From b5ddd5e92d454c743752d02306ac922ec3c77c2d Mon Sep 17 00:00:00 2001 From: Elizaveta Semenova Date: Sat, 2 Mar 2024 17:48:51 +0000 Subject: [PATCH] various edits --- 13b_GP_priors.ipynb | 1005 +++++++++++++++++++++++++++++++++++++++++++ 16_areal_data.ipynb | 231 +++++++++- 2 files changed, 1217 insertions(+), 19 deletions(-) create mode 100644 13b_GP_priors.ipynb diff --git a/13b_GP_priors.ipynb b/13b_GP_priors.ipynb new file mode 100644 index 0000000..a07c12e --- /dev/null +++ b/13b_GP_priors.ipynb @@ -0,0 +1,1005 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Gaussian Processes: priors" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Nonparametric models\n", + "\n", + "The term *nonparametric* means that the shape of the predictor functions are fully determined by the data as opposed to parametric functions that are defined by a typ- ically fixed set of parameters. In non-parametric models the number of parameters grows with the number of data.\n", + "\n", + "Nonparametric functions are extremely flexible since the shape adapts to the underlying patterns in the data, either linear or nonlinear, smooth or wiggly, without knowing what these patterns look like. This property may be useful to find unknown patterns in the data, in contrast to a parametric model.\n", + "\n", + "However, in parametric models, selecting the best model involves constructing a multitude of models with different forms, parameters and covariables, in the predictor, followed by a search algorithm to select the best option, which can be a potentially greedy step.\n", + "\n", + "Nonparametric models are commonly based on kernel functions, such as the case of Gaussian processes, which are extensively used along this work. \n", + "\n", + "A kernel function $k(x, x′)$ is a function that maps a pair of inputs $x$ and $x′ \\in \\mathcal{X}$ (with input domain $\\mathcal{X} \\in \\mathbb{R}^D$) into $\\mathbb{R}$ characterizing the similarity of the pair of inputs. \n", + "\n", + "Semi-parametric models based on series expansion of basis functions are usually referred to as non-parametric models.\n", + "\n", + "## From parameteric to nonparamteric models\n", + "\n", + "So far, in this course, all models we have built were regressions, working in the supervised learning setting and using parametric models. We tried to describe functions with unknown parameters using Bayesian formalism." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "Gaussian processes (GPs) are powerful and flexible statistical models used primarily in machine learning and statistics for regression and classification tasks. At its core, a Gaussian process is a collection of random variables, any finite subset of which has a joint Multivariate distribution. In simpler terms, a GP defines a distribution over functions rather than individual points.\n", + "\n", + "Nonparametric models are statistical models where the number of parameters grows with the size of the dataset or is not fixed beforehand. This allows them to flexibly capture complex patterns in the data without making strong assumptions about the underlying distribution.\n", + "\n", + "A Gaussian process is a nonparametric model because it doesn't fix the number of parameters a priori, instead, it defines a distribution over functions, allowing for flexibility and adaptability to the complexity of the data.\n", + "\n", + "A few key points about Gaussian processes:\n", + "\n", + "- **Function Space Representation**: Unlike parametric models, which learn a fixed number of parameters, Gaussian processes define a distribution over functions. This allows them to capture uncertainty about the function being modeled.\n", + "\n", + "```{margin}\n", + "Well, do assume *something* about the functions, e.g. their smoothness in the form of kernel choice. \n", + "```\n", + "- **Flexibility**: GPs can model a wide variety of functions without assuming a specific functional form. This makes them particularly useful when dealing with complex or unknown relationships in data.\n", + "\n", + "- **Bayesian Framework**: Gaussian processes are inherently Bayesian models, meaning they provide a principled way to quantify uncertainty in predictions. This is achieved by representing the posterior distribution over functions given the observed data.\n", + "\n", + "- **Kernel Functions**: The choice of kernel function determines the behavior and characteristics of the GP. Common kernel functions include the radial basis function (RBF), also known as the squared exponential kernel, and the Matérn kernel, among others. These kernels encode assumptions about the smoothness and structure of the underlying function. We will see specific examples of kernels in this lecture.\n", + "\n", + "- **Regression and Classification**: GPs can be used for both regression and classification tasks where GP is commonly used as a latent variable.\n", + "\n", + "- **Computational Considerations**: While GPs offer many advantages, they can be computationally intensive, especially as the size of the dataset grows. Various approximation methods such as sparse GPs and approximate inference techniques are used to scale Gaussian processes to larger datasets.\n", + "\n", + "Now let's build the inredients which we need to understand Gaussian processes step by step." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## From Univariate to Multivariate Gaussians\n", + "\n", + "### Univariate Normal distribution\n", + "```{margin}\n", + "In the chapter about distributions we used notation $X$ for a random variable and $x$ for its values. Here we will denote the random variable of interest $Y$. It will become clear soon why we need to do it.\n", + "```\n", + "\n", + "Recall from previous chapters, the Univaritae normal distribution with PDF\n", + "\n", + "$$\n", + "\\mathcal{N}(y \\mid \\mu, \\sigma) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp\\left(-\\frac{(y - \\mu)^2}{2\\sigma^2}\\right).\n", + "$$\n", + "\n", + "To show that variable $y$ is dustributed normally with mean $\\mathbb{E}[y] = \\mu$ and variance $\\text{Var}(y)=\\sigma^2$, we use notation \n", + "$$y \\sim \\mathcal{N}(\\mu, \\sigma^2).$$\n", + "\n", + "\n", + "### Univariate reparametrization\n", + "\n", + "Note, that in order to sample variable $y$ we could fisrt sample from a standard Normal variable $z \\sim \\mathcal{N}(0,1)$, and then perform a transformation of this variable \n", + "$$\n", + "y = \\mu + \\sigma z \\sim \\mathcal{N}(\\mu, \\sigma^2).\n", + "$$\n", + "\n", + "**Excersise**: prove that $\\mu + \\sigma z$ is indeed distributed as $\\mathcal{N}(\\mu, \\sigma^2).$\n", + "\n", + "### Multivariate Normal distribution\n", + "\n", + "In the multivariate case, instead of using scalar mean and variance parameters $\\mu, \\sigma^2 \\in \\mathbb{R}$, we need to specify a vector mean $\\mu \\in \\mathbb{R}^d$ and covariance matrix $\\Sigma \\in \\mathbb{R}^{d \\times d}.$ To write that variable $y$ follows a Multivariate Normal distribution, we use notation \n", + "$$y \\sim \\mathcal{N}(\\mu, \\Sigma).$$\n", + "\n", + "### Cholesky decomposition and reparametrization\n", + "\n", + "Cholesky decomposition is a numerical method used to decompose a positive definite matrix into a lower triangular matrix and its conjugate transpose. For a positive definite matrix $A$, the Cholesky decomposition expresses it as:\n", + "$$A = L L^T$$\n", + "where\n", + "- $L$ is a lower triangular matrix,\n", + "- $L^T$ is the transpose of $L$.\n", + "\n", + "Cholesky decomposition is particularly useful because it provides a computationally efficient way to solve linear systems of equations, including inverting matrices and calculating determinants, especially when the matrix is symmetric and positive definite.\n", + "\n", + "In Gaussian processes, Cholesky decomposition is commonly used to generate samples from a multivariate Gaussian distribution. When you want to generate samples from a Gaussian process, you typically start with a covariance matrix $K$, which represents the covariance between different points in the input space. The Cholesky decomposition of this covariance matrix $K$ yields a lower triangular matrix $L$:\n", + "$$K = L L^T.$$\n", + "\n", + "By multiplying this lower triangular matrix with a vector of independent standard normal variables, you can generate samples from the Gaussian process while ensuring that the resulting samples have the desired covariance structure encoded by the covariance matrix $K$. This is done because the Cholesky decomposition allows you to transform independent standard normal variables into correlated Gaussian variables according to the covariance matrix Cholesky $K$. Hence, we can either sample directly \n", + "$$f \\sim \\mathcal{N}(0, \\Sigma)$$\n", + "or use the reparametrization\n", + "$$f = zL \\sim \\mathcal{N}(0, \\Sigma), \\quad z \\sim \\mathcal{N}(0,I).$$\n", + "\n", + "### Bivariate case\n", + "\n", + "'Bivariate' means $d=2$. Hence,\n", + "\n", + "$$\n", + "y = \\begin{pmatrix} y_1 \\\\ y_2 \\end{pmatrix}, \\quad \\mu = \\begin{pmatrix} \\mu_1 \\\\ \\mu_2 \\end{pmatrix}, \\quad \\Sigma = \\begin{pmatrix} \\sigma_1^2 & \\rho \\sigma_1 \\sigma_2 \\\\ \\rho \\sigma_1 \\sigma_2 &\\sigma_2^2 \\end{pmatrix}.\n", + "$$\n", + "\n", + "Here $\\mu_i$ is the mean of component $y_i$, $\\sigma_i^2$ is the variance for the $i$-th dimension, and $\\rho_{ij} = \\rho_{ji}$ is the *correlation* between the $i$-th and $j$-th dimensions:\n", + "$$\n", + "\\mathbb{E}(y_i) = \\mu_i,\\\\\n", + "\\text{var}(y_i) = \\sigma_i^2,\\\\\n", + "\\text{corr}(y_1, y_2) = \\rho_{12}.\n", + "$$\n", + "The covariance matrix tells us how the \"ball\" of random variables is stretched and rotated in space. Let's visualise a few examples.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.stats import norm\n", + "\n", + "import jax.numpy as jnp\n", + "from jax import jit\n", + "\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib.colors import Normalize\n", + "from matplotlib.cm import ScalarMappable\n", + "import matplotlib.gridspec as gridspec\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def plot_2d_gp(mu1, mu2, rho=0, sigma1=1, sigma2=1):\n", + " mu = np.array([mu1, mu2]) # mean\n", + " covariance = jnp.array([[sigma1**2, rho*sigma1*sigma2],[rho*sigma1*sigma2, sigma2**2]]) # covariance matrix\n", + "\n", + " # Generate data points from the 2D Gaussian distribution\n", + " num_samples = 1000\n", + " data = np.random.multivariate_normal(mu, covariance, num_samples)\n", + "\n", + " # Calculate marginal distributions\n", + " y_values = np.linspace(-3, 3, 1000)\n", + " marginal_y1 = norm.pdf(y_values, loc=mu[0], scale=np.sqrt(covariance[0, 0]))\n", + " marginal_y2 = norm.pdf(y_values, loc=mu[1], scale=np.sqrt(covariance[1, 1]))\n", + "\n", + " # Create figure and gridspec\n", + " fig = plt.figure(figsize=(6, 4))\n", + " gs = fig.add_gridspec(3, 3)\n", + "\n", + " # Main plot (2D Gaussian distribution)\n", + " ax_main = fig.add_subplot(gs[1:3, :2])\n", + " ax_main.scatter(data[:, 0], data[:, 1], alpha=0.5, label='2D Gaussian')\n", + " ax_main.set_xlabel('X')\n", + " ax_main.set_ylabel('Y')\n", + " ax_main.legend()\n", + " ax_main.grid(True)\n", + "\n", + " # Marginal X plot\n", + " ax_marginal_x = fig.add_subplot(gs[0, :2], sharex=ax_main)\n", + " ax_marginal_x.plot(y_values, marginal_y1, label='Marginal Y1', color='r')\n", + " ax_marginal_x.legend()\n", + " ax_marginal_x.grid(True)\n", + "\n", + " # Marginal Y plot\n", + " ax_marginal_y = fig.add_subplot(gs[1:3, 2], sharey=ax_main)\n", + " ax_marginal_y.plot(marginal_y2, y_values, label='Marginal Y2', color='g')\n", + " ax_marginal_y.legend()\n", + " ax_marginal_y.grid(True)\n", + "\n", + " plt.tight_layout()\n", + " plt.show()\n", + "\n", + "# Parameters for the 2D Gaussian distribution\n", + "mu1 = 0\n", + "mu2 = 0\n", + "\n", + "# How does the distribution change with different values of rho?\n", + "for rho in np.linspace(0.1,0.9, 2):\n", + " plot_2d_gp(mu1, mu2, rho)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### $d>2$\n", + "\n", + "```{margin}\n", + "This great visualisation idea I borrowed from Darren Wilkinson's slides from the GPSS.\n", + "```\n", + "\n", + "Visualising the distribution in dimensions higher than 2 is harder. \n", + "\n", + "Still in 2d, we can use indices of components of $y$ - 1 for $y_1$ and 2 for $y_2$ to make the plots. " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "# Parameters for the 2D Gaussian distribution\n", + "mu = np.array([0, 0]) # mean\n", + "covariance = np.array([[1, 0.5], [0.5, 1]]) # covariance matrix\n", + "\n", + "num_samples = 10\n", + "data = np.random.multivariate_normal(mu, covariance, num_samples)\n", + "\n", + "# Extract values at indices 1 and 2 for each sample\n", + "index_1 = 1\n", + "index_2 = 2\n", + "values_1 = data[:, index_1 - 1]\n", + "values_2 = data[:, index_2 - 1]\n", + "\n", + "# Generate a color map\n", + "cmap = plt.get_cmap('viridis')\n", + "norm = Normalize(vmin=0, vmax=num_samples - 1)\n", + "scalar_map = ScalarMappable(norm=norm, cmap=cmap)\n", + "\n", + "# Plotting\n", + "plt.figure(figsize=(3, 4))\n", + "\n", + "for i in range(num_samples):\n", + " color = scalar_map.to_rgba(i)\n", + " plt.plot([1, 2], [values_1[i], values_2[i]], color=color, marker='o', linestyle='-', label=f'sample {i}')\n", + "\n", + "plt.xticks([1, 2], ['1', '2']) # Set x-axis ticks to only 1 and 2\n", + "plt.xlabel('Index')\n", + "plt.ylabel('Value')\n", + "plt.title(f'Values at indices 1 and 2 for each Sample ({num_samples})')\n", + "plt.tight_layout()\n", + "plt.legend(loc='upper right', bbox_to_anchor=(1.8, 1))\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Can we generalise this approach to visualise data of higher dimensionality $d$?" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def plot_values(data, d):\n", + " num_samples = data.shape[0]\n", + " indices = list(range(1, d + 1)) # Indices to plot\n", + " values = [data[:, idx - 1] for idx in indices]\n", + "\n", + " # Generate a color map\n", + " cmap = plt.get_cmap('viridis')\n", + " norm = Normalize(vmin=0, vmax=num_samples - 1)\n", + " scalar_map = ScalarMappable(norm=norm, cmap=cmap)\n", + "\n", + " # Plotting\n", + " plt.figure(figsize=(6, 4))\n", + "\n", + " for i in range(num_samples):\n", + " color = scalar_map.to_rgba(i)\n", + " plt.plot(indices, [values[j][i] for j in range(len(indices))], color=color, marker='o', linestyle='-', label=f'sample {i}')\n", + "\n", + " plt.xticks(indices, [str(idx) for idx in indices])\n", + " plt.xlabel('Index')\n", + " plt.ylabel('Value')\n", + " plt.title(f'Values at indices 1 to {d} for each Sample ({num_samples})')\n", + " plt.tight_layout()\n", + " plt.legend(loc='upper right', bbox_to_anchor=(1.3, 1))\n", + " plt.show()\n", + "\n", + "# Parameters for the multivariate Gaussian distribution\n", + "mu = np.zeros(5) # mean vector\n", + "covariance = np.array([[1, 0.8, 0.7, 0.4, 0.1],\n", + " [0.8, 1, 0.5, 0.3, 0.2],\n", + " [0.7, 0.5, 1, 0.2, 0.1],\n", + " [0.4, 0.3, 0.2, 1, 0.1],\n", + " [0.1, 0.2, 0.1, 0.1, 1]]) # Example non-trivial covariance matrix\n", + "\n", + "# Generate data from multivariate normal distribution\n", + "d = 5 # Number of components in the vector\n", + "num_samples = 10\n", + "data = np.random.multivariate_normal(mu, covariance, num_samples)\n", + "plot_values(data, d)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the example above we coded up the covariance matris by hand. It is time to look into what covariance matrices might be more meaningful." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Gaussian process\n", + "\n", + "**Definition** (stochastic process)\n", + "\n", + "A stochastic process is a collection of random variables $f=f(x)$ indexed by some variable $x \\in \\mathbb{X}$.\n", + "\n", + "**Definition** (Gaussian processes)\n", + "\n", + "A **Gaussian process** is a stochastic process over the function $f: \\mathbb{X} \\to \\mathbb{R}$, such that every finite realisation $ (y_1, ..., y_d)T$ follows a Gaussian (multivariate normal) dsitribution:\n", + "\n", + "$$\n", + "(f(x_1), ... , f(x_d))^T \\sim \\mathcal{N}\\left( \\mu, \\Sigma \\right).\n", + "$$\n", + "\n", + "\n", + "To fully specify a Gaussian process, we need to specify its **mean function** $\\mu(x)$ and its **covariance function** $k(x,x'):$\n", + "\n", + "$$f(x) \\sim \\mathcal{GP}(\\mu(x), k(x, x')),$$\n", + "\n", + "where\n", + "\n", + "$$\\mathbb{E}[f(x)]=\\mu(x)$$\n", + "\n", + "and \n", + "\n", + "$$\\text{cov}[f(x), f(x')]=k(x, x').$$\n", + "\n", + "### Mean function\n", + "\n", + "Typically, for the mean function we chose one of the following options\n", + "\n", + "- $\\mu(x)=0,$\n", + "- $\\mu(x)=c,$\n", + "- $\\mu(x)=\\beta^Tx$.\n", + "\n", + "### Covariance functions (or kernels)\n", + "\n", + "Covariance function must be a positive semi-definite function in order to lead to valid covariance matrices.\n", + "\n", + "**Definition** (kernel)\n", + "\n", + "$k: \\mathbb{X} \\times \\mathbb{X} \\to \\mathbb{R}$ is a positive definite **kernel**, if for any finite collection $x= (x_1, ..., x_d)$ the matrix $k_{xx}$ with $[k_{xx}]_{ij}=k(x_i, x_j)$ is **positive definite**.\n", + "\n", + "**Definition** (positive definite matrix)\n", + "\n", + "A symmetric matrix $A \\in \\mathbb{R}^{N \\times N}$ is called positve (semi-) definite if\n", + "$$v^T A v \\ge 0$$ \n", + "for any $v \\in \\mathbb{R}^N.$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Kernels\n", + "\n", + "Kernel functions $k(x, x′)$ encode prior beliefs of data-generating latent functions. These typically include\n", + "- continuity,\n", + "- smomothness (differentialbility),\n", + "- periodicity,\n", + "- stationarity,\n", + "\n", + "and so on.\n", + "\n", + "The covariance functions typically have **hyperparameters** that we aim to learn from data.\n", + "\n", + "\n", + "\n", + "Let us explore some typical covariance functions.\n", + "\n", + "### RBF\n", + "\n", + "The squared exponential kernel, also known as the Gaussian kernel or the radial basis function (RBF) kernel is one of the most commonly used kernels in Gaussian process regression. It is defined as\n", + "\n", + "$$k(x_i, x_j) = \\sigma^2 \\exp \\left( -\\frac{1}{2\\ell^2} \\|x_i - x_j\\|^2 \\right)$$\n", + "\n", + "where\n", + "\n", + "- $\\sigma^2$ is the variance parameter (also called the amplitude),\n", + "- $l$ is the lengthscale parameter,\n", + "- $\\|x_i - x_j\\|$ is the Euclidean distance between the points $x_i$ and $x_j$.\n", + "\n", + "This kernel assigns high similarity (and hence high covariance) to points that are close to each other in the input space and low similarity (and low covariance) to points that are far apart. The parameters $\\sigma^2$ and $l$ control the overall variance and the rate at which the covariance decreases with distance, respectively.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def rbf_kernel(x1, x2, sigma=1.0, lengthscale=1.0, jitter=1e-6):\n", + " \"\"\"\n", + " Compute the Radial Basis Function (RBF) kernel matrix between two sets of points.\n", + "\n", + " Args:\n", + " - x1 (array): Array of shape (n1, d) representing the first set of points.\n", + " - x2 (array): Array of shape (n2, d) representing the second set of points.\n", + " - sigma (float): Variance parameter.\n", + " - length_scale (float): Length-scale parameter.\n", + " - jitter (float): Small positive value added to the diagonal elements.\n", + "\n", + " Returns:\n", + " - K (array): Kernel matrix of shape (n1, n2).\n", + " \"\"\"\n", + " sq_dist = jnp.sum(x1**2, axis=1).reshape(-1, 1) + jnp.sum(x2**2, axis=1) - 2 * jnp.dot(x1, x2.T)\n", + " K = sigma**2 * jnp.exp(-0.5 / lengthscale**2 * sq_dist)\n", + " K += jitter * jnp.eye(K.shape[0]) # Add jitter to ensure positive definiteness\n", + " return K" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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tt96aAPjgBz84/s1vfjMATDsUL774ouvw4cP2devWLQbQNE2sXbs2Pt/zmItL3qGYqpNwyC5swkZH/CBqLslVRTdyV/m7eXnsGZLZBA7ZiW7oeBQvVxS+iVfGNpDKJhkxBgnYyvFYfADsDm81HYoLgJmdHIVuJ7ph4Hfb+T+3rSMcTx3R5fH2a5bP6RQUep3IkkyJ18V4LImiyFSX+AGzA8TE5HxkrkgCwHD3qDUeTigznYp4OCE3rKzN3vPJO8fnc8yVK1emd+zYceCxxx7zfeELX6jcsGFD9Mtf/vLwZz7zmdotW7YcaGxs1D796U9XqKo6nY6w2+0GgCRJ2Gy26ZZXSZLIZrMCQAhxxHGO/r9hGKxfvz76u9/9rmsu+4qKirI9PT2W2tparaenx1JYWJg91XO85Gsodoe34pBdJLIxBtU+bJKNKmcdiWycWncjNwbuwiG7CGnjOGQXNwbuosW7ApvsoMHVglWyMpoeIqtrOGQnIW3sXJ+SyQmYOU/C57Kzu3OQra19LK0tJeB301xVwsfuvpp//OPb+NjdV5+UQzAaibO0rpSAz81IKEY4nsLtsJkdICanjJ45hB77Jnrkb/P/Zg6da5MuOW5497XhRDgpx8MJWdcN4uGEnAgn5RvefW14vvvs7u62eDwe/b777pv41Kc+NbJr1y5nMpmUAMrKyrKRSET63e9+d8p1C0NDQ9YNGza4AB5++OHCa6655ojoww033JDYtm2be9++fTaAWCwm7dmzx3b0fm677bbw97///SKA73//+0W33357+FRtueQjFCFtDBmZsDaBz1JAsa0UgZh2DCqdtceNOBRYiknlEpTaq+hNHiaYHsZrKaDAUny2T8HkFHl+Vwcepw2rLNPaH8RmUagrK2BnxyBXLp5fdKm80Es0qVJV4ieuZugenqC6xE95oXeBrTe5mNEzhyB5Pwg3iFLQo5C8H50/RbIuPtfmXTIsuaop9Z6/fvvIi794xR/sG7eWVBdl7v6zW8eWXNWUmu8+t2/f7vjc5z5XJUkSiqIY3/3ud3uKi4tzH/jAB4JLly5dVlVVlVm1alXiVPfb0NCg3n///UX33XdfbX19ffqzn/3sEZP2Kioqst///ve73/ve9zZkMhkB8KUvfWlg5cqV6Znr/eM//uPQPffcs6i2tra4oqIi8+tf//rwqdoiDOPCGRx2+eWXG9u2bVvQff524GEOxw/hVjxUOuoQQkymOFzcWfHOWbebmSpRc0mG1QG8Fh93lr/bTHmc53zpx09T4nNxqHeUnG7QUlWC1aowEorxj39827z2ORX18DhtKLLE7sODSELwuffeRHN1YIHPwORCR88cgvQzoA+CVAG2WxGWFozoVyDXA4YKSCAVAlZQKpA8f3Hc7S4GR0MIsd0wjMvP5DF2797dvWrVqosqhNza2mq9++67m9rb2/efrWPu3r27eNWqVXXHW3ZJpzx0Q8cirGhGBq8lH2lKZhOkcglW+a+Yc9tKZ+10OgQBbouXYmsZJfbys2G6yWlQXuila2gcVctSX1aI3WYhnkqfVjRhqgPE67QTSag0VRbTWFFMIq0toOUmFwPTUQg9CqIMcmMQ/3eM6NdAex30NEglIPlBH4dcH6Q3oid+Colvv7HdVPTCTImYnCdc0imPzkQrCLil9O0Mpfqn2z+vKrrhpKIMM9MhES3E5rHnaY3tYYXvjDraJqfJZY0VvLCrg9ICD26njWhSPaKTY77M7AAxDINnd7SxtbWPymIfAb85/MpkkvQzILwgBOQ6QA9PRiQ6wbIaUPLOBAA6ZPuBNKhPg5ECIwlyLUgFeUHp9DNwEUQpTE6dlpaWzNmMTpyIS9ahCGcm6IgdoNxRzWr/lVx2yqUwR+KzFFDnaqIr0UaFvYYimxnmPh/RdYO+YIR1LdXYLBZGQrGT6uQ4VYQQXLdiEaPhPTy3o513vGkFVssl+3UzmYk+CIYDsh0gFJDLQRQBYXC8fzJ6IeXrKIw4CAmc/1/+daygj+a3tSzNr6MPnuMTMjHJc0le4bJ6lt3h17HJDpZ5L1uw/TZ5ljKiDrIvsoP1JTcji0vy7T2v2dM1yFgkwT3rV9BQXnRGj2W3Kty0upHfbd7Poxt3E0tlzKFXJoAHsrvzUQjLEkDOpy+kCiTrYnT+9Kg6iXfmX09X5ddTWiC7H7LtIFWDXHGuT8jEBLhEHYqDsV0kc3GuLLoei2Slc08Pmx7fwkhvkNKaEtbfeyUNK0+9sFIWCst9a3h9YiMdsYO0eFecAetN5ks4nmJbaz/1pYXUlxWelWNWFHkJ+N088uIuGiuKqSzxmUOvLmGMXJB8niIHUjkYAoxo/seWLwKXrIuPn8Kw3ToZpQDkRaDtAuMQOL90tsw3MZmTS8ahmJqGOaj2kMzGWVuwnkJrCZ17enj067/F7XdTUlVMLJTg0a//lnd95q3zciqKbAGqHHXsDr3OgegukrmEOZb7PMAwDDbu7USSBOtX1B8z/OVMMhyK4Xc7GIsmCPjdpuz5JYqhh0D9DUKpxLDfBZlNx0Qh5uKY6IVlCRggjFFg6dk5CROTObgkujymWjzj2TBqNoUkJDoThxhI5iMTVruF0EiYvkP9ZLUsTq+DTY9vAaBzTw8//odf8NU//Q4//odf0LnnxEqjHsVPT+ow/alu/EqhqVJ6HnCwd5TB8ShXLanFZbee1WMPh2IsqcnX1PQGQwDm0KtLDEOPQ+rXYBjgeDuSbQ2S55NIvn/N/3uSRZWSdfEb2/m+jHDcipHZg6EdOLMnYHLBsW7dupaNGzc6T3b9+++/v6CxsXGZJElrT2W7mVwSEYrd4a3YZSfhzDgIg2pnA1k9y46xzex/tZ2slkWSJCRZEB6NggBDN6haXMFrv9uGr9h3StGLA9FdlNoqCGsTRLNh/NbCaTvMKMXZY2q8dl8wzHgkwZqmyukb+9lkauhVeaGH/rEIsaSKMfm6ycXL9MyIXB/oIZBrEe6PIqQFTLdZr0HoY5B+AUMqRMinrDhtMguHdvc6Xnpyjz84FLGWlPsy19+xMrx4Vc28B1ud76xevTr12GOPdXzkIx+pm+8+zlmEQghRLYR4QQhxUAixXwjxF2fqWCFtDHVMY2j3GAObxzmwsZ3BA6Ps3rObrJbF4baz+MpGll7dwqLL6nD5XdgcVv7wvWcZOjzCSPcoiWgCT4ELt989Hb2Y63hF1sD0KG7DMMyx3GeZmeO10xmNVEbj8OA47QNn/zO4aXUjsWQah9WCRZboGBwjllC5aXXjWbfF5OzwxqyJEOTCoEdAH8HITSzocYSQwH47CDdG/AH06NfMkd0LwKHdvY5f/PCl0kQ0pRSXerVENKX84ocvlR7a3XvRypevWbNGXbVqVfro10+FcxmhyAKfMQxjhxDCA2wXQjxrGMbCx+5CCvt37scunFhzDkYGgvT19lNXX8MHv3gPT//oRdREBpdPwdDB5XXwzn94Nz/7119hsSiERyP07O+n5YpFuHxORnqDcx5uaix3gbWYwVQvsWwERVjMsdxnkanx2rmcTjihUl9WiNNuPSd1CzNlz+0hC7FUmhvNLo+Lm6lZE/oQkALLCkA6IzMjhLCjyy2QfBwkX36WhTmye05efnqvd2I0Nqt8+WvPH/CnVU1KJdLypPAnaVWTHvzPZyquumlp+HjbFAY82ptuW3HBypcvBOcsQmEYxpBhGDsmf48BB4HKM3Gs2HM6sgfi6SjhYATZK/BWOfD2lbH6xhW86zNvxVPgItg/hqfAxbs+81YWraqjpqUSd4Gb+pU16DmdgfYhEpEEpTVz3whW+a8glcuPZLcKKyPqIMmTmL5psnAMTURx2a0MjEVwWi35IVbnsG5hSnDs6x99K7eubWE0HCc3+SRichGiD4KRyQ+tkmvyLaJncmaE9jooTUAO9AGQvHmHJv3MmTneRU48mpKtNuWIL6jVpujxaOq05Mtffvll78c//vHKp556yl1UVJSDvHz5ypUrFzc3Ny999dVXPfv27ZuOghxPvtzhcBhT8uUAR8uXv/rqq0dM0ZspX7548eKljzzySFFvb+8ZKSQ7L2oohBB1wGXA3LmEeRLbr1FhLGHI04m1Lo3b8OEbrCB2ID8WuWFl7XFrItbfe+V0B0hpTTG9BwfQ0lnu+PCb5zze1Fju3eGtyLIC2TSrfOvM+omzSHmhl97REKqWpbGiGCEEsaR6zusWJElw5eIantx6iNa+UZbWmjnvixKpDDKvg3CBXJp/zYjnOzrOBPogyFUgdMiN5DVAzKFXszJXJAFgeGDCmoimFLfX8YZ8eTQlu7yO7Ns+eM1FKV++EJzzLg8hhBt4DPiUYRjHfMhCiD8TQmwTQmwLBudONcxGaU0JRp+FpqE1tLReTWXbUow+ywkjDQ0ra6ejFwjwl/ooX1RK+aLSEx6z0lnLnRXv5MP1n2aF/wqSemxetpvMjxtXLqJ3NIwEeGeM1z4f6hZqAnkV0m1t/WjZ3Ik3MLnwkCpBj4EozHd26FOzJm49Q8eryDsscjUIK2Q788c7Uw7MRc71d6wMx6OqHI+m8vLl0ZQcj6ry9XesDM93n+e7fPlCcE4dCiGEhbwz8ZBhGI8fbx3DMH5gGMblhmFcXlIyv5zz+nuvJB6OEwsl0HWDWChBPBxn/b1XnnDbhpW1/PE/vJu/euATfPp/Po630MPrT+w86WNLQqLe1UwoM04oMy/H1mQeyLLEkuoA9eVFjITjeJ3282aQlBD5KEUyrbGnc8HTmCbnGEOPIowgON4GSiUYw/kUhPMM1jPYbs07EHoCpLp8EWju8JlzYC5yFq+qSb37I9ePuLyO7NhI1OLyOrLv/sj1I6fT5bF9+3bH6tWrlyxevHjpv/3bv5V/8YtfHJopX37HHXc0no58eXNz89JQKKTMJV/e3Ny8dO3atYv37t1rP3o/P/7xj/2lpaUrd+3a5brnnnua1q9f33Sqtpwz+XKRj8s8CEwYhvGpk9nmdOTLF2oa5t6XD7Lzub1c966rqVtWfVLbZPUsLwafoNBazJqCa075mCanhmEYPLpxD4Zh8O7rV53VIVanwtPbWukPRnj/TZfhsM1aH2ZygWGknshLkDv/CCF5ztpxj5A21zMguRHujyPk818B2ZQvnx/nm3z5uayhuBb4ILBXCLFr8rXPG4bxxJk42Gx1EqfKsmtb6D3Yz+tP7KC0rgSH6xhH7xgUSaHWuYiO+EHi2ShuxZw/cCbpGp5gIpbkzZc1nbfOBMC6xTX0jOxmR3s/1y6vP9fmmCwARrYXI9uBsF19Vp0JOHJkt2FkIPkQqBswnO9DmLpCJmeBc9nlsckwDGEYxkrDMFZP/pwRZ2IhkSSJa952BRlVY+uTJ5/6qHEuQhISXYm2M2idiWEY7Gjvx++ys+gMi3+dLgVuBy3VJWzc28l/Pf4yX/rx03zv95tp659frZDJucUwcpDeiJB8YFk40cH5IIQVbG/Oj/vOnJFad5PzAFO+/CKgoNTPyuuX8vzDm9j14n7SyfQJ0yg22U6Vo47+VDdN7mXY5XnPRzGZg56REGPRJDeuWoQknb/RiSn8Lgd7Ogcp8blZXFtqCoddyGh7MfQJhOOu8yIiIJQasCwDbQeGssicomlyxjnnXR4XKg6PncO7u+nc3U1BqX96LPdcWh91rmZ0Q6c70X4WLb10MAyDHR0DeJ02GisvjCFimw/2UFHkI5nRUNMaXqcdj9PG87s6zrVpJqeAoSch8xpCqQW54Vyb8wa29SBcGPGfosf+05yiaXJGMR2KebL5N9uoX16NrMiM9gZPaiy3S3FTZq+iL9mJpmfOorWXBn3BCKPhOKsXVSJLF8af9tBElLqyQhRJYmg83zVtCoddOOiZQ+ixb2KEP4aR3oQhlZ1XdTtC2DCkOsi8BFo7iLI3pmiaToXJAnPu43IXKCO9QUqqiknFVSaGwpTWBU5qLHeDu5m26D5+0Xc/gCltvkBM1U64HTZaqi+cVMGUcFjA72ZoIoqa0chkc+d8AJfJiZnW60AGPZsfe516DF34zq9x19l9IJeDEQFS+RZWnTMyBtzk0ubCeIw7DymtKSERSVJSXYShG4wPTpCIJE84LCuuxRhS+wiqw/iUAlPa/DRp6w/yvd9v5q9/+Ad+v+UARR7HBROdgDeEw+zWfNto1/DEeTOAayGIpltpC32HPcG/oy30HaLp1nNt0sIxrdcRAskGlubzc9y1PghKMwgFsr3518wpmhc9pypf/tGPfrSqvr5+WXNz89Jbbrll0djY2CmPGb9wrrznGVPDsrR0Dnehi8GOYWITsRMOy9od3kqxrRRJSCRyUZyKC4fsYnd461my/OJhpqKols2i6wav7O++oLokpoTDCr1OZEkildZ493WrLoqCzGi6la7Ig2i5KDa5FC0XpSvy4MXjVEzpdRix/Nhr5PPzRi1VgKGCXDk5/Cp0ZseAXyQcODTo+PYPni//4ld+XfvtHzxffuDQ4EVdSX/bbbdF29ra9re1tR1obGxU//7v//6Uq3hNh2KezBzLLcsysiyz7q41J5x1EdLGKLAUY5VsRLQwgCltPk+mFEUFgriaoba0AK/LfsEVNE4Jh/2/D9/JmqYqMhfYOO7ZohDDyQ0okgdJWNH0CIrkRJE8DCc3nGOLFwipPD+NUjhBmiwCPh9v1FNTNLEDNsi25SdpmlM0Z+XAoUHHw49uKY3FVaW4yKPF4qry8KNbSk/HqTjf5cvvvffeqMWSj5ReffXViYGBgVMWEDNrKE6DqWFZhmHwhx9sIDoWwzCMOYuypqTNvRY/Y+kRMrk0WSNrSpvPg6GJKKUFHjoGxrDIMiU+FwhxwRY0Fnic1AYK2Nc9zMpF5VjkeQsbnjWmohCK5JmOQnRG7qfcdQchdScYEjr5AmSBQJE8pLKD5PQ0Ca2b4eQG1OwQdqWcMufNeG0t5/iMTgG5HvQNk+O1jXykwoiC7Z3n2rIjkKyL0fnTfCpGsoOeBtv151edx1nmxU2t3vHx+KzjaV95rcOfTmtSMpmRg+R1mNJpTfqfB1+uuPaqxvDxtikqcms3rG+5KOTLf/SjHxW/853vnJj9HTw+ZoRiARBCsPTqZqJjMQba59ZmmJI2V4QChkEwPUzKlDafF+WFXkYmYkSTKmWFHiRJIp5KX9AFjasWlZPKaLT3XxgRq6kohCK5SefGUHPDJLR+OiM/wkBHCIHLUovPuhi7UoqWi6DpMQ6Of5X9418hqfVilUouuHSIYaQR+gjYbwel6uzodZwGknUxkueTCP93EI57EMZIfpqmyXGJxVXZaj1Kvtyq6LG4etHLl//N3/xNmSzLxsc+9rFTdijMCMUCUbusih0b9nBgcxtVzbOHPGdKmyMNkNZVbit7h9nlMQ9uWt3I//vZc4CgyOucVhR9+zXLz7Vp86a80EuJz8WezkGW1ATOqxbE46Fmh1CEl2jmAFk9hSzsOJVKdDIs8v0ZPdGfIgs7suTCggEWQYX7LQzGf4NhGKSyI6RzY3iszdPpkAsiSpHZjmGkEM73IOQTqw+fLwghMGzXYiQfRWi7wLruXJt0TpgrkgAwNBKxxuKq4nHbp/OPsbgqL3Lbs+9429qLVr78W9/6VtHTTz/tf/nll9ukeRS3mxGKBUKWZRZf2cRw1yjjQ6E5152SNn9v9UdocLdgkU1hqPngdthorCimtqyAYCRxXimKzhchBKsaKggnVHpG5v47OtcYhoHAQii9G93Q8Fqb8dtXYJUL8Fib8NuXIsl3sSc8xmvBLewJjyHLdxNwXoMkLBTZ1+G1LkagEMu0ARJq9vxXXzX0OGi7EJaWC8qZmELI5QilMe8U6acsbnlJcNN1i8OJRFqOxVVZ1w1icVVOJNLyTdctDs93n+e7fPkvf/lL73/+53+WPfHEEx0ej0c/evnJYEYoFpDmtQ3seekABza38aaTkEYvtpVik+z0J7sps1eeBQsvLra39VEd8PO+my67IOoNTpaG8iLch3rZ3TlEXVnhuTZnmmi6dbrmwSYHUCQvBnknyGmpRZE8aLkoWT1Gtede2qNDPDYwiEe5AZdiZyyj0jowiN2Sr5noCHdzcCKMqieocEYodYao9159rk/zxGReAwywXgC2zobtakh2QuZ1sN94rq0571i6uCL1/nddOfL8xkP+0WDUGijxZt525+qxpYsrTku+/HOf+1yVJEkoimJ897vf7ZkpX15VVZU5Hfny++67r7a+vj49l3x5JpMRAF/60pcGVq5cmZ653qc//emaTCYj3XTTTc0Aa9asiT/88MO9p2LLOZMvnw+nI19+ttj61E4Ovd7BvX9xJy6f64Trt0b30plo5cbAXaa+xykwOB7ht5sPcM3SOlY2nP/yzKfK7s5BNh/o4d71Kwj43Sfe4Awzs/gSBNH0QbJGnDrPB/DaljKSeu6Y4softG8gpqVwyFZCmQRCCNRcBq/VSZ2s0Rt/kJzhRNcdWOQYhbZRAs4rubnmc3SOZXn2UAeDkSgVPi+3LG5kcem5jzwZuTFI/QwslyFs68+1OaeFkX4RtH3gfD9COreOqylfPj9M+fKLnCVXNXPo9Q4Obung8ltXnXD9KmcdnYlWBlI9LHKff8Vc5yvb2vpx2a0sqQ2ca1POCEuqA+xo72f34UFuWdt8rs2ZLr7MGSmSWh+SZMOrVJPSh6i234vPfuzf7nAqTFzNcCg0jJrTsMoyfoedrMjxTEzFozTS4h3AawkylnazI3gZde4xYrFv82RrGQl7Dmw5+lNWDrw2wF9cdf25dyoyrwBWsJ7Re9/ZwbIOtEOQfhUcd59ra0wuAkyHYoFx+13ULq2ifXsnK69fitU2d32ES/FQYC1mINVNg6vlvC/COx8YHI8wOB7l2mV1F1WqYyZWi8KSmlJ2Hx4kmlDxuuzn1B41O4Su66Ryg1hlP25LPXPVPMS0FEOJCG2hEZySnQLhI5nKMBBLUux0k0olQa5gb6YGSYIMGhldIxhxohuHqa7ZiTAUPLJGMuelO1HHz/e7+VLp7Wf3xJkcsZ1+BrLtoE+A451I4tx+HguBkJwY1rUYyd9hZHYDsfwMDdut52WnismxmPLllwBLr25mx4a9fPP/+yGGbpxQ2rzKUcfeyDZC2hiF1nMf1j2fMQyDra2T0YmaC68g7lRYXlfG8zs7+Lefv4CiSJQXerlpdeM5KTqVhI1o9gBOpQK3pQEEaLkodqWc9ugQL4zsZ1gNU2b3U+0sYliNEIvlcEg2REYhnFExJB2LIlGeK8XltpMy0niUN9J80WwCq1TEuKZxdVEnmZzCYKoYRUqwzLeLvUFBVr8V5SyOVp/W6xBe0FXAgPQr6MqSi+Kma+CA7F4QHrCseUM4jPOz/dXk/Mbs8jgDRMfjdO7tZbBtiOLKohNKm5fZq1CEQn+y++waegEyOB5laCLK6kUVKPLF/ec7OB6la3iCgbEIRV4X0aTKTzZsP+ujxVPZITAEkpCxyoUY6NPFl2l9NQ91byKmpfAqDnaHuvlJ10bAoDRVSXmyikzGwGYXVLkLuMazDJfh5v3NV5HMpollU+i6TiybIpXV+OOm9dR5xoiqpViEjXJHjJxkQdUtVPvaeXjbbjYc6uCbL73K5377NN96aTOHRs7g+zGl10EGSILSCJL//NPrmC/p50GuA3JghPOzNM5HPRKTC4KL+4p8jtj0+BYqFgUQkkR0PHZCaXNFUih3VDOs9pPVtbNs7YWDYRhsbevDfQlEJyA/Wry6xIeiSExE822xHqftrI4W13IRhuJP4rbWsaTgr7HKftK5ESyyl3rfn7B5IoVHsZM1dFqjg4CgwV1GJpcFXRAO5VipNHOz+wousy3Gotmp8Hm5tX4pf77sVjyKg3Ethkdx8OfLbuXW+qVUuXNEMg7C6SJswqDQkkBFpsKjMRKN8s2XNrOrbwif3U40pXL/5u1nzqnQB0G4IDeQ/1cqPj/1OuaLPghyTX58eK4PMC6u8zM5q5gpjzPASG+Q0roAkdEooZEwBQHfCaXNqxx19CW7GFL7qHY2nEVrz3/a+oM8v6uDw4NjhOIp7l2/4qKPTsAbo8VD8RRjkQRlBR7cDttZGy2e09MMJJ7AQKfCfRdWuYACx8oj1hlW92IVCt2JIC7FRoO7FFlI7BkboNhahctqxWu3YQCxlEpETfOOy/KDx26tX8qt9UuPOW6Tfxnx3AFiqo1oxoXHGkNRFGxKJYcYorbISyylsX94lBK3E4/NzrOHOs5MwaZUAdmuvLiWMjlw63zU65gvUkU+zSFXTWp8BAH7xXN+JmeVi/+qfA4orSkhGUnhD/iITcTJatkTSpv7LIW4Fa+Z9jiKaUXRRIpMNoeuG7x6gSmKzpfyQi/xVJpinwtVyxJLZc7aaHHDyDGceBotF6bcdTtW+fjzdmySQmt0EJdio9FThkWSaR8Pkk7CTc2L+NtbrsPncDAcjeF12PnTq9ee8Ma/tODtLPcXUOu34nQG8NldNHlyXF78VkbVKDHvGHppiHDhAAf1Dg6E+9jVP0Q6m+XQSJBvvbR54dIhtpsh10NeSdSbv/ka0YtHWGtaOEwG3JA9DHr44jm/S5hTlS//i7/4i4rm5ualixcvXnrttdc2dXd3n/LERTNCARwaCS5oz/v6e6/k0a//FsWmYOgGQ50jKFaFOz5806zbCCGoctZxKLqHmBbBY/HN+/gXE1OKohiQUDPUlxVisyo8v6vjgp6IeTLctLqRn2zYjttuRRKCvmAYn8t+RkeLR9OtDCc2EErvRDey1Hjei9NSddx1u+Kj+RrFbJaReIq+4U40I4sh5XhX9dVc11iHEILFZafW2uu1tbCq+OOUTg7RssjN6LqKxxKh1l7M9mwrNhSKrH6yis6YZRwjDl/d8DLdEyFqC/2UeT3T6ZCTcWJmQ4gchrIchGVSr6MCbO+8aAoWjxQOs4Euge3qi+b8Toc9XUOOZ7a1+UdCUWtpgTdz6+XN4ZX15fMebHW+86UvfWn4v/7rvwYB/vmf/znw+c9/vvxUB1td8hGKQyNB7t+8nWhKPeIidDpPNlPS5iWVhWjpLBlV412feesJpc0r7DX0jw/ztZe/wd/+4e/4l6e/wWvtO6eXH+4a5YGfbuJfv/EED/x0E4e7Rudt44XC0EQUp81C72gIm6JQ5HWd1bD/uaS5qoQP3rwWn9uBJAnUjMZ7b1h1xhypqeFVce0wOV3DIvkYS208rmBXV3yU54b34pd8eENlCF1CNdLEExqWkJ+1JXWn1QLttbXQXPD/sbLkn1lS+JfUeN+NmhuhsrQbZ9YJCEJG/m/AKdtY0uRhKBojklLpHg8zFk/gslnx2W08e2h+NSeGkYXMNobVWr6z68184aUb+c6OK2gLFc37vM5HpoTDpIJvIpzvRehjGIZ6rs06p+zpGnI8+PTW0nhSVQJ+jxZPqsqDT28t3dM1dNHKlxcWFk6P204kEtJ8vr+XfITi2UMd+Ow2LIpMPJ3BYbVgYEznZOcbvZiSNl95/TL2bjxIecMbT2mHu0bZ+EobI6NRSgNerru2mUX1AXZ2HqR1tA0hC3xyFalcgsfbHwWgRKnkkcdex+O2U1LsIRZXeeSx13nvO9axqP7iHO4E+bB/a98oqpalubIESRJEk+oFrSh6KjRXldBcVUIwEuexl/cCZ25OyXByAwiJTHYCm1KIx9KIpkenBbum2kM7YsNEtRSXFdSRGrVRbStBzRbQNR6iweWk2Ofk2dbDpxyZmAuPdRFJbSkOy2O8qXot+0d1hrRxkkqKtRW1GJYcXruNUo+bgUiUrvEQPRNhfA47g9EYOV2nPTg+63f5eN/zlsIhxmIj/HhnJTmRXrCox3mN9er8JNDMNrjAJ4HOxYYdbd5gJDFrSP/FPYf96UxWSqQzMuG8fLmayUrf+e0rFTesXBQ+3jYlPpd285rmC1q+/M///M8rH3300SKPx5N76aWXTln695J3KPpCEbRcjrF4gqkh5LIQpHM6HpuVlw/3UOhyzPtiUrusmj0vHaDnQD+L1zVxuGv0CMcgEkvxk0c28+YblvDU0FPkJDu4UoSSESTNRlYS/GrXE3i6V6GmNRRZxgCcjrz67MZX2lhUH5jVSbnQWVFXygu7Oigv8uB22i4KRdH5UOJzU+x1crBvlGV1ZWfkGKnsIOlsCCGs07MmFMmNmh2iPTrEQ92bMAydSCaJLEn0JycIxRRKLQV0T968G4oLMYDByMJHkEqc63EqL6JIB7m27gYiWoCO2DATepQl9krSPhfRlMqysgDxdIbxRJKBSBRFlvh/z7xE2+gYFX4PZZ4jv8sA92/ejm/SIQklU/xw02v8+bp29g1nmUgX4bDkCCdTOK1WvPbTf+A4n5gqeh6aiFJe6OUtl1VQ4duDYVmFkDzn2rxzQiyhyh6nLTfzNZtF1mOJ05Mv/8IXvlD98Y9/vPJtb3tb5Pbbb49DXr78G9/4RpmqqlI4HFaWLl2aAiJwfPlygCn58qKiotzR8uXf/OY3A8C0QzFTvhxA0zSxdu3aIwTEpvjWt7418K1vfWvgc5/7XNlXv/rVwH/8x3+cUrvPJetQ6IbBgeFRRuNxkmmNmkI/PrsNNZtlPJHEJQQbO3qIpVXSk681lRRNh1BPdNGYeYMPh1IYr7SyeF0TL2w8RE7XGZuI0z8YIp3OoqY1Hv3VNrS1Y1g1F5Ijg2FPoaetGFkLcUuIid5xHA4L0Wg+hSeEwGZTyGZ1Xnj5EC+90kaB33nc6MWF6mxktCzdI2GuWVqLRZEZCcUoL/Ty9muWX/T1E8djcU0pm/Z1EYzEKfEtvL6HhIWMHsJnW4IQ+YhoVo9jV8p5YWQ/AhhRo7gsdpo8ZSSzafqsQcYGNTw2G40lRQghiKVUKnwLH0GShIU1xe9m88i/4xYP4rM6cXqs7IuWUuNaRd3iSu7fvB0At92GYRhIkuCOJc38du9B0tkc/aEoA+EYAlC1LF95+kUA0loWu0XBIN+eXO3uZnvvYZ7uWk4iGzsifSMJgabrFDocvHS4i2KXi4DHfUFGL9r6g/zk2W04bFZK/W6iSZUfvSD4sxvjFCtbwH7zuTbxjDBXJAFgYCxqjSdVxeOcIV+eVOWmSnv2fTdedtHKl0/xoQ99aOKuu+5qMh2KWZj5JOG12XBaLUiSxOXVlbQHxylw2HHbbUhqGs2er0Z/cMsOlrkDpDIaXeMhDgwHqfZ7iaUzcx7r6ChEbDzGs693kfvxRl7b2onDYcFqVXA5bfi8TmxWmXgijcVbgWokka1+MpYYLsWOmk3jkCsov3IR0biK02EllcqQSKYZH09gGPCr3+0gnckSjaZwOCzYbRZyOYM/PL2Hm65fwm/+sPOCTJVsPthDPJXm3TesvmRSHHPRWFHMawd6ONQ7SsmKhXUocrqKJBxIQkLCgmHoZPX4tHJob2InE+k4NtlCk6cMWUjYJSspoZLWrDSVFCEJQfSo1tCFptKh0OCSCGViRLNWimx23lzSz0hyL2uq6vnTq9ceETF4x2XLWVxawrOtHVxZV0UklSap5b+/hmEwkczXCpR6XAghEAisssHVpeOMJ0uoKV5KMpPD77ST0w2SmQxj8QQIeKa1g2QmQzKjMRyNUV3gw2u3nrkW1tPg6CjEdSvqcdqsPPD0VkZDMYQk8Dhs1JUWAgVsOeznLt9BDH3NORcOOxfcenlz+MGnt5YCuBy2XCKVlmOptHzvdSvnLS7W3d1tCQQC2fvuu2/C4/HoDz74YNHx5Mvf8pa3hE5lv1Py5TfffHNiNvnyz3zmMzX79u2zLV++PB2LxaSuri7L0Wqje/futa1YsSIN8Oijj/oXLVp0ygWol4RDMVV46bRaSGU0OoLj5HSDP7v2Cm5b0kTr6NhxL0IVPi/RlIrPYWd5eSmd4xO0B8cp93rIZLNYleO/fRtfacPltJHRcoz2jBFOaaS0HK9vOUxdXQkWRaKkxDudDY/FVWoL3SxprOHx9kexpq0YikFcmiCHxF0Nd1PSnK+hEIDLmZey13WDd99zBQ8/ugWH3UIypaGmNcZDCXLZHH0D43R0jpLL6fi8ToqKXBRMKqBOpUrOV3pHwxzsHWX1ogrTmZjEblWoLy+kY3CMq5bWLqiOybi6Favsodn/SSbS26aVQ6s992JV6olqr6IZOZZ6qpAnoxcHgyN4JCcfv+Ea9g6NHPP9ORMMJzdQYm/GY/Gi5WL47c2kc0kOx/ezYbiee6vX8efXHysrPvVdLnY7gXwnXTSlUltYMP2715HX5yi1d+C2agS1a3nnkpXcv3k7WjaH225D13U8kw8cP3ptBwVOBykt71AcHpvAabXgiCfPyLnPl6nWa5tFQQC7Dw/y4u4OVtSV0zMSorzQg9NuZTQc50DPCJXFXnb2lHPXmoFLVjhsZX156k9uu2JkZpfHvdetHDudLo/zXb78s5/9bFVnZ6ddCGFUVVVl/vd///f4o53n4JKQL//WS5uJpFL0hCKoWpYyrxuPzUaB03Hci88UU46Iz27DbbcRU1W6J8JU+n00Fhfiykr8fvshRuJxSt1u3n/Naq5ZUseX/uU3ZHM6uZyOzarg8zkZ7x4lk9P59N+8dTp64XLaSCTTxOLqdMTgtfadPN/5AhOWHmyKjbvL3sPVzfk872ypiwd+uolYXMXjzl8QDSAUTqAoMkNDYRwOC4lkBlXVsNstBEq8aFqOd99z+XmZClEzWR7duBurIvOON628JIZYnSxTsu0LqemRzo3TG/0FXtsSSp03HLEsq+d4YnAnhyIDjGfiBGxeXIqdjokx+qIhPli/nrubVh5/x2eAPcG/wyaXYhga4fQ+rHIBLksdkUwfexO3U2b3c0fFaiRx5N/M0d/luJomoqaPqaHw2mUWe55kPGVnddN9c9ZJfOulzdOOiGEYjCeStAfHkSTBBy5fTYnLyebuvnNeX/G9371K59AEoXgKAwOH1YJFkaYHpcXVDF6nPZ9iHJ4gGE0Q8Ln55z8qRo3+ip7RFLlchBzlBErvoa5q9mvmfDHly+eHKV9+DhiMRCnzeqgtEFhlGYfVgm4YJywcW1xackwI9bNvXoHHZuNbz77Ci62dFFnslDidTCSSfOU3z3PNyxWktRxWi0x9bTFutx0BaLEUkcEJSgtcvPcd6464kd9128rpG/lVTZdxVdNlDKX62BXeQmNh5bQ9i+oDx73hX3dtM4889jrAtJOiqhrvfcdlbHyljVhcpbqqiEgkydBIlPbDI8iKxA8ffJnyUt95kQqZGZJV0xo+l4OP3Hml6UwcRXmhF5/TzqG+0QVxKAzDIJjchCSsFNuvPGbZy6MHGU6FeUfNlRwem+AXh19nMBFC1yRuLl/BXY0rTtuGU8GulKPlolhkL3YlgJodRpFc+G21rHcu5vHeLWwdP4wkBGV2PzeWLqPJW37c7/LMSMrHrvIxOvYrvHIbbmsOo/LPqJ1ctri05LiOwC2LG4+o2bDKMhU+L1fWVrG1u4/t/YNU+b0sKi46Z/UVaS3L9vYBdEOn0OOkusSP1aKgGwYjoRhvv3YFP9kweQ4OG2WFHjJZnRKfi5+/1MqNDdvwWj2MpZoRRBkf+TbAGXEqTC58LgmHYmbqYoq4mj6pwrHZLiZDQ2FcioWEniUTiWHJgDCgNRHi7/7oJv7w9B4ADN0gnkwjOazUFjjp3t/H8msXn/CmHbBXYJWs9Ce7KLHNXdW/qD4wp5My5Wx4PQ4kWUKWBbGYSiicQNd1ygI+/L58GPhcpEKmQrIepw2bItM5NE4slSYUT1HiX/jiwwsZIQSLawJsOdRLOJ7C7553WzwAca2TZLafgPM6ZOnIfe0MddMeG+byoga0pMyG3b2UShWkw04kSWIkmKZ1dOys3iDLnDfTFXkQALtcRlLrJ651Uef9ACNpQW9yjFQ2w1JvFTEtxUPdm/hA3fppp+J4tuqZQ9TZf0VdtQuyPhASSC+jZ5rmHPA0l5Py9edeptTjIZJKc3A4yJKy/HHPZn3FeDTBs9vbACjyuGgoL4TJgr2piatTs05m1ld88p4VlPjdbH79MQZCfgLeFDY5QUb3ohswOvIr06E4TzDly88BRz9JTIU7T6dwbDSWxK1LhLUMcdkg4HJSbHczrqZYvaIGj9t+zA2+9bm9dO/LOxQnQhYyFY5aehIdpHMqNtk+5/qzRS+O52zcfdtKfvGrbVitMiOjUbp7x7DZLASK3cQT6ePs/cwyNQ3TabWwf2iCAreTymLvJTENcz40V5WwtbWP1r5Rrlwy97C0udANjbHUK9jkInzWZQDTsybaY8NEM0muDyzhsoJ6vr3xNZxWC72hMFZFYWl5ADWjnfUCRK+thXrfnzA8OUXTba0HFGTJwQsj+2lwlTKYCtGTHGOxrxIP8MLIfpq85bPvdEpR1EgAWVCWgaHnXz/BxMjZnJSxRJJl5QFiapq20TEOjQRpDhSfkXbaKWZG+ayKjCwJKov9/J9bL+epba1EU+l8iiOVPqL1emrWydGUemNE1EqSmS4UaZCM0YyBG5ljxheYmADn2KEQQtwP3A2MGoZxxgYLnCjceSrousGB1kEkVSemZyn1uIgrOZJGDqFlKHXnn6iPd4NPL6ti29O7iY7H8BaduL+72lFPd6KdgVQPDe6WU7Z1iuPZUhbwEourLG4qJxxNMjoapaMriNtlY9+BARRFYvPrh89KfcXQRJRir4uOwXFyuk5zWQk2q3JJTMOcDy67ldpAAa39QS5vqUaW5pcWCqk70fQYVe63I4Q0PWtCRiKmJVEkiUOxITpiwwyEo8RUlWxOZ2lZAKsso9ilM3qDnA2vrQWvLf990I0sPdGfMZbazLAqCNgKaFCsHIoM0BUfpclTxrAannuH+iCIEsh25KXJhRvQT0txc2ZUtDlQTNvoGHsGhrms6syIbk1F+dx2K+lMls6hcWRJ4s4rlrByUQUlfvcRUYiTab3OiXI8jihqrhSP3I+hjyMkKznmcM5MLmnOdYTiR8C3gR+f6QPN9iRxImYWQro9duw2BVmSuKmxjmf6ujFkQZFipzcVJZHL8NEb1826r9pl1Wx7ejfd+/tYed2xKotH47Z4KbAW0Z/qot7VfFqjjI9mZt2Fz+NAliUURaKpsYynn9vLwbYRykq9VFUUnPH6ilK/mz1dQ+RyBg3lhThslktqGuZ8WFwToGtkgt7RMPVlp9bWF023MhD/A+PqZhxKNVk932X2wsh+bJLCQCqEVbKw2FtBKpfhhZH9yEIwGk/QUlqCy5YfqnayacMziSQUih1XMZR4hmq7mwnNgcfioNZVzOH4CIdjwzR78zfxWeexSBWgtQMayJM1S6epKDozKuqx2yj3ujk0OpYfmpfNYpulQ2y+PL+rA5fNytBElLiaoS5QgNtp49WDPaxcVDFrFGIuAqX3MD7ybXThJmfYcFt6SWjFBMr/ZEFtN7l4OKcVb4ZhbAQmzsaxOluH+Om3N/CNz/+Sn357A52tJw7bTc2TCEeTZLQs+w4M8Pq2LhY1lPDpP76Zv7rjOjx2GxOpFFVOD1c21pC1S8zWOePyOgnUltC9r++k7a5y1JPIxglpC1ucPJUK8bjtBMdieN12PvRH6/mT912DzWalwO8kGk1xqH2YdDqLezKFs9BouRyKLBGKpSj1u/G5HdPTMG9a3bjgx7tYqC7xk1QzfOfXr/ClHz/N936/+aQUWKf0OmKZNmThxir76Yo8SDTdylAqxKgaRTd0Gj2lKJKMS7HTHRvDoshYZQW7IqMbxvS8iVsWn/vPyG1pxC4HWOaNMRQeY8u+w+zdMcDEcILuSJAWT/n0dzkaVykueqMI+XDXKNhugFwvCBvgXBBF0amoqNdhZzgao6rAz59fdzWSLPHbvYfIZLMLdv4Ag+NRRsIxEqrGovIiKkv8eJz204ry1VVdTVHpJzCED8OwIUkyo8k1lAWuWEDLTS4mznWE4qzQ2TrE4w+8jN1hpajUSzya4vEHXubeD72JhpbZw3cvbmpF03T6B0JkszoVZX48bhuHO4Ncd00LN6/N/0yxZ2CYlzq6eL2nnyvrqo+7z7plVbz+xE5CoxEKAidWFC2zV3Ewuou+ZDeF1oXNVc9WdxGPqyxuKiOjZekfDNM3MIHX6yAeW1jBIC2X4+mtrRgGfOTOK+kYHD+lkOylTMfgGO0DYyTUNGsCVUSTKj/ZsJ0P3rx2zvdtOLkBA0HOUHEqldjkIjTyeh1Zo5hQJs4SXxV2OR+FiGopotEsawv93LNqKRs7us/KvIlTQQhBseMahsYfoqAzSUj2ozt17BE76miGJ9Q9SHssJMMawbE4CPB67FgUmRdePkTDe2yE1Wb6BlLouW3olFFceS81/tNT3DxeVLSuqICnDrbzg1e2ktV1RmLx024pNQyDjJZlLJqgpSpAgSdfYL0QUvd1VVdTV3U1hmEQHX+IUKaNl3Yf4tbLly1oxNRk4Vm3bl3L1772tb7rrrvulAajfPGLXyz9p3/6p6rBwcHd5eXlp+T5nvcOhRDiz4A/A6ipqZnXPl59dj9ur4PRwTCjg2ECFX5cHjuvPrufhpbyY0Khb7qmCUmS2Lq9G4tFwu22U19bgMtpRdcNRkaP7/WvqChlNBbn9Z5+StwuGoqPDUXXLq3i6Qde5Id//ROEJCitKWH9vVfOqkSqSArljhoGUt0s1Vdhkazzeg9OhdLJ+gqP286i+hKCYzG6esZwOa0MDIWoLC847WNkczrPbGtjYCzCDasW0VId4OY1C2D8JcLzuzqoLPbRPTJBKJaivMg7/fpcDkUqO0gmN44sbNiVfPeQIrkZTXXilCtwKXYUIaEbBomsyuGJMSr1Cm5Z3EhmJEnB3gTaYIyCChlrWRZKz8rpHsHxUhe1NeXs32NQ4BikeE8lqVS+limhp+nIjCIpgiZXJU67jZyuE42myGSyDA4Os6axiwMdDkajN+PzOvOzYTZP8N53jC54iq+xpIjG4Dj//fIWCl0OVlSUnXZL6fb2fjwOGx6HDaslH0E6uvDydBFC4C24ifpUL5sPb2dPZyGrFp2ZepDzhV39Q44nD7T5h6JRa7nXm7ljaXN4ddXFK18O0NHRYXn++ee95eXlc4+DnoXz3qEwDOMHwA8gP9hqPvsYHQxTVOqloNjN6GCY3sOjWG0KFqtC++Fh7n/wZSLBGJmURrsisXFTK8uXVeLz2fF5HZSV+qenWiaSaUoDx/f6hRBc31TPeDLJw1t3YbUohJKpI55AhjpH6dzbg6JILL9uKbFQgke//ts55c2rnfX0JTsZTPVS6zrzIeaj51o47BYCxV6qKvw889x+CgpcjE/ECQZjp1SwOVWFPjgeJZnKUOBxcO+bVtBSfe6HaV1oDE1EKS3wMB5NMB5LUl7oOSlZ97xeRwS/bem0XkciG2IwJbHMX8291et4afQgw2oYS85KhVbBLfVLyYwkefyBl3F7HRSX+U46yrfQzBxr7/c76euf4D+/u4FFDSW0dbpZed0ES677A4psxcgUoU5cRudYJZGGKHo0S6WS94CMChgNRqkqGSEYnGDXoZVouQm83hQ1lfkHgTPVQt0eHKexpIjRWJyeiTCNJXk59Pl0zBzqG2VbWz/XLq+notDD87sPn7Eon5ArCBQtZ2lyD5taOygt8FBWeHGKh+3qH3L8z6tbSz12W67U49Giqqr8z6tbS//vNVeMzNepiEaj0lvf+taGoaEhq67r4q//+q8HP/KRj4Q++9nPlj/11FP+dDotXX755fGHHnqoR5Ik1q1b17JixYrk7t27nRMTE8oDDzzQ9ZWvfKW8tbXV8ba3vW3im9/85mBra6v19ttvb7rssssS+/btczY0NKiPPvpot8fj0Wce+/HHH/d++ctfrshkMqK2tjb9yCOPdPt8Pv1oGz/xiU9Uf/WrX+1/5zvfOa8bzXnvUCwEgQo/8WiKgmIP/iI3kYkEfYdHyaSzfPPrTzI2FsPtcZA2DFJxlVw2RzSS4iN/ch0/f3wr8bh6xFTLu26bfTKgRZZpKi7ike17cVktrKmuOOIJ5PXHtxCoLmJiKEwmmcZTkB+FvenxLbM6FD5LAV6Ln75UFzXORWc81DjbXIva6iJ+9+QufvuHnXi8DpobS0+6YHO6Ct1hJammGYnESeey8+5QuNQpL/QSTaoUepz0jIZIpjWyuj5niDunp5En9ToECoahk9Gj9CV6yUo3cVPZctyKnRZfJZGUyiPb91BY4OTKumoe/s5zWKwKybiKrhu4PPk25lef3T/971T075pblp0xJ2PjK21YrQpj43HCkalIrkE0mmL5ChdFZTEs1hxatBGcGSzODSy13o6jaRk/37OZfmUMrGBTLZTZ7dx+g87G12qorWshGlUJjkVp7Rimtrpo1kjk6TIYiVJT6EeRJQbCUYpdTrwO+yl3zPSOhtm4p5OqEh9vWlGPLEk0L7BzfnBilKe62xhIRKl0ebmrtpmGsi76w1387HkDiyITjCYoL/Qu6PTWM81TB9q8o/HZ5cufbz3sV7NZKZ7JyDApX65lpf984ZWKm1qOL18ecLu025deuPLlDz30kK+8vFy7+uqr5x2FOddtoz8DbgCKhRD9wJcMw/jfhT7ONbcs4/EHXgbA6bajWGSKy/2sv3UZ//G950irGeKZLHa7lUKvExmDwd5xGhtK5xwYNRuvdPXSHChiMByleyJM42Tq49lDHai9QUrrAkwMhwkHozjcDlw+JyO9cxfUVTnqORDdSTQbwmc582I9s9VXhCMpFjUEGJ9I0N4xQnVV0fTMjUX1gWNEiKYuMk9tPUQqnWE8miCTzdFUUYzdZjFnTcyTm1Y38pMN23HarAigLxjG7bDNGeKeSG/HInto8n+CUHoHqewgQ6rCRO46bq24HbdiZ8OWAzzy0g7akhEcNgufWL+O4b4Jdr92GMQbSoZCgMNtI7Y/SU/HCIUlnjMeuUgm0+w9MEA2m0OWpfxANr8z72CMxVj7plEOHS7C5R9Hso2RigTIGlaWXNaLr+BNPD4miMQSeKJOcBlUX90JThuqfhmGblBR5sPvc9DVM8b+Q4M01JVgGMaCO/BTLaUVPi8TiRTdE2FqC/0n1TEz9f3qHs6nulY2lHHrmuYz4pgfnBjlB/tex2e1U+7yEMmo/Pf+Dj69tJymQAff35Rgwqlg91mxh4PsfXaYv7hl/UXxfY6oquy1HyVfrsh6RL045ctjsZj0b//2b+UvvPBC+3zPD86xQ2EYxvvOxnEaWsq590NvOuIp6tZ3XI632I0hCYTdgk0HRcshGwbIEiKdr0WZ7cY6F1NFa5IQ9IUijNptlLhdDEaiLKkpIRZK4PI5iU3EKa8vJRFJUloz95ewwlHN6+Mb+XX/QyiShQJLMav8V1DpnP9go/kwMhpFcVmIqTrDEzG62mM0FhdQnHQdMfGytMBDNJHie7/fzMq6cl490IPbbsHnclBbWoDP5UA3DHPWxDyZOeGQIUEqk+Vjd10968U8k4sQVvfgsbYQztbx4liCg1E3SS3N3ZVLqXQWsmHLAf7jDxsxLAKLIiESWb7xqxe5zluGxabgdNmoqCsmndKIRZKMD0cYG46Sy+okYioen5Py6ryzO1WfNF9m1kkUF7spLfESjqTI5nTcLht1tcVYlPy1PRZXKQ14cbijtCxqYmBUkBMj2ByFNFY24HBH2Rg8yPLiGvpd4zgqrSz1FtAsH2BHtIor1609IsVXWe7ncFcQWYKXN7dTWuLh1S0LN5NlZktpTaGfPQNDdI5N8Le3Xj/ndlPfL7tFIZJIoeVy9I9F6R4JnZGb+FPdbWR1ncORCRRJwqVYMTD4WZedtcYo9c0RBvvr8GQEhg069Ake2bqLL1bdsuC2LDRzRRIABsJRa1RVFa/9DfnyqKrKi0vt2T9ed/HJlx88eNDW399vW7ly5VKAkZER65o1a5Zs2bLlYE1NzUkXZl4y8WbDKqP57WSKnaR9NvZ3jvD7p/cQKHLjtFkoLvFgscqMj8WJRJIsa5p73PVcVPi8xNU05V4Pfoed3okwo9F8Nff6e68kHo4jW2SS0RSh0TDxcJz191455z5H1SGG1D4mMkF8SgGpXIIXRv/AQPKUBeFOC8kps613cDK87kGxyewZHmUoHOWprYewWmQEMBqK0TMaJhiJ81prL00VRdSVFdFUVYLPlR/xvBBV6JcyzVUlfOzuq/n8+9/M6kUVOOyzRnAZS72KEBKRbB0PdW9iJBUmpaWxygrbQp20R4f4+cadyBaJZC4LsSzWuI4NmcMk+dNP34bdaSWjarg8drx+JyUVfmqbSqlvLsflsRMej9O+fwBZlhgdDM/7vKbqJCLRFEIS7Nzdy69+twOLRebDH7wWl8uGqmroukEsrhKLq1x3bTN2pRyPx2B500pqq0upbzTweAzsSjnDaphCm5saVzHxrIojtxebJLE7UXpMC7Xf5+RT993Mm29YyrYdXfzHd59lbCJxhObN4a7ReZ/fzJbSZCZDld9HbVEBRS7nnNs9v6sDt8PKSCiGYcCK+nIKPI68U7nAhNQUrwz1MJKIYZNlrJJMOJ0imIzz4uA4vx9VuKL0MB9ftYlPrPw976vfyBJfiO2R+Q8DO5+4Y2lzOKam5aiqyrphEFVVOaam5TuWNofnu8/u7m6Lx+PR77vvvolPfepTI7t27XIeT778VPc7JV8OMJt8+bZt29z79u2zQT4asWfPHtvMddatW5eamJjYPTAwsHdgYGBvaWlpZseOHafkTMAlUkMxs5DL5baxZ38/sWiK229ZwSfvu4Wf/vAFJlQNi8tGLqtjTWS4Yt2ieR9v5hNIXVEBO/oGaQ2O8d61K2ioLOddn3krz/74RYY6RjB0Y86CzCl2h7dSZAswnh4lnovisxRMv34mohSzpS5yLhk9p5NKayQE5IRBToL2RIT2zVG8LjuJZJpMJofHYaOxphibw8ofvXkNP9mwnWhSPe74X5P5UxPwY7cotPePURM49nqU1AaIa50U26/kl/1dOCQL/akJrLKFxb5KUtk0L4zspysUJkkWJQdFwoarKJ8eDKaSNC6rOm6U79Vn9xOPpigq9ZKMq3S3j3BwVy9NK6pOaPfxuzWK+e2Tu4lEUwTH4+g5Hb/PSU1VEalUhlXLa3C7jh1rv6g+QDQ9U+ejnJjWgRCCas+9lNn7iGkpCq1uEtZxXHTQk2nAZ8t3KswWiXxpUxuyJDE4FMKiSPi8eWf4dAs2Z7aUqlqWn27dxQttnbzzsuVIs6RYhiaiGLpBMqPRVFGMw2bBZpz+RNmZdRLlLg81bh/DyThWWaHI7qDBWwgCMGBMTSALibFgDyt8Q4xn3PTFq/BYUry1ejOPM/eD0YXC6qry1P+95oqRmV0e71mzcux0ujzOd/nyheCSkC9/4KebiMZVkskMwyMRFEWisMBFRZmfD/3Rejpbh6YvlEWlXmRZIITEdXesoLphfheNmZLHHpuNdC7HVXXV3L6kCSEEhmHwy2/8nkBNMde/68RCOw/1fA+/Ukh/Kh+1qnY2ABDSxvlA7cfmZeNszExdTN38J6JJ1i+r4/FX9pFOa0SiKbJaDqfdSqDYQyanEw8lGQslKPY58bjs6Ll8+9qa5TV87oM3z+qkmJw+G/d20tYf5I9vXovV8sZzgmHo9MYeRTfS1Hrfxz/v/Q1RLUUip9LiqcCp2FBTGXb39HDolQyGMFjk8mO35aMdUVXFa7fzw7/6wHGPOzXjxe114HTbiUzEOHxgiEXLKrnjnVfQuKzyuNvNdPIdDiujwSijwRgNdSXs2d+H1+PA73dS4HfhdtkwdIPgWIy//fSdc74P0XQrw8kNpLIDpLNj+KwraC78BB2xYZ7te5RVjjYqlW6SuSS/CV/LOxo+TrNv9vbHf/3GE3h9Dnr7xkmlNGqqC/F7nSdly6nQOjLGM4faua6xjlWVx08VffNXL7O9vZ+A382iiuL8+SZVvE47H7t7fmJdM+skJCE4MDFKOJ3inoZlXF5ayU9bd+Gz2vFYbcQyaSIZlT9bvo7Bga/gZj8BV4QJzU5cc5BIO7BZ63jziv86ZTtM+fL5YcqXnwNGRqOUFHsYn4jj9zmpqihAksR0FXdDS/kR+d5MJsvzv9nJy0/tpX5xOYcPDJ5yBfvRQ2229Q6wuauXvX4vKyvKEEJQ2VhG78F+dF1HOkFRVYGlmFQugc9ayKg6RCqXnH59oZkS67IqMkNjEcIJlXAixa8378dtt1LgdrCmpRqXzQJCTF/UJrpDbIz3kExmsEgyFrsCkkBO5NOQ8xn/a3JyNFeWcKBnhK7hiSPacKOZQ6RzY5S7bkUSFgwMBiLj2IMyu0IdCARpe46UJLGqpoKu4TEyRg6rLhPPZIhrGh+5dfab1fHqkz7+91fQ3xnktRcO0ravn/HRKMGhyBHfn42vtOG0W4nFVbp6xsjldHI5nXAkycpl1RgY+DxvqJ/G52jXnslMnY9o+hDDyeeIa4dZZM9SEmijP5lEJ4MkubmzoB2r3gnM7lBMzWRpbCilqztIb98EiYI01VULWxjdHCji4Mgom7v6WFRciNtmO2Ydr8NORsvhn6w/Wogo31PdbXgtdiJplcFEDKsssbggQDKrsba0CqfFekSXx3uaV7KkMEBJJkZ3LINmCDJZGVnOUuwN0+CJnc7bYHKBc0k4FKUBLz3pIMGWEHFJJaiPEwgXUBs4/s3NalW46a2r+dn3X+An33qWhpZyAhUFp1XBvra6gsFIlJc7uinzuAl43FQ2ldGxs4ux/nECJyjKXOW/ghdG/4BNdiAhMZoewqN4uarohlOyYybHixg0VRZzeHAMXTeIJFUEAo/TRmN5EZlsjj+59Qp+smE7OV1HB+KTY7Lffs1yHm/byvUt9ezuHWI8lsSfs7Omthw9mXcoZkaCjnbO5lpmcmJKC9x4nTbaB8ZoqQ7kR2knnp5UEy2h1PFmBpITpKMZIiMJRMJBLpklQYa4YrCucBmfe+cdbN/bxc837mQ4HqfM7eYjt17NzVfOrTtztEMO0Li0kt8/vJlHH3qFnMOCxWPn8HiU1vYh3v/h69l3cJBsLgcG+HwOigpcOJ02xsfj3H37Sh557HUkIU66Xft4eKzNhNK7GE9twSWN4bWWsVSZAF0Dy0o6472EYr+i1LMOh3L8gXEzZ7LU1RTT2jFMd+8YV59GSvR4CCG4oamBh7ftZmNHN3cuO1IMsHt4AjWb5f03XcbAeHTBZk0MJKKkNI0xNUHA6abG40cSgoFE/mFrSWGAJYXHRmkNKUOpy0VEA8VuxSHZKbLlMKR5zUMymSemfPk5oHZtAb/b9TqunA0XdmK5FMPOMNetbp51G6vNgpEz8HodBIciuDwOPL78E9N8KtiFENyyuJFHtu/hwS07sMgyg+EoISmKZ2c795zAoah01nJj4C52h7ciSzKanubqohvnXT9xdEdGJJ7iW7/ZREtlCaF4ilzOoDrgo8TnxqLIRJMqpU77Ed0FR1/Upp7mbl3RxMhohKHhCKN9YZa0lB8RGj+6vRA4L4YmXcgIIWiqLGFHez/DkX2MpB9G0xMI7FjkAjoiD9CaXIXWpVHZUUhHcQjNn0MyLBSEvNQnHRQ4Hdx85dITOhAngyxLdPWOkXJY0DM5iKdRvA5aRyN887vPYvE5sdsU6muLp9MrU90as81BOdWaBSEkiuxXMph4gkzuAFalCfQxkIpB2KhwVNMb28+rY628uWzFcfdxtC1LWsqx2y30D4bYu7+fFctOXCtysvgddtbVVvG7vQfZ2juAqmlU+Lzc2FTP7oODFLgd3HnlkgVrETUMg0wuS38iQqOviCpPXgogklapdM0dDZow/BRLw0hWCNgLUUQOYaQZNfyYMchLl0vCoehQhlheX0nH8Cgj6TA+q5PF1RV0KEPcxDLao0O8MLKfYTVMmd3PjaXLaPKWMxGM0byqhu7WYXo7RmhcVonTbZ93BbvDYqGxuJBf7zlAidvN8vIAIfcYj7YeYslI0wmn5FU6a6l01qLmkrw4+iQZY/5PA1NpDZfNytB4lGA4TiKdoW0gyLuvW8XGvZ24HTZkWZoW65oKrc6Wupj5NBco9pLN6XR3j5PL6Tz3+124vQ70nE5/VxAhBGk1wy//9yWEkBhVIhwoHCblylJU5KZ8xHvarYeXGk2VxWxv76dt7PcUeG1k9SHsSjF2uZT2xGFkfSexHYvolDU8WgE5t0zSyGFIFvpDoQW350DHCAUFLvSsTnAsRlTLIltkwhGVv77vFp54Zg+alsNqUY6JQsynXft4uCx1OJRyEuntWLNdQA7kfAeXXcrgsTdwODJCo7uMWvfxv39H25LL6by8uZ1tO7vpHRhnZDTG6AK1lDotCgeGR7HIMpfXVBJNqXxjwyvU2318+M3rFtSZ2DjYjdtixW214bHY0A1juk7iPc0niAZZWuhNDRCQ01iEShY3EVGHsNQtiH0mFyaXhEMxrIapKCzEcEAoE0fTc4wbUUbGwwRsXjaPt1Fi8xKw+YhpKR7q3sQH6tZPT9isay6lff8APe3DlFYVEqjwz9uWXQPD1Bb4mUimCMYTlJX46Ooc5g+7D7L41pPz7e2ykzJ7Ff3Jbprcy1CkU/8Yh8aj2Cwy+4aGyeZy+N0O6suLSKoZbr28hbqywuNGIebi6Ke5qvICbn/zcjq7gzy3qZ2sP8NAcYRMXQ5bQqFi0IXzsETcn2Z8bRpZlVBigqA7Qqgiidphhk9PBb/bQanfTSjZi8tlAyFwWqoYTIWI5wQeNcagkcUuyeCxkDFylCtOcpkso/75F2fPJguuSYJkQiVrABYZoWVxWhXsHhuXrazB6zl+t8ZCkhcOu5qR9C482S0oSgVgm1YULfN/iEI1wqZgK+XOAqwn8V2SZYnrrmlmNBjlsV9vp7zcT31tyUlPjZ2L59o6aSwpoj8UYSASpdTtJpnMELKlqShauBbrV4d62TE6wC21zZQ6XDzd035MncRcuC1NjCZfQEiX4VDKyOpxsnqMeufNC2ajyYXHJeFQlNn9xLQU1c4iqp1FJLNphlJhskaOp4Z2o+YyxLU0fquLgN2LR7Hzwsh+bp6csOn2OqiuD9C2r49UMsPHv/CWedsyGInmRcPGJuidCFPtdmND0DlwYunpmdS6GhlS+xhI9VDrOrV8biyVJpHK0Dkco8DtpKmyGKfdSjSpTotMzbeAUmRyWMIq1rEkFquVIqcNW22An8tRRmvi2AwFn3Cg+XL0FsRY37AISmPkcglsihU1lSE9kSGhJhmpOPNCaBcbTVUl7A1aGEt1E9X97Ai3omYzlORkUsNebNVuxqMJyGqUWBxYNAM9o2Orc83reDO7NUqKPUTjKg/8dBPNjWVYnBYmwgl8LjvFJR4i4wniUZXmyTTBQkUhToRDKcdhqSKhHsAr1SCMYZAqwPZOZOtirgtEuL/jBb6855dYZeWIKOVsSJIgnsgXisZiKsMjESrL/cDJtZR27ulh0+NbGOkNHiEQOBiJUub1kM7mGInGiUVVHIqCbD29yMTM1lAAqyRxU3UjN1TWI4RgadHJq7wZhkHWCFPiuB5JKKi5IexKOdWee6cLYk0uTS4Jh+LG0mU81L0JAJdiJ2foOBQrH6hbz0+7X8YhWYlmU0xk4oylo3gUOyPpKB9Z/WbWvn8xj+19jaAWxVlipS7iQ01p87ZlauxuQ3Ehh0aC9CcSaIrAn8qdeOMZ+C2F+CwF9CQ7qHE2zDkeeLr4cjyKJAnsFoVivxNV06gs9mK3WY5Ja8yHo+skxkejfPsff0N9SxmsFFgyEuQECbuGpBjk5Cw7SvqwF1qIjSZQZBXZLpFz6mjjGiFrkj2vdzJmjfH4/i0EtSglFi/vWHEVN648tQK9S4WG8kJeH5EIpsKMR6yEskmskkZIzpGUrsFe4sLnkHHFdPREFqvHTumiYqoriuZ1vI2vtOFx23G77EyEEwTHYoQjSVJqH29/yxpe3HiI+HicdDKDq8CJxWWl2G4lHk3h9jpOfIAFwDAMCmWJUWz0pFUkyYJdkSmzCrxAJJOkLzlOIquy3F9zRJRyLqdidDTKooZSBodCjAaj2O0WCnzOE2qAdO7p4dGv/xa3301JVfERAoEVPi89wRDBiRid4xPousGyylJqCv3zPv+ZraEA7eEx7LKFP1rsmddY8VS2n3RunAr3bXhtpyfxbnLmOFX58k9/+tMVP/3pT4sLCwuzAP/4j/848J73vCdyKse8JByKJm85H6hbf0SdxFurLqfJW06lo5CYlqLOVUKVs5CxdIy+xDgSgm+3PsXhzAi1q0tZbqknkVXp6B3imW07KCj2TI8ZPhVmDr1qLCliZ98g4zad1aHsSbWPTiGEoNbVyJ7wVsYyI5TYjj/Zc6r40iJLhOJJQvEUFlnmk2+/FqfddsppjbmYkol3uu0Eh8KMDubz8oYOUolMpV7IoBYiZWSRhMBps6Ghs7qogoiSIDGYIhlNY/gExhIHQoP/3P17+kWIEsVDkcVDLKfy3R1PA5hOxXHIii6ixDnU1kxhYRi3LUEs7GLnaD1WX4b19dW0BycoanDgttuIq2kiappbFs9PxXZkNIrLbaPt8DDJZAaHw0pjQwBNy3HnrStpaSo7Iq2xZkU1ra93sfHJPdx67+UolnlLI5w8uQFy2T7Gc2kSRj+F9jVouShdkQep9/0JL4z0Uecqpi85QW9ijOZJJ+KFkf1zOhRTRchVFYWk01n6+ifIZfXp9tbZohCbHt+Cw2NHkgW5bPYIgcDme1fxu20HcCpWrEjEDY2O0XHeveb0WkN9VjtqNktfLEyly0uJw83TPe2nFJmYIpTejSI5CbZa+fXjvzjm/C4Wdo4OOn7ffcg/GI9aK9zezN11i8OXBSouavnyj33sYyMzhcVOlUvCoYC8U3G8i8PR0QuXbKPcWcANJUv4/eBOwpkEmp7Db3XhtTioqSihPxlh09N7ab6zli2JjmOKOediauzu1NCrVVXljFsd9LeP0d81Qs2iky9CLLdX0yrtpTvRPqtD8fyuDrRsjuGJGIossaS6FEUWvHaoj4/dPbv2w3wYHQxTXOZjsGeMiWAMf5Gb0soCIhMJfDYnQ9IEPsmJL+1CjWlEIymc2Lhu8VKekHdi2BRkTWCVZTx2O7ctXskPJp4hm9MJ6nE0dEoUL2Thsb2vmQ7FUeiGxljqNUZisDNagayWI0dlskJGlyAQj/Gxt1xJ6+jY9N9fhc/LOy5bfsqy2QDZbI6crrP/4CBOh5W62mL8PifxuEpxoRs4flqjyOvkxT/s5vWXDnH1m5eecfVctF1EtV6Esgw524uaHcZlrQNgOLmBYbWUgM1HvVuhPTZEW3SIRk8Zw2p4zt3OLEKuqSpi38F+DneNctdtK6ajEA6PHbvTRs/Bfvb+5UFW3rCULU/swOawIoRASILiqkKKq4oY6Q2S7J3gspIyWifG0Q2DQpcTl6zQ2hXktpXzSycMJKL4bXa6oiEK7A4a/UUYk6+fKplciITWQ2awlj98/Q/HjbJcDE7FztFBx/f2bin1WG25MpdHi6RV5Xt7t5R+bMWVI/N1Ki4E+fLT5ZJxKGZjrujFprFWKh2FjKWjhCbTIRiQCWTZk+rj8U3bcWWtZGM5+nwjtFYO8rFVt5yUUzHzAt49Msa/dPyGX27ZwyfrS1FOMkohCYkaZwPt8QPEs1HcypFFW4ZhsLdrCDWj4Xfliy4VWTpjolyBCv+0M1FS5qO8poh4NIVcp1BW7qVvKIg/48YuW8i5c1gyMuukRna/MEBwRMVoyoHXAFVg3WGjuaISa0amXipmLBMnRALJKlEoOwlqpqjY0YTV3WT1OIdGAhj2HJmkjIGEIsCuCDJxHSHEMX9/J8vM4kun04bVKmO3KdisCtWVBXg9DuKT2hpzzYyoqi9hxRX1bHxyD69vbEXP6mds9oihhyDXRcywYFWKyaGiZkew6wEUyY2aHaLM3kJMS+GxOGjylNMeG2JfuI+VBTVz7vvYltIKMpksPX0TBF89iJAE/a1D5LR8OjObzdG27TAVi0rJ5XT8AR/RsSjBvnGGDo9Q1VLBYDCMXc2R64xRqGoU+STiFQq7hobmtGUuKl1edgWHkIVgka8IIQTRk2gNPR6h9G4kFHb8Kozb5yIejuNw246IslwIDsUT3a3ekWR8VvGbZ3s7/GpWk+JaRh5K5Id1pbKa9NUdL1fcUtMYPt42pU63dmddywUrXw7wv//7v4FHHnmkaNWqVcnvfve7fSUlJaeUi7/kHQqYPXoxVcxZ7w5gYJDIphlKhcgqOh1FYwyNhHEIC/4CF1pGJ9I+wmPKa/zt1ffM2op6POpKi7m6rJztQ0F+vGUH8UyGoUiMCp+XWxY3znnxr3Y2cDhxiJ5EB8t8a6Zfz+k6G/d0ktayuO02GiuLp58Ez5Qo1+qrFvHczt0kVuYYrlJpS45hzUjUrCznyqpG3uRdwm8PbSeYiVJi9fKhtTdw4+Kl/Od3N1CguWF/Xu0xUOJFUgQbX2mjxOIloYxTXRohSRTVGCMUL6aE/Hs5kOxhd3grIW3snCmwng9k9QQT6R1IoopRLUxOUdFzYJVAliBNFkd8/p/5VPGl02FFzWh09Y6BYfB/PrCet9/tOeVuDY/PQXf7CHouR8uKmjM3e0TbDUjoyhKyehyHUkE6N05C68WhVGBXyo+JUpbbC2iLDWEYOnFNxW2xz7r7oyMwXT1jvPDyIV7f1okjkcLhtFG7tAq7244kS4z1j/OOT93No1//LbIsU9VcidPrpO/QABarhcHtXfTEk1gdVsrdTnLJLLHD4xiLiugLRagu8M1qy2zXnHWlVTzd20atpwBJCCJp9eRaQ48ip6eIZVrxWJsZ6TyAkTMY7RnD4bbjL/Hh8jkZ6T214vLzlUhGlX2WI+XL7bKiRzIXp3w5wF/+5V+O/vu///ugEIJPfepTlffdd1/1o48+2n0q52g6FHNw9IXGMAxcip0P1K3ny52/oFh1kUIjYUkjuSSythwvjxykqN3DrlAPxTY3pZNOyYmKvK5YWs++DcM8vnM/tcUFNAeKiaZU7t+8nT+9eu2sToVNtlNur2Yg1UuzZzkWyUpGy/LMjjb6gxHuvnIp29v6iKXSZ1SUK5fTeb27A/UmgdtwokdyRItUcrVwVaCQOysuQ6mSuX3ZqmO2Tac1Vi6tJhRJMDIapasniNUiIysyN7y9jifHdhJLK2TTCoYzg1I0wGXeVQwke3hh9A84ZBcFlqJpBdYbA3ddck7FeOp1VC3NrzuSZNICbciFrSCH7DCQ0zLGoA2vZ/ab0YnY+EobiizTPxgim9WprizE7bJxqG2Iq9ctOuVujVc3HKC+pYzhvgl6O0dpXp7v/FjI2SOGoYJ2EJQWSi3VM4TDKohp7YAx2ZlwVJTS4efW8pUcig3y+4Ht3F25dk6nYibVFX6kUIxwJofisLFybQOyPCmzHkpQWlNCw8pa3vWZtx5RX/H2T9yBu8DFFz57Pyk7KHEVTUhgt+JSczhDKi+2d3JFc4CNwYPHOA3t0SEe6t6ER7Ef0/4+lk5yVVkNLouVoUTspFtDjyaSOYBuZPHbV+It7GXfK60Eqovwl+T/rhKRJKUnGNB3vjBXJAGgPx6xRtKq4rO9IV8eSavyEps9+6Glay86+XKA6urqaWXRT3ziE8G777676VTP0XQo5mCudIgyIfB7XdjHMmT6s/hKXaTsGumIxsHoIKlsmmEjx1g6TpnDj0u2zlnkVdlUTvi5HH7ZTiSlMpFIUuzOhxGfPdQxZ5SiztXE5sHX2NTxbyTUNFrCRlG2hfesu4HF1QGW1pYuaPHl8di1uYMd6S5aGiopKyqkKz5KWEvgURykchkUaXbHvjTgZSw3gNYygHtZDD1uI3KwgMyEh719O7FoDnR7BotHA00gVGh1voYY7kcSOllDI5VLYJfzXQNTCqwXe/RiSoBuNN5PRdFrDKeL2DcEvjEPkuIg2p/CyBpY7RbcHhtlTve8j9XZM0Y0lsKqyDQ3luJ0WNF144QdDbMxVW9js1noODDAQM8Y1Q2B05I9PwZtH4ahISyr8crF1Pv+hOHkBrJGHJtcgNNSh9uaF9k7XpSy3hPgycFdPHD4eYSQmMjEj4k2ziy89Ae8yIqCoshcfm0Lu3b38EpHEEORsRo6hXqOD3/4JgAaVtYekxrQcjl0r53KAo2JwjgdrgRuzcplyRKk3gyd8RFeO7CLCo8Pp2xjKBXiBx0buLtiDa+Nt5PVdTJ6Fouu4bHkvwu/69+JSHu5o66FK8uq5/1WGkaOcHovLksNiuHHYrOQ07L4SrzoukEikiQejnPH5Pld6Nxdtzj8vb1bSgE8VlsulknLsUxa/kDL6nmLi3V3d1sCgUD2vvvum/B4PPqDDz5YdDz58re85S2nNGVuSr785ptvTswmX/6Zz3ymZt++fbbly5enY7GY1NXVZTlabbSnp8cyFQF55JFH/C0tLadcK2I6FCdgtnTISqma140unEVWMsNZQtE4FknhmnQjMWuORncZqVyaETVCf3IcGQmrHELTs3THg8eEJhsDZSStgjJNQvXb6J4I47bZcNttDEbmvmjv6+/m0HgbAplMvIAsKSY8O5nINgOBMy7K1d8V5OCuXqQWmUBhAYfjI8S0FDXOYopsnhMWty250sXj7bux5RzYDBeqNYF1TTsrilexK9yLJa1jkyRkyYbiklBTKvF0kLZYnICtCEV6Y/9WyUrOyLErtIVd4S24Fe9FGb04NBLk5zt/R4lvL42Vrag5aB1eTmWkgssrKwhLGq22cSZSKSqK/FTY3dQXzk/QqqtnjGg0BQKaFpVimezMSJykYNfxmBoa5/Y6CFQUMDIQwmIdp6Lm9MTuppzIsDbKaksrZc4VFMr5fc4UDktpg/TFf0VI3UmRY93xbbT7WOyp4NttT+OQrSz3Vx/x5C93Z6bbPx0uO/s2tZJJpfnjf3gPV7RUsm8wTCScwJ3RwONErwxgeGZvld1zeIhshUy2Ok6N5CYRjBMTCXYWp2guCjAmHWY0EqUrOkZW17HKMi67hYe7XyGeU3HJtumnU5dip8jq5nB0mHXeItx2wQ/aN5xSAflMYpl2snqCUudN7H7pAIpF4YNfehft27umoyx3fPimC6J+4mS4LFCR+tiKK0dmdnl8oGX12Ol0eZzv8uV/8Rd/UXXgwAEHQFVVVeaBBx7oOVVbLgn58jNBZ+sQ9//iaUYrk8QtKmp/mvJhL5+57142SPuni7wAEtk0nfERMrksLd4KuhNBqp2FeCxOElmVWFblA3Xr+cEjrzAyGmb5lc3sHx7FabVQ6fPgczj48+tnV3z8pxf/g3A2SEaOYSS9FNoLyAoVh+Ti72/4yzP6PiTiKn/42RZcHjt9l0U4GBtAzWnUuUoosnmm34c/a5p9gt4Tg79kOBSkf3icmBHCYgeXR8Hv9NJzOIrVopCN2kgldAzdAEuGRCxL8VInhl0jEcuh6mmcFomA106By4lu5NB0DYfixK14KbIGUHMpHLKLOyveeUbfk7PBf218GNn+W9JCxW2PksjaMVQLiYE7ee9V9/KTDduRhKB/LExZgRdJEnzw5rWn7FgebBtiy9ZODAz6B0L4vI4jBLvmOxVy5swSu9PGoZ3dJOJp/r8vvo3Fq+YuhpyNgWQPO4I/okHppUCMIZHgQHYVLcWfPG7Eqtaexibi1Hrfh0U+vmP0g/YNjKQi005xpbMQm6TgsTiwPzRBLJRATaoMdgxjd9koriykqLyQXGMFYxNxBofC2GwWmhYFSCTSeNx2PvRH64+pd1jnb+L1bUNsze5hZGQQYZPBKkgn06Q0jWKPF2uZm4HxBA7ZRonLTVbPoWZzVBe7afIHiGtp3BY7ES3JeDpGUI0RSad5U8liJnJhAjYfLsV+xDXnZJwKwzDoiz2KTg5n5Baevv8FFq2uo2xx1YIJ+pny5fPDlC+/SGhoKedP333b9Bcqq2VxFNiw2SzcWHhk7YVu6BTZPNxevprH+7YQ1ZJ0J3TKHQWU2D1Avuf9zhWL+c4zmwiH49QU+Dg0EiSTzfFXNx9fuAjIh51To+RSViw+C66CDIomkHESzU6ckXOfUgYdGQgRjyYpKfdz2zvezBORXQTVKLWuEgqsbmJailhW5a1Vc18nQloQyaHhr9Ypk0txK17skpOUnoDYMgZ923G5LbgdFlLZBPFMFmNPBQPRFFw+jIwVt3CTyabpCUVZJr+ZqHsfVmFH1ZOEMxOkcylKbVWEtAvrejKV1phq8by+sY5wKs1EdgOKrlFoSZDRJIIJJy7ZwFO5h+aqj/LBm9fy3M52Dg+Nk8lm+cidV52UMzHVyTE8GsXAwGaRWbm8hhvf1EJP3/iCjco+Wva8cVkVaipDcCjC4mPLbI5gtlRWR/jXLJG3k9atZKQ4VnJUS20cmngU3XgHLwWfPKLeZldkgiWuDGOpVyl3337cYw2rYQJ2H16rg97EGD2JIE7Zil2xUdg7gSzLDLYP4yvxUL24EiEkRnqD5LxuSoo9KLJEV88YwyNRygJeRkajR9Q7FFu9DCTH+Zfe/bhwovpTFDqLSA8nyY1rlDgKKC73MxwJEerWsDstJCNpBodSOK0WlCIbqTjcsfQyHurehKZnKbF5ccpWgqkkDY4KulNDpHIZ1KxGsd1Lse2Na86JHIoDba9wsO8h8LZCvJ74rjHc3nqKGsp4/IGXcXnsFJV6TUE/E8B0KE6LmbLNuWyOJx/dyubnDnDXe6+ctfbimeHdlNr9DKsh+pJjjKWjVDmLGFbD/J8117P92d1MxDNoVplyr5cCl4NC5/HDpEk1w3M728ml7FhtOfyWAGlpDE2JkUsreOX5hbjnYuaTpa7rhMbi5HSD53v2EXOrvLvmakbT0WPOezbUXJJENk5MixCwl1NkDSCEIJlNUGAp4arLr+EnT8XIVg4hXAmUjIOCkQbed+81fGXTY2jdhfgrEkhyFEXzoCYCPDvRw1uurmQ4FGS43yCaySH5R5jwhmgpOn0lzbPFoZEg92/ejs9uI+Bxczg4znOtnayqLMVbEkbPpVHkLMNJL0KVScng840Cb4xOX15XRmt/kPqyE/8tTHVyuN12NC3LwFAYu83CW+5YjaLICz4q+2jZ833butj12mFq2gPUNh1/4NLMQly/UkhYG+e3gw9T52zCnX6OqGQgRAYfGuM5N5oBVn0jvx5IYgAei0bWyOBR/AAMZ4K4LYfxaf04Lccqh051enksDlq8FUxk4hyOjZDMZsjWZwnu6idzs4NgtcFIZpSybiu1NSXkAl560kFGy0IM+yP0R0dpilXQFCjjtwPbUbMZktk0sayKmtFIpDMUedwsKaxDIPDVOKdtiGkpytMBnn2qg4RnDGxWslaFDBqJiRQFiaJj6r0ckp1FtjruqV/Nb4ZewSoUxjMx+pPjDKVCFFk9hLX8AMXZukMOtL3Crs7vYPOkkA0PE8EUWukzlDg/yO8e2sxEMMbYcITaplI8vry9pqDf2cWUL79IkRWZ9bcu58lfvM7m5w9w492r52xFbfKUE84k6E9OsC/cS7mjgIycQ3JmOdy7CyOlUGTxkFNqeOZQB+9Zs4KuoYnp4kq33YYsCbwuOzfV3MCWyDNo2Syy7CAlJtBxcnft3Qt+nlPTMAGCQxFKKwtQ63SeO7iH999yPVcXN886qOiYkLOzkeF0HwWWYgTglPNFg8lsglQuwVVFN1DpDPDB22/LPxl3TIpP3Z4Xn7K0KhgjPkYTDjRXDmvEikPIjDmCjO4qY1+2B6fsxG3xoCYNRnLjFMsRhosHKLNXLvh7s9A8e6gDn91GzjDYPzSCqmUpdNpxWi3oWQW/a5xQxklatSHLChYlTTRxpPPZUF7E/p4R+oJhGsrnHq+98ZU2XC4boVCCiVCC6spCPB47r7zWQXPj8QenLSRL19TS2xnk9ZcOUVpZgN15rJbL7vBWHLKLrKHRnewnZ+TQ9Ax9qU5utEkk8VAix1BwYZOqIJemQomzL2fBIqykcgliWoSIHCZgKyeUdWCRvARTm6hR3o0QR86AObrTyyJkyhx+FulFPFu8lYG7BcW6hDejEM2lGKoKc/nay8g5rfxmXyf2nBWXw8aIHmGLchCqNfonxnHJNhyKjSKrm7FIijrJRYnPwT3V63ioexOSJo5MTyxaz67UAOqEnXR5Fq0wi12z4R12IudU4I16L8Mw+EX7XmLONCuKytgaLiCmpWjxVpDIphmdrOuyyRZ+2rmR1/rbSQ+qaJHsEfN0DnQ+jsACUpTIsJOJwRwWl40u9Sm6WldTGPDgK3BNTzs9HSVmk4sD06FYQPxFbtZc28TWja207uk7bi545gXKa3FS7RT0JA0KrC7+9ZVfss3VjhLPUfH/s/feUXLc95Xvp3J1ztOTI3IGCIJZFCmSIkUqmFSwkhW89lutvd51fmeD3/Oes+u3Z61nW/au9CSvHGTLkiVREinSFAmSYgIJgkSOg8HkHDqH6orvj8YMAWJmAAzBJOGew3PA6a6uqg5V9/f93u+9QoiybTA2dYSqYyPacOLUJCGfCmcNq1zP49/90s1cu7adloEITw49Td6oIvs1NjVv4IbOi9SOV4Dp8Rx2k8er5gC1G13CUQMRgfiY76Jk4tyV5aQxypH8PtaHt3FP0wPkrex5ZKNOJuoCr6VWxhECDLslpKyA5FdwYw7VjEHMDnHouSJVrRWnZwYjMkeAGA3Ta8iWKhxIvEhUSZA1Z8lac+/YCZCxXAHXcxnPF/EpCmsbkoR0jelSloQkIYZcqjUVwRPxaxYhxeb06e7zXqMpHsanKvRPzF2UUExM5evaiKJBU2OUdEMY7w1MclwuRFHkxjs28Oh39vLyMye55e7NF3yfstYsCgpTtXF0yUdSieETAxSdPA3+a5iqvIrklTCEJJbrIFEh6dtGh7CaqlPGJ/kp2nlma1P0l0+R1ltI6NczWPg2R2p/DDjochON/jsIa2sXnfS6VV/D6e8eJ9EZQU2FyGbyDBt5VF3BFw/zI/cwlMCXlqmUDPKmgxaSUR2JXKXCtpZOMqUKc9MGI/lZTNthVXucZl9s2cmy9JRJvimBPVglM2Rj+BWCmk5y4nyd4GAhy3i5wPvaepBF8QJSlNRCiILINfEuftL/KmPTcwTRCUd0vKrH6JEpvj73OGusIVxfFZwyo8gITSIpQoQCVXa9dx3Vcu28PJZKyXhDScxX8e7HVUJxhbFmcyvjw3M8+eMDPPfTIxRz1fMES4tdMP5d2z2kfVF+/eBXICxhuS5lt0ZUC4AFE9lhfpr1aFaCTOfK5MpV0rEgiVCAV0+Pce3adm7s2saNXdsAGKn0czS/n3FjmBbfFb5Jdog8751EcgRCIR8ZvYxgwZZQy7IWyvMrS13SmTLGKNlFwkoMSRAJKmGCSviyb+gd02FGAjN4oocw4+G0uHgJ2DjTgJYMEvDHKUx0kD1RIWs7VDQZUdaQd6g8MfYTzJyMkwnjD2YZahrmQ90PvGNIhe26GJbFWL5AazRCZ6JuSlSoGvSkhykUfTwztJ41eon2oEXJDHBsfDVrKtvOex1RFOhsjNE3NoflOCjS4uO7pmVTKtfIZMv0dKZIJurVotIbmORYCaLxIFuu6+Hphw9w+OUzmDXnvN+PLuoMVc4QlMO0+DoQBfFseyxJKPheVPsAZQdyjkRQsmlQU/iDH2Or7uPp6UcACMkRBAQmjFFkZA5k92Cbh6g5Fao04BPHma2eYlPiNxZIxXy1sZgt8dj/fgpFk4muibMhlKDUbFBxaggICB5krTICAl3BFGKDiCrK+GS1rp+YniI9l+CF2X50UcWyHTzJZXBujvuarwGWnizb0JRGL+QZiYeolEuUDYvQhMWGzvp3dj5R9LnxQYKKyl1tqxZebymS8qMX9xI3A1Rkk0k3jyO6CKJHYWaY1rBKID1JPh9EMEREn0RBz6AbTbzv7s08+DfPAfXKRKVkUCpUueuBN1VXeRXvcFwlFFcYgiDQ1Bbnwb95Dn9AY/32jgsES0tdMNy8RZMvxISUY06r4qgSIRSqZhnDqLG3lkMUBBRNxgKCor6ohXarr4uRygCnCkdo0JpQxCsXAz7VVMI56aDHdIq+Groho5QkrC3L24VnrVnCcpSx6jA1p0pSSxORY+SslQtHw7MKNya6OSyOkZOq6FmVWNiHaZp0tkbOBjfFaG6KkstVGBnP4NY8nn+lnxweaqiGFi9iF6MMninwM/FpPr3h8ys+nisFw7J55NgpIj6dYs0kEaivAgtVA8sboik+Rf94E7WXQwx2B+kNuehlmYYxPx/++PUXvF5PU4ITw9OMzuQX1VIYhsXjTx8jGQ/guh6aJte9Bc5Ocixno/1mwOdX6D85gSAKbNzRufD7ufNzm3ADHuARUxMICOe1xwTJh6ZuQqNGXBDORpTfhaiuo0WF2xruPa8K9tHWO5AEib1T/4WCVSEo2ehiDcvTmazNoOV/wDUN/2HBa2K8f5L8TIHWtS18+j/eTya3j6JVJaz4CJ+d6CpaVRp8kYV/z096AQRiKk2lKC/tGWN1RzvD4hSmbNESiNFopug7leeOZayEbr7/Oia+/BA7nCA3RRrZPTHGTLGIPxrg+Owk3zj+Cp4HsiAQ1XT++vgr/PqmXayPNyBNgP8JCI6DvxmkO6HoVamNGpiyg2qKKJqCFwQj7uA5HlNJgVWyS82UkGQBn2wjSTbHM0l+7XWi2obmKHc9sPOqfuIXHFcJxZuAV57rpWN1munxHFNjWVo663PwFxMspZQQRcMgWdTJC1WMNpu8v4oiachFh5xawp+ywScwYeeYyGS4JXFhSqQgCGyMbGfP7FP0lY6zPrztipzX9HiOSSNHclWEPFWECqTFMG0bG6gF7GW3jSgxBsu9eECjr5WgHF5YWa4UDc1R/IUqa8LbGTw9RTFfxtkhUWqz2HRtM48/dByo23krikQqEeKu2zfyz2NHsef8eFUbJ1HBHxTQihH6JofgbdBsnjvJEff7EfDwqSqf2rkND2/hsZaoytaOLAdHKriljfzhfTdxfP8Q0/1nx/Y+vvjYXlMijK7K9I/PXUAoypUajz95jGLJ4GMfuRbTsq/YJMdK8eKTJ+hc08j40BwTw3N0rE5jq1UeP/kvXHfzRnbGb+ZE4dAF7TGv+giC3AyBLyAI2gWv2+LvWLQCJQklZDGG6eXx3Fk0KQhekKnq8YWQL3/IR2GuRClfYW5sjsxEjts6z28lzOsd5qeaFnvsM9tv4n+89BzVXotyRcbnRlFjQYKtPiYqy7eWXu+weW17EwMbmujP5Xj+sZ8R7okzUirgU1Q6w3EKpsFjg71oM86CkDqRDjM5muF//pcf07kmTXzWx8SmEv6Yj6CkYUo2JavGFjtK1d3PoZEOAn6TSLhKpRRkdmwN05W6ANNpgsr7oWRAUAfn8oNLr+JNxOXGlwP81//6Xxu+8Y1vNMiy7N1xxx35r33ta6OXs8+rhOJNQJ2xx3Bdj9nJPMGwj1DUf1HB0ke338L/u+9haj4RoywjzdnYIY/mcIBKJI9mlbEtGddS8SQHM5Yl6ysu+loRJU67v5vBch8tvk7CSvQNnZNRNfnZ4wdxox5iSmJToIO2QH2VWLSqxJXQktvWHAPwqDhlmvU2AlLovJXlSnHjnRsXyq6NLTHmpnJIB13W/Ot2+tVJPnr/NezZc+aCm+OPBkMEmlzMskA5C8VIEV/QQsxe+amYi+HcSY6AqvLqyBg12+F3bruRtek62VqXTuF5HmOln/Bc3ziDY218ZvstbN/Yw44bL+6OK4kiXek4ZybmsB2XoeFZnn2hl5GxLIVilbaWOJ+4/1oa0/WV9VtNIF6P6fEc/m4bbc04c14OS4+iaCL2nMTO2C345QBdwfPP23Nm8ewzCOquRcnEcqi5GhFZwHR92O4gNWcMTWyi6io8/+BegpEA06Oz1Co11u7sQRBEnn9wL7/yf398yVYCsORjrQ1H2HO4H0WR6UzFqJk2B46NsGPTxf03znXY9DyPfz5whMHecQanz6Dns0wINYI5h8O+DK3rWhgLmuzZcwx/UMeomowOzmIaVv28qxa/+cUP8k8/+RnTLRWKWg29LNM9EmPthlmO5USmhnsIxmMMqDaGbFNTLIJRmScnjvDM9Akiiu8Cq+/LMcx6J+Nobtj3xMSR6JSRU9N61LyzaXNuU7T95za+/OGHHw498sgj0RMnThzz+Xze2NjYZfODq4TiTcC8C2Bja5xy0WB0YIbmjvhFBUstjW00el2MMo7tt3BrIg2lRn71g7fwZwOPEtBljLJLpWoSFDTS4TBj3vSSr7c6tIlJY5QXZnbj4a1YgOh5Hk8+eZBX5SF6WprICVViagDPg5K9vNdEzTF4OfMsiqhyb+PHGar0Lyq8XAle72XQ1JbAF9S4o2Uzz1d7mQxl+cJnbr5gu2ZnPY5vN5sbpwiLFaZqAgeNEBWnEdd1ES8x7fVKYH6Sw3Jd+mczBDWV1akQB8cmuWVVF4XaKSYru8nXjjNXmqZ/uo2dqa1s39hzWfvpakpwYmSaPQf6ee5nJ1EUmVy+TK1mM5cpUa7ULv4ibxECqxxGU4fQBB/StEY+NoEaEOjI3ohfDiy+kbUPQVBA3XbZ+/PJ12A7z6KKQaAB1x2j6ozhVz9I//AMjuVQypRpXdtMOB6qe7+cDcFaqn253GM+W8CTRHA9bNtBkAQQBaTyZQU7IggCuzramC6WiVSDHBkaRlEV2tQwpmFx6JVTbN+5loFTkxiGiVWz8Qc00j0NhCI+MtNFNm7v5Iv+s346fTkSDSHUaBZHHqRHuZ5D/gqmYRO1NYquh61YbFrVyT8PvYjjueCPo0nKQmvnUrwt3g04mhv2/X3/s+mgrDspLWIVrar89/3Ppn+l+z1TKyUV7/T48q9+9aupP/iDP5jw+XweQEtLy/Jl50VwlVC8CTh35dzWleLYgSH6T07yG3903bLb7d7fS0SMItR8hKfz+B1Yd003/f15Ipofy3HwhU0qPgtMF9cVUPSlI+1VUSWmJHki82Ma9VZSWuMlW1A/ffgwPzjyEjNWAcWWEEWBLWu7+OTGW6jYtSVXZeeOhoblCB6gSzo7YzeT0BrYGN2x5D5XgnO9DGqGxY+/tYfxV2bYdnMnuycO89JsLzXXPm++/oPXNjA3PUHVcyh4KlHJ5XYlx77IFN958WG2Ja9l777+hcrGe25a86at2sdyBSzHYapYIqRrrE4lkESR8XyBQu0Uh0e+yvRoGUsapSDZNIUF3r/l8ttELckwuiLz+AsniGoqY+NZRFFk04YWLMvh2Rd63/bKxDyC11Zwj4m4koDaYmJVwB71E92x+PXNczNg94FyDYJwaSFe52Jr4oM8O5XBzyiqKGF4YSo2JNV2tMA0p1/up7G7gURTDHjjIVhTmSIdiQjlosFUrkRjLMTO9mbcyuURCoDOeJR0KIgxVcGJaojTJgOZWYSgjBSSyD48gK+kUS0ZCJZFcWKW8kyOZHuSlu6zPYqaiTubwRyd5PSRMp2359iyrp0da79E0/6TfP/Ac8xYRVJKiF/dchfvvWY7/+fBb4PnMW3kCSk6qigTkPWL2uy/U/Dk5JHwbK24ZHz5s1MnooZriWWnJlHLA2A4lvjV3iea35Nen1tsm6QWst7XuPldG1/e39+vP/PMM6E/+qM/atE0zfvTP/3TkVtvvfWS2yVwlVC8KXj9yrlnXX02vJhbnNi6rsfJkWn2HB9CUyQS4QAtfh+TpyeRHI+JTIEtm1t5eWyYkBxCVqpkvTLTlsH1ieVXqpPGGAE5RMkuEFdTCyu8+QCtxfD04cP8r/0/xS9qKJLEuJgDQeDj/iZa/PW2wGKrkHNHQ4NSmP5yLzW3yn1Nv0xCe/NvVpqusHlnJ6++cBp1RqNiHOGaQB+rgi55J8oTI8eh7WP0xJ8jJkfI5+eomQ6G3UJzc5xE0uBbR0/w/IHDxFpklK0mg2UfQ48N8Nm733/Fb7hFo0auWmWuXKE9HqU9Fl2Y5GiOhDkx/CNO9s0iJDNYUo3JQozGisLp8Z9w3eqNl7UvSRTpSMd46rmT1MT6TXd1TwOaKqMq8ls2GnpJCNfYsKGH05N92J6FvxpHVXyY2gWJy3WY+wAZ1O0r2l2Lv4P3pD/3mmBT8xHRjpEv76fWHAJRIJK8MiFYM/kSjiLQqobo6mznzOAMRtXCLJm0niUsl4N6laKVr5Yr+MoQMBWqcQdvzsb/SpnJ2QzbblrN2MlZwhEf/pCPUqHKzMtnuOG2dQsaEdWnkp8pUHNyuPoEPvd6ZNHPbTt3cNvOCxcBPcF0Pa8nkEI+W9Er2waNenRF78s7DUWrKgUV/TyGp4myW7SqP7fx5Y7jCNlsVjp48ODJZ555xv+pT32qZ2Rk5MjlVGwviVAIgtAA3AQ0A1XgKPCK53lLL49/wfF6F8CXnj7Bsf2DpFuilCSvblA1V8CvKfg1BUWRSUb8xAI+0vEwtmUzdXqSqYksPWtbeF9PJzNmnrmCgWyqJFSBolphulzkudE+GsOBRd3ustYcLXoHY8YgI9V+mvQ2fJJ/WQvqHxx5CZ+oYukOs7UiPkshLgV47PhB7tu+eJASvDYaKgsy48YQkiDR6utksNzHhsi2K/n2Lok1W9roPTrK3sGf8NF1x5g1BcZqAZo1g7tCT5LJ9kOgn4AeJhBoB88ArwiCSiSkobh+5A1HKRWDBIsp9ICD0dPLY6+E+I2uj1yx4xzK5Hj85GlaImEEIO57bZIjb9R4YPsmDvT9FU5qDkk0yVSCqKJONghnpo5y3WUHC9dNrhzXZbpQYuvaFjS1/vN/IyFfbwZiSpJcZJa4rrNKbSUiJjh2vI/yqIe32jtvPNlzs2D3grIDQVg6eOtieL1gc6r4As8c+huUDUlue+82egdPMeZmiIhxblv//hWHYO07NcLq7gbKw0WMmkV3Z4qTvRMMDM5yw87ui7/AIogGdEzFQ8vC2lMilbKN64m4loIvqVMYGMfvWJRzLoVcBUUS8AkOj/7Vo3hArWIiqxKiKLLlwxpyKMiBH5bZvAxnPc/bQtAv2vp8p2G5SgLAeCWrFq2qHFJ8C6SiaFWlUMhnf6Ljxp/L+PLGxkbzox/9aE4URW677baKKIre5OSk3NzcfMmtj2UJhSAItwH/JxAHDgDTgA58BOgRBOH7wJc9z3sHLW/emdh58xpmJ3L88KFXGPW5+DSZQrlK/+QcngdffP+13L61h289uZ9CxSDo0xACGrOzBX7tE7eyOpzi36y/4zzSsCXSwUOnj/C1E0/iKDVkU8O0PPrULCcyE/yb9XcQU5JUnTKtvi4mjBFGq4OE5AgNWvOSxzruZvECAka1hlaUaPLFkBWJGWv5jzlrzYAHGWsWEZEWXweaqL+l+RmSJLLthlU4s/8Lw/DhUxVEb4qAYOETbRy7D+TNgApSAvDAGQN7AAgS0ETCPoE1iRNEvMOUzRh9RgejpRPUv/Yrw/wkx7xZlU9RWJtO8Zu33sBUsXReXscD2zexKhXg+cEMumwwXorguH7CaAhylbHyyhZJsgOaImPKJrIkXrHR0Hn/g7FygZZAmLs717A+3nDRx5bClshO/nn0fyMiEVUS1FyDcKOGtD/NYO8kXedOspivADIo21Z8/Iuh72kRqmE6t9Y45e2n+fp2tmgbqDoVTjv7aa00Xbb+ZzJTZHg6x+071xC+TlmYptm0vgVNkxkZy3LoyAhbNrUu6+nyerw6PYbfkSmUqhxqERAVlYAF8UmB1pYW/LUSbWt9FDIlXMcBBPA88nN1QXeyJY4ki6S6dAIth7GmOpjozy+7z+W8LX4ecGfT5tzf9z+bBgjIulO2DalkG9L97bt+buPLP/jBD+Z2794duu+++4qHDx/WLMsSGxsbL0tHcbEKxQeAX/M8b/j1DwiCIAP3AXcCP7icnf4ioHd0ZsEmuyke5vZtq7jmtnX8818+RM6s4bkejuWQDPpp70jQOzbL7dtX89k7rlnYLp2OEhjL0xKqj2ktJvLaHO3gC09/ndF8lrDiJ6oEsBwYmMnzPXUfn1t7LT8e+z4zRoWybSOLJbJylq7AGk7lR3lm+uTCBeHm1DpmzSJuAIxyDf+sTCwYRNVkirZBSll6FVuyCguZHDE1QUprQhblNzwauhK09zQwVa0xV/TY0Jih5laZs3RcMU1YcsH/Oah8E9wCCEEQwiA1gtTNzZ1PkJCLzNgBcraMJhXZETqCJ65f8fHMT3L4VIV8tcpsuYKuKHxs+yZifh8xv4916dd68pZbYrT0I4puELHm4CESREOWakhCjb7qmss+hppp88LePnpakigBhYCrMDNTfMOjoScy03z96MtEVJ2mQIi8afD1oy/z65vqlaz/78jL+GWFmOY777HlSIUgCrToHSBA3s4SU5J8aPWtHOmd5tUXTtPSOofsPgXOIDjToN+DKC4h1lwBTu/v58z+EdbffjfT/h+RqHnk7Sx+OUhArht+LdcyXAr7Tg3j1xQ2dTainM1GmYfjuLywt4/9h4boH5ohm6swvYiGZz6Yb3o8R6opQtOqJA9OnSJQFckndGzHI5yxIaCQ2xogmEyQyvkpZsu0rn7t2lHMlmlf37rw71AsgNp2ElyRXF+CdPvF2y/inISyV0ed9qM06Ig3SfDOKXS9IWyKtld/pfs9U+dOedzfvmv2jUx5vNPjy3/rt35r9hOf+ETn6tWrNyqK4n79618fuFyB+tsaXy4Iwt3AXwAS8Nee5/0/yz3/nRRfvhx6R2f41u5XCfk1/JrC+FyByUyRVU0J9hweoDxdIurTaIiHcCyHmmHRsCrFl//tR857nfxsgR//1WNcd+8O1l57od/EPD7++P8iW6xiyxa6JiIJIq7nIYsSv73lLh6f2IMsziCINTxXw3Jl2gJBhsozqKKEKFrUHImpqs660FoYdvjZ6aOEFB+pSISyU6Pi1vg3O97PbVu2vC6TI0FcTZG3M5StIrPmdF2rIQWoOhWqTvmiAtA3A6Mj/5lM4TkEF4byKQqaQMzvsjO9nVTyP+KaJ6H2OLjjCwZIgrKaM0MfR3WGQXQpegJFW8Ys6yA2c8OGb6Eol18d+MtnXmS6WGIsX8B2XDrjMTRZIuzTL4ilN508Y6WHsN0q/+P5KTLGDDsTWWJ+g1IlwJmpFjq6ruUPr//IJe/f8zyeeaGXweFZtmxv5+Uzo3xg13raG6KXfS6vx5/tf568aRBUVKYrZQzHJlerIosipuNQtGroUn3d0hKMEFY0IprOb++4cPoGwHZtnpv9KZqoc0Pi9vNW6nPTBV786YPs2vUiycY2cGbBHQOpFQL/B6K6bsXnMW9eNXxqjNxUnu23b+aT/+GX+P7w7+EXTcatNDXHI6k1Epaj5OwMn+7415f8+mOzeR5+6Tg3bexkc9fiq3jP8/jRIwd4+NGDpFIhVnWnqVbNhZh4wXQWEj5t02FkYIZhpYy+M05YD3Gmf5qq6pFUdHy2QLFmsm1bJ59ZvZbvffkhgtEggYh/QQfysd/9EAAPfetvaLh2EH/XCLWZGBNPb+JDn/3Csm2d+SC5UFC/InH2V+PLV4Z3ZXy5IAjfAn7T87z82f/vBP6353nvW+lBCYIgAf+TeoVjFNgnCMJDnucdX+lrvtVYrAqxpjXFT185heO6zOXLnCkZ9fEqoGpaNMkac5qJUHNxLAdVU6i5DtWZC4lpJBkmnAgxcmp8WUIhmBKpQIBC1cIuO+h+GUs0qVo23xncg+naxLU2FFFCFERMx+Ll2T6i+hS2q4AbouZUCChZjGqKNYMd3BPYxmnfFDNWgZQS5vPb3rtAJuaFl34xQH/5JEfyr3BN7Cbubf4Es7WpJTM53ip4notuR4haNfqKEWqyQsyt4asanJnaTCoJJU9g0pYwbBldlmhUBcKCRDIQYqIiEvAcQnjUJBctWkQrF3nsyaN0dyZ5+ZWBy5oAGZjLkClXEQSBDY0NBDQV1/MYz9dbSPOjoWVrENPJEVR6GJi8BqtSQwuEOTMtY+VtlIhMuDXE/RuWnxZ6Pc4MzDAwOMOOrR1sXNPC7sOn+epDL6Cq8nnf25VgrFwgrvk4NjdNxTaRRBFVlChZJooo0ROJo0sKedNgrJTH9AUo2ebS71X5FIZTZVv0+gvK/omGMFu39zM77RGMCOjKLMhtIMTr5HCFhGJemOgL6ZSyJRzbYejECINHRwgmdmCZj9EsTWIIDlVLYdLqotF/zSW/vud57Ds1QlBXWd++tPuTIAhkcxVaWuLk8xUGBmfpaK/nrzz7Qi9KzkCSRCZHMlQrJqpPRugKkEBHTQTYGepi/+kRZowqnf4QW9Z1UFW8Cwyx0u0p7vnV2+ne0kGhdoqd/yrDzFQOsygiE2Dnv8qQ7DSWPadnX+hFliWmZoq0tciEgvrC398p00JX8dbjUqc8ngf2CoLwO0AL8PvA777Bfe8C+jzP6wcQBOE7wIeBdwWhOLcKkQwHGJ3J8eXvP8OmjjQvHB8ioCsoskQ85CMe9hPQVaZyJdKWTDnso5qvksuUCMaDOKJA3Fi8Z9q6tpmTe09j1ixUbfEppw3+Dg6ZvUT8GoWqSaFqoioiN/o3U9OyKKJE2a5hOBau52G7DqaXxXL8OKKJQA5d0lFRmcwdY1toDR+6r5MTVYus5RJT4qyJRnA9l5czz2K6JjXXoOKUERFp0tsw3RqapC/pRviWwtzD2MAoE+PvQ3RH6WmsgNTG41Npxt1purqOMln6NrIYQpPSWE6Bgfzf0Rb6OKZbRpc0Co5HTKoSdCU8QccJmpwaHuSZl59g065xVvUUqZbC/OiJdXzkzg8veRGdKZXJVKrUbIftrU341PpnWDJqNEfCFGqnGMj/HQgSNTuD65nMVIZ4aRC2yOu556adPDt74gKx7aWiWDR4aV8/6YYImze20jc+S+/oLI7rsnNtG4WKwbd2v8pn77hmRaQioursnx5DlWXWxxuIaDr5mkFErd9g8qZBRNNJ+QJoksyZ/ByNgRCW66CI51d7qk6F/vIpmnxtxNTFg8wamw0mRxV6D79CLFahUI7S0gnR2PhlH/s8nn9wL76gzszIHLbpsGZnD67j8fyDe7nht1s5lpnD8yx8YgseFUTnIJ7TTMUu4T/bAlkOw9M5JrNF3rO5G1lavoQ8PV2gsy1BLuJjZCzLyd4JWptjTEzmKZ2YxDJtFFWmrTtFJSWiSXmC4y7JDWEKVYNbrl3D0fEpQj4dJaiS8NU/h3MNsc7FZGU34XgcOVREl9fiV9qxnEL979raRY+xUjU5fGwUx3GRZYlazUZTZQJ+7Z01LfQLgHdlfLnnef+fIAjHgKeBWWC753mTb3DfLcDIOf8/Clyw9BIE4deBXwdob7+4k9xbhd37e3Fcl8m5AsWqiYeHZTsMTmVZ19aAKEBDNAhnV1mFikFTPEywXcI3m2VIkhmfzSPnq2xMJehKL+7S2LqmieN7TjFxZpKODW2LPucTG69h8qUSJS2L3y/hFsGe0diyo53ZgELRqtLqf+0CXbSq9JdlYmoCVZSwvDKOV6NUKaDpDpXrT/DQzJOE5ShhJcqUMcb3R4/R6uvkTPkEmuBDkzQicoyYmkQSJLLWioTPVxyedQzP3M+ZviQlYxdTYzlmdufoXtdENCxxSjrD/pl/pj0QQhAkqvYEjlemZmc4lf1zsPOkvDISKjYaEalG2XEYR0Nf8zjdPeOMO36sik7YN0diw7PsORCip+uXLziWqWKJHx8+wfp0imKtl0T0FfxankotQqa6njvW3sdI8a+pORlcr4YoqCjyKk5M9dIaGOCBXV8iFYuwLnb5UetnBqZ55vleXj00hKrIfPGzNyGKAk8d7KMxFmIyV6RcNQkH6jecpw72XTahOJ2bxXRsTNdhVShJSNXI1wzypsEn1tRFnl8/+jIAIVUjrGrENB9Jzc+Dfcf4cPd6dPk1knyqcAQBgbWhzUvus1CIYtdGCUULGLUIRhX6T/TStX4dicjlvkt1jJ4ep5gpYdVs2te3EAj7F8yrPHeGJn0rc7WTWN4UAamdtNZKxT3DnrmnSKstjFQHFipy55rG9Y7O8NSB07x0cpiArvLeLRef4kg3hBkdyZCZyFHMVzEFj+mpPD5FJmraBII63WsbEWWRU9IMmgGrGpJcu27VguNqUzhE/1wG2/N4YPumZfdn2BNYTgkEAV2uE1VZDGLYdYuCMwPTC+LRVCpES1OM2bkSjusRCup0diQXSNI7bVroKt56XGrL47PAfwZ+BdgCPCoIwhc8zzv0Bva92JL8AkGH53lfB74OdQ3FG9jfivD6tsbO1a3UbIcXjg2iqzI+VaExHiLs1/BpKjP5Ep+6fTvf2v0qhWqNoE+jVK1RrNT4yI2bkFfbTP7Nc+wIx9jqi3D62CiFcpYbP714T7mhPYnqUxntnViSUKxLp/h319+6MCnQmAgSatYYyxdIyTFOlMeZK0ximA66KpEI62yIraI3O4JVcHFqLrbnIugKWxpWYclVsKBo5ynar6m9i3aeTv9qwCN0jpX32yG8XAyePQy1pxHkDiqmj0qpRro5Sj5TqruVtidY19RMydrLUFGhYuWoOQ6K5COlJ9FlhyP5bnxehA6tQFSqgCwwYeoM22HC8WN4solkajiehO3qzJo6uu854Jc5NP4SR6Z+jOlO4rlJssUtJAMb+cyuOGfyJxjNOuQqAaK+Cu9Z/yyekiVjvIrl+JizZLIWFI3TiCWPLQ0qqYaV3SHn+9tVw0IUIB7z89CjB/H7VCYyBRoTIWbyZbKlKuGATtCnLRoy93qcO7EBoIoiW1PN3N+zkZ+NDSxMcnxizZYF0eWvb9p13pTHH+68FVkU+ZfBXr5ycA8uHrPVCumAQDo6zQ2pnfgk/5LHsOfZZjau3YssOQwPKUQTBrJksefZZj7Yefnv1czoHLnpArWqybprewhE6uLOefMqwz5MVGshrKYomCcACCstVJwZJpwKj07+Myk1TVpvPc80rpzx863dr+K5HpIoEAno/ONTBy5aCepujrH70UP4fSr+gEplpki+UsPXHKV5exuTfdO8fGKMjGox22CythTgpi9uojud4os3XMMTJ/so1kyiPh8dsSjdyeXt5GUxRME8Q0jpQhTq5M52S+hy08L3KBjU0TSZQ0dGeOHF09x+63q+8OmbePTxw1Sr5nkairc6SO4q3lm41JbHA8DNnudNA/8kCMIPgb8FVuYkU8cocO4dshVYed3yTcB8WyOoqyiSyIEzYzx9sI9tPc20JCLoqkxzInxBFWJNa+q8aY2meJiP3Lhp4UKy9WMb+fYrrzJZLRG6VmFtLUSltLj1sSiKtKxuYrR3Yllb6HXp1HmTAp7n8dyZIZ481cdIzkVPgKi6eI6EMemjUWilf6ofSwNLdPBqNuGCxHUtt9En7mNVYD02Vr2VIerIgkLWmuOm5B08Pf0IFbuMT/IvCC/fSCbHG8GCuNIZACcDyhaEwN3ceGeGR378PeTOM2zekGVqQKQw0cFd71nDAEUmqkVKdoKiHcBxRfryOWJqA3smG7kuneeI0Y7r+WhTx2hS5tg3sY1VkZdRJQ9FsZFdGx81RD2LGJzjxZGv0Jd5Bk+IAEGKtXF8gX5WNwTIWScI6yqbm32Ybg7LqWB7NSrWEIKwmsHKFKIYwrCrVAyDoO7ii61cYPjsC71Avd2RiAdpbY5RLBk8+0IvTfEwhYpBJKCTK1Vpb4hSqtZoii+/spyf5ggrGlXLYrScR5dkPrV2G5uSjWxPL15FWR9vWHSiYzRR4C+O/IRYYJZUACZdg9HpADsidy57HKdPBmlp6iIR70fVTGamoFC9izO9F289vB5DJ0Z5/gd7WbW9i+nhGVyXC8yrbHkGyymgSGHC6loK5ilytSNEfdsQHJGIEqfklPBqo6T1+ntwKLeP4YMthHwqozN5/JpKWypKsVq7aCVo5PgEG9qTDM8UmJjKoyKwqSVOZ08aIeLjlFwhl7LIRW0URCwUPLXeOjr3GjCeL/CDg8fYOzjCLT2di+7L8zwUIUzNNJgYzFPKlwmGXZpaZLY03893f3wSx3GZni5QLBnoukJjOoJlOWzf0k44pL/tQXJX8c7CpbY8PvK6/39ZEITLU4ZdiH3AakEQuoAx4JeBT73B11wRLhBXbu0hFQvxnacPkClUmMoWcT0PXZFpb4gS8mk8cMuWJasQAI7fo9rsUI44VAMOjr9eXDmRmebR8gBNm9OsVzupWCanh6Z47OUjRBNBihHvgrn9trXNDBweYnZ0joZLtPwVBIFbejr4l+OnEAyVSD7O6oYEkipSwOCxZ8bZoG0llxik4GbxOQlShW5OT2SJ31/3rvDLAVSxHrQ0X4Vo8XdcEAP9dggv4SyZqHwTBD84eaAGzgieNUCyU2D7/f1MD5mUixoNqybRrhnB84kMzW7GFQ9QsV0s10MTqyhyjcHy9ayPb6JsNdIUOI4sZii5XVTcJB9o9nHSCGLWXKqiiOuBYwqElCqqojJa2IOmGHieg+tNEQsK6IrLhPEPuKqARBBBEBAFGV1Oo4oJbC/P4eJqRGeIuVyZvOERcFwiSZmT5SZuXOH7MjgyRy5XwedTaG2pr1Dn+9v3v/davrX7VVRZwrRtJjMFXI+F7+1SeGywl5CiMV4uUjANeiIJworGE8N9bEo2XvYx7p05TFdyiorlkas5hHwGsgw/GXqZTYmPLLlda6eMY9ucPH0PJ441MD40Ryyl09YVveg+5yc5poZnEEQBRVFYfU039//2vUycmVpCtHhHXeNCvRWgy031SoXnkTMnafN1UbBzzNYmGakM0Ki1kLVmmciE8GsKFdOiMx1HEITzKkHnjn82NEe58c6NJBrCHD8whOu4RFyPpnSM1s4Uqq4wO5mnmpbIrQbXEpFUiaCo0e+r8N1n9/Mfuu4+rz2RbgiT6PBzaHSCtQ1JGkIXEq6KPUwmX+Tk3h2EEzlCsQKlfIjdP+yiLz3LS6/04/cpqKpCa3OMRCIIHgs6iZ6uhqsE4irOw8WMrf4T8L88z8u8/jHP80xBEG4H/J7n/eRyd+x5ni0Iwm8CP6U+NvpNz/PecnHJfBUioKlossSJ4SmeOzLAhvYGjg9Pkwj5SIYDxEI+Qj4NF5jKFpetQrx+Nj9XM/jLgy9yV/sqHh8+zUy1hCiIgIBfUVBjKgfMHMYTLzDR5ZEKhc6b6f/C6u0IosDIqfFLJhTwmmPa2nSKoUyOYxPTrGlIEtQ1Jksl1s7FqL7SSCLaTfuqBkBgejzHbdFreXr6EYBFqxDvCOEl1CsTQhjcacACZQt4LtQeZ9KWiEXTBMN5DHsS100yO2YyNVTheaMDRTTpDg6R1gwsL8ZguZNpQ+a/rNvI14+WqTp3ElI1imaNGfEkn+4sMjgVRREq1CwwBQdJdbGRGch3sF6v4XlNFGt5FAmiPj+2LWC4cyQatmG7JRQxgiRoIAhYTgFdbuL4lMDcVBvtqWEiYhnLCHPwSDdapwgrcMPM5SsUCwae59HdmUIS69+B+f72/Pd29/5e+ifnsByXz9917UX1E2PlAoZtUTBr9EQTpHwBXM9baH9cLqbME/jVAD5JJmONUrNkIkqUKXN5A7Gbb5foP2IzOpwklgwxPZ5jtH+GD37y+mX3Nz/JEYwEsAyLiTNTKLrCPb92O76AvqRoMaytpSvyOSYruzHsCXxyE02BuymYR4lJZ6g6fqJqHE3SmayOMljppcXXSVM8zNGBCWRJJB6qO3jOV4L6T00sxInHG8KMD83yV3/8I7rWNGJbDpqu0NKZJBDSEQSBUqFKQ3OUH1ZGaAgGyToGll1DLQlY2DyROcOaH+3jwJERUskQqWSIYslg+KUMvg1hnj7dz45omuf3nF4gG7fctAo5/iKneytkR3aQGxXJFwwMw6Rm2lTz4/R0puqGV8nQQn+6WDau6iTeJbjc+PJ77723+8yZMzpAsViUQqGQc/LkycsakrhYheII8LAgCAawH5ih7pS5GtgG7Ab+2+Xs8Fx4nvco8OhKt78S+OkrpygbNaZzJRzXRRJFYgEd1/O4YX0HNdsm7H8tcKh0tq0BsKY1teiFeH41V7UtJspFilaNsmXy7d5DGI5NayBMSNWxXIeyZVK0a2SCNk/aE9QGLIIoyBWPpC9Aoj3GkxMDbOpsYOTUONfcufWyzq85Uld/r21I0jczx7GJKdLhIAFbZHRghobmGG3dqfMuXO+kKsSycMeBKLgZkJrqJlW44I5TtSVc18JwptGlFH69FSlRYWS8l2w1DmKakptGEDyichjH8RAlh/Xxhgv6/nd3PEBKf5ztkXEeme6hSZ8hKmcpOwp9+UbyxRRjxjSyOkvFVZEQKVYdYpJDUOmgNfhhBvJ/h+uZiIKK7RSx3SIN/g8xMvkYRS9C9thWdEMhkQpRcmuEhqqwuKxmSVSqJk88fZyuziRz2TKGYSH5xQv62/Pf257mJFPZIqtbLq5/8csKp3OzdEfipHx1nUHRrNESWNnNxa+aWI6OLFfRZIFyVUfyPIKqteQ2nufQ1DSNJN7E4FiM6fEcqza2YBomY0NzbNjRsWRL8NkfvIhru4z3T2GUDJrXNBGOB3npoVdZs2P5PJywtvaCiYeg0k7B/Db95ecwXQVdMGhSdMZNP57n0bqqzHNnxkl15ZiIHcer+XBKLXxk253s+dEh/EGdSslg+Mw0tuUgiiKWafOF33k/j3xn79nzhXKxSqlQ5a4HdvL9F0cQLBdLdmmQA0R1nUK5StFn8cLefirVGtWqha4pyIqIbTmUT2SZmCvw9NAxukJRFFWib2CaU8Mvs2nXOK/uSWNXioiiSCCg0dIcIxTSKeSrfOyXdvKdH7xMqWQsqpOYd3+dd3i9c92q89qu73YMlk77DuRejGbNOTWmJszt0RtyncHVP7fx5Y888kj//L9/7dd+rTUSiVx2Wt3FCMVHPc+7SRCEP6Buu90EFIB/AH7d87x3zZv7+rbGrrVtFKs19hwfJKApJMIBkpEgQZ+KR70Kcc+udXxr96sAi7Y1FoPjuhzNTFGzLSzXxScrJHQ/HaEoFduiMxRbGKWbR94w0JMy++1hRk5OUfI7KBGVklNkrLfAnFnh/Wt28JMn9/L/vPAUs65xyTbGd56j/l7f2MCR8Qle7RthnaKh+yCWDF5w4YJ3UBViOYjNYB0DBBDPlt29EojNeN44ZXuEoNKOX24HAbSww9xkCKUiIUUEQpKfilth1swheTI3NdZvLIv1/T3rBjYEhxk0qxwrNFIsO6hKhmRYpt3bwdMDh9nZeQDB8WGUVVBL5HST9tgDF6xydbmJhP8+npktIuZBkkCoQTjmw5RtXMEjdvryUjNNy2b308cxahaf/Ogu8oXqRfvb3U0JBiYzTGaLy2ooKpaJLIoIQFjRcD2Polk7b5rjcrE22sGr0wM4Yhld9FPyFPK1AtuTy2hHnAE8t0xD++185je7Fv48cGqCF544xvEDw/gV4bzWxXX37sAybfb9y0E0n4oe0Ghf30IsHT0vhvxy4VfaaA7sImc8j+FA1YvjE122B8GvpXk2e4SmnYPodhKjrBDwOzRvmSQQrzA6MEOlZGBULUJRP4mGMIGQztxUgfXbOtB86nntkLse2En32ia2jDXzbG8/jugRFFVM28YSXG5a14Vu2Pj0GIWiQa1mU61aWJZNYaZKIeMxh8GAkccUPfwI3Lx+gEImQlN8E14Ukokg4tlqVrFUr0L0dDXwyw/sWvR7NO/+GtZVGsMhClWDb774Kl+84ZqfC1IxWDrt2z39cNon+Z2okrAqTkXePf1w+g4+OLVSUvFOjy+fh+u6PPzww/Ennnji1OWe48UIxTWCIHQAnwZue91jPupBYe94nOsZEfJpHBucXBBXdqbjBHSVZOQ1697iJYorX59TsDaWYqpaomjWUESRjYk0IbWuQcjXDBp8Qe7uXHPeKF3RrJG3DD6xdhen9g+T8AVwCxai5UFMIaPVGJ6e4weJIZ6JZlk7pdHd2XTJNsbr0inuamrnu88eYLJYQrM8WnSVyOoEyR0BXj05ytTcBI3BIJ/4pe3nBZq946HeDMZukJoBqW6l7ebJiasQhSyy4EMRo3i4GHaBgcIIln4rt5QUegNTeLqA5KpIgoNPg/c2LnMzk1cT1tdwT2KUqL+VjJXFL3WQqZSYEUuYTgvP9plsaR4m5S9TqoQ5ObKBShU+sBqmamF+NruWSSNNTAngMkJY8bN+rJHh8Wnc7TI1n0PI1umcStARvXjVYL5nPjGVp1ypkYgF+PgvXUsyESKZCF20v93REEUWRfonMksSCs/zeGKkj5jm4w+vuZWXJkcWnea4XLyv8TZmzTEmKjkMy0/cL+N4Mkml/hmcq3dIt6e4+f7r6Fp9DEEMgnQ+0e1c08hI/wzPPLSfzOlh4qkIkWSYvkOD7HloH+t2rSbZHMcf8dHY1YBwtoD/RmPIC+Zx4vpGDHsSWQwRUldju2VEhsiVDQI+hXRIotHXjE8KULZLPHnqCbKzLpbl0LOumUi8ft2Zrw7ChcGC8/jElq28ODeCWHIwqiayX6a5Jc4nt23npfFeiiWD9tbXpjqKJQO/X+Pg6DgT1BAFkRbVTyw5hh2tMTnYyec+dA3f+cHLlCu1RasQS+kknjjZhyZLjOaKdCdlwmf9Lp442feuIBQHs3vDeSu7ZHz5kfwrUcs1xZpTlXLUR+JNtyb+ZOK7zZsjO3OLbRNRYta22HXv2vjyefz0pz8NJpNJa/PmzYtPCiyDixGKrwGPAd3AuZ7XAvURz5XF473FeOpgHyGfykyuRLZURRJFWpJhgueKK88Gcr2+CrFUW2NBJ6Ho+CSZvVMj/HS4l/e1reLXN17LI0OncD3vgtXcYiX1+b83TkhkmurlSjNbw561CUc0OjI6g50FKqLDK30DDJwcocEXJLa6gccGe5e9qPefmuDgD4+yLRBkLuOQmSkSjHg0Xhvi8ZEhEs0+bm3qoGbZPD4xTOtU6l1xQQAQqOCp20AIgTcJYjN5cQ2z9gyNgfcyVlR4dfrH1JyT5GpBbPcGPrnuHqpSgX9+/DlG4jksxaBRDdPameRkcZyOYGohov28fQkCnnoTbuEvaCscI2lZlO0kI8U2pKBLxGdSnOrghVNpJEWkQ4uA7XF4eJzThQn+cfB5QrJOQNI5lB3C9Gw+FbuRkpelWPbTPdtEoOajUjIoFarc+IXl48nPHemr1ay6N4DtUjMvPctHVWRaUxEGJua4cUPHooFUx+am6M9nuLWlmx0NzdzQfGWqVi3+DhqrjWSmp5Hn8kTEONG2XZzJuuyfPcUTX3mcYDRIqjVJMVvmof/5PT77+wbxtjsYODJyAdnY9d51/OR/P005X8aumpRydefZeHMMPajxuf/yCb735YcoZSvn2U+vNIYcOKupaEEWA5TMfgrmCYLKKmaKA9hehEavg4mRIQatCfxOBN0JYSllrrn5NvpPTiLJ9YC2+c98vjq4FDRZ4drmVmRRomJb51Up1ZvgOz+oL1ReTwz2/GSccEXFEjxs2aI1OUa2GGPaCS1bhVgOJ6dmKBo1RFHAchx8ikJQ1xbcX9/tqDplyScGziv5K4LqVp0VJvPxzo8vn8c//MM/xB944IELdJOXgmUJhed5XwG+IgjCVz3P+9JKdvBOwESmQDoWomSY+DWVhmgQQRQuKq5cDo8N9uKXFcbKBQqmgSbJrI2mkAWROzpW0xKKLEoaYOlRuo3JNL58hoGIQUYVUeYs4gctOkIRBss2Wl+FnO4xEYZSJk/4hTyVGyzYsfRx7nniGJouMzORp1Iy6F7bhKorvHpshNU9CWZKZU5MztAejxLW1XfNCsPzDLCOUBU7GbOrVO0cnjeJKGRJB25ltrqOvz+1j6DyPsaKBTK1Kg2+AFXbQtVlcgcKRCSZG6/ZhGlY5I6WMH/J4jEOsibYxInC2AXulAOzI3j5I4Rlj4yxmlJ1ls3+EZzoXRzTJhCjAbRikHGrxICTI60GUCsiT08dIyTruHj0l6bwyxrtcpLHDh/g9lXref8D1/Lyz05eUOJeDs++0EswqFMsGmRzFTrbkwT86mVbH3c3JRicyjKdK5GOhc57LFer8szYAO2hKNtTV7ZydeTQUY69dJLYXCdJs5lCpsDYbC/mh03+6vA+mjJVyvkKju2g+VTae0Y5tS+Hf/h2/uWbPyacCJFsTTA7NsfX/+DvWXvtauZOj1IWZDJZCd2nEk0ESbXHKGZKy9pPrxS63ITlFFClOCFVpmj1kTUOksk1IRsBRkcn0KQIjl4g687gWjOsi6znY//qvQz0Ti7a1lgOh2cn6Y4m+OKGnYivI3/LEQNfXKdFGKS5o5d0YqLu4TF+A764vrDtpX5nHNdlz8AwecNAEgQ2NaXR5PptZN799d2A5SoJABlzWq04FdkvvUYqKk5ZapHa7Vsb7v65jC8HsCyLxx57LPbyyy+vyLH6UsdG37VkAliYvW8+x0qvcAniyuXQm5ulUDPwgM5wnLQ/gAcLqvelSMNyuPHOjUz+zXNcZ8fwB3XKYpVRZgjF/AztOU0NgUDGwdKgHIJqySV4dBo+tPjrWabNyUPDmDUbQRRo72kgmgjiuh6Tc+NsineRDAY4MzvH6elZ/KqCVizjed5lxSe/LbAOU7MnGawVQUrhuS4lexBZ0NHFT/DTodMLY44Vx2JLshFREHhssJfUHoOOVWnGh+eYHMnQ1l3/7LWXPWp32Hyt7wlWBxtp9MUoWlX+cfB5Pt15M3OzP0TxmonpU4juFK6QQlf9UDlFq9LMYOIMgaRMUjaYqwpMzUbYUVzNWDmDi8tMrYhPUukJphnunSIvVnnPPVuIxoOs2dR6Wac/NpGjapgUiwbJRJB0QxjP9S7b+rgjHUMSBfonMucRCtfz+OnQaQRB4K721Vf8+/D0i7uRPAnjpMvxqVM4loNZNSl/r8JQg4ukyzSZaj3rpmIQjY9zcp/Isf0/xaya5GbyCIBVszENk/7Dg7Sua+b0UB5BEglFA7iux7GjE2ze3AwsbT+9UjT6zx8p9cstzFWOYdgGvmEVM+FSKVYwZySUVAAhWSFXKDJljKG1OcTvzyFYs8QU0KJL55tAndwNFbPc0NR+AZmYx1LEYEtXDXnNMSpFUAQH05ZZvf4krnXxMaJzhZfJgB/1LHm4Z/0aDo5NULNsFEmiZNTIG7WLOnO+W7A9ekNu9/TDaQCf6HeqbkWqOhXppsT7fm7jywF+/OMfh7u7u42enp6l1dHL4FKNrd7VuH3bqssWVy4Fz/PYOzVCxqgCHltTTfjO2gcXasaKVe9Q753e/4Vbzlu5/OoffIBw1M/uLxxibquCbAvoszZGs0IlJlI6Ub+BHO99geP9D2IyhUqahPZeskNRzJqN7lPpXNOIqtU/7krJoDEYpGTUCPt0tjQ3MluqcGZ2jopl8f2Dx2gI+jk8PvWWKbiXU4xf8NjaDtYGD5GxMyA1Y3tlqs4EAbkFVUowVX2SsXIXFcukaBqsiiaJ6b6FMUdvvEKyMYLjuEyNZVFUmXRLjNmxPDphZE/m1ckRJHuShBqiMRbgp+OH2WqOMGlEqNkacV8JWWnDE0Rkb4rbez7Ij6f+iZqjUjVCxBSbcOMsBSXMzJiHp7ooZYVy0WLWPgOSzeY1HUTjl2/INDaRJZsrU66YdHckSZ4d6yutwPpYU2RakhH6J+a4fn07J7MzPDbYy8HZCaq2xefXX7OgA1oJXq+FuO7eHViY9E2fQprwI0+UiKRC6AEdVVMoZIsEukPk20w67ASKJxKKzNLUGsB0NxNKOARCPmqGheu6hGJBgrEAuek8ekua0YkSpguFooFfk/EcBzF8+e/xpWAxsa2R3QHOCcLyMZwRlcCaUYJrK3h2HGv0GiZzLs9MP8a0OUGj3kpMSZznsLmUEPrI7BSiILApsXS42FLY3DbE0Qk/sUQFXQ0wV2ihYhSJ+PfzyvCtBFSV3afOXPDbmxdeRnQNn6LwyvA4VcviS7fs4v3r13BNe8t5v8sHtm96V1Q3LwWdwdXVO/jg1LlTHjcl3jf7RqY83unx5QD/9E//FP/Yxz62onYHvM3x5ZeLNxJfvlQy6MVwrvAy7Q/ik2Us1yUkaxzNTBLVfK+JK03joiLJleJL9/wPZjWT8SYXww9BW0auubg+mV//eA9u/gdIXgjP0imV53DFMoHKR1i36kZ+9shBgmHfwqhaqVBl2y9t4vGJYSK6RlDXKBk1cobBe3o6OT45zQv9wyQCPrqTCQQ8Coa5oOBe6bjYUtude+GaP5a8UeOLN9QTHefV5EFNo1wzCcsn+eVNeWbFaWaqPmYqJygZOpLQTlc8RshX5O9P3sjp3Cyroglag/XK1HxoVWpP/T0IhHTGBmfJzBSJxAJ0rE5zYNckg9MFTNnAFVwsx8WqeYQ1nc+Gj+PTSriqR1dggqwVx7MjqEKSTHwXh6ePMVaZpGoo6AQJh1VmTJPx0STlYhm1JCFWPSzRQYkp/MHNH+L29RfXSpybpZCIB8lmy1iWw9hEjkQ88Ibjo0+OTPOzQ2fYsqmJ7w0fRRUlBgtZfLJCTPet+Du94P0QDSKKMNY3yexYhs4PpZgNjxE+2kJbSxuSVG9LF7NlQrEAGz64lT969GFcv4yuKNyeOkmXXWDj1v+L5x98ZeF585j//1lTRBY9+o+MMDNVQFZlOtc3E46H+N0/+dhlH//lolit8XeP7UMtlrCs75La0I9otiAYjQhyFVsoYY+8D+c9ZaZrEwTkEI16C5qkn3WeDfCB5o9e8Lq26/LXx/bRGoxwX9flO6genvlP5CoOM5VTFKsBZLGVjmiYojXO3t4P0zs9x5qGJPGA7+xvz+DT127jseOnyVQqeB5M5AvoikJjKEhDOMi/vfWGK/GWLeBqfPnK8K6ML/95wEraGucaVAUVlZcnRyhZFv9687V8qHvDwmruSqjeL4YNO7vo79/D9WvGkEMFqtkg/S82kU130Tv1Q8JaFVe2yDsqkq7QKIXRI0fYecvniTeEFu3Xtk6lFl1h9M9l6E7EyBs1Tk3NIEsisiDyrb0HuG/zOn546BgRXV90XOxSSENjOESuWuXrz+/j4zs2sfvUGVzPo2rZFGo1bMelYNT4y5+9iOU6lAwTSaqPLQZUidtaT/PsQJRIQ5DpyqsIBBFppWY5HJscoDXRjCrWBW9npjKcHJ1BVWTiYR+f2LkFLeDwjb99knF3jkrKwxEcAqPT3HDnBp7MDePgotk+SpaBLThYoknF85gObGGV8iim58dwfMTlOSYcAyn4UYYqJ5nzPAL+ID6/Rdm2mXZqNAb8ZOeiZGZNKikTJ+Yil0UaelUOVEaWJRTzwstQUCcU1jl8bJRiocp9d2/lQx/YxtDI3BWxPu5MxxGFfh7sPUYopDFczKFKMhsTacqWeVHh71J4/sGXEASBqaFpyrkKgiSQaI3htFZ4785bOXZojErBuEAkWWv1oa9PMTmbJZwrkE4WOC2vYVVrkJvvv47vffkhgAu22/PsaUqFKjvv3IJjO4wNzTE9nkWQJIr5KqGI77LP4WKYd7ycGs8y41nMuSY3trfQvqOJnDmHrBVBVKjlItiuzJobp+gTI3T4e5iuTTBSHSCupojKcbLW4ve6vtwcVbvetlsJREFDkk/QEWshlF6DIIhYToG0uI4XPQ/HdRnKZpkqFrEcl6JR4388+RxFwySoKgiCQCLgpysRQxCEnxvh5VVcefzCEIqV4LHBXiKKTsW2GC7m8MkK3ZE4/fksgiCsSCexUrzvs02ET45QyXpU8iLx9jwduwo0xkOMGqPkBQnJFYl4IoYdYtYIojj1aJSlxtBen/8xj8lCia5kHM/zyFSqFI0a+arB0clphnI5bNslFbIJmiaqJCHg8cODx7hj3Sq+s/8IMZ9GOhRktlzhr559iQ+sX8PTff1ky1Vy1XqUt+O61Gybv3rupfMuXACyKCKJAnMVE1kUaAgFUGQJz4O4OoAsVNg90EqXdZJ0xKBQacB1DVS5hieU+N6xAB0RiUjFR0Go4kgeruvh5aBWcagFILPWhzVVwi2bOAmF6aTE3x8/wmi4htdQQULGJ6qENA1PdAmYQU7aHv3GDrb7+oi4DqoEp+w1jGZzWOSxXANZ1DHdMpJgE1PD6FIIY7hCsVlGyktoAx6eT2I8As/3nuHfOy6Dw7PnEYP33LSGnq4Gnn2hF11XqBoWE5N5JFGkp7uBfKGKLEtXzPpYV2Wak2F+OtRHmxqhalusjzcgiyIhVbuoG+br2xo3/dIuNL/Gq7uPIEkiqq7QvKqReGMUI1JizD7NrnU3sOF3zUVFkn+2/3lu73RpWnWCHv8YMRV2Z2M8NtjLb++4eWlxpaby4N88B4A/qBNPhajVLNItMR797l6a2uMMnZ5iZiK/YHf9Rsak5x0vNV2hmK9wupRH90R2frQHr/MZovnrmZg8iSPO4ktVaUhuwBcpErN6qDpl2vzdzNQmmKtNkzVnafN3Lbqfw7MTRDUfbcHLD4srmf14Xl2op8t1QmI5BWy3SFvofmx3kB1tzYzmCnh4+BSFuF8nb5isSiYwbJuE348mSwiCQKFqvGuEl78IeFfGl/+iYqSUp2pbZIwKMd1HTySBKAgrtht+I5BTB+kWW8lkBygXLfA80i0JwiGD/KkmKtiUHZ24ViGiVwjoearVOI5bpWwNn9fnbfTfcYHz37mYd9cM+3RSwQCpYIBC1WCDItM/m0H1S5RMk2yl3k70PI+T03Mcm5qmZtlMKwoCdWFfzbb59v5DlAyTZMCPJsuEdA1FlJBEgVzVYH06RdW0iQV8yKKIePbCNT/b/tq/XTZHZymbabZ1u5RtH6PT9+H3DaLKGXKVEPtmNjBRCGBk57Btl7D82qq0aNf406fqN5yaY6M1+vBRf9znuFSKJvG8jqzoFKQsJaGIH51WvYkNjR1ktTF8/ms5aq7n1YrJjf5XSao2r+SziEIAv1zAdD0UMYwslJEEg5oTpySXUPIuji4gJ1T8pkTRsZgIV/n63z7D4PAcTY0RUskQmVyZb/zdc1yzrZ29r/SjKPULeSjko6M1jiSJly28vBR0NyaQBgT6cnN0RuILxmsXc8M8t62RbE0w3j/Jn//rr9OztRN/UCcQC9C6umnBwTKrTxH1x0hpjTRsERYVSTrWCe5MPU/eUnE9m5qrcF1kL4/NKMDNS4orF9Mgfe7f3UVDU5Qff+sFvvO1p0k0hOla10SpUOXBv3mO+79wy4pJxVMPHaCQq1Kr5iiILqFEgA2RKIf29rNrVRNStEA8cR2mk6VsDWK7pxFYzZbITn42UzcITmstyMI0U7UxTMdksNyHjMzh/CtkrVl0IUx/2c+dzddetjC2ZA0yUX6cqL6e1tAvMVN9ZuEa0Ba6n7C2luZIpu6km37N96RQNWiPxxZM8UzbRpUlilXj50p4eRVXHlcJxRLIGBUyRoVszWBNNEFzIAxCvQ//RoSXK0XZHED252kONuGWEowcnSUsdqCIZQZrt9AmP4XtuUxVQ9RMhYQvi6f7OJH5M8rWIAGlHU1KYzkFBvJ/R1fkc0uSivkLCXC+pmH7Jp442UehatDjS+C4dY1BtlLBpyhMFIpEohEct+6/ockSqixTqBrs6qinLc6TBKhfuBrDoYX9GaZFUNcovO7C9cjBh9gSPkZTYBxZKLLf6GFTS5Cjo9czUg0xUWoibxtUHRMfCh9o72CuWCXm9+G4Ls5ZnZDnesxW6rb27dEIgiAgixIhXUUWRcbzRRoGTB4+coZEOEg6kKJkmgxbOR7o3EK/r0zRqtIVrFcFBNGlVdzPnWqCkreWWWMcV5jE8kq4noTtCmhVFVtzUUsgqDI13UN2XTRLQG/0MzySIZev4DgugiBQq1nUTJsX9/aTSoURBYGGVAifT0XgNRfDK43OdAwVkZmaSUzXL9kN8/kH9xKMBgGPvv39GKUaiioDHl/8k0/x4J8/QjlfJRDxkzczlOU8t2790LI3xxtjpyjaGrokoeMyUo3glzVujF3cuG+papzrerR0JMhnK/QdHSPeEELTFfY8ceyihOL1QV7rt7VTzFc4sKcPN6JQDEtkJA9dchF1menx3HkTIIoYwa90UDRP4SEgeifYFe2hL/8QNXuKpJhmZ/rDVDw/e2d/xoQxTJOvnZiSoDc3TokcMf/mi577uShbw0yWfoomJWgOfBBJ1IjpFxKBpX7r8+3P+Uj0n0fh5VVceVwlFIvgdG6Wx4dO0x2JM1YqEFBUXDyKtTdmN7xSWE4e083jeTYhdTNCTGFMzJGbm6Y9toqWxFZmczJh51Wi6hw5O8RE/ia6Uquo2U9guUXK1iBBpRtFqpdNJyu7lyQUF7uQnHsBMm0b2/X42I7NC2Tj9aShMxFb8YXLNU+S3nqIgYyN7Rj4dYtbWvuQQrvIGTv4x/5nCEgKhmdTsk1MwWVHVwtnxusrr1gwcN6xbIqkF/79+uNsi0UIDRRYX9KZEEwyqkhS97FJCDO5b5zbfmUj/zj4PAABWWeoFieoitwWNynJG/nHwSwhaT1JWadolhnOH0TLjrGmsZGx2RJODXKSTUl3iEky12/oxnfEJd0QZmauhCgKJBNB/H6VUqnGx89mKTiOi+d6lF7nYngl0VeaI+TXuV6IEdf8l6wLGuubwDRMCrMlVJ9K+/oWwskws2NzrN7efV57Qttlsfn6jezavHxQ8bqozd4ZhVZ9FllQmTZU/IrILY2Xbtr1esxM5GnrSZOqmkyPZZkez+F5HqMDs0yP5ygVKuzZffy89M/utU0LbY1ASEfTZI6+Osie3cfYsqub2KoEp+wymqYgmi6aILJveobrG9OLToC0x/8TLlVGi4+QNw/T7FuNT16H7ZawrJ+xOvwr9JU8PGCmNonreeRNj7ga4WTxAN2h5TNHCrVTTFZ2UzL7MJ08UW0bXZE6mVjyvb7Ib32ptuhVXMViuEooOH+Sw3Zd/LLMllQTn12/g7FS/i0TXi4G260wVvoJQaWHmjOD4xrIokywQaJcmqVB/z+4uzPO14/mkPw9BBSV4ZkJ5owK9yXWoEh70OWtVOxhimYvPqUVXUxj2Iu6ri5gqQvJ5ZCNy1ntLHnhqj2OT1XoTE4gu5NUPAVFbCQqzHGqOMO2pkZOzs5SrJk0+sJ0x2OcKs5wz7q1Sx7Lcsf56E+f4dp1nQycmsCcs4klBRqag0yP51gdbuLTnTfz9NSxBdOrDYm7Sct9NAY0bmUtPzjwEtNmAbUg0uO20Xa9w7atDTxyOEBxvES4ZDIbcJAjGg9s3cr+qTMUSwarul4792LJoPEiWQpXEiWrxvPjQ6xvaECZEfjEqm3Ew/4LnneuViLVmqCxq4G5iSy1qkn72hZSbQlEUaSYLS9YWs+3J2qOwc9mHqXV14UiqsseT9TXza7kGCVjhJlaEE1SaPULRH0rN+ZtaI5SKlQJhn10rmmkZliMDs5QLZt89+tP039ignRrnFRjmKmxLH/7Zz/l+tvWc2BPH4VcmdlJAdf1UFSZ1u4UvoBGoDmFdKBM1bSQBBE/EmXbxEjVb+CLhYoBTJZ3IwkBqvYYrmegSSlkMcRU9UkcT6I7sJbp2gSDpSFqnsRa/6olBZvzKNROna2IiNScHAJQdUYpW0PLtjfhKmm4iiuHX3hCMT/JEZAVckaVGaOMX1b51NpthFWN8FsovHw9XM9ivPQotluiO/o5LKewsOKJxtLMvNSD2ZNgfXvqPDvvbakmPOBkdoa4nkASDMLqesrWABVrlJowR0TbsOLjWinZWMmFy7ROkDXH8FHG8VxMT8b1qpjWScbKqxElkWhQZ2NjmrZQZMFr4mLHstRjr5y98aza2ML0eI65qTzT4zmaO5KYpo00Af4nIDgO/maw71yH0DLI5MBTvPptlzVqkuiETKlQxY1KrH//JvLqCJ/e2cmBCbP++agaluMwWMxyy42r+e6D+4ALLZPh8lwMV4pnRgdwXJePrt/E357Zx5//8FkEQThvvPpcrYTu1zj8zHH2PPQK22/fSGYihz/sBwSK2fJ5ltZjlSEO5fYxXO3DdGp0By5h7FG7i5j1p8QklbboFtqqRWYq40w5N7BSCeWNd248T7BpmTaBoM4n//XtPPrPL6NoMpmZApmZuj7FrFk88+ghaoZNvCGEriv4gzqReADPg9nJPEYsxMYtbew7PoxseWgBhZ71TRji8qP4lpsnpm3DcCYwnBlqzhwiKoIoEpNvZqraj2ueJOLNoMsKU0aensjyY5pjpUcw3TyOW0ESNcLqOhy3umwl8ip+vnG58eV79uzxfelLX+qo1WqiLMveX/7lXw7ddtttl7TtPH7hCcVjg72oosRQMY/tumxMpFFFiSeG+9i0wjGtN4L5smXVHsd2SqhSgq7IZ/DJTfjkpoWLgxm26C3+mKETYzS0py6YOClZNb7be4QDM210BJ9louKRN0USmkPCN0ZE3YjtlpHFwFKHsiJc6dVO0S6i4CFQwkRBlxsQXIOiXUQSBE4XMrSHogsK+HNFhMsdy1KPnXvjaWyN4/MrjPTPovsUvvmn/8LY0BxNbXGSjRGK+Qrf+dpL3PdRjbnx3WRmNmFbKpIksm5rOwBnniqw4VNN9JeO0tWg0uCUiClJdK+LQ9MZGhqDb0kVYin05zP05ma5samDUtGkd2wWRRbZvrqVQsXgW7tf5bN3XMNLD+5F1RVmx+YozBbRAxqNXQ0EwgHe//nbF526GKsM8fT0I+iSH8dxkEWFvXM/wy8Flk2yFdV1uPJGsE8ABRL+Jp7NXIM46+OB6MrOczHB5vz49E++/RIbr+mkWq5RMyxUTUFVJXKZMumW2EJlYx7lYj3Iyx8PMDCZoaElxob2NH5dpVAxiPuXT4qdt+z2K2345BZMN0vFHKlXH+29qM5BHIKU7AC6bKFymEylgZJVwHUnzk+t1a7D8vLMGXuQCKIrDfjkZkRBQRCli1Yir2JpZI1DvonyY9GqPan65EazKXB3LqZvfVcEYq4Ev//7v9/6H//jfxz/+Mc/Xvjud78b+cM//MO2l19++bISR3/hCcXJ3AwFw0CWJDYmGup6ibOr3Lca82VLWQxhOwZVZxoXC9e70AVV1RSae9KMnBhj511bLxC5BRWN+3s28peH8jw72sb1TRNEtSIFq4H+wiaCioWT/Z8A2G7hkqY/3g5kvChpBsEzQUgj4yIIHv2WD1kQUSWZuOa/YhqXxW48937yBiKxAH/1xz+imKtbk/t8KuWSQaVk8OA/WOy8tsTadTnmcuuIxgOomoLresyM50monTxVeQRN1OkOrKXqlJlz9tIa3sxLk8N8uHsDX/jMzVfuTbtEmI7D06P9JHQ/Oxta+Maje0nHgswVK5iWTfjsjfHxfScZ2XMK27IRRZGm7gaSrQlAYGp4Zsmpi0O5ffikAI5n4+DQrLUhIHIot29ZQuE50yBICKHfRFC2IALdiTGeHR9golykKRBactvlsJRg89x2yDxxKBWqpFtiF1Q2zg3ysgMy//Xbu9FkCV1TKFSMS3Lgfb1lt4iCLqdoC36Ux4b+F6IQRJMMUnoJSfDjegEc61Wen/wamnCaquNguCY6RxmRHiPtu46g0oMkBtCkxMJ+bLeELr+L0oPfQcgah3z9+W+mZTHk6FLastyi3J//ZrqbL06tlFS80+PLBUEgn89LALlcTkqn08v7wS+CX1hC4XkeB2YmyBkGogCbEmnUece+i4zKvVmYrOxGFkNYbgHTnSOkdCGLoSXLlu3rWxnt3UdmMkeiKXbB4zHdh4BA3mzi5akuNsTTSKKA6RocmhlkU/IJBGRC6upLmv54O2CJDeQtgZAYRBFFbDTGnWaOF3xsbWjmk2u38sRw3xXVuCx14wlGfCQbwkxN5KiUawTDPhqaoxgVk3BiPbHkHPJICM+rf48qJYOG5ijHC4do0lvJmLPMmdM06PXX1tQJGqw1/P2J/WiSzJxROS9B8s3CvGZo/8w4NcfmN7ZcjySKTGQK+F04PjhD9uQ4qVCAYCzAdK5MyrLxhXx0bWpDUetW8+dqJRZD1polKscZMwZRRRW/FFz4+7KwjiEIMsivfQ83Jxt5eWqUl6dG+HD3ytt1i2E50rBcZSNbrLCmJYXlukxli5ccLLiYYHN+jLNi20jiRjLGHCHVIaJ6CGIV18vhOM8wa+eQxRCaKOF4HgVHIuw4rI19kYH832FRQBaD2G5pwWviKi7ERPnxcM2eXjK+fKrydNRxDdEWSwvpoo5riL3ZrzSn/bflFttGkxuspsBd79r48q985Ssj99577+r//J//c5vrujz//PMnL+GtPA+/kITC9Tx+NtrPodkJbmvt4mR2hqptIYviJY3KvVkw7AkEVKr2BLqcwie34OEuWbZsXduMIAgMnxhdlFAA5E2DjYkGTufmGChkWBVJEFI1bO8oEW0TNXv67Fhp27Lk5e1AzckgU8V2YU+pi6FqDL9sIZJHkW/nQ13r0WX5LWtNpZvr5e9zg7xKhSrJdISO9WuYG/gyWzf8I6oGuVyY48dWc+OdH+dF68fE1RQeHllzjoAcxC8FyVpzrIkm+PapQ4QUlR0NLeRNg68ffflNs3Cf1wypooTp2IQUlR/1H6fBH0S3XA7uO42kytREganBGQb6Jli9rpXP/l8f46d/8zRG2USS5UuK/44pSbLWLIZjkNIaEQSBil0mpiSX3MbzLLB7Qe5BEF6bTlAliW2pJl6aHGamWiblu3KtuuVIw/zjixHMU6MzpKJBPvO+Hfj15YWmr8dSgk1VSlMw56g5GjExRM0VsZ0CitgBDOEJApZn4XoqPjGN6zrM1E5z7TIk5SouH5ZbkGQhdF58uShoruUWfm7jy7/yla+k/uRP/mTk85//fO6v//qvY5///Oc79+zZ03s55/gLQyjmV2XDpTwV2ySh+bincx03N3e8pRbay0GVkmSqr6BIEQJyBwhgO0uXLXW/RrozxfCJMbbfvviceksgTN40aAtFGCnmCKsamiTTFC2jij1oaoySdYayNYJfbsXxLjub5k2B45lMlB8Du0p/oZtJJ05IKTBclOnLbeTfbrsGXX5rv77LrWRbO3Mk/WVyGZvBgVaicZP7P3GaYGOek7NJqk6ZuJqiYpeYMsZJaY3ElCTPjw+xLpZktFRgoJBhTbR+s523u369C+XN91+30F5Y7rGl8NhgL2FFZ6SUQxEl1sUbFuy1pdPT1DwwSwYVIORTCPj8dMkq2967iXA8dFnx31uj1/L90b/F81xCcoSKXabqlLk+8d6lD9A+g+fVEOQLqxDbU03snx7jlalR7um8sjfKpUjDUnBdj9Njs7Q3RC+bTCyHjfEP8cz4X+CTA0hCGNsp4FJic/JXOFP+OgEphOF5VJ0KLlX8gkjVrS+0lyIpV3EhlqskAFTsMdVyi7IihhdIheUWJEUM2Z2Rz/xcxpf/4Ac/SHzzm98cAfjiF7+Y/ff//t93Xu45/kIQivlVmU9SyFTL5M0aluOQ9PnfcgvtpeB5HhI+HAyC0io8PGyneNGyZfv6Fl5+9AD52QKR5IVtmrs71/D1oy8TVnTCqs7JzAxNgTB3ta/GdksoUpig0gP0U7TOEFZXvYlneWnwPI+p8pNY9hyZksOMtZU56xqOzk3heR5toSjPjg1yTfryIr/fKJZbybrF76EHumn0TdPY0QpiBNwC1B5na/TDPD39CAANWjMDlV4mjBEeaHkfT505jq/sYZ7JcMiuMiGPsWlVB2NB87zJilRrkmK2zPe+/BAf+916Xv1Sj3Vv6ViSbIyVC2Rm85yZnCaYcTjqzxJvjNJn1wg9cYxUwk8m4aMW0QjpOtt9AdyJfP38LzP+O6omaNRaMD2TvJ0lpiS5PvHeZfUT2McRxAhIF362uqywJdnEq9Nj3NDUTlS78tkcl4rR2Txlw+SmjZ1X9HVVuYeKdTdp/zEsZxpVSrMl+Stsa7iB8ZFXsZ1n8YlBPHyYTp6q4OFX77iix3AV0BS4O9ef/2YaQBaCju2VJNstSu2hj/3cxpenUinr0UcfDd13333Fhx9+ONTR0WFc7jn+QhCK+UyOoWIOy3PZlmpa+PvbTSTmkasdwhNsusNfpGwPXHLZsm1dnVAMnxhj8y0XEor18YaFkdKCaWA4Fu2hCGui9zFW+gegLgzTpCQ1Zw6QyRoHiOnb36xTXRTz0y2GPYEHCCh0+DbRb/aSdettKcdz2RBvwCcrb4toFpZZybrjILWDlwN3qk4ohCC447SEOrit4V4O5faRtWZp1FuRkPAED3/Z48ArpwjKKtGAxoxb5YV9x9nS3cb3dz9MYa5EpVBFEAUkWcKqWXz/zx5GliVcxwU8qqUqsiqh+VWe+ec9uK7LD/7sJ+eQjRL//D9+zEf+7T0UZwocHhohXpPQqh6TkzP0D0zS1pSgbV0Lqq6QaktwolrB9Dx8ZYvwMjqJ5TBU7iOqxbk1dQ+6dPGbv+fm8OxRBO2GJZ00dzQ0c3BmnH1To9zZvnpFx3Ul0Ds6ja7ItDcs3mpcCTzPY//0OF2RHXxq7RcueA+2Jj7Is1MZ/IziE2tYboBRK8R14atW2FcaMX1rtZsvTp075dEe+tjsG5nyeKfHl3/1q18d+p3f+Z223/3d3xU0TXO/9rWvDV3usfxCxJf/3nOPsimSo0PdR0zOUPFS9FZ3cDQf5U9v+cCbcKSXh5ozy3Dh+wSUdpoC91y2Z/+jf/0knuty76/fedHnjhTz/KDvKGtjSW5s9JiqPrlAXtK+26k4wxTNPlK+G98yUnHudIvnueTNo4iCytbANeyZyPK3Q+uwXZd1sRQRTV+IIf/tHW/9ZMRScItfqVckvDw4E6BsB68KYhgx9FvnPdfzPPZlniNnZXj5m9M87eSQKg5C1WEuKWKqsGW/RbC3RCQZQtVVPM/DsR0s06aUqV9z/GHfed8Vz/OoFOo216Zp4Q/qeK6H47iYFRMrpXFqg0IuArGch2oJiGEF2ydyu5Pi4x9670LVo+yXOVUo0lay+ZXf/fBlVSYALNfk6elHSestbI1ee0nbeLUXwXoF/F9AEINLPu/vj7/Ko4O9pAMhOkPRN13E+nrULJtvPfEq69obuHnT4oFeK8GZ/BwP9Z/gno61rIsvTuLmfT2y1iwxJYFPCmC4FdaFt9AVWHPFjuWtxtX48pXhanz524AtkTyb/Y/iEqLiJdGEMlv9jyJy79t9aLieVXfOEzXS/tsum0xAve2x/4nDlPNlApHlxWptoQg3NrXzwsQQLcEetiR/47zHw169GjJSfIiR4oOA96aPlM5Pt0iiTr52DEWKEpKSVGr7qHI3s9Uyq6NJQqpGvma8baLZZaHdBZVvAhp4LthDIOqgfRR4vd4hyaqbuxgWRxmfOk7HUIrZtX7MtEaXI+G5Ak6XxfZ1q7GzNUKx1z7TYrZMIOrDsV0KMwX0gIbjuLiOSzFTpnm1ytx4lmRLPS1WEAVESaSmwIFImZQJ182FGEq6VAMCUVdhXcmHNFCke0vHglV2YXgaLa6z7d5rL5tMAIxWBnE8m87ApbXQPM+t+05IHcuSiROZaV6eGsNw7LPk880VsS6GM+Nz2K7L2otMc1wuXp0eJ6RqrI4mlnxOi7/jvJaR67kcyr3MycJh5mrTTBuTZ8lGkq3Ra5dvL13FVVxh/EIQirsbBzk+p6JLNqpYpWBrCF6NuxsH3+5DY7b6EjVnjpbgB5HElfWE29e1sPtbz/LV3/17PNe9qEDv2nQro6UCz4wO0OgP0eB/7QIuCCJ+qYOy9W0czySodL/pI6WGPYEsRCnUTuLhEVZWEfQmydUyDBlpPrc+yWS59LaLZpeDqK7D5YtQexyc00AV/F9CVNctaCECYT+yLHH4uRM8/6N9rP1gG9E1fkJRH+8VuuBsAXIiW6S3xaG2tZHSt44CEIj4L5is+N6XH0L1afWKQr6CrErc/1v38vyDeylmywtExBJc9ogZkoEEO0tB7DmDDWYAzk6ZF7NlQq+zygZ4ZO8JcqVqnZhcBtF1PZfBSh9xNUVEucSWgDOM55YQtPcs+7THBntJ+uq24DPVCq1nDc3eyvZl7+gMsaCP5EXI++VgslxkrJTnPS1dSKJ48Q3OQhREtkZ3MTM5xZNTD9Oot5LSGqk6ZZ6efoTbGu69Sip+jnE1vvxtQFLLsyHeQ7F6ANctk9B1onozEWUSz/PwrFP1G4E7DmIzaHchqpdgEbxCzOsFiuZpTCdHU+BuAkr7il9vdizDmYMD+EI+Ntyw9gKB3ushCAJ3d6zm/93/HL///L+Q0P20BSMLpeOp6pOE1bXUnFmq9hjIjShi5E0bKVXECFnj0FnL4LVIgoplDDJmRFkVa+f97atXVLl5qyGq60Bdh2fdhmc8jSDFgXoipyAKjPaOY9VstIBG+/oW4jSw+eZVPHXgCQwphxj0ICsjHg3ymZvu46CaR/zUWvYdG2TSyNIYC/DpG25Z+EzPDd56/dTF9778EAC+iI9XxCwFy+B33vNe0mpg4bHFSMq5WNWc4OlDZ5jJl2mILl01eD0mjTEMp8KG8LZLf/Os4wiiH6TlWwhj5QJNgRCaJDNTLTNRKdIajLxlmppcqcpktsj169uv6Hfy1ekxNElmUyJ92duKgojl1QjJEfJWFr8cICjX9VQXMxG7iqu4kviFIBSIzST1Akn/TeDmwJ0DZwpcFa/wp+AcB7EFxMZ6H7zyTVy++KaQinm9gCj6sJwSAgK52kEKte0rvlk//+Beki1xCpkSjm0vrEyff3DvklWKoWKOkXKBXM3ALyvka6+Vji1nAk1Ko4hhBEGmak/iiAa2V1zxeS+Fqj2B69lU7DLT1QDZ2hiNapZubQ6Dz3Jn26p3BZk4D/IaBOE5sE/gkOT4S6cwDQvdr9G9rYNgNIDnwszoLLf3XMs+92kqMyUY0PElZBKflVizNszsqMf/Huqle2uaO6MJimaNR81RWjPNrI83LDl10b2lgx1fuoV/fHEvfe4ckk/hc+t3csPO+ijmckTkXHQ2xpGO9NM3PnvJhMLzPAbLvQTkIA3apY1hem4FnAFQtiAIy4/5z49BRzSdhM/PVLlEUFHfMiO63tEZBGB1y5Vrd+RrBqdzc1zT0IImreySnLMytPt7GDeGmDLGUf0aPsl/cROxq7iKK4hfDEIx3992ASEGogKooL0Paj8BtwTeALjTIKZA8NcrFuo6XPPkFa1ezOsFDGcKcIloG3A9+w2t/qeGZ0h3NlCYK5GbKZBqSRCI+Jkanllym8cGe2nyhwgpGiPFHKooEdV8PDbYy71d9awBRQoTkDuQBI2i2YdKHNutIIsXJlGuBGVriInyYxStGM+P30ZzcJCQkgO7wKlqC+tb7rqs8u87BYKg4cndGPkjPP1jA8uw8Yf99GztQDrrxlrK110mjxUO0hHrIROYIbI6RoPeRMUucyi3j9FSI03+EHNGFb1UWGhNXay8fyIzzaPmKIFtTTRXgkQ1H0ekAicy08sSkddDU2TaUlH6x+e4YX3HJRG7rDVH3sqyIbz9os9f+G1ZR8CrgLKTi+1hfgwaoMkfYqyUZ7CQ41PXbrvosb1ReJ5H79gsbQ1RAlfQe2L/zDiCwML02UoQU+peJ416GyOVfiaqoyS0hmVNxK7iKq40fiEIxXn97Xli4Pto/e/WcyB2nR33mwVnEDwBRAG3+jMwHjk7AnhlqheGPYGIjunkCChtSKIf0VvaDfNSkG5PUcyW8Yd9zI1lSLbEKecry9oiz5eOI6qO7bpMlAvUHJuSVbsga0AS/GhSEl1OM1L8ASFlLZnavoXpkEsVbJ47GioIKngCYW0NL00kQfDI1rbQlx3m/akXKAvreWpsgK3plhW/L281zhVeJtJFNmw/CY7KL/37D/DCD1+mUjAuaDO8aP0LcTWJi0POzBCUQ/ikAFlrlrGynw2JNP35DGOlAmOlAhFVY0Io4rguvbnZ8wzZ3t+xmpju5+tHX2a8VG8BxH1+1kRTFExjRTqD7qYEg1NZJs9aS18MQ+XTKKJKi295wuKaJ+skXwjXRaxIUP0BrhBZ9rd17hh0/TscpskfojsSv6zzWgnGZvOUqjWuX7fy9uTrYdgWx+emWBtLEVK1i2+wBLZGr13wOklrzQxVzmC6Bve3fO5KHepVXMVF8QtBKOC1/vaFDzTXiYLUWP/PK9cV+l4VKt8AXBAEEFQQw/Uqx9nqxUqgS01kjFeRBBVNql/c32iIz833X8f3vvwQ/pCPmdE5pgZn8DxvWVvkc0vHHeEoqiRxKjtDgy+IKvUsauOrSjH683/LaOnHhJQ1+M6mJl6KYPP80VCRonkCQZBoDf4So+VhegIzNIh7uKN9lJgGe4s7OZF7e7wmVoJ54aUvpFMpVBk5niMWLbPzbmjbeh3N3Y2LthlOjtdXlgm1oe6iWXvNRXP+M1oTS1KzbaarZUaKOQRB4L/te5qTuVnaghF8kszRuUmeGj3D5kSaU9lZmv0hEj4/Df4gggAhVVuRzqAzHUMWRc6Mzy1JKOZHGWfNCXJmhmtiNyOLF7m01B6vkwlBBAyQuwHtkn5b5xrRTVWKfPvUIQ7PTnLtm2R01js6w1MH+9h/ehRRELh1S/cVe+3Ds5OYrsM1DW+MOLf4X+d14mtBRsHBufjGV/FzicuNL3/xxRd9X/rSlzoqlYrY2tpqfv/73++Px+Puxbd8Db8whGJJnNcOCYLn1ImD/99C+X+CBzjj4IyBEAIxDk7dOXAl7ZCwtoGpypNn3SnBcgpvOMRnftzv2e+/yGjvONVSlc/+0ceXLWufWzoOqRp+WSGpB2j0B/le3xE+0r2BNbHfuGA7QVBQhFC90iIoaFK9pDrfsjm3CnFu9WKi/FNcbAxnEtPJo8tpNCnFjPEMHT4/a9VHqHl+wqqCIHis8/0My3v7x3ovFc8/uBc9oDFxZhrTMGnf2I6gqswOH6B1c3nJNsO5K8sGrYmB8mkm3VHub/0cXbrvvM8orGq0hiJ8oGMt3z9zlLJpMpDPACAJIgmt7vx6W2s3Zcskor0Wo73SwDtVkWlriNI/MceNGzoRxfObEvMR5T4pgOeB7Vr0lY7RGVi1vBjQHa9X/ZwBQKr/rjyh/vfLQNofojMcY//0GNtSTSjiiqMWFkXv6Azf2v0qAa3uBaJpCt9+6gCfveOai4aALYcTmWkeHTzFM2P1SavZK5BPcu5Iqed5vJrdw8niISJKlKi69CjqVSwO1zzow3g0ijOhIjWZ6B/Iieq2n9v48l/7tV/r/O///b+P3HvvvaU///M/T/zxH/9x41/8xV9c1g/y3degvsIQ1XXg/2KdRHiTZ8nEFxHVjSCvA6kZlG11F0ScenCRM4Fb/DqU/7wu8jy3HWIuHdDmeR41Z5qk72YCSgc1ZwpFCl+RcczuLR18/r/8Mv/qv3+G7s2dNLQv3zudLx1HVJ2JcpGIqvN719zCr23eRaFm8JWDL/Df9j3N7z33KH+2/3lOZKYBsJw5otpWFClM2RoiaxygYo2Rqx1muvw8/fm/wXIKaFIay8nTm/0rzuT+lpnqc1StKRy3il9uJqSsQhHCjBT7WOc/QMnRCCk6qmgzYybIW+o7Yqz3UjExMMXU0CyWabFqWycNbUmq1U7KhTLYp5bcbn5l6ZMCVN0qDXozDVoziqgu+hn9+qZd3NmxmpCicV1jG53hOOtiKa5Jt7A51UjNcbivax150yBfM3A9b8G74+7OlRkfrWpOUKlZTGQurHDMR5Rrkk7RzhPTUgTlCIdy+5Z/UbEZ3Ez9PykFSOCV6n+/TOxKt1GxLY7MTl38yZeJpw72EfJr2K6LB7SnooT8Gk8d7Fvxa85HAQwVsuiiREhR+frRlxd+Y1cCgiCwJXotmqhzIPcSNeeyXZR/oeGaB32Uv5HGLciIaQu3IFP+Rto1D67Y771QKIjvfe97V61du3bD6tWrN37jG9+IAfze7/1e06ZNm9avXr164yc/+ckO160XBXbt2rX2V3/1V9t27ty5tru7e+Mzzzzjv+uuu3o6Ojo2/dZv/VYz1I2turq6Nt5///2da9as2XD33Xd3F4vFC+7rDz74YHjbtm3rNmzYsP6ee+7pzufzFzxncHBQv+eee0oA9913X+EnP/nJZdvAvi0VCkEQPgb838B6YJfneZdvf3kFsWQ7ZMGsCBDTIARA8IF6PdSeALcIbrW+uhIT9RLuMmLOMgo1Z5aW4AcIa2/OWOqaa7o5+vxJel85w447ljd/WirDZFuyiT955Rk0SWJzsvE88yD9bJsjpKzGkgpYbgHDngLP40z+r3E9C02qIAoqlpvDcsvMVp8noHRRNF36shJFq0JQGcEn1TAcjfeGC6jyerLVkxiOh0OUDfEESS3/prxHVxqO7VDOVyjOFVm7a9WCuVhmSqCjuwnsE3jK0iLFc1eWjufw4uxTHM2/ys3qXUt+RvPtkMbAa9MX+ZpBSyB8gc7gjXp3tDfEkCWRMxNztCQj5z0279iYteZwPZeoEkcT9YtPF2h3Qem/g2eAkDrrMlpYMAK7HLQEw7QGI7w6PcqWZCPyFRTyTmQKpGMhTs/NoCsyAV3FPfv3lWI+oG2omCWgarQGI+RXqHFZDqqosj12Ay/NPc3Ppv8Fx7PJWnNXTa8Az3gsjLN0fDnGk1EwRITX4svxDJHinzV7+vtyi24jNViCfve7Nr589erV1W9/+9vRz3zmM7l/+Id/iE9OTl628vjtqlAcBe4Hnn2b9n9JWLR6Efg3iIFPgdgA8mYQo/UxVPsE2H1gHfj/27vz6MiuOsHz3/vei31ThPY1Fyl352Knd4yBtLFZqsF244I+VUA1dHGGLgqaQ001VdVzipmePkNPNTNdC0UdBrsKKBoOYBe4jTF2OsF2OvGSTqftXJWbUqk9tEYo9vfenT+eJCs3bRFSRKbu5xwfZ4YUoasIpeL37v0t2Nn9kHrE+SU5vXuReoRE6gncepSQe/la5AYiAVo3NXHq0DnMgrmkx3h1sIftNQ0E3R5OjsVJ5HMEXW6e7uqkwX8vpp2kYCcxtBAuLYLPaGRT9Cu49Qh+oxlJgbw9hkuLUOXehteoR/AgneODmHYCv2EwnBniwmQvfuMuWiJbqPNZbAprbIhu5LaGtdR45ZKuVleabdu8+NjLxBqiROoiCKFh25LkWIrJ8UnadtyLtEacCqIF0IXO9qqbyds5jiXeuOrnfWDtxjl3IbbE6vjyTXfx3979Ib58011FvVG5DJ219VHO9o9g2xe36o+6akhZk4xPjWX36j4yVnre6gLh6gB9A+j1wPisncGlBdq3NbQyWchzbLS0uxSNsTBjiTTJTI7qcACEYDKTW1CC6tX0phJkrQIZs+A05ioix2U+EVeUGncDh8dfpj9zgaireqbpVW960aMaVg85oYPnkvwBj+3cvjQ33XRT5sUXXwx//vOfb3766aeD1dXVFjjjy3fs2LF548aNWw8cOBA6cuTIzC7IlcaX+3w+OT2+HODS8eUHDhy4qMZ79vjyzZs3b/3Rj35U3d3dfVmw8Oijj3Z961vfqt22bduWZDKpuVyuRc/lKMsOhZTyOFw+ZrUSXXX3Qm+eSuZsByzn6MO6ADIPqW85nyMECC9oYfLWGG7zdcKBryHE8sZxm27toPt4L11HL9Cxa/GzBqYrQKIeL13JcXonJ9CEwK1P4DXuQPKveH3oZ+Stk1PTEB8g6ttOKLuRgpUgoL9z5VOwEvj0Jn5xziJv3UvU+xY5s5+8FSFl3oEmouDZAJPfcEoHtY1FXa2uJCklr/ziEN3He7nvD96L1++5LPGyeUs9pE6DeWLqzXN+EVeUjuAWTk0eo8HTTIPv8mTDUu9CzKe9qYbTfSP0jkzQWls1c/vOqlt4ou+HZK0MDd6WhY0oB+foUAsiAv8RYbQWvb7WYITGQIjXBnvZFqsvWbnxnl0d/PXjL5IrmFQFfSTSWZLpHA/cufSBXA3+EC/3n6fK6yM2NTF1qTkuCzGY7aPKVU3KmiRlJgm6VNOruXYSAKTV43aOO94ZX46d0NE2myLwqetyfPmNN96Yfemll04BvPXWW55nnnmmarHfY8UnZQohPgd8DqCtrXTlWkW7NJkTF2g14P99SP29k2Bm9YE1AHozGXMcjyjMJGMup4a1dURqw5x89TTtO9cuOnCbXQGyoaqapkCIzrFhMmaBrx/8DWcmRlkTupeIx0syleON4RE8xhDNgYvLTU17EtNO0hJ8kBPjxymYAVLmbty6waZoDVGvMzVUc9+FbdwA5hHnHF1vAs/HlrVb6VLNLg2VtsTtdXP3w3ew9XZnZ+BKiZfSWA+Fk0j3uxBiYf/k1gc3M5Tr58Dwc7g0Nwlz4rKt6qsdhyyH1toqEqkM3/z5S3jcBo2xMHt2ddDe3EyDp5kRMUTWzixoRLmUEgqHEXrNFceUL4UQglvrW/n52WOcGIuzbQkdJ69kQ3MNm1trOTMwwngqQ2MszAN33lBUQmZLMMykmWedJ4aNJJnLLet8mrHCMM2+NfRluxnI9lBPM0EjrJpezcX7oXEnhwIQQQs5qSOTOt5PXLfjy3t7e43m5mbTsiz+8i//svGzn/3sopN6li2gEELsBRqu8KG/kFL+fKGPI6X8NvBtcKaNlmh5Rbtib4upN0E7t3XquMMDVhdm4QQuexyX59YV2ZURQrD51g5e+cUhhntHqW1ZXIb3pRUgpm1T7fPzUPs2vnf8DcZzGWwpaQqECbndhFwenu7q5Ms33XXR7oVLr6fWt4e3RjOMZZ2ZEB1V1dT4AmhCzJz5S2sEhEAE/wjh3rUMz0hpTJeGBquCaELQdbwHT8BNpCY09x2NLchCJ8LqAmNhw7I0oVHjbmD/8LOEjCrafOvLOp/hbP8Ip3pHME2Lmze3kkhn+f7e13n/e6rxen08WPcpqj0LfJO1epHWMMJ7T0n/PawLRzFtm//79Reo9QVoDoSLnkQ6nEjhchl87kO3s3XNlX6dLU6qkGckm+bB9dtIm4UV2V2abnrV7GujL9PNQLaXKleGGk/x38/1SnPvytj84eDFVR6fGC6myqPSx5c/+uijsUceeaQO4EMf+tDYF7/4xUXvxJR1fLkQ4jfAnyw0KXOp48tX2kVNe/AzmduPS47i8dyN8O1BihjkfrOss0MK+QI//caTtGxq4t0P3bbo+x8fHbpoO336F/OfvPgUAcNFTyrBZN75eZQS8rbFfWs6eKm/m2qPD5/h4lxijEQ+y56WdrZV17P3wmkibi8ht4dk3rkq+9wNt7I5cMLplhj4DEIsOYl62X3vaz8mOZbCLJh0H+8hXB2ipilGKBbkU1/73aveT0obmfivYPeCFlzwa/5U308ZyF5g0kxS720i7Koibabw6QE+1LSyx0H/8ORv6Y2P0z+WpKOphqqgj4l0GrPuBPds3zb/EccsMvOkM+I98AcIcfW8uMU6PjrENw69SDyTYlusHreuz/yMLfXN+sCxLo52DfDJe2/G6y7++uu5C6c5MjLIpzbfRNS7Mj/rs0t7PZqX8+nTTJoJ3l//ADfF7liRNcxHjS9fGjW+fBWYvXuRLxwlhx8j9HmE7kZmn3PePPX1oLcu2+wQl9tF+661dB48w83378QX8M5/p1nmqy64IVZP2nQSy4YzKTQheG2gh1Q+j2k5x44Bl5umQAiXpvPhdZtZH4lddua/ORqD1Akw1ld0MAFOi/NQNMi5t3sJhP2s2doCiDlbnAPIQidYJ8FOgbZmwa/5WGGYek8zpjxPPDeAT/eXbT5D/2iChuow8USK0WSaqqAPVzjBSDZJR3DLgh9H2hNTcztuLmkwAU71REsgMtX5Ncn2moaZ25cSUNi25HTvMG110ZIEEyPZNEdGBtlR07hiwQRc3vRqbWADBgaDuV4upM/R6l98npWiXEm5ykYfBP4WqAV+IYQ4LKW8vxxrWS6TUtBfEAxnJvDoNWzQWvF7NiOzB5ycC3sAyDkdAovsvnk1m25p58Qrpzh96Bzb373wX/pzufQ4pGBb+FwuPnfDrTxy9CDbquvJ2xaWLQm63NjImez1KwUpstCJlFmEsa0k61tONc0xjrx4HMPtYs22FjRNIzmWmrPFOeC8tlqLMy9GjoLeuKDX/J35DM10p88ymO0l6q4ty3yGxliYRDpLNOhnJJHCsk3GtQtEjWqq3Yt4sy68CQhwbS/5GqeTiVuponMsTn8qQUMgtOTqid6RCdK5AhuaS/N87+/rwtB0bm8oPgl1sWaXJoNTnvzG2G85MvE6g5lehnIDUyXAqqT0WlJp48vLUjYqpfwXKWWLlNIjpay/3oKJ6TbTqUIXAg+GFqEr8T0SuZPABLhuchpl2RNTg5HsRXcIXIhITZjG9npOvnaa6WYpxbpas6UtsTqaA2EmC3l8houg2w1iAdnr5jGEFnZ2ayqYlJJgNMDkeJqa5hi6YcyUht4135GS3eck7Iog2FO7GSI472u+s+oWMlaKgl2gxl1PojBBPNfPzqpbSvRdLdyeXR0k0zk8Lh3LtulOnSdjpbln/Z0LzoOQMg+FY2BsQGgLH4e+UM2BMMl8jpjHR9Trp2dyguFMesnVE509cTwunba6Rff3ucyF5ARnJ0a5tb4Fn1HanZml0IXOjdE7MHDx3ND/ZDDbsxpKSm3btiu/tLCCTT1/V30zWfWdMpfDQHovuuanYE84vRlcTRhaiIH0Xuf8XKacq1TXVkAH822QJlKWvu/+5ls76Ons5++++Ch/9Zlv8r2v/ZizbxX3y+JqPQ7m641wKWknkGY3uLZWfAnxqUNnySSyPPilD1G/ppZ4zzChaICHv/KR+Sd3ak1T1Su1zowYObmgrpCzu2hamEQ9NVS76ggYpX8zns/Gllo+ee9uGqIh8gWTvLefOzo2c8uarQt/kMJxJ6hw7VyWNc78/OWzrAlVkbMsTo7HuX/NhkU/VsG0ODcwyvrGagy9uF+TUkpe7DtHyOUpaqJoqelCpyDzhF1RkmaCicIYfiOATw/M3+n02nQkHo9HVFCxNLZti3g8HsHpI3VFKodiGWTNfkw7h5QmfrdTFmdoQWeiaOD3Ly431VtB5gA/ZH6Cra+H/MslS9jMZfKcOnSWYFWALbdvJDmW4iffeGJhb4SLtOjeCIVjTiBhlOY4ZrmMDozx2i8P09TRwD2/9+7FBz/TJcYiAFJzhs9pkQX12Zi9VV2w87w0vJc3x1/jXTX3YGgre6W7saWWjS21rF2vcXAkzu76XYvYnZBQeBOhNyL05akuuPTnb1O0BgFYS0g8PzcwimnZbGgubl7H012dHBsdYiKf5VObbyz5rJFijRVGaPOtZyDXQzw3gKG5COjB67Kk1DTNfzcwMPCdgYGBG1AX00thA0dM0/x3V/sEFVAsA0MLk8y/gd/ViqE5bZinJ4pesdw09BcIzUCmfgSpHzp5FfrCk/fmcuBnr1G/poaJeJJcOkso6qxn/+OvlDyggIX3RpDSBvMY6G0IbZ6yyzLK5wo8/+Pf4vG7edeDSyv7veg114SzS+H/wqJfU5fmZkfVLbwy8jzHE2+yvWpZk+KvSEoJ4TjakI/EiAfmOU2YaUFvnnSav/k+xXJeHs7++ZNS8tjpo7zQ18XacHRR48FP9Q4T8nlojC3tZ3N6XkfI5SFrFtCE4LmeM7RXVa9Y75CFeCdPp4XeTBeD2R5i7rqy5Okst927dw8BHyn3Oq5nKkorMSltdPxITFxaGCntmYmiDf57AecNRgt9ES3ydef/7s0Io8PpqqlHnTbNdq/Tjnh6PsgSDXbHadrQiO7S6TnVj0QSiPjnrUxYdtYFpD0JrspNxpRS8tsnDjI5nuLuj92+6EqZ2aZfcxH5OrhvRoilXanG3LW0BzfTk+miP3NhyetZit70eX5y4VHeSr0EvgkO9x+b8/NnyqfthJMnhA25vXMO0CslIQT3trUjpWRfzxkWWiKfzubpiY+zoblmyUdxT3d1EnF7yVomedtic7SWiNvL012dS3q85TKdp5O1MjR4WrGkTW+mi02hyv13qVQutUNRYhP5owhNsD7yh0wWTs2M8W4NPTT/RFE5DMZOsLqdLpvCA6KmqITN+rZakmMpmjoauHC8l5HeUTx+7/yVCcutcNQpE9Urr2RtuhvmqUNnSScy3PcH76WuVM+X1ojQqpzkRNci8g9m6QhuZTg3yEvx53DrHmfK5zJn5/emz7Nv6BeM54cJ6REI+Omc2E/nSBsbq6+So5B7xgmIheG0UtfXOMd8y1DRdDVVHh93NLbxQu85OseH2RSd/3U83TeCBDYU0Q2zN5Ug4vZyITlBlcdHxOPFlnJZ5nUU4/KS0g5M26Q3201roB23tuj5UMoqpgKKEjLtNCOZV/AbLTQG3o8Q9y3uAbQm52rOWAtmHswu0PJgLL098V0P3TbV3TFAIOqn61gP9Wtq+OBn9yz5MYsl7fRUL4IdS75SXy7T3TANl0E6mcHldXF43xE23LS+JEdEQgikaysydwDsUYQWW/RjaEKjztPE/uFnCegh1vo3LHsXzTfHX8O0C0gg5qnF4wkyODbJ/v4Xrx5Q2H3OcDyrC9BBr3NySJahomkuN9Y20Tk2zG96ztIWqpq3yqKzN05tJEA0uPReEQ3+EK8NXsCl6ayPOK/xcs7rKMalJaWj+Tivjb7IobGXuCV2N3qF/RtVKpc68iih4cwBbGlS5797aVulnvucKzk76TS+Qjhnz67dS17T+h1rePgrHyEUDeINeHF7XazfuZZ121d+LoqdP4Gd/Bvk+JeQuQNIKu/qZ//jr+D2uBi6MIzLbbBx93qC0SD7H3+ldF/E2OIMiCscX/JDdCaPUu9pxpIWY4XhZc/OH8z1kjQnCBhBQkYEj8sg7A3RNzlw9aMErQnsMWcar1YDGAuqbik1TQjubevgQnKcP3nxKf7kxaf4fw/t5/jo5aMKxpJphidSRSVjSimJuD1M5HM0+IMYmjZvxVMliblr2R65hbH8CM8P/pKn+n7CD87/A0/1/fR6LSdVSkQFFCWSLvSSyJ8k6r0Rt760uvWLx6XHnfI6950I6wTSXvpW6foda/jU136XP//nL/Fv//O/oZAp0H28Z8mPtxSXn6cbkHlsxc7TF6r7ZC99ZwdBwrodazBcRslzToQWAH0tmCeWXCo8Vhimxl1P2FXFaH6YicLYsnXRzFlZMlYKiaTe2zwTLAcDApn1MZJIX/mOnvvA7gaZBa1u1hTZRe7clcBwJsX55Dg9kxP4dIOJfJZvH3n1sqCis3cYTQg6mhY3/2a2t4YHmDTzfHbrbpqDkcv6tVwLmnytxFy1vDb2In2Z7tXQo0IpAXXkUQJSWgxlXsClhYl5byrqsS4dly7tUUj/BDJPIP0fQ4ilJwYCbLl9A+fe7ubVp96gYV0dHt/CM9+LMnOergFZp5IFz4qep88n3jNCIp7AzJtsvWPjzHOTmkiXPufEtRWZOTs1MGzxE2ins/PrPI1Y0iSe7cd054m5SzNlc5otbQ6Pv0Ktu4FJM0HOyuLT/WSsNG6fTTjXwem+YWoigcvuK1ztSL0DRD8wftEAvZX2dFcn68IxupPjnEuMsa26fiZJckusjs6eOPveOMVLR7uoqwrSMzyxpImig+kkz/eeY104ykfXV35/lbmM5IeIumpIWylG83Fibuf5WM1jz5W5qR2KIiRyJ+kc+yYHB79A/+Sv8BktaCWeTyC0GHg/DHICmXwEO/nfsSe+ip38myVd3Wuaxh0fuZlsOsehvW+XdK1zsvuchDxrENBBiy2oW+RKGega4tnvPc+G3e3UNMfIZ01sWy68G+Zi6WudnYolHntMZ+dnrDT1HmfXoC97gfWB0m6pdyaPMJqPc2fNPdzX8CA+PcBYYQSfHuD9Df+KjdENThLjlY49zBOghRChr15U0VQOvakEEY+XDVU1SODY6CAuTac3laCzJ873975O/2gSt0vH63bx/b2v09mzuF2prFngyXMn8btc3L9m4zUdTIDTo6LZt4bI1C5Yf/YCHs1zXfaoUEpD7VAs0XR7bU14MO0suvAymHoWv9E0fzXHIgmjBVtrh8w3QW8AY1tRPSqqG6NsuX0jxw6cZN32NhrWrsA2rNYE1gjYo05yHrqz/b3C5+nTpis5Brvj+IJepC1p29LCA3/8QQbODc18rL6tlg9+dk/Je3YIoSGNzVB4A2lPLroV9aXZ+Wv8HU7JX/Y8rYH1JemmOZDp4Vyqkzb/+pkr0kuvTNPNw5x/4xT9o0maqt9JOJRSQv4wQq8DvbnotRRreqhdxONla6yO46NDHI73cmNdM/sOnybk9zCWSGNoOs01YSazefYdPj3vLsXsqbzJQo46b4B/v/OOimivXazpXbBaTyNuzctwboCzZidrAovfUVNWBxVQLNFAei+GFiJrDSCEIOzZhGVnGUjvLXlAAYDV6Zy7y1FnsJjeVNRQsV3v28ahvW/xN5///6hqiNCwpo67HrptWZpdAc65+eR/dZo6idpZ5+krO4Yb3qnkCFYF8XjdnHztDEjJPZ+8G3/Ix/oda5bveZjNtRWZfx1hngD34ptUXZqdP2kmeHnkN7w+tp/bq9+HW1v8cVZv+jxvjr9GPNdH0kywPrCJLeFdV/38tfVRDF3jVG/8ooACqwtpjyG891fElfqlQ+2agxGOjgxi2zbnRkZprYpwJpkhGvKhaRpBn4f+0bnzlqabV0XcXpCSgVSSnGkynsvQGKjcZm0LtbPqFn499AsAIq4olrToz3ZTsArEcwPkAEHobQAAHmJJREFUrdxMQKuGiimgjjyWLGP2kbPGyFsT+I0WNOF+p732crD7nLN2rRqsHidbvogjg+7jvfSe7ic5Oolt2jMtuYud83E1wrUB9I2g1+Ocp4fBX9qR7Qu1//FXCFYFMfMFzh/voao2zIab13Pwl4dXdB1CiyL0ZigcW3DTpbkEjTC7o+8iY6XZO/AEv+j78aKy83vT5/n10C9IWQnSZgrTLhDP9c/ZQMtl6Kyrj3GufxRr9gC6whvOrovRUfT3VQqXDrVr8Af5T7e+jzp/iCFfmjPDo1jSnskFmczkaIzNXeI53bxKIOiZajW/NhStuOZVSzV7lsxYYYSYu5aHmj9Ng6+ZfQNP8kTfD0lbkyphU5mxanYoErmTDKT3zjSaavDfW9xOgoS0eYGgaw1e3UmEm26vvSxm96goTIJ5xplYusQjg/2Pv0Jday0ut0G8Z4RQLEiwKrhsLbkxT4MWQAT+FGGU9ypmsDuObdoMdQ8TqPKzbnsbQmjl6R7q2oLM7kXYfSU5Goi6q2nwtPL0wE8Ju6K0+dYvuEfFm+Ov4dF9JAvjmLJAq3/9zO1z3c9laOw/eo63u/rZ0FzL+3dFWRfpQXjeVVF9Rq7UFn5DtIb4xCRPvXkcw6szUEjjzRnUFwJ86c675ny87uQ4pm0Tz6bw6AbrIzGEEBXXvKoYl+6CAawJdPC95N+SNidJ6hP4dD9+wwnEVMLm6rYqAorpfAdDC+LR6ylYCc5NfJd1kU8vKaiYyB1FCDeG8ODSIkhsTGsS007SGnpoGb4D3hkwZeN0lyy8BfIUhP7Tkh5usDtObUsNvqCHzGSWc29307KxafneVAtvOh0i9ZXvfzGbZVpkUzmGuuLUr6ujZWMjmqaRHEuVp3uo0QH2Y8jEXyE1b0kGwvVmzlPnaSJpTtCVPkXQCKMLgzfHX6XZv2bmWGN6q3p75GZ8ho+zqRNIKZFIajz1+I0AUso5k/A6e+I883onlmWjCUEineXlt35OeKdOTdMNS/4eVkq118+tTa08fuooGhJ/zkJ6DXLVNpbf2TWanSfRHAjz/rYOMpbJYCZFupBnTaiKllAEfarfRCU2ryolQzPw6F7qvU2M5ofx6wHCrqplK1tWrh2rIqCYznfIWSPkrTH8rraZ2xcbUCTzZxhKP0+1bzdrQr/LYGbf4tprL9FlQ8WMdYB3yVeA0y25Q9EAHbvWce5IN2cOn2PtMjS8ktYA0hpAeN5T1vP0zGSGX//oAKFokHQiTbQ+AoiZSo5ydA+VhbNgdjoTZ/XbSjIQbqwwTL23iZAVJlGYIGmOY9k2A9kegkaYU5NHibhi+DQ/vZkujiYO0eZzdiPcmodabz0+3bnizFjpOQdF7Tt8mnDAi21LhhMpNjT5aIsN8eqZDXy4eYVKkov09OlOWjwRAlVuLGx8hgspJD848QYPtd/A90++QcTtpdEfoisxxp8d+BXbq+u5q6mNoyNDRL0+NCFmmld9fOOOcn9Lyy7qqiVjpWj1h/BoTin7fD8ryvVvVQQUWbMfj1ZPQSTImv0UZJKgsW7R+Q7pQg8DqWfxGvU0Bu5HEy4i3pUbvT27R4WUFmQeg9w+pN6w6Imd0y25AQIRP3WtNSTHJtF1nUPPvc2Ne24o3Zt/4U2EcINrZceUz67kCFeHEEIQiPh58EsfwipYy17JsSC5Z0Bvcea3yLGpBlAU1Z9jOjs/YIQIGCFsaTOSG8KUBd6ceJW8lSNjpbGljRCCoBFG0zQ+2vR7PB//JVI6VRoZK03GSnF79Xuv+rX6RxPUR0NoQjA0MYlfO47bpfPW2Xo+vLRnZEVZts2ZsRFaQmHa6qIMZ1Ik8jkS+SyH4n10jo8gANNvcyE5wWQhR8DlxqMb/Psdd1y2e/HxjTuumeZVxZhO2JwOPNNmat6fFeX6tyoCCq/RSMFK4He14NLCTBbOMpZ7k5C7AynlnG+c07kXk/lz5O1RIu4dNAU+XPJ+E4slhI703gfpH0L2GaTvQaed8wJNt+Se/ab6R3/9GeIXRjjy4nG6jnSTHJ1k6MIw9W21S64AkXbKyZ9w3eAEFStkdiWH1+/h6IGTmDmTz37991izxZmNUpYA4lJ2H2gNTntqqx+02qL7c8zOzvfpfrJWBk1o3F//EL8e+gUut5uMncar+5xgAo2xwgitgXW8T3z4ouOQ26vfO+eZeGMsTCKdJezzEPQIwu7TDCSaiYYblrz+ldQ9NE5AuvEEDNy6TlMwTBMwns1iaBpnE6O4hcZINo0uBO2RamJePwPpJHDlvIzV4NKy5YX8rCjXv1URUDT47+XcxHcBMLQgAVcbyfwpQKcv9RQ+vYXh7P7LEjancy+E8JC3xpDSJGP1kiqcX7ajjcUQWhXS815k9lnI/AvS6p16g1rYOfyVyiPbd65lbHCcn/3d01Q3VrFhd/tMBcjDX/nI4t+EzaNIaSFcK7sNvP/xVwiE/aQSKQa74oRjQWpaqjm6/wS7762gLenpZFu9CcxTzuwLjKL6c8z1yz7mriNjpah3v/P4aTM1s1V9pSS8uezZ1cGvXn6CbbVHee+ac1jWJPvPtbDn1sqo7pjPie4hdoUb6NMnmchlCbk9JPM5EoUsn7vhVp7u6mQin2WT24sAEKyKPImFWOzPinL9WxUBRdiziXWRT19U5bE19udIUaAn8XPO5f+JoGsDPqORvDXKqfG/p963h6HMC+StUcDZEYh4dmLL/PL1mlgKYzOIA5D6Lri2TV3tLv0cXgjBcM8obVuaGRsY59zb52lqb1hSBYiUFhTeRhhrEdrS5psshZSS04fPkcvkMXMmVXVhWjY1la+SYy7TybYiBHid6h2tAXzF9ee42i/7S3cvFnKsMZeOuhHq7nyT83EThAVo3Lv1BOvqRoAyJLkuQiqbp3tojLvb1xGu91316GJ2/4pkLrdq8iQUZbFWRUABTlBxpSCgX3saXQSn+krEsWUBS+a4MPkv2DKDR6/H0AJ49Gp0zYsm3cvXa2IJhBBImQAtCPaQ04VShIs6hx/sjtOyoYlwLMiFk32cPnQOX8jLoK5hmRbnj/VcdFRy1eMQ8zTSTiE89xb/jV7F7DyJ+rZaNt3WQbx7hNR4GqEL2m9cS3Cqt0DZKjnmcFGyreYCOwveDy5bf46Sb1XnniEcqGN7oADmBL0T7UykCtiZX5WtzfZCdfbEkcCm1jqqgr4rHl1M969YjXkSirJYqyaguJqCPUHUs4usNYAt8xiaHw0vpkzid7VSsBK49He2N5e118RS2YNgbHFGnZsXnF4VRZzDT1eAVNVGCMWCjA2M03uqHxB8+0+/R9eRHhrb66ltqZn7OGSZS0Vn50mEY0GOv9zJ/p+9yu737+CBP/4AB35+EGmDbUtSE+myVXLMZzrZVkoL0t8DOTJvbk8xSrpVbfc5nU/NMyACVAWbGBgfIjF5llikNF9iOUgpOXlhiMZYmKqgb87PXa15EoqyWKs+oJidsDmtYCXwG62X5V6Y9jL3mliqmXP4Biexz469c/sSXFoB4vF7qWur5T0fv5Nf/eM+0ok0F070khhOEKgKYLh0Xvjpb1m/Yw0Xjv6a4bM/wuPpoaq6gBb8OA2bnDfGS3cTFproeaX7rdvext5/foFCrsBw7wiJkSSartGysRGPz827//UdNG9oqoxKjgUSQke6bkLmnkdYvWC0zH+nctOanAFnsgCuDQRcHsLeAv3jQWLlH+FxVf2jScZTWW7acA08x4pyjVj1AcVcQcOVci+Ws9fEks2cw4eBUTCPg9a45HP4K1WATL8Zv/jYy9xwdwNj/WOMDU0wEU8ipeTUoXNEqwdpanoKW4YIBjUsM0e88zHGRxvI5dfyP//+VwSq/ERqIyTHJi/a2bhasDF7FyLaUEXfmX7+/j88ysabOzj07Fv4wz48Pjc1LdXUt9Wg6TrxnuGZ76OSA4grcm1FFA5C4eC1EVC4boPsXtAbAT/YCWrCJntP7qCuZZLaSPFDypbDiQtDuA2ddQ2xci9FUa4bqz6gmC9ouFruRSW5+Bw+AHYO3DcVdYZ9tTfj6eOQpvYGGtvrnR2CnhEQGkH/fiYndMxCgWj1GIMXfCRGJfmuR3j2se3kM3ncPqd0VOjOrsUP/stj3PrBG3npZ68SrYsQra8i3jPCP/5vP+KuB2/l4DNvkhhOMj40QT5bAAmFgkn/2UE23tKOEBBrjCKcHPyKzJNYDCFcSNcuZO4lsAYQeuWWX0opEXYv0n0raH5naJ3WRDD2IMncJMe7h6jdXnkBRa5gcrZ/hA3NNbiMymkNrijXulUfUMC1ETTM56KmV9lfg3nE6U5Z4jekS49DcukCQtN4+CsfIdn9HJbdTDA0jNfnZmK8Dl9YJ+IeIRj1E93chNAElmmTS+fIpnIMdg3xzD/9hnwmT2o8DTgJr/lMnmf+6TdkU1miDVV4/B6iDW5C0SDegJfh3hEe+MIH+ck3nmByLE0g4q/oPIlFcW1H5A9C/nXwVXB7KLMTafUg/A8gXO+02fYA7U2nOdUzzB1b1lTcm/aZvmFMy2ZLW325l6Io1xUVUFyPPO8Cqwuye5H+TyBE6V7muY5D3jhfj8cTJxRJkZqsxuUJYriSIFpo37luptX3tORYivada+nvGiQcDZHL5rEKFm6vC5fHxcRIgsa19Ve8X31b7ZxruZYJ4Ua6diLzr4I9itAqb1teyhzk9yP0ejC2XvbxLW31nOyJc7pvuGLeuDt74uw7fJqXj58n5POwZ2c7dVWVt4OiKNcqFVBch4RwIz17kJmfI/KvgeeOkj7+1Y5Datf/a0T6/8DMe0hOREAm0fVJomv/kLvWrL9oZ2P2bsL+x18hOZYiVl8181jJsRSNa+sv2xG5dBfimsyTWAj3TkThDci/Bt77y72ay+VfAZkG7+9csUNrfTRILOTn2PnBiggoOnvifH/v67gMDV0T+Dwuvv/cIT557242tly7R2SKUkkW3qtZuaYIYw3CtQUKryOtlWnm1Nwu8FffysREK5oYBhEiuvbLtG5738xuQigaIN4zTCgamEnIvOuh25gcnyQ5lsK25cywrunEzKvd73omhA9cN4B5CmlPlHs5F5HWsDPt1rjB2aG4AiEEW9fUE59IEZ+YXOEVXm7f4dOE/B6yeRNd02irqyLk97Dv8OlyL01Rrhtqh+J65nk3WN3I1A+QQoDdX5Lx2FcizXPIwnGqmh8muv7KOyJX202Y7+jiut2FmI/rRmT2OZj435Gae9leu4Wy8yecxN/8AcAL7ruZq1PGhuYaXj5+viKSM/tHE1SH/QxPpIiF/Bi6TtCn0T+aKOu6FOV6ogKK65gQXmytDdJ/A/paMNpLMh77UlJmILcPodeA+9YlPcaqDRrmIM0ep2GUzIJ2y7K8dgtl5084pcnSBKmBHoX0P8+5Fo/LoL2xuiKSMxtjYU73xrGlpCHqTOadzORojKmZHIpSKmU58hBC/JUQ4oQQ4i0hxL8IIarKsY5VwTwOej3IcSANWtjpV5F7pnRfI/cCyAx43o8QlZXRf03LPeMEgsIDdu/yvHaLWYsITI1YD4GxbkFr8boMfnu8i//120/yD0/+ls6e8sxSuXv7OvpGkngMA7fbIJHOkkzn2LPr2hhipijXgnLlUDwL3CCl3AF0An9WpnVc/+w+0DeBcEPhBMhk0eOxZ5PmaWThJLhvRegqua2k7D7QqkFvBnsY7HhJX7tFsfrAijsdMY21zm3zrKWzJ85Trx5HA2zbJpHO8v29r5clqDAtybY19axrjDE4liTs96qETEUpsbIceUgpZ1/WvAwUN1pRubrpttzGFjBPQOGkM82yiC6MM2fpVjdYw+DaBa7dpVuz4pg92txOgHkedOn8fcXpTuMqY4OzUwEgJ+ds777v8GlCAS8ul0H30BgCMZMIuZJv5JZt89a5frata+CBO2+Y/w6KoixJJVR5fAb45dU+KIT4nBDioBDiYDxeYaOnrwWe+0AmnHN4fRMgncDC2LKkh5s5S7cTzmRMmQLrLLJwqrTrVt557ewk6OtA5sE6AZ57VnQZ0hoA4XJ2uUQAZ+Jawlmb576r3q9/NEHQ56Em7Mdt6PQOTxD0ulc8EfJM3wiTmRw3tlfwcBFFuQ4sW0AhhNgrhDhyhf8+Outz/gIwgR9c7XGklN+WUt4spby5tlZtTy6W5t4M/s845++MgPtG8NyDsE4iCycW/4DTZ+n2qHOebrSDVleec/3r3MWv3Si4toG+FWEPrdgapMxC9mmEsRZCX3XWIgec//vnTg5tjIWZzOTQNM35czZH30hiRRMhpZQcPtNHLOSnra5qxb6uoqxGy3bkIaW8d66PCyE+DfwOcI+UUi7XOpSL23IDSJmHzJPI9P9AYgPmgkoSpZROkqedce6jNzr/SVmec/1V4LLXLrcfmT8ERivCWN6EQimlM/hLToLvY2h6A7h3LPj+e3Z18P29rwMQC/s5PzTG+cExPnnPyh2PdQ+NM5pMs2dXx7KNg1cUxVGWHAohxAeA/wi8R0qZLscaVjMh3NjGRsj8xEmy0zuAiYtKEmfyJOw+J9hw346we52tbnTnannmLD255FHpyiK573BGm2efQ/rrENoyXu0X3kSaZxGedy9pJszGllo+ee9u9h0+Tf9ogvbGamxbIlfwff3wmT6CPg/tTdUr90UVZZUqVx+Kv8OZIfTs1FXDy1LK/6VMa1mdcvucPAo7DvYFsHVAQPo72Ob7IfdL0GpA1EGh05kL4r4FfB+H3IsgLcB2rl5lAjwqr3YlCKEjvR+A9A+Rk//ovDmXsGHZTCBpngF7BNx3O0m3S7SxpXYmAVNKyc9eOsLBkxdob6rGpS9vifHAaJL+0QR3bl2LrlVCupiiXN/KVeWhir/Lze4D0QBGZCofYhKsSTBPg9UPMgf2GAjNSQbU60H40PwfcXY3Zu9eeD5Wtu6Nq5HQItjaesj8LeitYGwsSdOrmYRb4Z/aibLBPIEsnESU4PUVQnDbljae+O0xjnYNsGuZkyQPn+nF6zLY0la3rF9HURSH6pS5Wk2XJIqw0+uAahAJ0LaCec55U5EZIA/6ehAhJxmPy8/1lTKwTjjlo3IC5Kizm2TjBHpLfW1yzzivsz0ImM4sEWkX95iXaKqO0FZXxRune9ncWo/XvTy/gsaSaboGx9i9oaXixqcryvVK7QOuVjMliYlLygDvB2O9E1AY68DYBFpk3p4Dygqz+5zXRoSd44npILCY5FjrPFi9zs6U3uY0rlqGRlq3bW4jX7A4fKa3pI8LTjOtf3jyt3z1O09x6FTPsgUsiqJcTgUUq9RFJYmXlgFeNdi4es8BZYVpTc74cNfmqcZXcSgcAhFd0sNJ84zTpMwedQLK6SmiyxBIVocDbGip5ci5ASYzuZI97vSI8pGJFLa0CXhd/Pj5N8vW7ltRVhsVvq9iVzu60NybsfmMypOoZJ77phqMAVozSAFWJ8gcsnAMKQXknp31+r2TsHlxBU8DiGqnp4jrRrDOAR4nkFzGhNtbNrbwyvHz/Jcf7MXtNmiMhdmzq6OoDpr7Dp8m5HMznEgDgnUN1WQL5op35lSU1UoFFMoVqTyJynZZ0Ge0gP8TCLsLmfoRWGecZE3RcFHCJjCVeBkGwpB/zfm4//cQ/oedjqcrEEj2jybpGhwjk8uzq715Zs5HMfM1+kcTICWjyTTN1RHcLgPD0NWIckVZISqgUJRr1JWCPil3Qe6VqTbd3aBVAZrTjCz93amqnQIw6eRLCPdU+fAQQuhONccKBJL7Dp9mbX2UrsEx+kcStDfXzNy+1IDC53Zx7PwAjbEwjTE1olxRVpoKKBTlOiKEhhQCjO1OfxFrGKdfiAV299RnBUEI0KLOjBD0Fe902j+aoD4aoiFv0jsyQd/IBA3R0JJ3E0YSKQQgEMRCfmxgcmpEuRoIpigrQwUUinK9mS4Jdm1/5zZ7ArTgVGAxAVoIhHfqY4kVr+BpjIVJpLM0xELkCiZ9IwkSqSybWhffMyKTL/D0aydpqolw/y2bePl4N/2jzsyQB+68QeVPKMoKUQGFolxvZidsiuBUcmUSPA87H08/CtIDuMvW6XT2nI+2uioKpknPcIKbOpoxLRtDX1gBmmXbPPt6J5lcgY/cuY26quCyN8xSFOXKxLU0l+vmm2+WBw8eLPcyFKXiXTaL5apVHqVp2b0UnT3xmTkfjbEwLdVhekYStNREuG/3RtyuK1/vzNxvJEHetAh63Tz8np1qJ+IaJoR4XUp5c7nXoRRH7VAoynVoriqdSqngmT3nY1pnT5zfvHmG7/zyFWxbEk+kLiopne41EfJ70DRBz/A4Qa+7TN+BoiizqcZWiqJUjI0ttWxqqeXFt89y+Ewv0aCP8WSGR375Ci+8fZYfP/8m2VyBsUSanvgE9VUh1jbE2Hf4dLmXriirntqhUBSlohy/MMSm1joGRpMc7RpAArmCyfeePchkJk/A68JtGEQCXtY1xBCaUL0mFKUCqIBCUZSKMl1SWhXwMZJIYeg6hq4xkcqyfW0j2XyBSNA38/mJdFb1mlCUCqCOPBRFqSiNsTCTmRxej4vm2irqYyFcLp31TdV88NbNTGbzJNJZbClJTPWa2LOro9zLVpRVTwUUiqJUlD27Okimc1cMGja21PLJe3cT9nsZHEsS9nuLatetKErpqCMPRVEqynTQMLukdHaDqitVhyiKUn4qoFAUpeKooEFRrj3qyENRFEVRlKKpgEJRFEVRlKKpgEJRFEVRlKKpgEJRFEVRlKKpgEJRFEVRlKJdU9NGhRBx4HyRD1MDDJdgOdcL9XxcTD0fF1PPx8XU83G5Ujwna6SUqqznGndNBRSlIIQ4qMbkvkM9HxdTz8fF1PNxMfV8XE49J8o0deShKIqiKErRVEChKIqiKErRVmNA8e1yL6DCqOfjYur5uJh6Pi6mno/LqedEAVZhDoWiKIqiKKW3GncoFEVRFEUpMRVQKIqiKIpStFUTUAghPiCEOCmEOC2E+Gq511NuQohWIcSvhRDHhRBHhRBfKveayk0IoQsh3hBCPFnutVQCIUSVEOKnQogTUz8nd5R7TeUkhPjy1L+VI0KIHwohvOVe00oSQjwqhBgSQhyZdVtMCPGsEOLU1P+j5VyjUl6rIqAQQujAN4EPAluBfyOE2FreVZWdCXxFSrkFuB34I/Wc8CXgeLkXUUH+GnhaSrkZ2Mkqfm6EEM3AF4GbpZQ3ADrwifKuasX9E/CBS277KvCclHID8NzU35VValUEFMCtwGkp5VkpZR74EfDRMq+prKSU/VLKQ1N/TuK8WTSXd1XlI4RoAT4MfKfca6kEQogwcDfwCICUMi+lHC/rosrPAHxCCAPwA31lXs+KklK+AIxecvNHge9O/fm7wAMruSalsqyWgKIZuDDr7z2s4jfPSwkh1gI3Aq+UeSnl9N+BPwXsMq+jUqwH4sA/Th0DfUcIESj3ospFStkL/DegG+gHJqSUz5R3VRWhXkrZD85FClBX5vUoZbRaAgpxhdtUvSwghAgCjwH/QUqZKPd6ykEI8TvAkJTy9XKvpYIYwE3At6SUNwIpVvF29lRuwEeBdUATEBBC/H55V6UolWW1BBQ9QOusv7ewyrYrr0QI4cIJJn4gpXy83Ospo3cBHxFCdOEch+0RQvxzeZdUdj1Aj5RyetfqpzgBxmp1L3BOShmXUhaAx4E7y7ymSjAohGgEmPr/UJnXo5TRagkoXgM2CCHWCSHcOMlUT5R5TWUlhBA45+PHpZT/T7nXU05Syj+TUrZIKdfi/Gzsk1Ku6qtPKeUAcEEIsWnqpnuAY2VcUrl1A7cLIfxT/3buYRUnqc7yBPDpqT9/Gvh5GdeilJlR7gWsBCmlKYT4AvArnOzsR6WUR8u8rHJ7F/BJ4G0hxOGp2/5cSvlU+ZakVJg/Bn4wFYSfBf5tmddTNlLKV4QQPwUO4VRIvcEqazkthPgh8F6gRgjRA/wl8HXgx0KIz+IEXQ+Xb4VKuanW24qiKIqiFG21HHkoiqIoirKMVEChKIqiKErRVEChKIqiKErRVEChKIqiKErRVEChKIqiKErRVEChKIqiKErRVEChKIqiKErRVEChKBVECHGLEOItIYRXCBEQQhwVQtxQ7nUpiqLMRzW2UpQKI4T4PwEv4MOZp/F/lXlJiqIo81IBhaJUmKlW168BWeBOKaVV5iUpiqLMSx15KErliQFBIISzU6EoilLx1A6FolQYIcQTOGPU1wGNUsovlHlJiqIo81oV00YV5VohhPgUYEop/4cQQgcOCCH2SCn3lXttiqIoc1E7FIqiKIqiFE3lUCiKoiiKUjQVUCiKoiiKUjQVUCiKoiiKUjQVUCiKoiiKUjQVUCiKoiiKUjQVUCiKoiiKUjQVUCiKoiiKUrT/H+Ukb5eOsNs+AAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Define parameters\n", + "n_points = 50\n", + "num_samples = 10\n", + "sigma = 1.0\n", + "lengthscale = 1.0\n", + "jitter = 1e-4\n", + "\n", + "# Generate random input data\n", + "x = jnp.linspace(0, 10, n_points).reshape(-1, 1)\n", + "\n", + "# Compute covariance matrix using RBF kernel function\n", + "K = rbf_kernel(x, x, sigma=sigma, lengthscale=lengthscale, jitter=jitter)\n", + "\n", + "# Generate a color map\n", + "cmap = plt.get_cmap('viridis')\n", + "norm = Normalize(vmin=0, vmax=num_samples - 1)\n", + "scalar_map = ScalarMappable(norm=norm, cmap=cmap)\n", + "\n", + "# Parameters for the multivariate Gaussian distribution\n", + "mu = np.zeros(n_points) # mean vector\n", + "\n", + "data = np.random.multivariate_normal(mu, K, num_samples)\n", + "\n", + "# Generate a color map\n", + "cmap = plt.get_cmap('viridis')\n", + "norm = Normalize(vmin=0, vmax=num_samples - 1)\n", + "scalar_map = ScalarMappable(norm=norm, cmap=cmap)\n", + "\n", + "# Plotting\n", + "plt.figure(figsize=(6, 4))\n", + "\n", + "for i in range(num_samples):\n", + " color = scalar_map.to_rgba(i)\n", + " plt.plot(x, data[i,:], marker='o', linestyle='-', alpha=0.5, color=color, label=f'sample {i}')\n", + "\n", + "plt.xlabel('x')\n", + "plt.ylabel('f(x)')\n", + "plt.title(f'RBF kernel with lengthscale={lengthscale})')\n", + "plt.tight_layout()\n", + "plt.legend(loc='upper right', bbox_to_anchor=(1.3, 1))\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Generate random lengthscale values for each sample\n", + "#lengthscales = np.linspace(0.1, 6, num_samples-1)\n", + "lengthscales = np.array([0.3, 0.5, 1.0, 2.0, 5.0])\n", + "\n", + "# Plotting\n", + "plt.figure(figsize=(10, 6))\n", + "\n", + "for i, lengthscale in enumerate(lengthscales):\n", + "\n", + " # Compute covariance matrix using RBF kernel function with different lengthscale for each sample\n", + " K = rbf_kernel(x, x, sigma=sigma, lengthscale=lengthscale, jitter=jitter)\n", + "\n", + " # Draw samples from multivariate Gaussian distribution\n", + " mu = np.zeros(n_points) # mean vector\n", + " data = np.random.multivariate_normal(mu, K)\n", + " \n", + " # Generate a color corresponding to the lengthscale\n", + " color = cmap(i / (len(lengthscales) - 1))\n", + " \n", + " # Plot the sample\n", + " plt.plot(x, data, marker='o', linestyle='-', color=color, label=f'lengthscale={lengthscale:.2f}')\n", + "\n", + "plt.xlabel('x')\n", + "plt.ylabel('f(x)')\n", + "plt.title(f'RBF kernel with varying lengthscales')\n", + "plt.legend(loc='upper right', bbox_to_anchor=(1.5, 1))\n", + "plt.tight_layout()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Apart from visualising trajectories, we can also plot the covariance matrix:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Visualization\n", + "plt.figure(figsize=(4, 4))\n", + "plt.imshow(K, cmap='viridis', extent=[-5, 5, -5, 5])\n", + "plt.colorbar(label='Value')\n", + "plt.title('RBF Kernel Matrix')\n", + "plt.xlabel('X')\n", + "plt.ylabel('X')\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will need to plot many more GP trajectories.Let us write a helper function for that." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def plot_gp_samples(x, K, ttl=\"\", num_samples=5):\n", + " \n", + " num_points = len(x)\n", + " samples = np.random.multivariate_normal(mean=np.zeros(num_points), cov=K, size=num_samples)\n", + "\n", + " # Plot the samples\n", + " plt.figure(figsize=(6, 4))\n", + " for i in range(num_samples):\n", + " plt.plot(x, samples[i], label=f'Sample {i}')\n", + " plt.xlabel('x')\n", + " plt.ylabel('f(x)')\n", + " plt.title(ttl)\n", + " plt.legend()\n", + " plt.tight_layout()\n", + " plt.legend(loc='upper right', bbox_to_anchor=(1.3, 1))\n", + " plt.show()\n", + "\n", + "# test the function\n", + "n_points = 50\n", + "sigma = 1.0\n", + "lengthscale = 1.0\n", + "jitter = 1e-4\n", + "\n", + "# Generate random input data\n", + "x = jnp.linspace(0, 10, n_points).reshape(-1, 1)\n", + "\n", + "# Compute covariance matrix using RBF kernel function\n", + "K = rbf_kernel(x, x, sigma=sigma, lengthscale=lengthscale, jitter=jitter)\n", + "\n", + "plot_gp_samples(x, K, ttl=\"RBF kernel demonstration\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Matérn kernels\n", + "\n", + "The Matérn kernel is another popular choice in Gaussian processes. It is a flexible covariance function that is able to capture different levels of smoothness in the data. The Matérn kernel is defined as:\n", + "\n", + "$$\n", + "k_{\\text{Matérn}}(x_i, x_j) = \\sigma^2 \\frac{2^{1-\\nu}}{\\Gamma(\\nu)} \\left( \\frac{\\sqrt{2\\nu}}{\\ell} \\|x_i - x_j\\| \\right)^\\nu K_\\nu \\left( \\frac{\\sqrt{2\\nu}}{\\ell} \\|x_i - x_j\\| \\right)\n", + "$$\n", + "\n", + "where\n", + "\n", + "- $k(x_i, x_j)$ represents the covariance between two data points $x_i$, $x_j$,\n", + "- $\\sigma^2$ is the variance parameter,\n", + "- $\\nu$ is the smoothness parameter, typically a positive half-integer or integer ($\\nu = 1/2, 3/2, 5/2$),\n", + "- $l$ is the length-scale parameter,\n", + "- $\\|x_i - x_j\\|$ is the Euclidean distance between the points $x_i$ and $x_j$,\n", + "- $K_\\nu$ is the modified Bessel function of the second kind of order $\\nu$,\n", + "- $\\Gamma$ is the gamma function.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Matérn 3/2 and 5/2\n", + "\n", + "The Matérn kernel with $\\nu=3/2$ is a particular case of the Matérn family of kernels and is defined as\n", + "\n", + "$$k_{\\text{Matérn-3/2}}(x_i, x_j) = \\sigma^2 \\left(1 + \\frac{\\sqrt{3} \\|x_i - x_j\\|}{\\ell}\\right) \\exp\\left(-\\frac{\\sqrt{3} \\|x_i - x_j\\|}{\\ell}\\right).$$\n", + "\n", + "The Matérn kernel with $\\nu=5/2$ is another member of the Matérn family of kernels. The formula for the Matérn-5/2 kernel is given as\n", + "\n", + "$$k_{\\text{Matérn-5/2}}(x_i, x_j) = \\sigma^2 \\left(1 + \\frac{\\sqrt{5} \\|x_i - x_j\\|}{\\ell} + \\frac{5 \\|x_i - x_j\\|^2}{3\\ell^2}\\right) \\exp\\left(-\\frac{\\sqrt{5} \\|x_i - x_j\\|}{\\ell}\\right).$$\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "def matern32_kernel(x1, x2, sigma=1.0, lengthscale=1.0):\n", + " \"\"\"\n", + " Compute the Matérn-3/2 kernel matrix between two sets of points.\n", + "\n", + " Args:\n", + " - x1 (array): Array of shape (n1, d) representing the first set of points.\n", + " - x2 (array): Array of shape (n2, d) representing the second set of points.\n", + " - sigma (float): Variance parameter.\n", + " - length_scale (float): Length-scale parameter.\n", + "\n", + " Returns:\n", + " - K (array): Kernel matrix of shape (n1, n2).\n", + " \"\"\"\n", + " dist = jnp.sqrt(jnp.sum((x1[:, None] - x2) ** 2, axis=-1))\n", + " arg = dist / lengthscale\n", + " return sigma**2 * (1 + jnp.sqrt(3) * arg) * jnp.exp(- jnp.sqrt(3) * arg)\n", + "\n", + "# Compile the kernel function for better performance\n", + "matern32_kernel = jit(matern32_kernel)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "def matern52_kernel(x1, x2, sigma=1.0, lengthscale=1.0):\n", + " \"\"\"\n", + " Compute the Matérn-5/2 kernel matrix between two sets of points.\n", + "\n", + " Args:\n", + " - x1 (array): Array of shape (n1, d) representing the first set of points.\n", + " - x2 (array): Array of shape (n2, d) representing the second set of points.\n", + " - sigma (float): Variance parameter.\n", + " - length_scale (float): Length-scale parameter.\n", + "\n", + " Returns:\n", + " - K (array): Kernel matrix of shape (n1, n2).\n", + " \"\"\"\n", + " dist = jnp.sqrt(jnp.sum((x1[:, None] - x2) ** 2, axis=-1))\n", + " arg = dist / lengthscale\n", + " return sigma**2 * (1 + jnp.sqrt(5) * arg + 5/3 * arg**2) * jnp.exp(-jnp.sqrt(5) * arg)\n", + "\n", + "# Compile the kernel function for better performance\n", + "matern52_kernel = jit(matern52_kernel)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Periodic kernel\n", + "\n", + "The periodic kernel is commonly used in Gaussian processes to model periodic patterns in data. The formula for the periodic kernel is given as\n", + "\n", + "$$k_{\\text{periodic}}(x_i, x_j) = \\sigma^2 \\exp \\left( -\\frac{2\\sin^2(\\pi\\|x_i - x_j\\|/p)}{\\ell^2} \\right)$$\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "def periodic_kernel(x1, x2, sigma=1.0, lengthscale=1.0, period=1.0):\n", + " \"\"\"\n", + " Compute the periodic kernel matrix between two sets of points.\n", + "\n", + " Args:\n", + " - x1 (array): Array of shape (n1, d) representing the first set of points.\n", + " - x2 (array): Array of shape (n2, d) representing the second set of points.\n", + " - sigma (float): Variance parameter.\n", + " - length_scale (float): Length-scale parameter.\n", + " - period (float): Periodicity parameter.\n", + "\n", + " Returns:\n", + " - K (array): Kernel matrix of shape (n1, n2).\n", + " \"\"\"\n", + " dist = jnp.sqrt(jnp.sum((x1[:, None] - x2) ** 2, axis=-1))\n", + " return sigma**2 * jnp.exp(-2 * jnp.sin(jnp.pi * dist/ period)**2 / lengthscale**2)\n", + "\n", + "# Compile the kernel function for better performance\n", + "periodic_kernel = jit(periodic_kernel)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Linear kernel\n", + "\n", + "The linear kernel, also known as the dot product kernel, is one of the simplest kernels used in machine learning and Gaussian processes. It computes the covariance between two data points as the inner product of their feature vectors. The formula for the linear kernel is given as\n", + "\n", + "$$k_{\\text{linear}}(x_i, x_j) = x_i^T x_j$$" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "def linear_kernel(x1, x2):\n", + " \"\"\"\n", + " Compute the linear kernel matrix between two sets of points.\n", + "\n", + " Args:\n", + " - x1 (array): Array of shape (n1, d) representing the first set of points.\n", + " - x2 (array): Array of shape (n2, d) representing the second set of points.\n", + "\n", + " Returns:\n", + " - K (array): Kernel matrix of shape (n1, n2).\n", + " \"\"\"\n", + " return jnp.dot(x1, x2.T)\n", + "\n", + "# Compile the kernel function for better performance\n", + "linear_kernel = jit(linear_kernel)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + ":4: RuntimeWarning: covariance is not symmetric positive-semidefinite.\n", + " samples = np.random.multivariate_normal(mean=np.zeros(num_points), cov=K, size=num_samples)\n" + ] + }, + { + "data": { + "image/png": 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xBdl3eHi48e7duy06d+6cumrVqkotW7a8b/Shffv2qe+8806VCxcumNSuXTszOTlZExQUZFS3bt37huC6deuW8N1339nPnDkz4rvvvrPv3r17QkGfp0ooFAASMhKYc3IOmwM342Xtxc/df6ahc0O9xVPZujJLuy1lxaUVzD89n/6b+zO1xVQ6VOmgt5iUUk5KOPUT7PxQNxeiZm9o8CJ4t/vvCERhmNlB9e66G0BWKtw8BkEHdCMh+z/TjWIYWehGLzxb6RINtwZgUnLJ+V252bpLPnE3dCMtKVGQEgEpkZAcqfuaGgMaA90Ii5G57uudm4mVLjny6QSONXTJllIgSUlJBuPGjauSlJRkYGBgIL28vDJ//vnnEAcHh9zBgwdH+/v71/Lw8MiqV69egZeRVq1aNWPp0qX2Y8aM8fT29s6cMGFC9L33u7m55Xz33XfBL7zwQtWsrCwBMGXKlLB/JxSffPJJeL9+/ap5eno6uLm5ZW3atCmwoLGoSZkVnJSSncE7mXViFkmZSYyoPYJX672KiYGJvkO763r8dT48/CGX4y4zqckkXvR/Ud8hKaVNUjhsfgMCdukSiD6LwLayfmJJj4fgwxB0UJdgxFzV/bvQgJO/bu6FRxPdzd5H94e8sDKTITEMkkIhLghiAyEuUPc1IUSXYN3LzA4sne+5OYE2F7JSIDtNlyTduaXF6vYBuomq1TqCT2fdSIyZXeFjp2QnZZYnV69eNe7Vq5fv9evXL5bUMdWkzDv2fgoGxtDidTAu0km+ZVJqdirTjk5jW9A2atvX5vsu31O9UnV9h/Ufvna+rOi5gvcOvsfsv2cTmxHLuAbj1LwKRef8Otj6DuRkQo850OTloh2RKCgzO93oSM3eup/T4iDsHwj9W3e7sFE3kgK6JMPCKW8+h8v/53VYOoOhCeRm6UYYcrN132uzIScLUqN1q1USQ3WJRF49mLuMLMC+KrjUgVp9oVI1sK+mSwgsnXT7LoiEWxC4BwL2wKXNunkpQqMbueg8RTeHRKnwKk5CIaUuc7+wTvdi7jQF6gzQ7xuPHl2KvcTEAxMJTQllbP2xjKozqkB1JEqaiYEJc9vN5dPjn7Lk/BLiMuL4uPnHGGoqzq+w8i9pcbpE4uIG3R+2ft+Bg4++o/ov80rg21l3A93S1dgAXXIRH5S3dDVClyCEndIlC4/dp70uObDz0v0xt3YHGw/d10reuoSkKBNu28rQaLjulpsDYSd1yUXAbjA0LbrjKAVSvXr1rJIcnXicivNuLAQ8+yM0eQl2fgAbX4Hji6HbTN0SsApCSsmqK6v44uQX2Jna8WPXH2nsUmwjjUXKQGPA5OaTsTe157tz3xGfEc/nbT/HVL2hVTzBf8G6kZAWAx0/glZvl50aERoNOPrpbg+Sm62b56DN1k30NDAGA6O8m7Fuaas+R+cMDKFKc92t44f6i0MpdSrex3PPlvDyXuj3ve5Fu6wH/DZEN2GpnEvMTOStfW/x2YnPaOHWgnW915WZZOIOIQSvN3id95q+x/5b+3l116skZSXpOyylJF3fBb/0100WHLUX2k4sO8lEfhgYgU3e6IONO1g6gpmtboKkgZGaFKmUWhUvoQDdJ4R6z8PrJ6HDR7qhu4VN4cAc3aWRcuhM1BkGbBnAwbCDTGg8gYUdF2JnWjQTqvRhcM3BzG47m3Mx5xixYwTRafkYJlbKvku/w68DwcEPRu4A13r6jkhRlDwVM6G4w9gc2k2Ecf+Afx/Y9ylsGKWb3FVOSCn5+eLPDN8xHI3QsLz7cobVGlYuJjT28O7Bok6LuJV8i2E7hqmkorw7uxrWDtctvxy2BSxUzxdFKU0qdkJxh5ULPLMEOk2G82theR9IjdV3VIWWmp3KOwfeYe7JubSv3J61vddSx7GOvsMqUi3dWvJD1x+ISY/hlV2v3O1+qpQzf/8IG1/VTUAcslF3CUBRypBJkya5+Pj41PLz8/OvUaOG/969e4u1rGrTpk2rHzx4MN/LGZcuXWrn4+NTS6PRNCrI4+6lEoo7hIA278CzS3VLvH7srFvDXUbdSLjBwK0D2XNzD+MbjefL9l9iZWyl77CKRT3HeszvOJ+QpBDG7B5DWnaavkNSitKRBbB1PPh2g0Fr9VMcSlEK4d725deuXbu0b9++a1WrVs3Sd1z3ql+/fvr69esDGjdu/MR9PlRC8W+1n9ENp2YkwpJOEHJE3xEV2I7gHbyw9QUSMxP5ocsPjKg9olxc4niU5q7NmdNuDhdjLzJu3ziyckvVa1V5ElLqqk7++RH494XnfwEjtaJHKXse1L7cy8srG3Tty2vXrl3T19e31sCBAz21Wl1X8aZNm1Z/6aWXKjdu3Lh61apVax04cMC8a9eu1Tw9PWuPGzfODXSFrby9vWv179/fy8/Pz7979+5Vk5OT//N3fcOGDdb169ev4e/vX7NHjx5VExMT/7NNw4YNM+rVq1eo6/3laGp0EarSDF7eDSuf013+6LMI6j6n76geK1ubzbyT8/jl8i/Uc6zHF+2+wNnCWd9hlZhOVTrxSctP+Oivj3j34LvMbTdX1akoyw7O1ZWwrj8Ynl5QNBUlFWXT2MpEXSrayoZO/mn0XfTQpmN9+/ZNmjVrlpuXl1ftf7cvnzhxYtSdVuJ9+/b1Xr16tc2gQYMSAYyNjbUnT568On36dKcBAwb43Nu+/IMPPogECA4ONv3uu++C77QvnzNnjuO0adPudhsNDw83nDlzpuvBgwev3WlfPn36dOd/ty8vCmqE4mEqVYWX/gSPprqJmn/N13dEjxSdFs3LO1/ml8u/MKjGIJZ1W1ahkok7+vj0YVKTSey5uYepR6ailVp9h6Q8iXNrdJOk674ATy9UyYRSpt1pX75w4cIQR0fHnGHDhlWbP3++PcD27dut6tatW8PPz8//yJEjVhcuXLjb1vlB7cvNzMzknfblAP9uX37kyJH7rgne2768Ro0a/qtXr7a/efNmsXStUx/fHsW8km4C2MZXYNfHup8blL4+En9H/M3EAxNJy0njszaf8VTVp/Qdkl696P8iSVlJLD67GCtjK95t8m65v+RTrgQfht/HglebvJEJ9blHKUKPGEkoTqW9fXlRUK/UxzE01hXBqtYRNo+Dq9v1HdFdUkqWXVjGqD9HYWVsxaqeqyp8MnHHa/VeY3DNwfxy+Re+PfetvsNR8ivmOqwerCvq9PwK1f5bKRfOnj1rcv78+bsNVB7Vvryg+77TvhzgYe3LT548aXnhwgUTgOTkZM25c+eKpfujSijyw9AYnluhK6KzdriuVbGeJWcl8/b+t5l3ah4dq3Tk16d+xceuFPYx0BMhBO82eZenqz3NN2e+Yf219foOSXmclGhY+ayuGuTgtUXWyVJR9C0pKclg6NCh3tWqVavl5+fnf+XKFbPZs2ffvrd9eY8ePXwK077cz8/PPz4+3vBR7cv9/Pz8GzVqVOP8+fP/md28fPlyW2dn57pnzpyx6Nevn2/r1q19CxqLal9eEKkxsLSbrnnPiB3g7K+XMK7GXWX8/vGEpYQxvtF4hvgPUUP6D5GtzeaNvW9w7PYxvu7wNe0qt9N3SOWKlJKbyTc5FXmKq3FXsTK2wsHMAXsze+xN7e9+b25o/ujf0ex0+Lk3RFyA4VvBo1HJPQlF71T78iej2peXZRYO8OIG+LGrrpfAS3+CbZUSDWFL4BamHZ2GlbEVP3b7kUbO6o33UYw0RsxrN48RO0cw4cAEfuz2I3Ud6+o7rDJLSklgQiCnIk9xMvIkpyJPEZ2u+0BkZmhGRk4Gkv9+SLExseHpak8zsMZAKltVvv9OrRY2vAKhJ3WXOVQyoShlkhqheBIRF2BZT7B0gpE7wcK+2A+ZnpPO7BOzWX99PY2dGzOn3RwczFTp4fyKSY9hyLYhpGansqLnCjytPfUdUpmSlp3Gyssr+eXyL8RlxAHgZO5EY+fGNHZpTCPnRnhbe5Mrc0nITCA2PZaY9BhiM3RfL8deZnfIbnJlLu0rt2dwzcE0dWmqG7X482M4Ml/X+bfFWD0/U0Uf1AhF2aFGKIqaS20Y+Cus6AernoNhm3WdAIvJjYQbvHPgHQISAni5zsuMrT9W1VcoIAczB77t8i1Dtg1h9K7RrOi5QiVk+ZCZm8naq2v54fwPxGXE0ca9DV08u9DYpTEelh7/uYxhKAxxMHPAwcyB6lS/777I1Eh+u/ob666tY9+tffja+TLYvCpPHV2CaZNR0HxMST41RVGKmJqU+aS8WunKdN/+Rzdcqy2eegebAzfzwtYXiMuI49vO3/JmwzdVMvGEPK09WdRpEbEZsYzdM1aV6H6EHG0O66+tp9fGXsz+ezY+tj6s6LGCbzp/Qz/fflS2qlzgeTvOFs6MaziOP5/9k2ktpyGyM5gatpNuXl4crttbteUuhaSU5CYmIrNU5Vnl8SrUX6aETZvQWFhg1bEjwqAICuXU7AVdP4WdH8BfX0Gb8YXfZ5607DRmHp/J74G/08SlCZ+1+Qwnc6ci239FVcexDnPbzWXc3nGMPzCeBR0XYKQx0ndYpYaUkh3BO1h0ZhEhSSHUdajL9FbTae7avMiOYWpoSj/XVvTd/AEnTQz5zMOLMXvf4OU6LzOm/hiVMOuJNi2NzIAAMq5eJfPadTKvXSPz2jVy4+MBMLCxwcDRAUMHRwwdHHQ3RwcsO3bExNtbz9ErpYFeX7lCiKVALyBKSlm7OI8lpSR+5Soyzp/HyN0du0GDsH32GQxsbAq34+ZjdJPJ9k7XtVWu1qHQsQbEBzDhwARuJN5gdL3RjK47GgNVKbDItPVoy8fNP2bq0alMPTKV6a2moxFqsC4mPYYpR6ZwMPQgvna+zO8wn/aV2xf9CqLcbFg7ApEeT5NBf7LS0Y9ZJ2bxw/kfOBN9htltZuNo7li0x1QeKOvmTRJ/30zSjh1k3bih658CCDMzTHx8sOzYAZOq1dBmZpAbE0NOdAw5MTGknz1LTnQ0MiMDY29vlVAogP5HKH4CFgLLi/tAQgi8fl1F8t69xC9fQdScOUQvXIhNn6ep9OKLmPg8YQ0HIXTV/KIuw7qR8OpBsK38+Mc9xKaATcw4NgMLIwu+7/p9kX4yVP7vGb9niE6PZtGZRVgbW1f4app7b+5l6pGppOWk8V7T9xhYY2DxJVm7JkPIYej/A7jWxRT4pOUnNHRqyKfHPmXAlgF83vZzmro2LZ7jV3C5iYkkbd9B4u+/k376NAiBebNmWD/VE1M/P0z8/DDy8EA8pkKplBJtairCSI3w5cekSZNc1q9fb6/RaKRGo+Gbb74J6dixY4HrTuRX06ZNq8+dO/dW27Zt83Vt99VXX/X4888/bYyMjKSnp2fmr7/+Guzg4JBbkGPqNaGQUh4UQniV1PGEoSHWXbti3bUrGZcvE/fLLyRu2EjC6t+waNkSh9fHYt6wYcF3bGKp64T4QwdYM0RXo6KAXRHTstOYcXwGmwM308ylGZ+1/UxNGixmr9Z9laSsJFZcWoGlsSVj61e8FQZp2Wl8/vfnrL++nhqVavBZm8+oZlut+A54bi0c+waavfafhnt9fPrgb+/POwfeYdSuUYytP5aX67ysRo+KgMzNJeXAQRI3bSJl3z5kdjbGPtVwfGc8Nr17Y+TiUuB9CiEwsFSt5PPj3vblZmZmMjw83DAzM7NUfYLp1q1b0sKFC0ONjIx47bXX3D/++GOXxYsXhxVkH6X+lSqEeEUIcVIIcTI6OvrxD8gn05o1cZsxA5/9+3B86y0yAwIIGTKUuBW/8ERLaR18oN+3cPs0bH+3QA8NTAhk0NZBbAncwmv1XuO7Lt+pZKIECCGY2Hgi/Xz68e3Zb/n54s/6DqlEnY0+y7NbnmXD9Q2MrD2SVT1XFW8yEX4ONr8Bnq2g6/QHbuJr58vqp1bT3as7C04vUJNnC0mbkUH86t+40fMpQseMIe3UKewGDcRr/TqqbtmCw6hRT5RMKAVTFtqX9+/fP8kob7SpRYsWqWFhYQWue6/3OhR5IxR/5GcORXHWochNTub2u5NI2bcPm/79cZkyGY3JE5Q73/0JHJ6nuwzScOhjN98cuJlPj32KmaEZn7X5jBZuLZ4geqUwcrW5vHvwXf4M+ZNPWn5Cf9/++g6pWOVoc/j+3Pd8f+57nM2dmdF6Bo1diq0EgE5aHHzfXjd/4tUDuhoujyClZM3VNcw8MZMmzk1Y2GkhpoYFG/WryHLi44lftYr4lavIjYvDtHZt7F8aiVXnzqXyEkVJ1qH4+K+PKwfEBxRp+3IfO5+06a2mP7TpWGJioqZZs2Y1MjIyNP9uXx4ZGWng7OycC7r25c8991zcoEGDEps2bVq9UaNGKYsXLw6bPn2604IFC1zubV9+9uzZi4mJiQY1atSos3Pnzit32pfXrFkzfdq0aZF3Lnn4+vpm9e7du9revXuv32lfnpmZKR7Vvrxjx44+zz77bNyYMWPi/n2fqkORDwZWVngsWkjMwkXEfPMNmQEBeCyYj5FzAVuAd/xIt5R06wRwrg3uD76Ekp6Tzqzjs9gYsJEmLk3URDQ9MtAY8Fmbz0jNSWXqkamYG5nT3au7vsMqFvEZ8Uw8OJHj4cfpVbUXHzT7ACtjq+I9qDYX1r8MyeEwYvtjkwnQjR49X+N5zI3M+fDwh7y5703md5yPiUGx9DQqN7Ju3SJu2U8kbNiAzMjAsl07Ko0ciXnTJhV6jpC+3WlfvmPHDqs9e/ZYDRs2rNrkyZNDx40bF7t9+3arefPmuWRkZGgSEhIM/f3904FEeHD7coA77cvt7e1z/92+fP78+U5A5J1j39u+HCA7O1s0atQohYeYNGmSi4GBgRw9evR/konHUQnFPYRGg+O4NzCpWYPwSe8R9MyzeMz/umDzKjQG8MxS+L4drBkKrxz4TyXN4MRg3t7/NoEJgbxS9xVeq/eaWiqnZ0YGRnzZ/ktG7xrN+wffx9zQnLYebfUdVpG6GHORt/e/TWx6LNNaTqOfb7+SOfC+GRC4B3p/DR4F+xDau1pvcrQ5TD4ymbf3vc1XHb7C2EB1IP23jMuXif1hCUk7diAMDLB+ujf2w4dj4lvg/k7l3qNGEopTWWhfvmDBAvudO3faHjp06JrmMZNyH0SvcyiEEL8CR4HqQohQIcRL+oznDusuXfD6bTUaC3NChg0n/rc1BduBhT08txxSomDj/UWvdofs5oWtLxCTHsO3nb/ljQZvqGSilDAzNGNhp4X42vkyfv94/o74W98hFZmN1zcydLvuEtzyHstLLpm4tBkOfQENh0Gj4U+0i36+/ZjcYjKHwg4x4cAEsrXZRRtjGSWlJPXECW6OeoWgfv1JOXAA+5dGUm33btxmzFDJRClSFtqXr1u3zvqrr75y2bZtW4CVldUTVWrUa0IhpRwopXSVUhpJKT2klD/qM557mfj64r1mDRbNmxMxZQpRX8wr2A7cG0L3WRCwG/76ihxtDvNOzuPt/W/jbe3Nml5raOnesniCV56YlbEV33b5FjdLN8bsHsPB0IP6DqlQsnKzmH50OpOPTKaBcwN+6/UbtRxqlczBo67AptfAvTH0nFOoXQ3wG8AHzT5g3619TDo4iRxtThEFWfZIrZbkPXsIeWEgN4cOI+PSJRzHj8dn316c3nkHI2dVAK+0KQvty8ePH18lNTXVoGPHjn41atTwHzRoUIE7X+p9UmZB6KM5mMzNJeKTaSSsWYPL9GnYDRhQgAdLWDeSmCtbeLduO/5OuMbz1Z/n3SbvqmHbUi42PZbXdr/GtfhrTGs1jaerPa3vkAosMjWS8QfGcy76HCNrjyzZ0bCMRPi+A2Qm6yZhWrsVyW6XX1zOnJNz6OHVg1ltZlWogm+5Kakk/r6J+JWryLpxAyMPD+xfGolNv35oTMv2hFXVHOzJqPblZYwwMMBl8sdk375NxCfTMK5cBYvmzfL5YMGZFi/zTspJkuKvMrPpB/T2H1S8AStFwt7MnqXdlvLW/rf48PCHxKXHMbz2cH2HlW9Hwo7w/uH3ycjJYF77eXTx7FJyB7/TjjwhBIZtKbJkAmBoraHkyBy+PPUlRgZGfNrq03I/2TAzKIj4latI3LgRbWoqprVr4zZnDtY9uiMM1Vu4Unqo38Z8EIaGuH85j+CBAwl98028f1uNsZfXIx8jpWTVlVXM/XsurhbO/HLjEtVPrYMaL8ATTHZRSp6lsSXfdPqGDw5/wBenviA2I5a3G71dqgstZedms+D0ApZdXIaPrQ9z280t3toSD3Lwc7i2A3rMAc+iv6w3svZIMnMz+ebMN3hae/JK3VeK/Bj6JrVaUg4cIH7lKlIPHwYjI6y7d6fSi4Mxq1dP3+EppUT16tWzSnJ04nFUQpFPBlZWVF68mODnnufW6Nfw+m31Q/uA5Ghz+OzEZ/x29Tfae7RnRpsZWJ9bB3+8ratR0XZCCUevPCljA2Nmt5mNnYkdP138ibiMOKa2nFoqG4rdSr7FpIOTOB9zngF+A5jYZCJmhmYlG8TV7bB/FtQbBE1HFdthRtcdTXBiMAtPL6S6XXXaVW5XbMcqSVmhoSRu+p3EjRvJDgvD0NERh3FvYDdgAIaOalm5UrqphKIAjCtXxmPBfEJGjCT0zbeo8sP3/ykSk5qdyoQDEzgcdpgRtUfwVsO3dJ9oG42A4L90S+iqNAev1np6FkpBGWgM+KDZB9ib2bPozCLiM+KZ224u5kZFWhunULbd2Ma0Y9PQCA1ftPuCrl5dSz6ImADdpQ7XetBrXrG2IxdCMLXlVIISg3jv0HusfGolVW2qFtvxipM2NZWkP3eRuHEjaSdOgBBYtGiO0zvjserSpVQWolKUBym9Y7ellHnjxrhOm0basWNEfDrjvjLdEakRDN0+lKO3jzK5xWTGNxr//+FxIaD3V1CpKqx7CVKKroy4UvyEEIyuN5qPm3/MX7f/4sXtL3Ip9pK+wyItO42P//qYSYcm4Wvry7re6/STTGQmw+pBYGCk62tjVPwjI2aGZnzd4WuMDYx5c++bJGclF/sxi4rMzSX12HFuv/8B19q0Jfz998mOjMDxrTfx2bObKkuXYt2zp0omlDJFJRRPwLZfX+xHvUzCb78Rv2IFAJdjLzN462DCUsJY1GkRA/wesBrExAoG/AwZCbBh1H31KZSy4bnqz7Gw40ISMhIYtHUQ8/+ZT1Zull5iORR6iOf/eJ7fA35nVJ1RLOu+DDfLopsAmW+5ObB2BMQGwLPLwLbAq82emKulK3PbzSU0OZT3D72PVpbe15SUkvQzZ4iYOZOA9h24OXw4yX/+ic1TPfFctZJqO3bgMHo0Rm56+D9UlCKgEoon5Pj221h27kTkZ7M5uuEbhu0YhkajYXmP5bRyb/XwB7rUhh6z4cY+ODS35AJWikwbjzZs7LORp6o+xQ/nf+D5P57nQsyFEjt+QHwAo3eNZsyeMWillh+6/sC4huP0UyBNSl0zvIBd8NQXULXk5zI0cWnCu03f5UDoARadWVTix38UKSUZly8T9cUXBHbuQvALA0lY/Rtm9evh/tWX+B4+hOv06Zg3bFjuV6tUdJMmTXLx8fGp5efn51+jRg3/vXv3WhTn8Zo2bVr94MGD+b4u++abb7rdia1Vq1a+wcHBBR4eU3MonpDQaHD//HPO9O2BduYCak6qxdyei/PXj6PhMAg5Avtm6koRV+tY/AErRcrGxIYZrWfQzasbnxz9hMHbBjOs1jDG1h9bbP0m4jLi+ObMN6y7tg5zI3MmNp7IwBoDMTLQ47D4sW/g5I/Qchw0HqG3MF6o/gKXYy/z/bnvqVGpRskuk32AzIAAkrZtJ2n7drKCgsDAAItWLXF443WsOnXCwKqY+6copUpZaF8+ZcqUiK+//vo2wKeffur0wQcfuK5atepmQfahRigKYVngr3zSMRbbVPj0jF/+m3sJAb2+BMcauqZJiaHFG6hSbNp6tGVTn0308+nHsgvLeHbzs+y/tb9Iy0Nn5Wbx04Wf6LWhF+uureO56s+xtd9WhtYaqt9k4vIfsPNDqPk0dP5Ef3Ggm+PyUfOPqOtYlw8Pf8i1+GslHkNWSAgx337Ljaf7cKNXb2IWL8bQ0RGXqVPxPXyIKt9/j23fviqZqIDKQvvySpUq3b1emJqaqnmSETNVKfMJfXv2WxadWUQP7x68fdSehGU/UeXnn7Fo1jT/O4m5rmvp7FQThm8DQ1U9syw7EnaEqUenEp4ajp2JHV29utKrai/qOdYr8HB2Vm4Wf0f8zYHQA+y9uZfItEhau7dmQuMJJV9X4kHC/oFlPcHZH4b9AcalY8VLVFoUL/zxAiYGJqzpvabYO6lmR0aS9MdWkrZtI+OirhyAWcOGWPfogVW3rhg5qTLY+VGSlTJvf/Bh5czr14v0F9bE1zfNbeaMMt++/I033nBfu3atvZWVVe6BAweuurm5/afG/aMqZaoRigKSUrLg9AIWnVlE76q9mdV6Fs7jxmFUpQrhkz9Gm5GR/505+EKfhRD6N+z6uPiCVkpES/eWbO23lQUdF9DMtRmbAjYxZPsQem7oyYLTC7iReOORj49Jj2Hj9Y28te8tWq9uzejdo9l4fSM1KtXg287fsrjz4tKRTCTchF9fAEtHGLi61CQTAE7mTnzR/gvCU8OZdnQaxfGBKTc5mYT16wkZPoKA9h2ImjMHhMDp3Xfx2bcXr1UrqTTkRZVMKHfdaV++cOHCEEdHx5xhw4ZVmz9/vj3A9u3brerWrVvDz8/P/8iRI1YXLly4u0TqQe3LzczM5J325QD/bl9+5MgRy3uPfW/78ho1avivXr3a/ubNmw/89LpgwYKwiIiIc88++2zsnDlzCvwLrOZQFICUkq/++YqlF5bS37c/k5tP1vUSMDPDddon3Bw+gpiFC3GaUIDCVbX6wc3jcHwxVG4GtfsX3xNQip2RgRHtK7enfeX2pGSlsOfmHrbe2MqS80v4/tz3GGmMMNQY3v1653uBIDRFd+nL2dyZ3lV7065yO5q6NMXUsBT1achIhFXPQ3YGDN0MlqXvj2YDpwaMrT+W+afn08KtBf19C/+a0mZlkXrwIIlb/iBl3z5kVhZGnlVwGDMGm969Hls5Vyk9HjWSUJzKQvvyO0aMGBH31FNP+X755Ze3C/QcC7JxRSalZO7JuSy/tJzn/J7jw+Yf3leC2aJ5c2yefYbYZT9h1aMHZrUK0NGxyzQIOwWb3wDn2uDoVwzPQClplsaW9PHpQx+fPkSnRbMrZBdRaVFka7PJ0eb852sfnz60r9ye6nbVS+eM/9xsWDscYq7Bi+vBqYa+I3qokbVHcjz8OLOOz6K+Y32q2ha86NWdZZ6JmzeTtG072sREDOztsX3+eWx698K0Tp3S+f+klDpnz5410Wg01KlTJxMe3b68d+/e8QXZ95325Z07d059WPvyd955p8qFCxdMateunZmcnKwJCgoyqlu3bua9250/f97kTnxr1661rVatWnpBn6dKKPJBSsmsE7P49cqvDKoxiPeavvfANxLniRNJOXCA8I8+xnvNb/kvSmNoDAN+gu/awJqhMGoPGBfriiKlhDmaOzKoZhluDJebDetGQuBeeHohVG2v74geyUBjwMw2MxmwZQATDk5gVc9V+R7pyQoNJXHzZhJ//53skJsIU1OsOnfG5uneWLRsqRpyKQWWlJRkMG7cuCpJSUkGBgYG0svLK/Pnn38Oubd9uYeHR1Zh2pePGTPG09vbO/NR7cuzsrIEwJQpU8L+nVBMmDDB48aNG6ZCCOnh4ZH1448/hhQ0FjUp8zGklMw4PoPfrv7GUP+hTGg84ZGfSpJ27SLsjXE4vv02Dq8WsGlR4D5Y0Q/qDID+3xdr6WJFybfcHFj/ElzaBN1mQoux+o4o3w6FHmLMnjE8X/15Pmr+0UO3y01MJGnnThI3byb95CkAzJs1w6ZPH6y6dsHA0vKhj1UKT7UvfzKqfXkZs+D0An67+hsjao3g7UZvP3aI07pLF5K6diVm0SKsunTBpKp3/g9WrQN0+BD2faqrT9Hs1UJGryiFlJujq+p6aRN0nVGmkgnQFSEb6j+U5ZeW09y1OZ09O9+9T5uVRcqBAyRt3kLK/v3I7GyMq1bF8a23sOndCyN3dz1Grihlj0ooHuGXS7/ww/kfeMb3mXwlE3e4fPwRgceOET75YzyXL0cUpF15m3fg9j+w433dKhBV9ErRl9wc2PgKXNwAXaZDy9f1HdETeavhW5yMPMnkI5Pxt6uJ7dXbJG7eQtLOnWiTkjBwcMBu0ECsez+NaS1/NS9CKTNU+/IyYuuNrcz+ezadqnTio+YfFehNxtDREedJ7xL+4UckrFuH3XPP5f/AGo3ucseP3WDNcN18Cgffgj8BRSkMbS5sGg0X1uuKVrUap++InphhrmSW8Qts/2MKoV/2IDEpG2FujnWXzlj36o1Fi+ZqXoSiFAH1KnqAw2GH+ejwRzR2bszstrOfqEeCTf/+JGzYSPT8Bdg89RQaiwJMsjSxgoG/wg8ddUv0Xt4N5pUKHIOiPBFtLmx6Dc6vhU5ToPVb+o6owHJTUkg9dIjk3XtIOXAAbUoK7U2NOeGZjcXQzjw7cjYa89JTP0NRygNV2OpfzkWfY/z+8VSzrcb8jvOfuC+DEAKnCe+QGxND3PLlBd+BnaeuDXTCTd1SvdyiK+WsKA+lzYXfx8K536Djx9BmvL4jyheZm0v6+fPEfPc9ISNGcL1FS8LeHk/q0aNYde+Gx+JvqHnsOIET+/Op1QH+SdJ/63lFKW/UCMU9biTcYOyesdib2vNtl28LXbbXvEEDLDt3InbJj9g+/zyGlQo4yuDZAnp/Db+PgR3v6bo5KkpxyUzRLQ29vhM6fARtC1CgrYRJKckKCib16BHSjh0j9fgJtElJAJj4+WE3eDBWnTth1qABwsDg7uM+aPYBp6NO8/7h91nXex02Jjb6egqKUu6oEYo8EakRvLr7VQyEAd93+R4HM4ci2a/T22+jTU8n5ttvn2wHDQZDyzfg7yVw4ociiUlR/iMpHJb1+H8b8nYT9R3RfbRpaaQeP0HM9z9wa8xYrrduw42ePYmc/ikZFy9h1bULbnPn4nv4EFU3/47ze5Mwb9z4vmQCwNzInNltZxOTFsP0Y9OLpTS3ojxIaW9ffsfkyZOdhRCNwsPDCzzgoEYogJSsFF7b/RopWSks7baUytaVi2zfJtWqYftMf+J/XU2loUMx9vAo+E46f6JrJLZ9km6CZikvKqSUMRHndXN1MhJh0Brw1W/rb6nVkhUcQsb5c6SfPUvamTNkXr0GubkAGHt5YdmmDWYNGmDRojlGlSsXaNJ0bYfajG0wlq//+ZrW7q3p69O3mJ6JouiUhfblAAEBAUZ79+61dnV1zXqSx1f4hCJHm8PEgxMJTgxmcZfF1LSvWeTHcHj9dRI3byF6/nzcP/+84DvQGED/H+DHrrBmmG6Splr5oRSF67th7TAwsYaRO8ClTomHkBMXR/rZs6SfO0fGufOknz9/9/KFxtwc03p1sX9lFGb16mFWrx6GdnaFPuaIWiP4K+wvZh6fSUOnhlSxrlLofSrKwzyoffmd+yZMmOC6Y8cO28zMTE3jxo1TVq5cGaLRaGjatGn1OnXqpJ09e9Y8Li7OcNmyZUEzZsxwvXr1qlmfPn3i5s+ff/vq1avG3bt3923QoEHqhQsXzKtWrZqxdu3aYCsrK+29x9+wYYP1tGnT3LKysoSnp2fm6tWrg21sbLT/jvP111+vPGfOnNBnn33W50meZ4VPKL44+QWHww4zucVkmrs2L5ZjGDk7U2noEGKX/Ij9yJGY1niCHgim1jBoNSzpDMv76t78bYtuJEWpgP7+EbZN1LUgH7QGrN1K5LC5SUmknThB6tFjpB47RlZgoO4OjQYTPz+su3fHrG4dTOvWxaRatf9ctigKBhoDZrWZRf/N/Zl0cBLLey7HSJPPUvlKmbZn+eXKcWEpRbrEp5K7ZVqnoTUf2nSsb9++SbNmzXLz8vKq/e/25RMnToy600q8b9++3qtXr7YZNGhQIoCxsbH25MmTV6dPn+40YMAAn3vbl3/wwQeRAMHBwabfffdd8J325XPmzHGcNm1a5J1jh4eHG86cOdP14MGD1+60L58+fbrzv9uXr1y50sbV1TW7RYsWBe7hcUeFTijWXF3DL5d/4cWaLzLAb0CxHsv+5ZeJX7OWqHnzqPL990+2EzsveHED/NQLVvSFEdtLZbdHpZTT5sKuyXB0Ifh2g2d/1C1VLiYyO5u0kydJPXKU1GPHyLh4EbRahJkZ5o0aYdO3D+b162Naq1aJLuV0sXBhSospTDgwgcVnFjOuYdmttaGUbnfal+/YscNqz549VsOGDas2efLk0HHjxsVu377dat68eS4ZGRmahIQEQ39//3QgER7cvhzgTvtye3v73H+3L58/f74TcDehuLd9OUB2drZo1KjRfQ3EkpOTNbNnz3bdt2/f9cI8zwqbUBwLP8bM4zNp496GCY2Lfza7gY0NDq+8QtScOaQeO45F82ZPtiPXujB4ja7nx4r+MHwLmBV+CFipIJIjYP3LEHwImoyC7p+BQdG/Ddzp1Jm0ZQtJ23eQGx8PhoaY1a2Lw+jRWLRojlm9eghj4yI/dkF08+rG4bDDLDm/hJZuLWnsUmztJJRS4lEjCcWpNLcvv3z5skloaKhJ3bp1/QEiIyONGzZsWPP48eOXq1SpkvOwx/1bhVzlEZQYxPj94/G28ebztp9joCn6IdUHsXtxMIaurkTNm1e42eVVmutqVMRchZXPQVaBG9QpFVHgPvi2NYSdgj7fwFNzizyZyLwRRPT8+QR27UbIwEEkrN+ARYvmeCxaSPXjx/BatRLHcW9g3qSJ3pOJO95v+j6VrSrz/uH3ScxM1Hc4Sjl09uxZk/Pnz98tavSo9uUF3fed9uUAD2tffvLkScsLFy6YgG404ty5c/cVWGratGl6XFzc2bCwsPNhYWHnnZ2ds/75558CJRNQAROKxMxE3tj7BkYaIxZ2Woilccl1EdSYmOD4+utknDtH8p+7Crczn07wzI8QdhJWD4aczMc/RqmYtLmwd4ZuVMvcHkbt0y1HLiIyN5fEP7YSNOA5bvTsSczibzGu7IHrrFn4/nUY93nzsOrUqWDVYkvQvUtJpx2dppaSKkUuKSnJYOjQod7VqlWr5efn53/lyhWz2bNn3763fXmPHj18CtO+3M/Pzz8+Pt7wUe3L/fz8/Bs1alTj/PnzpkX37P6vQrUvz9ZmM3rXaE5HnebHbj/SwKlBEUaXPzI3l6C+fZHZOVTdshlhVMiJYKdX6gpf1egFA34uluFrpQxLCtdd4gg5DPVfhJ6fg3HR/GGXOTkkbvmD2O++Iys4GONq1bB99lmse/bEyLnsze1Zcn4JX//zNVNbTOUZv2f0HU6ZoJVaNKLwn0tV+/InU9ral1eYEQopJTOOzeBExAk+afmJXpIJAGFggOPb48kKDiZh48bC77DBYOg+G678AZvfAO1/VgIpFVXAHt0ljtv/QL/voO+iIkkmZFYW8WvWENi9B+Hvv48wNcX9q6+oumUz9iOGl8lkAmBk7ZE0d23OZyc+IzAhUN/hlHpRaVE8t+U5zkSd0XcoSilRcRIKJGaGZoyqM4re1XrrNRbLDu0xrVeX2O9/QOYU6BLVgzUfDR0+hLOrYPPrurbTSsWVnQ473odf+utWAb2yH+q9UOjdyuxs4latIqBbdyImT8HA1haPbxbhvXED1t27ITRl++1EIzTMajMLcyNzJhyYQEZOhr5DKrUyczN5a99b3Eq+hYVR6byUVRGUtvblen0HEEJ0F0JcFUIECCHeK85jaYSGSU0n8UaDN4rzMPkihMDh1dFkh4aStHVr0ey07URo/wGcWakrVJSt3gwrpNun4bt2cOwbaPoKvLwHHKsXerfpFy8S9NzzRE6bjpGLC5V/+B6vtWuw6tixQFUqSzsHMwdmtp5JQEIAc/6eo+9wSiUpJZ8c+YTzMeeZ1WYWvnZlosieVqvVlp9fVD3JO4cPHQbX2wV3IYQBsAjoAoQCfwshNkspi60N4JWIJKQEW3Mj7MyNMTUqmdUdD2LZoT0m1asT8933WPfuXfhPd0JA+0lgagM7JsGq5+CFlcVaX0ApRXJz4PA8ODAbLJxgyEao1rHQu9VmZBCz6Btily7FoJId7vO/xqpLl3KVRPxbK/dWjKg1gmUXl9HcrTldPPVbilyfsnO1xKdlkZmtJUcrycnVsj7wF7bc2EI/r5GYZdcjNiUTe8sn68pcgi5ER0f7Ozo6Jmo0mrIzcbAU0Wq1Ijo62ga48LBt9DmDrykQIKW8ASCEWA30AYotofhgw3n+uZlw92cTQw125sbYmhthY2aEp705dTxsqetuQw1XK0wMiy/h0I1SvELY+HdI/nMX1t27Fc2Om48GM1vYNAaW94HB68C8gF1OlbIlJgA2vqpb8VNnAPScUyS1SdJOnSL8w4/ICg7G5pn+OL/7LgY2FaM75xsN3uBk5Emm/DUFf3t/3C3d9R1SkcvIziUoJpWAqBRuRKcSlZxBXGoWsSlZxKRmEpeaRUJa9n2PMbC4ilnln8hJrsPy7b4s5xjfvtiQ7rVd9fQs8icnJ+fliIiIJREREbWpQJf6i5gWuJCTk/PywzbQ2yoPIcSzQHcp5ct5Pw8BmkkpX//Xdq8ArwBUqVKlUUhIyBMf8/TNeCISM4hPyyYhPYvEtGzi03Qvmvi0LAKjU4lL1fVEMTIQ1HCxpo6HDXXdbWjt64CHXdFW8ZO5udx4qhfC3Azv9euL9lPflW2wdjhUqqr7tGpdul/wyhOQUteF9s+PwdAEen0JtfsXere5KalEz5tH/KpVGLm74zp9GhYtWxZBwGXLreRbPLflOarZVmNZ92VlujR3ZFIGRwJjuBKeTEBUCgHRKdyKS0Ob9/YvBNiZG2NvYYy9pTH2lia67y1MqGRhhImRAYnZYXwf+BaVjF140/8rLI0tMDQQVHe2KvQIRXGv8lBKhj4TigFAt38lFE2llA+d5FDYZaOPI6UkLCGd86GJnAtL1H0NTSApIwchoGU1ewY0qkz32i5FdrkkYf0Gwj/8kMrffYtlu3ZFss+7gg7CrwN1IxRDf9clF0r5kBgKv78ON/aBT2d4emGRJI3p584R+tZb5IRHUGnoEBzHjSu19SNKwo6gHUw8OJFRdUaVqdLcaVk5HL8Rx6HrMRwOiOZapK7WkbGBBm8HC3ycLKnmZImPkyU+jpZUdbR45HtaUlYSg7cOJikriV+f+hU3y6Lt+6ISivJBnwlFC2CqlLJb3s/vA0gpZz3sMcWdUDyIlJIbMan8cTacdf/c4lZcOlamhvSu58ZzjStTz8OmUCMLMjubgG7dMHJ2wXPVyqK/Nh32D/zyDBgYwaDfwE0/y2WVIiIlnP1V18pemwvdZkCj4bqPmIWUsGkTEZOnYOjkhNuczzFvoH5XAKYemcqG6xv4rst3tHBroe9wHio2JZN1p0LZeyWKf27Gk50rMTHU0NS7Eq19HGjt60B1ZysMDQo24p+rzWXs3rEcDz/Okq5LaOTcqMhjVwlF+aDPhMIQuAZ0AsKAv4FBUsqHLoHRR0JxL61WciwolnUnQ9l2IZyMbC2+TpaMalOVZxp5YKB5sjf1uJUriZz+KVV+/hmLZk2faB+pCZnE3U7FzNoYGyczjIzv+bQRfVWXVKTG6GoR1FZFe8qklCjY8hZc3QpVWkLfb6CSd6F3K3NyiJozl7iff8a8eXPcv5xXJC3Cy4v0nHQG/jGQ+Mx4fuv1Gy4WLvoO6T5nbyXw89Fg/jgbTlauFn9Xa9r46hKIJl6VCj2a+sXJL/jp4k9MaTGFZ/2eLaKo76cSivJBr5UyhRA9ga8AA2CplHLGo7bXd0Jxr6SMbLaeC2fV8ZucD0uklps1k3v506yqfYH3pc3IIKBzF0z9fKmydOljt89IySYqJCnvlkxUcBKpiVn3bWNpZ4KNkzm2zubYOplha5NN5TOvYxB25P9LTMt43YAK5dLv8MfbkJkCnSZD89egCHrQ5CYkEDb+HVKPHMFuyBCc351Y+Oqt5dCNxBsM2joIT2tPfu7+M6aGxVK5ON8yc3LZdj6cn4+EcOZWAhbGBjzTyIOhLTzxcSq6lV0brm9gypEpvFD9BT5s/mGR7fffVEJRPlSo0tvFQUrJ5rO3mb39CrcTM+hZx4X3e9SkcqWCTeCM/XEpUXPm4PXbaszq1fvP/Vqt5NqJCP7ZEUJ8RNrdf7d1NsfJ0wonT2vs3S1IT8kmMSqNhKh0EiLTSIxKJyNVN1PbwsaYei4nqRX/Gcb+nXTVE01KrpeJ8gTSE2DbRDi/Blzr6/7PnGoUya4zr1/n1tjXyQkPx2XqFGyfUSNXj7L/1n7e2PsGT1d7mk9bfaqXpbMZ2bl8f/AGy48GE5OSRVUHC4a28OSZRh5YmRZtInj09lHG7B5DU9emLOy0sFgnpaqEonxQCUURSc/SvdC/PRBIrpS83NqbMR18sDTJ38pcbWoqAR07YdawIZUXf3P336WUhFyI5dimQGLDUnGsYoVPIyecPK1w9LTGxOzx+89IySYiKJEzu28RdjUeY6Ncahv/Tl3P61gM+R7sPJ/4eSvFKOggbHwNksOh3SRoM143F6YIJO/Zw+2J7yIszPGYP1/Nl8inb89+y6Izi3i3ybsM8R9Sosf+OziOSevOcSMmlU41nBjeyotW1RzQPOGl1kcJiA9gyPYhuFq6srz78mJvoqgSivJBJRRFLDwxnc93XGXj6TAcrUyY3qdWvtdoRy9aRMyChXj/vgnT6tWJDEri6MYAwq4lYO1gSvO+1fBp6IQoxBtIZHASp/8MIfCfKAzIobrVERoM6oJtg9ZPvE+liOVkwt5P4cgC3cqc/j+AR9FNhIv/9Vcipk3HtHZtPBYuwMjZucj2Xd5ppZbx+8ez/9Z+vu3yLc1dmxf7MVMyc/h8xxWWHw3Bw86Mmf3q0NbPsdiOF5Mew+Ctg8nSZrGq5ypcLYt/yblKKMoHlVAUk9M345n8+0XOhyUyopUX7/eoibHho+cs5CYmEtCxE7TpQZD/cwT+E42ZlRFNnvLGv7UbBo95fEEkRKVxZst5rpxMQCsNaFAnnqav9MdAj9VDFSDyEmx4BSLPQ+OR0PXTIusOChC7ZAlRc7/AskMH3L+ch8ZUv3MByqLU7FQGbx1MbEYsvz71Kx5WHsV2rP1Xo/hw4wVuJ6YzrIUXE7tVxyKfo55PIj0nnZd2vkRAQgDLui+jln2tYjvWvVRCUT6ohKIYZeVombX9Msv+CqZ+ZVsWDW6Iu63ZIx9zYsoyToa7YWBiTIOuntTvUgVj0+J7A0mLiuLYN2u5HFETB8tYOo9phX3Vol1jruSDVgvHv4XdU3Xl0vsshOo9imz3Ukqiv/6a2G+/w7pnT9xmf6YmXxbCzaSbvLD1Bdws3FjeYznmRkVb9C4+NYvpWy+x4Z8wqjla8PmzdWnkWbwVb7VSyzv732HPzT181eErOlYpfOn2/FIJRfmgEooSsO18OO+uO4ehgWDec/XoWOO/Q8zaXC1HNgZydvct7BKu0aJaNN4zPi6ZAKUkaM3P7DtgQ5Y0p3knK+r1b1GoSytKASSFw6bXdEWq/LrD0wt0XUKLiNRqiZz1GfErVmA74Flcpk5FGKiRqMI6HHaYsXvG0tWzK5+3/bzIJmlei0xm6I8niEnJZEz7aozt6FOsbQDuuLM8VB/zQ1RCUT6odYMloGcdV/54ozVuNmaM/Okks3dcISf3/w3bMlKz+WPROc7uvkXdDh60qx5B5ua1ZEdFlUyAQuD9/HBeGOdGZYsr/LU7g9+n/UFybHrJHL8iu7INFreEm8fgqXkwcHXRJhO5uYR/9DHxK1ZQadgwXKZNU8lEEWnt3po3G77JjuAdLDm/pEj2+c/NeAZ8e5RcKdk4phXju1YvkWRizdU1/HTxJ16o/gIv1nyx2I+nlE8qoSghXg4WbBjTkoFNq7B4fyCDlhwnKjmD+IhU1s0+SdjVeDq8WIM2z/vhOGI4MieH+F9WlmiM5jWa0fOTF+ngd4CoSA2rJx/g6sGAEo2hwshKgz/Gw+qBYOMOrx6EJi8VScXLO2RWFmHvTCBxwwYcxo7F6b1J5bpLqD6MqDWCnt49mX96Pr9e+bVQ+zp4LZrBPxzHxsyI9aNbUsejZBqx7QjawYzjM2jj3oZJTdXviPLk1CUPPdh4OpQPNlygtsaYzgkGGBlr6P5qHdx8bO9uEzruTVKPHcNn714MLEu4l4KUJO5awp4/sgjPqkmtBga0ealNkU4KrdAiLsD6lyD6CrR4XVeoyrBo2z9rMzMJG/cmKQcO4PTuu9iPHFGk+1f+L1ubzTv732HfrX1MbTGVZ/wKXs/jj3O3efu3M/g4WfHzyCY4WZXMZNkdQTuYdGgSDZwa8E2nb4p8Lkh+qUse5YP6C6EHfeu7M7euN+0iJZHaHGoNq35fMgFg/9JItElJJKxbW/IBCoFN11H0ndCMhva7uHg6l9+n/k5afGrJx1KeSAnHFsMPHSA9Hl7coOvFUcTJhMzKIuytt0k5cACXqVNVMlHMjDRGzG03l9burfnk6CdsCdxSoMevOBbCG7+epn5lW1a/0rzEkontQdtLRTKhlB8qoShhUkpObAkieE8YrrXs2esuGP7bP+y7ev98CbN69TBv3Ji4n5cjs7P1EqumSmNaTP6ArvWOEx1jytrJfxJ97qGtVpRHSY6Elc/CjvegWid47Qj4dCryw8icHMImvkvKvn24TJmM3QvPF/kxlP8yNjDmy/Zf0tS1KR/99RE7gnY89jFSShbsuc7Hmy7QsboTy0c2w8asZFbebA/aznuH3lPJhFKkVEJRgqSUHN98g5PbgvFv5Ur/sfVYM7Yl3g4WjPr5JOtPhd63faWXRpITHk7Sjse/ORUbEyt8X3uf/i/kgDaH9Ytvce2333SftpX8ubodFreA4MPQcy4M/BUsHIr8MDI3l9vvf0Dyzp04vTcJu4EDi/wYysOZGpoyv8N86jvW571D77EnZM8jt/9s+xW+2HWN/g3c+XZII8yMS2ay7LYb21QyoRQLlVCUECklx36/wantIfi3dqP94BoIjcDJypTfXm1OU+9KvLP2LN8eCOTOvBbLdu0wrlaN2CU/ou+5Lo7tezPgw2Y4WUWza58jR2d+iTaphFahlFVZabqGXr++AFZu8MoBaDqqSCde3iG1WsKnTCFpyxYc334b++HDi/wYyuOZG5nzTedvqOVQiwkHJ3Aw9OADt1t1/CbfHbzBkOaezB1QD6MCthR/UttubOP9w+/T0KmhSiaUIqcmZZYAKSXHNgXyz86b1GrjRruB1f9T4yEzJ5d31pzlj3PhjGzlzUdP1USjESSs30D4hx9SeckSLFu30tMz+L/crBwOLfydi9fs8DQ/T5ch3pg0eFrfYZU+t8/AhlEQcw1avgEdPy7yuRJ3SCmJnP4p8atW4TDmNRzHjSuW4zyINldLeko26cnZZKZmo82VSCnRaiVI7n5FgImZIaaWRpiYG2FqaYhhOa7KmpSVxKg/RxEQH8BXHb6ijUebu/f9HRzHoB+O0bKaA0uHN8GghOq93JtMLOq0qFQlE2pSZvmgEopiJqXk6MZATv95k1pt3Wn3gt9DC0ZptZLpWy+x7K9g+jd05/Nn6qLJzSGwU2dMfH3y1dq8pFz4428O/ZGAtUE4TzU9ie2zk4tlGL/M0WrhyHxdLw4LB+i7GKp1KLbDSSmJmjOXuKVLqTRyJE4TJxTZsj8pJenJ2SREpd3tYJsUnU5aUhbpyVmkJ2ff7WT7JAyNNJhYGGFubYytszmV3Cyo5GpBJTcLrB3MiqXpVUlKzEzkpZ0vcS3+Gq/We5XRdUcTmZTF0wsPY2VqxKaxrUpkzkS2NpuFpxey9MJSGjs3LnXJBKiEorxQCUUxklJyZEMgZ3bdpHY7d9q+4PfYN3spJQv2BjBv1zWequvKV8/XJ3Hpj0R/MQ+v9eswq1UytfXz4/aVGLYvPoU2K4uuzj/g+exwqNWvWIb0y4S4INj8BgQfgppPQ++vwbx4yyVHz59PzDeLsRs8GOePPnziZCInO5eYWylEBiURFZJEQmQaCZFpZGXk3t1GoxFYOZhiYWOCmZURZlbGmFkZY573vamFERoDoUuYhW57IXTfIyEzLZuM1BwyUrPv+z4tMZO48FRS4jLvHsvASIOdizkOHpa4+9nhUcMOS7uy13ckLTuNGcdnsDlwMw2cGhEd+Cy3oo3YNLYlPk5WxX780ORQJh2axLnoczzr9yzvNnkXM8NHl//XB5VQlA/5SiiEEE5AK8ANSAcuACellNpHPrCIlaWEQkrJkfUBnNl9izrtPWjzvG+B3uy/PxjIzG1X6OLvzNe9qnGrSxcs27fH/Yu5xRh1wSXFprNtwd/ERWTRwmo59RtpEb3mFWm1x1JPq4UT38OeT0BjCN1mQoMXiz2xil32E1GzZ2Pz7DO4TpuG0OTvOryUksSodCKDEokMSiIyOImY0BS0uXlzd+xMsHO1wNbRDBtnc2ydzLF1NsOqkimaYrzWn5WRQ1x4KnG3827hqUSHJN8dBbF1Nsejuh0eNe1w97PD1KLs9CLZHLCZyX9NIyfHgFE1P+DNln2K/Zg7g3fyyZFPkEimtpxKN69uxX7MJ6USivLhkQmFEKID8B5QCTgNRAGmgB9QDVgHfCGlTCr+UMtWQnFnNUedDh60ea5gycQdy48GM/n3i7T1c2RWxF6SVv5CtZ07MfZwL4aIn1x2Zi57frpI4OkY/MwO0cFpBYZPzYQ6A8r/aEVsIPw+Fm4eBZ8u0PsrsCm+7pN3JGzcRPj772PVvTvuX8x9bDnt1MRMQq/EE3oljtAr8aTE60YDjEwMcPKywtnLBmdva5y9rbGwKZ65Hk9CaiUxYSl5scdzOyCBnMxcEODkaU21ho74NHLC2r70feq+1/cHA5m1+xCeNdYTmx3MMP9hvNnwTYwMij4pysjJ4PO/P2fttbXUdajL7Lazi7UjalFQCUX58LiEYg6wQEp58wH3GQK9AAMp5friC/H/ykpC8c/OEI5uDMS/lSvtX6xRqGvaa/6+xaQN5+jiAG8vew+7gQNx+fCDIoy2aEgpObktmBNbgnCyCKOn+cdY+NSBHnPAqYa+wyt62lxdkaq908HABLrPgvqDSiSBSt67l9A3xmHRrCke336Lxtj4P9vkZmu5dSWO0Mvx3LoSR9xtXVEyEwtDPKpXwqOGHa7VbLBztShTcxVyc7REBicReiWekPMxRIUkA+BS1RqfRs74NHLCwrb0JEQAB65FM2LZCXrUduWL5/2Ze3Iuv139jdr2tfm09adUs61WZMcKiA9g4sGJBCQEMLL2SF5v8DpGmtI/kqMSivJBzaEoYhcOhnFg1VV8GzvReWStInmz/v1MGOPXnGXapXU0Cj6N7/59GNjaFj7YYnDjTDS7l13CSJNJV5u5uGtOQbPR0P49XVvu8iD6qm5UIvRv8OsBvb4Ea9cSOXTqiRPcenkUJjVq4LlsKRqL/5dlz8nK5ealOAL/iSL4XAxZGbkYGGlw87HBo0YlKteshIOHZbnqIpsYnUbAqSiun4wiNjQFBLj52OLbxBnfxk6YmOv3j2lQTCp9Fh7GzdaMDWNaYm5sCMCukF1M+WsKydnJNHJuxDO+z9DFswumhgWfJ5KVm8XeW3vZFLCJo7ePYmtiy6zWs2jp3rKon06xUQlF+ZDfORQrgNellIl5P3sBP0opi77U3yOU9oTi6vEIdv90Ca86DnR/tTYGRXi9efv5cL74bhsLds/F8rWxVH7z9SLbd1GLDUthx/cXSIxKo6nvRRolTkZYOUHXT6HOs2X3Mkh6PBz4XDdfwsQKenxeopd1Mi5dImToMAydnfH8ZQWGdnZkZ+Vy80IsAf9EEXw+lpzMXEwsDKla35FqDZxwr25brpdn3is+IvVuchEfnoqBoYaqDRyp2dIVj+p2JZ5IZeVoeXrhYSKTMtj8emsqV7p/ZUVMegybAjax4foGbiXfwtrYml5Ve/GM3zP42fk9ct9SSi7FXWLT9U1sC9pGUlYSzubOPF3taQbVHISDWdlacaUSivIhvwnFq8DbwHjAHZgIvCOlLFjR+kIqzQnFjdPR7PjhAm6+tvR6vW6xvInvvRJJ2OjRVE8Iw/PPP3F2si3yYxSVrIwc9q+8yvW/I6nsbUhny88wj/4LPFtDz8/BufSsVnms3Bw4tQz2zYD0BGg4FDp+VKITT7OCgwke/CLCxJgqv6wkMsGYq8cjuHEmhpzMXMysjPCu74hPAyfcqtsWaTJb1kgpibmVwuW/bnPt70gy03KwrGRCjRau1GzhirVDycy3mL/nOvN2XeOHoY3p4u/80O20UsvfEX+z/tp6dt/cTbY2m7qOdallXwsDYYBGaDAQBgghMBAGaKWWQ2GHuBZ/DWONMZ2qdKKvT1+auTbDQFM2k0eVUJQP+b7kIYRoDewDYoAGUsqI4gzsQUprQnHzUixbvzmHY2Urnn6zPsamhsV2rBMbd2H1/jhWtXyBV+ZO/M+nntJESsmlw7c5tOY6JuaGdG11E/fLH0BGou6TfbtJYF9014+LRcBu2PmhrjOoVxvdXAmXOiUaQnZkJCEDB5EorUl98SMCr6WTlpiFsZkhPo2c8G3ijJuPTbGuwCircrJzCTobw+Uj4dy6HAcS3KvbUqu1O1XrO2JgVDzn7HpkMk/NP0y32i4sGNgg34+Lz4hnS+AWNgVuIjI1Eq3UkitzkVLe/apFi38lf/r69KW7d3dsTEqmzXlxUglF+ZDfEYohwMfAFKAu0A0YIaU8W7zh3a80JhS3AxLY8vUZbJzN6ft2g2Jfyial5FLfZ4kKjeTD/lNY8UoLqjlaFusxCysmNIWdP+RdAunuQkPTVWj+XgK5mVD3BWg3ESpV1XeY94u8BLunwPU/wc5b1xW0es8Sv1yTfCuaE+8uJNTIlxRzNzQaQZXa9lRv5oJXXfsKczmjKCTHZXDlaDiXj4STHJuBqYURNVq44N/aDTsXi8fvIJ9ytZIB3x4hKCaVXePb4WBZuiaJlkYqoSgf8ptQbAJekVJG5f3cFPhOSpn/1LsIlLaEIuJGIpvnn8HCxoR+7zTE3Pq/s+2LQ9KffxI27k0WtBnO8SoNWf5SU2q5le5PKfdeAvGoYUf7Pg7YXF0MJ3+E3GyoNxDaToBK3voLUquFwD1w7BsI3Asm1tDuXWj6SrGVzX6Q3BwtIedjuXToFjcvxiGFBgcHDf6dffBp7ISZZcn8npVXUiu5dSWOS4duE3Q2Bq1W4uZri39rN6o1dCx0krbsryA+2XKJr56vT98GpWuJd2mlEory4YlXeQghjKWUWUUczyOVpoQiPDCRLQvOYG5tTN+3G2JpV3J/cGRuLjd6PkW2qTkjm40hOSuXn0Y0oZFn8VZlLCwpJZf/Cufw2utocyUNu1WhYStTDI/Ph5NLQeZC3ed1yy+rtIR8FmoqtKxUOLsajn+r671h6QJNX4ZGI8HCvmRiQDeSc+VIOFdPRJCRko2JTMM59C8avNwZj34lOv+5wkhNzOTK0XAuHb5NUkwGJuaG+DV1wb+1Kw4eBV+VdCsuja5fHqR51UosHd6kyMqgl3cqoSgfHleH4iPgGyll3EPu7wiYSyn/KKb47lNaEorwwES2zD+DuU3JJxN3xK9ZQ8TkKZgvWMzwsxCRmMEPQxvT2rf0z+5OTcjkr/UBXP87EmsHU9o854eXVxYc/hJOr4TsVF13zjrP6OZauNQt+ksNUkJsAJz+BU79BBkJ4FofWowF/75gWDKjAKkJmVw/GcnV4xHE3EpBYyDwrmuPw9nfMdu3GvdZM7Dt27dEYqnIpFYSejWeS3/d5saZaLQ5EscqVvi3csW3iXO+lp9KKRm69AT/hMTz5/h2uNuW7mJbpYlKKMqHxyUUfYB3gQzgHyAaXaVMX6A+sBuYKaWMLvZIKR0JRXhAAlsWnMXC1oS+bzfQWxEdbWYmAZ06Y1q9OmZfLWLIj8e5EZ3K3Ofq8XQ9N73EVFChV+I4uPoa8RFpeNV1oM1zvlhba+Hqdji/DgJ2gTYHHPx0iUWNXuDgC09aXTDhJgQdzLsdguTbIDRQszc0HwOVm5XIHIms9BxunInm6vEIwq7GIyU4eVpRvbkLvo2ciJ/1CYkbN+L8wQdUGjqk2ONR7peRks3VExFc/iuc2LAUDIw0VGvoSM2Wbrj72j50+enak7eYuO4c0/vUYkgLr5INuoxTCUX58LiEYoWUcogQ4l10Zbdd0fXyuAwclFKml0yYOvpOKG7nJROWek4m7oj57nuiv/wS7w3ryfTyZdTyk5wIjmNcJ1/e6uRbJiog5uZoObvnFn9vC0ZqJQ26VqFuBw/dPIG0OLj0O5xfCyF/6R6gMdRNknSsrksuHKrrEg5LR8hMgczkvFvi/7+Pvqpr2BUfrNuHuQN4twXvNrpy2baVi/153ik6df1kJEFnY8jN1mLtYIpfUxf8mjpj52Kh6xz62WfE/bwch9dfx/H1scUel/JwUkqibyZz6a9wrp+IICsjF8tKJlRv5kL1Zi73TeSMSs6g8xcHqO5ixW+vtCgTr73SRCUU5cPjEopLQA9gM/CfHswPuxRSXPSZUNy+nsCWhXnJxPgGpaLfQW5SEgHtO2DZoQPuX8wlMyeXjzZeYO2pUJ6q48rcAfUwMy4bqwCS4zL4a10Agf9EYWCkwa+pM3U7VMbBI28FS2IoBB/WJQcx13S3uBu6EYzHMbXRLfn0bqu7OdYokZGIjNRsgs/HEHQmhpuXYsnJ0mJqYYRvYyf8mrng7G193zX26EWLiFmwELshQ3D+4H11/b0Uyc7KJehsNFePRXDrUhxSgrO3NdWbueDb2Jm3N51jz5Uotr/ZptSvuiqNVEJRPjwuoRgHvAZUBcLuvQuQUsoSXeunr4Ti9vV4tiw8h5WdCX3eLh3JxB2Rsz8nbvlyqu3cgbGHB1JKfjh0g1nbr1DbzYYfhjbGxabstH2OvZ3CuX2hXDsWQU62Fnc/W+p2qIxXPYf/furLzda1DI+5BulxuuqVJlZgYnPP91ZgbFliEzyTYtIJPh/DjTMx3L6egNRKLGxN8K7nQNX6jrj5PbjoVNyKX4icMQObvn1xnTkj351DlZKXmpjJtRORXD0WQWxYCmjguiYX32bOjH6hdrHVtijPVEJRPuR32ehiKeVrJRDPI+kjobh+MpI9P1/G2t601CUTANkREQR06Yrdc8/h8vFHd/9996VI3lx9GktTQ34Y2pi6Hrb6C/IJZKRmc+mv25zfH0pKXCZWlUzxb+OGZ217HNxLTz+K5LgMwq7GE3YtnrCrCSTHZQBg52pB1XoOeNd3xKmK1SPjjV/9GxFTp2LZqRMeX3+FMCy+wmhK0QoLSmTWNyfxThOY5oKJuSHVGjlRvZkLrtVs1ChTPqmEonxQzcEeQkrJqe3BHN8chGs1G3qMroOZVelc/3/7/Q9I2r4dn317MbSzu/vvVyKSeOmnk8SmZvLFgPo8VbdkGlgVJW2ulqBzMZzbG8rt6wkAmFkbU7mmHVVqVqKyv32J1f/IzsolPjyVmNAUIgITCbsWT1KMLoEwtTDCzc8Wdz87qvhXwtY5fxVM439bQ8SUKVi2a4f7gvkP7ByqlF6L9wcye8cVVr3UDI8skVcOPZqcLC1W9qZ351vk9/eholIJRfmgEooHyM3Wsu+XK1w9HoFfM2c6vlizVA9jZgYEcKNXbxzGjsXxjfubhsWkZPLqilOcColnWAtPJvWocbfjYVmTmpDJrctx3LwUx63LcWSkZAPgUNkSVx9bbBzMsHYwxdrBDCt70ycqga7VSjJSsklPziIxOp3YsJS8WyqJUWncebmYmBvi5muLe3U73P3ssHezKPCoyZ2lvxbt2uKxYIFKJsqYuNQs2n2+j6belfhxeJO7/56VkUNQ3iqe0Cu6VTwuVa2p3twVn0ZOxV5NtyxSCUX5oJeEQggxAJgK1ASaSinzlSWUREKRnpLF9m/PEx6QSLOnvWnUw6tMDFveem0M6adP47N3Dxrz+z8NZebk8tn2Kyz7K5gqlcyZO6AeTb1LdxGsx5FaSfStZF2CcTGO6JvJZGfm3reNmZUR1g5mmFkZo9EIhAaERuR9r7vlZmtJS8oiPVl3y0jJ5r6XhAAbBzPsPSyxd7PQfXW3xMbBrFCXXeLXriXi48lYtG2jSyZMStelNOXxpm6+yPKjwex8qy2+zg8ugpWakMnVExFcPRZB3G1dB1Svug7UaOFCFf9Kqv9KHpVQlA/6SihqAlrgO2BCaUko4sJT2broLKmJWXQaVhPfxg/vEFjapP3zDyGDBuP03iTshw9/4DbHbsTy7rpz3IpPY2QrbyZ0rV5mVoE8jpS6kYWkmAySYtJJik0nKTqdxJgMMlKzkVqpu0ndKITMlUgp0RhqMLcyxszKCHNrY8ys7tyMsLI3pZKrRZE3e0tYt47wjz7Gok0bPBaqZKIsCo5JpfO8Awxo7MGs/nUfu/2dJahXjkVw/UQkGanZmFkbU72pMzVauGLvXrFXhqiEonzQ6yUPIcR+SklCcfNiLDuXXMTASEPP1+rg4l26e2M8SMiw4WQGBuKz6080Zg+u0peamcPsHVdYfjSEqg4WzBlQj0aedg/cVil6CevX65KJ1q1VMlGGjV35D/uuRrF/QnucrAu2iio3R0vIhViuHA0n5HwsWq3EydOKGi10VTkr4iURlVCUD6U+oRBCvAK8AlClSpVGISEhRRpDRmo2RzYEcPmvcOzdLeg5pi7W9mWzZG7ayZOEvDgEp3ffxX7kiEdueyQghonrzhGemM7LbaryRkcfrEwr3htZSUpYv4Hwjz7ColUrPBYtVMlEGXX6Zjz9vjnCm518ebuLX6H2lZ6cxbUTkVw+oqvKqTEUVK3nSI2WrlSuWanCFMhSCUX5UGwJhRBiN+DygLs+lFL+nrfNfvQ0QiGlJOBUFId+u0ZGag4NulSm8VPeGJXxSwAhI0aQefUaPrt3/Wcuxb8lZ2Qzc9sVfj1xExszI0a28mZ4Ky9szFRiUdRif/qJqM9m65KJbxapZKKMklLy3HdHCYpJ48DE9liYFN3lsOibyVw+Gs61ExFkpuZgbmOMXxNnqjd3eaJGZWWJSijKh1I/QnGvokookuMyOPDrVULOx+LkaUX7F2vgWLl8vGDvzqWYOAH7l17K12POhSawYG8Auy5FYmViyLCWXrzU2hs7C7XqoLCklER/8QWxS37Eqls33D6frZKJMmznxQheXXGKGf1qM7iZZ7EcIzdbS/D5GK4ej7h7ScTe3YLqzVzxa+qs95L/xUElFOVDhUootFrJ+X2hHNt8A4DmT1elTgePcjesePOll8m4dEk3SmFh8fgH5Ll0O4mF+66z/UIE5kYGvNjCk1FtquJgWf7ewEqCzMkhfPIUEjdswHbgC7h89BHCoGyPgFVk2blaun15ECFg51ttMSyBFRrpKVkEnIzi6vEIIoOSEAI8atjh28QZ77qOmFrqdzQxKz0HIxODQheaUwlF+aCvVR79gAWAI5AAnJFSdnvc4wqTUEgp2TTvNLevJ1Cllj3tBvmV2bkSj5N+5gzBLwzE8Z3xOIwaVeDHX49MZuG+ALacvY2hgYa2vg508XemU01nlVzkkzY9nbDx75Cybx8Or7+Ow9gxZWL5sfJwK46F8PGmC/wwtDFd/Et+BVhCZBpXj0dw7UQESTEZCI3A3c+Wag2dqFrfscQKvEkpCQ9M5PJftwk4FUXP0XWp7F+4ZegqoSgfKlRhqwsHwzAxM8SnsVO5f3O/OeoVMs6fp9ru3RhY5n+U4l43olNYcSyEPy9GEpaQjhDQqIodXWs508XfBW+HJ9tveZebmHi3LojL5I+xGzhQ3yEphZSSmUP7Ofuo6mjJb6801+v7x50lqIH/RBN4OorEqHQQ4OZjS9UGjlSuWQk7Z/MiL0+flpTFlWPhXP4rnITINIxMDPBt4kz9zpXv67z6JFRCUT5UqISiIkk/d47g557H8e23cXj1lULtS0rJpfAkdl2K5M+LkVwKTwKgqqMF9TxsqeVmjb+bNbVcbbAxr9gTOrMjI7n18stkBYfgNmcO1t0fO/CmlAHzdl1j/p7rbBrbivqVbfUdzl1SSuJupxLwTxQ3TkcTdzsV0FVydfayxtnbGueqNjh7WRd4Oao2V0tyXCaxoSlcPR5B8LkYtFqJazUbarZypVpDpyKr0aISivJBJRTl2M1XXyXjzFmq7dmNgWXRFc4JjU9j16VIDl6L5uLtJKKSM+/e52Fnhr+rNTVdralcyRwPOzPcbc1wtTEtkWvO+pR+/jyhb4xDm5yMx6KFWDRvru+QlCKQkJZF69n7aOvnwDeDG+k7nEdKiEwjPDCBiKAkIm8kEXc75W7lV1tnc6wqmWBiYYSpuREmFoaYmBthamGIsakhqYlZJEankRiVTmJ0Okkx6WhzdQ82szKienNX/Fu5Fno04kFUQlE+qISiHEs/f57gAc/h+NabOIweXWzHiU7O5FJ4EhdvJ3LxdhKXbicRHJt6XwlrA43AxdoUdzszKtuZ42VvjrejBV72Fng7WBTp8jt9SFi/nohPpmHo4IDHooWY1qyp75CUIvLFn1dZsDeAHW+1oYaLtb7DKZCsjByiQpKJDEokMiiJtKQsMtNyyEjNJjP1X2XmAUMTA2ydzLBxNMPG0RwbJzNsncxx9rbGwLD4PhCohKJ8UAlFOXdr9GuknT6Nz+5dGFiV3NLYjOxcwhMzCI1PIyw+ndD4dMIS0gmNT+NmXBqRSZn3be9oZYK3gwU+TpbU97ClQRVbqjlalvoVODIri4iZM0lY/RsWLVvg9sUX93V8Vcq2xLRsWs/eS2tfBxa/WLpHJwpKaiVZmblkpmaTmZ6DubUx5tbGepkfohKK8qFsfyxUHsvh9dcJfvZZ4laswHHMmBI7rqmRAd4OFg+duJmWlUNwTBrBsakExaQSHJNKcGwqf5y9zarjNwGwMjWkfmVbGlS2pUEVOxpUscXWvPTUxsiOjCLszTdJP3MG+1Ev4/jWW2pZaDnz419BJGfmMK6Tr75DKXJCIzAxM8TETP0ZUIqG+k0q58xq18KyY0fifvqZSi++iIF16RiyNTc2xD9vMue9tFpJUGwqp28mcPpmPKdvJrBwXwBaqbts0qKqPT3quNCtlotel7Cm/fMPoW++iTY1Dfcv52Hdo4feYlGKR2J6Nsv+CqJ7LRdqupaO142ilGbqkkcFkHH5MkH9n6HS8OE4T3pX3+EUWGpmDudCEzkcEM228xEExaSiEdC8qj096rjSrZYzTlYFa9D0pKSUxP+yksjZszFyd8NjwQJM/QrXz0Epnb7afY2vdl9n27g2/0l8laKlLnmUDyqhqCDCP/6YhI2bqPr7JkyqVdN3OE9MSsmViGS2nQ9n6/lwbkSnIgS0rGbPsBZedKrpjEExzbvIjooi/MOPSD10CMt27XCb83mpGfFRilZSRjatP9tL86r2fD9U/Z0rbiqhKB9UQlFB5MTGEti9B2Z16lD5xyXlorCXlJLrUSlsPRfO2pO3uJ2YQeVKZgxr4cWAxpWLtMlZ0s4/iZgyBW1GBk4TJ2A3aFC5OIfKg83fc515u67xxxutqe1uo+9wyj2VUJQP5bswgHKXob09jm+8QeqRI6Ts2aPvcIqEEAI/Zyve7uLHwXc7sHhwQ1ytzfh062VazNrDx5suEBCVUqhj5CYnc3vSe4S9+SZGHh54b1hPpcGDVTJRjiVnZPPj4SA613RWyYSiFIAaoahAZE4OQf36o01Lo+rWP9CYlsy8g5J2ISyRn48E8/vZ22TlaGlf3ZE3O/nSoErBlnOm/f03tye9R3ZEBA6jX8XhtdcQRhW7EmhFsHDvdeb+eY0tr7emjodKKEqCGqEoH9QIRQUiDA1x/vBDssPCiP3xR32HU2xqu9swZ0A9jr7XkXe6+HH2VgL9vjnC8GUnOHMr4bGP16anE/n5HEKGDgNDQzxX/oLjuHEqmagAUjJzWHI4iE41nFQyoSgFpBKKCsaieTOsuncn9vsfyA4L03c4xcre0oQ3OvlyeFJH3u1enTO3Eui76C9G/vQ350ITHviY1GPHuNGnL3FLl2I7YABVN27AvEGDkg1c0ZufjwSTkJbNm53LX90JRSluKqGogJzfnQhCEDn7c32HUiIsTAwZ096Hw5M6MrFbdf65Gc/TC//ipZ/+5nxoIqDrEHr7ww+5OXwECKjy00+4TvsEjYXqqFpRpGbmsOTQDTpUd6Suh62+w1GUMkcVtqqAjNzccHj1FaK/nk/q0aNYtGih75BKhKWJIWM7+DC0hSc/Hwnmh0NB9F5wiDcMb9Fz3y+QmIj9qJdxGDu23M4vUR5u+dEQ4tOyebOzqiuiKE9CjVBUUJVGjsTIw4OIGTOQ2dn6DqdEWZka8XpHX/YP9+enG2vpuX4+AVpzNr86g5yXxqhkogJKz8plyaEbtPVzLFXtyRWlLFEJRQWlMTHB+f33yAoIJH7VKn2HU6Jkbi5xK1cS1b8vLtfPYfHm25x+7wt+jDSm/dz9fPrHJeJSs/QdplKC1py8RWxqFq938NF3KIpSZqlloxWYlJJbo14h/cwZqm7dipGzk75DKnYZV64QPmUKGWfPYdGyJS5Tp2BcpQoAofFpfLX7Ohv+CcXc2JCX23jzUmtvrEzV6o7yLCtHS/s5+3C3M2Pt6Jb6DqdCUstGywc1QlGBCSFw/vADZG4uYe+ML9eXPrRpaUTOmUPQM8+SfSsUtzlzqPzjkrvJBICHnTlzB9Rj51ttae3jwFe7r9P28318fzCQjOxcPUavFKffz4RxOzGDMWp0QlEKRSUUFZyJtzeu06aRfvIUUV9+pe9wikXKoUPc6P00cT8uxbZ/P6pt24pN714PrXbp62zFt0Masfn1VtTxsGXmtiu0/XwfK44Gk5WjLeHoleKUq5UsPhCIv6s17f0c9R2OopRpKqFQsOndC7tBg4hbupSkP//UdzhFJic6mrDx47k16hWEiQmeK5bjOn06Bra2+Xp8XQ9blo9syppXW+Blb8HHv1+k4xf7WXcqlFxt2blUqDzczosR3IhOZWwHH1VOXVEKSc2hUADQZmURMmQIWQGBeK1bi4m3t75DemJSqyVhzVqivvgCmZGB/ehXsR81Co2x8ZPvU0oOXo9h7s6rnA9LpKqDBa939OHpem4YGqi8vCySUtJrwWHSs3LZNb5dsXWpVR5PzaEoH9Q7oQKAxtgYj6++QhgZETbuTbRpafoO6YlkXLtGyKDBREydiqm/P96bf8dx7NhCJROgm2/Szs+Rza+34tsXG2FiZMD4NWfpPO8A606FkpOrLoWUNQeuRXPxdhKj21dTyYSiFAGVUCh3Gbm64vbFXDIDAgifOpWyNHqlTU8n6ot5BPV/hqzgYFw/m0WVn5YV+UiLEILutV3Y+kZrvhvSCAsTQyasPUvHLw6w5u9bZKvEosz4Zl8gbjam9K3vru9QFKVcUAmFch/LVq1weON1kjZvIWH1an2Hky8phw5z4+k+xP7wAza9e1N1+zZs+/Yt1mviGo2gWy0X/nijNUuGNsbGzIh315+jw9z9rD5xUyUWpdyJoDhOBMfxStuqGBuqt0FFKQpqDoXyH1Kr5dbo0aQePYbXyl8wq1tX3yE9UHZkJJEzZ5G8cyfGXl64TJ2KRfNmeolFSsm+q1F8vfs6Z0MT8bQ3581OvvSp766G00uh4ctOcD40kcOTOmJmbKDvcCo8NYeifFCpufIfQqPB/fPPMXJ0JPTNt0pdV1KZk0PsTz9xo0dPUvbvx/HNcXhv/l1vyQToLoV0rOHMprGtWDK0MRbGhoxfc5auXx5gy9nbaNWqkFLjQlgi+69GM7K1t0omFKUIqYRCeSADW1vc589Hm5JC0HPPk37mjL5DAiDtn9MEPfMsUZ/NxqxxI6r+sQWH114r9KTLoiKEoLO/M3+80ZrFgxtioBG88etpes4/xM6LEWVqXkp5tXh/IFYmhgxp4anvUBSlXFEJhfJQZrVr4fXbajTm5oQMHUbi1q16iyUnPp7wjz8mZNAgchMTcZ//NZW/+w7jypX1FtOjaDSCHnVc2f5mW75+oT6ZOVpeXXGK/ouPcPZWgr7Dq7ACo1PYdiGcoS09sVYl1RWlSKmEQnkkk6pV8VrzG6Z163D7nQlEL1xUop+yc1NSiF6wkMDOXUjYsJFKI0ZQbesfWHftWiYKERloBH3qu7Pr7bZ8/kxdbsWl02fRX0xYe5ao5Ax9h1fhLN4fiLGBhhGtym6dFUUprQz1HYBS+hna2VFl6VIiJk8hZuFCsoKCcJ05A42JSbEdU5ueTvyqVcR+/wO5iYlYdemC45vjMPEpm/0WDA00PNekMj3quLBwXwBLDwex/Xw4b3TyZUQrL0wM1bX84nYrLo2Np8MY2sITB8vi+91VlIpKJRRKvmiMjXGdNRPjqlWJnjeP7NBQPBYtxNDBoUiPI7OySFi/nphvFpMTHY1FmzY4vvkmZrVrFelx9MXK1Ij3e9TkhSZV+PSPS3y2/QqrT9zko6f86VTTqUyMupRV3+wPxEAIXm1bTd+hKEq5pJaNKgWWtPNPbk+ahIGtLZWGvIjN009j6Fi4xkrZYWEk7fyT+FWryA4NxaxRI5zefgvzxuV7Jdn+q1FM/+MSgdGpdK/lwqz+dbCzKB0TTMuT2wnptJuzj+ebVObTvnX0HY7yL2rZaPmgl4RCCDEH6A1kAYHACCllwuMepxKK0iP9/AUiZ8zQrf4wMMCybVts+vfDql07RD5XXNxJIpJ27CDj3DkAzOrVw+H1sVi0bl1hPq1n52pZciiIebuuYm9hwrzn6tHSp2hHfiq6Kb9fYOXxm+yf2B4PO3N9h6P8i0ooygd9JRRdgb1SyhwhxGwAKeWkxz1OJRSlT+aNGyRu3EjCpk3kRsdgYGeHzdO9seraFWFkhMzORmbn5H3NRuZkk30rlKQ/d5JxVpdEmNaqhVX3blh3715qV22UhAthiYz79TRBsam80rYq73Sprqo4FoGo5Axaz95H3/pufP5sPX2HozyASijKB71f8hBC9AOelVIOfty2KqEovWRODimHD5O4YSPJ+/ZBdvYjtzf198eqR3esu3XDuEqVEoqy9EvLymH6H5f49cQt6rjb8PUL9anqaKnvsMq0GVsv8ePhIPa+0x4vBwt9h6M8gEooyofSkFBsAX6TUv7ykPtfAV4BqFKlSqOQkJCSDE95Ajnx8aSfOYPQaBBGRmBoiDAyQhgaIYyNMLCxwcjFRd9hlmo7LkTw3oZzZGZrmdLbn+ebVK4wl4CKUmxKJq1n76N7bRe+fL6+vsNRHkIlFOVDsSUUQojdwIP+anwopfw9b5sPgcZAf5mPQNQIhVKRRCRm8PZvZzh6I5YBjTyY2b8ORgbqEkhBfL7jCosPBLLr7Xb4OKmRntJKJRTlQ7EtG5VSdn7U/UKIYUAvoFN+kglFqWhcbExZ+XIzvtp9jfl7A4hKzuSbwQ2xMFGrvfMjIS2L5UdD6FnHVSUTilIC9PJxRwjRHZgEPC2lTNNHDIpSFmg0gvFdq/NZ/zocDojh+e+Pqgqb+bTsr2BSMnN4vUPZLIamKGWNvsZPFwJWwC4hxBkhxLd6ikNRyoQXmlZhydDGBEal0v+bIwRGp+g7pFItOSObZX8F0cXfmZqu1voOR1EqBL0kFFJKHyllZSll/bzbaH3EoShlSYcaTqx+pTnpWbk8s/gIp0Li9B1SqbX8aAhJGTmM6+ir71AUpcJQM7wUpQypV9mWDWNaYmduzKAfjrPjQoS+Qyp10rJy+PFwEO2rO1LHw0bf4ShKhaESCkUpYzztLVg3ugU1Xa15beUp1p68pe+QSpVfjoUQl5rFG2p0QlFKlEooFKUMsrc04ddRzWnt48Ck9efYei5c3yGVConp2XyzP5C2fo408rTTdziKUqGohEJRyigzYwO+G9KIhlXseOu30+y/GqXvkPTuuwOBJKRlM6l7dX2HoigVjkooFKUMMzc25MfhTfB1smL0L6c4EVRxJ2pGJGaw9K8g+tZ3o5abmjuhKCVNJRSKUsbZmBmx/KWmuNma8dJPf3MhLFHfIenF13uukauVvNNVjU4oij6ohEJRygEHSxNWvtwMazMjhi49QUBUsr5DKlEBUSn89vctXmzuSeVKqj25ouiDSigUpZxwtTFj5cvN0AjB4CXHuRVXcYrQztl5BXNjQ1UVU1H0SCUUilKOeDlY8MvLTcnI1jJ4yXGiksp/me5TIfHsvBjJq22rYm9pou9wFKXCUgmFopQzNVys+WlEE2JSMhnx09+kZuboO6RiI6Vk9vYrOFia8FIbb32HoygVmkooFKUcalDFjkWDGnI5PInXV/1DTq5W3yEVi71XojgRHMdbnX0xN1ZdWBVFn1RCoSjlVIcaTkzrU5t9V6OZsvkiUkp9h1SkcrWS2Tuu4O1gwfNNKus7HEWp8FRKryjl2IvNPbkVn8Z3B25QpZI5r7arpu+QisyGf0K5FpnCN4MbYmSgPhspir6phEJRyrlJ3WoQGp/OrO1X8LAz56m6rvoOqdAysnOZt+sa9Srb0qO2i77DURQFdclDUco9jUbwxYB6NPK04+01ZzgZXParaS45dIPwxAze614DIYS+w1EUBZVQKEqFYGpkwA9DG+Nua8ao5ScJiknVd0hP7HpkMvP3BNCzjgstqtnrOxxFUfKohEJRKohKFsYsG94EgBHLThCbkqnniAouJ1fLhLVnsTAxYFqf2voOR1GUe6iEQlEqEC8HC5YMa0x4YgYv/XyS9KxcfYdUID8cCuJsaCLT+tTGQRWxUpRSRSUUilLBNPKsxNcvNOBsaAJv/Hq6zNSouB6ZzJe7rtGjtgu9ysHEUkUpb1RCoSgVUPfaLkztXYvdlyOZXAZqVOTkapmw7tzdSx1qIqailD5q2aiiVFDDWnoRkZTB4v2BuNmY8npHX32H9FBLDgdx9lYC8wc2wNFKXepQlNJIJRSKUoG92606EYkZzP3zGs7WpgxoXPoqTgZEJTNv1zW61XKmt7rUoSillkooFKUCE0Iw+5m6RCdn8t6G8zhamdC+upO+w7orVyuZsPYc5sYGfNq3jrrUoSilmJpDoSgVnLGhhsUvNqS6sxVjVv7D+dBEfYd014+Hb3DmVgKfPF1LXepQlFJOJRSKomBlasSyEU2wMzdmxE8nCIxO0XdIXI9MZu6f1+jq78zT9dz0HY6iKI+hEgpFUQBwtjbl55FNkRIGfHuUc6EJeovlVlwaQ5eewMrEkE/7qVUdilIWqIRCUZS7fJwsWfdaS8yNDRj4/TEOX48p8RjCE9MZtOQYaVm5rHipGU5WpiUeg6IoBacSCkVR7uPtYMH611riYWfOyJ/+Zuu58BI7dlRyBoN/OE5CajYrXmqKv5t1iR1bUZTCUQmFoij/4WxtyppXW1DXw4bXf/2HFcdCiv2YcalZvLjkOBFJGSwb0YS6HrbFfkxFUYqOSigURXkgG3MjVrzUjI7Vnfh40wW+3n292CpqJqZlM+TH44TEprFkWGMae1UqluMoilJ8VEKhKMpDmRkb8O2QRjzT0IMvd19jyuaLZBdx74+UzByGLTvB9cgUvhvSiJbVHIp0/4qilAxV2EpRlEcyMtAwd0BdHCyN+e7gDQ4HxPBhz5p0rOFU6NUXienZjPr5JOfDElk8uGGpKqqlKErBqBEKRVEeSwjB+z1rsmRoYwBe+vkkg5cc5+LtJyuClZCWxbxd12g9ey8nQ+L46vn6dK3lUpQhK4pSwoQ+ugwKIaYDfQAtEAUMl1LeftzjGjduLE+ePFnc4SmK8gjZuVpWHb/JV7uvkZCezbMNPZjQrTrO1o9f3hmbksmPh4NYfjSElMwcutdy4fWOPtR2tymByJXSSghxSkrZWN9xKIWjr4TCWkqZlPf9OMBfSjn6cY9TCYWilB6J6dks2hfAT38FY6ARjGztRQ0Xa2zNjbA1M8bW3AgbcyOsTAyJTsnkh4M3+OXYTTJycnmqjiuvd/ShhotaFqqohKK80MscijvJRB4LoOSzGkVRCsXGzIgPetbkxWaezN5xhUX7Ah+4nYFGN89CSknf+u6M6eCDj5NlSYaqKEoJ0MsIBYAQYgYwFEgEOkgpox+y3SvAKwBVqlRpFBJS/OvhFUUpuNiUTOJSs0hIzyYhLZuEtCwS07NJTM9GKyUDGlXGy8FC32EqpZAaoSgfii2hEELsBh40y+pDKeXv92z3PmAqpZzyuH2qSx6Koijlj0ooyodiu+Qhpeycz01XAVuBxyYUiqIoiqKUTnpZNiqE8L3nx6eBK/qIQ1EURVGUoqGvwlafCSGqo1s2GgI8doWHoiiKoiill75WeTyjj+MqiqIoilI8VKVMRVEURVEKTSUUiqIoiqIUmkooFEVRFEUpNJVQKIqiKIpSaHqrlPkkhBDR6FaFFIYDEFME4ZQX6nzcT52P+6nzcT91Pv6rKM6Jp5TSsSiCUfSnTCUURUEIcVJVZPs/dT7up87H/dT5uJ86H/+lzolyh7rkoSiKoihKoamEQlEURVGUQquICcX3+g6glFHn437qfNxPnY/7qfPxX+qcKEAFnEOhKIqiKErRq4gjFIqiKIqiFDGVUCiKoiiKUmjlNqEQQnQXQlwVQgQIId57wP1CCDE/7/5zQoiG+oizpOTjfAzOOw/nhBBHhBD19BFnSXnc+bhnuyZCiFwhxLMlGV9Jy8/5EEK0F0KcEUJcFEIcKOkYS1I+Xi82QogtQoizeedjhD7iLClCiKVCiCghxIWH3F+h3k+Vh5BSlrsbYAAEAlUBY+As4P+vbXoC2wEBNAeO6ztuPZ+PloBd3vc9Kvr5uGe7vcA24Fl9x63n3w9b4BJQJe9nJ33Hrefz8QEwO+97RyAOMNZ37MV4TtoCDYELD7m/wryfqtvDb+V1hKIpECClvCGlzAJWA33+tU0fYLnUOQbYCiFcSzrQEvLY8yGlPCKljM/78RjgUcIxlqT8/H4AvAGsB6JKMjg9yM/5GARskFLeBJBSludzkp/zIQErIYQALNElFDklG2bJkVIeRPccH6YivZ8qD1FeEwp34NY9P4fm/VtBtykvCvpcX0L3aaO8euz5EEK4A/2Ab0swLn3Jz++HH2AnhNgvhDglhBhaYtGVvPycj4VATeA2cB54U0qpLZnwSqWK9H6qPIShvgMoJuIB//bv9bH52aa8yPdzFUJ0QJdQtC7WiPQrP+fjK2CSlDJX9yG0XMvP+TAEGgGdADPgqBDimJTyWnEHpwf5OR/dgDNAR6AasEsIcUhKmVTMsZVWFen9VHmI8ppQhAKV7/nZA90niYJuU17k67kKIeoCS4AeUsrYEopNH/JzPhoDq/OSCQegpxAiR0q5qUQiLFn5fb3ESClTgVQhxEGgHlAeE4r8nI8RwGdSSgkECCGCgBrAiZIJsdSpSO+nykOU10sefwO+QghvIYQx8AKw+V/bbAaG5s1Obg4kSinDSzrQEvLY8yGEqAJsAIaU00+d93rs+ZBSekspvaSUXsA6YEw5TSYgf6+X34E2QghDIYQ50Ay4XMJxlpT8nI+b6EZrEEI4A9WBGyUaZelSkd5PlYcolyMUUsocIcTrwE50M7aXSikvCiFG593/LbqZ+z2BACAN3SeOcimf52MyYA98k/epPEeW0w6C+TwfFUZ+zoeU8rIQYgdwDtACS6SUD1xCWNbl8/djOvCTEOI8uuH+SVLKctvWXAjxK9AecBBChAJTACOoeO+nysOp0tuKoiiKohRaeb3koSiKoihKCVIJhaIoiqIohaYSCkVRFEVRCk0lFIqiKIqiFJpKKBRFURTlf+3doU0FURRF0XOC+QlgcEg8FoOkECr4ZZDQCUFTABKDI6EDisCQh/hoRjwxA1mrgit37pvMZZqgAACmCQoAYJqggA1pe9X2re2u7XHb97aXa88FsMSPrWBj2t4l2eVwhOtjjHG/8kgAiwQFbMzP/YjXJJ9JrscYXyuPBLDIkwdsz1mSkySnOWwqADbPhgI2pu1TksckF0nOxxj7lUcCWPQvr43CX9X2NodLrw9tj5K8tL0ZYzyvPRvAb2woAIBpvqEAAKYJCgBgmqAAAKYJCgBgmqAAAKYJCgBgmqAAAKZ9A1Q9yqooiOyuAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# test the function\n", + "n_points = 50\n", + "sigma = 1.0\n", + "lengthscale = 0.2\n", + "jitter = 1e-4\n", + "\n", + "# Generate random input data\n", + "x = jnp.linspace(0, 1, n_points).reshape(-1, 1)\n", + "\n", + "# Compute covariance matrix using RBF kernel function\n", + "K32 = matern32_kernel(x, x, sigma=sigma, lengthscale=lengthscale)\n", + "K52 = matern52_kernel(x, x, sigma=sigma, lengthscale=lengthscale)\n", + "K_per = periodic_kernel(x, x, sigma=sigma, lengthscale=lengthscale)\n", + "K_lin = periodic_kernel(x, x)\n", + "\n", + "plot_gp_samples(x, K32, ttl=\"Matern 3/2 demonstration\")\n", + "plot_gp_samples(x, K52, ttl=\"Matern 5/2 demonstration\")\n", + "plot_gp_samples(x, K_per, ttl=\"Periodic kernel demonstration\")\n", + "plot_gp_samples(x, K_lin, ttl=\"Linear kernel demonstration\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Assignment\n", + "\n", + "Implement rational quadratic kernel:\n", + "- plot function draws,\n", + "- plot covariance matrix\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Combining kernels\n", + "\n", + "see my previous text here\n", + "\n", + "https://github.com/elizavetasemenova/gp_turing/blob/main/gp_rbf.ipynb" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.7" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/16_areal_data.ipynb b/16_areal_data.ipynb index 8951214..6ca8dae 100644 --- a/16_areal_data.ipynb +++ b/16_areal_data.ipynb @@ -24,7 +24,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 33, "metadata": {}, "outputs": [], "source": [ @@ -34,22 +34,30 @@ "import matplotlib.pyplot as plt\n", "from matplotlib.colors import Normalize\n", "from matplotlib.cm import ScalarMappable\n", - "from shapely.geometry import Polygon\n" + "from shapely.geometry import Polygon\n", + "\n", + "import numpy as np\n", + "\n", + "import networkx as nx\n", + "\n", + "import jax\n" ] }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 15, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -68,7 +76,7 @@ "gdf_admin = gpd.GeoDataFrame(data)\n", "\n", "# Plot the administrative boundaries with population size represented by color\n", - "fig, ax = plt.subplots(figsize=(6, 4))\n", + "fig, ax = plt.subplots(figsize=(8, 5))\n", "\n", "# Define colormap\n", "cmap = plt.cm.viridis # Change the colormap here\n", @@ -96,39 +104,210 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Models of areal data\n", + "## Adjancency structure\n", "\n", - "In models for areal data, the geographic units are de- noted by $B_i$, and the data are typically sums or averages of variables over these blocks. To introduce spatial association, we define a neighborhood structure based on the arrangement of the blocks in the map. Once the neighborhood structure is defined, models resembling autoregressive time series models are considered, such as conditionally autoregressive modedl (CAR).\n", + "Most models of areal data rely on the concept of adjacency matrix, i.e. a matrix $A = (a_{ij})$ with entries\n", "\n", - "### CAR\n", + "$$\n", + "a_{ij} = \\begin{cases}\n", + "\t\t\t1, & \\text{if areas } B_i \\text{ and } B_j \\text{ are neighbours},\\\\\n", + " 0, & \\text{otherwise}.\n", + "\t\t \\end{cases}\n", + "$$\n", "\n", - "The CAR model represents the spatial dependence among areal units in a Bayesian modelling framework. It describes the vector of spatially varying random effects $f = (f_1, ..., f_n)^T$ using the follwing prior:\n", + "The adjacency matrix must be symmetric: \n", "\n", - " $$f \\sim \\mathcal{N}(0, Q^{-1}) $$\n", + "$$\n", + "A = \\begin{pmatrix}\n", + "a_{11} & a_{12} & \\cdots & a_{1n} \\\\\n", + "a_{12} & a_{22} & \\cdots & a_{2n} \\\\\n", + "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n", + "a_{1n} & a_{2n} & \\cdots & a_{nn}\n", + "\\end{pmatrix}\n", + "$$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us compute adjacency matrix for this data." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def compute_adjacency_matrix(gdf):\n", + " num_geometries = len(gdf)\n", + " adjacency_matrix = np.zeros((num_geometries, num_geometries), dtype=int)\n", + " \n", + " for idx1, geometry1 in enumerate(gdf.geometry):\n", + " for idx2, geometry2 in enumerate(gdf.geometry):\n", + " if idx1 != idx2:\n", + " if geometry1.touches(geometry2): # Check if geometries share a common boundary\n", + " adjacency_matrix[idx1, idx2] = 1\n", + " \n", + " return adjacency_matrix\n", "\n", + "def visualize_adjacency_matrix(matrix):\n", + " plt.figure(figsize=(6, 4))\n", + " plt.imshow(matrix, cmap='binary', origin='lower')\n", + " plt.title('Adjacency Matrix')\n", + " plt.xlabel('Geometry Index')\n", + " plt.ylabel('Geometry Index')\n", + " plt.grid(False)\n", + " plt.show()\n", "\n", + "# Compute adjacency matrix\n", + "adjacency_matrix = compute_adjacency_matrix(gdf_admin)\n", "\n", - "\n" + "# Visualize the adjacency matrix\n", + "visualize_adjacency_matrix(adjacency_matrix)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To understand adjacency, we can think about areal data as graphs with binary edges. Here each area represents a vertex in a graph, and an edge exists between vertices $i$ and $j$ if areas $B_i$ and $B_j$ share a border." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 29, "metadata": {}, - "outputs": [], - "source": [] + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Create a graph\n", + "nx_graph = nx.Graph()\n", + "\n", + "# Add nodes with their coordinates and area names\n", + "for idx, geometry in enumerate(gdf_admin.geometry):\n", + " centroid = geometry.centroid\n", + " #area_name = gdf.loc[idx, 'area_name']\n", + " #nx_graph.add_node(idx, pos=(centroid.x, centroid.y), label=area_name)\n", + " nx_graph.add_node(idx, pos=(centroid.x, centroid.y))\n", + "\n", + "# Add edges based on adjacency\n", + "for i, j in zip(*np.where(adjacency_matrix == 1)):\n", + " nx_graph.add_edge(i, j)\n", + "\n", + "# Visualize the graph with nodes aligned with actual locations and labeled with area names\n", + "pos = nx.get_node_attributes(nx_graph, 'pos')\n", + "\n", + "nx.draw(nx_graph, pos, with_labels=True, node_size=300, node_color=\"skyblue\", font_size=8, font_color=\"black\")\n", + "plt.title('Adjacency Graph')\n", + "plt.show()" + ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "take data from here: https://hughst.github.io/week-7/" + "## Models of areal data\n", + "\n", + "In models for areal data, the geographic units are denoted by $B_i$, and the data are typically sums or averages of variables over these blocks. To introduce spatial association, we define a neighborhood structure based on the arrangement of the blocks in the map. Once the neighborhood structure is defined, one can construct models models resembling autoregressive time series models, such as the intrinsic conditionally autoregressive model (ICAR, also called Besag) and conditionally autoregressive model (CAR).\n", + "\n", + "### The Besag model\n", + "\n", + "The Besag model, also called improper conditionally autoregressive model (ICAR) computes the conditional mean of the random effect $f_i$ as an average of its neighbours $\\{f_j \\}_{j\\sim i}$ and its precision is proportional to the number of neighbours. It describes the vector of spatially varying random effects $f = (f_1, ..., f_n)^T$ using the prior\n", + "\n", + "$$\n", + "f \\sim \\mathcal{N}(0, Q^-).\n", + "$$\n", + "\n", + "Here $Q^-$ denotes the generalised inverse of matrix $Q$, which, in turn, is computed as \n", + "\n", + "$$\n", + "Q = \\tau R, \\\\\n", + "R = D - A.\n", + "$$\n", + "\n", + "Here $D$ is a diagnoal matrix. It's $i$-th element equals the total number of neighbours of area $i$. Hence, $D$ can be computed from $A$:\n", + "\n", + "$$\n", + "D = \\begin{pmatrix}\n", + "\\sum_{j=1}^n a_{1j} & 0 & \\cdots & 0 \\\\\n", + "0 & \\sum_{j=1}^n a_{2j} & \\cdots & 0 \\\\\n", + "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n", + "0 & 0 & \\cdots & \\sum_{j=1}^n a_{nj}\n", + "\\end{pmatrix}.\n", + "$$\n", + "\n", + "Note that the structure matrix here can be viewed as graph Laplacian.\n", + "\n", + "$R$ is a rank-defficient matrix. It is recommended, for example, to place an adidtional constraint, such sum-to-zero constraint on each non-singleton connected component:\n", + "\n", + "$$\n", + "\\sum_i f_i = 0.\n", + "$$\n", + "\n", + "\n", + "\n", + "### Conditional Autoregressive Models (CAR)\n", + "\n", + "Conditional Autoregressive Models (CAR): same as ICAR, the CAR model assumes that the value of a variable in one area depends on the values of neighboring areas, with weights specified by a spatial adjacency matrix. However, it introcues an additional parameter $\\alpha$, allowing to estimate the amount of spatial correlation.\n", + "\n", + "The psatial random effect now is modelled as\n", + "\n", + "$$f \\sim \\mathcal{N}(0, Q^{-1}) $$\n", + "\n", + "with \n", + "\n", + "$$\n", + "Q = \\tau R, \\\\\n", + "R = D - \\alpha A, \\\\\n", + "0 \\le \\alpha < 1.\n", + "$$\n", + "\n", + "If $\\alpha=0$, the model consist only of i.i.d. random effects, and if $\\alpha$ is close to 1, the model approaches ICAR.\n", + " \n", + "### The Besag-Yorg-Mollié model\n", + "\n", + "The Besag, York, and Mollié (BYM) decomposes the spatial random effect $f$ into the sum of an i.i.d. component $v$ and spatiallly structured component $w$. Each of these two components has its own precision parameter:\n", + "\n", + "$$\n", + "f \\sim \\mathcal{N}(0, \\tau_v^{-1}I + \\tau_w^{-1}R^-).\n", + "$$\n", + "\n", + "This model provides more flexibility than the CAR formulation. \n", + "\n" ] }, { "cell_type": "markdown", "metadata": {}, - "source": [] + "source": [ + "##" + ] }, { "cell_type": "code", @@ -137,12 +316,26 @@ "outputs": [], "source": [] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Examples\n", + "\n", + "take data from here: https://hughst.github.io/week-7/" + ] + }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] } ], "metadata": { @@ -163,7 +356,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.9.18" } }, "nbformat": 4,