{ "metadata": { "name": "", "signature": "sha256:8f2150f8c116d400ac97daf6d79ffccac1c0924a1b19f62f8934661208f3ef15" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Module 2: Inversion\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the previous module we started with a continuous distribution of a physical property and discretized it into many cells, then we performed a forward simulation that created data from known model parameters. Inversion, of course, is exactly the opposite process. Imagine each model parameter that we had represents a layer in a 1D layered earth. At the surface of the earth we measure the data, and when we invert we do so for the model parameters. Our goal is to take the observed data and recover models that emulate the real Earth as closely as possible. \n", "\n", "You may have noticed that the act of discretizing our problem created more cells than data values. In our latter example we produced 20 data points from 1000 model parameters, which is only a few data points and many model parameters. While this was not much of a problem in the forward simulation, when we want to do the inverse process, that is, obtain the model parameters from the data, it is clear that we have many more unknowns than knowns. In short, we have an underdetermined problem, and therefore infinite possible solutions. In mathematical terms, geophysical surveys represent what are called \"ill-posed\" problems. \n", "\n", "An \"ill-posed\" problem is any problem that does not satisfy the requirements for the definition of \"well-posed\" problem. A *well-posed* problem is a problem in mathematics that must satisfy all three of the following criteria:\n", "\n", "
    \n", "
  1. A solution exists.\n", "
  2. The solution is unique.\n", "
  3. The solution's behaviors change continuously with continuously changing initial conditions.\n", "
\n", "\n", "Any mathematical formulation that does not satisfy all three of the above is, by definition, an ill-posed problem. Since we are dealing with an underdetermined system, I hope that it is clear that we are dealing with an ill-posed problem (i.e., we have no unique solution), and we are going to have to come up with a method (or methods) that can help us choose from the available solutions. We need to devise an algorithm that can choose the \"best\" model from the infinitely many that are available to us. \n", "\n", "In short, we are going to have to find an optimum model. More specifically, in the context of most geophysics problems, we are going to use gradient-based optimization. This process involves building an *objective function*, which is a function that casts our inverse problem as an optimization problem. We will build an objective function consisting of two parts:\n", "\n", "$$\n", "\\phi = \\phi_d + \\beta \\phi_m\n", "$$\n", "\n", "Where the terms on the right hand side are (1) a data misfit (denoted as $\\phi_d$) and (2) a model regularization (denoted as $\\phi_m$). These two parts will be elaborated in detail below.\n", "\n", "Once we have formulated the objective function, we will take derivatives and obtain a recovered model. This module will flesh out the details of the model objective function, and then take first and second derivatives to derive an expression that gives us a solution for our model parameters.\n", "\n" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "The Data Misfit, $\\phi_d$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A *misfit* describes how close synthetic data matches measurements that are made in the field. Traditionally this term refers to the difference between the measured data and the predicted data. If these two quantities are sufficiently close, then we consider the model to be a viable candidate for the solution to our problem. Because the data are inaccurate, a model that reproduces those data exactly is not feasible. A realistic goal, rather, is to find a model whose predicted data are consistent with the errors in the observations, and this requires incorporating knowledge about the noise and uncertainties. The concept of fitting the data means that some estimate of the \u201cnoise\u201d be available. Unfortunately \u201cnoise\u201d within the context of inversion is everything that cannot be accounted for by a compatible relationship between the model and the data. More specifically, noise refers to (1) noise from data aquisition in the field, (2) uncertainty in source and receiver locations, (3) numerical error, (4) physical assumptions about our model that do not capture all of the physics. \n", "\n", "A standard approach is to assume that each datum, $d_i$, contains errors that can be described as Gaussian with a standard deviation $\\epsilon_i$. It is important to give a significant amount of thought towards assigning standard deviations in the data, but a reasonable starting point is to assign each $\\epsilon_i$ as $\\epsilon_i= floor +\\%|d_i|$. \n", "\n", "Incorporating both the differences between predicted and measured data and a measure of the uncertainties in the data yields our misfit function, $\\phi_d$:\n", "\n", "$$\n", "\\phi_d (m) = \\frac{1}{2} \\sum_{i=1}^N \\left( \\frac{F[m] -d_i^{obs} }{\\epsilon_i}\\right)^2 = \\frac{1}{2} \\|W_d(F[m] - d^{obs}) \\|_2^2\n", "$$ \n", "\n", "Note that the right hand size of the equation is written as a matrix-vector product, with each $\\epsilon_i$ in the denominator placed as elements on a diagonal matrix $W_d$, as follows:\n", "\n", "\\begin{equation}\n", "\\begin{split}\n", "W_d = \n", "\\begin{bmatrix}\n", " \\frac{1}{\\epsilon_1} & 0 & 0 & \\cdots & 0\\\\\n", " 0 & \\frac{1}{\\epsilon_2} & 0 & \\cdots & 0\\\\\n", " 0 & 0 & \\frac{1}{\\epsilon_3} & \\cdots & \\vdots\\\\\n", " 0 & 0 & 0 & \\ddots & \\frac{1}{\\epsilon_M}\\\\ \n", "\\end{bmatrix}\n", "\\end{split}\n", "\\end{equation}\n", "\n", "If we return to linear problem from the previous section where our forward operator was simply a matrix of kernel functions, we can substitute $F[m]$ with $G$ and obtain\n", "$$\n", "\\phi_d (m) = \\frac{1}{2} \\sum_{i=1}^N \\left( \\frac{(Gm)_i -d_i^{obs} }{\\epsilon_i}\\right)^2 = \\frac{1}{2} \\|W_d(Gm - d^{obs}) \\|_2^2\n", "$$ \n", "\n", "Now that we have defined a measure of misfit, the next task is to determine a tolerance value, such that if the misfit is about equal to that value, then we have an acceptable fit. Suppose that the standard deviations are known and that errors are Gaussian, then $\\phi_d$ becomes a $\\chi_N^2$ variable with $N$ degrees of freedom. This is a well-known quantity with an expected value $E[\\chi_N^2]=N$ and a standard deviation of $\\sqrt{2N}$. Basically, what this means is that computing $\\phi_d$ should give us a value that is close to the number of data, $N$.\n", "\n", "\n", "\n" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "The Model Regularization, $\\phi_m$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are many options for choosing a model regularization, but the goal in determining a model regularization is the same: given that we have no unique solution, we must make assumptions in order to recast the problem in such a way that a solution exists. A general function used in 1D is as follows:\n", "\n", "$$\n", "\\phi_m = \\alpha_s \\int (m)^2 dx + \\alpha_x \\int \\left( \\frac{dm}{dx} \\right)^2 dx\n", "$$\n", "\n", "Each term in the above expression is a norm that measures characteristics about our model. The first term is a representation of the square of the Euclidean length for a continuous function, and therefore measures the length of the model, while the second term uses derivative information to measure the model's smoothness. Usually the model regularization is defined with respect to a reference model. In the above, the reference model would simply be zero, but choosing a non-zero reference model $m_{ref}$, yields the following:\n", "$$\n", "\\phi_m = \\alpha_s \\int (m-m_{ref})^2 dx + \\alpha_x \\int \\left( \\frac{d}{dx} (m-m_{ref}) \\right)^2 dx\n", "$$\n", "\n", "As before, we will discretize this expression. It is easiest to break up each term and treat them separately, at first.\n", "We will denote each term of $\\phi_m$ as $\\phi_s$ and $\\phi_x$, respectively. Consider the first term. Translating the integral to a sum yields:\n", "\n", "$$\n", "\\phi_s = \\alpha_s \\int (m)^2 dx \\rightarrow \\sum_{i=1}^N \\int_{x_{i-1}}^{x_i} (m_i)^2 dx = \\sum_{i=1}^N m_i^2 (x_i - x_{i-1})\n", "$$\n", "\n", "Each spatial \"cell\" is $x_i - x_{i-1}$, which is the distance between nodes, as you may recall from the previous module. To simplify notation, we will use $\\Delta x_{n_i}$ to denote the *ith* distance between nodes:\n", "\n", "
\n", "\n", "\n", "We can then write $\\phi_s$ as:\n", "\n", "$$\n", "\\phi_s = \\alpha_s \\sum_{i=1}^N m_i^2 \\Delta x_{n_i} = \\alpha_s m^T W_s^T W_s m = \\alpha_s \\|W_s m\\|_2^2\n", "$$\n", "\n", "with:\n", "\n", "\\begin{equation}\n", "\\begin{split}\n", "W_d = \n", "\\begin{bmatrix}\n", " \\frac{1}{\\sqrt{\\Delta x_{n_1}}} & 0 & 0 & \\cdots & 0\\\\\n", " 0 & \\frac{1}{\\sqrt{\\Delta x_{n_2}}} & 0 & \\cdots & 0\\\\\n", " 0 & 0 & \\frac{1}{\\sqrt{\\Delta x_{n_3}}} & \\cdots & \\vdots\\\\\n", " 0 & 0 & 0 & \\ddots & \\frac{1}{\\sqrt{\\Delta x_{n_N}}}\\\\ \n", "\\end{bmatrix}\n", "\\end{split}\n", "\\end{equation}\n", "\n", "\n", "For the second term, we will do a similar process. First, we will delineate $\\Delta x_{c_i}$ as the distance between cell centers:\n", "\n", "
\n", "\n", "A discrete approximation to the integral can be made by evaluating the derivative of the model based on how much it changes between the cell-centers, that is, we will take the average gradient between the *ith* and *i+1th* cells:\n", "\n", "$$\n", "\\phi_x = \\alpha_x \\int \\left( \\frac{dm}{dx} \\right)^2 dx \\rightarrow \\sum_{i=1}^{N-1} \\left( \\frac{m_{i+1}-m_i}{h_k}\\right) \\Delta x_{c_i} = m^T W_x^T W_x m = \\|W_x m\\|_2^2\n", "$$\n", "\n", "The matrix $W_x$ is a finite difference matrix constructed thus:\n", "\n", "\n", "\\begin{equation}\n", "\\begin{split}\n", "W_d = \n", "\\begin{bmatrix}\n", " -\\frac{1}{\\sqrt{\\Delta x_{c_1}}} & \\frac{1}{\\sqrt{\\Delta x_{c_1}}} & 0 & \\cdots & 0\\\\\n", " 0 & -\\frac{1}{\\sqrt{\\Delta x_{c_2}}} & \\frac{1}{\\sqrt{\\Delta x_{c_2}}} & \\cdots & 0\\\\\n", " 0 & 0 & \\ddots & \\ddots & \\vdots\\\\\n", " 0 & 0 & 0 & -\\frac{1}{\\sqrt{\\Delta x_{c_{M-1}}}} & \\frac{1}{\\sqrt{\\Delta x_{c_{M-1}}}}\\\\ \n", " 0 & 0 & 0 & 0 & 0\n", "\\end{bmatrix}\n", "\\end{split}\n", "\\end{equation}\n", "\n", "If $W_x$ is an $M \\times M$ matrix, then the last row is zero. The reason the last row is zero is because there are $M-1$ segments on which linear gradients have been defined. Effectively the two $1/2$ cells on each end are neglected. \n", "\n", "So to summarize, we have $\\phi_m = \\phi_s + \\phi_x$ with \n", "\n", "\\begin{equation}\n", "\\begin{split}\n", " \\phi_m & = \\phi_s + \\phi_x \\\\[0.4em]\n", " & = \\alpha_s \\|W_s m\\|_2^2 + \\alpha_x \\|W_x m\\|_2^2 \\\\[0.4em] \n", "\\end{split}\n", "\\end{equation}\n", "\n", "Next, we will write this more compactly by stacking $W_s$ and $W_x$ into a matrix $W_m$ as follows\n", "\n", "\\begin{equation}\n", "\\begin{split}\n", "W_m = \n", "\\begin{bmatrix}\n", " \\alpha_s W_s\\\\\n", " \\alpha_x W_x\n", "\\end{bmatrix}\n", "\\end{split}\n", "\\end{equation}\n", "\n", "Now we can write $\\phi_m$ as the 2-norm of one matrix-vector operation:\n", "\n", "$$\n", "\\phi_m = \\| W_m m \\|_2^2\n", "$$\n", "\n", "As before, if we want to describe with respect to a reference model $m_{ref}$ we could write:\n", "\n", "$$\n", "\\phi_m = \\| W_m (m-m_{ref})\\|_2^2\n", "$$" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Model Objective Function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we go back and recall what was discussed in the introduction, the model objective function casts the inverse problem as an optimization problem, and as mentioned, we will be using gradient-based optimization, so we will need to take derivatives. The complete model objective function that we are dealing with will contain both the data misfit and the model regularization. This means that we can write it as $\\phi$ as the sum of the two and then differentiate:\n", "\n", "$$\n", "\\phi = \\phi_d + \\beta \\phi_m\n", "$$\n", "For the linear problem we are considering\n", "$$\n", "\\phi_d = \\frac{1}{2}\\| W_d (Gm-d^{obs})\\|_2^2 = \\frac{1}{2}(Gm-d^{obs})^T W_d^T W_d (Gm-d^{obs})\n", "$$\n", "and\n", "$$\n", "\\phi_m = \\frac{1}{2} \\|W_m (m-m_{ref}) \\|^2_2 = \\frac{1}{2}(m-m_{ref})^T W_m^T W_m (m-m_{ref})\n", "$$\n", "\n", "To simplify the terms and see the math a little more clearly, let's note that $W_d(Gm-d^{obs})$, and $\\beta W_m(m-m_{ref})$ are simply vectors. And since we are taking the square of the 2-norm, all that we are really doing is taking the dot product of each vector with itself. So let $z=W_d(Gm-d^{obs})$, and let $y=W_m(m-m_{ref})$ where both $z$ and $y$ vectors are functions of $m$. So then:\n", "\n", "$$\n", "\\phi_d = \\frac{1}{2}\\|z\\|_2^2 = \\frac{1}{2}z^T z \n", "$$
\n", "$$\n", "\\phi_m = \\frac{1}{2}\\|y\\|_2^2 =\\frac{1}{2}y^T y \n", "$$\n", "\n", "\n", "To minimize this, we want to look at $\\nabla \\phi$. Using our compact expressions:\n", "$$\n", "\\phi = \\phi_d + \\beta \\phi_m = \\frac{1}{2}z^Tz + \\beta \\frac{1}{2}y^Ty \\\\ \n", "$$\n", "\n", "Taking the derivative with respect to $m$ yields:\n", "\\begin{equation}\n", "\\begin{split}\n", "\\frac{d \\phi}{dm}& = \\frac{1}{2} \\left(z^T \\frac{dz}{dm} + z^T \\frac{dz}{dm} + \\beta y^T \\frac{dy}{dm} + \\beta y^T \\frac{dy}{dm}\\right)\\\\\\\\[0.6em]\n", "& = z^T \\frac{dz}{dm} + \\beta y^T \\frac{dy}{dm}\n", "\\end{split}\n", "\\end{equation}\n", "\n", "Note that \n", "$$\\frac{dz}{dm} = \\frac{d}{dm}(W_d(Gm-d^{obs})) = W_d G $$ \n", "\n", "and \n", "\n", "$$ \\frac{dy}{dm} = \\frac{d}{dm}(W_m (m-m_{ref})) = W_m $$\n", "\n", "Next, let's substitute both derivatives, our expressions for $z$ and $y$, apply the transposes, and rearrange:
\n", "\n", "\\begin{equation}\n", "\\begin{split}\n", "\\frac{d \\phi}{dm} & = z^T \\frac{dz}{dm} + \\beta y^T \\frac{dy}{dm} \\\\[0.6em]\n", " & = (W_d(Gm-d^{obs}))^T W_d G + \\beta (W_m (m-m_{ref}))^T W_m\\\\[0.6em]\n", " & = (Gm-d^{obs})^T W_d^T W_d G + \\beta (m-m_{ref})^T W_m^T W_m \\\\[0.6em]\n", " & = ((Gm)^T - d^T) W_d^T W_d G + \\beta (m^T-m_{ref}^T)W_m^T W_m \\\\[0.6em]\n", " & = (m^T G^T - d^T) W_d^T W_d G + \\beta m^T W_m^T W_m - \\beta m_{ref}^T W_m^T W_m \\\\[0.6em]\n", " & = m^T G^T W_d^T W_d G - d^T W_d^T W_d G + \\beta m^T W_m^T W_m - \\beta m_{ref}^T W_m^T W_m\\\\[0.6em]\n", " & = m^T G^T W_d^T W_d G + \\beta m^T W_m^T W_m - d^T W_d^T W_d G - \\beta m_{ref}^T W_m^T W_m\n", " \\end{split}\n", "\\end{equation}\n", "\n", "Now we have an expression for the derivative of our equation that we can work with. Setting the gradient to zero and gathering like terms gives:
\n", "\n", "\\begin{equation} \n", "\\begin{split}\n", " m^T G^T W_d^T W_d G + \\beta m^T W_m^T W_m = d^T W_d^T W_d G + \\beta m_{ref}^T W_m^T W_m\\\\[0.6em]\n", " (G^T W_d^T W_d G + \\beta W_m^T W_m)m = G^T W_d^T W_d d + \\beta W_m^T W_m m_{ref}\\\\[0.6em]\n", "\\end{split}\n", "\\end{equation}\n", "\n", "From here we can do two things. First, we can solve for $m$, our recovered model:\n", "\n", "\\begin{equation}\n", "\\begin{split}\n", " m = (G^T W_d^T W_d G + \\beta W_m^T W_m)^{-1} (G^T W_d^T W_d d + \\beta W_m^T W_m m_{ref})\\\\[0.6em]\n", "\\end{split}\n", "\\end{equation}\n", "\n", "Second, we can get the second derivative simply from the bracketed terms on the left hand side of the equation above:\n", "\\begin{equation} \n", "\\frac{d^2 \\phi}{dm^2} = G^T W_d^T W_d G + \\beta W_m^T W_m\n", "\\end{equation}\n", "\n", "In the model problem that we are solving, second derivative information is not required to obtain a solution, however, in non-linear problems or situations when higher order information is required, it is useful to have this available when we need it. \n", "\n", "\n", "\n" ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "\n" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Solving for $m$ in Python" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before we solve for $m$, we will recreate what we had in the first module. First, install the appropriate packages:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Import Packages\n", "from SimPEG import *\n", "from IPython.html.widgets import interactive\n", "import numpy as np\n", "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Efficiency Warning: Interpolation will be slow, use setup.py!\n", "\n", " python setup.py build_ext --inplace\n", " \n", "Populating the interactive namespace from numpy and matplotlib" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] }, { "output_type": "stream", "stream": "stderr", "text": [ "WARNING: pylab import has clobbered these variables: ['interactive']\n", "`%matplotlib` prevents importing * from pylab and numpy\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is the model that we had previously:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Begin by creating a ficticious set of model data\n", "\n", "M=1000 # Set number of model parameters \n", "x=np.linspace(0,1,M+1) # Define 1D domain on nodes\n", "xc = 0.5*(x[1:] + x[0:-1]) # Define 1D domain on cell centers\n", "m = np.zeros(M) # preallocate m array \n", "\n", "# Define Gaussian function:\n", "gauss = lambda x, a, mean, SD: a*np.exp(-(x-mean)**2./(2.*SD**2.)) # create a Gaussian function\n", "\n", "# Choose parameters for Gaussian, evaluate, and store in an array, f.\n", "SD=6 \n", "mean=0\n", "a=1/(SD*sqrt(2*pi))\n", "x2=np.linspace(-20,20,0.2*M) \n", "f = gauss(x2,a, mean,SD)\n", "\n", "# Define a boxcar function:\n", "box = 0.4*np.ones(0.2*M)\n", "\n", "# Insert the Gaussian and Boxcar into m:\n", "m[0.2*M:0.4*M]=box\n", "m[0.6*M:0.8*M]=10*f\n", " \n", "# Plot \n", "pylab.plot(xc,m)\n", "pylab.xlabel('x')\n", "pylab.ylabel('m(x)')\n", "pylab.title('Model, $m(x)$')\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 8, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, we define out kernel functions and averaging and volume matrices as before:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Make the set of kernel functions\n", "\n", "g = lambda x, i, p, q: np.exp(-p*i*x)*np.cos(2*np.pi*q*i*x) # create an anonymous function as immediately above\n", "p = 0.01 # Set values for p, q\n", "q = 0.15\n", "N = 20 # specify number of output data\n", "Gn = np.zeros((M+1,N))\n", "\n", "for i in range(N):\n", " f = g(x,i,p,q)\n", " Gn[:,i] = f\n", " \n", "# Plot \n", "pylab.plot(x,Gn)\n", "pylab.xlabel('x')\n", "pylab.ylabel('g(x)')\n", "pylab.title('Kernel functions, $g(x)$')\n", "\n", "# Make Averaging Matrix\n", "n=M+1 # Define n as the N+1 dimension of the matrix \n", "w=n-1 # Define w and the n-1 dimentsion of the matix \n", "s = (M,n) # Store matrix values \n", "Av = np.zeros(s) # Create a matrix of zeros of the correct dimensions \n", " # and fill in with elements usin the loop below (note the 1/2 is included in here). \n", "for i in range(M):\n", " j=i\n", " k=i+1\n", " Av[i,j] = 0.5 \n", " Av[i,k] = 0.5\n", "\n", "\n", "# make the Volume, \"delta x\" array\n", "Deltax = diff(x)\n", "V = np.diag(Deltax) # create diagonal matrix \n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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GYsoUwy+hT4oP7PbbIacoB2lpabC1tYVIJNJ7rEzGnp1Kli+Ehy9GWNg8FCoL\nEZwRjNtht7GHvwcL7yzEe0ffQy2LWmi6pCmGnR+GZfeX4YjnETyNfoqkvCRoijTw6eeDuJ/idNtJ\nq4Sv7/uIj99lsB3KU6DRYICPDzZHR1fYrspVwau7F5JPJhtVjj7khfHwum2B4F94yEt7CZUqB+ci\nb+KY6wB4eg+AUqnrS5P5yeDRxgNh88OQ550HtVSNPO88hC8Mh3sr9womy8r3MSc0FB09PTDk4Q7M\n+KE/0tu2wZ2nTzHQ1xdD/Pyqfl/UamDbNvaM79wJhIezHy8kBPjxR6Z27tljlOn2afRTtDjYAo6n\nHNF0T1M8ED/A0TM5aNrTBUMPLADPiYdLgZdqJJBv32aK8OTJLIIvKYlZYIOCgAMHgHbtmOZgTABa\necgkNPTDcRq4PbfB+clXcG3saHT9vid69U7E0KH9IRDw4D+Jj7Cj8eAJBAhLTmZO4pcvcc7vHDof\n7wyZQobISGYHLAnS0Gg0WL58Ofr27YvccvZzjuOQnHwSAoENsrOfGqxTrlsuPDt5ImRWCJSZNdMc\nkhUKrI2MhCWfj5ViMRLlxkfLvBEaDeDiAqxezdqoc2fg229ZXGANXgCpVAgPj3Y6UUJFMUXgW/Oh\nztMdUd7OzMR73t7QalXw8GgLqVRQ8YApU6DZ+TOE9kLkB+oO4zILMmFxvC9s+a5Vmvmy1+/E7Xdm\noTq3wrL7y7Dy4UpMnToV3377bZXHOjsz30hJn5We/gc8PTtBrTY83Hz27BmaOTTDX/5/4ajnUSx/\nsBzDLwyH3X47bBywEUf6HMH82/Oxh78Hd8LvQCwRl0bvKBTJEAhsIJMZFqAAE8RTg4OxICxMbwdW\nGFnIfEuimpsolcpMeNw3R8Km1jrO6R9iovGDcAk8Rd2hUuWUbpf5ySCwFSDjWobeMjNvZ+qtT4FG\ngw/8/DAnNATTbszGmItjUKAsYKHmPB60L15gW1wc2np4IFmf4FCpgBkzgOHDgRQDfo/ERGDQIOaE\nqCL0+JDHITQ/0BzPYp4BAB6KH6PhDzZoPvRJqanTN9UXnY93xrpH66oN9dVomJO8XTvm7zeEUsnG\ncnZ2wMuXVRZZATIJDcOEhyzFiwVLMefwOWyexYNlD3c0bz4CV66Mg9j9BwjthTgWkYCR/v7gnJ2B\nVq0AqRRf3PsCn1z/BBzHwceHDTg8PVmZHMdhzZo16N+/P6SVYsVzc10hENghOfmEwTppijSI3hgN\nob0QGdfrOi59AAAgAElEQVQyamwKSFcq8XV0NCz5fHwREfHG0S41QqsFRCJg0yamwrdpA6xfD3h5\nVStAQkPnIjHxkM528QoxYrbomsA4jkNvb2/czWK2+6SkowgJmVV2gK8vE2IKBRL2JuiG4AJY7bwa\nq51XY2JgIE4Z6hgAzJyYj/wm9kBxiLUhJIUSNNnRBO37tTfK/zBlCrBrFwueYB161eUDwLJly7By\n5coK2zJuZEDYVghBiABnfc9i/eP1mHB5AtocboMGOxug24lumHF9Bn55NR3P3VpCnBls0Cm7Mz4e\nA319oaxi9Jx5OxPurdyrDB+vjFarhv9fbRD9vW2FgITS/RyH6UFBOCn6DEFBH4LjtFBmKCF0ECLj\nhn6BUULWvSwImwuhSFOUljUhMBDzQkMw5cpHmPzn5IqBBy4uTHsIDMTehAR0EYkqzjfhOGDWLODD\nD9lkm6ooKgLGjGFhvnqe8b38veh0rBMSpGy4X1DAfnfHjwSw2WeLB+Iy31WuPBdDfhuCL+99afC9\n12iAefOYLDM20OzFC3a79+4ZdzyZhIZhcnJewPVKN3z0zUuE9uuCXj8uwNChQZg8eRQEAhsEz/dC\nzI+x6OnlhWsZGcyuuWwZ5Go5ep/qjdM+zDZ19y7rn5KLtXaO47By5UoMHDiwgqkKAIqKoiESdUFk\n5KoqY+/zPPMg6iJC8LTgGmsdALNJfxcbC2s+H8vF4n/GbFUejmPB5d9/z4bUHTqw72G6nbdKJYGb\nW1OoVBXfAlWOCnwLPouAqoSzRIJeXl6lL5dKlQs3t6ZQKos7mE8+AQ4xIaSSFJdTrh2T85JhudcS\n6fnpEEilaOvhAbWejvLFCyb/1AeOsKiyKpDL5bCcaonRJ0ZX3TbFxMaycEcXl88RE7PFqHOys7Nh\na2uLwOLAfXmSnI20vfSP/AtVhfBL9cPlwMv45tlm/Opsh41XzWG2ywzv/foeFvy1AD8Lf8bjqMe4\nnBSJZkKh/pF3JSJXRyJ0jvHmyIR7c+F/oj64VMOmrQKNBn1EQji790Zy0i8IGBuAmG+N85nF/hgL\n/+H+4LQctsfFYYivL6Zdn4GpV6dCqdHz/ly5wgaBKSlYJhZjZrlIOuzYAQwYUL3AKKGoCHjvPWYT\nKn+J4CtodahVaYSWVAoMGcLki1IJeCZ5wsbJBi9jy9SAfGU++vzaBztcd+hchuNYdPyIEcyXURO8\nvJjgePHC8DFqtRpOTk4moVEVWq0ars8t8NuHd3B25gw4rm8MC1sZeLzWcHaeiGj/XeBb8eEmzkQL\nd3cUSCQsEkcoRFhmGHhOPIiLZyXv3g307cueH/YDc1i2bBkGDRqkM6FLrZYiIGAsAgPHV2mO0Mg1\niP46GsLmQmQ/fb34dYlKhY3R0bDi87E5Oho5/8YscI5jsfjr17P269WLTU8tdrImJh5EWNhnOqcl\nHU1C6Kf6O6aJgYH4LTW1wrbw8EVISNjLBJONDRvWlexbGI74PWXRUasersKGJxtK/x/i54cbGRVH\ntBzHrA+XL4OVxeOxsGQD7N69GxM/nggbJxuEZ4Ubbo9yfPllDGbOvACNxniN8JdffsGwYcOg1WoR\nODFQrx/DEEplOgQCHtJzRHBPdMdpn9NY47wGgy59iFpP/0LjE4Mx9LehWPFgBU56nQQ/gY+cohyd\ncjSFGnh29ETmzep9cEWed8C/WwuFvtUPdcWFhejDv4BXz6zhNfwptGrjnPechoPvIF+4H4qGnUCA\nzx6sxcjfR1Y9WW/nTqBPH8jz89HTywvnU1OZ+cre3rBJyhDx8cwO5OEBAAjPCgfPiYfAdCbcs7KY\nXFm1qqIL5FXcK9g42cAzybN0W6osFQ4HHPAk+kmFSxw9yl4dI+aH6uXlS1bFypP5Sli+fDnGjh1r\nEhrVEeT3CV58tBkfnr+Ki590RO/5FzFhwg2sXDkPAoEdxGuDEbUhCjNDQrAzPh64dg3o3h1QqXBc\ndBz9TveDSqMCxwFz5gCfflqmpWq1WixcuBATJkyAqlJnrdWqER6+GD4+/aFUZlVZx5wXOXBv4Y6o\n9VHQKl5vvkSSXI4vIyLAEwiwKz4eBX9XqG51aDQs/PXLLwFra3CDB0H02A65CfcrHMZxHLx6eCHn\nhW6HFVNUBJ5AgKJK9yCVesDTswO4JYuBn36qsC/POw/urd3BaTikyFJKtYwSrqSnY6S/f4VzHj9m\nIf6ll/nuO2DZMr23lZaWBisrK0RHR2OX2y58dltXCOo2hRwPH/aFpaWqRs5KjUaDXr164cyaM/Dq\n6QWtsmbPRFLSEfj7jyodWXMch3EBAfgxNhYZBRl4HvMchz0O4/O7n2PAmQFovLsxHA44YPzl8dj0\ndBP+DPoToZmhyBZkQ2AnqFoTzspCyJ6GiHOebXT9fg9LwuOvZiDAbUGN7kvqn4d7li6YfesU+vza\nB3mKavwuJS/tokXwk8lgy+dD0rOnUTPJ9XLtGtC5M5QFeXA85YhT3qcAsHmyXbsCW7bot9I+ED+A\n7X7b0gEoALyMfYlmPzcrfUb5fBb1/qbBikeOAD176ipRp0+fRpcuXSCTyUxCozpSU8+Df2I0xv70\nCondO6HXgdFwdFTA2toaHh5jkBD6C/iWfETES2HN5yNToQAmTAD27AHHcZj4x0RsfbEVQJmWeuRI\nWflqtRqTJ0/GvHnzoK1k/uA4DjEx30Ak6gy5vOpeQyVRIfjjYHj39kZB2GsONcAmCn4aGopmQiHO\npqbqpnP4J1EqIXM+DI+7jcE1NQemTwfu3wdUKkg9pPBo76F3XsDG6GhsrBTZA7D29BC2Rd57jYEM\nXTu493veyH6cja0vtmLlw4p+AaVWCzuBoDTnF8cB/fqxfqCU9HQ26VHPNN1169ZhzZo1AJht2nKv\nJZLyqvacJyTsQ1DQR9iyhcnQmnDv6j20qdMGuaKa5zjSatXw8uqOjAw2Pf1EcjL6+fgYTA2i5bSI\ny43DvYh72OG6A9OvTUeHox1gtssM20dtx5nRZ3BcdBz8BH7FjlqrRf6CIRA8blSlRl2ZqI1ROPXZ\nEzx2tUBRkfG95InkZPzwyTN8+8HWCgOCKikoYD362bNY8/vv+Pykbuoao+E4YNo0vPxsCKZcmQKO\n45CdzXJG/fhj1aee9jmNjkc7VpjH8fXTrzHn1hzk57Nou7t3X79q5as4fTrLbFGCt7c3bGxsEFHs\nlSeT0KgahSINrs+b4ugUV1ybOhUDNjSFXcdEjBy5BgcOrIFI1A0RyyMQ800MVorFWBMZyfQ7a2sg\nPh7p+emw228HUTILr4yJYZaR8tGWhYWFeP/99/F1+V+qHImJh+Du3hIFBVVPcuI4DimnUyDgCZB+\n+c3SfHjn5WGInx96e3vjZY7uaP6fIjr6a2bPl0pZ/PLgwYCdHSK6X0D8Wt2QVaVWC55AgGgDDv7Y\nK2MQdaSz3n1JR5IQPDcYtvttEZEVobN/S0wM1kVFAWCzc7t10xNNuXAh4ORUYVNKSgosLS2RWs5c\ntsZ5DTY93WTwvpXKTPD51igsFCMzE7C0ZPmGjCViaQT6NOuDy5d1Q5SNISfnFdzdW0OcnwNrPv+1\nEmTKFDLwQ/h4ynuKLU5b0P9Mf5jtMkO7I+0w7do0PF02Fr6HGyMwfIvRAR3KTCX4VnxkxOZjtesi\nuATONeq8Qo0GPLdXaL17BFwsXSBPrEH0YHg4YGmJ3ObNwXN1faNkoXGBrsg2q4W0cG/IZMw1UjIR\nuDo2PtmIYeeHlfpgCpQFaHO4Daase4oFC167SjpkZjILnEDA/HCdO3fG1atXS/eTSWhUj0jQG88+\nOIo5Fy7izpy+GPH9bkybloDu3btDJOqGtPAH4FvxkZpWACs+HzFFRWzo8OmnAIA/gv5A95PdS3/s\n27dZKqfy0Q3Z2dno0qULDlRylpWQnn4ZAoGdURE0+YH58OzgCfFy8WubqwAmhG5kZKCNhwemBge/\n/dxWRlzf3b018vMDKmzXBkeA3/AJ5M16sen3R44wozCAvzIzMcxQFJNWi4KhrSF8xdOZIAgAynQl\nnjd+jilnp+g9Pa6oCNZ8PpRaLcaNA86f13OQuztz6pfrBVatWoX169dXOCw2JxbW+6yRr9Q/wo6M\nXIXIyDWl/69YwSKVjUHmz8JQn9x5gg4dOpRmIqgpgYETsdlzEw4kJr7W+SWkX06Ht6M3OA0HjVaD\n8KxwPPljB7I6N8CjZ3XR+qAtLPZaYPiF4Vj7aC3O+59HYHqg3mR+0ZujIV7OzDR30qLw4JU5cgur\nz6mxRRyEBrf34l7EPcR8E4OIpbqDgioZOBDg8bArOhqz32C+0aQ/JsF93kho5s7HiBHAF18YH3mu\n0Wrw0ZWP8OW9MrXzwL2HqPNVB6Rnvd3JuzdvMtPrV19twowZMyrsI5PQqJ6YmK1w3TQPjmdeIadL\nB3Q+3Au2thzat38XDx5sRWDgBIQvCUfs97H4KS4Oc0JDmVrbogUgEJSaqba7bC8tc906FrFX/oFJ\nTEyEg4MD7hrQMzMzb0EgsEVeXvUJztRSNYKnBcOnn0+NMpjqQ67RYG9CAqyLJwhWl+76bcF8EO/q\njEIlDyTwHVyc//nZM5byumlTYOZMTH/5EmeSDUTgPH8O9OwJb+/eyMnRDUznOA4nup3A058Nz5X5\nwM8PR3yyYG9vINEqxzGfVnHge4mWkaHHHDbt2jT84v2Lzna5PBF8vhWUyjIzV3Q087NXNyuY4zj4\nDfVDyinmqB0+fDjO65Vu1XMt/jnuulhBoXqztDAcx8HvA7+ySX9FRUCnTohynoToaKZdp+en40n0\nEzgJnDD75mx0OtYJZrvMMODMAKx4sAJnfc/CN9wXfCs+5Allz/MRzzk457u8yutnK4pQ9/l9rHU9\nCIBNluVb8KE0tqMNDGQe4mnTkL9xI+wEAgS9xvTsJ9FP0OlYJ8izJchpYI8NYwJrlMIcYNrbu8fe\nxQX/C9BqWSrznvvG47joeI3rUxUcBwwYkIsmTb5HZiVzK5mERvXk5rpAcKsHNq0S4unYsRj6NQ89\nhkVi4cI/8cUXSyAQ2EES6guBjQC5eQrwSmzfly+zkCmtFonSxNLZ4gALqRswgGXaKI+XlxdsbGwQ\nEBCgpyZAVtadYsGhfzZxxR+eQ+LPiRDYCiBxlhh9v4ZIVyrxeUQEmgmFuJxuXDLFNyEq6ivExv6g\nsz3sszAkHavkD5BKkXvyJMydnZHbowewb5+u32L+fODQIcTH7y7NflsefgIfcxfMRcB4/W0PAKdT\nUtDmQkhpihi9HDvG4vgBfPPNN1i9erXew55EP0GfX/vobBeLlyM6Wtd0NWNGaZSwQTJuZMCrlxc4\nDfttnj59iq5du+r4y6ojR6WCvVAIt4BPEBdX1c0ah8xfBqG9kKXCWb8e6rnTwOdbQS43rCXkKfLg\nGu+Kg+4HMffWXKz8eCV+6PUD+p3uh6X3l+K0z2k8jb6FO68sECwzHCwy8vlx2DufqjApLnxxOOJ3\nGZn1b9YsZnLMzgYcHLD3xQvM0xMaXhUcx6Hf6X64FnINW7cCx1o5QfPJrOpP1ENwRjB4TjzsPp6I\n/v0B3xR/2P9sD5mimrVIaoBWq0W3btPQpIlcJ6E1mYSGMQ2ogOvLRrjzwTOsOnMGfy0YiEl7d2P6\n9AJYWloiJGQTIiPXImhKEFJOpWB7XBzmh4Uxg/eAAcCFCwCAE14nMOjcoNKHt2T0GBxc8XrXrl1D\nq1atkGbAiJ2VdR8CgY3O2hyGyHXLhbC5EAlOCW+lo/eQSuHo7Y3h/v4Ifd34vmrgOA4eHm11TFOa\nIg3cmrqVTtQqz+mUFEwPDmYzKRcvZk7pGTOYNiKTsf/T01FQEAp395Y6bbHoziIceH4Abk3coMrR\nH3osTlWBHrghOr2K0OTcXMDcHPlJSbC2tkaMgZAWLadFm8Nt4JNSNgtbn5ZRgocHmxNiqP/XqrUQ\ndRYh+3GZ3ZPjOPTu3RsPHjzQf5IBlovFWCEWo7AwEny+NdTqN09CGTo3FHGLXQF7eySL9yM4+GOj\nz+W0HDzaeyDNNQ38BD4OexzG/L/mo9uJbnB6aI8pjxfi83tf4JT3KXineJeG0t4XO6PO42twTq8Y\nSJIfmA9hc2H1kWUREcwJWaJZPHqEnM6dYenmVqO5Tfci7qHnLz1x9pwW7doBWbEy9vLXID9Vec54\n/IG6Fql45sLev7m35lawZLwpZ8+exaBBg7B2LYeSMQ/HcXj48KFJaBiLn88IvBqxB93uv0Due93R\n/bgjLCyAMWM+wrlzB8HnW0PyKgWe73oiR6GENZ/PfADu7sxMJZdDy2nx/tn3cc7vXLkfh8VWV37+\ntm3bhgEDBlRIcFgeieRRseDwMKr+8kQ5vB29ETYvrNq1OoxBw3E4lpQEnkCATdHRyH/LJquCgjC9\nHXvmX5nwH+Gv95wP/PzwV3lVWiplqdx79mTxiO++C2RkFAuk9pDJysqRKWSw2GuB9Px0BE0JQtol\n/QJ73z6g9YVgnKkuTn/aNDybPRvTpk2r8rCdrjsr2KjF4hWlJpvKcBxL4/Xkid7dSD2fCr9hfjpt\ndvnyZQwbNqzq+pYjpKAANgIBsovDwENDZyMhYZ/R5xuiKCwH/Nr3oTx3Gz4+AyCR6CaRNITkkYT5\nRfQMeuKSf8cJlz74XHgBC+8sRI+TPdBwZ0N0PdEV75wchWYvbuv1kfiP9Ef6n9UEjCxaBGyv1Bkv\nWYIVZ87gO0MTGirBcRwcTzlix42/YGtbbv7qtm2s/NfgwAGgzfu+mH2ThSpHZEXAxsmGpUJ5Q6RS\nKezt7eHt7Y2MDDbBNCEB2LFjB7p3724SGsYSF7cD7ns+w6Q9bojq1Amdt/Ew5MNorFvnjhEjRiAw\ncDxSUy/A29EbkgcS/Bgbi8XhxRO4pkwptUP5pvqWJq4DWEcwZQrLMF4ejuMwa9YsLFiwwKB2IJE8\ngEBgqzMaN4SmQIOQGSHwHehb5fKyNSFNocBnYWFo6e6OW5mZb81klZDgBLFY11YdvigcSUd0Q1VT\nFQpY8Pn6VzFkBlqWW8HCApg3D1H8OYiL21Z6yDm/c/joykfsni6kIfjjYL3FdOwI7ORnYJwB82EJ\nmuvXIWzQAEKhsMrjSuaE5CvzoVCkgM+3LJu1rodTp/RPPNcqtHBv7Q6pQDfFuUqlQqtWrVgqfyOY\nEBiIw+USaeXnB0IobAaN5g3zlX3/PSI7HEbo5kcQCOyMXm0QAIKmBCH1bKrefRqNHC/drPCe++3S\nuTkFygK89+t7sHr8O4be/wHvHnsXjXc3xtDfhmLDkw24GnwVwWeC4T9a/wAEAAuusLAoDbIoJTsb\n4t69YfPqlc5cIH08i3mGjoe7ws6ew7NnFcuBhYXe8O+qKCxk0U0e3kXofLwz/gz6EwDzkR32OFyj\nsvSxdetWLFxYljH5m2+A998PQocOHZCWlmYSGsYilQogfNgdv8zyxIkffsBvX43EzCN7MWmSBjwe\nD97ep+DrOwhpl9LgP9IfOSoVrPh8ltspKIiNdIvXXVh6fylWO5fZuTMy2EPg6lrxmgUFBejevTtO\nnTplsF4ZGdchFDZDYaFx0SAcxyHupzi4t3SHzOft2UBf5eSgs0iEqcHBSHkLKUn8/IZCInlYYRun\n5SCwFaAoVjec9pfkZMNRLamp7OUsKmIv6v79yB1nD+9LZmxVGYUCg88Nxt0IFoCgylbBzdwNmsKK\nHcKrVyzMVqZWo4mbG3KrmD3/15UryKtTpyx3TBVMuTIF5/3PIyZmi15fS3ny81n4beXkiEnHkhA4\nyfCan/v378f8+fOrrcuT7Gx08PTUyS0VFDRZ7/K6RhMZCVhbQxkQD5cVCxDut8roU5WZSrg1dYM6\n37CQEYuXY7doFXbExQEAjnoeRe8Lk2AjEJTeS648F89inmG3225MvToVrfa0wj2ze5h1ZBa2vdoG\n50hnZBWWExD79sFgLOuff2LsyZP4w4iZ4WMvjkfbaWexT5+y9vnnbOZ5DTh8uGzg4JPiAxsnGyRK\nEyFKFqHlwZZvtMpgZmYmrKysEF9u/ZkTJ66gdu1suLqyZ5lMQsM4tFolXF81wdNejzDlwQOkTfgA\n/X4dCHNzYMmSDdixYzuEwuaQ5QRC2FyI/IB8fBMTg1UlaSXmzmXqKFjiOhsnm9IUAgBLFta2rW4K\nALFYDBsbmypHiamp5+Hu3gpFRXFG30/mzUwIeIIap1qvCrlGg+9iY2EjEOBMSsprax0qVTbc3Jro\npM6Qekgh6qY/AGBsQACuGxqxHT3KnODl0KoV4L9oAsXHQyHuZA27HxtBlRhXut9/lL9O28yZw15Y\nAJgSFIRLVUycGDVqFGKGDdPJN6SP6yHXMer3EcXzMqKqPX7FioqTwbQKLYQOwioHARKJBBYWFsiq\nPGouh4bj0N3Lq6KJrxip1B0eHm2g1b5Gh8RxbJ0VJydwnBZuD1sg5Ls7Rp+edDQJoXOrDnPNyxOB\n794eVm5u8EwPh/U+aywL8S6dV2MIvyV+cF7tjG+efYNRv4+C+R5ztD3cFp9enQGpvSX8759BoUpP\nqDnH4dratRh5p+r7CMkIQcPv7TBlmlx/aK2/PzNfG2nelctZpp3yUeU7XXdixIUR0HJajLgwAr8H\nVL8uvSE2btyIFStWlP7/9OlT2NraYunSLCxdyraRSWgYT4D/WLiO24VWt12g4PHA22GOcdMy8P33\nEejWrRtiY79DZORqxG2PQ8SXEUhVKGDJ50OiUjGvt5VVqap70uskhv42tELHOncuS2lcmdu3b6NV\nq1ZVvvBJScfg4dEeCoXxOXFkPjIImwuRdPT1l/vUR2B+Pvr6+GCEv/9rze1IT7+CoKDJOttjvo1B\nzDe6TuVclQpN3NwM+1WGDdM7XTYkZAZSU8/jp5ursGZzTzaEnzEDcHND0pEkhC8qyw+Vnc2iekvm\n1lxIS8PHlSMYiomKioKNjQ2Uzs5sHkk1FKmK0HR3Q7zwGlftsQDrZ1q3LnOIp5xJQcC46k2UCxYs\ngFOliYflOZ+aiqF+uj6REvz8hiIj45refVVy8yabVa1SQSp1h6ewM9ws9Qcz6MOnn08F574+mJ+q\nHb4NuY1mf+3AQffDcBAKqw2NzfPKg0c7j9J71nJahGeF48XhtYjrZIt+p/vBbJcZev3SC0vvL8UF\n/wsQS8TgOA6K6Gjw7txBTLF2o4+h+xfDetr2qhezHDIExi4Of/YsSzhRHrVWjUHnBuGg+0E8jHyI\nPr/2ea0BW0mqm+Ri7djf3x82Njbg8/nIyCiNIzEJjZoQH78HHgfnYMkud7jMmoVt3w/FkmPnMXUq\nh5YtW8LLyxkCAQ9FKTLwLdgaD4vCw1lOKoCt5rWBJcHTaDVwPOVYao8EmDwpl9OsAps3b8aYMWOg\nqcKGGh+/C15ePWu0dGdRbBE83/VE1Iaot7dUJwC1VoufExNhzedjf0KC3gyxhggPX4KkpKM62716\neEEq1L23P9LTMTkoSH9hGRmst9cTUJCScgahobPR9URXCBOFbJnaY8eATp1Q2G0shBbPwRWveHjk\nCNM0SshWqWDu5qY3R9emTZuwYcMGNo/ExsZwBrhiOE6DSWeaYOeLqk1TZcez1BOvXrFEfJ4dPZHr\nUn26EE9PT7Rr105v+K1Kq0VbDw+46UlLXkJm5k34+g4yqo6lFBSwlYCKl9NlM/y3InJ1JKI36qZ6\nqUxhRCGE9kKjEhNGR2/CedcxqPv8IS6kpqCfT9VrgwBM2Hi+64k8z0q9+sSJpVGPCrUComQRDnsc\nxqc3P0XrQ61hvc8ak/6YhBnHdmPd3h16w12F/tmotaUp3Hyr0eb/+INpYtXWlU0BeqpnGlFUdhSs\n91kjKjsKbQ+3Lc1AURO+/vrr0lQ38fHxcHBwwI1ywmzpUpZejUxCw3ikUgHcH/bApdne2HLhAoIW\nTsTkS9Ngbg6sXfstvv32W/j5DUVW1h0ETw9G8slkhBQUwF4oZA7a5GQ2mi1W/1/FvULrQ60rZNq8\ncoUNyiq7BdRqNUaMGIEfq0hSw3EcxOIV8PcfVeXSmJVRZavgN8QPITND3kpkVXmii4ow0t8f/Xx8\nEG5EeG7JLPCCgopx8PJ4luK7ZP5BeT4JCcG5VP1OUvz6a+mcicrI5fFwcbNCy4MOFRe20WqB+/fh\n2fAmZHaDgf370ddRrfOyjg4IwK1KphylUglbW1uIS0Iplyyp1kSVlXUHJx+/q3fOhiF+/pkF3mRc\ny4Dv+75GjSw5jkOfPn3wqPKSgGDhymOqce5rtWq4u7cyanJpKdu2lbY/x3Hw9OwAmcwH8kQ5+JbV\nT7CL/TEWkWsNZw4uT3jyX7jsXBvLQ3zQxsMDJ43wJwFA7HexiNpQzoyVlsYGGlU8rymyFNwKu4Ul\n975Di2tXMXxpA/T8pWepNhKUHIlmUw+j/z4jEjEWFrJ+oZr6PnvGfGqGfup9gn0Yc3FM6WqONUEq\nlZb6MnJyctClSxccqjQpKDKSRQmTSWgYj0Yjh+srM7zq/hwDXFyg6tUD5nvMMXKMAvv3x6Bdu3ZI\nTj6N4OCPkfM8B1492HoOEwIDyzq1ZctYOstiJv85GT8Lfy79n+PYTHF9siE1NRX29vZwcXExWEeO\n0yA4eCpCQ+fWaM1njZxFVvkN9avR4jnGwHEcTiYnw5rPx6HExCrXXi4qioZQ2EynE0z+JRlh83Qn\nVCm1Wpi7uSHT0BroY8YA168bvN7Dl1bY9kR/xtnIVZGIXymEePJ62NdKg3rthtJ07QBwPDmZzccp\nx9WrVzFixIhyF3jIzA9VEBAwFskpv6P5geZGp0xnvn0Obj18kHWv6izI5Tl79iymTKmYJkWh1aKV\nuzvcpdVrqAkJTggLm2fcxdLSmEm2WNMqKAiBu3ur0t824ssIxH5XtRbm1dMLufzqtSiO4zDh8ng8\nftUU0dm+qPXqlVH3A7A5G+6t3cueuQMHDDvA9Vy3y9OnEEyfDlGiBw57HMasG7PQaOhZ1PqqFQac\nHhGjmLMAACAASURBVIidrjvxIvaFwZQxAFhGyt27q7zWpEnAmTOG96u1ajiecsQx0TE03dO0QnLD\n6nBycsLs2bOhVqsxevToUo2jMgEBJqFRY3x934fr0CNocdsFMjs7TDzUF6sPP8bcuRw6deoEofAF\n3NzMoVRkwbOjJ6RCKV7k5KCLSMQ6y7g49iIVG8dDM0PBc+JV+IGTkvRP+gMAZ2dntGzZEhKJ4Rne\nGk0RfH0H6Z1VXBWclkPU+iiIuomgSHn7izJFFRZikK8vhvv7I85AQsGUlFN6O6Xg6cFIu6jreH6Z\nk4MBhswQ2dlAkyYGc29wHIcfbjaFIEh/JI/koQR+Q/3w44/A2sUyYONG9tvNmgV4eSG2qAi2AkEF\nIThy5MgKyd2gULBRa+VptcUUFUVDIOBBo5Fj7aO1NZqgNaqvEttbRNfIrJifnw8LCwukl6vPyeRk\nTAg0HHlVHpUqG3y+BRQKI7InfvllqTkWYGHr5fNpFYrZ0rCVo9RKKIougsBWv3ZZmesh19HtRDdE\niNfgfsgmdPT0ZOl8jIDjOHh28ixbErZnzxqtf/pTbCzW7NhRas568ACw6ytE64PtcCPkBjY82YDB\n5waj0a5Gpb6RiwEXEZsTWyao3N2BTp0MqhFRUczSWd1Cm76pvrDdb4vp16bjgHv1QRgA044dHBzg\n5+eHdevWYcyYMVXmK6PXEBq1/4YO/L+Gpk0HU/3xUfSRuAEJPv2UvpS2pwKHB+TsXItmzvyMbty4\nT9bWEylLcp2aL21OqadSaYSFBTWoXZse5+QQtWlD9NFHRMeOERFRV5uuNK3zNNrltqv0Gi1aEG3f\nTrR8OREq/TwTJkygGTNm0JIlSwiVdxZTp05D6tHjHkkkdyk5+ZjR91ardi3qcKAD2X1mR/5D/Eke\nI69x+1RFBzMzcnN0pAlWVtTPz4/OpaXp3ENu7nOytBxVYRu0IOlLKVmOstQp83FODo23stJ/QWdn\nohEjiBo31rs7ID2AgmX1qZE2Qu9+i+EWVOBfQH9dUtOcpU2I9u8niosjGjCAaMYMajt2LFkpleSX\nn09ERElJSRQQEEBTp04tK6R+faIJE4ju3tV7jdTU02Rnt4Dq1GlA07pMo9sRt/Xfix7GqNPoRdMW\nVKt2LaPPady4MU2dOpX++OMPIiJSaLW0OzGRfmrTxqjz69WzIhubWZSWdqbqA/+PvfeOiurc3sef\nmaEzjQ5CxIYSsWLHgmKJxm6KJiYxRY0p5qaZXkw1icaYxHtN1eSmaoxGxS6I9K4IiiDNQh3KFAaG\nGWb274+XGWaYc4bBz/2s+/uuT561XEve8546M2e/ez97P/vyZeDgQeD11y1DjY1/wd9/ueVvr6Fe\nkE6Rov6nes5DKA4q4L/MHwKR4/tT6VR49uSz+HrR1wgKXAFty1E8GxaGUy0tuNrW1us9CQQCBNwT\nAMUfCuDCBUCpBGJje93PjJVBQdg3bRqMr7+O2vI2rF0LRK/9Fk9N3IC7o+7GtnnbkPpoKppfbsY3\ni7/B7f63I/5qPKbunoqwz8Kwcv9KfCnIgc6oR2d6Kuc5vvsOeOghwNPT8bVEh0Rjzeg1aNG1YPf5\n3bzvCGv89ttviIyMREFBAY4ePYq9e/fCxcXF6fv/vwSnrHBPNDQcoKxDs+iX+3LopT/+oOZVSyn8\ns3CKmWqib765TiEhIdTQEE+5uRNJ36inZBmTpPihtrZ7NWcODnalVNRqasn3Y1+qaO521Ts7mWzV\njxzZcx0dHTRu3DjaudOxSFlbWyWlpfUjhcL59EYzbu66yVKHL/ZdmM0ZXNRoaHR2Ni26eJFquwgc\nk8lIKSl+1N5um82lylbxptqOys6mDL4wxKpVTE6dB6+cfoVeP/0sJSeLeTvjJU++QPcG1dsvAA0G\not9/p+ffeove2bSJ6JdfaMsHH9B6rsYXe/cSzZ9vN2w06ig1NYC0WsZ/dBo7KXBrIJU3994jQntF\nSwkB6SSXm/okmU5ElJSURCNGjLCEDRc66WWYoVbnd4WZHPBfixbZcDlMHsXPrqCvJamFModlcnpL\neVPyes2aIiJ66uhTtO7wOiIiUnW00ZGzYqpvvUGbKyvpkWLnwn2aC10hqueeJ3r9daf2scbYnBxK\n2LiRvh/2Mb30hoZkW2RU3+q4aM9kMlFFcwX9+8K/af3h9bR9SSB9N8mV5v57Lr2T9A4lVCRQa0cr\n6fUsQcbJWyGtXkvhn4VT8NZgyq9xrIptlpnZvn07BQQE0GUnNLXwd3iqb+joqKPkszI6OzyNJqam\nkik0lG77NIxe+PAKPfUU0YgRIygl5RylpQVTa2sxFa0sopv/ukntnZ0UkJranYJ6//1EW7ZYjrv5\n7GaLJIAZ2dms6I8roaW0tJT8/f0tvaD5oFJlUWqqv9NV49ao+62OUgNTSZnhfDZWX9BhNNLr5eUU\nnJZGRxQKUqvzKCvLvtdF1QdVdPVZ+3z7ap2OfFNSuBtFGQy9kou377ydMm9kUl7eZE7VWyKiL2Zc\np5+j+QsnzzQ10aSEBDJNn07DXV0p5YUX7DO11GoisdguTFZX9yudPz/bZmz94fW0NW0r7/nMKHmq\nhMpfL6fVq5lSSl9gNBpp4MCBlJWTQ4MyMijVydi/NXJyxlFjoz2hTkSsSnXgQJtsjurqb+jSJXtS\n2GQyUU40U1Gwhq5aRynylF61ofJr8iloa5AlvPtrXR19lTqXamt/sBTY8oVCe15HxqAM0gTGEBU5\n7lvDhY+vXaM5v2VSs8iffkj5mu785c4+H4PKy8kYEEBHig7SS6deopjvY8jrAy8avGEThY4ooz8v\n/+l086iDxQfJ/2N/euYYNzdhRnp6Og0YMIBCQkKc1ifD3+GpvsHNLQiuHv4QoAxVyk5oxGKscZsI\n19tPIT4eWLZsOQ4dOoLAwPvQ0PAbgh8ORt2eOniIRHgkOBi7amrYgV57DfjsM6DLfX4h5gUkViai\nsL7Qcq4JE1gk64037K8jIiICW7duxQMPPICOjg7e65VKJyIiYicKC5ego6OuT/catCoIkXsiUbSk\nCM1nmvu0rzNwEwrx/qBB+GP4cDx99Sp2l+2HWDbTbl7LmRb4zLEPTZ1sbsZcHx+IBBzhi4wMIDwc\nCA3lPPfVpqtQ6pSYEDoBMlkslMpzdnNMJuDXYh/0b1Ly3sM0uRzFrq5I3L4d7f7+mHrlCjBwIPDx\nx4BazSZJJCyklZBgs29NzVfo12+DzdiK21fgz+I/ec8HAJ2qTjT80oDQJ0Jx773Avn0Op9tBKBRi\nzZo1eGvXLoS4uWGqTNa3AwDo1289d4iKCHjzTeDtt1lorgvNzSfh63uH3XSBQICw58JwY/sNm/HG\nw43wvdMXQjf+1w0R4R8n/oF3Z70LX08WovxDoYCf3wI0NR2Fj6srHu/XDx9dv97r/QgEAviNN6CJ\nJgFRUb3O74lpxgAkeHTCsHQZ9p76GKtHru7zMTBoEITh4VhUJ8HHcz9G2qNpaNzUCP/iVxCz9DJ2\nn9+NyH9GIuLLCDxy6BF8n/89ShpLOENQS4ctRWRAJHZf2A2D0cB7yp07d4KI8PTTT2PhwoV9v+b/\nY3DKqnLh8uWHKPP5N+mxndl09K23KP/lNbTol0UUHk60f38xDRo0yNILwmgwUlq/NGotarU08dGa\nc/uXLCGyah+5LW0bLf/dVvmzqYkpkOTl2V+HyWSiZcuW0cs9has4UFm5mfLyJt+SflBLcgulBqSS\n4i/ns3T6ima9nr5Lm0Nr0t+jIqtUx05tJyWLuSUk7i0qot18qbYvv+wwzLAtbZtFKLCx8SidPz/L\nbk56OtGI4SZK8Uuh9hv8z23pxYs0f9s2evPNN9lAQQHzJP38WOek+noWqrEKXWm1V7r0l2wz1To6\nO8jnIx+6qeL3kK5/dp0urWIkb3s7K7riewx8KC8vJ5FMRn86mZbaEwaDmpsQP3OGCXRZEalGo6Fr\nLvdFGjtYRbvmQrcndnHJxV7FBPcV7aPRu0ZTp5H9nto7O0manEy1rdcoJUVORqOeGjo6yCclhW7w\nCH9ao+muLZQX1vdQrsnEoo9BR7LpyMVskr0qoNaq3iv7ObF1K+vM1IWqKpZ7YXaWjCYjFdYX0q6c\nXbT6z9UU/lk4+X/iT8t/X047MnbQ+drzludxRXGFXN514a0QVygU5O7uTnPmzOmTdD7+9jT6Dpks\nBsLoy5he4oKkiRMRdbEWydeTMX+hHmVlw2AymVBV5QmTSYc2XRGCHwpG3Q91GODpiRiZDL/WdxF/\nL77IvA2jEQDwxIQnkFWdhbyaPMu5fH2BDz8EnnySrXytIRAI8PXXX+PHH39EWlqaw2sOD38L7u7h\nKCnhJ9D5IJ8ux6jjo1CyvgSKA4o+7ev0OVxcEEkFiAudj5kXLuBf1dUgIqhSVBCPEcNFbEvMdZpM\nON3SgjsckeB33sl7vkMlh7Bk2BIALLlBo8mByaS3mXPgALD8LgHkM+VQnuX3NubJ5UjSavHggw+y\ngVGjgF9+AbKzgeZmIDISOH8eOHLEktlQV/cjgoIegFDoanMsN5EbFg1dhINXDnKei4yE6i+rEfoM\n86A8PIDFi4E/HTsndiiTy+E+cCBEeXm9T+aAi4sE/v53oa7uB6uLI+Ctt5iXYUWkajTZcHfvD3f3\nEM5jCd2E6Le+H6p3VQMATHoTlElK+My19y7NaDe0Y9PpTdgxfwdEQhEA4KxSiVFiMYK9+8PDYxDU\n6gwEuLnh4eBgfF5d7fiGiCDP+Q5apRx6hd7x3B744Qegrg54NNIfO1RVWCSMhPeWbX06hgX33MMS\nCAzMO/jxR+C++7oJcKFAiBGBI7Bh/Ab8vOJnVD1bhfz1+bjr9rtwWXEZq/avgv9Wfyz+bTGOlB7B\n+JDxePPsm5ynev755+Hi4oK9e/dCKPw//1p3Cre2EqAuIjBhGJ2dkUMTMjKI5HKa9NV4+ui3JJo+\nnei5556jzZs3d1W/vtZd1ao30ommJhqT0yXxbDKx1lsHD1qOvTNrp1081GgkmjKFSQhw4cCBAzR4\n8GDS9CKZ0NnZRrm5E6iqqm8CaZb7zldTalAq1e/rmyqnM9BqSyg9vT8REZVotRSdk0NLLl6kwpdK\nqeJN+1z+dKWSRvLpcV27xlb5PNXzCq2CpFuk1G7oXn3m5ESTUplq+dtkYmH58+eJbu68aSMp0hPf\nHT9Orn/9xV9gV1PD9GGEQqJVq8h0/Rqlp4eRRsPNRx24fIDm/HsO57bG+EbKGWcrEX7kCNH06byX\nx4m48+fpwS1b6L77nCg+44FKlUUZGYO764GOH2c9Qns894qKt3jl3s0wcxgGlYGaE5spd6Ljau73\nz71PK/bays4/UVJCH1+71nXON6isjHngVe3t5JuSQipH+k45OUQREVS47CJnajcfbt5kqbAXLhDl\nqFTkcXIfHcv7nbkHVjU9fcLkyUQnTlhUlTMz+7Z7raaW9hbtpaeOPkVDvxhK2Awa99U4+jD5Q0q9\nlkodnR1UWlpKQqGQdu/e3efLw9+eRt/h7T0CBtENCIqbUNzWAU14OB6kUWj0OYkLF4DZs+/BwYMH\nERi4Eg0Ne+E51BMeAz3QfJLF4FuNRmSo1YBAwLyNbd2rkrXRa1HUUISMGxmWMaEQ+OILFiruyu60\nwfLlyzFt2jS89NJLDq9bJPLEiBGHUFPzNRSKv/p835KxEow+ORplz5Sh/jfuNMlbhUqVCplsGgBg\nqJcXMqKjMczLC2knanA92j79L6GlBXN9eFaix44B8+cDIhHn5qOlRzF74Gx4uHhYxuTyGVAqky1/\nFxSwj2f0aEAe59jTSPr1V4g9PVHCl94ZEgJs3w6sWQPU1ED5QBRc63QQN8s5p88ZNAeZNzOh6bD/\nsGu+rkHok6EQWPE4c+cCRUVAb4tpM/I0GpS2t+PDhx/GsWPHoNVqnduxBySSCRCJvNhzM3sZmzfb\nPXc+PsMa7v3cIZ8tR/3P9Wg+3gzfBTweJIAaTQ0+y/wMW+dutYwREeKbmrDYzw8A4ONzB1paTgMA\nwj08MM/XF9/V1vJfwP79wN13w2+RP5rim3q5825s3MhS40ePBuSdCughwm1DFwDr1wNbtjh9HBvc\ncw+wfz9yc1l0YeLEvu0eLA7GvVH3YuedO1GysQQjAkagWlON+tZ6bDy+Eb4f+GLUtFHw9vXGgJkD\n0G74z6bWc+H/vNEQCl0hloyC25RKzK/zQvbSpZhf7Ymz104hNhZQKiehtrYWDQ3spdDamo/gRxgh\nLhQIsKFfP3xjJsSXLwdqahhxC8DdxR1vznjTzqUcP569HPi+h59//jmOHj2KkydPOrx2d/cQREXt\nR2nperS1lfT53sWjxRh1ehTKXyhH3c99I9YdwdpoAIwk39JvAIaWAQ+Jr2HLtWswWYXVziqVmCXn\nfunixAlWG8GDw6WHsXTYUpsxmSwWKlW30ThwAFixghkOr0gvmHQmtFfa/7g6OjoQf+QI5vn7I0HJ\nb1gAAHffDQgEqNuxAEF1o4CxY4ENG4Br12ymSdwlmBI2BacrTtueq7oDqlQVAlcG2oy7u7MQ1QEn\nSzw+v3kTz4SGIiw4GJMmTUJ8fLxzO/aAQCBAUNBDqK//CTh6FNDp2D1awWBoRlvbZZvPlg+hT4Si\nZlcNmk80w3c+v9F4LeE1rIteh0E+gyxjF7VauAoEiPTyAsASQNrbr8JgYAkcL4SF4fObN2HoGeMF\nmMHrMhq+d/qi5VQLTAaOeT1w+DAz1q++yv4+WHwAkYImHG1WAi+8wDIUnCDh7bB0KRAfj19/NmH1\navYd/J/ghZgX0N7Zjpj+Mch/PB/33LgHUhcpJtwzAa8kvIKArQGYsWcG3kh8A6fLT0Orv7VFxP8F\n9Nkts0Zp6UbK/XQT7XzrPL1z+DAZFy8i6RYpffLPBlq9mmjdunW0bds2Ki9/jcrKNpFBaaBkaTLp\nGxk5J0tOJqXZXf7iC6K77rIcW9+pp8GfD6azlWdtznnzJvN6+UQ1z5w5Q2FhYaR0IoWyuvpbysq6\nnQyGW+up0XqpldL6pVHNnj4ysDzIzBxCGo2t6GBLUgvlTsql6+3tFJOXRwsKCqhRryed0Uhi6+dn\nDYOhW46TAx2dHSTdIqWG1p6aUQpKTpZa6giiohgRbsalVZeo5nv7e42Pj6epU6fSz3V1vKq3Fmi1\nZJJIKO2YlDVaUiiYpIyvL+urYCVsuCNjBz3616M2u1e+V0lXHudO//3zT6LZszk32aC2q1mVuSvf\nnj17aBlXVycnYW4c1RkznlOptaHhIF24MM+pY5lMJsoYmEHJ0mTeKvCLdRcpcGsgqXS2AoPvVVbS\nP0ptNaoKCuZTQ8Oflr9n5OfTr1zfi0uXiPr3t1Rj54zJ4RTGtIZGw3ZJSOgem/zdZPqg8DTFmLNW\nXnqJiZTeAkxRUbTAJ+NWu8HaoKW9hbw/8KYBOwbQ3v17acCAASSTySyq2Wqdmk6WnaTXzrxGU7+f\nSl4feNHk7ybTK6dfoRNXT9h1A8TfdRq3htranyj3yGI6uSKf5mVlEfn40JKfF9HOpN/I15fo8OGj\nNH36dNJoCig9PZxMJhMV3VNE1V8z6fJ7ioq6BdU0GhaDL+tW/dxzfg/F/Rhnd9533iG6917+61q/\nfj09bha+7wVXrqynwsIVt9z3QntFS+lh6f9jw6HT1VJKio+dVlblu5VUtok9E73RSC+WlVH/9HT6\n540b/AqmmZlMApYHiRWJNPHbiZzbsrKiSK3OpStXiEJCbHtxV39TTZcfsC98WrNmDe3YscMig89Z\nM2KF9pkjqOrTcbaDjY0s08vXl/U2r6igq01XKXhbsEVI0WQ0UXo4f+MsjYaVgjgQqSUios2VlbT+\nSrfhaWlpIalUSi297egAFxLHU939wZwcUmnpP6iqyrGmkjWKVhZRev903u2Lfl1En2V8Zjc+KTeX\nzjQ324yx7o/dysGHFQqKzuFoGfvxxzYv97IXy6jynUqH1/n880QPWqnd3FTdJJ+PfEit15E4OZma\n9XomTMrVMcsJlK96jfYEv9Ln/fiw8JeFFPVFFInniOnVV1+l5cv5+7Nr9VpKqEigNxPfpOm7p5P3\nB94U830MvXbmNTpdfvpvTuNWIZVOQIfsIrxz25HZ0QFjYCDuoyjkKU8hOBiQyeJw4cIF6PVhEIk8\noVZnIfD+QNT/yriAtSEh3TFWsRhYt84iLQIAq0euRnlzuQ23ATAKJCMDSOVWG8Ann3yCo0ePIikp\nqdd7iIj4Ah0d1bh+/eNbegZew7ww+sxoVL5e+T/iONTqNEilMRAIbL9aqmQVZDNYDYGrUIitgwfj\ny4gIbKqogFgk4s4CO3MGmDOH91wnyk5g/uD5nNtksilQqzNx8CCwbBnjksyQz5RDmWQbftLr9Thy\n5AjuuusuhLi7I8TNDee5SCcrNI1tR2Chv+2gnx/w/vtAWRmrKxk/HkNe/xRSkRfO154HALScboGr\nnysk4yScxxWLgZkzGZ3DB73JhK9qavBMWFj3fcnliIuLw19/9Z3jMiPocDvqVwdwckgq1TnI5TOd\nPpZJZ4JeoefMYEq9norC+kI8Mf4Jm3GFXo8rbW2Y3qPexMdnNpTK7tqYhX5+0BqNONczjBgfDyxa\n1L3fHB+0nG7hvcbz54GffwY+/bR77K8rf2HR0EWQuLpjukyGMy0tQEAA8NhjwEcfOXPrNvhZvQSL\n6XCf9+PD3bffjZqKGtA0QmJSIh5++GHeuV6uXogbGId3Z72L5EeS0bCpAe/OfBcCgQBbUm+Np/nb\naADw9IyAEUqYhE0YqnHFpaVLMfOaAGerzmLePCAlxQOxsbE4deoUAgLuRmPjAfgt8IP2oha6GzrM\n8fFBk8Fg0S3CE08AP/0EtLYCAFxFrnhl2iv4IOUDm/N6eTFe47nn7FNwAUAmk+Ff//oX1q5di7Ze\ndHeEQndERe1HdfUXaG4+dUvPwWuYF0adHIWy58puOR23J58BACaDCepMNWRTbV8ES/z9McLbG9Ud\nHVheVIQWQ4/Cpd6MRvkJzB/CbTSk0slQqTJw5AgLK1vDc4gnTAYTdNd1lrGEhARERkYirOslPNvH\nxyGvodPdQMPIRniklXNP8PFhomMlJYBEgoVnqxH/5dNAQwNqvq1ByDrulFUzli7llbgCwArfory8\nEOXtbTO+atUq/P777w6PzYvcXAQcaYFKch16ve3CwWBoQXt7GSSS8U4dikwEVaoKfgv97PSoiAgv\nn3kZ7856F+4u7jbbzrS0IFYuh1uPtFGxeDT0+np0dDD+UCgQ4JmwMOy0zhhobmZ6U7NmWYZk02XQ\nnNegU9Npd41GI/D44ywNPiCge/zAlQNYcfsKAMB8X1+cbO4qht20Cfj1V8ZbOon2dmBH2gTI0cIW\nEv8B3DhzA2pvNeYFzENhcSEWOOD8esLL1QuzB83G+3HvI+GhhN534MDfRgOAQCCERDIOnvOvY8E1\nD6RNmYKgvBK0GdowOrYKp04BixYtQnx8PPz9l6Ox8SAEbgL4r/BHw94GCAUCPGbtbfTvz5aKP/1k\nOcfDYx7G+brzltWmGffdxxZ1XZpzdli8eDEmTJiAt99+u9f78PAIw/Dhv6O4+CG0t1fe0rMQjxBj\n1LFRKH2iFE1Hnc88MUOlyoBMFmMz1prfCo/BHnD1sa1jaDcacUmrRXp0NPp7eGB8Xh4Kugwt2tqA\nnBxgxgzO89RoanBDdQMTQidwbpdKp0CpzEBRkb1enUAggGyqDKpUlWXsjz/+wN1WxO9sHx8ktPCv\nUBWKffCcdBcELUrHBKm/P/DJJ1j05k84KqqAfthkKI/WImiBO/8+YGT4yZMAn0DAFzdv2ngZZixc\nuBDp6elQ9kbkc2HLFoie3gR//6Wor//NZpNKlQKpdIpdLQoftIVauPq6IuzpMNTuthWzjC+Nh7pD\nzVlpfbqlBfM46nUEAhHk8ploaUm0jD0YFIREpRI3dV3G/+RJ9mFbKQGKvESQTpRClazqeUh8+y1L\nPHjkke6xxrZG5NbkYt7geQCY0TjR3MyuPzAQePBBYMcOp54BwPI4xo4TQrR0seNVgJPIz8/Hl1u/\nROzAWLTfaIdxhBE1WueN2N/oxv84TlhW9jLlf/8P+vPZAlqdm0vk50cr995DX2f+QN7eRJcv3yA/\nPz8yGFjzmtbWImpOaKacaNbE5np7O/lYV4gnJrIOTFYx1+3p2+muvXfZnTslhbX85Ct0ra+vp8DA\nQIe9xa1x48YOyskZR0bjrUuiqzJVlBqQSk2nnNfxNxp1dO6cF3V22pJt1z65RqUb7ZvvnGlupslW\n5fG/1NWRf2oq/VJXR3TypMPeFXvO76F79t3Du91kMlJCgpxWruSuQ7m+/TqVPMmYSb1eT76+vnT9\n+nXL9ha9nsTJydTBU12bmzuemppOM1LKifz4js4Okm2RUd7riVQc8R3jvd57j2lZ8WDKFKITJ+zH\nM1UqGpiRwcu5LFmyhH766ader8kGxcWsSKG1lZqaTlNOjm0TqatXn+9TTdD1z67TlfVXLDpQqmxG\ndncaOynqn1F0+Mphu31MJhOFpqVRCU9b4Zs3d1Jx8SM2Y0+XltIb5qSD1auJdu2y26/qgyq75k9N\nTd01GdbYnb/b5jdqMploQEYGFZrrpsxl3U7yRg880KUnFh/f9wKcHmhtbaVhw4bRr7/+Sl/nfk1e\nD3rRY189Zpdk0Rfgb07j1iGVToTptssILupEusEA+PhgeWcE0mvPYuJEoLw8DGFhYcjKyoK//zIo\nFAchj5VDX6uH9ooWt3l4YIpUiv2KrrDOzJkskJ7YvTJaP249Uq6n4LLiss25p01jhce7dnFfW2Bg\nILZv347HHnsMen3vFa6hoc/Aw2MAystfvNXHAekkKaL+jELx/cVQnnNu1draehGenkMgEtmGTFQp\nKsim22siJfVItb0/KAgJo0fjzcpKJPzxB4yzZ9vtY8aJMv7QFMC8x+rqSVi8OINzu7WnkZiYW54d\nnQAAIABJREFUiKFDh+K2226zbJe7umKwh0d3yNEK7e3l0Omus/j+nDksjNYL3ERumD1oNg4XnEPw\nt3cxMqu4GBgyhAXU2+1TgPlCVF/evImnQkO5dboArFixAgeczdk14+OPgaefBry94eMzC3p9HbTa\n7u+pUpnUJz5DeVYJ+Sw5BAKBJUUdAH4p/AVyDzkWDV1kt8+VtjaIBAJE8GiGy2QzoFKl2Iw91a8f\nvq2pQYfBwJb1HJpLPnN90HLG1mt86y2WUTx6tO1c69AUwLxSs7cBgGmgLVgAfP11r89Ar2fZy8uX\nA4iLYwTKrXiAXXj55Zcxfvx43HfffejX2g+6MB0+uP8DHCo5hNKm0ls+bl/x3zYa8wFcAXAVwMsc\n22cCUAE43/WPQ+7vPwOJZAJ0HgUw5muhMhhQe8cdiL0pQlJVEubNA06dYq6/TYhKJEDgykA0/NYA\noAchLhCwH6EVIe7t5o1/TPoHJwH14YeMY1PZe9EAgPvvvx/9+/fHJ5980uu9CAQCREZ+j6amY2ho\n+KPvD6ML8ulyDN87HJfuuQRVBs+FWUGjyYZUalu9RERQZ6ohnSK1m5+sVCK2R33GKLEYuePGITw1\nFf8ID0c9h5E0mow4XXEadwzmLzLr7ATS0qZgxAhuoyEeK4auQgeD0oADBw7grrvuspszQy5HCscH\n0tCwDwEBd0EodGFGIyHBvlkKB2LdYpEpz2QGNCKCxSQTEoD0dGY8du2ySE4AzGgcPmx76CaDAfFN\nTXgkOJj3PIsXL0ZCQoLzhX43bjDr9PTTAFgoKDDwXjQ07AUAGAxKtLeXQiLhDgX2BBkJqmQV5DPZ\nZxu8JhgNexvQoe3Au+fexftx79sUNJphDk1xbQMAb+8oGAxNNmKdkd7eGCkW49yJEyzxwMrwmyGJ\nlkBfo0dHLYv1FRaysov33rOdp9VrkVSVhDsjbCVrbIwGALz0EvD556yWxQESE4Hbb2f1oPD0ZKvD\nhFvjERITE3Ho0CHs3LkTAHDm4BmEuIegSFGE56c8j7eTeg9f/6fw3zQaIgA7wQzHcAD3AbidY945\nAGO7/r3/v3Ux7u5hgJAgCm3BAo0EadOnI6igHLpOHaKmVlmMxtGjRyGTTYNOdw063TUE3h+Ihl8b\nQERY6OeH4rY2VJpXjQ88AKSkAFVVlvM8NeEpHL96HOXNtgTqiBFMXmnrVnBCIBDgn//8J3bs2IEy\nJwg1FxcZoqL24erVp9DWdusEnE+cDyJ/jETRsiK0Xmx1OFetzoJEYms0dBU6CN2F8AjzsBnXm0zI\n02gwRWpvTHxUKgyuqYH/1KkYn5eHLLPCbBdyanIQKglFqJRb9RYAMjMBpXIyTCZuoyF0FUIyXgJV\nugpHjhzB0p5sOYDpMhmSOY3G7wgMXMn+GDiQZTRcusR7LWaMSB2BvMF5gPU7ccQIJjZ16BDw11/A\n8OHsjUaEyEj2riko6J7+77o6LPb3h68rP7fg6+uLCRMm9FocasHOnawrkBWXEBCwEgrFPqYZpkqF\nRDIJQqGbU4drvdAKtxA3uAcz3sbjNg9Ixktw+IvDuE12G2YOmMm536kupWM+CARCyGRTOb2NugMH\nbLKmbPYTCSCfJUdLQguIgGeeYcXuXQXnFpytOovx/cZD7mG7kImTy5GpVkPbpSuHUaOAMWNsOEsu\n/PknYLMWmT+feUN9hEajwWOPPYZvvvkGcrkcRqMR+/btwz0j78HhksN4ZtIzOFt5FhfrL/b52LeC\n/6bRmAigDEAVAAOA3wHY/3Jtf2L/axAIBBCLx8Jjzg3MKHdF2sCBEKSlYeaAmWjwPoumJiAkhFWH\n37xZA3//xWhsPATJeJY2qcnRwE0oxKrAQPxkFjH09mZyE//6l+U8Mg8ZNozfgK3p9tbhnXfYYpNP\nISE8PBwvv/wynnrqKaeECiWScRgw4G1cvnwvjEbHqyJH8Fvgh4gvInDxzotor+CXKVCrsyGVTrId\ny1RDOtneMORrNIjw8oKUq6tYUhIE06Zh89Ch2BkRgUWFhd1V92ChKUdeBsDCApGRk6DR5MFk4paT\nlk2ToWR/CWQyGSIiIuy2T5fJkKZS2VSva7VXYDAobDPEnAhRmTpN8PjFAxKJBIUNhfYTxo9nRO6u\nXSxUNHEikJiIBQuA48fZFCLC1zU1eDzEceYV0IcQVWsr8P337E1qBal0EozGNmi1hVCpUiCXcyck\ncKHlbAvks2xfvIFrAqH4QYG3Y7lXxHqTCSkqFWY7MBoAIJNNg0plm6O+yM8P49LScMVBhz75TDlU\n51TYv58lWa1fbz/naOlRLIywD29JXFwQLZEg1XoB8fLLbIVnNiQ9YDSydcDy5VaDCxYwo9FHkdFN\nmzZh9uzZliyp5ORkBAcH49Gpj+Jw6WF4u3rjlWmv8IoZ/qfx3zQaoQCshfdvdo1ZgwDEACgAcAzM\nI/lfg1g8FsKxFRhaTMhycQFaW7HQawySrydh9mwgMVGE+fPn4+jRo90hKoEAgasCWXtJAGuCgvDv\nurrul/pTTwG7d9vErDdO3Ii9l/aiQdtgc/7+/YFHH2XGgw/PPvssampq8McfzoWd+vV7Ep6eQ1Be\n/nzfHkYPBK4MRPgb4SiYV2Bx861hMCjR0XETXl62H5EqQ8UZmkpVqTCNr/dDcjLjhAAs9fdH6tix\n2HHzJtaVlKDDZEJCZQLmDp7r8HqPHgXuuEMOD49waLXcKzDpVCkaEhqwZMkSzu3B7u7wd3VFkVWY\nR6HYi4CAeyEQWNUxzJ7da9ih5VQLPAZ4YN6weThdfpp/4pw5LGvsxReBdetwZ9rrOP4H8/BSVCoI\nBQKnemYsW7YMx44d650D+/FHlqE2aJDNsEAg6ApR7YNanQ6pNIbnAPYw8xnWODX4FAZUD8BkwWTO\nfTLVakR4esLPgQcFADLZdDtPw6WxEYPr6vCpA2MqnyFHyzklXnyRab/1XKsQEY6VHbMLTZkRJ5cj\n0TqbbsYMllbNUxOTksIiZQMHWg1GRACurqx9rpM4deoUjh8/jk+tCkl+//13rFq1CiMCRwAAihqK\nsGH8BuTX5iPzZqbTx75V/DeNhjPmNh/AbQBGA/gSAG/V0ubNmy3/nCmG44JEMhYUVgrxRT0KWlth\nmDYNcbWeSKpKwty5hNOnu0NUPj5zodHkQ69vRMDdAWj4g4WoxkkkcBMKkW4OqQwezDowWb3kg8RB\nuHf4vdiZvdPuGl59lbm1pTy8lqurK7766is899xzUPERIFYQCAQYNuxbNDefssSobxWhG0IR8kgI\nLt5xEYYW29W7RpMLiSSaxfmtwOdppKpUmMoRmgLAjIZVqu0wLy9kRUej2WBAbG4G8mvPY1p/fv2j\n69eZtzZxIku9Val4yPApMnjd9MLiBYt5jzVDJkNyF3lJRLahKTPi4tg1d9rXAphR9+86BD0UhLmD\n5trpUNlBKARWrgSKixH7wG24cIGgvHc9vi4txeP9+vHG/K3Rr18/REZG4uzZs/yTTCYWm3/uOc7N\nAQEr0dDwOzSa83ZcFe8hO01Qpaogj+02Gp2mTryX9R68lnuh7kdujbOElhbM6cXLAACJZDza2krR\n2WkVskxMhGDGDPyhVELF8xl4j/CG5oYBcWM6OFuGX1JcglAgxO3+XBFyIM7HB4nWJLZAwLyNTz7h\n9BzMemc2EAj6FKJSqVRYu3YtvvvuO8i6FgoGgwF//vkn7r33XggEAiwZugSHSw7Dw8UDb854E28k\nOqZ9k5KSbN6V/69hMgDrp/cquMlwa1QC4FI/+x+lspmh1ZZQetoAOud9jkalZ1He55+T6ZlnKGRb\nCKUUlZOfH1FDQyNJJBLS6XRUWLiCamp2k8lkosyITFLlsLTCj65do3VW8g508CBRTIzNuUoaS8j/\nE387LRgi1jn27rsdX+vatWtp48aNTt+bWp1Pqan+pNXap772BSaTia4+d5XyYvKos7VbaqKq6n0q\nK3vRZm6ntpPOeZ2jzvZOu2P4p6ZyN9NpbmYaGnq93SajyUT3p+wh98/HUL6DVNVdu1iqIxFRdfXX\ndPnyQ5zzKisraY9oD7Wk86dP/lBbS/d2tQxlMjL9uaVaoqKYJDcH9C16plXWpKfmtmYSfyi2kXLv\nDQvmGuj7VftJFh9PTS++yCQtnMDWrVtpnVUTIDscOUI0bpxNWrg1TCYTpaX1o8zMCKevVZVj3wN+\nz/k9NPOHmaTKVFFmRCbn84vNz6fjjY1241zIz4+lpiarXORHHyX64gu621rOpweqq4k+cb1Il/7J\nnYL9cerH9GT8k7znNGukNVt/Lzs7iQYNshU2IyZZExrK0wf80CHnhMWI6NFHH6UNGzbYjB07doym\nTJli+ftM+Rma8M0EImI6dwN3DKSUaym9HttkMlF5+Wv/z6Xc5gKIADAAgBuAlQB61toHoZvTmNj1\n//98r9IueHoOQaexEW5DdZjT4Ims0aMhyMjAzAEzUapPgp8fUF3th8jISKSnp3eFqP6CQCBAwN0B\nUOxnIarVgYHYr1Cg3RzvXLSIkeFFRZZzDfUbimn9p2HPhT121/HMMyyhJjeX/1o/+ugj7Nu3D7mO\nJllBIhmL8PC3UVx8v12Dor5AIBBg8LbB8IzwxKW7L8GkZ6XsanW2HQmuydPAe4Q3RB62khSl7e3w\nEgoR5mFLjgNgmiqTJzM3vgeEAgFC2y9jyeC5mHfxIvY3NNjvD1thXIlkAjQa7md05MgR6Afr0ZrL\nT/DP6CLDiQgKxR8ICLiHe6U/YwZwzr7NLAAo9ivgM8cHrr6u8PH0QVRAFNJvpPOesyfuXOKCr4zz\nsaRfP/jqdCwl5/33gV6yo5YtW4YjR47AxCU3ALCmYc89xyu9KhAI4OV1O4RCb87tXFCnqSGb1h0+\n6zR14v3k9/F27NuQTJSATARNrm0as85oRK5G43SrWplsGpTKrhAVEXD6NDB3LtaFhOCb2lpOvu+t\ntwDJVBlci7m986NXj2LhUP4Wqe5CIaZIpbaJESIR+7H2KPbLy2NdgSMjOQ40axaQlWVRi+DD8ePH\nkZiYaJctaQ5NmTEjfAZKm0pR31oPV5ErXpv+Gt5Lfq/n4eyg01Wirs7+3eMM/ptGoxPA0wBOArgM\nYC+AYgCPd/0DgLsBFAK4AGAHgFX2h/nPQSAQwtt7NDznVmPCVRdk+/kBly5hTnAMkqqSMGsWcPYs\ncMcdd+DUqVPw81sApfIsjEYdMxp/KEBECPPwwDiJBIebuiqqXVyYbk2P3O5NMZuwPWM7jCZbMs3L\ni7Udf+st/mv18/PDxx9/jA0bNsDIQ8b1RGjoU3B1DUJlpYMDOwGBUIBh3w2DwE2AK2uuwNRpglqd\nZRfCUGdwh6bSeuMzeKrAASCxMhHPjFyCk6NG4fnycmyurLQhqg0GICmpW33E23sEdLoqdHba/0gP\nHz6M0DmhUGep7baZMcDDAyIA5e3tUCgOIiCgZ8yhC7Gx7No5UP9zPYIeDLL8PXfQXMe8Rg/Mn0/I\nT3TF2vCBLIU7M5MtQCIigO++4yVjhwwZAplMhvz8fPuNBQXAlSus34MDCAQi6PU3ne4QqUpT2cjF\n/HzxZ0vGlEAgQNDqINT/bCsrkqlWI8rbGxKupAgOyOXTu8nw0lJmOIYNwxwfHyg7O5HXo7bm4kXW\naHHxG3LOmiOlTonzted5s7rMmCWX42xPlYBHHmFG60Y3PRsfD/DQZMyaTJjAvqQ80Gg02LBhA779\n9ltIJN36ZNb6aGa4ilwRNzAOp8qZdNBDox/ClcYrvXIbSmUyZDLnkxus8d+u0zgOYBiAIQDMxQtf\nd/0DgH8CGAFgDBgh/r/O8kgk0RCOqUD/y0Zkt7UBI0diTqMUKddTLEZj3rx5OHnyJFxd/SAWj4ZS\nmQTxWDEAlm4IdBPiFjz2GNOtsdKQirktBiGSEBwots9yWbuWZXFmcIfjAQAPPfQQxGIxdvFVBfYA\nq9/Yg/r6n9DScmv54mYIXYQYvnc4Omo7UPI6W/W5u/e3mcNXn5GqUvGvKpOT7XU/utDS3oLSplJM\nDJ2IaIkE2dHRONXSgnsvXbKkQ2ZnM043sKtNhVDoCm/vkWhttX1xqlQqZGVlYeKaidBk8QsTCgQC\nzJDLcVpRis7OJkil3EQuZsxg7GePVX1HdQe0F7XwW9Cd3zl3sBO8hhVq/FUQeZkgrup6ZkOGAL//\nzkjYH39kvTxOceuNLV68GEeOHLHfsGMHS9Jwc5xG29Z2GUKhmNdbswYR05syGw2jyYgPUj6wyZgK\nWh2Ehr0NMHV2P6dzKhVm8vVT4YBUOgUaTS7zmLu8DAgEEAoEWBsSgm97pB++9BLw+utAyAwxdFU6\nGJpt+bhT5acwPXw6vFy9HJ7XjtdgF8MyJP/5T8tQD81Ee9xxB8uU48Ebb7yBWbNmYU4P3bWkpCQM\nGzYMoaG2+ULzh8zHiXIW6XcTueGVqa/06m2wjLjpDufw4b9tNP5/B7F4LEyhpXAr1OGaTgd1bCxu\nK7oBTYcGQ8ffRHIyMH78ZFRUVKC+vh5+fovQ1BRvF6JaHhCAdLUadWbxoPBwFnbZt8/mfJtiNmFr\n+la7lZy7O/DGG469DXPtxrvvvguFwjmBQTe3AERG7kFx8Rro9Y3OPxgOiDxEGPHXCChrMuCqGGET\ntiGivnsara3MUvK0N0uqSkLMbTFwE7EXXbC7O86OGQOxSIRp58/juk6HU6fYO8QaEsl4u5feiRMn\nMH36dPiP84e+Xg9DE3daLsBSb88qSuHvv8xOvdeCkBCmM2UVggSAhj8a4L/MH0L37v0mh01GaVMp\nGtuce/576uowaa4Bx4/3CCNNnMiM7ObNrPH8ggV29SJmzTQb1Nczg/P443AEne4GTCYdgoJWQ6HY\n53AuAOiqdAABHgNZ2HH/5f0I9A5EbHj3IsBrqBc8+ntAmdD98k3iKPJ0BBcXKTw9B6O19WK30ejC\nI8HB2KdQoLWLED91CigvZ/2xhK5CSKdIbTTHAODY1WO4cwh/D3ozxonFuKbToaFnRtrGjSxtWatF\ndTWLRE+Z4uBADrLtsrKysG/fPptsKTMOHDiAFXbsOjMaJ8tOWiIWj459FAV1Bcir4e8Zr1L9v+tp\n/P8OYvFYdLgVoe1SG6LdvZE3dSoE6emY1n8aStvTEBoKFBW5YtasWThz5ozFaBCRTYjKWyTCUj8/\n/GYdd3/8cbsQ1ZJhS6DqUCH5mn1o4+GH2ReeJ+oBAIiKisLq1avx+uuvO32Pvr7zEBi4CiUla50O\nO/DBVe4Kvxeb0XF2gEUqHgA6rjNj6RFuy1s06PWo1+vt1FkBMLcqOhrg4jrAQlNxA+NsxtyFQuyJ\njMSDQUGYnJ+PAyc6MW+e7X5S6QRoNDk2Y4cPH8aSJUsgEAkgGS+BOps/RDVFKkVOG+Dvv5x3DgBO\nXqPh9wYErrLtzucmcsOM8BlIrExEb2jt7MRfjY14crmHpV7DBgIBS9O5fJmtYGfNYt+zrlqhqVOn\norKyEtXWarDffcc0NHpWt/WAWp0BqTQGAQF3QaE42Ot3RZWmgnSqFAKBAESELalb8Oq0V+04oKDV\nQaj/hV2fzmhEjlrNH67kgVQ6GWplGnveVnIz/dzdMUMmw+8NDTAamTDtRx91O1TyGXIok7sNlolM\nOF52nDfV1houQiFmyOVI6ultDBrEqr1/+gnHjrGPwWGkbexYoK7OriDLYDBg3bp1+PTTT+HX47Mx\nGo04dOgQli+3/w72l/VHkDgIebXMSLi7uOPlqS/zehsdHXUwGJrg7R3V6z1z4W+j0QPe3sOh01fC\nfQgQp/BE1uDBQEYGpoXFIPV6ql2IystrOAQCAbTaS5CMl8CkN0FbyAjK1UFBtkbjzjuBmzdZkLUL\nQoEQL0x5gbPYz9WVeRpvvum4Hmjz5s04cuSI06Q4AAwa9AE6Oq6jpqZ3DZ3e0I6LGLTmDpQ9V4aW\nBBbzVWeqIZkksXthpKtUmCKTcesmnTvnmM+oSsTsgfZ6VAKBAM/fdhs+D47EpUIBrg+xjZn39DSM\nRiNOnDiBhV06RdJJUoe8RoSrCvUmCUzeU3nnALDjNdor26Gr0EEeZ7+KnjVgFpKqkhwfD8CfjY2Y\nLpNh2RxXFBQAvMK7bm7As88ynsLbm1WWf/ABXAwGS20RAJYW/PXXLDTVC5jRmAKxeAyIOqHVchQl\nWs+3IsFPlJ2AkYycL+OAlQFoPNwIY5sR2RoNhnt7cxd5OoBUOhnqqmPAgAHdscgurO/XD9/W1uKn\nn1hvEuvFuWyGzEbxtrC+EDJ3GQb6DIQzsKvXMOPZZ4HPP0f8EXIcmgIYgT5zpo0uHQBs3boVoaGh\nuO++++x2yczMREBAAIYMGcJ5yPmD5+NEWXcy6trotciuzkZBXYHdXJUqBTLZNH6vuRf8bTR6QCh0\ng5dXJDziajC2XIRsIsDHB3P1tyH1Riri4mzJcAD2IaquQr9Zcjmu63S4auYxeAjxB0c9iOzqbE7R\nsQceYIuSRAeLUplMhg8//BAbN27kz5Sxu093DB/+G6qq3rQRpusriAitrfnwGz4FUfuicPm+y2gt\naIUmVwPpRPvQVKZajclO1mdYo661DrWaWowJHsN7LS4FvoiZSninpgKbKystK2Mvr0jo9XUwGNiP\nPTs7G6GhoZbeGZJJEoe8hrLpMEa6tiC7tZeq+hkz2D10nbdhbwMC7g6A0MX+ZzZr4CycrXJQQ9GF\nH+rq8HBwMDw8gJgY9t1zCF9fYPt2lqFz/jwwbBgWy+U4crgrMTE+nlWdjeF/jmaoVOmQyaaw73XA\nCjQ2HnQ834oE/yjtI7wy9RUIOV5M7sHukE6WovFwY59DU2ZIpZOh1ubaeBlmzPf1RXWHHi9/04pt\n22yTwyQTJNBe1lr6a5yuOI25gxwXilpjllyOs1yigzNmoN1NhrNnjJjPr6PZjbg4mxBVaWkptm/f\njl27dnFm5x04cIDTyzBjQcQCHC/rdkU9XT3xYsyLeD/FXnmJhaZujc8A/jYanBCLx0I0tgJhJSZk\nq9VATAyiylQoay7D2MkqpKUBt902CGKxGBcvXoSv70I0NbG4sXWhn4tQiHsCA/G7tbexdi3w2282\n6ZKerp5YP249vsz6suelwMUFePvt3r2NNWvWgIjwUy96ONbw8hqGQYM+wuXL992yzIhez+Q93N1D\nIY+VI2JnBC4uvAhVqsoisWKNLI0GkyQcHet0OiA/n70ZOZBYmYjYAbEQCe07yplx6hSwfL4LMqOj\ncby5GQ8WF6PDZIJAIIJYPBYaDXPfT5w4gflWv2zpJCnU2Wre8Etj40HEyOTIUPN7IwAYb+XpyRov\ngTs0ZcbooNGoa61DXSt3sRsAVLa3o0irxaKuUMXcuU4J6jIMGQLs3w/8+ivmZ2Xh3PHjaDt5kkna\nPPlkr7sbje3QaossIoX+/suhUPAbDYPSAF2lDuIxYqTfSMcN1Q2sHLGSd745i+qcUtknEtwML69h\n6IQa+llj7baJBAIMrQiG9N5aO25B5CGCeIwYmhy2SDhdcRpzBvE3+uqJkWIx6rtCrDYQCJA0532M\n8SgGRzsQe5h5DSIQER5//HG8/vrrGDBggN1UIsLBgwc5+QwzpvefjksNl9DU1t0D5/FxjyPlWgou\nNdjyXEpl32RheuJvo8EBsXgsTP1LIShsRwcRqqdOhUtOHsb3G4+StgwMGsRqKMzehlw+E1rtRRgM\nTZBOksKkNaGtmHkX9wcG4teGhu4XUlgYi3/uta3OfnLCk/il8BcodfarmJUrmfqto0JSoVCIL7/8\nEq+++qpTleJmBAc/Ci+voaioeMXpfayh0eRDLB5rWR0F3huIsOfDoM5Ww2OQLTdhJEKuRoOJXJ5G\ndjYLqYjFnOc5W3kWcQPiOLeZYeZEzQS5zmTCnIICNOr1NiGq48eP23Q7cw9xh8hbhPYye10tg6EF\nanUWZgaORoYzz7WL19AWa2FQGGxqFqwhEoowI3wGzlVx13YAwL/r63FfYKCli93cuewe+4Rp0+CT\nk4PoYcOQeP/9zBOKju51t9bWfHh5RUIkYhlFMlkM9PpatLdXcM5XZ6ghGS+B0FWILalbsClmE1yE\n/CEn/2X+UGQokX0LfAYACAydkBQT1CPtz9HSAlz4KBjN0Q3Qc3jesikyqNJV0HXqkH4jHbMGzrKb\nwwdRl4xLKsd3IV47E4v0B4GrV3s/UGQkyw+vqMDu3bvR2tqKZ3rof5lRUFAAgUCAUaNG8R7O3cUd\nsQNicaaie1VhVtX+OK27BbTBoIROVw6xuPfvAB/+NhocEIvHwOB9BdoCLSZ6i5EzejSQnY1pt03j\n5DVEIg/I5XFobj4BgUAAv6V+aDzEMmMmS6XQmUzdHekAFqLavdvmnP0k/TB/yHzsPm87DrAQ6ObN\njN9w5G1MmDABd955J959912n71UgEGDo0K+hUOy36YrmLFpbz0Misf0C+i/0h0giQskjJTDqumsI\nLmm16Ofmxq3Qmp7OjCkPkq8nI3YAvyBdRQVLvho5kv3tJRJhX1QUpslkmJyfj1b3UdBocqBQKFBS\nUoKpU235CekkKdSZ9p5EU1M85PJZmCoPQI5GA2NviQNdvEbD3gYE3hsIgZBf8mNm+EzeEJWJCD92\nhabMGDkSUKttRJOdg1CIRY8+iviQEGDSJPacX30VcNADXa3Osam7EQhE8PdfyhuiMpPghfWFyK3J\nxSNjH+GcZ4aLxAV1D0gR3uYKWR/5DABATg6kjQFQG4vsNm3bBiyf5IkoiReONdl3n5TGSKFOVyP9\nRjpGBI6wU7XtDdNlMqT0CFERAfHHXbBolRj46qveDyIQAHFx0Bw6hFdffRXffvstRBx92YHu0FRv\n8jHzB8+3CVEBwBMTnsDRq0dxTXkNAKBWp3UpFjvXgZELfxsNDojFI9HWcQku/iLENnshy98fKCtD\nrN84G6Mxa9YsZGVloa2tzcJrAGwV1fgXMxoCgQD3BQbaE+JlZXYCU89OfhZfZn9pV+wb9di6AAAg\nAElEQVQHMIllc1MXR/jwww/x008/obi42On7dXX1xbBh3+HKlUdgMPStSQzzNGyNhiZXA9+5vnAL\ndUPxA8UgE3vRZqnVmMTHZ6Sn84am6lrroNAqLAJtXLBK17dAKBBgy6BBeDU8HGuueaBRlY1Tp05h\n1qxZcOtRnyCZJOEkwxsbD8Lffzn83dwQ7OaGS731qIiNBZ07h4bf6nlDU2bMGshPhqeoVBCLRBhr\n5XkJhSyq4XSIygqLZ89G/OXLoB9/ZIkY1dVstfvjj5wN6pmWmG3/DEchKjMJ/lHaR/jHpH/Aw4U7\nA84aV+9wx4jCW8zeS0qCVDYFarVt6VZdHXtnv/028HBwMH6sr7fbVTqFLRBOXz2NOQOdD02ZMZ2j\nz8qlS+zzuf215eyZWtVj8SIuDpd37sQDDzyAMQ44pt5CU2bMH8LIcOswq9xDjrVj1+LTDJbCq1Qm\n33J9hhl/Gw0OuLjI4OLiB69YFUaXC5Gj1QKjRmFKgxtya3IxeaoemZmAu7sU0dHROHfuHPz87kRz\n80mYTAbIY+Vov9qOjmqWdmo2GpbKZVdX1mt4j20Z/8TQiQgWB+NwSU81FfaFfPNN1jjG0WI3MDAQ\nb7zxBp555pk+pdP6+c2Hn99ClJVxu8h8aG09D7HYNq6sydVAMkGC23+8HYZ6AypeZSENXqNB5NBo\npFxLwdT+UzlJVTNOnYJdqq0Zj4WEYPvweWg1KLHn+K82oSkzpJOkdmS40diGlpYE+PszQcMpUmnv\nvMbgwSCdAa5ttZBM5OBurDAqaBQatA2o0dj3eN5TW4uHg4PtVpe3FKICMDQvDx6enihQKlmzon//\nm6nq7drF6od6VJFqNDmQSMbbjPn4xKGt7RL0etsXsclggiZXg5bbW3Ci7ASeGP+EU9d0IbQTw5IN\n0NffgqxNUhKkw++CRpMDou5F1ocfsp9W//7APQEBONvSAkUP/sE92B0uchcUZBT0qpbMhfESCUra\n2qC2EkeMj2dNAwWDBrIijd9/7/U4uTIZBl+7hs0OirHKysqgUCgweTJPUakVBvsOhrebNy4pbDmM\nZyc/i58v/ozGtkao1em2sv63gL+NBg/E4lFwnXgd/UqMyG9tBU2cCO/zRYjwi0BFez6GDWNh+Dlz\n5iAhIQHu7v3g4TEIKlUahK5C+C30Q+Nh5m2MFIshc3FBuvXq5JFH2A+3hyrns5OexedZn3Ne04oV\nLATT20vjySefRF1dHQ71sZH94MFboVZnQKH406n5en0jOjuV8PS0ldXW5GpYfNtdiKiDUWg80Iia\nb2v4SfCrV1maaL9+nOdJvpaMGf35iTuTiXl+cxwsGmf7+sJHEo3W2mQUDh9uIz0CAJJxEmgvaW3C\naS0tCRCLx8LVlRHRU2Sy3nkNgQBtfmMQGn2t13CCUCBE7IBYO17DXJuxOijIbp+5cxl/6mSSHAMR\nBP/6FxbMnm3bmGnSJGasN25kciIPPADcvNklc19tJ3MvFLrD13c+Ghttv1fai1q4h7tjx6UdWB+9\nHjKP3jkKIkJ6qxrTQ3yh+NO5wlQL9HogMxOu0xfCzS0YWi3zqquqWDPE115j0yQuLlji749fOTTK\nPCZ6wKPQA5PDen8Z94S7UIhxEonN79la7wxPPskqxB0s2jo7O/HoO+/APSAAUisJkp6Ij4/HokWL\nIBQ696qeM3CODa8BACGSENw9/G7szNoBjea8nUZcX/G30eCBt/coYHAFTAVMXK8yJgbIysK026Yh\n5VoKZs401xXNRkJX6hzzNhhbbR2iApi3YfPlHT6cpT72kH9YcfsKlLeU40LdBbtrEgqZHMK77zr2\nNlxcXLB9+3Zs2rQJHR32vS/4IBJ5IzLyJ5SWPomODp5OUFYwexnW+d5kJLReaIU4moVV3PzdMPLY\nSBR9WIGK1jaM4iK6MzJ4vQyA8RkzwvmNRmEhEBDQ1VbTAag9DJNGeiLf2xuruzKrzBB5ieA1zMsi\nAwMwPsPsZQDOeRpEhKbGYfDxcC6NeWb4TLsQ1X6FAjPkcgRxSHyEhbF7vWD/9eBHVhagVmP+unU4\n3rNCUChkS/MrV1jNw+jRaP3qWYi9RtnJ3AOAv/8KKBS2sjeaXA3cx7rjl8JfsHHSRqcuqay9He5C\nIcYsDEHDPm7hSV7k5jLdLbkcUukkS4jqnXdY+Yl12caa4GD8UGefoXZjyA3MbJppURfoK6xbAWs0\nTKSwqwUMq+5raWGrSh58+eWXCAoKgnjxYoe9WMxGw1nMHjTbzmgAwIsxL+L45Z1w9xgAFxfHHnBv\n+Nto8EAsHolO31Jo8jUYJxYjb/hwZjT6T0PqjVSL1NCECRNQUVGBpqYm+PrOtxgNnzt8oM5Qw6Bk\n8hSrupRvDdZLxEcftSPEXUWueGrCU7zexsqVgELhUO8MADB37lwMGzbM0lPYWchkkxESsg4lJet6\nDW8xEtw2NNV2pQ1uIW5wlXcTbV4RXtD9EI7BJYChmKPzn4PQVEt7CypaKhAdwp/t0UtNoAVFRR2Y\nOEGOhNGjYTCZcEdBAZRWPbkl4yVozWNGg4jQ1BQPP79uoxHl7Y06vR6NDhobtV5ohcZ9JFxLc3jn\nWIOrXuPH+no8xOFlmDFnTh9DVLt2ARs2YGZcHPLy8qDmMnxiMVPOzc2FWpMH6Z9FrAdMj++Ar+8C\nqNXpNtyXJleDvIA8LB22FP0k3N5iT6R19VPxucMH2gItZ2MvXiQlWd7QUulkqNUZuHyZ8X0vvGA7\ndZZcjiaDARd6kP6p/qkYWjXU+XP2wHSZzGI0kpKYootF5EAoBJ54wqZjpzWqq6vxwQcfYOfOnRDE\nxfH+mM36aD01qBwhbmAcUq6nwGC0lcUZ6jcUC/sPxI0OHk6xD/jbaPDA23sU2o1FELoJEaPxQr6X\nF9DRgekug5B6PRVTpxIyMgCBwBXTpk3D2bNnIZFMREfHdXR01MBF7AJ5rBzNx5mS+yBPTwz29ESC\ndTXpypWM1eyhG7Uueh3+uvIX6lvtSTyRiLnf7/Wufoxt27bho48+clqXyowBA96CXl+D2trvHM7j\nIsHVOWrO+oxLA0yYEipH4aJC+xi2A6ORdiMNk8Mmw1XEn+3hQOPQBidOlKFfPy08RSLsjYrCGLHY\nolkFMKNhlu1ubb0AkcgbXl7dLxaRQICJUikyHXgbjQca4blyKgRXrzrMTjJjROAINLc3o1rNZD5u\n6nQoaG211GZwoU/1Gkol6zu6Zg3+P/beOzzK8+r2/j1TNU19VCgC0SRACEkgOojqbhOXgElck7hi\nx0nsuOUkduLXjuN2XseOY8dxgt/jxC2uuGEMpgoQEk30LiSaUJ8madr5454+zzMa4Zz3u853WNfF\nlXg0I81IM8++91prr20ymZg6dSqrE02KFhZiu2oUlot/KopIVZUYEgxAozGTljYrdDgC6Krt4u++\nv/OLqclvh9zY1cX0tDTUKWqyrszqH0UVUTQslknYbLX85jciMiTWvauSJG6OEcT9fj//8v0LQ4sh\nbplYspiamso2m41ur5cVK2T0tB/9CD79FFri88Xuv/9+7rzzToqKihSDLkFs7ZsxYwZmBRu6HLKN\n2QzPGE7NyfguZ+6AXD48up9e7/mvRoALRUMRBsNIenpOYpqsYvxRFXV2O0yaxIC9jZh1Zlr8Bxky\nRHyeghSVSqUhI2M+bW2CcuqTokpLExnK//hH1M/OMmaxaMwiXquTj/j4wQ8Ef7thg+yXQyguLmbJ\nkiX93tClUukYPfotjh17FJfriOL95Oy2QT0jFlu6upg7OZ/cm3Opv6oerzOgHXR0wLFjoOBBX9ew\njpkFym4Pvz+5otHW1saaNUdQqzvxeLpQSxL/OXIkP87PZ/r27eyw2TBPMGOrExf61tblZGXF0wJ9\nUVTnPjhH9uKBIl9oy5bET4qwrhGkqN5pbubq7GxSFOyXIK6XmzdHbRBWxj/+IegSqxWASy65hK/6\n2Bxns23FMulmMWx5ww2CrL/jjtAFMDv7SlpbRXKu1+XFtt+GeZyZ0lzlOYJYbIxIOrYusnLu3SSL\nhtst6MyZ4j1hNo/D4TjMtm1O7rlH/iE35+byj7NnQzMbR9uP4vK7SKtMk7VZJwOLRkOx0chWm42v\nvxa/4ihkZcHChXFml5UrV7JlyxYeDQovAweKtbExQZMgqKkrr1TeKqmEeYXyFJXGfQivtoh/1v+z\n398zEheKhgJUKg1G42j0008zcL+POpsN/+TJsGULUwdNZVPTptAhYe7cuaHTWyRFlXVlFm0r2vD1\niDfr961Wlre20h25/+DWWwVFFUMD/HTyT3m19lXZU4FWm3y38dhjj/H++++ztx97iUFkcBUUPMq+\nfTdHuVOC8Hi66OlpwmAoirpdrmj4/f5QfMjQx4ZiHGVk340BK+6WLTBxouzSJQiI4An0jGDU0uDB\niV/PypUrmTGjCpOpBLs9nMfz88GDeX74cC7atYstA3txHXbhdXoD1FR80ZicmkqNQgfh2OfA0+UR\n8SnTpokOKglEzmv8o7lZVgCPRGoqjB/f96EBvx9efx1uuy10U7BoKFGPvb1n8XptGAwjRFt7++3i\nl2wwCB3uz38mK/1S2tq+wufzYN9h56T1JPdV3ZfUawVoc7tp6umhNMDnZC7IxLHHEXIbJkRQzwis\nhlWp9Jw+PYbf/GYHBoP8Q0YYjRQZjXzZJrr+b49/y9zCuWJeY9P5FQ0Q1ttPjnfS1aVw5rn7bkEN\nBj7vPT09LF26lJdeegmjMSKGvaoqLujS6/XyxRdfhPLR+oP5w+az6li0TtLb24zH08Ztk3/LMxuf\nwefvj5MiGheKRgKYzaVIY47BLhcpKhUNkydDTY0oGo2bmDlTnHJLS0tpbW2lqamJzMyLaW9fid/v\nRZejwzzOTPtqQUnl6/WMN5n4OpKiqqoSlqiYRTljc8ZSlF3ER/vkffE33SQ+ywm0NkAsa3r00Ue5\nP5bsTQKDBt2HSqWlsfG5uK/Z7TsxmcZFiaU+twhrDO4WCeJEQIwv0OvFzvK/FuE+5+bow0cTiuD2\nXjv1zfVMHjhZ8TmuXZssNSWiQyyWcuz27VFfW5STw7/GjuWGowfoHqGlfesJXK5Dsvk8lRYLW7u6\n4txXILoM6zVWMdA3fTps3Nj3E0NsX1t/Yj17HQ6ae3uTymKaPz8Jiqq2VkwDzg1P0o8ePRqfz8f+\n/ftlHyLmMyZGO7/S08X+jW++gXfeQT99ISleK11dG6ldUUtDQQMXD489aiujurOTSRYLmoAjSKVX\nkb0wO7RWICHWrIn6g2/aBPv2TWT27MQa0i0RgvjahrVUDakKTYafL2ampfFlUycLFggZIw6VlSIL\nLNDZPffcc4wePTpe2A5mlkVgy5Yt5OfnM2TIkH4/rxkFM9h2ehv23rCpo6trMxbLZOYNW4BRa2T5\nAZkdK0niQtFIAJOpFF/eISGGWyzUjRoFdXVMHTCJTU2iaIjTnoo5c+awevVq9PqB6PUD6eoSb+JY\niur7OTm8H6kxqFThbiMGSyuX8qetf4q7HUSo6UMPJddt3H333Rw9erRPWiIWkqSiuHgZjY3P4XBE\nt89y1JRjj4OUISloLNGum+B8RvBCpNKrKPmohJaPW+h+71vForG5aTPleeUYtApHSJITwf1+PytW\nrOCSSy7BbI4vGiDcMGvKyqge5mH1V+vIyLhIdmo2R6cjQ6vlkAw31PJBC9ZrBQ3E1KmCQ0piq2JJ\nTgnNjmZeO76HJTk58gnAMUiqaLz+usg6i7iiSZKUkKLq6toaN9QXQmmpuGg/+CBZH5yi5a272buy\nnqI5RX3aiyNRHdAzImFdZE3ORRVzSnj8cRg7thKXK3HC83VWK6vb22lzu0Pda+qUVGw1tqiFUP3B\njLQ0Dmk7WXCxgmFEkkS38dprnDhxghdeeIEXX5QxuAQ7jYiDyPlSUyDiQyYOmBi1bqGra1MofPKX\n037Jc5viD4LJ4kLRSACzuZRu1V58Th9Teo3U+f2Qn095m54j7UewZHeRlgb79kVbb6MoqkCkSHAq\n+trsbD6LpahuvllkUXVHhwYuLFrI0faj1J+Vj6T+0Y+EpiK3zTMSOp2O5557jvvvvx9PzFxIX0hJ\nGUJh4X+wf/8t+HzhxwYzpyKRSM+IHerTZmkZ9+kYNPvr6OiVW6YshvoSUVPJ6hn79+9Hp9MxfPjw\nQHBhfNEAGG0ysXjBELQ72vm0dwIehWGISRaLCLKMgOuoi55TPeGsKasV8vJkuepYqFVqpg2axtuH\nVvVJTYWewyQRKKAYlW63C/fTrfFxHpdeeqli0RBDfQpFA8SFcMkSsh/9jNOFTaQfTGOeo1loDUli\no8zmxox5GTj3O+luTBCc6fOJQhw4ZFRXi9/BRRdNDB3SlJCm0XBRZiavHd1Oj6eHUVmj0GZp0eXr\nQjlx/UWGpMPbpmXIrASPX7wYNmzgqaVLuffee2UDCRk6VOyQiUiIWL58eb+strGYP2w+q46GKaqu\nrs2hrZPXjrmWpq6mPlfCKuFC0UgAk6kUh2MXxlIj5cfVYvfw5Mloa7dRnldOzcmaUGcZLBp+vz+q\naBhHGNFZdSHBLS9AUa2I/LQXFMCECfBRNBWlVWu5fcLtit1GSopwjPxHfPpxHK644gry8/P5y1/+\n0u/fQ37+7Wg06TQ2hnd+OBw7MZujow+UikaNzcYkmaE+Y+8xpEH57LnrLM5D8R+8dScSi+BHjohr\n2LBhincBYNWqVcybNw9JkjCZxuFyHcTnk+fPB0wykXEgnRom8b3du0NrZCMxSUbXOPfhObIXZiOp\nI07c/aCoCnIr8XTspCxJp4xOJ66digu63nlHVFOZ4ZW5c+dSXV2NMybqwu/3y06Cy8GcOxMbGgbY\nBpFe/5mIWk/kygqg1yf0wdhDhEqnEiGG7yegqPbsEUMYgUGMxx4Tc0tpaWPo6WnC40msT9yQm8uy\nAyuYNWRWqDPqa5dKItTUQFpTGgc1CSguk4lTM2cycv16HnzwQeX7RSzwOn78OGfPnmWSwgbLZDB/\n2Hy+OSZaUZ/PE6AdBc2rUWn4+ZSf81z1+XUbF4pGAuh0VlSqFAxT7Aw+7I8XwxvDYviIESOQJIlD\nhw6RljYdp3MfbrcIS8taGJ4OB8Ghvx87pXrzzWJCPAa3VdzGu3vepbNb/o15223ixNWXzi1JEi+8\n8AK//e1vaVc8nio/tqjorzQ1vYDdvhufz43TeSBu85d9W3ioLwiv388Ou50JcpPgmzahnjeDwicK\nqb+yPjTTAtDj6WHrya1MG5xg6C+wfqMvZiRYNADU6hQMhuFxdFsQ7sG1cGoAb4+YTo5Ox+wdO+LW\ne04K6BqRiKKmgpg2LemicdZQhMG2p180TzADTRYxAngk0tLSQvE3kejpaQRU6PWD+vzZzY5mdm8d\nSkqxC9XXX8CTT4ogzsWLIcGE83a7neEGg2xIofX71sS6RoQ1e8MGEd92883CtGI2j8dmS9xyX5qZ\nScPZLZQMCOelWyZZsNX0bY2Ww4oVUGlMpTqBm87j8fDzffu4U6vFqNcrf7OIBV6fffYZl112mWKA\nYTKYOGAiDR0NNDuacTh2o9cPRqsNa2U/Kv8Rh9ri9/ckgwtFow+YTKVoyhpQ7+1Gq1JxorJSFI3B\nU0O6hvhbSxHWWz3p6VW0tYkJrKwrsmhdHk7bvEaOovre90TrHbMCMt+Sz8XDL+bNnW/KPj+jUaRA\n/OEPsl+OQmlpKQsXLuQ/kmlNYiBoqic5cOBWHI496PUFodhsAJ/Hh2OPA/P46KJxwOkkV6slQynZ\ndto0Btw+gMyLM9m7eG+IX649VcuorFEJIymSEcG9Xi9r165lboQYrKRrALR1LUdX1EtPvZM3ioq4\nLDOT6du3czRCw6iwWKh3OEIWzu6mbpwHnaTPiRGwp09PykHl9vlY78ujw3aMrp7kT72KRWPXLjh1\nikTbgC655JK46XCbrQ6LZUJShetPW/9E1unLkYr2iar9ve+JTmD0aGE3/v3vQSaNoLqzk2kKUegZ\ncwVF1XNKwUUVUTQefxz+x/8Im+5E9H1iikqnUpFi202LcXTottRJqQlX/SbCihXw/TGJo2Vef/11\nzg4YgHHo0Lj0hygEOw2/v99T4HLQqDRUDa1i9bHVUdRUEEaNlr+Un9+8xoWi0QfM5lL8Qw5j32kX\nk+GDB8ORI0xLL2Vz02YKh/nw+cTchJL1NnVSKu4WN66j4sKTp9dTbrFEU1RGI1x9tVjQFIOllUt5\nZesrijbJpUtFYFpDQ9+v54knnuDNN9/k6FH5vQiJkJ9/GxpNBidO/B6zOdpj6DrgQj9AHyeC19ps\nTJTrMkBcBAJbcoY/PxwkOPILMRdS3Sj2sidCMiL4tm3bGDBgAHkREeNKukZwCjxtYja2WhuSJPHb\nwkJ+MWgQMwOzHAAmtZoRBgO7AnH3LR+1kHVFFipdzMepqEgsQjmdOJLl6/Z2RprSmDhgApsaNyW8\nbyQmTBB/87j5sddfF4JXgpOqnBguZ26QQ7enm9fqXmNsyyW4h2/C7RZWVoxGcTWvqREHoJISYheb\nb0mwuVGlC2S2fRw/EAeI98v06axfL0Z7brop/CWLpTJqpa8cTttO43d38U1veuizZB5vxnXQhdfR\nt2EhEm1tQsv8wVQTp3p7aZXRdNra2nj88cf54x//iHTbbeLvooSRI8HjwbFnDxs3buQipfTNfiCY\nQxVc2xuJjo41oUy1/uJC0egDJlMpbstBXAddTNSbqXO5oKSEvCNnSNWncqjtYKjbmDdvHt9++y0+\nny9UNPx+H5JKIuvyLFo/C3cbi6xW3oulqG66SZaimlEwA51aF+e9DiI9XZhknkuCoszNzeVnP/tZ\neLioHwjSVK2ty9Fq86K+Zt9hx1wWz8fX2Wzy1FRLCzQ3i5MpoNKoGPPOGNpXtnPqtVNUN1UnpKYa\nGsRwW7G8hh5CJDUVhFKn4XAIeihjSkFoyA/groEDeXHECC7atYtvA4W+0mIJ6RrnPjgXT02BcC1N\nndpnt/HPs2f5YW4uMwtmsv7E+sQvKAIajWhmolgmlwv++U9RNBKgrKyMrq6uqMOD3IS/HN7b8x4V\n+RVI9WpSJ2bQ1haTZzVsmJhCf/FF+OlPxZBb4OcohlYGkH1ttvx0+Nmz4j0zejSPPRbdZUBynca6\nhnVUFczE6fOH9tuo9CpMJSZs2/tHUX3zjTiwGFMkJiukBPzmN7/h2muvFcuTliwRbaHSAUKSYNYs\nDv71r1RWVpKqtEKgHwhG1Mh1Gi0ty6MicvqDC0WjD5hM43C46kkZksLEMzohhldWwtatgqIK6Brr\n1sHAgQPJzs5m586dGAzD0GhSsdt3ATIUldXKF21tuCIpqlmzhB1mZ/QyeEmSWFq5lJdrlHOkfv5z\nMfwrE+gpc9+fs379emr6GvKQQUpKASkpw2hr+wKfL3y6su+wx81nQIJOY+tWMdQXcRrWpmsp+bSE\no785ysYjG//tekYQZnMZDseuuKHF1tbPyMy8PCpOJIjrcnJ4d8wYFu/dy7+am4UY3tVFb3Mv9h12\nMi7KkH8CfYjhdo+Hz1tb+b7V2u+iAYKiitKf//UvYa3qw98vSRILFixgZUSIlVzMfSz8fj8v1bzE\nPUX30Hu6l5yJ02hpUfD8X3YZ7N4totcnTaL56adpd7sZFTnYFoPMizKx1drobYmhTjZtgilTWLte\nRUODGFSPhNE4Cre7NaQjymFdwzqqhszih7m5/CPigyIXi98XVq4MR4dMTU2NTrAG6uvree+993gi\n6Im3WESScMyEeBSqqugOWMP/HRhrHYvP00l3zylMpnBiseioPyU7+6rz+r4XikYfMJlG0919BGO5\nluFHoM5uxz9xItTWMnXQVDY3bWbmTCGGQyxFdXE4wPCiDLo2d+HpErbVXJ2OcrOZFYEpVSCcOCqz\n5/uHpT9k/Yn1nOg8Ifs88/KEBilnA49/TSZ+97vf8ctf/rJfOzeC8Hja0ekG0Nj4TOg2uU7DE9hY\nWCFXNLZsEdHcMTCONGL8mxHaIatZuX0OFo1E6O7uZvPmzcyKuaNWm45Wa8XlOhx1e1vbl2RlXYZp\nrInuY9147NH25DkZGXxdWsp9hw9zvLubGpuNlk9byLw4E3WKAhUUnNdQwCetrUxLSyNHp2Pq4KnU\nnaqjx5N8eF+crpFAAI9FZNHo7T2Lz+ciJSVxsak5WUObq40pnVMwl5nJzr2C9vYVUQeIKOj1Yktg\nXR01zc1U1tejSpC2qDaqybwoM+qABYT0jMcfF3tlYiUySVJhsVQkpKiC2x9/mJvLP8+eDW1htEyy\n9FvXWLVKLMQCmJYaLYb7/X7uu+8+HnvsMbIiM8Ruvx3++lflXPtZsxh4+DAXx2WSnB8kSeJ7w8bg\nUg1CksLvT4djF5KkxRih7fQHF4pGH1Cp9KSkFKKffBbtnm7UQGN5ueg0AnEiJSWicz5zRnleQ2PW\nkDo9lbavw0Xi+1Yr78WGCd54o2gZYuYpzDozN4y7gVdrlVdJ/vKX8NprYgi4L9xyyy20trayfHn/\nJkN7e1vweh2MHv2/aGr6T+z2emHV3G6LKxr7nU4G6vXy6zxrasSJWAZ7Bu1hctZk9ly1J8pRFYlk\nRPBNmzYxZswY0mUmrGN1DY+nE7t9G+nps1HpBGURGZMeRJnFwvryct5rbuawy8WxL5rJvjpb+UlM\nnCg6R4WI+iA1BZCqT6Uou4jaU4m5+ajnUyYYjzNnEHtJDhyAJIfC5s+fz+rVq/F6vdhs26N2vSvh\npZqXWFq5FEedA8tEC3p9PgbDCDo7++iQhgxhy733MnnECLjzTli0CJqaZO+afY0MRVVdzQ7TdBob\n47uMICL3wMeixdnCic4TlOWVMcZkIlenY21gZWvqpNR+OaiOHROL+cYEDu9TUlOptdlCcz0ffPAB\nLS0t3HHHHdEPnDBB5M0pRKEf1ukwe72UZmYm/Vz6whRrOkcc0QealpblZGdf1S3MVUIAACAASURB\nVC+nXiQuFI0kYDKVoCpuwLHLISbD8/Lg9GnGpwzhaPtR7O4uZswQ3UZVVRUbN27E4/GQnj4bu70O\nj0e8IWUpqtbWaIqqqEhQCzLjvndX3s0b299QPIkOGyaC0/78575fk1qt5plnnuGhhx7q18Cfw7EL\ns7kUg2EIhYW/Z//+W+hudCCpJXT50bsJapX0DL8/YdGobqxmbtVcMuZnRDmqgjh9WhTpEuXtr4A8\nNRVErK7R3r6K1NRpIUeYZUI4Jj0WwwwGqisqSPFLbDzTQZoSNSV+kBA5YyhHgHa3mw2dnVwVcRrt\nL0WlVouOa80aYNkycUVVyPGKxYABAxgwYAB1dXXY7dv6FMHP2s/y+aHPubXsVmxbwzM5WVnhAMNE\nqOnqYnJFRdhlVVYmhLgYETnr8iw613WGunJ6emD7dh75aBK//rXQcuSQSAzfcGIDUwdNRROIvbkh\nN5e3Asm3hpEi7ba3OTk30erVIpkleM1N12op0OvZ5XDgcrl44IEHePHFF9HEPlFJEt2GwqzUipUr\nOTZoEFKSNu1kUJDiYv2ZaM66tfXT89Yz4ELRSAomUwm+vCPYd4l5g+1OJ5SVodu5m/J8MeQ3c6Y4\n/WZnZzNkyBC2bduGWm3CYplER8caALKvzKbtizb8XtEW5+p0VFgsfBVJUYGiIF6UXURpbinv731f\n8bk+/LCICepOMFgbxKWXXkp+fj5vvPFG0r8Lu32XWFAF5Of/GK3WyrGVb2IuM8edXBT1jKNHRQCe\nwqa+oAg+/H8OBz8cuT86aXfdOhFy2tcys8RFY3xUcGFb21dkZobXwFomWqLE8Fjk6HQscqZRM1PF\nklMHo+3TsZgyRZai+qilhfkZGVgiLi7nq2t8u9ondlPfcku/HhukqJLRM17f9jqLxiwiw5ARNciZ\nlXUlLS3LE1KdPr9fDHmmpoq//W9/K3SKb74RFt314desSdWQNiuN1i8CB6xt27ANLOLQaTM//KHy\n87NYlCfDhZ4Rbk2vz8nho5YWXF4vkkoitTJ5620kNRXEtLQ0qjs7efbZZ5k4cSJz5syRf/APfiAE\nEZnd5StWrEA1a1YSSZT9QO8B9nR6aegQ1sqentOKuWrJ4kLRSAImUwndqv34vX4mOPRsixTDI8IL\ng3/r2bNnsyawWCUz8yLa24U/O2VICrp8XdQE6iKrNTqLCoQ48cUXsjxTojwqgHHjBCOybFnfr0uS\nJJ599lkef/xxbEnsfoBwpxF8fFHR67Rsrkc/Jr5KKRaNBF1GV08Xh9sOU55fLhxV746h7as2Tv0l\nvEc7GWqqq6uL+vp6pinkWpnN43E4hEnB7/fT1vYlmZlhAdI8wRwnhsdidI0P+zQDKSoVF+3aFbXQ\nKQoKRePd5mYWR66ZQzjlqhur8fqSt4DOmQPffuESwta4cUk/DsJFoy/nlNvr5tXaV1k6aSm9Lb24\n29wYRopMMLO5DJ/Phct1SPHxh1wu0tTq6G2EI0cKS+7jj4uL6c03h5wc1mustHwQsN5WV7O6exqP\nPKLcZQCkpBTi8znp6Ynf1Le2YW1UJM0AvZ6JFguftYrCZJmc3JCf3x/uNCIxLTWVVWfO8OKLL/Jc\nIhtjWhpce23cB7S3t5e1a9dSeMMNSQ+E9gWRWGxndP7cUPR+a+vnZGZeIpurliwuFI0kYDKV4HDs\nwTzeTNExFdvsdnFlDojhm5o2UVEhYi06OqKLRkbGgtCQHyRJUWVliXflv/4V91yuGHUFTV1Nsutg\ng3jkEXjmmThZRBYTJkxg7ty5PP/8833fGZFuazaPD/13SspgjKcupyP7jSg3ktvno97hoFwuFmPL\nFsWiUXOyhor8itAaTm2GlnHLx3Hs18foWCs46GRE8LVr1zJ58mQMCnnZev1gfL5uenvP4XTuRZI0\nGI3hmHfTWBPdDd2K/n2fx8fg9+zUZ7r5x+jRlJvNzNqxg1Ny2oVM0Wjp7WVzVxeXxyxbyjXnkmPK\nYXfz7sQvMALjxkHbOR9NC5cm/Zggqqqq2LdvK729zRiNIxXv9/H+jxmeOZzS3FLsdXYsEywizRdx\neMjKuozW1i8UHy+XPxZ4MFx3nYg0yMkRnOMrr5B1eQZtX7fhdXlp/2wjKx3TufHGxK9FkiTM5oo4\nO3VndycHWg4wcUB0PEokRZXskN/evWIcpbAw+vZpaWmsPH2au+66Sz5fKhLBmY0IQXzjxo0UFRWR\nPneu0Kb62kWfBIKJxXOGzmVNwxrgu1NTcKFoJAWDYTi9vacxlqsw7O2h1+fjdFAMHywcVBqtj8pK\n0XHPmjUrpGuYzWV4PK10dwvXU9aV0fMaOTodE/pBUWlUGm6ruI3XauUXNIEYmh08GN57L7nX9+ST\nT/LSSy9xuo8hNJ/Pg9O5D6MxOj7Es9+KdkwbTU1h69Zep5OClJQo6iWEmhpZ5xQIPWPaoOjuwDjK\nyOj/NZq91++laXs3jY2CDk+ERNQUEMihKsVu30lrq+gyIuk1lVaFaay8GA7QVd1FYUoKPZKP0729\n/OeIEfwgJ4fp27dzICbTiVGjhJU6gpL4sKWFSzIzMckM4PWXolJ1dVDl+5Zvs7+f9GOCMJlMXHrp\nSNzuwVEOm1i8vPVl7p0k9n/LZYxlZl5GW9vnio+vUSoaQVgs8Oyz4hj/zjvoLp+BZZSftq9aYVM1\nlfdNQ2Zlusy3qcBuj44TqW6sZtLASeg10TEeV2dns7ajgza3G0ul6DT6chPKUVMAnbt34wRu+UUS\n2wsnTxaVJ2LNazCFGZ1OHEgTOO6ShUgsnsjsoWIPvdfrpKNjTRQNez64UDSSgCSpMRqL0FScxLHL\nQYXFwnarFTo6yHOpSUtJ42DrwZAYHqlrSJKKjIz5tLeLbiN1Uiq9Z3txHQ/HUlxntfKvWIrqssuE\nYHj8eNzz+XH5j3lnzzvYepTb6UcegaefjtvtJIuhQ4dy66239rnhz+U6hF4/EI0m3D14Oj30numl\neP7vaWh4CqdT2FgVqSm3W4jCEybI/ozqRvmhvsyLMhn8y8G8fU0TUyf7E9IU0HfRgCBFtTNOzwh9\nvcKMbZv877jlkxasC61UpqaytasLSZJ4eMgQfj1kCFXbt0dnU6lU4kIRscnvveZmFsVQU0H0W9d4\n5x3mjDvHt1uTXwsaiaqqgTQ0KNMVu87u4kjbERYWLQTkV/pmZMynq2szHo98kd2iEFoZh5ISwT/e\ndx/WA3/lxD3v0O1Ws+iBgqRei9lcEZdBFUtNBZEaSL794Nw59Pl61GY1rsOJ1yHKUVN+v5/777+f\ncSoVu5KIwkeSRE5XhJb41Vdfha2206f/W3QN0WlUUpxdjMvtYmfDP7FYJqDVJjBuJIELRSNJmEwl\nSMOPY99pp8JsFhTVhAliv0YfukYkRSWpJTIvi/ahX52dzeexWVQ6ndA23nor7rkMTB3InKFzEq5t\nvPhiwf9+rnz4i8KvfvUrPvroo4Qb/sTipej4EPtOO6ZxJkyWkQwZ8ggHD96G3y+STGWLxq5doreX\n+ZrP72Nz02amDp4a/zhg0M8HUW/IZPSZ5oQnwrNnz9LY2MgEhcIUhNk8nq6uOmy2LaSnxwuXlgp5\nMdzv99PySQtZV2WJmPQIPehH+fn8paiIy+vro/fBT54cOj2e7e2l1mbjMgVr5cwhM1nfsD75GZpl\ny5hz20jl8MI+MGKEn+pq5aDAl2te5s6Jd4b2tMt1GhqNBYtlMh0d8XbSbq+XPQ6H/LyOHCQJbryR\n7C3Pozl9lk4pA8N7byrPN0TAYpmAzVYXdVui7Y9LcnJ4O6Cj9BVe6PGIehZbND788EO6urr4/pgx\ncUN+irjhBvHhbG/nzJkzNDQ0MDnYfc+Y8Z11jcjEYkmSmD10NisOvPWdqSm4UDSShslUgif9EN1H\nuqnQmsK6xtatTBk0hc1Nm5kyRey26OmBOXPmRBWN9vZv8AdWLGZfmR1FUeXp9ZSZzdEb/SBMUclc\nPO6ceCd/rv2z4oVFkoST6ve/T67byMjI4OGHH+bhhx9WvI8QwcdH3WbfYcdSLi4Ggwb9DK/XyenT\nrycWwRWoqb3n9mI1WckxyZ/AJUmiXpdBqaedE7+XH3IEWL16NVVVVfGWxxiYTKXYbJuwWCah0cQ/\nV8sEC/Zt8Sdn514nfrcfc5lZbPKLMRFclZ3N+2PHsmTvXj4MdpBTpoQ6jQ/PneOyrCwMCtlQhemF\nSJLEsY5jCZ8/IAKQTpxgzE+m4XTKNqZ9Qq8/wY4dDk6ePBn3tXZXO+/vfZ/bJ9wOQM/pHnwuHymF\nKXH3VdI1dtjtFBuNGPuZ2tqgtqLhAHmXL4BXXhHuh3r53TJBGAzD8XjaQpPhTreTXWd3MWXQFNn7\nX5qZyQ67nVM9PSImPYGusX27WOkdufKkp6eHBx98kOeff57p6ekJE2+jkJUlTnZvv83XX3/NvHnz\nwu/XqVNFYkI/dpTEoqenCZBCicVVQ2axvrHmQtH474TJVIKzew+GEQZKmtRhB1VwMvzkZiwWkYW0\ndWtY13C73aSkDEans4YEuoyLMuiq7sJjCyvV18m5qCorBbURQWsEMX/YfGy9NmpOKkeBXHstnDsX\n5WZMiKVLl1JfXx8XmR1EpN02dFvEJLgkqSkqeoODRx9nt8Muvxuij/mMRNEhHR1w+IjEdZ8XcvKV\nk7Qslw+2S4aaAjCZxtLd3UhGxnz5r5eYxM5wVzTl0PJJC9lXZSNJEpWBwa7Y9a9V6emsKC3lnkOH\n+OupU+I1b90KXq+sayoSkiQJiqohiT/csmVw441IWg2zZyeISleA1+uku/sow4fP5xuZ2aC/bf8b\nV4y6IlTIbXWiy5AbDBO6xhdxB5ktMvszksHTT0OeaS+dqmlCLLzhBiEo3H8/KLj9JEkVNbi5qXET\n4/PGY9TKR5ekqNUszM7mvebmPof85PSMl19+mTFjxjB//nwqLRZ22u30JNERASIf7I03oqkpEGFy\nw4aJKnWeiF3bW2m1sqPDndDskCwuFI0kIRxUuzGNN5F+wEO7x0NreTnU1jI+bzyH2w5j67ExY4ag\nqLKyshg6dCjbAmv1MjIuClFUGouG1KmptH8d7iyusVr5rLU1+g0nSaLbeDM+Fl0lqbhjwh28Wqc8\nIa5WiynxZGLTAfR6PU899RQPPPAAPpk3fqTdNgj79uj4ELO5BLv1AQZI5zDKDVIoxIeAKBpTB8lT\nUyB+r5Mng6VQz9h/jeXAjw/g2OuIu1+yRUOlSkGSVBgMo+S/rldhLDbi2BX9M1o+aSFroXA95ep0\npKrVHJZZ/1pusbCmrIwnT5zgGYcD8vM5t2MHOx0OLs5IzCvPKJjBhhN98Noej4icCWznmzMnSltN\nCg5HPUZjMfPmXRyVQwXg9Xl5pfYV7qm8J3Rb5FBfLIzGIiRJh8MR3Q1s6epKTs+IQEMDrP64iwzv\nCU5utOJHBXfcIXS+tjYxjv3hh7JtdKQYvq5hHbMKElvtrg9QVOYJZuy77Ph65S/6sUWjpaWFp59+\nmmefFcvJzBoNo4xGdtjldZ04zJ+Pt7mZlV9+GR8d0o8FXnKIXaaV6duFx6/nWHsS3WsfuFA0koRe\nX4DXa8NQ4cW5S1hJt2dkQE8PurMtlOWVsfXU1qgcqlhdIzivAfEuqgF6PSUmE9/EUlQ//KFY2ylj\n5by17FY+2vcR7S7lpUo33QQ7dggpIRksXrwYv9/PezHWK7e7DY+ng5SUoaHbfL0+nPudmMaZou57\n0ryIYukIzc0xmktnJ5w4AWOj3VdBbGralFRIIUDalDSG/WEYuxfuxt0ebuOPHj1Kd3c3Y8aMUfgu\nYbhcB5EkDV6v8oc8VgzvOd2D65CL9KpwNIkcRRXEKKORDeXlvHnmDLVjx7Jr1SquzMoipQ+qZkbB\nDDY09lE0VqwQ6QGBqN9g0ehPnJiID6lgwYIFfPPNN1FdwpeHvyTLkMXkQeEir7SdEZStt4p22wR4\n5hn49YLNqConoBtopnNjQCuwWkXo31tviajbK68UuR4RiBTDg3lTiTAvPZ3j3d00qN0Yhhlw1Mcf\nRHp6hCQVafX+7W9/y/XXX09xRNTy1NTUhPs1oqBWs+3ii7FKEgUFMUJ/8PR5nrDZaklNDa/tbW1d\nzsyCKaF5je+CC0UjSQiL5lg0JY1CDLdYhK4RSVE1bWbGDJGt5vNFF4309Cpstq14veINmXVFFq2f\nt4amw0FkUcVt9BsyRDhKvojniq0mK5eNvIz/2hlvzQ1Cr4ef/Sz5bkOlUvHss8/yq1/9ip6IQuVw\n1GMyjUOSwm8Z5z4nKYUpqI3RF8BtdidVeTM5fPgX9PZGvJ7aWuGVlYm5aHG2cMZ+hrFW+YIC8UN9\n+bfmk3l5JnuvD0eNrFq1irlz5yaVq9PW9lWgg1TmyS0TosXw1uWtZF6SiUob/j0EHVRKGKjXs668\nnNVFRZxdt45rsxNkVQUwLmccp2ynOOdIsMlu2bKoCfBRo6C3N+4amhAiPqScwsJCzGYz9RGawcs1\nL3PPpHCX4ff7RdGoVO4aghRVEC29vbS43RQnSLaNxenTYq3M9QUipDD7mmxaPoqhIquqxGloxgzx\nGXz6afHiCXcayWx/BNCoVFxntfJOczOWSvnwwk2bRHMTjDHbv38/77zzDo899ljU/aamprIpWV0D\nWJGWxsUuV3yEQ7BonEegqBDBa0OdRnf3CXp7T7Jg5LWheY3vggtFox8wmUrwDT4qiobJJHSNGDE8\nN1cchnbvjtY1NBoLZnMFHR1ipaOh0IA2Rxv1Br0mO5vlra2hjXAh3HSTbPItCEH81bpXEzpt7rhD\nHEqT3bs0Z84ciouLefXVMPVlt8dTU3IhhSDstjOsY8nLu5lDh34a/kICEXxT4yYmD5yMWiV/ArfZ\nBDMR+/Dhzw3H7/Vz7BFxpUyWmgJobf2SjIwFOBzxuVBBWCqixfCgayoSiTqNILK0WhZdeSXj9+xh\n2ZkziWNHALVKzdRBU6luVNjF0doq4igWLw7dJEkwe3b/KCoRHyImwSNTbw+2HmT7me0sGrsodN+e\nph6QQD9QeW2pyFvbgdstut8am41KiwVVP8Lxnn9e5HaadoqiYb3GyrkPz8W/x3U64fbYulW09+Xl\nsG4dBkMRPT0nqWlaQ3F2Man6vrucJTk5vH32rKKDatWqaNfUL3/5Sx5++GGyYw4A/S4aNTVcMno0\nfPxx9BcKCsTrO3JE/oEJ0N19FLXajE4nFHsR+X8pcwvn8e2xb88r2ToSF4pGP2A0jqVHvR9JIzHe\nlhI1GT5l0BQ2NW3C7/dH6RqFhYURusaC0LwGBFxUEdbbQSkpFBuN0VZNEBOzq1eLC0UMZhbMREJi\nXcM6xeedmioKR5JD3wA8/fTTPPXUU3QGWm1Zu61MHHqPz8c+p5PxZjNDhz6O3V5HS8sn4ovfQQTf\ntAkqKiAlxrSj0qgY++5Yzn14jlNvnmL16tVJFQ2v10VX10Zycm7Abt+p+EEylZpw7nfi6/HhsXvo\nXN9J1qXRRWNCQAD19CGAfpyfz/CzZ0mz27m8vh5bHyP7Cec13n5bzPLEJPj2R9fw+dwi6SBwGIgs\nGn+q+RM/Kf8JKZrwLzyoZyTq4tRqA2lps0JU7JauLpE3lSRaWuBvf4Nf/sIr9K+pUzGOMaLSq2Sd\nbICwcH/2GTzxBPzwh6h+cjtm/Rh2nviXotU2FtPS0ujyemkeq6Fra/xFf/XqsJ7xzTffsHfvXu65\n5564+w03GHD5fJxUSDWORGdnJzt27GDWffdFzWyEcJ4UVXCoL4iWlk/JyrqKkZkj8fg8ybnyEuBC\n0egHgmK4ebyZvENeTvX00FVRAbW1DLIMJEWTwtH2o1G6RqT1VuRQxUSKfB5dCGQH/VJTxb5nmRFv\nSZJC3UYi/PSn4jojk5Mmi3HjxnH55ZfzhwCvpWS3jV28VG+3M9JgwKhWo1YbhZvq4FLcve0J40P6\n2tSXKG9Km6Wl5JMSVv5sJWa9mSF9LCACse7SbC7HZCoG/PT2xucVAagNagwjDDh2O2hf0U7qlFQ0\nadFW3jSNhsEpKeyJnQSPwbvt7TjLynjDZmOkwcDcnTs516ucrJpQDP/730MCeCSCDqpkDpNO5z5S\nUoagVgtNau7cuWzcuJFzned4q/4t7px4Z9T9E+kZkYjUNWr66Zx68UVxRhrUsRvy8yFbuNSyr8nm\n3EcJqDpJgmuuETkf6emYP97DmaPLqSpILphPJUlcn5PDv6x2sUslwtlos4l51OnTxc75+++/n2ee\neQa9Pr7jkiSJKQqb/GKxatUqpk+fjmHxYuGUivVLn2fRCA71AXg8Nrq6qsnMvCg0r/FddY0LRaMf\niHRQOXc5KDWb2WGxCI6+oSFEUQWLht8frWtYLBPo6TlJT48I30udkkrvqV66T4T5zGutVj5pacEd\ne2pVWM4EcGPpjXx56EuaHcpr+3JzxcbJP/4x+df7u9/9jtdee43GxgYcjj2YTOEscr/fL4rG+Oii\nERuHnp4+i+zsq2iovku4fWRyedxeN3Wn6pg8UJ66gr7zpswlZk5cfYLS9lJ6Tvd9yhNT4JcEtKro\nxNu4711hxlZnE1bbhfJ6RKXFQk2CC0VDdzeHnE7Spk9HvWULfx41iosyMpi1YweNCpHElQMrqW+u\nx+mOKUa7dgkvdeyUGSID0OtNjoqMDSlMT0+npKSEJ//xJHOGzmFw2uDo+ydZNISu8SU+n5eafjin\nOjtFrP/DDxNauhSE9WorLR8q7A6PhMUCL7yAceH9qPVnmXH304IrTgJLcnJ4u+McpnGmqK5m/Xoh\nmxgMsGzZMlJTU7nmmmsUv0+yYnjIapuSIj6csSmj5100wp1Ge/vXpKZORaMRhXvOULEC9rvgQtHo\nB4IcYUq5MzwZHtQ1amuZMlBQVMOHi+tjQ0O0riFJatLT59LeLvzwkloi89LMKBdVQUoKIwwGvg0s\niAnhoosEv3k4etscQIYhg2tGX8PftydYJQk88EDyS5oABg0axO23384LL9yPTpcbeuMBdB/vRm1S\no8uJDgSqs9vjhvqGDXsab/UqesuHye5n3XFmB8MyhpGWkib7PFwucRBTCKwNYUvzFuZfNp891+7B\n15OYKhKptiI6JBgnogTLBLH+tfWL1jg9I4i+dI33m5u52mpFPXUqbNmCJEk8OWwYt+XnM2P7dvY7\n4h07Rq2R0tzS+FmcZcuEziXjwJKk5CkquTj0+fPn89Ynb0UJ4BAhgidRNAyGoWi1Vna21GJSq8mX\nOZHL4U9/gksvFSMKsUXDUmnB0+XBsT/+9ySHppxiijP0ZC2+VfxCHnoIZH7HkSgzm9FJEs7xKVFa\nY9Bqa7PZ+PWvf80LL7yQkKJLRtfw+/2sWLEibLX98Y9F9xipdZWUiO1ascxDwu/rxW7fjsUi0hBi\nd4FXDa1i7fG130nXSLZomIBioCjw//+fhDiVlqAqPoFjpyPaQRURXihJhLqNzMxMhg0bRl2diDbI\nzLyItrYI6+0V0dZbUBj002rFaSSBIP5a3Wv4/MoXy8JCUXteU846jMPDDz/M0aMr8XqHRt2eaCd4\n7OIljSaVgjOzOVtwQDabqK/5jM2bRZKrKcE7z+12s379eha9tAhdvo6Ddx1U/GC4XEfweLpCdJvZ\nXJqw07BUWOhc30nKkBRSBsdPQkPfRePdc+dYbLWGE28Dz+0Xgwfz26FDmbNzJ7UyF5oZg2MoKrdb\nbHZMsDcj2SE/ucVLWSVZOPY5onZPAHQfE4cEfV5yBSAr6zLWNm9LmppyOAQ19cgjgRs2bhR8UACS\nShLdRqyLSgEbTzdi1Xvx3naj6DROnhRW7wSbKiVJYkluLltGerBtDf8tg0XjmWeeYd68eVRWVip+\nDyA05BdnaInAgQMH8Pv9jB4dWLlaVgbZ2dFb/dRq8X6pVjBDyMDpPIBWm4NWm4nf76Wt7XOys8NF\nY2TmSNw+N8c7jif9PWORqGhYgF8ANUA98HfgTWA3UAv8HDi/hLT/i2EyleDNPEx3QzflamNUp1Ge\nV86+ln043c6ozjJ+XiPsh8+8OJPODZ1REdzXWa183NISL6zeeKPwp8tcDCsHVJKeks7KI8r7l0Ec\nuP7n/0xuSRNAWloaS5ZMZu3axqjblUTwA04npTJXd0N9C/5JEzh27FdxX+vPfIYStm7dSmFhITm5\nORS/WYyt1sbJl+NjMSCSmhJv/z7pqTIzrsMusi5X3lleZjZzwOmMjrgP4KjLRUN3N7PT08XiKaMx\nyhVzS34+r44axWX19XwbY4KYOSRGDP/iC+GtHTFC8bkEHVSJDpN+vy8Qcx8dF7zGswbaoC0mdTnR\nUJ8cMjMvY3NnK5OTpKZef10ctMaMQXhuOzrEFssIZF+dnRxFBaw9UY1fW4Ddvktws2+9JcTmBx6A\nq68W80IyWJKTw9sD7aFOo6VFWJhzcxt55ZVXeOqpp/r82WaNhhEGA9sTDPkFqamojiUwIR6FflJU\nkVbbrq7N6HQDova+S5JE1ZCq76RrJCoaHwM24EpgGDAVmAIUAlcADuCT8/7J/5fCZCrB2bMHwygD\nQ47D0e5unBUVUFeHQa1nrHUs205vUxzyMxgK0WgsodkATZoGS6WF9lXhi8VQg4GhKSmsiaWoKirE\n4IXMySNZQXz8eHGoUWhYZDF6dAo7dnTxbcTxNXYSHMIieFymktcLdXXkX/Uq5869R2dn9KRrX86p\nZJYuRVptNWYNJZ+U0PBkQ9TvNYhg0QjCZBpNd/dRvF75SqoyqkAC41jlWYMUtZpihWng95qbudZq\nRROckJfZr7EwkFe1eO9ePoroMqcNnsbmps14fAFhVkEAj0SwniRya7pcR9FoMtFqw6GJDR0NrD+5\nntlVs0N77oNIlpoKIi1tBrvcOVQY+0597ekRqei/Cp4nNm0S+UsxiQJps9JwHXNFaYBy8Pl9bDix\ngez0qdEx6fPmCT2ookL8e/75uHynUUYj0nAd3YH1r99+K4rZY489yt13KC1l1AAAIABJREFU383g\nwYNJBlPT0hLqGqEo9Ej84AfCGx/pkuznZHjkUF8sNRVE1ZAq1jbIRwUlg0RFYx7wOiDntzkD/CVw\nn/+nYDKNDTmoeuqdjDEa2ZWSIqyPhw8L623jJkpLRUfc0iJ0jerqatyBN6hIvY2hqJZHU1Tfl3NR\nBdI/la74S0qWsPb4Wpq6mhK+hocfFhO3yaQ4A7hce7juugd58MEHQ/EikUGFQdTZ7fJJpvv2QV4e\n2twRjBjxRw4c+EnoAt3Y2YjL42JEpvzJubdX2PAjmApZxM5nGAoNjPnnGPb+YC+uo+GID6+3m46O\ntWRmLgjdplLpMRhG4nTukf3ejj0OJJ2E1574FxabeBvEe+fOschqDd+gsMmvKj2dr0pLufvQIf4W\n2G2SbcxmoGUg9WfrxVa7NWvg+4n3ZiQzryH0jOgu49XaV7mp9CYuvfjSuEiRvob6YuFGzXEKGdrb\n9yl52TJxkCkPyisxekYQKo2K7Cuzafk4cbdRf7ZeBF9mzIiLSUevh1//Wvz+V6wQLMGmTVF3WZyX\ny5mxGmxbbaxaBSNGnGDVqlU89NBDfb6WIKYmcFC5XC42bNgQbw3PyIDLLxf0YxCTJgnrlkxMjRwi\nRfDW1uVR1FQQVUP/zxWNIH4S898a4PHz/onRuATYDxwClP4ifwx8fSeQeInxfwNE0diDabwpejI8\nMOQXDC/UaMS1YeNGoWsMHz48pGvEzmuEpsN9YT7hOquVj1pa8MZyDMFYERl+yaK3cH3J9byxLfHO\n75kzxQDihx/2/Xo9Hhu9vae59tqf4vf7ef/993G3uvF0eOKSTutsNib0EVJotV6H0TiahoYngDA1\npSQsbt0q2Jg0eY0cAKfTSW1tLbNiOKyMuRkM+R9D2L1wNx67OKl3dm7AZBqLVhtNNYmd4fJZK62f\ntGIpt2DfnjhTSG4y/JDTyameHmZFzlMoFA2ACouFtWVl/O74cZ4LUCgh6+0//gELF8rGyseiL13D\nbt+BxRL+OHV7unlj+xssnbQ0NK8RpFD9Pj+2bTYsE5IvGjvtdgr1PlztibP53W4xzP2rSNYyRs+I\nRPY12Zz7MLEwHMybklvIFMKIEaJoPPqo8PjefrvItAIW5+RQPdxNe00nq1f7Wbv2NzzxxBOY5d7b\nCkgkhq9fv57S0lLSY2ZsgPCejeDn3mQSgvhW+d3nkfD53IEh3ApcriO43a0h620kRmePxtHr4ESn\nclJ0IiRTNOYBXwADgBJgE0Lv+K5QAy8jCscYYAkwOuY+lwEjgJHA7cCf/w0/9ztBq81ErbagK22X\nd1AFOo3IIT+IjRSZQ1dXdei0bRxpRG1RR12UhhkMDNLrWRdLURUUCI5JYVHGnRPv5PVtr4fpDBkE\nY9OTWdLkcOzBaByNWq3l2Wef5dFHH6WjtgPzeHNo3WcQ22REcCBqPkOSJEaO/BOnT7+OzbZddlNf\nJJKhpjZs2EBZWZnsh3rgPQOxTLaw/6b9+H3+KNdUJBLpGi2ftJB9dTb2uj6KhowY/t65c1xntaKO\nLIrl5aL7UpjrCOZV/e3MGR4+coTpg6cLXSMmNiQR+tI1YjuNd3a/w8QBExmROYLi4mLcbjeHA049\n50En2iwt2qzk90pv6epialoO7e1f40vwXnz7bWHQCDUW3d2CQlIQmzMWZGDfYaf3nPJ8y7oTYn+G\nyTQOp/MAPp+CBVuSxET93r2iAxkzBv7rvyjQ6+kpM3BwVTtnz/bi9e7gliR/70GMMBhw+nyy63+/\n+uqreGoqiNmzxWBIXcROkCT3azgce0hJGYJGYwlQU1dExf4EIUlSyEV1PkimaCwB/gvYBXyOEMDv\nP6+fFo1JwGHgOOAG3gEWxtznKoT4DrAFSAdy+f8YJlMJDDuGIxBcGJlBNTR9KF6/l8auxjhdI6gJ\naLXpmEzj6OwMt+6xAYagMOgHCSmq0txShqQP4fODiU94V1whPp8yadhRcDjqQxPDc+bMoaioiJV/\nXhmnZ/T6fOwNTILHISY+RK/PZ9iwZzhw4EdUN278ziJ4oilwSZIY9adR9J7tpeGJhjg9Iwgl223P\nqR5ch13k3pwrElA9yo6YMUYjJ3t66IjgyWVj0A0G4eSJvDDEYFBKCuvLy/m2o4MvvYPYcORb/J0d\nfVfQAIYPF5KAjEMbEJ1G0G7r9/t5qealkM1WkqSo6fD+6hkQKBoZeaSkFNLVtUn2Pl4vPPVUTJdR\nVwejRyta5dQpajIvyqT10/h0hOBrWdcgQgrVagMGw0js9sQ7OEhLg5deElPlL74Ic+cycYyEb7sD\nr2cVL7zwHOp+7gIJDvnJdRtRVttYqFRCs4oUxJPc5Bcpgre2fkp29lWK9/0uukYyRWMU8FPgQ+AE\ncAP/HtvtQCDSktMUuK2v+wz6N/zs7wSTqYRezUFUBhVFbRr2O530lJfD9u1IXm8ovHDSJLEzxumE\nmTNnsmnTpghdI346PHY/xHVWKx+cOxdPUV17rThGysSKANw5oW9BXKUSTqq+ggwdjl2YTONC//2H\nP/yBw18dRl0U/SHa7XAwLCUlftGO0wkHDojuKAJ5eTfjkbLZ3byTiQMmIgePR9DbM/sY6u0rb0ql\nVzH2g7Gc+ng7PfYzIQ97JAQ9FR8nEgwo1GXp0A/U4zqgzC1rVCrKzGbqAmL4PoeDVreb6XLcWsRS\nJiVkabWsGj+eFnUWPQ4Hh266Kk4cVkJQ15CjqHp7z+LzdaPXC1F3c9NmOrs7uWREuJjGFY1+6BkQ\nmAS3WMjKig4wjMSHHwoaP2pGMQE1FUSi6fADrQcwaAwUpInU2IQUVSwmThQHnGuu4ep7rqfbI1FR\ncIr58+X3rfSFKTJDfo2NjZw9ezbxVslbboF33w13otOnh1NQE0DoGZW43R3YbLWKe2JAFI3VR79M\n9qVEIZl34KfAbxD0UBVCX+ibYOsbyU6XxJLdso97/PHHQ//WJDPZ9B0QGSfi2e1ihMHAHq1W2Cn3\n7w9NhhuNUFoqrg1BXaO2thaAzMzoqPS06Wl0H+mm51S4nR1pNJKn07Ex1oWRmiqmoN59V/b5XTfm\nOmpP1XK0PfFY8JIlcOhQYrrUbq+PypwaN24c4wzjeHdb9M9WpKa2bROn6pjQKEmSsKfexlCjD1/v\ncdmfvX27CPnNUna60t7ezv79+5kyRX4zWxD6PD15rzTiq67AsTv+wq/T5aBS6QMbz8KInAKPTbyV\nQ6Su8d65c3zfapUP60uga0TCrNHweXExVUe93DJM02deVSSUxPBglxHUkV7e+jJLK5eiiqAy5s+f\nz5o1a/B4PP3uNNrcbs709jLaZCIzU36bn98PTz4puoyoX4+CCB6JrMuy6FzXiacr/ncRu9pVbmd4\nQqjVcO+98PEn7PeZuUbfCl99lfzjIyCna6xYsYIFCxYk7lwGDxadeVB0DKag7pE3agQR7DTa2r4i\nLW0WanW822/NmjU8/vjj/NfzT+H/RjlBIhGSKRqTgSCJ4QOeB64+r58WjZNApH9tMKKTSHSfQYHb\n4hBZNGbPnv1veHrKCMWJlJqidY3AkF+waACK1luLZRIu17FQdLhKqyLj4gxav4hxUeXkxA/6QXgV\nrAwMWgM3ld7E63WvJ3wdWq1YgqbUbfj9/kDmVLjT8Lq8ZLoy+c+P/5OmpvCfS9E5lSCksO7sMaYN\nnsmBAz/G7493JiWjZ6xZs4Zp06ah0+kS3xFwWtaSN+Yqdi/cTW9LPCceq2t4bB46N3SSeamwpcbu\n1pBD0EHl9/t5t7mZRUob+pIsGgD6FSuY7R9Eu/pkn3lVkVDaryF2aAg944z9DF8c+oJby6NtvLm5\nuRQUFFCzqUY45SqSLxo1XV1MtFhQSxKpqZPo6TlJd3f0nE9Qkrv88ogb/f6kioYmVUPazLS4zwrA\n2oa1UYOJ/eo0InD/sx9yWG3CM7IS7rkHFi0Sdsh+YJLMkF9CaioSQUE8iD7mNXy+HpzOfZjNZQmp\nqdmzZ/OrX93H1d9bz7b/lXimSwmJisbswP/KmY0PBP53znn9VIFahMA9FNABixFdTSQ+BW4K/P8p\nQAfyFuD/VphMY3A692Mab4ieDA84qCoHVLLz7E56PD1xYnhQ11CptKSnzw5FikD87nAIU1Sx60RZ\nsEAEnB08KPsc75h4B3/b8Td6vYkvMD/+sdANDhyI/1pv7ykkSROKTwFhPzUWGfnRHT+K2iWQ0Dml\ntKmvqZoFxXcgSRpOnnw57uv9nc9IBJ/PTUfHaoZe/n2s11nZu2gvPnd0u282l0bpGm0r2kidmoom\nVQQUWiZYkhbD9zgc2L1epihNRBcWCj9xY6P81yOxbBkzZ90AXfVcnJHBzO3bOZHEdGZhIWg08W+R\nSD3jL3V/YfHYxaSnxDt5FixYQPU71egH6uNCGhNhi80WypuSJDWZmZfQ1hamQvx++I//kOkyjhwR\ngnQSsxDZV8fv2PD7/aw9vjaq0zCZxuNw7MbnS37f9v79+/noow7SJqWSckhF+/btYtFVWZkIb0uy\n2wsO+QVndzweD998801yReOqq0RnERy2mTkzYdGw23diMIxCkjS0tX1FVtYVivc9fPg+rNZryMiY\nndTriEWionEFYhr8KeAaxHDfdOBa4PcIiirehpI8PMA9wApgL/AusA+4I/APhGvrKEIwfw24+zv8\nvH8b1GoTOl0e2rHN2HfFdBq1tZh0JkZljWLHmR1Mny4OlB6PmNfYvHkzvYGToqCowtU+85JMOr7t\nwNsdPnUXGY1kabVUx1JUGo3gl956S/Y5jsoaRUlOCR/uS+yrNZlg6VIxXBWLWGoKwpPgDz30EMuX\nL2f37t24fT72OBz92gnu9/upbqxmesEMior+yvHjT+Byhek0r1d8Rr6rnhFEV9cWUlIK0evzGPb7\nYaj0Ko7cHz39FtQ1gmj9tJXsq8IBheZyM/Yd9ihrdCyGGww4vF7eOHNGmZoCcbWcOrXvbuPcOfj2\nW0qv/xmnbKe4L9fCnQMGMGP7dvb1kaWkNK8RdE65vW5eq3uNpZVLZR+/YMECTqw80W8RvCZmU19W\n1uW0toaNGatXi4HvuMy/JPSMILKvyqZtRVvUZ+V4x3G8fm/UzI9GYyYlZQhO576kn/+DDz7IiBG3\nU7Eoi1GHJD7stMHvficog48/FoegJCywEBjyC1BUNTU1FBQUkJ+f3/cDdTphr//b38R/z5gRpixk\nEKSmOjs3kJIyDL1+gOz9Wlo+obOzmmHDfp/U85dDoqLxAMJuuwdYAPwa+BUwHxElMgd48Lx/ssCX\niDyrEYhCBKI4RKYj3RP4+nig/33m/yGYTCV4cw/T09hDiWSg3uHAU1Ymcm56e5kyUFBUWVni4LRz\nJ2RkZDBy5Ei2Bt5wYm/41yHxVZulxVxqpuPbaJut7KAfhF1UCgLZXRPv4s+1fbuU77lH0Kex3Xcs\nNQXhSfD09HQeffRRHn74YfY6nQxJScGsiTmNnjsnvO+j4ndwH247jEFjYFDqIIzGURQUPMiBA7eH\nfhf19YLKzctTft4nT56kubmZsrIy5TsFEOmaktQSo98eTduKNk6/cTp0n0h6yufxxQUUajO0aK1a\nnAeVI9AlSWKixcJ7cq6pWCRDUb39Nlx5Jer0jNBSpp8NHsyThYXM2bEjYbIuxIcXejx2enqaMBqL\n+Wj/R4zMHMm43HGyj505cyb643p04/qm/oLw+/1x610zMy+mo2NNyGL+5JNiPCKO1k+CmgpCl6PD\nXGamfWV44j9ITcXO/PRH11i1ahW7d+/h5MkiZl+pRZ2n5ZvNgfdIcbHIhvr5z0UnsHSpqH4JECmG\ny06BJ8KPfwxvvilOUCNGiNF5hfiTYNEQA33y1JTb3crBg3dRXPz3UBz++aAvTcMG5CFO+qsC/w4D\nBsSF/P9ZmEwlOLv3Yiw2otrfwyC9nv0gvI719aGlTBCvawQpKoNhBCqVDqdzb+j7KllvP2hpiaeo\nystFjpGCh3th0UIOtR5iT3NiAS0rC26+WWRSRSK44jUSkUGFd911F3v37uUftbVUyHUZW7cKyk7G\n8RMbHTJo0C/weDo4fVrwuMlabWfPnp2UHTLWaqtN1zLu03EcfeQondXiQ200FtHT04jX66RrY5ds\nQKFlgkV5GVAABXo9Dq+Xyr6G8KZMiZtGjsOyZeKPQ/R+jRvz8vhrURFX1NfzTUxOVCRi5zWEG24M\nKpWGl2pe4t5J9yo+1mg0UmYo46AkT4HK4Wh3Nwa1mgERybZabSZmcymdnWuprhZZTkuWyDy4H0UD\niAswjBXBg0hW1wjuyrj33lexWCSGDIGcyWn01to5E5y3kCS44QYx2+H1itmOf/5TcSAmUgwPRaEn\ni5ISGDhQCPGSlFDXEEVjQmDhUvwUOMChQ/eSk7OY9PTkdowoIRkhfAKCLhoQ+Hc7YiDvdZSnuP9/\nDyGG78E83iw/GR5IvIXov/WcOXNCRUOSJDIyLpZNvY20fo4xmUhVq9kSe6qUpISrYLVqLT+p+Amv\n1ia23wL84heiE468/sTSU36fH8cuR2iHhl6v58knn2RZdbV80ejHpj6VSkNx8d84duwRenpO/lv1\njN7eZlyuw6SmRifpGouMFC8rZs91e+hu7Eal0mI0FuNw7BauqQhqKohkxPAOj4dMrbbvPeWVlaIF\nVdrytmuXyKGZI6TDGQUz2NAYvmhckZ3NB2PH8sN9++J3ywcwdKhgOoKaVTAOfceZHRzvOM7C4tjR\nqDB8vT7yXHl8c7yPYZ4IKO3PyMwUFNWTT4rB0rg18R0dQqOLsWYnwv9m7z3D4yqv7u/f9D6jLtmW\nLLnL3bJxkXsPxmAwPYFQEgyhPgFiIBCeBBISAgESHEoaoSRATADj2Ljg3otsy7bc5Yolq5epGmnK\n++HWjKacMzMG533f///yui4+MHM0Gsmjs++91l5rZ83PomFpQ9g7I1c0zOZROBzynpgQ3nvvPSwW\nCyrVzPAYcPpYGzPP6OOHUdLT4e23RYv+0ktCY5QQBvt10pUVNTUcOXKECSnSb2Hcc0+XIC5TNPx+\nNx5PJQqFlmDQGxcPA1Bf/xkORxm9er1wcd9fAqkUjQJgJMLQ9ziiiOQgxm/v+tbv4P9QRC5kipug\nKiujX0Y/HO0OLjguRC1lmjRpErt27cLbeaMQUemrwq9rHGhEoVLgqojmq2WNfrfdBp9+Khtbu2Dk\nAj6s+BBne+LTcUGBSKh4803x/4FABx7PMUymQeFrPCc9qDPVaNK7/uJvueUW3N27Y+8cJY5CoqIh\nsanPbB5G9+4PcOzY/WzaFEzYaQSDwZSLRnPzV6SnT0OpjHc0Z16VSf7/5FMxvwK/x9+pa5TTsLSB\nzGvjZ32TieHBYJDdDgdNHR3JdxaYzWJr0n6ZhN333ovamzGmxxgO1B6IWso0KS2N1cOH8+PKSt6W\nmO6J3a8hRPARvLHrDX406keolfICt6vChaZAw8qNqY+cxlJTIWRmzqW6ehn79welTe07dogDV1w1\nkYe+px59kZ7Wza1U2atoaWthUPaguOvM5hGdHhz57DCn08mzzz7LK6+8wvr1ilCdxjLawoAjQT6S\nKcqMGwdlZcItO2EC/OxnUTlRIZPfO9u3M2XKFMltfwlx663CbFNTI1s0nM5yTKbBNDevIjPzmrjD\nSnt7PSdOPEhx8buSY7gXi1SKRjYQOYLTgXBlu4EUA7b/74PROIC2tlMYh2twHYjfraFQKBjbYyw7\nzu8I74ivrBRR4wMHDmRHJ5edljYdu31rmO9VKBQJAwzjbkT5+WKqY9kyyfdZYCtgUs9JfHTwo6Q/\n0xNPCGOs2w0ez3F0uoKoD5lUsm0A8BcW8t6zz4YFfkBUSJmi0drWyunm0wzPjT9VFhY+w+HDYDS6\nEg7RnDhxgmAwSH8JvSQWci7wEAqeKMDY38ixe45hMg2j5dwegh3BuK2E0Nlp7HPIiuF7HA40CgUm\nlYrTqeTPy+kaob0Zd9wRfkhuKdNws5lNJSW8/PXXvHD2bNxnJFIMdzj2EdD04d9H/s2CUQsSvjVH\nmYPsSdnU1dVFjVcnwk6Z9a4m0xDs9g6eeeYokvfNi6SmQsi+Xmz023R2E5MKJ0V5TULQaNLQavNw\nu+Vptpdffplp06YxatQYNm4MN3eYS8yoT7RzpsXNabnQQLUafvxjUfwrK4UvKSLmp9RmY3VV1cVR\nUyFYLGJi4P33BR195gzExOdH6hlS1NSJEw+Rm3s7NtvF/36lkErR+CciwuPniKDCbcCHCFf4Yfkv\n+78bSqUOvb4Xqv7VOA84GWEyUe50Ehg6VDjm3O6wMzxyKRNE7w0XkSLDkkaKDDaZMCiV0ot+vv99\nWc8GdAniyU6+AweKv9t33gGn84Dk5FRssu0Rt5ueRiMDCwt5++0IGuz0aWHo6x4/xbGzaicju41E\no4o/VSqVWqqrX2fIkGW0t8sH04W6jGQUUDAYoKlpFenp8n+wCoWCAX8dgPuoG/fybrTW7SNrXpbk\na2uztKht6qjk3Egsrq/nlpycpEuZwpDTNVatEvpYTFGMW8rUiT4GA1tKSvhXXR2PnTwZpX+Fiobf\n34HbfZhPTpRxTf9ryDElFuodZQ6so63MmDGDNcnyZhBRMgecTsnR6yNHFOzYMZdZs2Tibb5h0Qi5\nwzee3cjknvKtaSJd4/z58/zxj3/k17/+NeXlYvgiNOCkMqjEiHlDmny3EUKPHvDxx4K2+vGPxc3+\n3DnGWSwc12guTgSPxD33wF//KjrOMWPiViM4HGUYDANwOg+QlhbtgqirW4zLdYCioue/2feWQCpF\n45cIHaMVaEboG88h9mncdsneyf+BMJkG41UfRWVRYazyk6nRUBkICHGsvFyY/KriTX6RugYIiirS\nHZ42OQ3XIVdUKJtCoZA3+t1wg1COZdZCzuozC7vXHr82VAJPPgm/+x04HAfjJ6fKnZiGR09d7Ol0\ngr/44ou88MILtIZGg5PoGRMK5Lnd3buLmDRJQWXl/8hekyo15XTuQ6PJxGAoSnidyqhiyJIhNLyS\nhldzmIxrM2SvtYyUFsODwSCLOw19Uom3kpDrNGTCCSPF8Fh00+nYOGIEu+127jx6NLxnvqhIxF0d\nOnQUna4ni8r+GrfOVQqhxUuRkSKJcMDppI/BED9FB/zmN1BQMBenU6Jo+Hzi81Iqv71RDqZiE2qL\nmo3HNkrqGSEkmqB65pln+NGPfkTPnj1Zty5+9bpljIXZp3X8s7Y2tTWps2eL8b8RI2DkSIy/+Q2+\nwkJ69u59MT9aF8aNE7Tdpk2SFJXDUYbf7yQ9fQYqVdfgRnt7LSdOPNJJSxm+2feWQKrrXncDvwf+\ngDDlXQZgMg0Nx4nEJd7u3s2YHmPYe2EvvoAv6t96woQJlJWV4elsd8XobZeuodQpSZ+ZTtOK6KmY\nG+UoKotFWGtlYkWUCiX3jbovpfHbceOEKezECQmPxr74TmOv08koi4Vhw4Zx1VVX8dJLL4knLkIE\nj0QwKEx9N9wwD4djNw0N8es5A4EA69evT6loJKOmIqEv0DPglSvAYYSsC7LXmUeZJeNEdjkc6JVK\nhplMqXca/ftDa6vgrENobBRJkjffHHf5+ILxbD+/HX9Amp9P12hYPXw4TR0dzK+owN25NGXqVDh4\nsBx7MIccUw5jekj/24Tg9/hxH3NjGmZi1qxZrFmzJrxLRQ5y1NTJk7BiBdx883QcjjJ8vhjP0cGD\ngmbNkC/UiaC4XkGVo4oRefKj1xbLSEkxvKysjNWrV/PUU08BSBeN0RayKjpw+f0cSOKNCUOvh//9\nX9ixgy1Ll5JRU0N5Ap9FQigUsGCB6DZiiobP56Ct7SwOx94oaioYDHL8+P3k5d2F1Sptrv2mSLVo\nXIYERNE4iHm4OV7XKCvDprdRaCvkQO0BBg8W94KaGrBYLAwdOpTtnbSExTIar/ccXm/XjUpK1xhm\nMqFWKNgjR1ElWMd3d8ndLDm6hCaP/HhmCE89BR7PAYzGrk7DW+Ml4A2g6xlNSO9xOMKTU88//zxv\nv/02VVVVskXDH/Czs2onpQXSp8qTJ0UX3revgQED/sqJEw/Q0RE9C19eXk52djY9esTmW8ajqWll\nQmoqFu217agaB3DsN1/ia5V2/sp1GqFE25BXY6/TGR82GQulUpjFIsMLP/4YrrpKcolItimb7pbu\nHKiV3v0BYFSpWDJkCOkaDd85cICWjg6mToWGhn1sqa3hodHJuwzXAeH8VxlUFBYWYrVaOXgwcVrs\nTrtdcr3rb38LDzwAGRkmbLaJUdOCwDempkI4Nu4YQ6qHSOoZIVgso3A69xEMdhW+YDDI448/zvPP\nP4/FYqGjQ0yvx07tWcdYcexy8N3cXD6svchAir59WZmfzxVKJTvef190j8loLincfrvYbz5ggAhl\n69TLnM59mExDaWlZR2ZmVyZLXd3HuN3HKCr6xcV/ryS4XDS+BUymoWIsNTaDqrPTAMI5VEql+LuQ\nGr1VKtWkpc2IihTJvCqTpq+aCLR3fcgVCoW80W/mTGH8kcoDQWyAu7r/1bxb/m7Sn2v69FZMpkbW\nr+9qp0P+jEie3x8Msj8ic6qgoIAFCxbw/LPPQnm5+D3EoKKugm7mbmQZ48dZQXQZkyeLw1Va2hQy\nM6/m1KmFUdekSk35fK04neWkpaUWJw7CBZ6WPxrdlHMc/t5hgv74m35o7Day4wsEg3xSXx/OmsrQ\naMjTapO6toF4XSPCmyGFST0nyVJUIWiUSt4rLmak2cyU8nIGlXpRqvaxraaOmwfHdzCxiE22TYWi\nkpqc+vprMdz3P51MY2j0Ngpbt36rorFbs5vh1cNxH5Y3XWo0mWg0GXg8J8KPffHFFzQ1NfGDH/xA\nvM5uISPFBmQaBxnxVnn5rjaDj+rq4v1SCeB0Otm5cyfXTZ7M9kcegaws4b/405+SptZGISsLrrwS\nli4V4mPntKLDUYZWm4vJNAitVnz2vN4LVFb+uJOW0id61W+Ey0VQ79X4AAAgAElEQVTjW8Bg6E1H\nRwP6of4or0Zw0CDx12K3y4YXSukakRSVNleLsdhI6+boVv7G7Gw+kaKoQrEiCbqN+6+4n7fL3iYQ\nTPxhdbsrUCgG8+KLXR+PUHxIJI653XTT6bBFcNhPPfUUJ5YsoS0vT6TxxuBi94H37v1bmppW09zc\ntbM69VHbtVitE1Lmc/0uPy0bW8gaOhbtxHMEPAFOPROfFKzL06HUK2k72zUdtd1ux6ZSMThiD8RF\nieEhXePQIaiuFocAGcT6NeSgVCj4fd++3JSdza2NeykqKqdY9zg6dfKxT/tue1R8SLKi0dzRwYX2\ndgbF7MH43e/gBz/ouhFnZs6lqWlF1ImfbdtSjg+Rwqazm5g2YFrSjX4WyxVhiqq9vZ2FCxfyyiuv\nhM2hUtQUiDWzlhIL+UcDpKnVbEmw+zsW69evZ8yYMUzPyWG72y1+IWvWiMGV0lKRAp0q7rkH/vKX\nqP0aQs9wkZkpXOCClrqPbt0WhHeFX2pcLhrfAgqFEpNpEIFuJ2m/0E6mV4lBqeSszydMSnv2UJpf\nGnaGx+oa5eXluDpPoqH9GpF/TCGjXyRKOqmgUAhaFO64Q2RRyZxgxheMR6/Ws+70uoQ/l9N5gIKC\noVy40PV+nfu6nOAhRFJTIaSlpfH0zJlskTGsSfkzIhHrBFerrfTv/zbHji3A73fR3t7Otm3bUkoy\nvhg9A6DpqyYsYyyk5V6B07WfQYsHUb+4ntqP4imJWIpKKtE25aIxdqxYPuTzxXkzpBASw1MRZRUK\nBT8rKuLRLDdtfgVcuDf5+yF+8dK0adPYtm0bbTJjxLs6ByIiNxTW1oozzOMRK9sMhl5oNJk4HJ3S\naFWV2FSXwui0FFraWqhsqmTq1VPjAgxjIUx+4vu++eab9OvXj9mzZ4eflysaIHQNx24Ht+Xm8s+L\noKhC0SH9DAYcfj8XvF6xL2HzZvjRjwQN+cgjQtdKhunTxXXdu0cVDZfrUHgXeG3tP2hrO0NR0bMp\nv8eLxeWi8S1hMg3F7TmEaZAJ18F4XWNg9kDqXHU0uBu44grBHtntIqKhpKSErZ0RIAZDEWp1WtSe\n6tBipsibg0KhkDf6DR8uRHGZqAGFQpFSHpXLdRCLZSgLF3bFpkt5NPbI7NCYZjSy0eOR3GuSqNM4\ne1ZQtQMGRD+emTkHm20ip049w44dO+jfvz8ZSUTTYDB40UWj8YtGsq7NQq/vhc/XjMLmZMiSIVQ+\nUhknfEeK4f5gkH93jtpGIuWikZYm3JXl5aLoJ6CmAHql9SIYDHKm5UzKP5ul/mMuuPL4y2oVW5Lk\nJfmcPtpOt2Ea0tU1pKWlMWTIkPDnNRZSesarr8L3vhefHxYVYLhtmzhxJ3PPy2Drua2M6TGG7MnZ\neM978ZyWX5IlOo0ympqaeOGFF3g5IqXT4xEynFxApmWMBccuB7fm5PBpfX1U3HkihFa7xm3yC23o\nO3RIfOgHDRI5Y4kOAkqlyKM6dAi2baOjvQmvtwqlUo/ROAivt5qTJx+nuPhdlMqLNBFeBC4XjW+J\nkBhuGmaKT7zdvRulQsmYHmPYeX4nOh2MHNnFRET6NSB+9NY83EzQG8R9LJqrvUmOolIokgritw+7\nnXWn11Fll98NIDKnhnHXXYI6PbDDh/e8F2NxtJt0T+fkVCxUe/Yw4dFHeeKJJ6LeY42zhiZPE8VZ\nxZLfN9RlSN0/+vZ9jfr6xSxf/m5Km9REqqkSo3FA0msBgv4gjcsbO/0ZynDirXmYmf5v96difgXt\ntV0j0JGdxpbWVnI0GgYYo38/JRYLh1wuvKncYMaNE1pGz54iGC8BFAoFE3tOFHvDU0AgGODA+c/o\nmz8OfUUG8ysOsVxm6yN0jlYPMaHURt8eQlNUUojVM5qaxLDPExKRplG6xtatogX/hgiHFKoUZM7L\nTNhtCDG8nF/+8jluvPFGBg8eHH5u+3YYOlSSUQXAOtqKfbedQr2eQSYTKxPkfYVQWVmJ2+1m6FAx\nUCK1lInMTPjzn+Hf/xYnNJk4kjDuuksI4hkZOCs+Q6PJDgcUHjt2L927P4DFMjLpe/s2uFw0viXM\n5ogJKondGkA48RbkwwshfvQ27A6PoahGWSx0BIMclBJZv/c9oTzKuFctOgu3Dr6Vv+79q+TzwWCw\nM3NqKHq9EDDf+7kL02ATSnXXxyUQDFLudMZnTjkccOoUsx9/nEAgwCeffBJ+avvX2ynNL5WdcgmJ\n4FLQaDLp2/d1Vq78mKlTkweuhbqMpPlPnWjd3oq2uxZ9oRAOzeYSnM59AGTfkE3e3XlU3FBBwCsK\nQGiLX6Q3IxYmlYp+BgP7pajEWIwbJ1z9SbqMEFIRw0P46uRXFBl8XFE8h0yrktc1w/nh0aN8EDnm\nGwG5TX1yuoZUsu3rr8N114kaGAubbQJtbSfFtOBFxKFLITJvKvv67IRFQ6NJB9JYt+49nnvuuajn\n1q+Xp6YA9L31BDwBvNVebktxiiqyywDhDN8h590pLY2PI3FLCPv5+WJooFs3HJXLCQTayMq6lpqa\nd/F6z1NY+HTS9/VtcblofEtEdRqdE1R7HA6C/fqJ41ZDA6UFpZKJt6WlpRw8eBBHJ4WRljYNh2MX\nfn9XMZAqGiGKStLol58Po0aJ04gM7h99P3/Z+xd8gfiRUq/3a1QqA1qtmG66/36o2eIk2De6OBx3\nu8nWaEiPzQrauxeGDUOp1/PSSy/x9NNPh+NFLlYEj4VeP5sTJ9rp2XOj/EWdaGpaRUZG6qO2cbsz\nzCNwOsvD/1/08yK02VpOPCTiS7TdtaAA99dt/Lu+npuzsyVfN2WKavBgMTxx660pvd9EJr9YLNq1\niGKrGotlJNOmQeNuM+tGjOCZ06d5TWIJVMjUF4tx48Zx4sQJGmO6lNhkW7sd3nhDjG5LQanUkJ4+\ni+bzS0RarMSUXSpwtjupqKtgbA/hQ0ifkY7zoBNvjUwAJHDkSICHH76SnJgiv25dV3SIFBQKRVjX\nuDE7m5VNTUlX74aKRghjLBb2ORzy1FZsHMmQIVFxJGHccw/U1GB37MLvd6LVFnDq1BMMHPg+SmXq\nMfbfFJeLxreEVpuDQqFFM7AF10EXPTRaAsAFn09wUWVljO0xlt3Vu/EH/OEDRXs7GAwGrrjiCrZ0\nahBqtRmzeRQtLZvCr582PQ3nXicdzdGbx27MzuaTujppMTQJRTUsdxiFaYUsOx6fVxUbH2KzwZV9\nHWy+EKNnyFBTkf6M6dOn079/f/70J7EeJZEIXl0tamwEYxCHTZs2MXZsKc3N7+JwlMte5/e7sdu3\nkZ6e4OgYg8hd4BBfNBRKBcXvF9O6vZWqN6rETWSkhR1basnX6ehrlA6CS9kZvn+/4KxT5MqH5g6l\nylFFgzux+FvZVMmhmu3olT70+l7hSJFBJhNbSkr484ULLIyJHZHrNDQaDZMnT2bt2rVRj8fqGW+9\nJViWfv3k31dm5lw8Gz8SorDhm7mVt329jZJuJRg04uuVOiWZczJp/EKaetuwYQP79rmYODF63Nvh\nEL/+ZFO/1jFW7LvsZGo0TE5LY0mD/O++ra2NTZs2RVGpFrWaPql0nrFxJPPnR+/RmDsXWlpwWC6Q\nljaNEyfupaDgJ5jNw+Rf8xLictG4BDCZhuJVH0WdrsZ7xhuXeJtpzCTXlMuRhiPYbOKPaU+nOTXZ\n6K3KoCJtahpNK6M51DEWC+7OjXlxuP560c4kMBHJCeJSOzT64uRfe81RL7c30XrXCFPfiy++yK9+\n9Svqm+oprymXdSJv2iS6MInVG2GsWbOG2bOvonfvlzh27AeyKzxbWjZiNo9ErY43x0nBfcyN3+XH\nPLLr5zGZBuPxVIaDJAHUFjVDlw7l3AvnaFrdhHmUmcNbGxIuW0q503j/fVExI01+CaBWqhmXP46t\n56SF6RDe2PUG9w+fjdk8HIVCydSpoqMLBKCnXs+WkhK2tbZyx5EjtAcC+Fp9eKu8GAdKF0EpiiqS\nmnK7xV6Wp5OwJBkZc1Bs20Vw/LiUfl4pbDyzkamFU6MeC2VRxSIQCPD4448za9aDeDzRqcJbtohm\nR6buhxHqNAC+l5OTcIpqy5YtDB48OG5gY5yUriGHUBxJSYn474UXRIy+RkP7fbfiMwXR12sIBNop\nKPhJaq95CXC5aFwCROoaUrs1AEFRfR0/ehtfNL4TJYZDYopKcorKbBbc6Mcfy77nGwfdyL4L+6hs\nqox63OU6GHViCXQE6DjhZtRNZhYt6rpuj8MRNvVFIaZohOJFFr62kOKsYsxaiUJDYj0jhDVr1jBj\nxgzy8u5Eq83l3LkXJa+72Kmp0O6MSP1DqdRhMPTD7Y5eYGXobWDQ4kEcuf0Iymw13nKXLDUFMNRk\n4kxbW2Iq48gRcZKcMyf5Jr8IyIUXhuBsd/L+gfe5sqBPeMdCfr4Y1jrcGTWaqdGwZvhwHH4/cw8e\npHZXC+YR5ij9KhKhohHZ4UYWjb/+VdDzQ4Ykfu9abQ7pR/S4RsTvJk8VG85uYEpRNJ+ZMScD+zY7\nHS3RB4p//OMfaLVarrnmcRyOfVEx6YlGbSMRKhrBYJB5WVnssNupjUx2jkAsNRWCpBieCKE4krIy\n8bc1ZAisWEHrzcXoayCwfjXFxe+hUCRfRHapcLloXAKEdQ2Z3RogL4aPHTuWo0ePhoP+zOYSOjrq\naWvr4poz52bStLIpvGwmBFldA5JSVHq1nrtG3MWfyv4U9bigp7o6DfdRN7qeOh79qYq33hKtfCAY\nZJ8UPVVTIy7oG73U8fnnn2fx9sUMS5dvnzduFPlIcqipqaGqqopRo0ahUCjo3/8vVFUtkqSpLrpo\nLG2IWusaQixFFULapDR6v9SbL/9zjv7HoSgBvaJRKhlqMklHv4TwzjtCAA8tlE8RyUx+H+z/gCmF\nU9D4z2I2l4QfnzpVCL8hGFQqPh08mN56Pa8tPY5qpPwq0OLiYnw+H5WV4rDhDQQ46HIxymLB6xW7\n5p95JoU3HwhgOeilvl91ChfHw93hprymnNL86DgatVktOvPlXZ250+nkpz/9Ka+++ioaTTo6XTfc\n7qPh51MtGro8HSqLCk+lB6NKxTVZWSyW6eblVruW2mzh9a8XhV694Isv4A9/gEceoW77r9G0QtHm\nnhiN/+8uUb1cNC4BQnEicZ1GUZFoJ6uroxJvJ04UQyOBgNh+N3bsWDZ3VhGFQkl6+kyam7soAF0P\nHfoiPfbt0SeUcVYrrT4fh6UoqhkzhHHq6NH45zpx36j7eHf/u7T5BAUTCLTT1nYSo3Fg+JpQSGHf\nvsKk/Oc/Q6XHQ7paTWasCL57tyiUMRNLBQUFFIwv4MzmM5Lvo7YWLlxIvLRt7dq1TJs2Leze1evz\n6dPndxw9eieBQNdpz+M5jc/Xgtmc2ga49rp2XBUu0qelxz0nVzQAut3VjfV3aNE7g3jOynsDAMZY\nrfIUVUeHKO533y1Mfrt2paxrjM0fG7eUKYRgMMiiXYt4ZOwjOBz7ora5Re7XCEGtVPJ2//6MrVTz\n28wGTkhN7iA63EiKar/TST+DAZNKFWbYUtK1Dx2C7GzqFBuSXiqF7V9vZ0TeCEza+AKXNT8ryh3+\n4osvMm3aNEo7U3QjneGNjWKTgUy2ZhxCfg2A23Jy+FCiaJw/f54LFy5whcQvon+kye+b4Kqr4OBB\nmvo0omwD3Y6TspOS/y1cLhqXAIL/PoZxqA7Xfhe99XrsPh/1HR3iL6isjKG5QznXeo6Wtha6dxcU\nwZEj4uuTjd6CdIChUqHgBjmKSq0W47cJuo0+GX0Y1W0UnxwSY7Fu91GxIyQiryYyPuTJJ4Vha2dz\natRUCMFgkFZLKweXH+TQofh95aHE50SrvkPUVCRyc7+PXl/I2bO/DD/W1PSl4MsThNdFonF5Ixmz\nMlDq4q9PVDTaAwHW9W5Hnabm2IJjCd3ZCXWN5cuFG7p/f8jOFhlDoQ9GEhg1RobmDGV31e6459ae\nXotKqWJi/mja2k5FbWCM1DUioVAoyD/kZ/aMHkwuL2eXDI0SWTRC1FRHh4g/T6nLANi6FcWkafj9\ndtzuyuTXx2DDmQ1MKZQetcu8JpPmr5rxu/2cPn2at956ixdf7KIyI53h69aJzl+b4tBRyK8BMDM9\nnVMeDydjbtqrVq1i1qxZkrvrQyY/2dHbFGBv349f7aXb7D+gaG8Xnf3SpYmNgZcQl4vGJYBKZUSn\ny4fu52mvb8dv91NisbAvYpOfWqlmVLdR4Z0WiXWN2TQ3r4niXaV0DUA+wBAERZUgVgTggdEP8Mfd\nfwTiqSmIjg8pKRGU6ge7HYy+iKJxpuUMKpWKpx98OhxBHYkNGxJTU6HVrrGmPkFT/Znq6j9jt4sb\nZ2Pjl2RmXiX/YjFo+LyBrOukwxNDBr+gRFbXmuZmio1Gen43D9dBF1+/Ej+6GkLCovG3v4lwphDk\n9mvIQM7kt2jXIh4e8zAu1wGMxoFRDuEePUQKeUVF9Ne017bjd/q5c0Ihf+rfn7kHD7JCwgQ4Y8YM\nNmzYgM/nY6fdzhirlQ8+EAyKnKM6Dlu3opg4iYyMq2hqklnMlAAhU58UtFlaLKMtNK1uYuHChTz6\n6KPk5+eHn4/sNNasSRjzFYfITkOtVHJzTk6cZ0NOzwjhosTwGPj9HioqbgCUZI16WIhU/foJF+XV\nV4tR3f8yLheNSwSTaSjutgpMg004DyZOvIVoXWP06NFUVlbS1Oky1el6oNV2i1oaYxllwdfsw3My\n+lQz3majoaODY1J0wvDhYmZ206b45zoxt99c6lx17Krahcu1P4rWCQaDcUGFTz0FW+odjDTFFI1g\nsIueikHIn/Hggw9SUVHBxo3RPotkRSPRaledLo++fX/P0aN30d7eRGvrZtLTZ0u8Sjx8Th8tG1vI\nmCsdSaLRZKBWZ+DxxIcWftQZg24ttWIebub8a+dpWCo9gtnfaKSpo4P6WNG0ulqcHG66qeux0tKL\n1zVixPDTzafZem4rtw29DYdjDxbLqLivk6KoQiGFCoWCeVlZfDFkCHcfPcq7F6J3i+Tm5lJYWMiu\nXbvY6XAw0mDhhRfg5z9P+W2HTX2ZmVdL7kxJBE+Hh70X9jKhp7wpMGt+FofePERZWRmPR4ZfARZL\nCU7nfgIBH199JcaDU4VllAXnfieBDnGQuK1ziirUafp8vs4pP/nP4EWL4RE4ffpnQAC9vrcY3Lj6\naqGb7tkjTE7jxskbAy8RLheNS4RIXSPKGR4Sw4PB8PpXEJ1GqGhotVpKS0vZFHFzjx29VSgVZMzN\noHH5RVBUkFQQVylVPDj6QRbtWiRiMyKKRtvZNpRGJdqcrt590pQg3p5OajbFFI3jx0UGQ2zQEJ1F\nI388Op2OF154gYULF4b/yOrqhPQyQn5/TpiaknN35+TcitE4kOPH78VsLkGjSW0ip2lFE9ZSK5q0\n+LWzIUhRVG6/n2WNjdySk4NlpAX3YTdDPh/CsR8ew7k/fgZfqVAwymKhLLbbeP99uPFGiEyGlVv/\nKoMJBRPiljK9sfsN7hpxFyatCacz9aLh2BUdhz7eZmPDiBH84swZfhOze/zKK6/k06++ora9nX1L\nTBQWJp9+C6O6WgTvDRhARsZsHI5dcTtTEmHH+R0MyRkiO4kHkHFNBq51Ll7+zcsYYgYV1GobOl0P\njh8/gseT2BsUC7VVjb5Qj6tC6IhjrVY6gkHxtw7s3LmToqIiuoX2xUpgjNWa2OQng5aWjdTWfojf\n7yY9vZOqvfFGweuuWCG6jfJy0W0MGgSffZaQsjr74tmL+v4hXC4alwhSzvC9DodIpNRq4cwZxuaP\nZcf5HQSCAQYMEPpVyLMjPXqbXNcA5EdvAW67DT7/PKFY9sOSH7Ls+H+wO/ZGCaZScehH3S5y1Vr+\n+BtN9Odxxw7ZdZ2Rpr5bb70Vv9/P4sWLgdT0DClqKhKCpnqTpqYVmExJZj0j0PB5A9nXy4/LgnTR\nWNbYyBiLhVytFn1vPT67D30vPX0X9eXgvIOSjuTRFgu7IotGMCimpn74w+gLhw2DM2cgSahgCKGl\nTAfrxIIkV7uLd8vf5cHRDwLgcOzFbJYuGrG6hmN3dNEAKDaZ2DZyJB/V1fFIZWV4qdScOXNYeuIE\no8wWfv0rxcV3GePHg1KJSmUiLW0KTU0rUv7yRNRUCB+s/IBmYzPTM6XHoiyWUezbt4eZMy8+K9Ey\npsuvoVAo+H5uLu91RrKsXLmS73wncRKBVa2md6rxMp3w+RwcPXoXhYU/IxBoC0ehU1oqhm3+KChm\n8vPFqP3f/w7PPit2cEhkWbV93cb5V86n/P0jcbloXCLEejX6G43UtLfT0tER1jXyzHnY9DZONJ5A\noYjXNdat64ost9km43Tup6OjOfxY+sx07Dvs+OzRM/8TbTYueL1USrWk3bsLimzpUtn3nm5I547B\n1+DxedBqu4cfl4pD3+1wMCXPgsMhRMQwtm8Xp+QYOLwOTjSeoKSbGPlUKpW89tprPPnkk3g8nqTU\nlN/vT2m1q0aTjUplorFxOX5/8tY84A3QtKIpygUuBVE09kU99mFtLd/LzQUIO8Ode53k3ppL3t15\nHJp/CH9b9DrWMbHO8C1bxLDC2JhVnBqN+LxcRLcR6df458F/MqHnBHql98Lv9+DxnIjb9Q7iY5GV\nJbxjIKhI+2471jHxiX3ddTo2jRhBhcvFrYcP0+b3M378eL42m1GfUFFQkDj+JQ4xeVOZmfNoaPgi\n5S/fcCbenxGJlpYWfv7zn9P37r40fCZNGVosV1BfX3ZRekYI1tHCGR7CHXl5fFxXR3sgkFLRAEFR\nXYwYfvLkY6SlzcDnawaC2GydnxujUcQGlZdHF4dp08RjV14pftdPPQURRcq+3Y51vEw6YxJcLhqX\nCAZDX9rba9APDuI65EIZgOFms9h7MWaMEImJ1jUii8aoUaM4f/48NZ0nFpXKgM02OWr0Vm1WY5tk\ni9sdrlIouD4ZRfX++wnf/x0DSzlu99ER4bJ2lsfvBN/tcDDGauHJJ7ti0wHZTmNn1U5G5I1Aq+qi\nuCZPnszo0aN55ZVXkuZN7d27l27duiVs9wHc7sMolQas1nGcPp18hKd5bTOmISa0uYnHZmI7jeaO\nDta3tDA/KyJypHOTH4iMKl2hjmM/iJ6oConh4cf+9jfRZUgdc0Mz2SkiJIYHg0H+sPMPPDLmEYBO\nEXyAbEx2JEXVdqYNpU6Jrrv0tWkaDSuHDUMJzNy/HzuQVlrK7veOXlyXARJF4xqam1dFjU7Loc3X\nRll1GRN7yifjPv/888ybN4/hjwyn4fOGOH8TgNE4Cp1uzzcqGpFiOEBvg4Fio5EPjxyhsrKSiSmk\n9l6MrtHQsIzm5jX07fsqdXWL0Wiy0GgifEUzZgg66k/Rnis0Gnj0UXEyqKoSG/8649ft2+1YSy8X\njf9PoVCoMBoH4lUdQ5utxXPS06VrREzERC5lihTD1Wo106ZNi8r1ycy8isbGL6O+T9Z86ZiEmxIZ\n/a6/XuwtqJY3UmWpW7EHc/j08Kfhx6R2aOx2iMmp224Tk6FlZQhDX2WlpDCx5dwWJvWMH6l5+eWX\nefXVDzh7NkBJSdzTYSSjpkIQU1Nz6d//DerqFkfld0mh4fMGsuYn7jIA9PpCAgE37e1iHv/T+npm\npadjjdhWGEq8BdF5FP+9GM9JD2d/2cUZF3SG+X3t9YpEvyVLRDGXQuRpIgWExPBVlatQK9VM7yUo\nGYdjjyQ1FcK0aV1FI1bPkIJOqeSjQYOYYLMxbs8emvLyUR9fkbBTjIPLFRdSqNPlYTQW09KyIemX\n76raxcDsgVh10je8o0eP8sEHH/CrX/0KQx8DugIdLRviqb5Tp0ooKjpAt27SUTSJYB5mxlPpwe/q\n6ibvzMtj0WefMWvWLDSx/iUJpDpB1d5ey/HjCygufg+/30VbW2X8+uKpUwVF9f770jR0t25C1/zo\nI3jpJZgyhda1F7CVphazE4vLReMSQlbXGD1aLINvb4/qNEaMEPR1cycDNXPmzKhcn4yMOXGrMbPm\nZQl3uDf69DTJZuNrr5dTUh8ak0kIZu+9J/venc79DC+4nkW7RFZIR2MHvlbB1Yfg7cy6KrFY0Gph\n4UL45S8RlWP4cMlh901nNzGpML5oFBUVMW3az7FYDhBx/43DmjVrUiway8nIuAqNJpP+/d/i6NG7\n8fmkOeOgPyiiQ1IoGgqForPbEHlFH9bVhampEGK3+KkMKoZ8MYQL71yg5h814dcJj97+61/CgiyX\nWRWZapkCeqf3JhAM8MKWF3h03KPhgQG5yakQpkzp0jXsu+1YRyc/eSoVCn7bpw+3ZObQ0aLFU7sE\nv9+f9OvC2LVLMqQwM/PalCiqRP4MgMcff5yf/vSn4RTbnFtyqP9X/GFqzRorXm8hLldF3HPJoNQp\nMQ014Sjr6jZuys7mwJo1TEmBmgIxUdfq81GTwOQXDAY5evQH5OXdTVraZBob/4NW2x2rNaajHzdO\nUFMjR0KnViiJiROhrAz/TbfjOujC8o9vtt3vctG4hAjrGiVmnPsinOFWK/TuDQcOMCJvBJVNlTjb\nnWg0gtIOMRGhJTchCkOsxsyIGr3V5moxDzXTvLY56nurlUrmZ2XJU1Q//KEQXmWmKZzOcib2u4sq\nRxVl1WU49jgwl5hRKLvokwNOJ3073b8ACxaIe1vVp9slqal2fzu7q3fLJttmZ9+Iw7GMHTIjph6P\nhx07djAlCWHu87XidO4Jp9pmZc3r3PS3UPL61q2t6HroMPRKLV01pGtUe72UO51cFRNCZ+hnoKOh\nIyqJWJenY9jyYZx87CTNG8S/VTjxNtabEQurVczep7g/WqFQMDx3OAdrD/LdId8NP56saHTrBrm5\ngvp27HZgGZO404jEhYN6bNUZeHMyeHHlypS/Tm5/RlbWtTQ2Lk26wnbj2Y1MLZoq+dyXX35JZWUl\nDz30UPixnJtzqP+8PjwiG8KaNWAwjMNuTy0gMha2CTZat65ZgrEAACAASURBVHXFgegDART79mEf\nJf/7joQydpOfBKqr36Kjo46iol8AUF//GcGgD6s1RgczGkXBmDBBRAwngkqFY8TNmErSUfXpkdJ7\njXvv3+irLkMSoU4jRFcMMho509aGy+8PU1RalZbhecPDLt7I0du+ffuiUqk4GhH9IcxP8RSV1LKZ\nhEa/sWNBp5P0bPj9Lrzec1hMQ3jgigdYtGsRjj3x8dhljmhTn8Egpvyq/y0tgu+9sJc+6X1I00uP\nwG7bpuXHPx7Bj3/8YwIS44dbt25l2LBhWOXWqXWiqWk1NttEVKqumNJ+/V6nsXFFHL0HUP9ZPVnX\nJ+8yQjCbR+Jw7OVfdXVcl5WFPmbUS6FUYB5hjuo2AEyDTQz6eBCHbzmM64hLTFDV1IiRuQTmL+Ci\nKarWtlb6ZfRDpxY0mN/fhsdzPCrmXgqzZsFXq4I49zol49Cl4PPBv4/YuWt4GrfPm8dvP/mEV7/+\nOqWd5XJFw2gsRqk04HTKF0qvz8uuql2SekZ7ezuPPfYYr776KtqIjldfqMfYz0jzmq5DltstGp4+\nfcZit6fuiYmEdbyV1q1dRWPz5s306d+fzy6i6yq1WtkmUzRcrsOcPv2/DBz4T5RKLR0dLbS2bqWj\no146ImfqVPGDVVcLViMBWre0YpuSKb/wJAkuF41LiLBXo0TcQNQKBYNNJjFaF6FrxIYXhu4Nsbk+\nIK9rNHzRQNAf/Uc6NS2N021tnG1rIw4Kheg2/va3uKdcrorOP1oN94y8h6XHltKwowHLqHgRPNYJ\nfu+CIL3rd1Bhie80Np/dLKlnADQ0iJ3gP/vZVfj9fj788MO4a1atWpXQJBWCoKbmRj2mVtsYOPA9\njh27h/b2rkIaDAZT1jNCsFhE7MSHdXV8T4ZSihTDI5E+PZ0+L/Xh4FUHGebRscftJnDnnSTk5OCi\nikadq46K+grs3q4bkMt1EIOhX1QkjBRmz4Z9S1xo87Ro0pNz8SAmOjv6t3LXaBt3X3stRQcP8s6F\nCzx84kR4JFcSPp/Q1iRs4wqFgqysxBTV7urd9MvoJ3kI+f3vf0+fPn246qr4NICcW3Oo+7grI2rz\nZkENZ2ePxeH4hp3GeBv27XaCAfHzLlu2jFvnzaPa65XOgpPAJJuNzRKj1YGAlyNHbqN3719jNApD\na2PjfzCbh2MyDZUebJg2TRwI771X7OFIgNYtrdgmfjM9Ay4XjUsKrTZP8MlZDaAC7/mI3RqRRSMi\nvHDsWEEPhKSImTNnRu1httkm4nYfibrxGXoZ0HbXRp10QFBU1yWiqL7/fTF6G/NBdTrLw/6MTGMm\nNwy8gfpd9dJFI+bUb6g+idaq59m341vdzec2S+oZIP5wJ0wArVbJ73//e5566ilcMX9sckmhkQgG\nAzQ1rZCMDklLm0Ju7u0cO7YgfAp27nUKTnqwfJJrLIzGAXjba2ny1DEtPT7YEKLF8Fjk3ZlH7p25\n1F17gIymZo7fcUfybzphgigaKZze3y57m5sH3UyNq4Z6l/i3T0ZNhTB1KrTtd2AoSa3L8PvhF6+2\no8hqZ6jZJEZvT53i8x49OOp2M7+iQnTWUigvh4ICMesrgWS6xvrT65lWFL9e7/z587z00kv84Q9/\nkDSAZt+UTePSxvAYdCg6xGQagtd7PmqsPVXouutQW9W4j4vx7uXLlzPvmmu4PcKzkQxjrVYqXC6c\nMbH5p08/i05XSLduC8KPNTR8hk6XH09NhTBunJiSuvVWoWvIdDDBQOfk1IRvNjkFl4vGJUVINHW5\nDmAZKW4iYV1j4ECor4f6ekoLhDM8GAxiNgtHamfSCDNmzGDjxo10dAh+XKnUkZ4+PS7AMHu+9D7k\nhEa/rCzBR3z0UdTDwgneNfn0YJ8HCbQEUPfqOg27/H5OeTwMNcXcbHfswDC9lJ07xT0hhEAwwNav\nt8p2Ghs2dI3aTpgwgUmTJvHbiBne6upqqqqqGC0RSxIJh2MPGk0GBkNvyed79folbW1nqKl5B4D6\nz+vJmp8l6y6XgkKholkzkLttdahkvi5WDI9F0c+LyDVuZeTJC+ywpeBYz88Hi0XSmBWJNl8bb5W9\nxWOljzGx50Q2nhURLXJO8FiYzTAh00FNempF45//BF2JnQkZVlQKBRqNhhkzZrB97Vq+HDaMDLWa\nKfv2SQu8mzYltI3bbKW0t1/A4zkj+fza02uZ0Tver/OTn/yE+++/n74xkfwh6LrrMA0z0bxKFIdQ\ndIhSqe6kHuMDH1OBdbwV+1Y7x48fx+VyMWLECO7My+MftbWJO65OGFQqSiyWKF2juXkdtbX/ZMCA\nv4Y/oz6fk+bmdQQCbvmiYTAIv8bJk6Ii/uMfkpe5DrtQZ6jR5UmPVqeCy0XjEsNsLsHp3CcyavZG\nTFAplcKvsXMn+dZ8tCotJ5tPAtGjt9nZ2fTu3Ztdnb4OkNc16j+vj+ORp6elccLt5pwURQWSFJXo\nNLp40sLzhdQW1fLZsc/Cj+11OBhiMqGNXa23fTvqCeNYuBCef77r4cP1h0nXp9PNIu2viDX1/fa3\nv+WNN97g7Fkxprp69WpmzJghmRQaCSlqKhJKpY6BA//BqVNP4fGcpOGz5C7wWASDQcp8fZiqOyN7\njbHYiLfai69VetmSQqGgu2IZg6vTWblKPtwwCilQVB8d/IjhucMZnDOYGb1msO60cFwmG7eNxEDs\n7GpJfvLs6IBf/AJKvm9nfETHOWfOHFasWIFWqeTvxcXMy8qidN++eJomiSlHoVCRmTmXxsZ4I6qr\n3UVZdRmTC6OLzrp169i5cyc//elPE773nFtyqPtXHTU1ghYNnUWs1m8vhi9fvpy5c+eiUCgYZDLR\nXadjbXNq3csUm42NnZ1/R0cTR4/eSXHxO2i1Xd1YU9NKrNZxOJ375IsGdC1KeeABsaRdonDZt9q/\nFTUFl4vGJUfIDBbiuIeaTBz3eGiLEMMBJvWcxOazolLE3htidQ0xersqKvXWNNSEQq3AWR59utUo\nlVyfnc1HcqteZ80SgU/7xQhpMBjoXPHaVTQcexx0L+3OK9tfCRclKT0DCJv67rtPmJg7X1boGTLU\nVEODGDUeObLrsZ49e/LQQw/x5JNPAqnFMYCIQk+Wams2D6Fnz6ep+PIxfK2+pH6EWOxzOjmlLCat\nXX48U6FSYB5mjvv3COPIERTHj3HVwivZrfNw/g8pRDgkKRrBYJDXdrzGo+MeBWB6r+msO72OQMCL\n2300pZ0ifo8fc6ObTw/K5ziF8M47IoX7vK2V8bauG8+VV17J6tWr8fl8KBQK/reoiOeKiphaXs5X\nnSGcBALiZJQkoEqOotpybgsj8kZE5U21t7fz0EMP8dprr2FMsqs1+4ZsGr9sZMXSADNmCN8bgNX6\n7cRw+zY7y5YtY+7croPLnRdBUU1OS2NTayvBYJDjx+8jK+sGMjKiP/cNDZ+Snj4dv9+DXi/dUQNd\nbs2pU8UhNWaXO3TqGRMuF43/X8FsLsHh6Ow09jjRq1T0Mxg46HLFFY1N58Qk08SJQh8MUcGxuoZe\nn49Olx91IlIoFLIU1fdzc/mgpkZ6mkWlEgt/OrsNj+ckanVmVMifo8zBsJnDaGlrCcdTSOkZuFxi\nydPIkRiNYpIq1G1sPicvgod2GMR6oJ544gm2bdvGunXrWLNmTdKi4fVW4/GcwGZL7sDNz/8f/GtL\n0M0+EzVGnAr+UVvL0OyJOJ17El5nGWWRFMMBsb3q7rsZVZBFXQ8Fh/54lvolMjRiCEmKxrrT6/AH\n/czuI4YFhuUOo8HdwOm6dRgMfVCpko8UO/Y4MA81ca5WRVWV/HVtbfCrX8EvfhmgzOEIr3cF6NGj\nB/n5+VHd8R15eXwyeDDfP3KEN6uqRA57VpaY800AEWBYRkdHdMba2tNrmdk72q/z+uuvU1hYyLXX\nXpv059TmarGOtvLFe+3MmdP1eKjTSGnyKwamISbaqto4svNIVMzNd3NzWd7YSHNHcuPgeKuVvQ4H\np6vfx+0+Su/e0SuM/f42GhtXoNHkYLWOSUyrlpaK37PTCY88Aq+/HnfJtxXB4XLRuOQwGvvT3n4B\nVTcvgY4A3gveLl0jtJnN72dy4eRwp5GdLf6WQjlAkyZNory8HHsE1ynrDv8s/sYzwWbD6fdzQG6K\n4+674cMPoa0tTs8AcSOxjbbx6LhHeWX7KwDsttvjO409e2DoUDHKC9x3nyh++/cHExaNtWuldxiY\nTCZeffVVFixYQG5ubtQOBCk0Nv6HjIwrUSqTb9BRKJQoN8/GPfot7PaypNeH4AsE+LC2lut7jKWj\nozHuZhYJ8yhzOMguCh6PcOQuWIBGqeQKmxXnBz05vuA4rdsTrP4cOBCamsRaQwmEuozQjUSpUDK1\naCr7z/0LiyW1VXT27XZspVZmzBBcvxzeektQ5pqBTnobDNhipr/mzJnDl19Gfz6npKWxdeRIFlVV\n8cknnxBIIQZXpTKSnj4rrttYe3otM3p13Zirq6t58cUXef3111PWpzJuymZDmZrIs4hO1x2VyoDH\nczKl14iEUq2kraiN+f3nYzZ3dUCZGg1XZmRIbvWLhVmtZpBBxZen3mHgwH/GTbs1N6/BbB6G2304\n3tQXC71eOO03bxZBpdu3C42jE94qLz6HD2Nx4q4sGS4XjUsMhUKFyTRE+DVCYnhI18jKEm6qI0cY\nmD2Q5rZmqh0i2mPSpC4LhcFgYOzYsVF7J6R0Des4K75GH+4T0QF9SoWC23Jz+UfMcpgwiorERqXP\nP4+anAJor2/H1+rD0MfAXSPuYuvXW9lde4y6jg4GxFIA26NNfUajcIk/9eJZOvwd9M2QFibXrhVx\nOVK44YYbRBeVnVx3aGhYSmZm8lMmgOuIC18T9L/+IY4cuT2lUEOAVc3N9DYYGGAyY7GMDC/vkYJ1\nnDVuJS8A//63uOP2FtTCBKuVfTkdFL9fTMX8ClxHZIq7UimmqCRyqA7VHaKsuozbht4W9fj0XtNp\natmK1Zp60bCWWpk9W75oOJ0iZ+z552GbPVrPCOGaa65h2bJlcY/3MRjYXlJC3o4d/K53b1p90ppP\nJLKzb6S+/t/h/2/yNHGi8QRj87v4/J/85Cfcd9999OvXL4WfUuBMYQ6ZPi95tuj3YLF889Hbw8rD\nTMmK12kWdO/OX6qrk3YwgYCX4vZVnLE9hNkc76lpaPiU7OwbaG3dis0mvz8kjJkzxXiY0SgMpG+8\nEX6qdWsrtvG2ixoCkcLlovFfQJwYHuo0IExRKRXKKF1j2rTo1NhYXcNqLaWt7QxebxeHoFAqyLw2\nU5Kiui03lw8TTXHccw/87W9xIrhjjwPLSAsKpQKjxsh9o+7juX2LGW2xxE8OSSTb/uhHsL1qM0Ot\nkyQ/nGfOiKiqITIJ5gqFApvNxt69e6lOkJXl8zlpbd1MZuYc2WsiUf9JPdk3ZZObdwsWyxWcPPl4\n8i8C3q+p4Y7O2BCx8U2+SzH2N+Jr9cVHo//pT6IN68R4m41tdjuZczLp81IfDlx5gLbzMoMLke7P\nCLy87WUeHvMwBk00BTW913QMgTOYzYmnzqAz2bazaMyaJYqG1IqH118Xn89hw2Bba7SeEcK4ceOo\nrq4ODzJEIk2tZuL+/TjGj6d079649aixyMyc22lkEwLx+tPrmdBzQjj0cv369WzdupWnn3466c8Y\niTXb1Ezu5Y5LvhUU1cXrGn6/ny/PfElBa0Hcc9PS0rD7/eyR29jYiZMnFzLO4GJfIL74BQIdNDT8\nh4yMOTid+xOL4CGE/iFBCOLvvRdOt23d+u2pKbhcNP4riBXDh5tMHHK56AgE4nWNs6K9mDFDaFih\ng9isWbNYvXp1+DWVSjUZGVfS2Bh9msueny1JUQ0ymcjTatkgt5fhuuvgwAGcLbsxm7sSA517nFH+\njAdHP8iahguMMMYIEMGgpLvXaIRBV22ieoc8NTVjhvwOg5aWFo4fP869997LwoXSMSAAzc2rsFrH\noVan9kdQt7iOnJuFMa9//zdoalpNff2nCb+mpaODlU1N3Nxp6EtWNBRKheg2dkR0G4cOwalTcM01\n4YdKrVZ2Oxx0BALk3ZFHjwd7cODKA1ExJGFEtqCdOG8/z9JjS7l/9P1xl/ex5ZGp8VPXkZyCaDsr\nCpW+UE9hoVgBGxpkCKGlBV57DZ57Tvy/XKehUqmYO3cuS6Ui+I8eRWEy8cupU3mwRw8m7N3LpgT7\nQtRqC2lp02hsFBv9Iqmpjo4OHn74YV577TVMsePfSbBiBVzzPTU1H0SL1EIMv/hOY/v27bTmt9Jx\nqCMupkSpUHBPt278RYZaBGho+IKGhqXcNPCn7JJYytTSshGDoTft7bWYTINQqVL4ea+4QiTaVldD\nYaGo9p2Zc5dCz4DLReO/ArFOsksMN6vV9NbrhcYQUTQmF04Oi+G5ucL3tKeT/SgpKaG5uZnTp0+H\nX1fKMZs2LQ3PCQ9t5+JPqrcnoqh0Orz33UigzY5eXxh+2LHHgXlUFz/bzdKNjNyJ1NfExI8cOyaG\n/CV0h0bTZpr2TZJM916zRp6aApFqO2HCBJ577jk2b94ctxo2BEFNzZN/oQi4DrvwtfiwjhM3O7Xa\nxqBBH3H8+P20tclvL/ukM9E2o1OxN5tHJaSnQIKi+tOfBE0QofqnazQU6nRhzalgYQEZszKomFeB\n3xNjjLviCpEg3NQVh//a9te4a8RdZBji19Q6nXtpCWSx/kx8dxKLUJcR6ghnzYKIcwoAr7wi6l3/\n/nCurQ1vIEAfg7TAPm/ePOmiETFq+2CPHrw/cCA3HjrE3xPcUCMpqkgR/NVXX6WgoID58+cn/fki\nUV8vPrJzHrfi3OvEW9XVDVoso3C5DuH3y3R7MliyZAlX3nAlhj4GSY/OXXl5LK6vjzPvAbS1nePY\nsXsZNOgjsg1Z9DMY4jY71td/EqamrNYUqCkQgy7Tp4s/NBCC+KJF+FracR9zxxl2vwkuF43/Akym\nobjdR9EWKvE7/bTXtTMutHQltJmttZWSbiWcbTlLk0fcEGbM6JqSUyqVfOc732HFiq6NZhkZV9La\nuhmfr+vDpdQqyboui/pP4ruNW3NyWNLQgFvGoeu4pQTLET+KCCOWoyw6c8ofDOLQ9WD13t/j9UXQ\nLlu2COokBrXOWmpdNfzq4WE880z0qHgwKCi4RKG1IRe4yWTitdde48EHHwwbHUMIBHw0Ni4nKyu1\nolH/ST05N+VETU1ZrWMoKPgJhw/fRiAgzbO/V1PDnRHraw2GPvj99nBMuhSspRFFw+0WbrgFC+Ku\nG2+zsbVViOAKhYI+r/RBV6DjyPeORO9/0GrFlrvObqPZ08zfy/8eHrONhd2+E4OphHVn1kk+H3Vt\nzE6F2bOji0Z9Pbz5Jvzv/4r/39zayiSbPCc+a9Ysdu7cSWtrjLgfY+qbnZHBxhEjeOHsWZ44eVKS\nQs3KuoaWlg2cbjpMk6eJYbnDOHXqFC+//DJvvvnmRfPyq1eLQ7fBpiLr+ixqP+w6TKlURkymQQm7\nyFgEg0GWLFnC/PnzSZuSRsvG+M6pu07HJJstbmVBIODj8OHvkZ//KDab0AQnR/g1xDUdNDR8Rnb2\nLdjtKeoZIUT+Q06aBHo9rYs2Yh1tRan79rf8y0XjvwCVyoheX4jHcwzzSJF4W2qzsb21VZw4r7hC\nmOKUasbljwuPtc6cGT1aHTJNhaBW27BaS+Pc4Tm35FC3OP5G1k2nY4zFwtIG6e1lTnM1Fnc+fPIJ\nAO117fjsQgQP4YjLRZ5Oz/CsIj6qiHCSb94smSG04cwGJhdO5s47VNTUdB14QEwDWiyia5ZCMBhk\n1apV4VHb66+/nu7du7No0aKo6+z2rej1PdHre0q/UAzqFteRfXO8sF5Q8BNUKhNnzz4X99xJj4fj\nHg9XRiTaCsd/4m7DOtaKY69D0BWLF4uJOYkfeILNxraIm6tCqaD43WL8Tj8nHjwRLaBOmyZMW8Cb\nu99k3oB5FNjieXQAh2MXfbtdw7rT65KKsLFFY9o0MdwXOvD+5jfw3e+KuQmAjS0tTEmTd7ObzWYm\nTZrEysjU22BQ0tQ30GRi56hR7LLbufbgwTiBXK22YbNNYunB15lWNA0FCh544AEWLlxIr169Ev5c\nUli5sisjMvf2XGo/iO7AbbaJtLYm785CqKiowOfzMXz4cNKmpknu7ABYIEFRnTnzC1QqIz17PhF+\nbFp6OusjikZz81oMhr7o9T1pbd12cUVj1izxhxcMCh74kUdoeXcfadNSSCJIAZeLxn8JYTG8c4Jq\nXOR6x4j5+8mFk8O6xuTJsHNnVw7V7Nmz2bhxI20R7u5QhHQk0qal0XaqDc+ZeIHx+wkoKodjD+Zh\nN4XjlMMieMQpbofdTqnVymPjHuPV7a923YhkOo31Z0Q+kFotpm2efrqr20hGTR06dAilUklxcTEg\nbtKLFi3i17/+dZQo3tCwlKysFKemDrnwO/xYx8bz8AqFkoED3+fChb/R3Bx9Mv+gpobv5uSgiXHA\nJ9M11FY1hl4GXPudsGgRPPig5HXjrVa2xuQDKbVKBn82GMceB2d+cabriU7TlqfDw6Jdi1g4Xlrr\nCQaD2O076Z03F7PWzOH6w7Lv0+/x4zrsiqIrzGYxDLdmDZw+LajwZyNWLmxqaWGyhAgeiTiKqrJS\n3Lh6x5vSMjUavho+nCK9nrF79nAsZl1xdvaNrDn1JTN6zWDx4sVUVVXx2GOPJfz+UggEYNUqwv6M\ntMlp+Fp9OA90UUo22yRaW1NPFV6yZAnXXXedGNyYbKN1a6vkhsA5GRmcaWvjUCcV2dy8lpqadxg4\n8AMUiq7P1tS0NLbb7cIEDNTVfUxOzq243cdQq23odN3jXlsWvXqJ01lohv+736XlXCZpvRKMd18E\nLheN/xLCYvgoM449DgYajTR0dFDf3h4VbTup5yQ2nxMnHKtVsFchLSAzM5PBgwezOWJ6JjNzHo2N\nX0ZRKkqNUng2JCiq67Ky2NLaKr5vDByOPVim3ANffw3798dRUwDb7XbGWa3M7jObIEFWn1wtRLaW\nFui8uUdi/Zn1TOslQuVuvFEI+0uWiOfk/BkhRMYxhDBgwADuvfdeHn9cTDsFg0EaGr5IWc+o+6SO\n7BuzZQ19Wm0uxcXvcuTIHeFQyEAwyPu1tVHUVAhW65ikoqm11ErrRwfE72iO9HRXX4MBbyDA1zFx\nL2qLmmFfDqPuwzqq3uiclBs1Cs6c4V8b32B0j9EMzhks+ZpebxXBoA+9vojpRdNZc2qN5HUgaEjT\nYBMqQ3RMy9y5sHw5/Oxn8PDDQmsDqPF6qe3oYKg5sXP86quvZsWKFV2UYpLJB41SyR/79+cnBQVM\n2rePZRFdcUbm1Wy9cJ7RmUN59NFH+fOf/5zSVrxY7Nkjpt1DDZ9CqSD3tuhuw2abgN2+LSp1IRFC\n1BSANkuLrkCHc1+8rqFWKrk7L4+/XbhAe3stR47cQXHx+2i10Yu8bGo1Q0wmttntnYa+pWRn30Rr\n65aL6zJCiBCofO0a3MpCrOveSPJFqeFy0fgvQXQa5ViusODY7UCpUDAm1G2ENrN5vYzpMYaKugqc\n7eIDl4yi0usL0OsL405F2TdnU784vmiY1Wquzszk4xijkddbQyDQht7UV3Dub72FfYc9LBaHsL2z\n01AoFDwx/gle3PpiV5cRcwqvslfR4G5gWK6YN1cqhYv4Zz8TjuLNmwUFIodly5Zx9dVXxz3+zDPP\nsHPnTlauXInbfZhgsCPOkCiFYDBI/eJ6SWoqEhkZs8nNvY2jR+8mGAyytbUVo1JJicQNMjSemYj6\nsY6zYv/0qOgyYrO6OqFQKJhgs7Ellv8HtDlahq0exrkXz4lJH42G4Pjx7P7wdzw54UnZ7+tw7MJi\nEa7h2X1ms/rUatlr5XZEz50LX3whPoOPR0wlb25tZaLNJhvYGEKPHj3o06cPW0JO9mTtZSfu6d6d\nL4YM4b7jx3nh7FmCwSCHGs9h0xlZ8eEvuPbaaymVWPSVCpYtg9jE9Nz/h73vjo6q3Np/JiEJIW0m\nHRJ6k94VRIqUUESwIEWKIla8CuKVa2/YUcErigVREUGpAkqXkpk0QjpppJOeTDIzmUySycyc5/fH\nSSYzmZLgt77r9fv5rJW1Mu95z3vOmTnn7Pd99t7PXhmCyr2V5vIC7u4hcHMLgk6X3uF4169fx/Xr\n1zHZInJQOt2+XwMA1nbvjh8qK5CYvgrduz8Ef3/7M6dZMhnOqVRQqU7Dy2skPDx63JgT3BIWobdq\nuRo+t/jB5ZcDDhNFbwR/ltHwB3AWwDUAZwA4ItsKAaQCSAJw2UGf/0p4e49CfX0yuvbrClODCfpy\nfRtFZVGZzdPNE2NCx5jra8ycae0HaG80gFaKql0U1XQpmoqa0JhnS1E9EBqK79pp4dTXJ8LHZ6w4\nq3/4YfCnn1EXq7GicdQGA4r1erOy7bLhy1CoLkT5yQMOqalpvafBxWLZPX8+IJUCb78N9O/vUBUb\nNTU1SE1NxXQ7Bae9vLzw+eefY926dSgrO4DAwIWdcoTqrupgqrdPTbVH375vwWCoRknJNnzb4gC3\ndwwxg9gLjY25DsfyHdCMumJv59X5YC1W1x6efT0x8vRI5G/KR/WRaqQO9ceMIondAkStqKuLM8fy\nz+o3C/IiOZqM9iOCHBmNAQNE//2aNSLD0YpLnaCmWmGmqARB9MV0wmgAwCQ/P1weNw7HlEosycjA\n0WsnMEE2BF26yPHuu+92agx7OHYMaK804jXUC+6h7lBdaBMWFCmqjv0av/zyCxYsWIAuFlnx0mlS\naC7Zp3/6eXpimGs5zhhGmKvw2UOr0WilpgDcuBO8FbffLsozNDVBfVENaUSQmCXezj/4R/BnGY3n\nIRqNQQB+b/lsDwQwHcAYAJ1Lcf0vgbt7MFxdvaHXF8D3Zl/UxdVZ+zUsKKppvafhQoHo6Jw4UZRz\nahXJHDduHGpqalBYWGgeOyBgIZTKo1azXZcuLgi6cydyLAAAIABJREFUNwhVB2wd4jNkMigNBiRb\nhPRZqaD26IGmiXfDRWiCR1ibZHKcVotx3t7o0jJbdnN1w3O3PoeGi2fsGw079Q4kEuCdd4Dt252v\nMk6dOoXp06eja1f7RYPmzp2LiRMnIiPjCwQG3uV4IAtU7a1C8PLgThkYFxc3DB26D5lF23C4ugKr\n7VBTrRBXGzEOt3c7/z2MbjI0653nSkyXSh3n0UB8sY34bQSyH8vGe8Y4zC52Lpei1V42Z4LLPGUY\nHjzcnDxqCZLQxGjgN8nWCJw5IwZsebRTzo7UaJw6wS2xcOFCHD16FExKEuugh3W+rGiYhwcujR4N\nH1dXfJh8EAmHKjBhggTe3n/sVVVcLP7ZW6SErApB5W5Liuq2Tvk1LKmpVkinSaGWq20KowGAUnkc\nC4y7cVRyH5y9cif6+iKzQYdCZSSCgu6FXl8Bg0EJLy/7dKRTSKWixI9cDvUFNaTTpcDGjaIGWgcJ\nhx3hzzIaCwF83/L/9wCcvQX+ZznvfyJanaY+N/tAe1kUeYvXasUQQ4tM3xl9Z+BCoWg0PDzECMuL\nF8Ux7IXeenuPalGntV5KO6KoXCUSPBgaim8tVhvti/TUjV0JXyHdKkY2tsWfYYk1/e5FSLkWV8Nt\n9fgt/RmWmDZNHNZeiYVW/Pbbb3apKUu8//4GAFUoLOx4xkuBqPyxEiErQjrs2wpPz35IC9qBMYyH\nDI5rN/v6TnKcQdzcDMlXX8B3vLd1kp8djPD2RpXBYL/2RAt8xvqg+MtiJBkAn3K1qFBsB4JgbPlN\n2zLB5w6Yi9N5p236NuY0wsXdBV17WxtoQRBFJ59+Wow2akWNwYDCpia7dJ09jBw5Ei4uLijbvbvT\nqwxLdHV1xUe9Q6BXZaBY1R2QTodSeeSGxwGA48fF1a69Qokh94dAeUwJY53oH/TzmwK1Wu6Ueqyp\nqUFCQgJmz55t1e4e7A6PHh6oT7H2azQ2FiA7ey0eGv48VCbgspMXtoeLCyZ0bUS25z1wdw+CWn0R\nfn5TrRzmN4T582E4fAaN1xrhO8FXDEaYMcNu9c4bwZ9lNEIAtJr4ypbP9kAA5wBcAWAb7P5fDh+f\nCairi4fvLeJKI8DNDd3d3cVIittuEz3egoBbe96K1MpUc7nOjvwaYmnMhbYU1VQp9GV6Gy0qQEw0\n2ltVBX1L1mn7Ij112nD4uudZ6RzFaDSY1I6S8LySjNohffBu/EdW7UXqIugMOgwLsp0VVVeLCr4/\n/2xTNBAAYDQacerUKbulOi1BRkIimYLHHlsHUwe1mDUKDbr4dYH3yM696Frxc30IVvkDmZkrQdrR\n1EAHK43Dh4HBg+EbEQZNtPNoFVeJBFP8/HDJjl+jFSSxVbkVz9/2MlTNw9H47Um7/XS6VHh4hMPN\nrS1EeE7/OTiVe8qmrzpSDb+ptob3xx/FWj4vvghkZoq/GwAoNBpM8vW1iSRzBIlEgsWLF6Ph+HHn\nkQ9O8L38e7hcB3Z/sROf6iYhtmjXH1KiPXYMWOggZsI92B2ymTJzKVhPz/4gjU4TPo8ePYpZs2bB\n006CY3u/hsnUhPT0xejV60X4SydjXY8e+MyZlDCAsbyMFDfRIKnVFyGVTu/gCp1gwQJofsmH70Sf\ntvyM554TU/w7ocDrCP+bRuMsgDQ7f+1/Qrb82cNkiNTUPABPArCvTQHg9ddfN/9dbJ2m/8nw8ZkA\nrTYevjf7QntFC5rYRlH16CEuIbOy4OnmiZvDbjZTCbNmWSdZRURE4OLFi9BbzEjF7PBfrI4ncZUg\naHEQqn62nY329fTESC8vHFUq0dxcBZNJh65d2+Ld6+K08F0xGvjkEwBiBFGcVmuz0oBCgZA59+J0\n7mnkq/LNzRcKL2B6n+l2qaCzZ8UJ5113iVRVe0RHR6NPnz4I64DGUCoPYfLkF+Hp6YnPPnMeCVL5\nYyWCV9iv5+0IqfX1KG9uxqohGyAIjSgqestuPx+fMWhouAaTyY7Q4PbtwFNPiQV6ojoOcZwulTr0\nawDA6bzTaDA0YPXy1XBfFgHNG79Al2V7XHuCduN7jEdFfQVK6qxrd2giNZBOtaaamprE8NoPPhBX\nuzNnirIbQIs/o5PUVCvuW7gQ3QsLQSdFlxzBZDLhnf3vYNGwRVg2ciS2jX0SHo1JWJF6EeobeNlp\ntSKt70xhv/va7ijfKTqHJRIJpFLnfo39+/dj6dKldrdJp1nna+TmroenZ3+Eh68HADzUvTuO19TY\njWQExCJMQ5sOI7pJDNxQqy9AKnXC6XaEUaOg1g6AdHhbpOVFnQ6vSyR4fdkyvP7663987D8BWQBa\nSePuLZ87wmsAHKnM8b8Rzc01jIz0piAYGTsglvVX67mjpIQPZmaKHVavJr/4giS5+dJmPnPqGZKk\nyUSGhJB5eW1jTZo0iadPnzZ/NpkMVCgC2dBQYHVMdZSacTfFURAEm/PZU1HBOcnJVCpPMClpprnd\n2GjkpW6XaKxQk/7+ZGEhr9bXs19MjO1FTZ1KnjrFl35/iY8df8zcvPrIau6I32H3e1i1ityxgywr\nE4cvsD5lbtq0ia+88ordfVvR2HidcnkATaZmZmZmMiAggNevX7fb16Q3UR4gZ2Nho9Mx2+Ppa9f4\nan4+SbKpqYxRUT1YU3PGbt+EhImsrb1g3ZiYSPbsSRoMNNYbecnrEo06o9NjJtTVcUhcnN1tgiBw\n0s5J3Ju6V2xISqIhuC+je0azIa/Bqu/Vq0tZVvatzRhLDyzlzoSdVm0xfWJYn1lv1fbuu+TChW2f\nd+4klywR/x8bH89Ilcrpddic+/nzTHJ3Z0pKyg3tR5Iffvgh3V9wZ0ZlhrntavpKbk18mf1jYpis\n1XZqnIMHyYiIDs7TKDAqLIraVHHM4uJtzMp61G7f6upq+vn5sb6+3u52fYWecqmcJoOJ5eXfMzZ2\nEA0GjVWfNZmZfLew0O7+JSU7mJq2hIEKBfM0eZTL/SkIpg6u0jku+x+h+qkvrBt//ZUcNYoUBGcT\ndof4s+ipYwAeaPn/AQC/2OnTDUBr/IYXgAiIK5W/DNzc/OHmFoKGhmz43Oxj6wy3SPKzLNXp4iJm\nr1oGTbU6F1vh4tIFgYF3Qam0Ft3zneQLQS/Y1cK5JzAQ8VotSlSxVtRUfXI9ug3qBtcQP+CBB4DP\nPkOkWo0p7aNlGhvFoPfJk7H+lvXYn74f5dpykMT5gvM2TnCgLbFqzhyxZshTTwEvvWTdp33lM3tQ\nKg8jMHAhXFzccNNNN+Gpp57CunXr7FIWtSdr4TXMy4azd4Ymkwk/VlZiTYsD3MOjO4YM+RFZWavR\n1GRbnlX0a7SjqLZtE5VFu3SBq5crvEd4oy7OuV9jlLc3ypubUWln9nm+4DxqGmuwZNgSsWHkSHSR\nNKDvI0TyjGRzMifJlnh+2+CE9n6NputNMOlM6Da4zUlfUQF8+KH414o77hBXuxU6A3IaG62KLnUG\nkvPnUTN6NA4ePNhxZwvk5ORg85ebEewfjJuC2vKAuoeuxBThLDb37YtZKSmdqoznjJoyn6erBN3X\ndEf5N+Jqw89vKtTqi3b7HjlyBHPmzHEolOge4g6P3h6ovHgFeXnPYtiwQ+jSxfp7ezIsDF+UldmV\nTqms3I0e3VdjtkyGy2UnIJVO++P+DAD6Mj30zX7wSd1vvWHePNBoQsFK28p+ncGfZTTeAzAbYsjt\njJbPANADwG8t/4cCkANIBhAH4FeI4bl/Kfj6tlBUt/ii7nIdhnt5oUSvR63BYBVBNSFsAgrUBajW\niUTy3LnWzsjWMEbLl2RQ0H2oqjpgdTyJRCLGoO+xzQL3dHXF0uBg5NUorGSWrfIz/vEPYNcuyGtq\nbCmJ6Ghg1CjA2xtBXkFYNXIVPor5CDm1ouzFoIBBNsdMTgZkMjFJFQD++U/RyX+lJam6oKAASqUS\nEyY4l/Kurj6IoKDF5s/PP/88CgsLsXfvXpu+N+oAB4AjSiXG+figjwVXLZNNR1jYemRkLIUgWL/U\nbeS0S0tFr6uFBLrfND9oIjvn17Cn+ro5cjNemvISXF1aEvBcXIDZsxEalIpez/VCyowUNBU1Qa+/\nDtIAT8/+NmNE9I/AufxzMLYkg2rkGvhNsdaPeuklMcTWsjRFaCgwdCiwPUqNyX5+trXhO8K5c+i+\ncuUNGQ1BEPDwww9j2tppuHPInVbnKJXORFNTARb5aHFx9Gi8W1SEx7KzzRnU7WE0ikmKFuLCDhG6\nJhRVP1ZB0Avw9h4Fg6EGTU225Xj379+PJUuWOB3Lb2ZX5P70IwYO3AFvb1v9/3E+Pgh1d8evNdbF\nvBoactDYmAeZLALz/f2hVJ3/n1FTAGrP1EI22x8uifHWzkQXF2jufg3VRzpXx7w9/iyjUQtgFsSQ\n2wgArVdUBqB1ypkPYHTL33AAfzxQ+0+EpTNcG6dFFxcXTPT1FcXqBg8Wte6Li9HFpQum9JqCi4UX\nAYiaY5cuiVwzAAwZMgRdu3ZFUlKSeWyp9HY0Nuaiqem61TFDVoagcl+lXVmDNSEhcGtMgLdPm9HQ\nxmnhc0vLoq5fP3DKFERWVtquNC5csIqbfW7yc9iVtAsHMw4ion+EXX+GpeYPIEpVvP66aDxI4Nix\nY7jjjjvg4uSlpNeXQadLh0zWFonj4eGBb7/9Fhs3bkSFxazTWGdE7elaBC3uuIiTJXaWl+NhO6VI\ne/XaBDe3QJv6G60rDbMR//RTYNUq0UK2QDpVCnWkY39FK6bZCb2NLIpEcV0x7h9xv3XnOXOA06cR\n9mQYwteHI3lGMpT5F+DnN9nu99/Dpwd6+vVEfGk8ANEJbunPSEwETpwQEzDb4+67gSNFKsyyuKZO\noaYGyMjAkEceQX19PTIyHMuZWGLHjh0wGAyoC6nD3AFzrba5uHRBcPASVFXtwzAvL8SPG4daoxG3\nJSWh0E59jpgYUYC5VyfkyTz7ecJrpBeUvyghkbhAJrsdarX1LLy6uhrx8fGY5yDDHxBFBjUDP4Zr\n0u0IDl7ssN9T4eH4pMTaKFVW/oCQkPvh4iJW/QvQx6GbX8eVDp1BdUYF2fwgkdFoJ19cljsEPUYW\n/qFx/84I/19GqzPca5QXGq41wNRgwlQ/P0RqNGISw/TpZjG6mX1n4vcC8Wb19xcLFbUqiEgkEixa\ntMhK18fFxQ2BgYusqpwBYjGgrr27QnXOdiYxzK0aRokHohvb6Im6uDqrBLjC9ethbGjAgPbB+u2M\nRrhvOFaMWIFvkr4x16luj/ZGAxBntUqlmKl7+PBh3HPPPfa/vBYolUcQELAALi7W5zN+/Hg8/PDD\nePzxx80v7+rD1ZDeLoWbf+flJnIbGpCm02GhncxDicQFN920G7W1Z1Be/q253cMjHBKJG5qa8kWP\n686dwIYNVvv6TfaD9rIWQrP9KKxW2HOGv3HpDbxw2wvo4tIuVjQiQvwdDAaErw9H2JNhKPjpOLrR\ncRrT3P5z8VuOuIDXyDXmyCkSWL9e1Aizl7d3991AtpcK031vUOjuzBlg2jRIunbFvffe26nVRmFh\nIV577TV8vONjJJQnWJV2bUVw8ApUVv4IkvDp0gX7hw7FypAQ3JKYaCPKeegQ0MFtZYXuD7c5xKXS\nmVCprI3GoUOHMH/+fHRrX73SAnl5G+E+rhamawEwqB077JcEBeFaQwOSWsJvSaHFaKwGAHgLFfCR\nNCChufP5Le1BgVCdVcE/wh9YsEB82FrQXN2MmpO1CDm5wckIjvG30fhfhrf3GOh0VyFxN8FrmBe0\nCVpMlUrb6IgZM8wl+2b0nWH2awAd+zUAkaKqrramqAA4pKi02ji4eo3HFy0CgM2VzTDUGqw4bvng\nwZianw+JZWp6fb1YoefWW63Ge/bWZ5GvysfwYNuluEYDJCXZCJyiSxdgyxZgw4YqpKSkYFYHYZnt\nqSlLvPrqq8jNzcW+faICb+X3lQhd5Tgxzx52lJVhTWgoPBysdtzcpBg+/Cjy8/8FjUakpMQKg5Oh\n0UQBu3aJv2M79dUufl3gOdAT2gTnyVSjvb1R1txsztc4X3AeReoiPDDqAdvOwcFivH2cqH/Vc2NP\nuE7MQuU/g6Avs5/vsXDwQhzLPobmqmboy/TmMOSDB0V75yhx3S2sCfA1Qpd6Y2HLOHnSrLm1ePFi\nHDhge39aQhAEPPjgg9i0aRPyJHmY3mc6vNxt/QYipWqCViuKQ0gkEmzo2RO/DB+Op3NysD4nB3pB\ngCCI13bffZ0/5cC7A6FN0qIxvxEy2SyoVOesqOCOqKny8l2orT2LYWN2w3eyL9QXHK8w3VxcsD48\nHB8Vi74yjUYBV1dvszSOWn0RTZ6TcELV8SrVEbSJWrgFuqFrr66ig+rECXOFt4rvKhC4KBBushvX\n8QL+Nhr/6+jSxRtdu/aFTnfVXNXtZh8fXNXpxOIsrUaDxIiQEVA1qVCsEW+mefOs/Rq33noriouL\ncf16Gx0lk81EQ8M1G2dt8LJg1PxaA2O9teR0XV0chgROwzmVCmV6fVvdYAtBP3ldHab06iU6dluh\nUIjCee3i04vURQj2CsbOxJ02137unGhj7NXsmTcP8PI6ht695zjMAgcAvb4c9fXJkMnsr2Q8PDzw\n3Xff4ZlnnsH1uOvQXdUh4M4Ah+O1R4PJhO8rKvB4D+cqol5eN2Hw4F1IT18MvV40uH5+U6FWXRC/\np2ftB/b5Te2cX2OGVIpzKhVI4uXzL+P16a/DzdXBQx0RIUYXADAa62D0LkL3GVORfHsy9OW2hmNi\n+ERU1Ffg2olr8JvsB4mrBI2NYsj+tm1i3R57+F2lwk06KY7+cgP5te0kZSdNmgSNRoO0NMcxLFu3\nboUgCHj22WdxNPsoFg22r2AskUgQGvoQyst3WbVP8vND0vjxKNbrcWtiIg5eaoKfHzBkSOdP27Wr\nK0IfDEXZjjJ4evaHROKGhgYxqLOiogJJSUmY237J3AKNJhb5+c9j+PBf0KWLH/wj/KE649xf8Ej3\n7jhRW4vipiZUVOxGSMgqM71YW3sG4YFz8Vs7v8eNQHVGBdmcFlqxd2+Rp5PLQRNR9kUZejxxA6q5\n7fC30fgPoNUZ3hq77+nqijHe3mIU1aBBYuZbXh5cJC64vc/tZopq3DiRxmktu9ylSxebkpqOKCr3\nIHf43eZnUz+8ri4WQdJJWBoUhJ3l5WIJyCnW3ESkWo2p06eLXuyrV8XGdtRUK87kncGy4cuwO2U3\nyrTWNb2PH3fuiPT3P4z8/HvgpBQ4qqp+QmDgXXB1dWxYxo8fj7Vr12Lv6r0Ivj8YLu6dv61/qqrC\nRF9f9HVQjc4SgYELEBb2BK5evQcmUxOk0mlQl54UZTJusV+/ubN+jdn+/jijUuFEzglo9BosH77c\ncecWvwYA1NXFwMdnLPr8ayBCHwxF8rRkNBVb6025urhiwaAFyDqaBdks8UXy0Ufi/WVH6suMcyoV\n7ukrw5Ej1sW0nCIxUeRWW4pwuLi44P7778ePP/5ot3taWhree+89fP/99zDSiDN5Z7BgkGNlgNDQ\n1aiuPmCTIyNzc8OhYcPwUPfueODLGtw0zzZ6sCOEPRGG8m/LITQKkMnaKKqffvoJCxcutDu50evL\nkJ6+GIMH74KXlxjtJYuQofZMrU1fS0jd3PBAaCg+K74GpfIQQkJWAhCpKpXqDEZ1X4h6kwk5DbaJ\nup1B7ela+M+xqOy4eDFw6BBqTtTALcCtU3psjvC30fgPwOwMn+wLjUIDkiJF1erXsKCoIvpHmEMk\nXVzE94MlRdXerwF0QFFZyD+bTE3Q6dLh4zMOT4SF4evycqjlaqu6wZXNzagyGDDc318kvD/4QNzg\nyGjkn8E9N92DNaPX4F15W6yCyeQ8ekWj0SAxUYFHHpmP5x0pjwGoqtqL4OAVjju04NWXX8Wg/EFI\nDEnssG8rSOKz0lI8eQPaSL16vYiuXXshJ+cJdPMcAqO+Bvrn1jjs7zfFca0FS0TIZDhTW4uXL7yC\nzbdvbouYsodbbxUFympqrLKGe7/QGz2e6IHkqck2wpWLBi+CS7QLZLNkKCgQVxgffWRn7BaQxO8q\nFR4cLhqZ1FSnp98GC2qqFStXrsTevXshtKuBrdfrsXLlSrz//vvo27cvLhRewLDgYQjxdhz55uER\nBl/fW+3Wd5dIJFjXIwzSqO5IGJuPtVlZ0HWgHGAJz/6e8L3FF1U/VUEmm2V2hu/evRurV6+26W8y\n6ZCWdifCwp5EYGCbofMa5gWhUUBDrvMX/vqwMOSX/wgv3ynmehn19UlwcwuAp2cfzPP3x4la58bH\nHowaI+oT660TOBcvBg4fRuknxQh7KuyGKx9a4m+j8R+Aj8/NqKuLRdfwruji0wUN2Q2iM9yOX2Pu\ngLk4k3cGJkG82dv7NSIiIhAbG2tVUlOkqLJtKKrARYHQJmjNM8/6+mR06zYYrq7dMMrbGwNM7tBm\n6OAzoU3OVKHRYLKvryiB/fjj4ps/LU3UlZg40Wp8ZYMS2cpsTOo5CZsmb8Leq3vN2ccxMeIE3FGV\nvhMnTmDq1Kl4800fnD8vRvO2R0PDNej1JZDJOg49bIhqQGD/QDy17SkUFTmWgbBEXF0dNEYj5lhU\n5+sIEokEN930LbTaRNQcfgbSax5Q32yrw9UK9yB3dO3dFdp4536Nvp6ekAhNaPLogbtv6qD+tYeH\nWLHr7FmoVNZZwz2f6Yme/+qJ5OnJVpnjU1ymwEXnAn2/Zjz1lMimtVbks4erOh26ubqiXzdP3HOP\n6FjuFOwYjeHDh0Mmk1nVhQGA1157DX379sWaNaLRPZZ9zCE1ZYnu3W0pqlZcvgz4ebkg7b6hMJCY\nkJCAtPrOrzrCngxD6WelkEpvh1p9EWlpyaiurrZRXyZNyMhYAW/vkejVy3rWI5FIEHBHAGp+dU4v\n9fH0xGKXE0h0b/PY19aegkwmprDfGRCAow6qbjpD7ala+E3xg6uXxcRj0CAIPv6QJMYgeMmNKSW0\nx99G4z8Ab+9R0OuLYDCIs3qNQoNb/fxwRasVtaBmzBBn8iTCfcMR5hOGy6Wis2/uXDGvoTWq0Nvb\nG9OnT8fx48fN47u4uCMo6B5UVe2zOq6rpyuClwWj4lsxJLWuLtYqP2NduRQlg1zg2rXt5opUqzGl\nNT9DKgXWrhUD+W+5xUb69Fz+OUzrMw3uru4I8Q7B2jFr8Xbk2wA6TqxqjZry9hYXM089Ja5OLFFZ\nuRdBQUshkTiZdbeg4tsK9PtHP2zcuBGrV6/uUJsKAD4rK8MTYWFwucFZl6urF4YP/wVuH3wFz5Bx\nUNc5V0aVzZZBddY5x20STNBXKzB55PrOzQIXLIDx9BHRV+ZrLeEa9ngY+r7VFykzUszV6fRyPcpH\nlePtA6eQl+fQBWPGidpazG8xpkuWAD/91AmKqrZWpDPtlAFesWKFFUUll8vx/fff46uvvoJEIgHJ\nThuNgIAFaGjIREODrTx9qwPcx60Ldg8Zgn/16oUZKSnYVlwMoRMcm/9cfxjVRjQldYOHR0/8+uuH\nWLlyJVzbOX7y85+H0ajGoEFf2v29Au4MQM0x50ajvj4FIRIV3qwdgOaWVVht7Sn4+4u+kzn+/kjQ\naqF0IDviCMpjSgQuso0ErPWbgd4D4//HdcL/Nhr/Abi4uMHHZzzq6mLNRsO3SxcM7tYNV7RacTru\n7Q20xLPPGzAPJ3PF5UVAADB2rHWNjfvuuw/791tneYaErEJl5R6bY3d/uDvKd5WDAqHVxsHHIj9j\ndJoECcNoxZva1E3YsEEMobSjLX0m7wzm9G8T9tk0eRMOZBzAtZprTo1GY2Mjzp49i4UtHZYvB7p1\nsxbfJImqqr0ICemYmjKoDKg5UYOQ+0Pw3HNiKdQtW7Y43aequRm/1tSYM8BvFJ6pVfCtkKG8RypU\nKuc5p/6z/Ts0Gj+k/oCQ5mJcd+3kLHDBAmhKTsDXe7xdf0/oA6EYsG0AUiJSUHelDqpzKvhO98eX\nF47is89E+XNn+K2mBvMDxICCCRNE/3ZiR8zfr7+KolV2uP/ly5fj0KFD0Ov10Gg0eOCBB/DVV18h\nOFi83oTyBHi7e2Nw4OAOL93FxR0hIStRUfGtVTspGo3FFoF2D4SGInbsWOyvrkZESgpKmuzXF2mF\nxEWCsHVhKN1eCn//+aisPIpVq1ZZ9Skr+wpK5VEMH34YLi72v0jZLBm0V7QwqByH3paVfY1ePdZi\nkJcPfqishNGoQX19MqRSMT/D09UVEf7+OHoDDnHBIKD2ZK1NMIhBbUBR1gT4Fp8Vf8z/Af42Gv8h\n+PpOFguqtBgNAA5Db+cNbDMagFhAprVkKiCG3l68eNGKovLzu63lpkuxOq7PGB+4+btB9buqpUB9\n28tfF12H8On+2NHiia5ubkZhUxMmWFbf6dFDfAlUW0uuCxRwIueEVRJWYLdAPDvpWTz1w3ZotaKx\ns4czZ85gzJgxCGzJi5BIxNy4l19uU/4W63ATPj7jHXyjbaj6qQr+Ef5w83eDq6srfvjhB3z88cdI\nSEhwuM/O8nLcHRgI/z9QPhQA8PbbcHn+FQwc8jmamgqh1aY47Oo3xQ/1yfUwao12tzcYGvDKhVfw\n6aSHEFNXh8bO8PDh4VBP9oJU09dhl+AlwRj81WCkzktF7alapKomw9D7NG6b5nzmqjIYkFRfj9tb\nVpwSCbBsGbBvn9PdxJv0LvtVDnr27ImRI0fit99+w2OPPYaIiAjcaeHwOpx5GHfd1Lk6KYBIUVVU\nfGdV9jgmRrxVR4607tvf0xORo0djmlSKcQkJ2O9AXr4VoWtCUftbLa6lBOLmm00YOnSoeVtt7TkU\nFLyKESN+s1IUbg/Xbq6QTpei9qR9n4TJ1ICqqn3o3n0tXundG+8UFUFZexa+vrfC1bUt/P3ewEAc\nrrYtd+AIGrkGngM84dHDmhWo+LYCngvGQSL1FTm8/wH+Nhr/IbTG9Hcb0g3GWiP05fq2JD9ANBot\neuiTe05GTk0OqnTizb1okRiJ1Pou8fPzs6HfVZy3AAAgAElEQVSoJBIXhISscLjaKPkpEYLQCE9P\nUepDMAjQxmlxzx198H1FBbRGI863qJl2scxXKCwUEysOHQJ0bRz5lbIrkHnKMMB/gNWx1k9cj9jf\ng3DzjEpHlU6xb98+G6XQ0aOB1avbaJNWB3hHVA1JlH1Zhu4Pt2Vz9+rVC5988glWrFiBBjvRJ82C\ngO2lpVgfHu50bIdITQXi44GHHkJIyHJ4eg5CevpdMBrtc+eu3Vzhc7OPlQKqJbbGbMWk8EmY1ftW\njPb2brsnOoBqnCukCjtKuxYIXBiIvpv7orFOwM49PTC6x3CczTvrdJ8zKhWm+vnB04KSuf9+Udre\n4SS1oUG8f53URFm1ahXefPNNZGRkYOvWreZ2kvg5/ec2ja1OwMtrGLp27YuamrZnYM8eMSnf3i3T\nxcUFr/Tpg19HjMArBQVYnZkJjdG+EXfzd0PwsmB8/boCwcEuZsUFnS4dmZn3Y9iw/ejWbaDdfS0R\ncGcAao7bXyVUVx+Ar+8t6Nq1F6ZKpejp4YErpQcREGBdHuCOgADINRqH59oeymNKBCy0XmUIBgEl\nn5QgfH04sHQpYEd650bwt9H4D8HXdyK02ngQJnPo7TSpFFEajchnzpwpOi8MBri5umFG3xk4nStG\nUfXtK4r9xVjo49mnqFaisnIvSOuZavD9wVBVX4KP563ml3B9cj269u2Kft29MUsmw66KCvyusiMZ\n0RpzP3068OWX5uZfr/2KOwfZhkZ1c+uGkNJHkBP4kV0xwfr6epw8eRKLF9sm673xhpgBf/asEVVV\nPyEkxEnYaQvqYusg6ARzKGkrli9fjvHjx+NZO+T9vqoqDPPywqhOFhWywTvviFXQWsJ0u3d/CC4u\nXZGZeb/Nd98K2WyZ3Qz9yvpKbI3dindnipFn8/39bXSJ7MFgUKPRRw3fH+I7dDaYdAISZcFYjULc\n2TQHP6f/7LT/iZoa3BFg/eIZOlSMpFU4ct+cOyfG8AY4zpEZPnw4UlNTsX37dqt6FAnlCXCRuGBM\n6Bin59UeYWH/QGnpdgBAczOwf79o3Jxhgq8vEsePh5erK0ZfuQK5A1l6n0d8cPbq75D5zUFNzQk0\nNV1Hauo8DBiw1UwfdYSABQGoPVVrowhAEiUln6JHj3Xmtld6h4Oa05AFWPt0fLp0wTSptFP3BEnU\nHK2x8WdU769G195dxTDbVatEB9V/aT2Nv2EBNzcZPDx6Q6dLMVNU/m5uGNytG2Lq6sRM3wEDzGFE\nln4NQFz1WyaD26OovLyGwt09FCrVBetjS93QdV4OJJmjzG0aucYcaruxZ098UlKCcyoVZtozGnPm\niMUWtmwRZ5QAjl87bjeevqoKqMwLganPWbN0hSWOHz+OyZMnm6kpS3h5AZ9/DuzYcQru7n3RrVvH\n/HbZjjL0eLyHVXJiKz777DOcOXPGyriSxEfFxXj2j64ysrNFGvHxx81NMlkESCNMpgbk5j5j11g6\n8mu8cekNrB61Gv39RbHBOwMCcFyp7LDgkEZzCT7SSXDRC2ZfmCOk7qzFtcAAvBkXitFfjcbR1KNo\nNNjqNQFiHZWTFk5wSyxf7oSickJNAUBDQwPWrFmDqVOnIsqi0BcA/Hz1ZywdtvSGw0CDgu5BQ0Mm\ndLoMnDwpGjZnEWGt8HJ1xY5Bg7B94EAszcjAxtxcNLSjBA/HHMbkHpPRLWMmlMojSE2di/DwDZ3y\nsbXCo7sHPAd72mSH19XFwGhUW60qxkquos4lFMfrbPOFFgcFdUipARCVrV0Br+Ft2fQkcf2D6+j1\nrxYRrn79xNywU7bFuTqLv43GfxAiRRUtGo2WIvSzW4rJAxBn9C3xtfMGzrMKvW31a7S+S+xRVECr\nQ/wHm2NzSArq9/Qzv4xUv6sgnSFy1rf4+kLapQtURiOGWmrrGAziCzIiQiSKJ08GduxASV0Jrmuu\n49aet9oc58gRYN48CT6Y+yaeP/e8+fxbsW/fPixf7ngFMX8+sGDBLsTFOdC2sECzshnKY0qEPmjf\nme3n54f9+/fjySefRE5ODgAxYU0gbyjM1gpvvSWGeln4fby9R8JorEP//h9BpTqP4uIPbHbzHu2N\n5qpmNJW0OWIzqzNxMOMgXp7aphY4zMsLEokEaTrntFNt7WkxymbhQjFUzQEKM4xwya7DMz/I4DOk\nGyLORWBA9QB898J3oGBrmK5otQhyc7NS+23FsmWio9lmkmo0ivzpIseRT08//TTGjh2L999/H998\n8405Z4Mk9mfsx9Jh9gsbOYOLizu6d38EpaWfmampG8EdAQFImzABlc3NGGWx6iCJL7/8EuueXwfV\n+/2hUv0OmSwCPXtuvOFzDF4abFMUraTkE4SHP2Ule65UHkVw4F14q6jIRjb97sBAXFSrO4yiqvqp\nCsHLgq2Mb+2pWoCA/zyL+331amD37hu+lv9r+B8VKvlPobz8O169upQmvYmRPpFsVjbz99pa3nLl\nitghKkosjtKCEZ+PoKJIQZIUBLG+T3p623i7d+/mnXfeaXWMpqZyRkb60WhsKxTT3KxkZKQPY4dF\nsfZCLU3NJkb6RlJfrTf3eSwri0EKhfUJR0aSY8e2fU5NJUNCuEOxjfcfut/uNc6cKRa/EQSBU7+d\nyq+ufGXeVlNTQ19fX2o0Grv7kqReX8FLl6Ts1UvD1FSH3UiSRR8UMeOBDOedSG7fvp2jR49mY2Mj\n5yQn85uysg73sYurV8ngYNLO+WdkrGRp6RdsaiphTEwflpXttN196VWWfl1q/nzn3jv5UfRHNv2e\nvnaNbzko1EOK321MTB9qtWnk2bPkhAkO+pFPj67i4QHJVu2fXvqUcx+fy/Rl6TQ1WRf5eSU/n//M\nzXV47MmTyaNH2zVeukSOGeNwnz179nDgwIGsq6ujIAgcOXIkf//9d5JkTHEMh2wfYrdoWGfQ1FTK\nEyd609dXYG3tHxqCJPlLdTV7REXx6WvXeF6h4IABA2gw6Ckf+wMjj/ZlZeWBP3Z+JU2Uy+Tm71ks\nJiazKs4kCAKjo3tRq03lrQkJ3F1ebjPOsvR0flZS4vA4gklgdM9oatOsC1QlTktkxZ4K6861taSf\nH1lb+5cqwvT/JVojqFzcXeB3mx/UF8VaBekNDWIZy5tvBq5fR6uuxl033YVfssSwKYlEXP0fPtw2\n3qJFixAZGQmlRQKQh0co/PxutZIV0Wii4Os7EeHreqN0eym08Vp49vOEe2BbuKDKaIRA4nJrgSig\njZpqxYgRwJQp+PXCl3b9GdXVYp2MefPEBKetc7bilQuvQN0kzuAOHz6M2bNnw9dJQZ/Kyj0IDr4L\nL77oi0ceMWus2YCCqKET9kTH2dzr1q3DwIEDsfq115Ci02FFyI3V2jDj1VdFwSY75y+TRaC29jQ8\nPMIwcuRpFBS8jOpq69pigXcGmh2jZ/LOIL06HU9OeNJmrFaKyhEaG6+BNMLLa5joayosBAoKbPrt\n2QN0L6rB2Cet/QxLxi1BTO8Y6Aw6pESkwFDTtnQ4XF2Nu+1Qh6146CHr0GgA4vLjbvsJiampqdiw\nYQMOHjwIHx8fSCQSPPLII/j6668BiNTUkmFL/nCGsodHD8TFvYjbbsvDjSq4W2JRYCDSJkyAymjE\nwnffxYyVK5Gbuw4eD8TC9dQyG5meTp9fmAe8RniZZUXKynYgJGSVVXGm+vpkSCRu8PIajvf69cOr\nhYVi/pYFVoWEYE+lrQBpKzTRGnTx6wLv4W1+urq4OjQVNiFoabsyATKZyB789NMfuqb/K/hDs4D/\nNARBoEIRwoaGAhZtKWL2E9kkyTnJyTxcVSV2WrKE/OYbkmRiWSL7f9LfPAuLjCRHjLAec/ny5dy+\nfbtVW1XVESYkTDZ/zs19jgUFb9KgNVDuL2fOsznMeTbHvN0kCAxUKPhKfj7vu3q1baCxY8VZpAXq\nk+Lo86KEtcpim+v78kty6VLrtkePPcr1J9eTJGfMmMGDBw86/X7i4oZSpYqkyUTOmCGWIbUH5Ukl\n48fEd3qGqtFo6PP221xy7Fin+tvgyhWyRw9Sp7O7Wa+voFwupclkIEnW1V2hQhFEleqiuU9zTTMj\nfSOpq9Nx0KeDeDz7uP2xTCZK5XKWNzXZ3S6WJH24reGxx8j33rPqU1FBhgQJvBigsCkNS5Kzds/i\n/rT9zN2Uy9gBsdRl65hZX88eUVE0OflOtVpSKhVL95IkDQaxNvG1azZ9a2tr2b9/f/7444827X5+\nfiyvLGfoh6HMqs5yeLzOYNQoLbdte5CC4Ly0bmegUqno5efHf/xyJw8qRrG2sZaXJ5/hpfO+NBrt\n//YdoeTzEqbfn06jsYEKRRB1OuvvKi/vRebm/tP8eX5KCv9dbP18NZtMDFYomOPg/st+MpuFb1mv\nTlPmprDkcwerk1OnyLFj/15p/LdDIpG0FHi5ANlMGVTnRV/GLAd+jdGho2EUjEivTgcguhRqa639\nnqtXr8budvxkQMAdaGrKh04n7qdWR8LP7zZ08e6CkJUhqD5QDdmMtmlZcn09Arp0waaePXFRrUaW\nTgeUlIhKie2k0E+6X8fE5mDIvrEN2ztwwFaO+q0Zb+HHtB/xe/LvSEpKwvz58232a0VdXRzIZvj5\n3QYXF1Fx/KOPRBWT9ij9tBQ91vXo9AxV6eYG18mTce4f/3CquOoQr7wCvPiimIVoB+7uIejatQ+0\nWlGy3MdnHIYO/Qnp6fdBq00GIIZyeo/xxu7Pd2NQwCCHwnzuLi6YI5PhmIOImZqak+asYQBiGOXP\nbRFRpJjIv2G+Fp7BbvDsZ+ufWDFiBX5I+wH93++Pnpt6ImlKEvbEF+OeoCCnGfLe3sC991pQ4hcu\nAD17Wpf9gyh3vmLFCtx55524v11Ik0wmw6JFi/DCNy+gr7RvpxL6HCEhAVCrvTB58jVUVx/ueIcO\nsGvXLtw+pQdW9ijGWdlXGJmUhcpH+0Fy7SbU1Jz4Q2MG3RuEmt9qUFbwLXx9J1mF65KCjb7aO/36\n4e2iImgtltluLi5YFhyMH+ysNgSjgOoD1VYrCk20BrpMHbqvtS0sBgCYPVuMdvv/GH/A/v85KC39\nihkZKymYBMr95WwqaWKyVsuBsbFih7IycSpnEGes60+u55sX3zTvv3Ej+eqrbeMZDAaGhoYyMzPT\n6jh5eS8yJ2cDDQY1IyO9aTQ2kiTrkup4QXLByp/xZkEBn8kRVx5vFRZydUYG+dln5KpVNue/5MAS\nfnn8dTIoiJYkclWVSJPamwh9EvsJ+93bj48++qjT7yYzcy0LC9+xatu5U6TL9W2ny/qMeipCFDQ2\ndn5m+UhWFl/Oz+eePXvYr18/1tTUdHpfKhRk797WJ2EHubmbmJ//ilVbVdVBRkWFsr5eXMGlvpXK\nF29+kXm1eU7HOlhVxZlJSTbtRmMDIyO9aTCoLRvJ0FDzbP+LL8RFYs5L+cz9p33/hFavpfQ9Kcu1\nIn9ec7aGg765wEM/OfZntCI6mhw0SPSZcM0a8iNbv8yrr77KqVOnsrm52e4YiYmJ9HzAk5/Hfd7h\n8Zzh0UfJt94iq6t/YXz8uD/sGyHFZyksTMpdu/pSr68mSV5UqXhTbCyPPvxPxpxc8IfHTp6TRPlr\nS6lWx1i1q1RyxsUNtTnv+9PT+Vp+vvUYWi3Do6NpMFn7oaqPVjNhUoJVW9LMJCv/mSPgD6w0/q/g\nRn6/PxUNDbmMiupBQRCYdm8ay3eX0yQIDFYomN/QQiOMG0deuECSvFhwkWO+aHMyxsVZPLAt2Lhx\nI1988cV2x8mnQhHIysr9TE6ebW6vOVPDSGkky79vc7bdcuUKz7UYALXBwAC5nLpZs8gD1s4/XbOO\nvu/6sqq+Snxan3vOvG3HDltqqhV6g57uQe58Z9879juQbG6upVwupV5v7bQTBHL+fGtDmfVwFgte\nL3A4Vntcb2ykTC5ndctL/9lnn+WsWbNoaDHMTiEI5MSJ5HffddhVpbrE+PjRNu0VFXsYFdWd9fWZ\nXPvJWp4KOEXB5Pzl1mA00i8ykhXtDJVS+RsTE6fY7vCPf5CbNzM7mwwIIDMyyMvDL1OtUNv2bcGD\nvzzILVFbSJJ5DQ0MvCinol80857Po2B0fH6CQA4ZQsrPNZEyGdnOQXv06FGGh4ezoqLCwQikUqek\n60uu3PXjLod9OkJdXRtVJggmxsUNYW3tuT883o4dqzhiRFc2NVk7optMJu7YGcVzv3nx3/mpNi/t\nziD76/2MHPetTXtW1mM2EyWSLGhooL9czqLGRqv2SQkJPNJKZbcg9c5Ulu1qC+5QXVQxpl8MTc0d\nnyf+Nhr//WiNlNDpsljyWYk5+ufBzMw2HnPzZvLpp0mSBpOBgR8EslBV2LI/2bcvmZjYNmZycjJ7\n9epFU7ubOTl5NpOTI1hU1MZ35z6Xy/Tl6bw86jIFQWCVXk+/yEjqLfZ9MzmZDV5e4lNpgcMZhznj\n+xnih7Iy0t+fbInyufVW8rh9ip6RkZHsPbA3wz8KZ11Tnd0+169/zPR0+xFZpaXiwiY+ntRX6CmX\nyqmvcj7rt8RT165ZRQQZDAbOnj2bGzdu7Hjnn34Sp+2deFGYTAYqFIFsaCiw2VZe/h23Hgtg763h\njLkphpo4xxFkrbjfTsRMVtYjvH79Q9vOUVEUBt/EmycI/Pe/yfrMekaFRTk1TpcKL3HoZ+Is94Oi\nIj6SlUV9lZ5J05OYMjeFzbX2Vwkk+fHH5EdTjpDTp1u1JyUlMSgoiHFxcU6v7dO4Tzl121ROnDjR\naT9n+PJL8u672z6Xle2ymiDdCEpKtnPECA/++OMOu9sFQeDFj2fxw+82cUx8POOdRADa7mtkjHwo\n5UHnqctuW4qbTHrK5QFsbLQfKfdafj6XWPoYSe4uL+fs5LZouNboLGO90XyeiVMTWf6dbQSWPeBv\no/HXQEbGAywp+Zy6HB2jukdREAQerKpiROvNcPUq2auXeTmx5pc13Bqz1bz/Cy+QmzZZjzly5Ehe\naFmdtKKy8gAvXerGuror5ra4oXFUx6h5efhlKk8q+X15Oe9JS7PaT7N3L8/ecgtL2jli7z90P3fE\nWzxUr7xCrlrFnBwxEtUBE8EHH3yQW7Zs4QNHHuDTJ5622S4IJsbE9KdaHWV/AIrv7gEDyKx/5TPr\n0c47Tsuamiiz41Suqalhv379uHv3bsc7NzaSffqYV32dQWbmGhYXf2LTXq+vZ6+PAvnh0UBmb0pg\n7nMd00BHq6s51WJ2IAhGKhTBbGiwQ20JAqsDBvHpm2NoMpEFmwt47Wlb57T1LgL7f9KfcSVxHHX5\nMs+3rDZNzSbmbMhhTP8YmxDOVqhU5K9ui6j6sC20uKysjD179uTPP//c4XFH7RjFk9dOsm/fvoyJ\niXHa3/4Y5MiRoj+3FSaTntHRPW0ooI5w/frH3LmzO3v3Dne6+iw4vZ8Xvx3C3dfLGBoVxUeysljV\nAWVJis/hlSu3MOefOczd1Pa7V1TsY1LS7Q730xmN7BUdzQsWNHCj0cgghYLZLTxwweYCZj3W9jxU\nH69m3E1xNBk6txrC30bjr4Hy8u959epikmTswFjWJdaxzmCgT2Qk6wwG8YkYMECM2CF5KucUb/n6\nFvP+KSlizobRgtL/6KOPuHLlSqvjNDQU8MIFCevqRL6zoaCBiiAFBZPA8t3lTLo9iUuuXrXNW1ix\nggdff51PWUTENBoaKX1PygqtBeVQV0eGhvLVR8u5fr39a9VqtZRKpayoqKBSp2TIlhDGlVjPQpXK\nk4yPH9MhH/3oA0ae8FCwPrPeaT9LrMvO5oacHLvb0tLSGBQURLlcbn/n998nFy3q9LFIsrr6qN0X\nwcZTG7ni0AqWlHxOxQ+3MqpnZIcUVZPJRJlcztIWg+eI/iLJixfJzd7vsn7FIyTJyyMvUxWp6vB8\n3458m3cff5Y9o6NtoqbKd5dTEahg5f5K2x3LyljvIeObm0SjotPpOH78eG7evLnDYyqKFBz474E0\nCSZu27aN9957b4f7tMfZs+TQodY0LSn6DJOSZnZ6nMLCdxgbO4B33TWPW7duddpXEIy8+Esoc786\nQ1VzM5/JyWGgQsFtxcVsdrASFQQj4+KGUKn8jbpsHRXBChobxAc3MXFKh/kfByorOeLyZStK7KW8\nPD6WlUWT3sTo8GjWJYqrd1OzibGDY6n8Tdnp68ffRuOvATHBJ4CCIM7oCjYXkCQjkpN5sJWvfO45\n8qWXSIoUVfCWYObWtM1Sxowhz5xpG1OpVNLPz4/V1dXmtvLy7xkXN5yZmWtIiqF/GatEOszUbGJk\nnyhKL0SyzHIW3thISqWsLiigv1zOghY/yy+Zv3D6d9ZUBEmaPv2MfbqWMeGK/Rfg119/zUUWL949\nKXs4csdINhvbliWpqQvsJsO1R96HxfzEO5Xff99hV7F/Cy/sbDZ46tQphoSEMCur3eqlqkp0DmRn\nd+5gLRAd1b5sbm57cONK4hiyJYTVOvG3KS39khf77mb5OVtHd3s8mJnJD69fJ0leu7aeBQVv2vSp\nqCDDwsjze0pJmYy6JKW4gu3AKJFkZX0lPX5czw1ZV+1ur0uoY3TvaOb+K9d69vrOO1Td9wiDg0md\nzsR7772Xq1at6pQjetnBZdwWs40kWV9fz+DgYF69av/4jjB3rhgk0R4mUzNjYvqztva80/0FQWB+\n/quMixvChITzDAkJYX19x5ORrJjneemFu2hQiyuS9Pp6zkpO5tC4OJ61E1xRVvYtExOnmL+X1DtT\nWbKjhFptKqOietBkckwBtp7njKQkftRyD5BklV5PmVzOzG+KmTSj7R4q/ncxk2cn31AwAP42Gn8d\nxMYOZl3dFdacrWHCRHEl8GlxMR/IaMlwjo4mhw0z93/ytye5+VLbLO7TT8nly63HXL16Nbds2WL+\nnJGxitevf9jiYK5kyh0prNjXtlLYtzObw39qN8s+coScNo0k+Wp+vvl87tt/H7+I/8LmOiIvGDjM\nI4fCvp9stgmCwNGjR/P06dNWbXN+mMN3IkXnn06XTYUiqMMYeFOTOKtK3KthYCDZ/h1vDyszMvh6\nQUGH/Xbu3Ml+/fqxstJiRv3II3S4fOoAaWn3mI2g3qjn8M+Hc2/qXus+m47y0uJNVtShPVxSqTg0\nLo4mk5HR0b3MUVitMBrJWbPM8wvyjjuYv/AX5mywv7pqD6Mg0PP337hRbkuptUJfpWdyRDITb0tk\n4/VG0b/Trx8ZF8d58wTOnPkjp0yZwiYHeSWWKKsro/Q9KVWNbaug9957j8vb38xOcPWqmBrSzkds\nRnn5D0xImOzw5SkIAnNzN/Hy5RHU6yu5ZMkSvv/++506tl5fwYunfJn9cttqWRAEHqmqYt+YGN6d\nlsa8lomW0djI6OheVKvblBZUkSrGDohlVuZjLCh4vVPHzNHpGCCXm8clyaeys3l0sILKk+LkpLm2\nmYoghUM60RHwt9H46yAn5xkWFLxJU1OLpEeVngUNDQxSKGgUBPHB7N6dbAmljboeZSW3UFNjVgIw\nIzo6mv3796fJZKIgmFoSCfOYlfUo8zI3i9IlFs7NR69m8om1l6jLsnhhL1tGfi6GQWoMBgYrFFRU\nX6ffu36sbbDVaVi7lnz/8XwyPFzM/LKAQqHgoEGDbBz0BaoCBn4QyJSKFGZlPcL8/Nc6/L5KdpQw\nZV4KSfH0Ro4knU0MU7VaBisUIt3XCbz88su85ZZbqNPpRDmXHj1ItePII2eoqjpkpqheOf8KF+xd\nYPMC013TUR70O+UXQ6hSOaDHKL6QBsbGMqrkBOPihtmM8/rroi+69TKFA4cY7X6E2uTOvTx+Uyo5\nJPoSe23tRYPJ8XclmAQWvltIRbCC6rcOiz+AIPChh/bQ3b2ASmXHVBhJvnHxDT52/DGrtrq6OgYG\nBtqEjTvCQw+Rb7zheLtICQ2lUvmrzTaTycDMzId45coENjcrmZ6ezqCgIGq1nX/Zpieu4aXH17I+\nw/oGbDAaubmggAFyOTfk5DCr8EOmplrL/AiCwMszTjPydymbmjovZ7OlqIgzkpLMv3/m0XJ+1++C\n2VeX/UQ2sx+/sVUx+bfR+EuhtvYcr1wR/RRpd6Wx/Acx2mHU5cu8pGp5ADdsEJ3NFG+2Ptv6MLm8\nLXJi6VIxnaIVgiBw1KhRPHPmDDWaWMbFDSFJ1tenU/7hHCbc1jarNbaE+UZuyWH6/S2CVjqdaIks\nZtwfX7/Okb+8wvv232dzDRqNRXbwypXkv/5ltX3p0qX85BP7M9hvEr/h5K+GMFIuo15fZbdPK0x6\nE6N7RVMdo265TvFwy5fbctqtWJCayq0WS/qOIAgCV61axYXz51MYMYLct6/T+7aH0dhIuVxGed5h\nhn4Yas6FaI+ESQnM33OWCkUQlcoTDsd7t7CQX8fex6Ii69nwqVPivMLSJVV7uprxbt+Z/WEdYUFq\nKneWlXHizok8lHGow/4quYpKz2msnPE6v/j8C/bp05cTJui5d2+Hu7KhuYGhH4YyrTLNZtvmzZs7\ntdrIzRWD9jpKs1Eqf2Vs7GCaTG3UpNGoY0rKHUxJmUuDQTQS9913H995x3EouD3U12cw8mwgE2bY\npwAr9HpuyIzlkQsybrt2ig1G63yitFP/oPyN+5yGNbeHwWTi+CtX+FVpKQWTwPhx8dzySQofy8qi\nWqFmVI8oNqucU12WaK5pZt6LeX8bjb8STCY9IyN9qddXsfTrUl5dKtIObxcWcl0rjx4fT/bvb34z\nvnDuBW481RYmevq0mNJhiS+++IJ33XUX8/JeYm5uW4hV9OKPmfZim9PtQm0tx8bH01BnoCJYwfqr\n9eT+/eRs65DFRqOR7ttG8L0E25fo9u3k4sUtH8rKyMBA88qotLSUMpnMoTihIAh8//hAfvf7WLvb\nLVH6VSmTI6xF9xoaRL/Oh3aiT8/U1LBfTAwbjTcmK9Hc3Myvhw5lSkgIjZ1coThCavpqPvGjjEez\n2qv7taFsVxlTF6RSrY6mQhHC0tKv7KPvpdsAACAASURBVPYr1ql47IIPq+vbQjOzs8Uw5MhI674Z\nKzNYfOd3dhMz26M1F0BnNPJA+gHe/PXNHfPhOTkUAgL579HvMtAtkCmnUnjqlJi30VFU8qdxn3Lh\nvoV2t2m1Wnbv3p3x8fFOx3jwQeucHWdISZlnDk/W66uZkDCRGRmrzX6E6OhohoeHi6vLG0Ra6r2M\neu4fLPvG/mohK+sxxqU/xnvT0hgeHc1dZWU0CgL1+krK5TLGz/+t02Gx5mNqtQxUKJi8+zrjx8VT\n2aRnkFzBvTNj7AcrOEDNqRpGhUXx2tPX/jYafzWkpd3N8vIf2FTeRLlUTmOjkbkNDQxWKMRoCUEQ\nM/lassVzanIY9EEQmwziktRoFKOoLHM2tFotAwICqFAMMdMeglGgPOgCow7cbH5gnszO5jstORZF\nW4qYdm8aee+9Nt7Fa8pr9H0/kKPiYkTarAWCILpcWsRKRXz6qZiwYTTytdde47p16xxeu8FQx0i5\nP0f+O5DyIsf0jLHByOjwaKqjbamiwkKR2z57tq2t2WTi0Lg4mwSoTqGoiEJAAFdPnMi1a9fa0Go3\ngk3HI3jknL/Tl7Cx3ki5TFQF0OmuMSamP/PyXrLZp7LyJ+5WTOK2ljwelUq8Lb7+2nq85ppmMYcl\nu1JMurOjlmqJF/LyzJFlJsHEIduH8EzuGaf78MknmbNkCYOCgnhi0wnKA+S8/kkxb75ZoLNIW71R\nz15bezG2ONZhn6+++orTpk1z+J1duybGJqg6x4RRp8uiXB5AtTqGsbGDmZv7L/PYgiBw4sSJ/K4T\nSZv2x85m5EV/yvv9Sn2FdaCFRhNPhSKEzc0inRutVvO2xEQOv3yZJ5NX8dq19VRHqRkdHk2D5sYm\nJzuyr/Ngj4usPCv6Ml7dmcLxu+U0duJeNeqMzH4ym9E9o1lzVlyq4W+j8ddCaenXTE9fRlKUMK4+\nKkbXjL9ypS0S4403yKeeMu9z+3e38+erbU/nO++Isy9LvPHGOp461dUs4FZ7oZbxY+KZlDSd5eXf\n0ygIDI2K4rWWGZZRZ2RcyAkK3n42T+TzZ5/nhpMbODUxkZ9bJJrJ5baZ6TSZyNtuo27LFgYHBzvl\nqAsL32V6+nIeyzrG3lt7U6mzHyZY9F4R0+6xpTNacf68aDhac/c+KS7mrOQbiyAhKV7IrFnk229T\nq9Vy0qRJXL9+/R+SpdiXto+D/j2A0TH9OswZyH48+/+1d97hUVXpH/8mIZCEUNITQi8Sem9BEQRp\n6qogiKCIiIsi+hNc66qwsK6soiioCIrI6rKCIKBUA4QwM+kTSO89IWTSy2Tqvd/fHzeZJKRNVg3C\n3s/zzJMp586ce3Lvec95KzO3ZJIkDQYNIyOnMCHhcQpCvVH56tW5VGbs5YCQEBpMIufNa3RJWMje\nls2ElbWOFOvWka+/3uLvVpvN9FQqmdRglf1t9LecsX9Gy50tLqbB2ZkjXF0ZWruQ0SZrqZ6q5udj\n0zh4gNBippWv1F/VB4a2gMlk4ogRI3j8+PFmP1++vHVbRnPExT3KS5e6MC+vcbqSQ4cOcezYsb9q\nYZCSsp7h3z7K6IXRlutEEEyMjJzMa9caR7qLosjTuRd44pIbp4Rd4I8aDRNXJzJ5XfvsECkvpfDz\nB4K5ITWVFREVDPJUcHJwRJMEhzdSEVbB0DtCGb8insYyI8uMRs6PjpaFxq2GXl9AhaInzWYd8z7N\nY/wKybbwQXY2n66bcOsi52rVJQdjDnLOv+ZYvqO4WLIrNHT8iY//Bzdtsre43yavS2bWu1ksLb3A\n0NA7eL6kmGNvUAOULf4bS30WNpokdSYdPd73YHJxMqOrquihVLK4NoLvscekqOAmJCfzEycnLpo3\nr8XzNpnKqVR6sLpaOseNZzdy4b8XUhAb38DGYiOV7spGUbTNsXs3OWQImVhgoIdSyXgrXCeb/ZLJ\nky3jXFZWxnHjxnHDhg3tEhwJmgS6v+/OqGtRzMn5kPHxK1ptXxVdRZWPypJHy2zWMjb2YarV06nX\nF1CrTaJS6UlB0NNfrea8v2t47731hu86BGOtz766NuI+O1tS/rew49qRk9MkqNMkmDh452AGpAc0\ne0z6kiX8xsGhSTCeYBKY9W4WJ9uXcuuKiibjVWOsYe+PejM4J7jVsSDJc+fOsX///k3cX4ODJbfi\ndtirmZe3mwqFB1UqX2o0P1rer6ioYO/evXnp0qVWjm4bk6mcwcF9Gbp8F/M+kxZUWVnv8cqV2RRv\nuJbNZi3Dwkbw2rVv+FNREcdFRHDqxXBe8FZYPKDaovR8KVXeKhZe03LohWAGDFSx8FAhk7VauiuV\njKxsmm3BrDUz7ZU0Kj2VLDwkTRKCKPLh2FiuT5HVU7ckUVF3s6joeCMVVbZOR1eFoj61h7+/pfKN\nzqSj+/vujRLerVkjZR5p+J2bN9/LzZs3UzSLVHmrqE3WUhRFqtX+fCTqlEXVQZIURYqjRjOh96cs\nPll/AX8b/S3v/Ve9jeOFlBSuTUpiVpY0HzXnXGQwGNinZ09GTJjQopI7M3MzExJWWl4bzUb67/Pn\nu5ffbdQudUOqJX18W7z+Oum+I54vJlrnatqI9HTJHpPQuKBTaWkpJ0+ezOeee86qFWmlvpJ+n/px\nX5SU2r4un9aNuYxuJHpBNPP31ieXE0WBmZmbGRzcm3FxS5ieLvnTLvtcQ6dvIlle3lSIFR4qZNRd\nUY3ffPbZpqkDKAUN+qpUzU4yR+KPcPTu0TQLje1Bv/zrXyyxsWHEsWMtnkfoD9V06WRk0MxY1qTV\nu4duU2zjokOLWjzuRlasWNEoxYsgkBMnkt9+a93xgmBkSsp6hoX5UatNZVmZgiqVjyV2Zv369Vy9\nerXV/WmNkpIAKoN8qPA7wkJ1KJVKd+p02Y3aiKLIpKQ1jI9/rJF67JhGw0VfhPAnl0v8MTS3kfr3\nRmoya6j0UrL0YilFUaRqeQzfXniJ4bU2w6MaDXsHBzOngR9ySUAJQwaGMP6xeBoKDZbf3ZiaSn+1\nmnpBkIXGrUhe3qeW1WjU3VEsOi7tDmZERfFo3SrxwAFywQLLMRvObuBrAfWeSjExkoeowUDq9XlU\nKFyYmBhDDw8P5v2cx/Ax4Za2WUXn6Rx4itd1DVZyajXZvz+Lf9YwdEgoBYM0QU79aiqPJ9arCkqN\nRvqoVHxkrb5hrsJG7N+/n3Nmz5ZKvL3/fpPPjcYSKhRurKlpnEYjryKP3tu9eSFDMpJok7RUuCmo\nL2jb958kf9IU0/lECB9YYma77N8mE3nXXc1b1CmtSu+8806uWrWK5la+WBRFLv1hKdecWNPo/aSk\nPzMzs3WdStmlMoYOCW3iTVNQ8C0DA22Ynb2dX35J9h8ocmRwRH3tlbrfFkRGjIuwXDsWcnIk6X5D\nxP8X+fmcHx3d4nnc+fWd/Epdb9s6cOAAv3R0ZMGyZa2eB0muf17kkolVVLgpmPVeFq+XXaf7++5M\nLrZeDVNUVEQvLy+Gh0vX7Z49Us5IazRJOl0O1eppjI6+j0Zjvao1NXUDY2IeoEJxmd7e3u3LctwG\nubkfU/XLYAZ+15+5KXsafSYFEb7F8PAxjar11SGIIk9uT+JRn0ucfjiYe/Pzmzhw1KTVMGRAiGU3\nk/tJLsNHhfNYRgF9VSrm1gqKHTk57BcczJi8ciasTGBw3+BG0eFmUeTLqakcGR7O0lqNAWShcevR\nUEWVvydfMkhTSkxmubFraiQLYG2q5PTSdLr9041Vhvq9+pw5Uu2mnJwdTEyUjByPP/44vx/zPXN2\n1LuefnXtGmcp9zTOj/TMM+QWKdI4en40cz7Mofqamn0+6tPEd/9AUhFtu5uYmt10AjUajRw0aJCU\nAysrS3LvCW1s+ExNfYlJSWubHEuS59PP03u7N1OLU3ll9pVG/W6NSpOJfYKDeep6Ce+5R7LxWK2q\nfustafBaEQjV1dWcPXs2Fy9ezJqapgWNSHJr0FZO3DuROpPuhmMTqVR6NDth1CGKIiOnRDYKvCTJ\njIy3GRu7iNu2raOHRzkTEmp4qriYw8PCGq1KNUc0jJjQQkGq114jV9SryKpMJvZSqRjWSsK98Lxw\nem/3ZpG2iDt27OA93t40ubg01oG2QGWllEX+5wN6Rs+P5tzVc/nC/mYMMG1w8OBBDh06lHFx1XR3\nlwL62qK4+DSVSi9mZ/+ziXpIEAwMDJxIX9+ePNGkXu2vQxRFhoeP5aUAR4Y99yHNBmlCrqlJZ2zs\nIkZETGiSvflG8vfmM9DtMt98M4x9Lyr5XlYWSyr1zNudR6WHkvlfSDvRkoASKr2UrMmQrsPtOTkc\nGhrKQoOBolnkh/+OZ48TgXx1l5rFZTpL/xRlZfRXqznryhWLipmUhcYtS52KylRu4uUeUqCf1mym\nq0LBrLrt5ksvSZkKa1l0aBF3hu60vA4KkoJ0IyOnsKREyuKWHJXMkzYnWZhcf7P7q9U8mBNJpdJT\nqslQVNTIKFKdUE2lu5KPfvsotykaV4MjJUPkgEWlfLmZfE6fffYZ586dW//G0aNSSt5a47o0gbrT\nYGh58vk8/HMuX7WcIaNCrE66tjYpiatqbUDV1dLGYe3almM4LJw7JynKrZgM9Xo9ly1bRn9//0ap\nWkjJztR3R19eq2ze/TIh4XFmZraek6n0QilDBoRYaklLOzJXHj+eTk9PgT/88CbDwoazsjKGd0VF\n8ct8aRIRjALDhoWx+HQLevGqKsnFrrYC41sZGVzRsNB8C7x05iUOf2s4h95xB3VTp5I7d7Z5TB1n\nz0qC42Dkz+z/bn9e6HuB8cvjpWjydvDkk6vp5RXP995r/R8pCEamp79JlcqXZWWXm20jiiIfemgB\nH3nEiSUlzdts/ltyc3cxPHwkNYUnePk/w3npbHcGB/ehQuHKjIy3aTY3v9C4kcorlYxeEM1ApyCe\n6HOZpx0D+Z+7ghmnknaWFREVVHooWRrYOMj2nYwMjggM4S9Twxh1dxQj1Ro+GhdHp6AgDggJoatC\nwaGhodybn98kvxhkoXFrkp+/l7GxD5EkE55IYM5H0gr7+eTk+kIsSUmsTfRDUooQH/jJwEa654cf\nTuP58x4Wt9r8L/N5oN8BS60NdWUl+9QWcUlMXC2VmGzG/erSO5fY862eLNc1NlqUlUmq/5AYA71V\nKl5u4GlV52cfFXWDXn3dOnLRIlIQGB29sPm03g0wlhp52u00V/51JQ3mtjOI/libvqG8gWW4slJS\nZ7z4YiuCIzdXKlzUjgy2giDw9ddf55AhQ5haKzSV2Up6vO/B6OvNq3tIUqtNqRWWra82Yx6IYfY/\nJX14Ssr/8exZKbeTWi1NegUF31CpdOcv6V/TQ6nkdYOBOdtz2s439MMPpJ8fE4qL6aZQNNJ7N0dV\nVRXve+g+OrzqQNVrK6XU8O2MW1n78nU6vOnLgLQLNFWZmPF2BhVuCmZuzqRZa53+8JVXjHRyiuBH\nH7Wc4qS6OoERERMYHT2/1cXIpk2bOHnyZBYU/EKl0sOSxPPXUlj4A1WqXpbMw2atmZELAhi3McBS\n+re9mCpN1KZomVVYxTfT0+mpVPLxH9S84KFg4bHGqsmazBrGLo3lEy9f5h0BKmY12AnrzGamarVN\narI0BLLQuDUxmSotBtOyS2UMGxFGURQZXVXFXioV9XW6lgcflCLqavHf58/vor+zvA4MfJ1vvLHR\ncn+rp6qZsC+Brq6uzM7O5sqEBG7LliYlg+E6VZfcKfTyJG+oEPfn43/mU0ufsnhb1PHmm1IKB5I8\nWVzM3sHBlmSAW7du5bLmdN46HTltGot2PsbQ0CGNInSbI35FPJPXJ/PB/zzIZUeWNTHINiRHp6On\nUsmQZizyZWXkpElSragmmqfqaikysBmbizXs2bOHXl5e/PzHz+n1gRfPpJ5p85i0tFfb9KTSpmqp\ndFdSExvMCxc8OWhQEdU3zG1abRIjIsbzqeB/cMXpECrcFNSmtBGcJoo0rVjBSUeO8Iv81qu5ZWVl\ncfTo0VyzZg0jz/2LRV1tmB58qs3za4hJMPGeb2azz8q36nNikdRl6Rj3aByD+wTz2tfXWt1JHj4s\nVQeIjMyhr68vv/++cW4zURSYk7ODSqU78/O/aFVofv311xwwYIClKJRG8yNVKh9WVbUs6K2hqOin\nWgHU+P4xVZqke+/JBKsKIbWF5nIpz3tc5pp3QzggJIQfZGezIKeKKS+kUOGqYMamDJq1Zn6Uk8Pe\nwcHtqvUBWWjcuiQmPs3s7G0URZGhQ0JZppBW8fdevcqv6wyZISFSfYdaqXA+/TwH7xxMk2CiIBio\nVHpx8eJEfvGF5Jcd3C+Ygkng5s2bed/jj7OnQsGSBvrMsg+eYMXk7o30v9nl2XTZ5sK0oDSqvFXU\nX5MM0QUFkk01u4FjyKtpaZx39SozMjPp5ubG9PTmS5ia8pIZfMSOpT++3ezndWiOSIZ4s9ZMnUnH\n2Qdmc9XxVU1ccUkpiG9GVBTfzWq+gA0p7Thmz5Y2OpbFtSCQDz0klSn9FaVB95/cT9tXbLlsyzKr\nPKvM5mqGhAxgUdFPrbbL+SyNF/YP5eOP7b1RllsQBCMTE9/j18POcO/LP1nlErw+Lo4Ldu6kuLv5\nIkMkeebMGXp7e3PHjh0Ur18nBw3i5U1PcfDOwS2q3pr0TRS46vgqzv9uPq8VmHnHHU1ds8tV5Yy6\nO4qhQ0J5/eD1Jqk4Tp2SzGF1m9bo6Gh6enryu++kBVJ1dTyjomZQrZ7exKHiRnbv3k1fX98mMUOF\nhd9TqfRsUZ3VFteu7adS6cWKiuaLTZmrzYy5P4ZX51xtEvzXHgr+VUClR31iwtCcUu54Npwnugfy\n4xUhPJl4vVHa9KMaDT2USu7IybHquoAsNG5dKipCGRo6mKIoMu+zPMY+JBnEA0pKOCwsrF4XOWOG\nxfdQFEXO/GYm90XtY2HhD4yKmsGoKCnY7crieOZ8KKm5ampq2HPDBi4836AUpsFAsV8/Jn89mrm5\nuyxvP/HjE3zrwlskyYxNGbxyzxWKZpGrV0v1yRtiFAROV6vpd++93LKlacruOpKS1jBJtVjSbd2Y\n96IWXY6OSi9lo8jvakM17/z6Tq47ua7JDbAuOZkLo6NbdVMkSb1eSnUyaxZZViqSGzZIRg8riue0\nREpxCn0/9OUngZ/Q39+f999/v1XeOOXlKiqVntRqm0/RazYL/O67J3l06zyG3hfbYmpzURCZuCqR\nwfcp6R54gn8PXc+qqpYDID/IzubwsDCWpaRIyapu8F01Go18/fXX6evrK8UuFBZK+Wnekq6Ddy+/\ny6G7hlqqR7aEwWzg6uOrOe2raaw2SN552dlSJpw33mjsnCCKIksCShg5OZLhI8OpOaKhaBb5zTeS\nwLixLlNcXBz79OnNDRtmMCjIjbm5uyzBq81hNBr56quvcsCAAS0uZkpKpLxfWVnvNTGct4TZrGVS\n0jMMDR1siTNqCcEkMP3NdKp8VCw6XtSueB9DoYHxy+MZNiyMVTFVNBQZmPF2BpXuSiY8mcDC1Cru\nyc/nVLWaPioVX0tLY2JtbEt6TQ0nR0byrqgoXmnGrbohkIXGrYsoioyIGMvi4pM0a81UeiipTZFi\nK8ZFRPBEnfH14kXJuFyb3VKZrWSfj3ozPHIKCwulSPEXl+l4rovCkvO/xGhktwsX2H/q1Po8O198\nQc6dWxs85s6qqliqr6npvd3bUpJVNIuMujuKR565xl69pASFN7Lv8GF26tuX37aQHLC4+DSDg/tK\n3kMBAfV1Wxsg6AVGTo606PMbUqGv4LSvpvGp409ZPLl25+VxWFhYIztGa5jNUpbzXa5vUzd0TNvZ\n7lpBfU1Nn+0+llgMg8HADRs20NfXl2fOtK2mKig4QJXKt0lK9NJSHXfufJrffOPPa1nSSjxuaRxN\nVY3P0VRlYvxj8Yy6K4qmKhNjKsvpdfkXrgtazaTkFyypK0gpHmNjaiqHhIbWO1TExkpW6jfeIHU6\nJicnc9q0aZw/fz41Go3k7TZwoCQwGkxyH4d8TK8PvHg47nCzk1+8Jp7T903nAwcfaFLSV6OR5PSM\nGU1CYSiKIot+KuLZsVe5oJuG/T1NjIkyN2mj0RzliRO9OWmSB6dNm2SJSL8RURQZFBTE8ePH159T\nK+h02YyKuosREeNZUvJLixO7IBhYUPAtg4P7MSHhCZpMrU/GDSm9WMqwYWG8OucqSy+Utio8DNcN\nzNySSYWbgqkbUlmdUs3Ul1KpcFEw6ZkkalObqiLjq6v5SloavVUqjouI4LbsbKZptfwiP5+eSiWX\nxsVRWV7e7O/ivxAaNr/DBH4zqD3/W5vCwu+Rn/8pxo9XInNTJgw5Bvjt98PxoiK8k5WFKxMnws7G\nBnjgAWDWLGDjRgDAyz/di3u6qbFwZhFsbOxwdWUy9h+1xxNBAzFxIvDXjAxoTCbUbNkCFxcXfPre\ne8CwYcDRo8CUKSgo+AY5Oe/j1QR3LBv5GJ6b9JylT9VZBowbYsarLwl45oPujfpbUFCAcePGYdu3\n3+JVJyccGzkS03v0sHyu1+dCrZ6EESMOo2fPGdKbJ04Aa9cCv/wCjB4Nkkh5NgWmYhNGHBkBG5um\nl6TWqMWSH5bAztYOK2btxkvp2VCMG4chTk7WD+62bSjfeQDTDEH4x1eeePjhdvxjarmYeRHLjizD\nnvv34OFhjb/g4sWLeOqpp7Bw4UK8//776NatW4vfo9EcQWrqOri7P4gePWYgL+860tO/hNE4BosX\n74OTU3cIegGp61NReqYUPs/4wOkOJ9Sk1KDgqwK4znXFkF1DYNfVDgCQpdPhicRYFNZcwxzxFIZ7\nzECxwzQcKCzGeGdn7LnjDrh37lzfgcJC8M9/RtXly/jKYMDwRx7B3ClTYHv2LKBWA598AixZ0qTf\nyhwl1p9eD1sbWzwy/BEMdBmIMl0ZLmReQFB2EN6e8Taen/Q87GztmhwrCMCuXcA//gFMmADMmQP4\n+AClpYBSCZw9S6xcYMDy0jSIMZXwfcEXPmt8oOsSgfT0VyAIWgwatB09e87Gvn37sHXrVvj4+GDh\nwoUYPHgwRFFEUlISTp8+jYqKCrz77rtYtmxZs9fTjZAiioqOICtrM0gzXF0Xwtl5FOzsusFkKkZV\nlRqlpafh6DgUAwb8DT173t3md96IaBJxff915O/Kh6AV4DLHBV1Hd4W9uz1EnQhDjgEVygpURVbB\nfZE7XO51QcnPJSg9Uwrvp7zRZ2MfdPHt0upvCCQul5fje40GPxYXY5CDAx50d4dBFPG9RoMqQcC9\nLi4Y5ewML3t7ONnZYbGnJ9BOOSALjT8QomhGeLgf/Py+hrONP8KGhGHspbFwGuaEu65cwRofH6zy\n8QESE4EZM6S/7u4Ij5qFj6Ij8c79YRhQOQDqKWrkvTcFW3bY41iIHv6xkYiaOBE99HqMGTMGFydO\nxCBnZ+DAAQAASWw5NQ1HM9OgXlcAezt7S5/efBOIvGTCOynhGHNuNLpN6FbbVxELFy7E5MmTsWXL\nFpwrLcUTiYn4edQoTOneHYKgR3T0LLi7P4S+fV9rfKI//ACsXw8cOYKc4H4o/K4Q41Tj0Kl7pxbH\nxiSYsOD02whynI5jw4fi/l53WDeoJPDGG5KwOn8e4fm+WLoUWLAA2L4d6NrVmq8gPg3/FFsvb8Xh\nJYcxs//MZttVVFRgw4YNCAgIwPbt27F06dIWJy2jUYOCgm9w9Wo0VCpXjBmzCMuXz2zSvkpdBc0h\nDfQ5ejj0dYDno56W/8GNfTxfVoajBUnIqoiGu5CBZb1GY+GAZbC1tW/UNiIiAi+88AJGm0z455Qp\ncCkpAbp1A+66SxIWrQhjkSIC0gNwLv0c8irz0KNLD0ztPRWPDH8EPRx6tHhcHTqd9K9QqYC6n504\nEVi8GHB1ldpUx1Yj88A5lHh8DNvhaejdbRP6z1gDW9v668NkMuHSpUsIDAxEZmYmbG1tMXjwYMyc\nORN33303bG1t2+xLc2NYVRWJ8vJA1NQkQhCq0amTK7p2HQlX13lwcrLymmvjN7SxWpRfKkdNUg1M\nxSbYdbVDZ5/OcB7vDON1I65/fR1ClYBe63rBe5U37F3s2/7iGzCJIi6Wl+OQRoMTxcXo6+CAad27\no2enTtAKAkpMJtSIIo6NGgXcPnKgXVi9VfyjU1DwDSMjJ1MUBWZ/kM2YB2JIkiHl5eylUtUbsjdu\nJJctY0nJOYaEDOLnYR9z4t6JjH4omplbMymKki5/4Hex/FuD6nXqfftYZGPD1AZ1saWiSG78/uLw\nRtHLFy5IKvDCQlLzo4YqH5Wl8Mwbb7zBO++8k8YGhvWTxcX0UCqpKitlXNwSxsUtaVlXHBDAfOdH\nGexxnvq8tqO+jxcV0UOp5HrlHnp94NV2NlZSsn6vXElOmSIl6aqlvFzKHD5kiFRvqTWqDFVceWwl\nR30+qlG53dZQKBQcPXo077nnHl69erXZNrm55Lx5koeXNVUI20t5eTCvXJnNkJCBzMv7jGZzNfPz\n87ly5Ur6+Phw3759vypZ3++BKIosKwvi1avzqFL5MjP5A2bvTGHYsDCG+YUxe1s2dVnti/X4oyOa\nRZaeL2XCkwlU9FQw5v4YFp8ptqpUr7WYBIGXy8r4aloah4WF0Uup5OrERB7RaGSbxu2AKAqMjJws\nZaPVmRk2LMySK399SgpX1imFtVoKfkMYFtCbRUXHKYoiX9r4En/2/dmS/G5/ZiHtvw/l51+ZLcfQ\nz4+Ba9ZwyJAhLCoqot6k58S9E7ldtZ16fQFDQvozN3cXMzIkgdGgUisLDhRQ5aPi7q27OWDAgGb1\nxWeKNHw96CGeC/On2dzyDZ77SS6DvS5R6z1Jyo/Uin1id14efVQqiythYGYgfT/05fOnnm8UFd+I\njAwpvmDJkhZL/B0+LKVfWbVKqrN9I0FZQRz4yUA+eexJi2HXWkwmE3ft2kVvb28+8sgjjK8NqNPp\npDxhbm5SEL7R+ro5/xVlZQpedwHktwAADuVJREFUuDCfS5c6sEcPB7788rMt1ji5WUgC7UtGRExg\naOhg5ud/2SjLryiKLLtcxqQ/J1HhpqB6upp5n+b9Kq+km4loFlmuKmfaK2kM7h3MiLERzPkox+qU\nOb+WtJoafpyby4djY2WhcbtQURFGpdKLev01loeUW1xfq0wmDgoJ4b9q6yRkqJ5h9Ef2FK9Kbn2K\nXgouXL+QeyL3ML22dOyR2Ap6epKnfhakUq6PP05SKm86YuQIPvzdw1x8aLHFSFZTk8GTJydz4MBi\n7tzZdLXz6bpP6WbrRuVnyiafCYKR8fEreDliGoeqfuFraWn1SRfr2hgFpm5MZejgUNZk1khW0nnz\nyGnTJCNtA6rNZq5KTKRfWBhTbyiUU1pTyiePPckBHw/gkfgj9UY+QZCSFbm7kx9/3KZbbUUF+Ze/\nSM03bZLK516vus61P69lrw978aek1l1k26K6uprvv/8+PTx8OXbsLnp713DRIrEuI8zvSmxsLJ99\n9lm6uLhw/fpVvHz5aSoUbrxyZRYLCr6xVK+7GYiimWVll5ic/CwVChfGxDzI4uIzbXoxCQaBRT8X\nMX55PC/3uMzIyZHM/FsmKyMrf9PV+W+NqdLEohNFTFydSKWnkuGjwpn+1/R21/T+rYEsNG4fMjI2\nMSpqBs1mHTP/lsnIKZE0a82Mq66mh1LJwOzDVKm8qT/0Oc2+gxg1QcmMtzOYWpJKz4+H0ivoHD+t\nrX8RohK4x/FFFg69U8pjRdJgMnDc5nF0fNaRYVH1vuZpaeSgQSauXfsp4+KWWnImCYLArVu30tfX\nl6H/DqXKV8XUjak0V0u7GJ0um2q1P2Ni/kSzWYpCvT8mhqPDwxlcG3xXnVhN9XQ1oxdE01jSYIkt\nCFJqcnd38uWXycJCniou5qCQEK5MSGBVK7uQX9J+4ZjdYzj1q6kM/ff7FKdPl9RRMTHtGu/UVPLR\npwvosPCvdHjHjasObmy2Jnp7uX5diiHs00fgsGG5HDhwFf38/Lht27YWXUF/DRqNhnv37uW0adPo\n6+vLd955h4UN0qQIgp6FhT8wJuZ+Xr7cjTEx9zM/fw/1+taD/n4LTKYqFhefZHLy81SpvBkRMY5Z\nWf+gTmd9Wd6GCAaBpedLmbohlaFDQqn0UDJ2USxzP85lpbqyXeVUf2uMxUYWnylm2mtpjJwcyaCu\nQbxyj5RPrSbdurQiHQFk76nbB1JAQsJyCEIVhg07iPS111GTXIMRR0ZAZfgR1VnrYOj3Hf7kMAcJ\nswLhkB0Ov8MTETtrBv4UcwWVucfwmLMB7415Gd1fehXa1Gu4s+IUJs11wdOvpuEVxWr0cOiBB4wP\n4K9/+Suef/7/4O7+Cv72ty74+9+BNWv0SE/fgJKSk9Bqn8GWLQEQReLw4cPo1asXjEVGpG9MR1lE\nHrptuYiKXl+ib99X0KfPK7Cxsa09B+LfhYX4SJWBx4/ZYtwZEwa/3R+9X+wNG9uml57p2jWc3bcP\n211dUdC3L3a5uWHetGlAax4wWi3EH49Cs3MbzJnp+Gy+C3o+8yIeGrEYQ92HtjnOOpMOv6T/gkPx\nh3A27Szu67cMzjF/wfH9AzFgAPDgg8B99wEjRrTejYbk5QGnTwMnTwIKBfDww8BzzwGTJkljolQq\ncfDgQRw9ehR9+vTBvffei1mzZsHf379Vr6vm0Ov1iIiIgEKhQEBAAK5cuYJ58+Zh+fLluO+++9Cp\nUyvOBaYylJaeRUnJzygtPQt7e0/06DEdPXrciW7dJsDR8Q7Y2Tm0qz91kIRen4Xq6ihUValRUaFE\nVVUUunefBBeXufDwWPybGJYbos/Wo1xRjgpFBSoUFdDn6NF1ZFc4j3GG81hndB3ZFY4DHdHZp3Oz\n199/g1AjQJeugy5Vh5qkGlSpq1AdVQ1TiQnO453Rc2ZPuMxyQbcp3WDn0NSr7GZT63hxS3hPLQGw\nGYAfgEkAolpoNx/AxwDsAHwF4J8ttLvthAYAiKIRaWkbUVx8HD7eT6MqoBPKyi/AdnQy7K7twpmL\n3ph6SkDlqp6oeKAMlyNCcX7kSGwvKsLimgqEn9qLMUFJuHrvaGS98gyKzSL2nlUggxcwtvp1POX3\nMpwcbaFSVeDwYQMMhhQsWHAWc+Z4wsnJCbm5uTh37hjS05Px5JNd8NRTD6NHj/Gws+te64oYjtKi\nANglTYN5x0q4jhiFbpO6obN3Z9BE6DOlm7gmqQbXl3TDJ3/SI72HgFk9e2JE167w7twZZhIaoxFX\nq6sRWF6OO5yc8IKjI5YePoxOBw8CNTXA9OnA8OGSj2anToBWC2RlSe6hkZGSJ9kTT4CLFkF1PRz/\nif0Pjicfh52NHSb5ToKfmx98uvnAubMzzKIZJTUlyK7IxtXrVxFdGI1JvSbh0RGPYumIpXBzcgMA\nmEzA+fPSxH/6NFBeDowfL3kq9+oFeHgAdnaSc1ZpKVBQAKSlSV0yGIB584CFCyXv6O7dm///ms1m\nqFQqXLx4EYGBgYiMjIS3tzdGjBiB/v37w9PTEx4eHrC3t4etrS1MJhNKSkpQXFyMzMxMJCYmIisr\nCyNHjsSMGTMwa9YszJ49G46Oju2+1kgBWm0cKipUqKhQorr6KnS6DHTp0htOTnegc2dvdO7sBXt7\nT9jaOsLGphNsbe1BmmE2V0IQKmEylUKvz4Zenwm9PhN2dt3Rrdt4ODuPR/fuU9Gz512ws7PCXe03\nwlxhRnVMNaqvVqM6uho18TXQZeogVAjo0q8LHPo6wN7dHvZu9ujk1gmdenaCbWdb2NjbSA9bG4g6\nEaJehKATIFQJMGlMMBYapcc1I4xFRjgOcITjEEc4DXWC83hndBvfDY5DHH8zwfR7cisJDT8AIoA9\nAF5G80LDDkAygDkA8gFEAHgMQGIzbW9LoVFHVVUUNJpDMJtL0UU3CuLJOTBm2MK+bxfELrDHBVcd\n9KKIcY6O8N2/Hw+WlEgT69ChyJo3BYerw5BcnIzOdp0xodcETHddjMvnXHDlCmA0AoMGAfPnA15e\nefjpp58QFxcHo9EILy8v+Pv7Y+7cuTCZslBWdh41NQkwmythb+8GZ+dxcHWdi86dvWAsMqL0bCm0\nsVoYNUbY2NnAoZ8Duk/tjh539YCdox1IIl2nQ1BFBVJqalBoNMLe1hZunTphlLMz7u7RA70dGqxs\nSSA1FQgJkf4WFACiCDg6Av36AaNHA/7+QI+mrp4kcfDng7AdYIvU0lQUVBVAZ9bBzsYOLo4u6N+z\nP0Z4jMBk38no2rntiUyjkQRCXTc0Gql7gOQq6u0NDBwoCZZ+/azflTREEARkZGQgLi4Oubm5KCws\nRFFREQRBgCiK6NSpE9zc3ODm5ob+/fvDz88PQ4YMgYND27uBS5cuYebMme3qjyiaoNOlQ6dLhdFY\nCJOpEEajBqJoAGkCaYaNjR06deoBO7vu6NSpJxwc+sHBoT8cHPrD3t61/YPQAVw4cwFT+06FPlcP\nc4kZpmITTCUmmCvMoJEQTSJoIiACto62sHWwha2jLeyc7dDZszPsvezR2aszOvt0hkMfB9jY/fGF\nQ0v8N0LjZhMIYHwLn00DcLbB69drH81xkzSCfzw2bdp0s7vwh0Eei3rksahHHot68F/YNNofAdNx\n+ALIbfA6r/Y9GRkZGZmbRMtWsl9PAADvZt5/E8DPVhx/++qbZGRkZG5RbrYuKxAt2zSmQjKWz699\n/QYkO0hzxvA0AIN+h/7JyMjI3M6kAxh8szvRHgIBTGjhs06QTqg/gM4ArgIY1jHdkpGRkZH5I/Ew\nJHuFDsB1AGdq3+8F4FSDdgsgeVClQdppyMjIyMjIyMjIyMjI/LbMB5AEIBXAay202Vn7eTSAcR3U\nr5tBW2OxAtIYxABQARjdcV3rcKy5LgApiNQMYFFHdOomYc1YzARwBUAcgEsd0qubQ1tj4Q7Jpf8q\npLFY1WE961i+BlAIILaVNrflvGkHSUXVH4A9mrdvLARwuvb5FAChHdW5DsaasZgGoC7ibT7+t8ei\nrt1FACcBLO6oznUw1oxFTwDxAHrXvnbvqM51MNaMxWYA79U+dwdQgt/Xm/RmcRckQdCS0Gj3vPlH\njtNoyGRIF0EWABOA7wE8eEObPwE4UPs8DNIN4tVB/etIrBmLEAAVtc/DUD9J3G5YMxYA8AKAIwCK\nOqxnHY81Y7EcwFFIMU8AUNxRnetgrBmLAgB1CV66QxIa5g7qX0eiAFDWyuftnjdvFaFhTaBfc21u\nx8myvUGPT6N+JXG7Ye118SCA3bWvb9f4H2vGYggAV0hei5EAnuiYrnU41ozFlwBGALgGSS3zfx3T\ntT8c7Z43b5XtmLU3+o1xJ7fjBNGec5oFYDWA6b9TX2421ozFx5DSzxDS9XGzY5N+L6wZC3tIaXtm\nA3CCtCMNhaTPvp2wZizehKS2mgkpxisAwBgAVb9ft/6wtGvevFWERj6APg1e90H9FrulNr1r37vd\nsGYsAMn4/SUkm0Zr29NbGWvGYgIk9QQg6a4XQFJZ/PS7965jsWYsciGppHS1j8uQJsrbTWhYMxb+\nAN6tfZ4OIBPAUEg7sP8lbtt505pAv4YGnam4fY2/1oxFX0g63akd2rOOp70BoPtx+3pPWTMWfgDO\nQzIUO0Eyjg7vuC52GNaMxUcANtU+94IkVP6YaXl/Pf1hnSH8tps3mwv0W1v7qOPT2s+j0XL23NuB\ntsbiK0iGvSu1j/CO7mAHYs11UcftLDQA68biL5A8qGIBvNihvetY2hoLd0g58KIhjcXyju5gB/Ef\nSHYbI6Sd5mr8786bMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIy\nMjIyMjIyMjIyMjIyMhKTIEXXdgHQFVKRn9sxXYfM/yC3a8ZPGZmbzVYADgAcIaVv+OfN7Y6MjIyM\nzB8Ze0i7jVDIizOZ24hbpQiTjMythjsk1ZQzpN2GjMxtgbwCkpH5ffgJwEEAAwH4QCo5KyMjIyMj\n04SVAH6ofW4LSUU186b1RkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZGRkZG\nRkZGRkZGRkZGRkZGRkZG5tbl/wH9UE+8rrphaAAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Last, we produce our data:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "G=np.dot(np.transpose(np.dot(Av, Gn)), V)\n", "d = np.dot(np.dot(np.transpose(np.dot(Av, Gn)), V),m) # Create synthetic data\n", "xd=np.linspace(0,1,len(d)) # make x array for data \n", "\n", "# Plot\n", "\n", "pylab.plot(xd,d)\n", "pylab.xlabel('')\n", "pylab.ylabel('d')\n", "pylab.title('Synthetic Data $d$')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 11, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Introducing noise to the data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is where we stood at the end of the last module. Next, to simulate taking data in the field, we are going to add a noise to the data before we perform our inversion. We will do this by defining a lambda function that assigns a floor value and percent scaling factor. Also, we will assume that the noise is Gaussian. We then add the noise to the original data to make a simulated vector of observed data. The superposition of our noise and original data is plotted below." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Add noise to our synthetic data\n", "\n", "noise = lambda fl, length, data, s: fl + randn(length)*data*s # introduce noise using a floor (f), length (l) and scaling factor (s)\n", "\n", "noi = noise(0, len(d), d, 0.04)\n", "\n", "dobs= d + noi\n", "\n", "#pylab.plot(xd,r)\n", "pylab.plot(xd,d)\n", "pylab.plot(xd,dobs)\n", "pylab.xlabel('')\n", "pylab.ylabel('d')\n", "pylab.title('Synthetic Data and noise, $d$')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 12, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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M4W9YsSgz2bPbb/nzDsxjwKYBNHmwjE3fvMTmzVCokP2Wn9KpoMRO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\nEREREXfzf5Qy2xNOHMQyAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Calculating $\\phi_d$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are now in a position to build up the data misfit term, $\\phi_d$. We will need a function to compute the 2-norm, so constructing a lambda function to do this is useful. Next we will make the matrix $W_d$, which is a diagonal matrix that contains the inverses of the variances in the uncertainty in our data. Again, we will define a floor and percent error for each datum. Assigning a floor to the uncertainties in our case will consist of taking the Euclidian length of our data vector and scaling it by the number of data values that we have. Last, we calculate $\\phi_d$ using our 2-norm function that we created. It is insightful to see what values have been assigned to our floor and misfit, so they are printed below." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Calculate the data misfit, phi_d #\n", "####################################\n", "\n", "# Anonymous function for 2-Norm\n", "L2 = lambda A, w: dot(dot(w.T,A.T),dot(A,w)) \n", "\n", "#This constructs the inverses of the variances. \n", "invvar = lambda floor, percent, data: 1./(floor + percent*np.abs(data))\n", " \n", "# assign a floor\n", "flr = 0.015*dot(d.T,d)**0.5/len(d)\n", "\n", "# Make Wd\n", "eps = invvar(flr,0.02,dobs) # define epsilon and Wd\n", "Wd=np.diag(eps) \n", "\n", "# Take the 2-norm\n", "phi_d = L2(Wd, np.dot(G,m)-dobs)\n", "print phi_d\n", "print flr" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "28.8794257836\n", "0.000200320925096\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Choosing a reference model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In choosing a reference model, we need to know something about the variation of physical properties in the subsurface. Given that we are looking for property contrasts relative to a background property, and assuming that we know nothing about the number of targets, their values, or their locations, a good first place to start is to assign a constant background value. In real-world situations, this would represent the background value of the surrounding earth (for example, the conductivity, seismic velocity, density, etc. of our country rock). In the case of our synthetic model, we are going to take the mean value of our model and use that as a constant background. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Reference Model#\n", "##################\n", "## A constant reference model ##\n", "mref = np.mean(m)*np.ones(M) \n", "\n", "# Plot \n", "pylab.plot(xc,mref)\n", "pylab.xlabel('x')\n", "pylab.ylabel('m(x)')\n", "pylab.title('Reference Model, $m(x)$')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 14, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Setting up the spacial domains" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we are going to set up the domains, with a vector for points on the cell centers and for points on the nodes. These will be defined as $l$ and $h$." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Domains #\n", "############################### # Set up domains:\n", "l = np.power(x[1:len(x)]-x[0:len(x)-1],0.5) # vector of distances between nodes, l\n", "midx=np.dot(Av,x) # vector of midpoints, midx \n", "h = np.power(midx[1:len(midx)]-x[0:len(midx)-1], 0.5) # Calculate distances between midpoints & take sqr roots of each value in vector h\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Calculating the model regularization, $\\phi_m$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As discussed above, we are going to first need to make our $W_m$ matrix, which is a partitioned matrix from two other matrices, $W_s$ and $W_x$, each scaled by a separate parameter $\\alpha_s$ and $\\alpha_x$. We are going to discuss the manner in which $\\alpha_s$ and $\\alpha_x$ are selected in more detail during the next module. But for the moment, we will set them as they are defined below. Once this matrix is built up, calculating $\\phi_m$ is a simple matter, given that we have made a function to compute the 2-norm already. For the sake of illustration, I compute and print $\\phi_m$ from the residual of our reference model $m_{ref}$ and our true model $m$. However, of interest to us will be the residual of the model that we recover $m_{rec}$ and our reference model." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Calculate the model regularization, phi_m #\n", "##############################################\n", "\n", "# Create Ws, Wx matriceshes\n", "Ws=np.diag(l) # put length vector into a diagonal matrix, Ws\n", "Wx = np.zeros((len(m), len(m))) # preaollocate array and enter values into matrix, Wx\n", "for i in range(len(h)):\n", " j=i\n", " k=i+1\n", " Wx[i,j] = h[i] \n", " Wx[i,k] = h[i] \n", " \n", "alpha_s=0.1 # Set alpha_s and alpha_x values \n", "alpha_x=0.15\n", "\n", "# build Wm #\n", "Wm=np.concatenate((alpha_s*Ws, alpha_x*Wx), axis=0)\n", "\n", "phi_m = L2(Wm, mref-m)\n", "print (phi_m)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.00557850734497\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Inverting for our recovered model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At last we can invert to find our recovered model and see how it compares with the true model. First we will assign a value for $\\beta$. As with the $\\alpha$ parameters from before, we will assign a value, but the choice of beta will be a topic that we explore more fully in the next module. Once our $\\beta$ value is assigned, we will define yet another lambda function to obtain the recovered model, plot it against our true model, and then output our results for $\\phi_d$ and $\\phi_m$. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "beta = 1000000\n", "# Set beta value\n", "\n", "# Get recovered model\n", "mrecovered = lambda G,Wd,Wm,data,mref, beta: dot(np.linalg.inv(dot(dot(G.T,Wd.T),dot(Wd,G)) + beta*dot(Wm.T,Wm)),dot(dot(G.T,Wd),dot(Wd,dobs)) + beta*dot(dot(Wm.T,Wm),mref))\n", "# mrec = dot(np.linalg.inv(dot(dot(G.T,Wd.T),dot(Wd,G)) + beta*dot(Wm.T,Wm)),dot(dot(G.T,Wd),dot(Wd,dobs)) + beta*dot(dot(Wm.T,Wm),mref))\n", "\n", "mrec = mrecovered(G,Wd,Wm,dobs,mref,beta)\n", "\n", "# Get residual of mref and mrec\n", "phi_d2 = L2(Wd,np.dot(G,mrec)-dobs)\n", "phi_m2 = L2(Wm, mref-mrec)\n", "\n", "\n", "print phi_d2\n", "print phi_m2\n", "\n", "# Plot \n", "pylab.plot(xc,m)\n", "pylab.plot(xc,mrec)\n", "pylab.xlabel('x')\n", "pylab.ylabel('m(x)')\n", "pylab.title('Model, $m(x)$')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "600.74350741\n", "0.00271419323233\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 20, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a last step, we will obtain our predicted data and see how it compares with the synthetic data that we used initially." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Get predicted data\n", "\n", "dpred = np.dot(G,mrec)\n", "\n", "#pylab.plot(xd,r)\n", "pylab.plot(xd,dpred,'o')\n", "pylab.plot(xd,dobs)\n", "pylab.plot(xd,d,'x')\n", "pylab.xlabel('')\n", "pylab.ylabel('d')\n", "pylab.title('Predicted and Observed Data')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 21, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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5hdHeo20+meSFvbdPSAnFQNM0Gi1qxPu+7/Piky/qHY4QBcqfl/6k43cdiR4Z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\nLEsVCEQBX5B1lZkQIoPyxcu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"text": [ "" ] } ], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This concludes the current module. For the next module, we will examine the constraints on our choice for $\\alpha_s$ and $\\alpha_x$, and then introduce the Tikhonov curve and a method for choosing $\\beta$." ] } ], "metadata": {} } ] }