1c9Df1vYmFNPS8OKwY3IxEpH+Ed6MbWj9KwttjaLG/y8+equ+6nPD+Xre+/45Say/NyANoErML0KkL7+KDT2f9H1m3bhiEsDGNcnFNqPJMELCGEEKIHmj1uGCHVfTC7Q8aMeOq/Xcu4Ce5UFdeTsjHnrOV7Dx3BqKsXcHDDN5zYt7vL6y3Lz0VvMOAbGgZAg7mZyqJ6wuNODc/Q3Ezdjp2YJk3qFl9KJWAJIYQQPdDIKD9S3K5lel09z8dnoPPywvjlG8SOCiZ5bQ5VJfVnrTNx8S0E9e7D+teW02B27CDJF1Kel4NfeETrFD6FGT/1v7J3cK/fn4Ktvh7TFOcOz/ATCVhCCCFED6SUou+YuUyrdqHEpYmT88dg3rKFhIHN6AyKbSuPnzX+lcHFhavuvJfG2lp2rPxXl9ZblpfT9vLgiWp0BkXwqQmezVu2oFxc8ExM7NK6zkcClhBCCNFDLRwVyYH6KxjQ1MyrMenoAwIwv/kiifP6kHekgox9Z4+GHty7DyNmX8PBTd9SlHG8S+psbqinprSkbcDKqCKkt3frBM/mLVvwGDsWnadnl9R0IRKwhBBCiB4qxNuNot7X8auaOo62nMT8qyupT0oixphPUJQX21el09RgOWu98TfchKevH5vefgWbrfOn0vlpDsKAUwGrpclKaU4tYX3tlwebsrJozs7GNHVqp9fSXhKwhBBCiB5s9tjB2GoG42e1sSK2AENoKOUvvMCUJf1oqG1m95eZZ61j9PBg6tLbKc7MIPW7DZ1eY9lPdxBGRAFQnF2Dzaa1jn9l3roVANPUKZ1eS3tJwBJCCCF6sOkDglmrn83imlo2l+5Cu/V6Gg4exCNzH4OnRpC6NZ+SnJqz1us3fjLh/QaS9O+PaWlu6tQay/JyMLga8Qm2z7FamFEF6vQEz+YtWzHGxeIaEfFLb9OlJGAJIYQQPZjRoCd6+HTGVpswavBRnyJco6Mpfe5ZxsyNxsPblS0fpmGzth0bSynFxMVLMVdWcHDD2k6tsSwvh4CIKJTOHlsKM6oICDdh9HDBWltLfXJyt7o8CBKwhBBCiB7v+oRIvmqezvzaWtZkf43xrttpSs+gccNaJi2KpzS3ltStBWetFzlwCFFDhrPni9U0N5w9rIOjlOfntnZwt1ltFGXWEH7q8mDd9u1gsWC64opO2/6lkIAlhBBC9HCDe/lwOHAOi6ubsGgW/t2rALchQyhdvpyYgV5EDfJn95pMzJVnXwqcuHgpDbU17F+7plNqa6itoa6ygoBIe/+rsnwzLU3W1vGvzFu2oPfxwX3YsE7Z/qWSgCWEEEIIZo/uT0pjAtPrm/gkbRXe996FpaiIqo8+ZvLiftisGttXp5+1XlhsP/omjCX5689pqnf8WazyvFzg9BQ5pwcY9UGzWjFv3YbnlMkoffea+F4ClhBCCCGYP6IXn3Alt1VVUttSy1q/XDwnTaLsjTcwGVtImNObE/tLyDlUfta6iQsX01RfR+r36x1eV9nP5iA8mVGFV4AbJj83Gg7+iLWqCq9u1v8KJGAJIYQQAvD3dCUwfjyuTeGMsOp5/8j7+N93N7aaGsrffIsRV0bhF+rBtpVptDS3HfsqtG8cEQMGs3/dGmxWx46LVZaXjdHDE5N/AJqmUZhRRfgZlwcxGPCcOLHNOi8feJn3Dr/n0DoulgQsIYQQQgCwaEwk77dM47ayIgrrCtnqloP31VdT8a9/YSsvZcqSftSUNZK8NvusdUddvYDaslKOJ213aE0lOVkERceglKK6pIGG2pbT419t2YLHqFHovb1bl69truW9w++RWX32+F1dSQKWEEIIIQCYHBfEDvdpjG7QEaPcWHF4BYF3/xHNZqPspZfoFe9H/8RQDmzMpbq0bX+rviNH4xfWi+SvvzhrDsNLpdlslOVkExQdA9gvD4J9gueWggKajh8/a3iGbzK/ocHSwKL4RQ6p4VJJwBJCCCEEAAa9jlmjYllpmcItZUUcqzhGiqEAvxsXU/Xvz2g6cYLEBX3RGXTs/OxEm3WVTseoufMozkyn4Nhhh9RTVVJES1Nja8AqzKjCzdMFv1APardsAdqO3q5pGquOr2JgwEAGBQ5ySA2XSgKWEEIIIVrdMCqSFZaZzK01E6Az8u6hdwm84w507u6U/PMZPH2MjJoVTWZKKSfTK9usO3DyNNxMXqSs+8ohtZTmZAGccQarmrBYH5RSmLdsxTU6GmNMTOvyB0sPkl6Z7vSzVyABSwghhBBniA02ERkzgN1qDDdX17Dz5E6O2U4S8Ic/YN68mbqk3QyfEYnJz8j21RlottOXA12MbgyaMo2M5N3UV1d1uJbSnCyU0hEQGYW5spGa0gbC43yx1dVRn5R01uXBT9I+weRiYnbM7A5vu6MkYAkhhBCijZsTo3m5YSaLy0vw1ht548c38L9lKYbwMIqffgq9QZE4vy+lubWk7Slqs+6QabOwWS0c3vZ9h+sozcnCL7wXLq5GCtLsZ8t69fOjLikJraUF0xVTW5etbKxkQ/YGru5zNR4uHh3edkdJwBJCCCFEGzMHhZDtOZQyl1hurreyOW8z6fU5BN93H01HjlK9Zg3xo0MI7u1N0ucnaGk6PTRDQEQU4fEDSP1+Q4c7u5eeuoMQID+tEqOngcBeJmo3fYfO2xuPUaNal11zYg3NtmZu6HdDh7bpKBKwhBBCCNGGi17HjWOieK5uJkuKsvDUG3kz9U28587FbfBgSp9/Aa2pkYnXx1JX3UzKxtw26w+ZPovKk/kd6uzeWGemprSEoOgYNE0jP62SiHg/sFowf/89XldMRbm4AGDTbKw+vpoRwSOI94vv0L47igQsIYQQQpxl8Zgo1tnGgiGUG1tc2JC9gazabEIe/hOWoiIq3nuPsFhf+o4MJmVDTpt5CvslTsTV3YPU7y59ZPeynGwAgqNjqClrxFzRRK9+ftQnJ2OtrsY0Y0brsnuK9pBTk8Oifs7v3P4TCVhCCCGEOEu4rztTB/Ti9ZarWJp3DDe9K68dfA2P0aMxzZhO+RtvYikrY/zCvthsGru/PD1sg4ubGwMmTuF40g4a68yXtP2SM+4gPLP/Ve3GTSg3N0xnjN6+Km0VvkZfroy+0v7ED8/A3rcucc8dQwKWEEIIIc7ptgkxvNswCU+9Fzdp3nyb9S3plekEP/AAtuZmSl98Ce9Ad4ZNi+RYUhFl+afD1KCpM7C0NJOxZ9clbbs0Jwt3L288/fzJT6vEw9sV32A3ajdtwjRpEjp3d/ty9aVszt3M/Nj5GPVGqC2GrU9DwX6HHINLJQFLCCGEEOeU2MefmLBgVuuu4tasFDwN7rxy4BWMMTH4LV5M1erVNKWnM3JWNK7uBvZ8dXp6mtC+8fiGhHF0x9ZL2vbPO7j36udHU2oqlpISvGZe2brc5xmfY9EsXB9/vf2JncvB2gKTHrj0HXcACVhCCCGEOCelFL+ZGMNz1VMxKVeW6vzZlLuJI+VHCLxrGTpPT4qfehqjh4HhMyLJOlhGcVZN67r9J0wm79CP1FVVXmBLbdmsVsrzcgiKjqGysJ6GmmYi+vtRu2kTGAyYpthHb7fYLKw+vpqxYWOJ9o4GcwnsfRuGLoKAvg4/HhdDApYQQgghzuuaYWEoUzAbPeayNH033i4mXkp5CYOfH4F3LaNu+3bMW7cybHokbiYXdq853Rer/4SpaJqNtF0/XNQ2K07mY2lpJrh3HwqOn+p/Fe9LzcaNeCYmtk7u/F3udxTVFbGk/xL7ijteAGsTTH7IMTvfAR0KWEqpG5RSh5VSNqVUws9e+7NSKkMplaaUmtWxMoUQQgjhDEaDnqWJ0TxaOh1PZeA2XSA/FPzA3qK9+C9ZgmtMDCVPPImLzsbIWdHkHa1sDUUBEZEE9e7Dse0Xd5mwODMDgJA+ceQeqcA70A1jaTYtObltLg9+ePRDIkwRTImYAuZS+9mrITc4/ewVdPwM1iFgIbDtzCeVUgOBxcAg4CrgFaWUvoPbEkIIIYQT3JwYRY3Bnx2+13Lz8R2EuAXwbPKz4OJCyCMP05yTQ8UHHzJkSi88fFzZvSazdZDRAROmUJiRRlVRYbu3V3QiHRc3d7yDQ8lPqyRqYADV33wDBgPeM2cCcKjsECklKdw04Cb0Oj1sf67bnL2CDgYsTdOOapqWdo6X5gErNU1r0jQtC8gAxnRkW0IIIYRwjgCTkRvHRPFw4VSMysB/qQAOlR9ifc56TFOm4Dl5EmWvvAK1VSTM7k1hRjW5RyoA6Dd+EgDHLqKze3FmOsG9+1CcZcbSZCVyoB8169ZhmjABva8vAB8c/QBPF0/mx86H6gL7sAzDboTAOMcfgEvQWX2wegF5Z/yef+q5syilfq+USlZKJZeWlnZSOUIIIYToiN9P7kMJ/uz2v5Zrjm4mziuaF/a9QIu1hZBHHsHW2Ejp8y8wcGI4Xv5u7P7SfhbLOzCY8H4DOZ60vV3bsVmtlGZnEdo3ltzD5ej0ioDGfCwnC/GeOweAkvoS1metZ0HsAkyuJtj2NGg2mPJwZx6Ci3LBgKWU2qSUOnSOx7xfWu0cz51zQiJN097QNC1B07SEoKCg9tYthBBCiC4U7uvOwpG9uK9wBsrgxv2NOvLN+Xx87GOMffrgf9MSqj79lJb0NEZf3ZvS3FqyDpQBEDdmHKW52VQVF11gK1Cen4ulpdne/+pwBWGxPjRsWocyGjFNmwbAx8c+xqpZ7Z3by0/A/vch4Tbwi+7UY3AxLhiwNE2boWna4HM8vvyF1fKByDN+jwBOdrRYIYQQQjjPnVNjKbZ6sSN4CROOb2WC/2BePfgqZQ1lBC5bht7Xl+J/PE78mBB8QzzY/VUmNptG3JhxAGTs2XnBbRRlpgPgHRRNeYGZqAF+1Hz7LaYpU9CbTNQ217Ly2EqujL6SSO9I2PIE6F1h0oOt7/H29iw+25/fOQehnTrrEuEaYLFSyqiUigHigD2dtC0hhBBCdIGYQE/mDg3n/ryJaB5BPFJaSqO1kRf2v4Dex4ege+6hPjmZuk0bGXN1DBUn68hMKcUnOJSg3n1I35t0wW0Un8jA1d2D6jL7RM5B1pNYy8rwnmO/PLgqbRXmFjO3D7kdTqZA6mpIvAO8QgBIK6rlyXVH2ZLm3G5HHR2mYYFSKh8YB3yjlFoPoGnaYWAVcAT4FrhL0zRrR4sVQgghhHPdOyOOCosrawN+Te/cvSwNmcAXGV9wsPQgvjdcj7F/f4qffIqYASZ8QzxIXpeNpmnEjR7HyeNHLzjoaHFmOiF9Ysk7WoWHjyu67WvReXhgmjqFJmsT7x95n/Hh4xnoPwDW/wU8AmDifQBYrDb+9OlBvN1c+Ou1g7ricJxXR+8i/FzTtAhN04yapoVomjbrjNf+oWlaX03T+mmatq7jpQohhBDC2foGmViUEMFDmcNo8YvlD0e3EeQeyOO7H8emIPSxR7EUFVHx+uuMnBVNeb6ZnEPl9suEmkbGL5zFslpaKM3JIjgmlrwjFUTG+1C7/lu8585B5+bGlxlfUt5Yzu2Db4e0tZCzHa74b3DzAeyXBg/mV/O/8wbh7+naVYfknGQkdyGEEEJclHumx2NTLrzltQzPyhwe8uzPkfIjfHTsIzxGjsRnwQLKV6ygd1A9Xv5uJK/Nxj8iCt/QMDL2nn/y57LcHKwWC0bPMJrqLQQ1ZaHV1+OzcCEtthbePfQuQwKHMDpwGGx4FAL7wchbAThRaubZjceZNSiEuUPCuuhInJ8ELCGEEEJclFAfN26d0Jun00Op7nsNV6V8xuTgBF5MeZH82nyCH3wAnZsbpU/8gxEzoyjOquHk8SpiR48j99CPNNaZz/m+P43gXlfli96gw3P7v3Ht0wf34cNZk7GGfHM+vx/6e1TyW1BxAmb+HfQGmi027l15AHdXPX+bNxilzjWYQdeSgCWEEEKIi7ZsSizebi48Yv4VKD2PVlSjUzr+d9f/ovf3J+jee6jbuYsIcyoePq4kr8shbsw4bFYL2Qf2nfM9izLTMXp6UpBuIzzaSMv+Pfhet5BmWzOvHnyVoYFDmeIVC5sfh7iZEGefNuf5TcdJLajmyYVDCfZ268rDcF4SsIQQQghx0Xw8XHj4qv6sy9GRGreM0PTvuC9kMkmFSXyR8QV+ixdjHDiAsqefZNikUArSKkEXiruXN1kpyed8z5NpRwmIiMVc2URIbRro9fhcey2r01ZTXF/MH0f+EbX+z2CzwJz/A6XYnVnOq1tP8KuESK4aHNrFR+H8JGAJIYQQ4pIsHh3JiChfbj+WgCV8NDfsXcnowKE8uedJ8uoKCH30USwlJYQc/hI3Txf2r8+l9/BRZB3Yh83WdnCBBnMt5fm5GIwRKAWmbSsxTZlCs68nb6a+ydjQsSTW1sDRNfb5Bv16U1HXzH2fHCDa34PHrhnopKNwbhKwhBBCCHFJdDrF3+cPprzBynLv+9FZW3i8vAa9Ts8jPzyCy7DB+Fx/HTXvr2DQcA9yUssJjBpMQ20NRRnpbd6r8PgxAOpq/Anyt6ErysH3+uv515F/UdFYwR8H3w5rH7B3bB9/N1abxt0fp1BW18zyG0fgaTQ44xCclwQsIYQQQlyyQeE+3Do+huUHNDKG/4nQzG38NWgiqWWpvHrgVYLvvx+dpyeB61/B1U1PaZ4fSqcjK2Vvm/cpSDuC0ukwV/kSmL8bl6goahLieDv1ba6MvpJhyR9CdT5c8wIYXHl2YxrbM8r427xBDI3wddLen58ELCGEEEJ0yEOz+hEbbOLGlME0x8xg5s53WBA2gbdS32JX/WFCHnqQluSdxIXUkn3ITHBMPJn72/bDOpl2FJN/BEq54HNwLf5Ll/LPfc+glOIh35GQ8j5MuBeix7EutZCXN5/gxjGR/Gp0lJP2+pdJwBJCCCFEh7i76nnxxhFUN1q4t2UZmk8Ej/z4PfE+MTy87WEqZ4zCY+xYAtY8g16v0Lv0oST7BOaKcsA+wGhRxnE0wvDVVeHp0sLRcWFsyt3E7+JvJGzDYxA2DKb+mb3ZFdzzyQFGRPnyP9c4d7T2XyIBSwghhBAdNiDMm7/MHcDajEZW9X0KjyYzL5RWY9DpuWfLPXj/5U+41FcSaTtBRXEQAJmn7iYsycrE0tJMU0MQQembMC2cz5OpzxPtFcWvD22E5jpY+Cbp5U3cvmIvEb7uvP3r0bi56J25y79IApYQQgghHGJpYjRzh4bx8HYLe4b/g14FB3im2ZPcmlz+nL0c/2V3ErZzBWh+uHr4cWz7FjSbjYK0IwDoDWGElOxj9RAz2TXZ/LfNB9ecHXDtS2TSi1ve2YPRRc97vxnj9KlwLkQClhBCCCEcQinFMzcMI7GPP0t2hHB8zN8ZnbmLx3Qh7Di5g/+LS8M3JpiQmsPoDCPJO5LK1g/epuDYEXR6HwKrcrBN7M/b5V+x1Hco4w99A5Me5HDgTBa9votmi433bhtDpL+Hs3f1giRgCSGEEMJh3Fz0vHFLAnEhXsxPiiVt5GMszEjiAV0w3+Zt5KtFEUSdWIemG0qvAVPZ982XnNi3B/ThhBUn8bdBGfRzC+LelG+g/9Xsir6DxW8k4arXseqOcQwM93b2LraLBCwhhBBCOJS3mwvv/WY0fYNMXLWrPz/E/5lfZ6bwuyYDbzVvJnecK4HlhygrHI5f2BA0mxUXFUh2bCF5pnqezjiIoe80lvs+zE1v7yHYy8jqO8fTN8jk7F1rt+41KpcQQgghLgvBXm6s+sM4Hlx9kKU/wn/FPMW9Ff/AxdOFJ4Zksnx/IR7Ns8kNm4rBPYDQympenFnKE0Vl+IVfyY21d7D7cB7XjYzg/80b1O0GEr0QpWmas2tolZCQoCUnn3t+IiGEEEL859E0jde3ZbL8u3SCLMW85/8Oe1QGr7n4ccMeHYOyYjgZPo0sr8/oPzAdb6bx+7JF+Hi68+jVA06gvawAAAU/SURBVFgwIsLZu3BeSql9mqYlnPM1CVhCCCGE6GwltY08vymdT/bmMptdzPFeyXaTjXSbK6G5OgYEWdhVfRuH3RP4/eQ+LE2M7vZnrSRgCSGEEKJbqKpvZueJcnamFWAtyyTAWoKnrQpr7BxGxUczIsq3W49vdaZfCljdOxoKIYQQ4rLi6+HKnCFhzBkSBpwzm1wW5C5CIYQQQggHk4AlhBBCCOFgErCEEEIIIRxMApYQQgghhINJwBJCCCGEcDAJWEIIIYQQDiYBSwghhBDCwSRgCSGEEEI4mAQsIYQQQggHk4AlhBBCCOFgErCEEEIIIRxMApYQQgghhINJwBJCCCGEcDClaZqza2illCoFcrpgU4FAWRdsR7SftEn3JO3S/UibdE/SLt1PV7RJtKZpQed6oVsFrK6ilErWNC3B2XWI06RNuidpl+5H2qR7knbpfpzdJnKJUAghhBDCwSRgCSGEEEI4WE8NWG84uwBxFmmT7knapfuRNumepF26H6e2SY/sgyWEEEII0Zl66hksIYQQQohOc9kGLKXUVUqpNKVUhlLqkXO8rpRSy0+9/qNSaqQz6uxp2tEuN51qjx+VUjuVUsOcUWdPcqE2OWO50Uopq1Lq+q6sr6dqT7sopaYqpQ4opQ4rpbZ2dY09TTv+f/kopb5SSh081Sa3OaPOnkQp9Y5SqkQpdeg8rzvvs17TtMvuAeiBE0AfwBU4CAz82TJzgHWAAhKB3c6u+3J/tLNdxgN+p36eLe3i/DY5Y7nvgbXA9c6u+3J/tPNvxRc4AkSd+j3Y2XVfzo92tsl/A0+d+jkIqABcnV375fwAJgMjgUPned1pn/WX6xmsMUCGpmmZmqY1AyuBeT9bZh7wL80uCfBVSoV1daE9zAXbRdO0nZqmVZ76NQmI6OIae5r2/K0A/BH4N1DSlcX1YO1plyXAZ5qm5QJomiZt07na0yYa4KWUUoAJe8CydG2ZPYumaduwH+fzcdpn/eUasHoBeWf8nn/quYtdRjjWxR7z27F/8xCd54JtopTqBSwAXuvCunq69vytxAN+SqktSql9Sqlbuqy6nqk9bfISMAA4CaQC92iaZuua8sR5OO2z3tAVG3ECdY7nfn67ZHuWEY7V7mOulLoCe8Ca2KkVifa0yfPAw5qmWe1fzEUXaE+7GIBRwHTAHdillErSNO14ZxfXQ7WnTWYBB4BpQF9go1LqB03Tajq7OHFeTvusv1wDVj4QecbvEdi/UVzsMsKx2nXMlVJDgbeA2ZqmlXdRbT1Ve9okAVh5KlwFAnOUUhZN077omhJ7pPb+DyvTNK0OqFNKbQOGARKwOkd72uQ24EnN3vknQymVBfQH9nRNieIcnPZZf7leItwLxCmlYpRSrsBiYM3PllkD3HLqDoNEoFrTtMKuLrSHuWC7KKWigM+ApfJNvEtcsE00TYvRNK23pmm9gU+BZRKuOl17/od9CUxSShmUUh7AWOBoF9fZk7SnTXKxn1FEKRUC9AMyu7RK8XNO+6y/LM9gaZpmUUr9F7Ae+50f72iadlgpdcep11/DfjfUHCADqMf+zUN0ona2y2NAAPDKqTMmFk0mUO007WwT0cXa0y6aph1VSn0L/AjYgLc0TTvnreqi49r5t/I3YIVSKhX7pamHNU0rc1rRPYBS6mNgKhColMoH/gdwAed/1stI7kIIIYQQDna5XiIUQgghhHAaCVhCCCGEEA4mAUsIIYQQwsEkYAkhhBBCOJgELCGEEEIIB5OAJYQQQgjhYBKwhBBCCCEcTAKWEEIIIYSD/X8IxKgbMW0ANAAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "acq_LCB = AcquisitionLCB(model,space,exploration_weight = 0)\n", "grid_par = np.array([0,0.5,1,2,3,5])\n", "\n", "plt.figure(figsize=(10,6))\n", "plt.title('Acquisition functions',size=15)\n", "for param in grid_par:\n", " acq_LCB = AcquisitionLCB(model,space,exploration_weight = param)\n", " plt.plot(X_grid, -acq_LCB.acquisition_function(X_grid),label=str(param))\n", "legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the sixhumpcamel function defined as\n", "$$f(x_1,x_2) = \\left(4-2.1x_1^2 + \\frac{x_1^4}{3} \\right)x_1^2 + x_1x_2 + (-4 +4x_2^2)x_2^2,$$\n", "\n", "in $[-2,2]\\times [-1,1]$. This function has two global minima, at $(0.0898,-0.7126)$ and $(-0.0898,0.7126)$. This function is also implemented in GPyOpt so, to load and visualize it simply run." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "GPyOpt.fmodels.experiments2d.sixhumpcamel().plot()\n", "f_shc = GPyOpt.fmodels.experiments2d.sixhumpcamel(sd = 0.1).f # simulated version with some noise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(a) Create three objects to optimize this function using the the 'EI' (with parameter equal to zero), the LCB (with parameter equal to 2) and the MPI (with parameter equal to zero). Use the same initial data in the three cases (Hint: use the options 'X' and 'Y' when creating the BO object)." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "from GPyOpt import Design_space ## GPyOpt design space\n", "\n", "bounds_shc = GPyOpt.fmodels.experiments2d.sixhumpcamel().bounds\n", "variables = [{'name': 'var_1', 'type': 'continuous', 'domain': bounds_shc[0]},\n", " {'name': 'var_2', 'type': 'continuous', 'domain': bounds_shc[1]}]\n", "\n", "space = GPyOpt.Design_space(variables)\n", "\n", "\n", "from GPyOpt.experiment_design.random_design import RandomDesign\n", "seed(12345)\n", "n_data = 3\n", "sampler = RandomDesign(space)\n", "X = sampler.get_samples(n_data)\n", "Y = f_shc(X)\n", "\n", "BO_EI = GPyOpt.methods.BayesianOptimization(f_shc,variables,X=X,Y=Y,acquisition='EI',jitter=0)\n", "BO_LCB = GPyOpt.methods.BayesianOptimization(f_shc,variables,X=X,Y=Y,acquisition='LCB',acquisition_weight=2)\n", "BO_MPI = GPyOpt.methods.BayesianOptimization(f_shc,variables,X=X,Y=Y,acquisition='MPI',jitter=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(b) In the three cases run the optimization for 30 iterations" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "max_iter = 30\n", "BO_EI.run_optimization(max_iter)\n", "BO_LCB.run_optimization(max_iter)\n", "BO_MPI.run_optimization(max_iter)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(c) Now make a plot comparing the three methods. The x axis should contain the number of iterations and y axis the best found value (Hint: use .Y_best to extract from the BO objects the best current value at each iteration). Which acquisition is has the best performance in this example?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plt.figure(figsize=(10,6))\n", "plt.title('Comparison of acquisition functions',size=15)\n", "plt.plot(BO_EI.Y_best,label = 'EI')\n", "plt.plot(BO_LCB.Y_best,label = 'LCB')\n", "plt.plot(BO_MPI.Y_best,label = 'MPI')\n", "legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(d) Compare the models and the acquisition functions in the three cases (after the 30 iterations). What do you observe? " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "BO_EI.plot_acquisition()\n", "BO_LCB.plot_acquisition()\n", "BO_MPI.plot_acquisition()\n", "\n", "display(BO_EI.model.model)\n", "display(BO_LCB.model.model)\n", "display(BO_MPI.model.model)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "### Credit\n", "\n", "This notebook was written by Javier Gonzalez." ] } ], "metadata": { "@webio": { "lastCommId": null, "lastKernelId": null }, "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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 2 }