{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "QPC6Knjp3fBL"
},
"source": [
"# 8. Process monitoring using PCA 📐\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "UYFfqiWL3pPE"
},
"source": [
"## Goals of this exercise 🌟\n",
"- We will review the steps for PCA with an illustrative 2D example\n",
"- We will use PCA for process monitoring, specifically for fault detection.\n",
"- We will review the $T^2$ and $Q$ statistics for process monitoring"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "hZcN6kX939BR"
},
"source": [
"## A quick reminder ✅\n",
"\n",
"\n",
"Process monitoring aims to guarantee the effectiveness of planned operations by furnishing information that identifies and highlights any deviations in behavior. The four procedures associated with process monitoring are: fault detection, fault identification, fault diagnosis, and process recovery.\n",
"\n",
"* **Fault detection**: determining whether a fault has occurred\n",
"* **Fault identification**: identifying the variables most relevant to diagnosing the fault\n",
"* **Fault diagnosis**: determining the cause of the observed\n",
"* **Process recovery**: emoving the effect of the fault\n",
"\n",
"For fault detection, some measures are established based on statistical theory or systems theory. A threshold can be placed on some of these measures, and a fault is detected whenever one of the measures is evaluated outside the limit.\n",
"\n",
"Unsupervised learning models help in extracting information that is useful for process monitoring and this becomes very valuable for the process engineers and operators.\n",
"\n",
"**Principal Component Analysis** (PCA) is a popular technique used in process monitoring. It is a dimensionality reduction method that projects the original data into a lower dimension while retaining important information. The components in PCA are new variables that are a combination of the original variables. The first component captures the largest amount of variation in the data, and each subsequent component captures as much remaining variation as possible. This provides us with a hierarchical coordinate system.\n",
"\n",
"PCA can be viewed as the statistical interpretation of Singular Value Decomosition. Here we will review the \"standard\" PCA procedure.\n",
"\n",
"Given a dataset with $n_d$ datapoints $\\mathcal{D}=\\{ {\\bf x}^{(1)},...,{\\bf x}^{(n_d)} \\}$, where each data point contains $n_x$ descriptors ${\\bf x}^{(i)} \\in \\mathbb{R}^{n_x}$, which is a column vector. If ${\\bf x}$ were measurements from a chemical process each $x_i$ from ${\\bf x}=[x_1,...,x_{n_x}]^T$ would be a descriptor of that process such as temperature, preassure, concentrations... \n",
"\n",
"We can stack the transpose of datapoints as rows in a matrix to form:\n",
"\n",
"$$\n",
"X = \\begin{bmatrix}\n",
" ({\\bf x}^{(1)})^T \\\\ ({\\bf x}^{(2)})^T \\\\ \\vdots \\\\ ({\\bf x}^{(n_d)})^T \n",
"\\end{bmatrix} =\n",
"\\begin{bmatrix}\n",
" x^{(1)}_{1}, x^{(1)}_{2}& ... & x^{(1)}_{n_x} \\\\\n",
" x^{(2)}_{1}, x^{(2)}_{2}& ... &x^{(2)}_{n_x} \\\\\n",
" \\vdots ~\\quad \\vdots & \\ddots & \\vdots \\\\\n",
" x^{(n_d)}_{1}, x^{(n_d)}_{2}& ... & x^{(n_d)}_{n_x} \n",
"\\end{bmatrix} \\qquad\n",
"$$ \n",
"\n",
"where $X \\in \\mathbb{R}^{n_d \\times n_x}$, typically, in chemical engineering $n_d >> n_x$.\n",
"\n",
"\n",
"**1) Standardize the data** \n",
" \n",
"We define $\\overline{x}_j = \\frac{1}{n_d} \\sum_{i=1}^{n_d} x_j^{(i)}$ as the mean value, and $\\sigma_j = \\sqrt{ \\frac{\\sum_{i=1}^{n_d} (x_j^{(i)} - \\overline{x}_j)^2}{n_d-1}}$ as the standard deviation for each dimension $j$. Then we define a new standardized data matrix:\n",
"\n",
"$$\n",
"X_s = \\begin{bmatrix}\n",
" (x^{(1)}_{1} - \\overline{x}_1)/\\sigma_1, (x^{(1)}_{2} - \\overline{x}_2)/\\sigma_2& ... & (x^{(1)}_{n_x} - \\overline{x}_{n_x})/\\sigma_{n_x} \\\\\n",
" (x^{(2)}_{1} - \\overline{x}_1)/\\sigma_1, (x^{(2)}_{2} - \\overline{x}_2)/\\sigma_2& ... & (x^{(2)}_{n_x} - \\overline{x}_{n_x})/\\sigma_{n_x} \\\\\n",
" \\vdots \\qquad \\qquad \\vdots & \\ddots & \\vdots \\\\\n",
" (x^{(n_d)}_{1} - \\overline{x}_1)/\\sigma_1, (x^{(n_d)}_{2} - \\overline{x}_2)/\\sigma_2& ... & (x^{(n_d)}_{n_x} - \\overline{x}_{n_x})/\\sigma_{n_x} \n",
"\\end{bmatrix} \\qquad\n",
"$$ \n",
"\n",
"**2) Compute the covariance matrix** \n",
"\n",
"We can then compute the covariance matrix by:\n",
"\n",
"$X_c = X_s^TX_s$\n",
"\n",
"Notice that this is equivalent to computing the covariance $\\sigma^2_{j,k} = \\frac{1}{(n_d-1)^2} \\sum_{i=1}^{n_d} \\frac{1}{2} (x_{j}^{(i)} - \\overline{x}_j)^T(x_{k}^{(i)} - \\overline{x}_k) $ for each two dimensions and then having the matrix: \n",
"\n",
"$$\n",
"X_c = \\begin{bmatrix}\n",
" \\sigma^2_{1,1}, \\sigma^2_{1,2}& ... & \\sigma^2_{1,n_x} \\\\\n",
" \\sigma^2_{2,1}, \\sigma^2_{2,2}& ... & \\sigma^2_{2,n_x} \\\\\n",
" \\vdots \\qquad \\vdots & \\ddots & \\vdots \\\\\n",
" \\sigma^2_{n_x,1}, \\sigma^2_{n_x,2}& ... & \\sigma^2_{n_x,n_x} \n",
"\\end{bmatrix}\n",
"$$\n",
"\n",
"**3) Compute the singular values** \n",
"\n",
"Now we obtain the eigenvalues and eigenvectors for $X_c$:\n",
"\n",
"$X_c {\\bf v}_j = {\\bf v}_j \\lambda_j $\n",
"\n",
"Assuming we concatenate all eigenvectors in a matrix $V_c$, and we have a diagonal matrix of eigenvalues $\\Lambda$ we have:\n",
"\n",
"$X_c V_c = V_c \\Lambda $\n",
"\n",
"such that:\n",
"\n",
"$$\n",
"\\Lambda = \\begin{bmatrix}\n",
" \\lambda_1, & 0 ,& ..., & 0 \\\\\n",
" 0, & \\lambda_2 ,& ..., & 0 \\\\\n",
" \\vdots & \\vdots & \\ddots & 0 \\\\\n",
" 0, & 0 ,& ..., & \\lambda_{n_x}\n",
"\\end{bmatrix}\n",
"$$\n",
"\n",
"where all $\\lambda \\geq0$ and, again, by definition we assume $\\lambda_1 \\geq \\lambda_2 \\geq ... \\geq \\lambda_{n_x} \\geq0$.\n",
"\n",
"\n",
"Eigenvectors are the \"axis\" of the transformation represented by a matrix. On the other hand, the eigenvalues are the amount that eleigenvectors scale up or down when passing through the matrix.\n",
"\n",
"**4) Choose the $k$ principal components** \n",
"\n",
"We then choose the $k$ eigenvectors with the largest eigenvalues as the principal components\n",
"\n",
"Let's try to reproduce these steps for an illustrative example:\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "OOLKtGZHB9Bu"
},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"from numpy import linalg as LA\n",
"from tqdm.notebook import tqdm"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "XcWVvE_sDcq_"
},
"source": [
"Let's generate some synthetic observation for this example"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "siLtGOPjDYy4"
},
"outputs": [],
"source": [
"X = np.random.multivariate_normal([0,0], [[100, 6], [6, 1]], 500)*[2,0.1] + [-45, 0.5]"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "GxLT_cmfEiRd"
},
"source": [
"and visualize the data"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 450
},
"id": "U0z_MInCEcLh",
"outputId": "fa2eb680-9df4-47e2-80f1-e40dcfcea7db"
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(X[:,0],X[:,1],'.')\n",
"plt.xlabel(r'$x_1$')\n",
"plt.ylabel(r'$x_2$')\n",
"plt.axis([-90, 0, -45, 45])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "9UMYKi_jEsO2"
},
"source": [
"we see that $x_1$ varies much more than $x_2$. This, however, might be deceiving, and due to a unit mismatch. We next normalize the data to remove this possible issue.\n",
"\n",
"### *1.Normalization*"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "yXhLYiCEE8CW"
},
"outputs": [],
"source": [
"X_mean = np.mean(X, axis=0).reshape(1,2)\n",
"X_std = np.std(X, axis=0).reshape(1,2)\n",
"X_norm = (X-X_mean)/X_std"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 458
},
"id": "xbLsq3HwFN_D",
"outputId": "5dc93ab4-60c8-4ebf-a886-4496e7489ca4"
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(X_norm[:,0],X_norm[:,1],'.')\n",
"plt.xlabel(r'$x_1 \\quad normalized $')\n",
"plt.ylabel(r'$x_2 \\quad normalized $')\n",
"plt.axis([-3, 3, -3, 3])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "anRpjgFkUgMB"
},
"source": [
"Now we can appreciate a much more interesting distribution of our data. Next we will measure the variability of our data.\n",
"\n",
"### *2. Covariance matrix*\n",
"\n",
"Intuitively, the covariance matrix generalizes the notion of variance $ \\sigma^2$ to multiple dimensions. Our example (a two-dimensional space), cannot be characterized completely by a single number (like $\\sigma$), nor only by the variances of $ x_1 $ and $ x_2 $ ($\\sigma_1$ and $\\sigma_2$), as they do not contain all the necessary information. For this, we also need the information of how $ x_1 $ varies with respect to $ x_2 $, which we can be representd by a matrix of size $ D \\times D = 2 \\times 2$ as follows:\n",
"\n",
"$cov(X) = \n",
"\\begin{bmatrix}\n",
" \\sigma^2_{1,1} & \\sigma^2_{1,2} \\\\\n",
" \\sigma^2_{2,1} & \\sigma^2_{2,2}\n",
"\\end{bmatrix}$\n",
"\n",
"where:\n",
"\n",
"$\\sigma^2_{i,k} = \\frac{\\sum_{i=1}^{M} (x_{i,j}-\\mu_j)(x_{i,k}-\\mu_k)}{M-1}$\n",
"\n",
"If $j=k$, $\\sigma^2_{j,j} = \\sigma^2_{j}$ then this is the variance of dimension $j$, which is the square of the standard deviation that we defined during the normalization of the data."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "ULZE7h5oUu1H"
},
"outputs": [],
"source": [
"# Here we calculate the covariance matrix. Notice that the mean = 0.\n",
"Cov_M = np.zeros((2,2))\n",
"for point in range(np.shape(X_norm)[0]):\n",
" point_ = X_norm[point,:].reshape(1,2)\n",
" Cov_M = Cov_M + np.matmul(point_.T,point_)\n",
"Cov_M = Cov_M/np.shape(X_norm)[0] \n",
"\n",
"# We calculate the covariance matrix taking advantage of numpy's vectorization\n",
"Cov_M2 = np.matmul(X_norm.T, X_norm)/X_norm.shape[0]"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 452
},
"id": "R6rbmE__VP1o",
"outputId": "e2a4de5c-8295-4d21-ea7a-75b8b4eed998"
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x_, y_ = np.random.multivariate_normal([0,0], Cov_M2, 500).T\n",
"plt.scatter(x_, y_, s=5, color='black')\n",
"plt.axis('equal')\n",
"plt.title('Covariance Matrix')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "rebZMDttVsgs"
},
"source": [
"### *3. Eigendecomposition*\n",
"\n",
"To simplify the notation, let us define $ cov (X) = A $. Now, we obtain the eigenvalues and eigenvectors for the covariance matrix:\n",
"\n",
"$Av=\\lambda v$\n",
"\n",
"\n",
"Where $ v\\in \\mathbb {R}^D $ is an **eigenvector**, which has the same dimension as the sides of our covariance matrix $A$. In our example $ D = 2 $. On the other hand $ \\lambda \\in \\mathbb {R} $ is a scalar, and is the corresponding **eigenvalue**.\n",
"\n",
"Let us remember that **matrices** are **linear transformations** that act on vectors. This is, given a vector $v$, and a matrix $A$, we can apply $A$ to $v$ and obtain $b$:\n",
"\n",
"$Av = b$\n",
"\n",
"**Eigenvectors** are the \"axis\" of the transformation represented by a matrix. Remember that a matrix changes the direction and magnitud of any vector that it is applied too, except for its eigenvectors. When a matrix is applied to its eigenvector, the eigenvector does not change its direction (as would any other vector when the matrix is applied to it). On the other hand, the **eigenvalues** are the amount that eleigenvectors scale up or down when passing through the matrix. As shown in $Av=\\lambda v$.\n",
"\n",
"Let us now remember that the covariance matrix defines how scattered and correlated (or \"tilted\") our data is. So if we want to represent the covariance matrix with a vector and its magnitude (to decrease the dimensionality of the data), we should simply find the vector that points in the direction of the greatest \"change\" of the data. This direction happens to be the **eigenvector** with the larges **eigenvalue**.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "G9eJxr3QWIf7",
"outputId": "b4f986e5-360a-405e-d5e1-25c789ab7177"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"eigenvalue 1 = 0.4021709463292218 eigenvector 1 = [-0.70710678 0.70710678]\n",
"eigenvalue 2 = 1.5978290536707775 eigenvector 2 = [-0.70710678 -0.70710678]\n"
]
}
],
"source": [
"eigenVal, eigenVec = LA.eig(Cov_M)\n",
"print(\"eigenvalue 1 = \",eigenVal[0], \" eigenvector 1 = \",eigenVec[:,0])\n",
"print(\"eigenvalue 2 = \",eigenVal[1], \" eigenvector 2 = \",eigenVec[:,1])"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "LWReSc4XWapu"
},
"source": [
"We now plot the eigenvectors weighted by their respective eigenvalue."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 458
},
"id": "rwyVnPFvWbiv",
"outputId": "862186e9-7ba0-4dd8-ba1d-9b0ecc51a848"
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(X_norm[:,0],X_norm[:,1],'.')\n",
"plt.plot([0,eigenVec[0,0]*eigenVal[0]],[0,eigenVec[1,0]*eigenVal[0]],'--', color='blue', label='EV 1', linewidth=2)\n",
"plt.plot([0,eigenVec[0,1]*eigenVal[1]],[0,eigenVec[1,1]*eigenVal[1]],'-', color='black', label='EV 2', linewidth=2)\n",
"plt.xlabel(r'$x_1 \\quad normalized $')\n",
"plt.ylabel(r'$x_2 \\quad normalized $')\n",
"plt.axis([-3, 3, -3, 3])\n",
"plt.legend(loc='center right')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "4-4Ixa9TWlbF"
},
"source": [
"### *4. Principal components*\n",
"\n",
"We are interested in obtaining the principal components of our data. The principal components are those which capture the highest variation of the data, the rest, which do not present so much variation can be discarded.\n",
"\n",
"Therefore, a natural option is to choose the main eigenvectors as components. By main eigenvalues we refer to the ones with the highest eigenvalues. Therefore we choose $k$ eigenvectors, where $k"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(X_norm[:,0],X_norm[:,1],'.')\n",
"plt.plot([eigenVec[0,max_idx]*-10,eigenVec[0,max_idx]*10],\n",
" [eigenVec[1,max_idx]*-10,eigenVec[1,max_idx]*10],'--', \n",
" color='blue', label='1D-space', linewidth=2.0)\n",
"plt.xlabel(r'$x_1 \\quad normalized $')\n",
"plt.ylabel(r'$x_2 \\quad normalized $')\n",
"plt.axis([-3, 3, -3, 3])\n",
"plt.legend(loc='center right')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "IHHG1LEvXMrV"
},
"source": [
"Following from the above, we wish to project datapoints $x$ onto the space of an eigenvector $v$. More precisely, we wish to project datapoints which are in a 2-dimensional space onto a 1-dimensional space (which is spanned by the eigenvector with the largest eigenvalue).\n",
"\n",
"For one point $x$ and the eigenvector $v$ this is done by:\n",
"$\\frac{vv^T}{||v||^2}~x$\n",
"\n",
"where $v^T$ means the transpose of vector $v$, and $||v||$ is the Euclidean norm of vector $v$.\n",
"\n",
"\n",
"$^*$ This is assuming an inner product in the Euclidean space"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "dDiYGsSzXBv2"
},
"outputs": [],
"source": [
"# -- Projecting the data into the 1-dimensional space -- #\n",
"\n",
"# -- Taking advantage of numpy's vectorization we can project the whole matrix -- #\n",
"P_vec = P_vec.reshape(P_vec.shape[0],1) # reshaping for easier handling\n",
"Y_1D = np.matmul(P_vec.T,X_norm.T) # projecting into 1D\n",
"Y_norm = np.matmul(P_vec,Y_1D).T # projecting 1D back into 2D\n",
"\n",
"# Note: P_vec has norm 1, so there is no need to compute the norm"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "0XhJ--Z8XRPC"
},
"source": [
"We can visualize the data projected onto the 1-dimensional space below"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 458
},
"id": "5I_fidvQXShl",
"outputId": "72ff5657-12c2-4b3c-b021-1f595f546884"
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(Y_norm[:],Y_norm[:],'.')\n",
"plt.plot(X_norm[:,0],X_norm[:,1],'.', alpha=0.2, color='black')\n",
"plt.plot([eigenVec[0,max_idx]*-10,eigenVec[0,max_idx]*10],[eigenVec[1,max_idx]*-10,eigenVec[1,max_idx]*10],'--', color='blue', label='1D-space', linewidth=0.5)\n",
"plt.xlabel(r'$x_1 \\quad normalized $')\n",
"plt.ylabel(r'$x_2 \\quad normalized $')\n",
"plt.axis([-3, 3, -3, 3])\n",
"plt.legend(loc='center right')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "5TZlFtVPZe7d"
},
"source": [
"Now, [scikit-learn](https://scikit-learn.org/stable/) has a very handy [PCA implementation](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html#sklearn.decomposition.PCA) for this that we can use as follows:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 458
},
"id": "vPJJGfvxZn5l",
"outputId": "80fad707-bea1-4e84-ce26-8ca09376856f"
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.decomposition import PCA #import PCA from sklearn\n",
"pca = PCA(n_components=1) # define how many principal components we wish to reduce our system to\n",
"pca.fit(X_norm) # obtain the components and its eigenvalues\n",
"X_pca = pca.transform(X_norm) # apply dimensionality reduction\n",
"Y_pca = pca.inverse_transform(X_pca) # get the data back on its original space\n",
"\n",
"# visualize\n",
"plt.plot(Y_pca[:,0],Y_pca[:,1],'.')\n",
"plt.plot([eigenVec[0,max_idx]*-10,eigenVec[0,max_idx]*10],[eigenVec[1,max_idx]*-10,eigenVec[1,max_idx]*10],'--', color='blue', label='1D-space', linewidth=0.5)\n",
"plt.plot(X_norm[:,0],X_norm[:,1],'.', alpha=0.2, color='black')\n",
"plt.xlabel(r'$x_1 \\quad normalizada $')\n",
"plt.ylabel(r'$x_2 \\quad normalizada $')\n",
"plt.axis([-3, 3, -3, 3])\n",
"plt.legend(loc='center right')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "IfovUvVwiKke"
},
"source": [
"## Tennessee Eastman process 🏭\n",
"\n",
"In this notebook we will illustrate the capabilities of some unsupervised learning techniques that perform dimensionality reduction applied to the task of process monitoring. The case-study that we are going to use is the called Tennessee Eastman process (TEP) [{cite}`downs1993plant`]. The data collected here corresponds to simulated data and it is widely used in the process monitoring community. Initially, TEP was created by the company [Eastman](https://www.eastman.com/en) to provide a realistic scenerario in which to test different process monitoring methods.\n",
"\n",
"In the following we will provide a short explanation of the process. If you like to have a more detailed explanation overall read Chapter 8 of [{cite}`russell2000data`].\n",
"\n",
"The process consist of five major units:\n",
"\n",
"* Reactor\n",
"* Condenser\n",
"* Compressor\n",
"* Separator\n",
"* Stripper\n",
"\n",
"and it contains eight components: the gaseous reactants $A$, $C$, $D$ and $E$ that are fed into the reactor along the inert $B$ to produce the liquids $G$ and $H$. The product $F$ is an unwanted byproduct.\n",
"\n",
"$$\n",
"A(g) + C(g) + D(g) → G(liq)\n",
"$$\n",
"\n",
"$$\n",
"A(g) + C(g) + E(g) → H(liq)\n",
"$$\n",
"\n",
"$$\n",
"A(g) + E(g) → F(liq)\n",
"$$\n",
"\n",
"$$\n",
"3D(g) → 2F(liq)\n",
"$$\n",
"\n",
"The reactor product stream is then cooled using the condenser and fed to a flash separator. A recycle is implemented via the compressor with the necessary purge to prevent accumulation of $B$ and $F$. Finally, the liquid outlet of the separator is fed into a stripper for further separation. See the figure below for a schematic reresentation of the flowsheet.\n",
"\n",
"```{figure} media/08_monitoring/TEP_flowsheet.png\n",
":alt: cstr\n",
":width: 80%\n",
":align: center\n",
"\n",
"Schematic representation of the Tennessee Eastman process flowsheet. Modified from [{cite}`russell2000data`].\n",
"```\n",
"\n",
"The dataset contains 41 measured states and 11 manipulated variables. Some variables are sampled every 3 minutes, 6 minutes or 15 minutes. And all measurements include Gaussian noise.\n",
"\n",
"The data contains 21 faults, out of which 16 are known (Faults 1-15 and 21). Some faults are caused by step changes in some process variables, while others are associated with a random variability increase. A slow drift in the reaction kinetics and sticking valves are other causes of the faults."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "KoH74KjEmjDC"
},
"source": [
"Let's import the data corresponding to the 21 faulty simulations (i.e., files 01 to 21) and the data for the normal operation (i.e., files with 00) using some for-loops and store it into a dictionary. \n",
"\n",
"### **Process faults**\n",
"\n",
"File | Description | Type\n",
"---- | ------------------------------------------------------ | ----\n",
"00 | Normal operation |\n",
"01 | A/C Feed Ratio, B Composition Constant (Stream 4) | Step\n",
"02 | B Composition, A/C Ratio Constant (Stream 4) | Step\n",
"03 | D Feed Temperature (Stream 2) | Step\n",
"04 | Reactor Cooling Water Inlet Temperature | Step\n",
"05 | Condenser Cooling Water Inlet Temperature | Step\n",
"06 | A Feed Loss (Stream 1) | Step\n",
"07 | C Header Pressure Loss - Reduced Availability (Stream 4)| Step\n",
"08 | A, B, C Feed Composition (Stream 4) | Random Variation\n",
"09 | D Feed Temperature (Stream 2) | Random Variation\n",
"10 | C Feed Temperature (Stream 4) | Random Variation\n",
"11 | Reactor Cooling Water Inlet Temperature | Random Variation\n",
"12 | Condenser Cooling Water Inlet Temperature | Random Variation\n",
"13 | Reaction Kinetics | Slow Drift\n",
"14 | Reactor Cooling Water Valve | Valve Sticking\n",
"15 | Condenser Cooling Water Valve |Valve Sticking\n",
"16 | Unknown\n",
"17 | Unknown\n",
"18 | Unknown\n",
"19 | Unknown\n",
"20 | Unknown\n",
"21 | Unknown\n",
"\n",
"As you can suspect from the code below, the data has already being splitted into training and test."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 49,
"referenced_widgets": [
"24fe066ae90042bebe4f2d0162bab580",
"f698e1de452d4944afa3e48cd760678a",
"34c8b4b563eb42bda24d17716bf77356",
"f03822bb126a4cb8aa001124779b8d83",
"399b762697c94937a3e0c44c75e3d61f",
"f9abe98e38aa471e994a5571db8a9312",
"fcb76a25e20a4ea0a2d68aa3dd580dd7",
"7b02181796e64b0fa5ac159a63386aa4",
"83952c02e1e045e3bed9456bcc704ea2",
"16b944467dbc466ca483d9a906223005",
"534a45d148054c0296ff4211f6dbcb78"
]
},
"id": "4YYrq5vrlHOh",
"outputId": "0912f5c5-00e5-48d9-d7a1-2b69c42d4989"
},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "24fe066ae90042bebe4f2d0162bab580",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
" 0%| | 0/22 [00:00, ?it/s]"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data_dict = {}\n",
"for i in tqdm(range(22)):\n",
" i_str = str(i)\n",
" if len(i_str) == 1:\n",
" term = '0'+i_str\n",
" else:\n",
" term = i_str\n",
" for split in ['','_te']:\n",
" term = term + split\n",
" if 'google.colab' in str(get_ipython()):\n",
" data_dict[term] = np.loadtxt('https://raw.githubusercontent.com/edgarsmdn/MLCE_book/main/references/d' \n",
" + term + '.dat')\n",
" else:\n",
" data_dict[term] = np.loadtxt('references/d'+ term + '.dat')\n",
"data_dict['00'] = data_dict['00'].T"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "2Qlnm2kgpSvo",
"outputId": "17b75bdd-a75c-40c2-cef7-3d74c2e42ed1"
},
"outputs": [
{
"data": {
"text/plain": [
"(500, 52)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data_dict['00'].shape"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "AjzF3XgKtdx_"
},
"source": [
"each dataset is reported in the form of a matrix where the 52 columns correspond to the 41 process measurements + 11 manipulated variables according to the following tables\n",
"\n",
"### Process variables\n",
"\n",
"**Process Measurements (3 minutes)**\n",
"\n",
"Column | Description | Unit\n",
"------ | ----------------------------------- | ----\n",
"1 | A Feed (stream 1) | kscmh\n",
"2 | D Feed (stream 2) | kg/hr\n",
"3 | E Feed (stream 3) | kg/hr\n",
"4 | A and C Feed (stream 4) | kscmh\n",
"5 | Recycle Flow (stream 8) | kscmh\n",
"6 | Reactor Feed Rate (stream 6) | kscmh\n",
"7 | Reactor Pressure | kPa gauge\n",
"8 | Reactor Level | %\n",
"9 | Reactor Temperature | Deg C\n",
"10 | Purge Rate (stream 9) | kscmh\n",
"11 | Product Sep Temp | Deg C\n",
"12 | Product Sep Level | %\n",
"13 | Prod Sep Pressure | kPa gauge\n",
"14 | Prod Sep Underflow (stream 10) | m3/hr\n",
"15 | Stripper Level | %\n",
"16 | Stripper Pressure | kPa gauge\n",
"17 | Stripper Underflow (stream 11) | m3/hr\n",
"18 | Stripper Temperature | Deg C\n",
"19 | Stripper Steam Flow | kg/hr\n",
"20 | Compressor Work | kW\n",
"21 | Reactor Cooling Water Outlet Temp | Deg C\n",
"22 | Separator Cooling Water Outlet Temp | Deg C\n",
"\n",
"**Reactor feed analysis (6 minutes)**\n",
"\n",
"Column | Description | Unit\n",
"------ | ----------- | ----\n",
"23 | Component A | % mol\n",
"24 | Component B | % mol\n",
"25 | Component C | % mol\n",
"26 | Component D | % mol\n",
"27 | Component E | % mol\n",
"28 | Component F | % mol\n",
"\n",
"**Purge gas analysis (6 minutes)**\n",
"\n",
"Column | Description | Unit\n",
"------ | ----------- | ----\n",
"29 | Component A | % mol\n",
"30 | Component B | % mol\n",
"31 | Component C | % mol\n",
"32 | Component D | % mol\n",
"33 | Component E | % mol\n",
"34 | Component F | % mol\n",
"35 | Component G | % mol\n",
"36 | Component H | % mol\n",
"\n",
"**Product analaysis (15 minutes)**\n",
"\n",
"Column | Description | Unit\n",
"------ | ----------- | ----\n",
"37 | Component D | % mol\n",
"38 | Component E | % mol\n",
"39 | Component F | % mol\n",
"40 | Component G | % mol\n",
"41 | Component H | % mol\n",
"\n",
"**Manipulated variables**\n",
"\n",
"Column | Description \n",
"------ | ----------- \n",
"42 | D Feed Flow (stream 2) \n",
"43 | E Feed Flow (stream 3) \n",
"44 | A Feed Flow (stream 1) \n",
"45 | A and C Feed Flow (stream 4)\n",
"46 | Compressor Recycle Valve\n",
"47 | Purge Valve (stream 9)\n",
"48 | Separator Pot Liquid Flow (stream 10)\n",
"49 | Stripper Liquid Product Flow (stream 11)\n",
"50 | Stripper Steam Valve\n",
"51 | Reactor Cooling Water Flow\n",
"52 | Condenser Cooling Water Flow"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "GQo0Y5hQyNzj"
},
"source": [
"For instance, let's observe the profile under normal conditions of the reactor pressure"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 489
},
"id": "5-Pxryf6pdCY",
"outputId": "12d32a0d-0e13-4941-c01f-575db55f0353"
},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 500.0)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"var = 7\n",
"plt.plot(data_dict['00'][:,var-1])\n",
"plt.xlabel('Sample')\n",
"plt.ylabel('Reactor pressure (kPa)')\n",
"plt.title('Normal operation')\n",
"plt.ylim(2680, 2730)\n",
"plt.xlim(0,500)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "JrAuldT91Xf0"
},
"source": [
"If you observe, during normal operation the reactor pressure is kept around 2750 kPa.\n",
"\n",
"Let's compare this to the profile under faulty conditions caused by an step change in the composition of the inert species $B$ in the inlet stream (Fault 02). "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 489
},
"id": "31n9wN3fqg06",
"outputId": "c30260cb-48ea-44b6-ee7d-43bfb55e3927"
},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 500.0)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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ujhmtyvvzs98tIYQQEqq4BlElJSX48MMPsWjRIqSlpaG8vBzl5eWwWq2i6x04cABr167FPffcE3Afy5cvx7x587Bz504cOnQI33zzDe6//34MHjwYHTp0AADcf//9OHjwIB5//HHs2bMHb775Jj755BNMmTIl6j/jzuM1eOSTbThTZ2/wOpxggaTbw8Hh8gdBi387ijX7veU2qyCI0qv8wY/V4cZhURDVcEBQZ3cC8AdLWsH9yGSAQRJUpTr281sbCTwJIYSQYOIaRL311luoqanB0KFD0apVK/5r8eLFouu9//77aNu2LYqLiwPuQ6fT4b///S8uueQSdO/eHVOmTMHYsWOxbNky/jodO3bEN998g9LSUvTt2xevvPIK3nvvPYwcOTLqP+Pf3v4Zn285jkc/2R708gU/H8LFL/yAfadqAfgDJQAY2s2bdSur8AZILMOkUymgVMihVngfPovTjbIzFv52jQVRLBNl1Cj5+2KMGmWLW3moo0wUIYSQZopr7YYLcUTVCy+8gBdeeCHoZZdffjl+/vnnJu9j6NCh2Lp1a1jHFwks8Fl/4EzQy2d8tQsAMP3Lnfj43iJYHd43c5kMvgbvCpyqtfnui2WivMGTTq2Aw+qB1eESZ6JcTZfz0oJkotI0LauUBwA6tfd3SUEUIYSQcMU1E5XqztY7+P+7PBxc7oaDmzpfIzkLonQqBQrSvQ3ep83eUiB7o2fZE72v9GZxuHGoMrRMFPs+rJwnzESl+fqkWhKt0lfOc1AQRQghJDwUREXRrhM1otN7ymsbvK7L7c3KWQWBUoFvlVx5jTcTxd7otb7giTWFV9TaRT1XjTWW17FMlC/rpBX0QLW0pnLA//PbXBREEUIICQ8FUVG064R4E+TNh6savK7LtwLP4vAGOVqVAnkm74gFVs7jG8t92ZNsgxoA8JvkfhvtifI1lrOsk7QnqqXxZ6KosZwQQkh4KIiKogOn6wD4AxVpX5TbwwX8nwVKerU/E3WqhvVE+RrLfdmTwizvXKi1+/zDMgHA3khWpdHG8haYiWK/Szv1RBFCCAkTBVFRxLJKY/q0AgBs+LNS1BdVa3Py/3f5ZlvxPVFqBfJ9QVS9w406u8vfWK70Pmzts7yTxaUZLxZsldfYsPO4uKQY0BOl9v8JmFpgEMWa9K0URBFCCAkTBVFRxAKigR0yka5TodbuwvZj/qCmxuoPomos3v8Le6IMGiXfu1ReY/M3lvuyJ+2yxdPWc4ze8h673p3zfsVVr63Dyt3+ae0Bq/OULbucxzJxLg8HZyON/4QQQogUBVFRZPEFUQaNEhd1zAIAbD9azV8uDKLMNhccLo8oEwWA74s6bbaJhm0CQDtfOY/pVuDdF8jmdON0rY1vZH/44618VszfWO7tiRI1lmta4Oo8QTmTxhwQQggJBwVRUWQLstKu2uIfeyAMogCgyuIQ9UQBQI7RG0SdqXfw96dRsiBKvFFw/3aZvu/rwZbD1fz59Q43f5qVEIOPOGh5mSiN0v8UaGxVIyGEECJFQVQUCUtz6TpvlkcYOFVbxEFUZZ3DP8bAF9ywVXR1Nhef2WJlN1a+A4DcNA16tUkH4F2uv/WIeMXevlO1cLk9qPfdBzuelt5YLpPJ+L4oykQRQggJBwVRUcSX39TBgyhpJupsvYMPlHR8EOUNbOrsTv/KOt95MpkM/QozAABPjuku2EzXgy2+IIplwPafroPZd3vh/Qo3IG6JE8sB2vqFEEJI81AQFUVs9lBDmShpEFVR528eZ+U8Poiyufwr6zT+wOf1Wy7AR/dcjHH92vCr9mxON79i7/oL2wIA9p+qhdn3/QxqBVS+ffeEPUHC/7ck/k2IKYgihBASOgqiokjYE2UKEkSZJUHUgdN1AZkoVrozi4IofwN420w9BnfJAeAPBsrO1MPicEOlkGFkzwIA3nIe+97sWLy38f8JKBUta/Nhhv2uaesXQggh4WiZ9ZsY4DjO3xPVRDkv36TBKbMdb/z4J3+ZTu19aFjp7kydnR/I2VDvkjST1CnHiK75RijkMphtLuz3Df9MFwRRaoU/iFLIW2YQxZdBG9m4mRBCCJGiTFSUON0cH/RoVQpk6MVBFMdxOFhRDwAY1Dkn4PY6X4aINZaz/fNkMkDfQNlNJzm/a74RGqUCbTO986TY4E2TYKNhmUyGvoUZyNSrcEFhZjN+0uTHD9ykTBQhhJAwUCYqSoT9NXpJJorjOHy1/QR+PXQWKoUMd1/SEUu3Hhfd3uK7PWv2PukLogxqJeQNZIyEpTkAOC/fOzeqVboWhyst2FPu7ZMy6cQP++cPDILL4+FHJ7Q0/NYvtAkxIYSQMFAQFSUsq6GUy6BSyPkgyun2lvmW/X4SAHDvkE78aAKhC9t7h3Ma+SDKKjodjEaSiTov3wgAaJXuzUTtO+Ut5wl7ogBvGU8hb5kBFCDchJiCKEIIIaGjICpKhDOiAG82SimXweXhUGN18pPDuxWYAACPXnEe3ll7EPMmDIRSLsMFvsGZrP+J7VXc2CwnaSaK3XerdO+Yg7P13kGfwnIe8U9tpxEHhBBCwkFBVJTwQzN9b9AymQzpOhUq6x2osTr5bVgMvssfGt4VE4d1gUwmLtVJp4g3lokSNokDQHvftjAsiGKkmaiWjs9E0cRyQgghYaDG8iiRZqIA/6q4aouTH1egV/uDImkABfj3uGMaC6KEty8wafneKVbOkx4H8dKpaWI5IYSQ8FEQFSW2YEGUYIWedAuXhkjLd01dn+mc599Xr1WGJBPVArd3aQzLRFEQRQghJBwUREWJtJwHQLRCr55lojSNN3RLg6ZQ97frnGvk/y/NRFE5T4ytzqOJ5YQQQsJBQVSU+Mt5/l9xrlEDADheZeUzUQZ140GRWimHRum/j6YyURe0ywAA3Hpxe/68TL1KdB9UzhMzaPxb6xBCCCGhorpOlATriereyrtabuvRarh8y+2aykQB3uZye513ZV1TQdRH91yMyjoHCn1N5YC3V2pM71b43DeLig3+JF5ZBjUAoNK3epEQQggJBQVRUWITbPnC9GztDaJ+Lavkz2sqEwV4A6czLIhqopynVyuhzwq8zkt/64Mu+UZU1NrRzTeEk3hl+4KosxREEUIICQMFUVHi30jY/yvu4QuibL6l9FqVPKT96tIEc51CbSyXUirkeHBol2bdNtXxmag6e5yPhBBCSDKhnqgoYY3lbPk84A2G2mf7y2yhZKEA4C+dsvj/SzcZJucux9erVlnvAMdxcT4aQgghyYKCqCgJNuIAALr7pogDofVDAcDkEefx/+8gCMJIZLBMlN3l4TOIhBBCSFOonBclwRrLAaB1hn/cQKiZKINGiV//ORy/H6vBgPaZkTtIAsC7JY9WJYfN6UFlnYNfrUcIIYQ0hjJRUcLKedJNgfNNGv7/4bxZ55m0GNEjP+hUc3JuZDIZsg2spEd9UYQQQkJDQVSU1Pv2xpM2ghcI9rHTq6m/KVFkG1lzOa3QI4QQEhoKoqKk1hY8iMpL8wdRoZbzSPRl0ZgDQgghYaIgKkrYti7Skp0wE0W9N4mDBVFnqJxHCCEkRBRERUm9PfgGw3lp/p4oDrScPlHwYw6onEcIISREFERFSR2fiRL3PQmzT7W0V1vCaOXLEB49a4nzkRBCCEkWFERFSUON5UK04W3i6Jrn3Qpn/+m6OB8JIYSQZEFBVBRwHMcHSI3tdeem6dgJ47x8IwDgcGU9PyiVEEIIaQwFUVFgd3ng8ngDpGDN40+P7YkMvQpPjekR60MjDchN0yBdp4KHA/6soGwUIYSQplEQFQU1Vif//2BjDMYP6oCtT12B3m3TY3lYpBEymYzPRu0/RUEUIYSQplEQFWGLNx3BxS/8AMC75YtCHnzCOE0eTzxd8719UXtP1cb5SAghhCQDCqIi7InPdvD/pzlQyaVHK+/m0L8fq47vgRBCCEkKFERFUVojTeUk8bDNnbcdqYbbQ03/hBBCGkdBVBRJZ0SRxHZefhqMGiXqHW7so5IeIYSQJlAQFWEqhb/XifbGSy4KuQx9C73N/luOVMX5aAghhCQ6CqIiLF2n5v+vU1MmKtn0aZsBANhbTpkoQgghjaMgKsKEJTyLg4Y2Jpt0nQqAf9seQgghpCEUREWYcNo17Y2XfAy+7KHFTgEwIYSQxlEQFWHC7JNZMHSTJAedr4/NQlu/EEIIaQIFURHEcZwoiMo2qhu5NklELBNldVAWkRBCSOMoiIogh9vDzxfqlp+G/7u+b5yPiISLLQaop3IeIYSQJtAa/AiyCrJQyyZdApWCYtRkw6bMW6mcRwghpAn0Lh9BrJSnVsgpgEpSOhXLRFE5jxBCSOPonT6CLL4+GpoPlbz4TBSNpyCEENIECqIiiGWi9BREJS322NU7XOA42j+PEEJIwyiIiiAWRFEmKnmxx87DAXaXJ85HQwghJJFREBVBrJxHe+YlL70qcOK8003BFCGEkEAUREUQZaKSn1Ihh1rpfVpYHC588/tJ9JzxHb75/WScj4wQQkiioSAqgqgnKjXwW7843ChZtAUOlwcli7bE+agIIYQkGgqiIoit6KJyXnLTs61faIUeIYSQRlAQFUH1NOIgJej5TBTNiiKEENIwCqIiyErlvJTAB1GCrV8Uclm8DocQQkiCoiAqgqixPDWwcl652cafp6YJ9IQQQiTonSGCLNQTlRJYJurJL3by52lU9FQhhBAiRu8MEcR6aKicl9z0msAgWKOkpwohhBCxuL4zzJo1CwMHDkRaWhry8vJwzTXXYO/evfzlhw4dgkwmC/r16aefAgC2b9+Om2++GYWFhdDpdOjevTv+85//BHyv1atXo3///tBoNOjSpQvmz58f8Z+HynmpQRGk/UlNQRQhhBCJuL4zrFmzBiUlJdi4cSNKS0vhdDpRXFyM+vp6AEBhYSFOnjwp+nr66adhNBoxevRoAMDmzZuRl5eHDz/8ELt27cK//vUvTJs2Da+//jr/fcrKyjBmzBhcfvnl2LZtGyZPnox77rkH3333XUR/HmosTw27T5oDzlNRTxQhhBCJuDbvrFixQnR6/vz5yMvLw+bNmzFkyBAoFAoUFBSIrrN06VLccMMNMBqNAIC77rpLdHmnTp2wYcMGfP7555g4cSIA4O2330bHjh3xyiuvAAC6d++OdevW4dVXX8XIkSMj9vP4y3nUE5XMerVJx75TdeIzaS9iQgghEgn18bqmpgYAkJWVFfTyzZs3Y9u2bbj77rubvB/hfWzYsAEjRowQXWfkyJHYsGFDg/dht9thNptFX02hieWpYero83HzRe1E59FmxIQQQqQSJojyeDyYPHkyBg8ejF69egW9zty5c9G9e3cMGjSowfv5+eefsXjxYtx77738eeXl5cjPzxddLz8/H2azGVarNej9zJo1C+np6fxXYWFhkz8DBVGpIS9Ni+evEf8N2l00vZwQQohYwgRRJSUl2LlzJz7++OOgl1utVixatKjRLNTOnTsxbtw4zJgxA8XFxed0PNOmTUNNTQ3/dfTo0SZvwzeWq6icl+zkkuGadidlogghhIglxLv9xIkTsWzZMqxduxZt27YNep0lS5bAYrHgjjvuCHr57t27MXz4cNx777148sknRZcVFBTg1KlTovNOnToFk8kEnU4X9P40Gg00Gk1YPwfriTJoKBOVamyUiSKEECIR10wUx3GYOHEili5dilWrVqFjx44NXnfu3LkYO3YscnNzAy7btWsXLr/8cowfPx7PP/98wOVFRUX44YcfROeVlpaiqKjo3H8IH47jYHXSiINU5XRzcHuou5wQQohfXDNRJSUlWLRoEb788kukpaWhvLwcAJCeni7KEB04cABr167F8uXLA+5j586dGDZsGEaOHIlHHnmEvw+FQsEHXPfffz9ef/11PP7447jrrruwatUqfPLJJ/jmm28i9rPYnB5wvvdYWp2XmhwuDwXIhBBCeHHNRL311luoqanB0KFD0apVK/5r8eLFouu9//77aNu2bdA+pyVLlqCiogIffvih6D4GDhzIX6djx4745ptvUFpair59++KVV17Be++9F5XxBgCgU9EbbSp45IrzRKepuZwQQoiQjOM4qlGEwGw2Iz09HTU1NTCZTAGXHz1rwaUv/QitSo49z46OwxGSSPN4OBw8U4fiV9fCwwG//HM48k3aeB8WIYSQMDT1/n0uEmZ1XrLzjzegUl6qkMtl6JKXxmcWbU7KRBFCCPGjICpCWDmPSnmpR+N7TGngJiGEECEKoiKE7ZtH4w1Sj8a3+TDNiiKEECJEQVSE1LNBm1TOSzl8EEWN5YQQQgQoiIoQfvNhKuelHC2V8wghhARBQVSEWGnfvJRFmShCCCHBUBAVIfzqPA2V81KNRslW51EmihBCiB8FURFQbXHgg42HAVA5LxVpVJSJIoQQEoiCqAh4a/WfKDtTD4D2zUtFtDqPEEJIMBRERcCKXeX8/4Xbv5DUQHOiCCGEBENBVATIZTL+/1f2bhXHIyHRQI3lhBBCgqEu6HPk9nA4VmUBAKx5bCjaZxvifEQk0qixnBBCSDCUiTpHJ2uscLo5qBQytM3Ux/twSBSwTBTtnUcIIUSIgqhzdOSsNwvVNlMPhVzWxLVJMmJBlNNNmShCCCF+FESdo6O+IKowi7JQqUrtC6Ic1FhOCCFEgIKoc2BzuvHtTu/KvPYURKUstcIXRFEmihBCiAAFUefg/fVlWL23AnIZMKpXQbwPh0SJis9EcXE+EkIIIYmEgqhzsOdkLQDg4eHnYXCXnDgfDYkWykQRQggJhoKoc1BRawcAdMihUl4qY5koJ/VEEUIIEaAg6hycrrUBAHKNmjgfCYkmDWWiCCGEBEFB1Dk47ctE5ZkoiEpl0tV5Hg+Hd9f+iStmr8Hmw2fjeWiEEELiiIKoZrI53ai1effJyzVq43w0JJpUkkzU/zYdwQvL92D/6Tq8u/ZgPA+NEEJIHFEQ1UysH0qtlMOko91zUpk0E7X9aDV/2eq9Fai306bThBDSElEQFSaO43D0rIXvh8pL00Amo0nlqUyl8D6+bGJ5vcO//Yvd5cEPe07H5bgIIYTEF6VQwvTp5mN47vtD/OncNOqHSnXSTJTFl3lSK+VwuDw4cKo2bsdGCCEkfigTFaa95WbRaVqZl/rY3nkOSSYqzxdAW51u7DhWgymLt+FEtTU+B0kIISTmKBMVJouglAMAHhpinfJYYzmbE2VxeDNROUYNjlVZYXG4cfXr6wAAx6us+OT+ovgcKCGEkJhqVhB15MgRHD58GBaLBbm5uejZsyc0mpaRkWFNxOcXpOHgmXr8bUDbOB8RiTa1JBNlsXsD6RxfFtIqCKz/OGkGIYSQliHkIOrQoUN466238PHHH+PYsWPgOH8KRq1W49JLL8W9996L6667DnJ56lYJ631voA8M7YwxvVtBqUjdn5V4sUyU3cXKeSwTpQYgzk56OEpNEkJISxFSBDBp0iT07dsXZWVleO6557B7927U1NTA4XCgvLwcy5cvxyWXXILp06ejT58+2LRpU7SPO27qfJmoNK2SAqgWgu2d52woE+UUBlExPjhCCCFxE1ImymAw4ODBg8jOzg64LC8vD8OGDcOwYcMwY8YMrFixAkePHsXAgQMjfrCJgJXzjBpVnI+ExIpGsDqP47iATJSVMlGEENIihRREzZo1K+Q7HDVqVLMPJhl4gyglDBpFvA+FxAgr53k4b+mOZZtyfKvzLE7/sE2KoQghpOWgelSY6nxZiDTKRLUYrLEcAKosDv7/WQbqiSKEkJasWavzlixZgk8++QRHjhyBw+EQXbZly5aIHFiisjo8kGsAo5amQ7QUKkHvW7XFCQDQqRQwarx/AzZBEOWmIIoQQlqMsDNRc+bMwYQJE5Cfn4+tW7fioosuQnZ2Ng4ePIjRo0dH4xgTEpXzWg627QvgD6IMGgX0au/fgEXQWE4xFCGEtBxhB1Fvvvkm3n33Xbz22mtQq9V4/PHHUVpaikmTJqGmpiYax5hw1Ao5NEoKoloKmUzGl/RYOU+vVkKr8gVRkgGshBBCWoawg6gjR45g0KBBAACdTofaWu++Ybfffjv+97//RfboEhSV8loeNuagmg+iFNCrvX8HbE89QgghLUvYQVRBQQHOnj0LAGjXrh02btwIACgrKxMN4ExlrBeGtBz+TBQr5yn5cp6Uh4ZFEUJIixB2EDVs2DB89dVXAIAJEyZgypQpuOKKK3DjjTfi2muvjfgBJiIKoloe1hdVJchEaZRyyGSB1xX2SBFCCEldYUcD7777Ljweb/mipKQE2dnZ+PnnnzF27Fjcd999ET/ARERBVMvDMlE1LBOlVkImk0GnUgT0RFnsLvobIYSQFiCsV/qNGzfi66+/hsPhwPDhwzFq1CjcdNNNuOmmm6J1fAmJeqJaHtYTxTJRBl+QpFcHBlF1dhfyYnt4hBBC4iDkaGDJkiW48cYbodPpoFKpMHv2bPz73//GP/7xj2geX0KiLEPLw2ZFVVv9Iw4AQBekL4pW6xFCSMsQck/UrFmz8Pe//x01NTWoqqrCc889hxdeeCGax5awKBPV8rD989icKLYyT6cKDKLY/oqEEEJSW8hB1N69e/GPf/wDCoX3TePRRx9FbW0tTp8+HbWDS1TpOtrypaVRSct5apaJCgyoKRNFCCEtQ8hBlMVigclk4k+r1WpotVrU1dVF5cASWaccQ7wPgcSYWpqJYj1RQTJRdZSJIoSQFiGsutR7770Ho9HIn3a5XJg/fz5ycnL48yZNmhS5o0tQnfOMTV+JpBThJsSAPxMVbFaUxUFBFCGEtAQhB1Ht2rXDf//7X9F5BQUF+OCDD/jTMpmsZQRRuRREtTTCTYgBfyZKGySIqrNTOY8QQlqCkIOoQ4cORfEwkkeOUU09US1QQ5koQ5AgijWWH6m04NudJ3HrX9rTik5CCElBYU8sP3bsWIOXsS1gUllH6odqkdTSTJSvobxbgSngumbfGITi/7cGs77dg7dX/xn9AySEEBJzYQdRxcXF/N55QuvXr8eoUaMiclCJrFMuBVEtkTSIYnOiLumSE3Bds80bRNmc3sn+O47XRPnoCCGExEPYQdRf/vIXFBcXo7a2lj9v7dq1uPLKKzFjxoyIHlwiokxUyyQt57FM1Hn5gf1xtTYXquod/Gn6myGEkNQUdhD13nvvoV27drj66qtht9vx448/YsyYMXjmmWcwZcqUaBxjQulETeUtkkbaE+XLRMlkMnT1rdbskK0H4M1E7T5p5q8rDcAIIYSkhrBf3eVyOT7++GOoVCoMGzYMY8eOxaxZs/Dwww9H4/gSTsdsyiq0RJkGtei0XjBk83/3/gX/vq43Hi3uBsCbidp1wl/Cs9LwTUIISUkhLRn6/fffA86bOXMmbr75Ztx2220YMmQIf50+ffpE9ggTTEG6Nt6HQOIgUy8Novyr8nKMGtw4sB02HfL2CpqtTuwp95e7aYI5IYSkppCCqH79+kEmk4HjOP48dvqdd97Bu+++C47jIJPJ4Han9huGTCaL9yGQOMgy+MdaqJXygLlRAGDSeq9jtrn4yeYAYHOm9nOCEEJaqpCCqLKysmgfByEJLcug4f8fbDYUAKT5NqautTlRa/MHUVYKogghJCWFFES1b98+2sdBSEITZqL0QTYdBgCTbwir082hotbOn089UYQQkppCaiwPZ4imxWLBrl27mn1AhCQiYU+URhX8aWNQKyD3VXuPV1v58ykTRQghqSmkIOr222/HyJEj8emnn6K+vj7odXbv3o1//vOf6Ny5MzZv3hzRgyQk3jIEQZTT7Ql6HZlMhjStPxvFUE8UIYSkppDKebt378Zbb72FJ598ErfccgvOO+88tG7dGlqtFlVVVdizZw/q6upw7bXX4vvvv0fv3r2jfdyExJRC7l9QYHcGD6IAwKRTosbqFJ1HmShCCElNIQVRKpUKkyZNwqRJk/Dbb79h3bp1OHz4MKxWK/r27YspU6bg8ssvR1ZWVrSPl5C4s7saDqLSNCoAVtF51BNFCCGpKeyt5S+88EJceOGF0TgWQpJCY+U5ky7wKUWZKEIISU20HwUhYWosE8VmRQlRTxQhhKSmuAZRs2bNwsCBA5GWloa8vDxcc8012Lt3L3/5oUOHIJPJgn59+umn/PUmTZqEAQMGQKPRoF+/fkG/1++//45LL70UWq0WhYWFeOmll6L945EU1di8VeEqvgy9v8m8oWZ0QgghySuuQdSaNWtQUlKCjRs3orS0FE6nE8XFxfwKwMLCQpw8eVL09fTTT8NoNGL06NGi+7rrrrtw4403Bv0+ZrMZxcXFaN++PTZv3oyXX34ZM2fOxLvvvhv1n5Gkjjdv7Q+jRom54xsuZxdm6fj/56X5B3RSSY8QQlJP2D1RkbRixQrR6fnz5yMvLw+bN2/GkCFDoFAoUFBQILrO0qVLccMNN8BoNPLnzZkzBwBQUVERdJ+/jz76CA6HA++//z7UajV69uyJbdu2Yfbs2bj33nuj8JORVHRl71YY1bMAcnnDqah2gg2qswxqyGWAhwNsDnfQUh8hhJDkdU6ZKJvNFqnjAADU1NQAQIOr/DZv3oxt27bh7rvvDut+N2zYgCFDhkCt9pdaRo4cib1796Kqqirobex2O8xms+iLkMYCKABol6Xn/5+mVUGn8m4RQ5koQghJPWEHUR6PB88++yzatGkDo9GIgwcPAgCeeuopzJ07t9kH4vF4MHnyZAwePBi9evUKep25c+eie/fuGDRoUFj3XV5ejvz8fNF57HR5eXnQ28yaNQvp6en8V2FhYVjfk7RMwiBKrZRDp6YgihBCUlXYQdRzzz2H+fPn46WXXhJldnr16oX33nuv2QdSUlKCnTt34uOPPw56udVqxaJFi8LOQjXXtGnTUFNTw38dPXo0Jt+XJLdMvb9kV2NxQssyUTQrihBCUk7YQdTChQvx7rvv4tZbb4VC4d/Nvm/fvtizZ0+zDmLixIlYtmwZfvzxR7Rt2zbodZYsWQKLxYI77rgj7PsvKCjAqVOnROex09KeK0aj0cBkMom+CGmKTLB0r8rioHIeIYSksLCDqOPHj6NLly4B53s8HjidziC3aBjHcZg4cSKWLl2KVatWoWPHjg1ed+7cuRg7dixyc3PDPWQUFRVh7dq1ouMrLS1Ft27dkJmZGfb9ERKKzrlG6H3lPJoVRQghqSfsIKpHjx746aefAs5fsmQJLrjggrDuq6SkBB9++CEWLVqEtLQ0lJeXo7y8HFareNuMAwcOYO3atbjnnnuC3s+BAwewbds2/rbbtm3Dtm3b4HA4AAC33HIL1Go17r77buzatQuLFy/Gf/7zHzzyyCNhHS8hoVj20CW4+aJCPHlVd0E5j+ZEEUJIqgl7xMH06dMxfvx4HD9+HB6PB59//jn27t2LhQsXYtmyZWHd11tvvQUAGDp0qOj8efPm4c477+RPv//++2jbti2Ki4uD3s8999yDNWvW8KdZMFdWVoYOHTogPT0d33//PUpKSjBgwADk5ORg+vTpNN6AREWvNumY9dc+AECN5YQQksJkHMdx4d7op59+wjPPPIPt27ejrq4O/fv3x/Tp0xsMclKB2WxGeno6ampqqD+KhOzBjzZj+Y5yzLy6B+4c3HC5mhBCSHRE8/07rEyUy+XCCy+8gLvuugulpaURPRBCUlHrdO8E87Iz9aiotSNXMMWcEEJIcgurJ0qpVOKll16Cy+WK1vEQklI65nonmC/YcBgDn1+JjQcr43xEhBBCIiXsxvLhw4eL+o8IIQ3rlGMUnZ71bfPGgBBCCEk8YTeWjx49GlOnTsWOHTswYMAAGAwG0eVjx46N2MERkuw65YqfHxplXPf8JoQQEkFhB1EPPvggAGD27NkBl8lkMrjdtAqJECZP0gNVXhPZ/SYJIYTET9hBlMdD824ICZVwgjkAHK2ywOpw86MPCCGEJC+qLRASZTdf1I7/P8cBB07XxfFoCCGERErYmahnnnmm0cunT5/e7IMhJBVNv6oH7ihqj5lf7cIvZWdxoKIWvdumx/uwCCGEnKOwg6ilS5eKTjudTpSVlUGpVKJz584URBEioVMr0L2VCdlGNQDAbKURIYQQkgrCDqK2bt0acJ7ZbMadd96Ja6+9NiIHRUgq0ippM2JCCEklEemJMplMePrpp/HUU09F4u4ISUkaFQuiaHEGIYSkgog1ltfU1KCmpiZSd0dIytGqvE83m4syUYQQkgrCLufNmTNHdJrjOJw8eRIffPABRo8eHbEDIyTVaKicRwghKSXsIOrVV18VnZbL5cjNzcX48eMxbdq0iB0YIamGz0RROY8QQlJC2EFUWVlZNI6DkJSn9fVE2amcRwghKeGce6LMZjO++OIL/PHHH5E4HkJSlta3b56dMlGEEJISwg6ibrjhBrz++usAAKvVigsvvBA33HAD+vTpg88++yziB0hIqtCqqCeKEEJSSdhB1Nq1a3HppZcC8A7e5DgO1dXVmDNnDp577rmIHyAhqYIPoqicRwghKSHsIKqmpgZZWVkAgBUrVuC6666DXq/HmDFjsH///ogfICGpghrLCSEktYQdRBUWFmLDhg2or6/HihUrUFxcDACoqqqCVquN+AESkio0VM4jhJCUEvbqvMmTJ+PWW2+F0WhE+/btMXToUADeMl/v3r0jfXyEpAza9oUQQlJL2EHUgw8+iIsuughHjx7FFVdcAbncm8zq1KkT9UQR0ggq5xHSchyurMdP+8/ghgsLoVZGbHMQkmDCDqIA4MILL8SFF14IAHC73dixYwcGDRqEzMzMiB4cIamE5kQR0nIUv7oWdpcHDpcHd13SMd6HQ6Ik7PB48uTJmDt3LgBvAHXZZZehf//+KCwsxOrVqyN9fISkDC1tQExIi2F3eZ/nv5adjfORkGgKO4hasmQJ+vbtCwD4+uuvUVZWhj179mDKlCn417/+FfEDJCRV+Mt5lIkiJBUcrqzHO2v+RL3dJTrf5fZ/UDLpmlXwIUki7CDqzJkzKCgoAAAsX74c119/Pc477zzcdddd2LFjR8QPkJBUwTYgdnk40YssISQxcRzX6OXPf/MHZn27B8t+PyE6/2SNjf+/SkH9UKks7Ec3Pz8fu3fvhtvtxooVK3DFFVcAACwWCxQKRcQPkJBUwTJRgD/VTwhJTF9uO46eM77Dmn0VQS/nOA6/Ha4CAJw220WXHa608P+vtjqjd5Ak7sIOoiZMmIAbbrgBvXr1gkwmw4gRIwAAv/zyC84///yIHyAhqYKNOACopEdIopv+5S5YHG6Mf/9X/GflflRbHKLLD1VacLbee540UDpyVhBESW5HUkvYxdqZM2eiV69eOHr0KK6//npoNBoAgEKhwNSpUyN+gISkCrlcBrVCDofbAxtloghJaJ1zDdhypBoA8OrKfdCrFfj7kE785Zt9WSgAqJEEUYfP1vP/r6qnTFQqa1bH29/+9jcAgM3mr/uOHz8+MkdESArTqHxBlC8TVVXvwI97T8OkVWF49zzIZLI4HyEhBABaZ+j4IAoAyirrRZdvOdJwEHWUMlEtRtjlPLfbjWeffRZt2rSB0WjEwYMHAQBPPfUUP/qAEBKcVrL1y4yvduGRT7bjnoW/YenW4/E8NEKIgFOy+EMtaRDf0kgmSph9qrJQJiqVhR1EPf/885g/fz5eeuklqNVq/vxevXrhvffei+jBEZJqpFPLj1b5P7G+u/Zgk6uBCCGx4XR7n4sdsvUAAKvD38dYa3Ni36la/rRZEkTZBAN1rU439UCmsLCDqIULF+Ldd9/FrbfeKlqN17dvX+zZsyeiB0dIqmHN5Xbfi2qdzT9fZk95LTYdqgp6O0JIbLFMVLpOBQCod/ifq9uP1sDDAaz6Xi3JNgkDrmCXk9QRdhB1/PhxdOnSJeB8j8cDp5P+UAhpDF/O831SZUP68k3eBRrCT7eEkPhx+BZ/pOu9FRdhYMT6ofq2zQAQWM6TjjCpor6olBV2ENWjRw/89NNPAecvWbIEF1xwQUQOipBUJS3n1fqCqC55RgDAabMt+A0JITHVWCZq3f4zAIBh5+cB8JbsHILASZqJoiAqdYW9Om/69OkYP348jh8/Do/Hg88//xx79+7FwoULsWzZsmgcIyEpQ7gJMcdxqPMFUZ1zjVh/oBLlFEQRkhBYT1S6b9sWFhidMtuw6bB3P7y/9m+DV1fuA8d5s1G5ad6MMss0Z+pVqLI4UVlHQVSqCjsTNW7cOHz99ddYuXIlDAYDpk+fjj/++ANff/01P72cEBIc2/rF5vTA4nCD9ZGzTNQpyeRjQkh8sExUhs5bzqv3BVHf7jgJjgMGtM9E20w90jTeIEtY0mMBV8/W6QCA3SfNMTtuElthZaJcLhdeeOEF3HXXXSgtLY3WMRGSsjSCTYhZP5RCLkO7LO8KoFOCTJTN6cYpsw3tsw2xP1BCWjiHpJzHAqNNvtEGw7t7S3npehXMNhcfRHk8HN8TVdQ5G+sOnBGNQyCpJaxMlFKpxEsvvQSXy9X0lQkhAbSCTBTrhzKoFShI1wIQB1F3L9iEy15ejZ3Ha2J/oIS0cHxPlF7cE1Xl2+qldboOgD9TVWP1ni9sKh/cJQcA8PuxmoC5UyQ1hF3OGz58ONasWRONYyEk5WkFmSg23iBNq0KByRtEVVmcsDm9/VLrD1QCAD757Wh8DpaQFszpYj1R3iDK4stEseGZGb7gil3OMlHCmVA9W5tg0iphdbqx5yStvE1FYTeWjx49GlOnTsWOHTswYMAAGAziUsPYsWMjdnCEpBrhiAPWVG7UKJGuU0GtlMPh8qCi1s6X/YS3IYTEjr8nyhskOVweuNwefhuXTN/oA5Ov8dxs9T6frb4gSqWQQaWQo2frdGw4WIkDFbXo3TY9pj8Dib6wg6gHH3wQADB79uyAy2QyGdxumsxKSENYJsru9PBBlEGjgEwmQ75Jg6NnrThZYxOl/s/UUrM5IbHmkJTzAMDidPPjClgQlabxXl5rE2ei2IcflrESDtYlqSPscp7H42nwiwIoQhrn74nyl/OMWu+LbAdfA/kTn/2OrYLNTY9VWWN8lIQQ9kHGoFZCIfeOJq+qd/Az3jIM3udtmtabi6i1iTNROl8QZfSt3mM9kCS1hB1EEUKaT7gBMctEsSXS00Z3R45Rg7Iz9XhnzUH+NserKYgiJNbYnCiNUg6973nLnotKuYx/3qb5PgSZfUEUC7LYc90oCbJIamlWEPXDDz/gqquuQufOndG5c2dcddVVWLlyZaSPjZCUI5xYLuyJAoAerU0Y1DkbgPhTa7nZBhet7CEkZtweDm6PN4hSKeTQqX1BlC8rnKFXQebbOM+fiRKX81gmigVZVM5LTWEHUW+++SZGjRqFtLQ0PPzww3j44YdhMplw5ZVX4o033ojGMRKSMjRBGssNGn9rIpt4LOT2cBgxew3MNtqbkpBYEPYkqpRy/jl6oto7goT1QwGB5Tx/T5T37ZVlrOqonJeSwm4sf+GFF/Dqq69i4sSJ/HmTJk3C4MGD8cILL6CkpCSiB0hIKuG3fXF6BD1R/qdhXpAgCgAOVVrw68GzGNEjP/oHSUgLJwqiFDI+q3S82gJAGkSJG8utksZyoyRTRVJL2Jmo6upqjBo1KuD84uJi1NTQUEBCGqNV+sp5rsCeKECciZLLgMkjuvKn6ZMsIbEh3ExYJZfDoPEGRCwTlSFYsWcKyESJe6KkmSqSWsIOosaOHYulS5cGnP/ll1/iqquuishBEZKq/I3lHv5FVZyJ0vL/zzdpMXnEeRjVswAAfZIlJFZYU7lSLoNcLoNO7X2Ossby4Jmoxlfn0Yeg1BR2Oa9Hjx54/vnnsXr1ahQVFQEANm7ciPXr1+PRRx/FnDlz+OtOmjQpckdKSArQKNmcKDcfFBkFmag8kz8TxbaC4csB9CJMSEywcp5K4X2+GtTi1XlsvAEQ2Fhul/ZEaZsOosprbPizoo7fJoYkj7CDqLlz5yIzMxO7d+/G7t27+fMzMjIwd+5c/rRMJqMgihAJ4YgDtk2E8FNtrtEfRGUbvP/nP8lSOYCQmHDwQZR3BZ7el4liZb5gjeX1DjfcHo7fqJit6JNmqoL5y6wfAABfTRyMPm0zIvVjkBgIO4gqKyuLxnEQ0iL4t33xwCPZg0v6f/YCbgrhkywhJHJYJkrtyxxnCp6XAJBlCCznAd4POgGN5U18CNp/yr+n3t7yWgqikgwN2yQkhoQbEFf7dn1nG5gC4GfPAIDSV0qgYX2ExBbbfJiV87KMatHlOYLTaqWcL9Obbc4Gh2063B7YXYG7enyz4yT/f6VCFnA5SWwURBESQ+yF1eJw+7ePkHzKZfr6Nis1apouBxBCIsch6YnKMYhHj2RJTgtLdtLGcoPaX/AJ9hxes6+C/7/FQVunJRsKogiJIbZ3HqOQy0SN5QDw+YODMGl4V9xR1AGAsDGVVucREgtOSU+UsHwHANmS06zkfuWcn/DHSTMAf9ZZ+BwPVtJjvZEAYLFTEJVswu6JIoQ0n0Yl/tySoVOJSngA0L9dJvq3y+RPUzmPkNiSrs7LlpTzpKeFT+FtR6sB+DNRgLcvqs7uCtrXaBNknygTlXzCykS5XC4888wzOHbsWLSOh5CUplHKRS+46Q2U8oRo2whCYkvaWJ4tKN9pVXJ+tR7zZ0V9wH1ohUFUIx+ELE5hEEXP8WQTVhClVCrx8ssvw+WiB5qQ5pDJZHwTKuDNRDWFNjAlJLYcksZyYeZJGkABwITBHQLOE+4+IJ0lJWSlTFRSC7snatiwYVizZk00joWQFkH4CTVDr27kml7CT7E7jtVg4YZD4DhOdJ3Nh89i0S9HAs4nhIRP2hOlVysauzoeH3k+xhe1F52Xb/LvPsAyWadq7aLreDwc7IItZuopE5V0wu6JGj16NKZOnYodO3ZgwIABMBgMosvHjh0bsYMjJBV5m8sDZ0Q1hDWlOtweXP36OgDeoZyje7fir3PdWxsAAK3Stbj8/LwIHzEhLYu0J0ratyilUytwaddcLNhwmD+vQBBEtcvSAwCOnrWIbmd1ijNPVspEJZ2wg6gHH3wQADB79uyAy2QyGdxu+iMgpDFalbCcF0ImShP4NN13qg6jewded9OhsxREEXKO+J4oRejFmhxB+U6tlIs+ILXL0gEADleKe6ekQRSV85JP2EGUx+Np+kqEkAaJy3lNZ6IUchkMagXqBS+wamXwF/fTknIBISR8Dre4JyoUwgGceWkaUfaqfba3YnPkrFV0G2nmiRrLkw/NiSIkxkSN5SEEUYC/L4qRN1BdqKAgipBz5vT1KakEz9VebUwAgLF9Wwe9TY5g30tpD1WhoJwn7FukTFTya1YQtWbNGlx99dXo0qULunTpgrFjx+Knn34K+35mzZqFgQMHIi0tDXl5ebjmmmuwd+9e/vJDhw5BJpMF/fr000/56x05cgRjxoyBXq9HXl4eHnvssYAVhKtXr0b//v2h0WjQpUsXzJ8/vzk/OiHn7IigL6JTjjGk20hLeg3NjKJMFCHnTtpYDgDz7rwIL/61Nx4f1S3obYQZZrmkh6ptpg4ymXdMydl6B39+YCaKgqhkE3YQ9eGHH2LEiBHQ6/WYNGkSJk2aBJ1Oh+HDh2PRokVh3deaNWtQUlKCjRs3orS0FE6nE8XFxaiv99aNCwsLcfLkSdHX008/DaPRiNGjRwMA3G43xowZA4fDgZ9//hkLFizA/PnzMX36dP77lJWVYcyYMbj88suxbds2TJ48Gffccw++++67cH98Qs5Zhxxvaj/HqMHgLtkh3aYgXSs6bRYslfZ4/J9sK2ptEThCQlo2FkQJs8a5aRrcdFG7oCMOpKR74GlVCr7RXPghSho0UTkv+YTdE/X888/jpZdewpQpU/jzJk2ahNmzZ+PZZ5/FLbfcEvJ9rVixQnR6/vz5yMvLw+bNmzFkyBAoFAoUFBSIrrN06VLccMMNMBq9n+C///577N69GytXrkR+fj769euHZ599Fk888QRmzpwJtVqNt99+Gx07dsQrr7wCAOjevTvWrVuHV199FSNHjgz3V0DIOXlyTHd8ue0EHh7etclVP0zHHAPWH6jkT5sFW0Wwfb4A4EydAxzHhXy/hJBAzemJElLIA2/XNlOHkzU2nKi24YJ23vNsvnJemkaJWruLtn1JQmH/hRw8eBBXX311wPljx45FWVnZOR1MTU0NACArKyvo5Zs3b8a2bdtw99138+dt2LABvXv3Rn5+Pn/eyJEjYTabsWvXLv46I0aMEN3XyJEjsWHDhgaPxW63w2w2i74IiYQB7bPwzLheyDZqmr6yT0dJ2a+mgSAKAKottMceIedCOuIgVGxW1BMjA0t+6Tq2SbH/+cl6otgwT4vTTbPekkzYQVRhYSF++OGHgPNXrlyJwsLCZh+Ix+PB5MmTMXjwYPTq1SvodebOnYvu3btj0KBB/Hnl5eWiAAoAf7q8vLzR65jNZlit4tUSzKxZs5Cens5/ncvPRsi56pQjnsdmFvREOVziIOpETfC/aUJIaPjG8jCDqJlje+K3J0dgUJecgMuMQbZvYuU8tsGxWzJ8kyS+sMt5jz76KCZNmoRt27bxwcz69esxf/58/Oc//2n2gZSUlGDnzp1Yt25d0MutVisWLVqEp556qtnfIxzTpk3DI488wp82m80USJG46SgNogSZKKckE2Vz0oswIefCPycqvLK4TCYTrdITCrZ/nj8T5b+N1eEWNamTxBZ2EPXAAw+goKAAr7zyCj755BMA3h6jxYsXY9y4cc06iIkTJ2LZsmVYu3Yt2rZtG/Q6S5YsgcViwR133CE6v6CgAL/++qvovFOnTvGXsX/ZecLrmEwm6HS6oN9Po9FAowm93EJINLXNFP+disp5kk+uLklQtfN4DSpq7TSEk5AQsQyRJoLBjFHDynmCIMrXSJ6mUUKtlMPh8sDidCMzYt+VRFvYQRQAXHvttbj22mvP+ZtzHIeHHnoIS5cuxerVq9GxY8cGrzt37lyMHTsWubm5ovOLiorw/PPP4/Tp08jL875JlJaWwmQyoUePHvx1li9fLrpdaWkpioqKzvlnICQWlJKygnB1njSIcrrFPRVXvebN7v74j6EBGS1CSCAW6Ji0zXqLDIptQlxnF/REObzPXa1aAYNa4Q2i7LRCL5mE3RPVqVMnVFZWBpxfXV2NTp06hXVfJSUl+PDDD7Fo0SKkpaWhvLwc5eXlAX1KBw4cwNq1a3HPPfcE3EdxcTF69OiB22+/Hdu3b8d3332HJ598EiUlJXwm6f7778fBgwfx+OOPY8+ePXjzzTfxySefiFYYEpLoPr73L7j7Eu8HDZvTA7vL+2lZ2ljuFOwqYBMM8ztRTb1ShISCfUgx6UIbhhuKtEbKeXqVgh+dQLOikkvYQdShQ4eC7o9nt9tx/PjxsO7rrbfeQk1NDYYOHYpWrVrxX4sXLxZd7/3330fbtm1RXFwccB8KhQLLli2DQqFAUVERbrvtNtxxxx145pln+Ot07NgR33zzDUpLS9G3b1+88soreO+992i8AUkqf+mUjX9d2R1seoHZ6n0xDizn+TNRp8z+uVHSAYCEkOD8majIBVHBGstZOU+nVkDnm3JeT7OikkrIucqvvvqK//93332H9PR0/rTb7cYPP/yADh06hPXNQ13K+cILL+CFF15o8PL27dsHlOukhg4diq1bt4Z1fIQkGrlchjSNEmabC2abE7lpmoDynbDR/JTZP8Hc6qQXZ0JCwTJRaREt5wXpifJlorQqBb8xOa3OSy4h/4Vcc801ALyrD8aPHy+6TKVSoUOHDvwwS0JI9Jh0KphtLr65PLAnyn+6XJCJqqdBfoSEhK1+jWQ5j2WihHOiWOlOr1ZA7et7lD6fSWILOYjy+PosOnbsiE2bNiEnJ3AOBiEk+rwlBiv/Qi8dcSDMTJ0WBVGUiSKx8/mWY+iUa0S/wox4H0pYOI6LSjnP31jufx6ynkWdSgG1kjJRySjsXOW5TiUnhJwbNvmYZaKkL7ouUTlPEERRwyqJkX2navHIJ9sBALueHgmDJnJlsWizOt1w+fajjGw5zxdEBSnn6dQKqJXenijKRCWXsBvLJ02ahDlz5gSc//rrr2Py5MmROCZCSCNMOu+LMZtaHrA6T1TO8/dE0dJpEiunBX93n/x2NI5HEj6WhVLIZdCrIzknyvu8rXe44fYFaaycp1NROS9ZhR1EffbZZxg8eHDA+YMGDcKSJUsiclCEkIaxEgNfzmtkThRlokg8WAQrzD757VgcjyR87HmVplVGdCNvoyCrxUp65TXe52e2UQONigVR9DxNJmEHUZWVlaKVeYzJZMKZM2ciclCEkIaxch57sZdmolyeBsp5lIkiMSJcpl9ZZ2/kmomHnxEVwX4oANAo/dmmOrsLFocLJ31BVOdcAzQsE+WmTFQyCTuI6tKlC1asWBFw/rfffhv2sE1CSPjYiiH2Yt9YY3lVvYP/P82fIbEi7PsRDnxNBqxMzsrmkcT6ohb8fAgLfj4MAMjUq5ChV/ON5VTOSy5h/5U88sgjmDhxIioqKjBs2DAAwA8//IBXXnkF/+///b9IHx8hRMKfiQo+bFMYVAk3I7bQiAMSI3WCvzVbkgUFfDlPE9lMFAAofRsav7v2IH8e24qJVuclp7CDqLvuugt2ux3PP/88nn32WQBAhw4d8NZbbwVsDkwIiTz2Cbmh1XksiHJ7OFFpoKFMFMdxePKLnbA5Pfi/6/tEtA+EtEzC0rHD5YHHw0EuT46/q9ooZqKEw2+ZjjlGAKDG8iQVdjkPAB544AEcO3YMp06dgtlsxsGDBymAIiRG+MbyBsp5bNsXaRmloZ6oP07W4qNfjuCzLcf4Hg1CzkWd5G8tmfp8/NPKI5+JuvmidlApZCi5vDN/XptMHQDKRCWrZgVRTG5uLoxGY6SOhRASAumcKOknV/aGZZUEUQ1tbPrNjhP8/88KeqgIaS5pwJ5MfVGsTB7pxnIAeP6aXvjlnyPwj+Ju/HntsvQAvI3nQHIFnKQZ5TwAWLJkCT755BMcOXIEDof4RXfLli0ROTBCSHAmyeq8kDNRDZTzvt1Rzv+/ykJBFDl30kyUsDcv0bFtWaJRzpPLZcgyqAEAn9xXhJ/2V+Cafq0BgBrLk1TYmag5c+ZgwoQJyM/Px9atW3HRRRchOzsbBw8exOjRo6NxjIQQAX85zwWO4xpsLA8s5wVmA9weDgfP1POnKRNFIiEwiEqiTJSvJyoa5Tyhizpm4dHiblD6eqEoiEpOYQdRb775Jt5991289tprUKvVePzxx1FaWopJkyahpqYmGsdICBFg5Ty3h0O9w82n/w2+6cpOPhMlfjEO1hMlfcGuoiCKREBAOS+JBkjymagIbvkSCn9PVPL8rkgzgqgjR45g0KBBAACdTofa2loAwO23347//e9/kT06QkgArUoOlW+ptNnqhMPlDZr0vm0l2LBN1hOVofcGXXaXR7Svnvc88Qv2WYsThJwradYzmcp5/onl0c1ESWmSdHXeiWprix7kG3YQVVBQgLNnzwIA2rVrh40bNwLwbkzMcVxjNyWERIBMJhM1lwdmonxBlK+RPNvXgwEAFklZRboS6Gx9ck2XJolJWs6zJ2E5Lxo9UY3hy3lJ1Fh+9KwFg15chXFvrI/3ocRN2EHUsGHD8NVXXwEAJkyYgClTpuCKK67AjTfeiGuvvTbiB0gICZQm2D+P7Z1n8GWinJLGcpNOBaVvRo/0E6PdKS3nUSaKhCfYh2cWRGl8gUEyDdysjdK2L01Jxp6o73Z5F6UcOF0X5yOJn7BD7XfffRceX7mgpKQE2dnZ+PnnnzF27Fjcd999ET9AQkggrcqbdbK5PIJMFAuixOU8nUoBg0aJGqszMIiSlvOoJ4qEweZ048r//ITzW6XhzVsHAPAGVezvLMeowfFqa3I1lkdxxEFjNEkYRAlX89pdbn5MQ0sSdhAll8shl/sTWDfddBNuuummiB4UIaRxWt+O73anm3/R1Wu8L2BsxAHLMmlVChh9QVStTRpESTJRNOKAhGHXiRocPFOPg2fqUW1xIEOv9vbeebx/g9lGdVIFUU63h//wEa9yXjIN2zxT63+9qLY4kW9qeUFUs4Zt/vTTT7jttttQVFSE48ePAwA++OADrFu3LqIHRwgJTlgmYZkovVo8rE+YiWIbnwb0qlAmqtmkTfotEVvUAABbj1QDEJeMM/Xefjxp2ThRsaZyADBqYhxEJWFj+aFK/3iUlvoBLOwg6rPPPsPIkSOh0+mwdetW2O3eRtSamhq88MILET9AQkggVs4TZaJ85TyXZE6URiXng6iATJTvzY1dXmVx0AKREHz86xH0mvkdfj5wJt6HElesfwgAthypAuAP1PVqBR/YJ8Oy/aVbj2HAcysBeBdpsPlNsZJImagDp2tx9KylyeuVCWbMtdR+yrD/Sp577jm8/fbb+O9//wuVyl8zHjx4ME0rJyRGhJko1gNl5EcceIMgYSaKXVbXQDmvVboWgLcpvbYFL1cO1dTPd8Dm9ODhxdvifShxZRb8PUmDKING6e/dS/BMlNPtwZTF2/nTbFeAWEqU1Xmna20YMXsthrz8Y6MfqOrsLpyu9a/mraZMVGj27t2LIUOGBJyfnp6O6urqSBwTIaQJwTNRvnKeS1zO06oUMPqaZKUBEssQmLQqfvZUS575Eq6WnrUTlr/2nPTODGQZUL1awffuNdYTZbY5cdt7v2DxpiNRPNLGfbuzXHQ6LcaDNoHEaSxf78uuclzjWbE/TppFp6ta6Iy5Zs2JOnDgQMD569atQ6dOnSJyUISQxml9q2B2nzTjlNkGwB9EsUwUK9UJe6KE5RfA/yKpUcn5cmCw7WFSlcvtwU/7K/iZWuFS+EZHtFTC8jDbm5FlnbRKBb9aq7GJ5a+W7sO6A2fwxGc7onikjZOWZWO9Mg8QbEAc5yBqT3kt/3+zreHAaN1+8e+MeqJC9Pe//x0PP/wwfvnlF8hkMpw4cQIfffQR/vGPf+CBBx6IxjESQiQ0vk/4n285DrPNhTYZOvQrzAQQOGxTp1YgraFynu8NT6NU8MM6mxtQJKN7Fv6G2+f+iv/+dLBZt1fKY9s3k2iEb7I2pwceD8dnnbQqOf932lg5T5rRiIfDlU33/0RbopTz2AIBILCHUohlrNj2OC21nBd2znLq1KnweDwYPnw4LBYLhgwZAo1Gg3/84x946KGHonGMhBAJVs5jXrvlAihk3qwIG3HAPv1rlHJ/T1QD5TyNUs5vG8MyCqnu5z/PYPXeCgDAT/srMGl415BuJyzhtfAYSlTOA7yZTRYwaVQKPmPaWGP58Wpr9A4wREckTdSVcVilylbnuT0cXG5PzBvbAe8HsN+PVfOnGwqiam1ObD3qvd7VfVvjo1+OtNhyXthBlEwmw7/+9S889thjOHDgAOrq6tCjRw8YjUZYrVbodLpoHCchRID1TzBZejUsvgySI0gmik0sb2hOlEYp58uBlhYSRK0Q9MHkpmlCvp2wr4wFri2V9O/J6nQLMlGKkBrLT1TboneAIXC4PDhZIw7kztTFfvsjteA57YhTEFVRaxc9VtLyP7Px4Fm4PRw6ZOvRq006gJabiWr2o6RWq9GjRw9cdNFFUKlUmD17Njp27BjJYyOENECaidJrFHxjOD/iwOXvTWm4sdxfzmNBVEvpidp3yt/7Ec7PXCXIUsS7fyXepD0zVqebz4BqlfImG8s5joPbE9/m/OPVVng4b+9gni+Y7ts2I+bHIQqi4vR3Jc1US8v/zLr93gzuJV1zkOnb4LylZqJCDqLsdjumTZuGCy+8EIMGDcIXX3wBAJg3bx46duyIV199FVOmTInWcRJCBKSZKINayX9y5ffOE2Si/CMOJOUXwSwpA99Y7sKDH23GfR/8ltKrz/af8u/3Jc2+cRwXkJ1ghKWeGmvLfONgpJkom9PtbyxXCRrLG8hEVQgyPvFq0melvHZZenxyXxHuHNQB//5bn5gfh1IuA0tsxiuIkj6eDZXz1vn6oS7pkssPVG2pjeUhl/OmT5+Od955ByNGjMDPP/+M66+/HhMmTMDGjRsxe/ZsXH/99VAoWt7Id0LiQSPJROlU/kyUdO88rUrO96YIXxR3Hq/BWt8KG2FP1CmzHct3eEtdx6utaJupj+JPEh+VdXZRMCTNRL2z9iBe/HYP/n1db9w4sJ3oMmEmqt7hjlv/SiIIyEQ53KLGcn57ogZ6og5W+Ic1chwHjuMgi3GJ9Ihv6nZhlh4dcgyYObZnTL8/I5PJoFbIYXd54jZwUzreJNjqvNNmG/6sqIdcBhR1zsaxKm8Q2lDWKtWFHER9+umnWLhwIcaOHYudO3eiT58+cLlc2L59e8z/6Alp6bSCTJROpYBcLoPK90bORhwIe1OkjeWVdXZc9Zp/mybh6jxhP8iZOkdKBlH7JbvOS5vpX/x2DwBg2uc7AoIo6dY4tTYXMg3qKBxl4pM2ltucbj67Ke6JCh5ECVfmeTjv3y77MBArhyr9mah40yi9QVS8VuhJy3nsQxfHcXjpu71ol6VHt4I0AECrdB3SdSpU1LIMeMssbYf88enYsWMYMMC7S3evXr2g0WgwZcoUCqAIiQNhJsrg23hYJVjd4/FwjU4s/3CjeLCht7Hce50KwRTikwmwcioa9vv6odpkeBfCNNQT5eGAQbN+wIY/K/nzpGWLYCW9j389gsEvrhL1XaUajuP4N9kMX1+MtyfKX87zZ6KCv8HuOiEebxCPDAwLqLvkGWP+vaXUcZ4VJc0mscf392M1eGv1n5j2+Q6+gTzT4H3M1Yrgx1xjcWL4K6vx0oo90T7suAo5iHK73VCr/Z+2lEoljMb4/9ER0hIJM1Es+FEKPsE73B4+Ne+dWO4LohwuON0efLDxsOj+NCo5H4wJ+1RO1sR35VS0nPD9XOf7PlULe6KkK7NO1Njw94W/8aely9+DlTymfr4Dx6utmPHlrogdc6KxOt181jM/zbttkKicp/SXkRvKRAUEUY1MNo8WFlCflx//9zNNnPfPky48YavzhBmqM7W+IMrXC6VSel93pNmzhRsO4c+Kery5+s+oHW8iCLmcx3Ec7rzzTmg03tULNpsN999/PwwGg+h6n3/+eWSPkBASQLg6j62qUwv6cg6crkOVxQmVQob22XrIfRljjgN++ON0QKCgUSrgUnvfEEWZqAaaq5PBkUoL/u/7vRg/qAMGtM8UXcayR619mSiLww2Ph4NcLgt4YwfEQUBlnSSIsjbcC5LKJQ6WpVDIZcjylTNtLo9g42sFnzG1BgmO7C43H8D4z4vt78tsc/IfFLrmp8X0ewejjvPWL9KeKOFjzBz19UCxIEotWNAi7GlrbNp5Kgk5iBo/frzo9G233RbxgyGEhEa4Os/gK9UpBS90q/eeBgD0b5cJvVoJjuOglMvg8nD4OMgeZd77CyznbT9ag4pae1hzlBKBy+3BkJd/BACcMtuw+L4i0eXSIAoALE43jBoldp2oCbg/nSBoPSEpcTa2Qk+Vwg3nLEth1Cih8wXyNod4dZ6en4IfGBTsP1UHl4dDuk4Fj8e78XWsgyi2QjPfpEF6HDYdlmJ/Z/EaeMsyTrlpGlTU2lFr9z7GbIAv4F/NyEYbqCTzrZpakZlqQg6i5s2bF83jIISEIVgmSvhp8UffJO5Lu+YA8K78aZ2hw5GzFn5Kd+t0LV/W0qjk/O2FWYNfD53F1a+tw7onLk+qFWjCDWWFO80zrCE636SBXObtfbLYXTBqlDhtDry+sAeNTdg2aZUw21yNfuJWKZPndxauOl8fmVGj5N/8xcM2/WMzgg1wZcFohxwDjldZfUFUbMt5/lJe/LNQAJBt9GZ3pNnOWGGZp1bpWm8Q5TstfE1gW+RkSDJRgDeDxoIo4W3iseoyVlL3GU5ICmN7kgHg36jYEmkA2Hy4CgBQ1DmHv94F7TL4/xs1SozsVeC/P6WCz2hJlZttje6hlYiE2SJ1kOCPZY/SdSr/fCzfXK1g/TusQdrj4fj7Pr+VCUDgCjVhKSbY904VrPRj0PhX4Ykay5UK6DVsCr63XCrE/qZMWqW/FyjG2Yttvq1LEiWIyjV6M77xmJgO+DNRrdK9PW7BgqijkkyU8G/cKchYCW8T7/0Aoyl1n+GEpDDWsAuAf6MCxM3lgP/FEPCW9pi/dMoWleiE274EI136nOiEL+BngwwBrLb4gyj2+2NBQbD+HRYknK61w+nmoJDL0N63JF7av1Jt9X+/FI6h+L8Jg0YJndr7g4rnRCn4ABUI/L2ycmCaVsl/KIhlOc/p9uC7Xd6M5eXd8mL2fRvDMlFngmRPY6GeD6K8ZW72GNkEm5KzhRVsrIdcLuNbCYTPBeEigVTe1DyFn+KEpK5g5TwgsAfHJOjzEDZXD+6SzTeGAo1nooD4BFEeD4f315Vhd5BG76YI+zGq6h0Bk9dZJipDrxKUnBrORLE98o5Xez+FF5i0/O9d+im7WrD9hSWF3zxYic6g9pfzbC7hnCjvsE1WxZH2+bAsR5pGxZeAYlnO23iwElUWJ7IMavylU1bMvm9jcuKdifI9Jm0zvUFUZb0Dn20+FrQcmyF4/WAN8cKFFGZB9jqVnwcURBGShISN5RqlMIjyZ6IUchk/QBPwL+cHvL1SLB0PeMuD0kzUPZd0RMcc7+rbWpsLjy/Zjme+3h25H6IJH286imeW7caVc34K+7bCQMjl4UQv6B4Px/cxmXQqPnj0Z6ICsyEsADhW5S3ltcnUNbiSSjTRPMkyeOFgPVHCcp60sVwmk/mDVMksLracPi0G5Tzhmzv721h/wDv764ru+QnT7+cPouLUE+V7TLrmp+GvF7QBxwEzv94V9DkhfP1gH96EmUTh8yBYdjdVJMZfDiEkLMJMlHBVnvB8k1YpauZUKuT4smQwFt51EbrkpYk+SQqHbTIGjZIf0rm33IxPfjuG99eXNTjzJ9JYXxcQ/pJv6TEKX9Br7S6wxFS6TuXfeNkXKAX7+dgnaRZEtc3wB1HSElRVC8lE1QvKeeKeKH8mCgC/cq/BTJRW1eDvMhLW7qvA+U+twIKfD+HbHSfRc8Z3WLzpCL8KtX1O/CeVMzlp8e6J8q+4nDnOu/1Nrc0VdAVqZpBMlPB5Kpzsn8rlvJBX5xFCEocwEyUXBFHZBjX/Rm8KsmS7b2EG//+Acp4kE2XQ+CedCz8Zm21OUbAWLcISwv7TtejZOj3k20o/+Z61ONAB3qwaawTXquSiMibLlAQLoljAwJrK22TqoJT73jjc0iDK/7tKtl6ycLDfiXh1nmBOlC9DalArUIHAN1JRTxQfREX+zXbhhkNwezjM+Mo/+PSJz3ZgaLdcAECOIXHGd+Swnqg4BVFscn+aVinqZztdGzh0N0OQifLPivI+FzweTvQ8SOUPE5SJIiQJCQMnYSYq2+h/Q2hq7o04HS/jNyBm9GolH2CcMvtfRKWr0aJFuL9dsAGYjWksEyVsKgcQUibK7vLA5fbwn65zjJqGy3mWllHOY2+4erV/TpRVUs5jlwP+1Y+MPxOlFPRERT4TlW/SBj2fPZZZCbTvIVudd7beAbdkNWMssJ4og0YpageokDS6K+Uy/gMWIMhE+YIos80J4eEH66lKFRREEZLk5IKSnfANwaRtPIgSlvM8HAe9SiFarmzQKJDm2y7mhGD7l5pGJnRHisPlwaEz9fzpcJvLpT0cwq1ahOMNAPBvBo2tzgO8QQALkDL0qgaDKGFjeUN78qUCfyZK4W8sl8yJAvx7O1oa2FIkTavyr86LQqm4oceTzWLKMiZOEJVlUEPmm1sm3eg62uwuNx8EsedEmu81RBpE5Zu0olYB9rrBngvSY49VC0A8UBBFSJITZ6IEQZSu8Wq9WinHjRcW4vJuueiUY4Rc7t0ihjGo/T1R5YLtX2KxnUPZmXp+XzYA+ONkmJkoh/iNvCpIEJWh8/6upJkSlkn515Xd0VWwKa3F4eIDpEy9OqTGcofbE7ctPKKtziHsifKNOHC6+WxSqJko0ZyoKPyuGppxxvaITKRynlIh58vssS7pCQN+loFie25Kg6gerU2i09L986SN8VTOI4QkLGlPFBPKNhb//lsfzJtwEX8fbDUe4Gss972InqyObTnvcGW96HRFmG8orLmZbeuy8WAlP+yRBVEmPhPlfcNgpQwWgA3vnofSRy7jf4/1dn8mKlOvhkYRvCfqsG8YIZOqpYxgjeXVglImO4/PRDXSWB7Ncl5dA0EUC24TKRMF+Et60sAl2li2SK2Q86sV2Yco6abbPSVBlDQTdUjy/KUgihCScC47z9sYe+0FbfjzsgWfqpsq5wXTKdefedGr/Y3lwt3dYxFEsZEErX3DQsPdBoM1MbfxBVE/7q3A7NJ9MNuc+HbnSQD+IDPd98mfBUgsAGN9PuxTeb3dxa+8a6icV293YesR/6pCIHWby1kjvnBOlLCUqfX9fnQq79/Q8h0nRSXaWDWWN/b71yjlAQsq4q3A9zdfXhPYzB1NLIAVLlph5Xwp6SIPlaSxvOyMOIhK5dV5FEQRkqTm3TkQu54eKdpEN0tUzmtGECXIRBkFIw6EzDHYAoa9wbbP9h5PjdUpmvXTFBYIje3bmj/vnbV/4qo56/DT/jNQKWR88Jll8P6eqi1OuNwefusKFhiwhvt7Fv7GB0yZhuDlvF/LzsLp5tAmQ8f3p6VqX1SdYNsXFnCy6fBKuYzPZrBM1MaDZzH0/1YDANweji/vGYUTy6MwJ4r9LWlVgW932QZ1wu3pxnYZOFFjbeKakcX+joVbSjUcREkyUZLnQlkFZaIIIQlOLpcFTBkX9nc0J4jqmOsPovQNBFHBZsZEGiv1FGbpwKqVVWE02lod3hfzXm3SsX1GMeQy775eR85a0DZTh0/vH4RLfJszZwgyUTZBQMSXoyQrlFQK76olVsKwC4K7dQfOAPAOM2XBg3Q+ktPtwZFKcckvGbGfy6hR8lsIsflb4on64r+hyjq7qMQW7dV5LNhbMOEiTBrWRbSHpHA1a6JgW64IS+ixwLKAwsUlwZ7/gHg7KcCfveKDKF8mqrPv9YSGbRJCkoIoE9XAp8jGdMgWBFGq4FvBxKKcx7IH6ToVn9GR9mU0xi7Yvy1dp0Jemv9F/+3bBqBfkHlZ1RanqOzA3hikv4MMvTd7ESwTtenQWQBAUeds/8bGknLSAx9uwZCXf8R6X8CVrIQ9Ua3Sdbjl4nb8ZcIgSlou23Kkml+coFZ6Z3VFs5zHAvI2mTo8UtwNFxT6tz9KpPEGDAtQTprjVM4TPHZGjfiD2Myre+Cnxy8PyN4Jy3luD4cyX08UK/tZU7QvEKAgipCUImwsb06ZIjdNgzsHdcAtF7dDpkEdNJ0fy0xUmlYQRIXRF8U++bKS3Nh+3rJemwwderUR93OweVlVFodoeT77/UlXd/G71/NBlPc2VoebH8UwoH1mwHYyzMo/TgEA5q4rC/nnSUT1gp4oAPjnld1xebdcdM414O+XduSvJ50/tuVIFZ8dYoF+tFbnOVwe/j7TfAHByJ75/OWJ2KvTKsMXRFXHtpzHSqmN9UQN7JiFwqzACe/CifMnqq1wuDxQK+T86tZULufRxHJCUogwAyDddDdUM8f25P8fvCcqlkGU0tcsX4fK+tBWKzndHn48AuuDeXh4V6RplLhuQNuA67NynsXh5gNEneD3uPdUrej6rGFfOmDw92PVcHk45Js0aJOh44OougZ6olxxGKYYKW4PxweqrGxp1Cgxb8JFAdcNyEQdrsLl3fIA+OcQsexHpHuihE3l7Dgv7pSNa/q1xhfbTmB497yIfr9IYOW82DeWs0nzDQdRugZ2KlAJVqr+WeEdkts+W+/fDSCFy3kURBGSYq7u2xq/HTqLYeef+xuEMUgmyhyDYZtmwSBGVqIMNRMlHOznX2avxEPDuwa9vknrnc7s9nD8G5cwGC0waXFEMLaAfaqWLuvecqQaANC/XSZkMhl0vgCuoUGDbk/yzo8S9nkFK/kKSTNRJ2ts/EpItkIyWuU81nulVytEmwzPvqEfxg/qENZWQrHCynm1dhdqbU4+0Iw2vrFcKSznSYKoBlYysg8UTheH/ae8QdR5+Wn8bgC2FM5EUTmPkBTz2s0XYN0TwyLy4hvvxvI0rRI5vnJeqBOc2bBMmUz8qbohMpkMGb4385O+FVHCT9yv3XwBLvftswb4ZyFJm2l3nqgBAL5xWbrsW3hdAHC5kyMTxXEc/rl0B2aX7uPPY+MNlHJZSL9jIYvDJdg+x/vYRqucx4Jx6d+xXC7DBe0y+Tf/RGLQKPky58kYZqPY714tykSJX0MaykTxHyjcbuzzZW675Bn5oCuVy3mJ9xdECDlnCnlklm1n6FWi1TpAbMp5rAyTplUiy7fiMNRyHt/XpFSE3BfGNlM9ESQT1bcwQ1SmYoNJpY3lx3zZKtacL92UFQCqreJp5slgy5EqLPrlCOb8sJ//WVkgnaZVNvk7lm73Umd3odI3PJX1u7HsR6S3B2F/R8EyqomsnW/ngAOC/SOjLVg5T/p7a2jjcT4T5eaw77QwE5X65TwKogghDdIoFRhyXq7oPLPVyU//jha2Os+kVfFb2VTUhlfOCzYXqCFshZ6/nBd42//c1A+ZehVe+lsfAIE9Ucd9jcBtMnWiy52CjJNwGGWs90ZrLuHmzyyQPV3r/T2x0QaNGd27Fdpm6nBVn1YAvJlCNi6CjRjgx0FEeKZWnWCBQjJhq0e3HK5q/IoRZA8yJ0qYwWsss8uP+3C6ccCXiTov3+jf3DtFB84CFEQRQppwRQ9xb5WHA6qjXNITlvPa+VYDrfzjFD7bfKzJ20pX5oWCNZef8AVCwXo/xvVrgy1PXYFBnb3zpfyZJg4Wh4vfL6xthvd4VZKeKUA86+pMjLf1aK6tvl4vADht9h4zC4KEoyMakq5T4afHL8f/Xd+XP+9olff3zFaTst6oSGc5a+2+jFkTfVuJpn877xiGLUdiGEQ5A3uihGNS8tI0DWYd2d/6oUoL6h1uqBQydMgx8IOAj1dZo/7BK14oiCKENGpUr1YwqBXokK3nX1SjuTmqy+3heyiMGiUu7ZqDv/qmi3+86UiTt2fL1rVhbOfBxhaU+2bzaJXBbyvauV7wqfzQGQt/vGzj52A9UVWCTFS9w52QS+ylhG/kLHg67fs3lEwU4P29aZRyvszMGvVZlpEFUZHut2OZqIaGRiYqFkTtPG6OyuysYFhGVZhtapWhg1GjhF6twIvX9Wnwtuy5sOO4ty+wU44RKoUcbTN1UMplsDrdOFUb29WGsUJBFCGkUek6FdY9MQxfP3QJ/6YZzSyKcFl6mlYFmUzGz3kKpUGVTR1vKBAKJtOXEWFTokMJwIRB1MEz3j6QNhk6PtDid7YXZKKEG/QC0Q1GI6HG6sRhwXR1Fjz5M1GhT/yWyWR8eYcFUazfjY2NsDjcYW3v0xSzIKOZTNpn65FlUMPh9mBfeWz6otiAWuHftVGjxKp/XIaN/xzOj6UIRqXw/q2zEjXbFkalkPOZZOlWMKmCgihCSJO8gzdVyPH1sJyJYj8PK+VplHL+BZ2V5kLZPoJldxpajh0My1SwT+OhBGDChnv2BtE2UxdweUOZKACoSPAgqlZSXmtuJorhf8++wJKV84RbFEUyG8WC1swEnEzeGJlMxgeosVgNCwTfgBjwlmyb2sxcepsegr31Ovr24zx4hoIoQkgLlxODTJRwRhSjC2PeDCt/hNNYrpcEXDp1aKMRWKDE9gprIwii/AMIhY3lkkxUgvdFSUcOsIbyijAay4Wkv2dWzlPIZXzfUiS3FTpb770vtnAgmWjC+OAQCfYgc6JCJR0VIZy/xYKoMgqiCCEtXS7LREUxg1JVz1bm+Usw7M03rExUGI3l0k1yQy0FsjcPtlcYa6QFgvdESVfkJfr8HOnIgXPNREkHcwr3rjNFoS+KDfXMMiTX6jwATQ5rjbRgIw5CpVI0konybUK8p9zc7F0UEhkFUYSQkLHyS7SCqBqrE498sg2Af1YO4J9PE0rQ0ZxP1NIMSVNTuBkWRLFVfcIeIdYn0lg5zxHh4ZKRFpiJCn91npDw95ymUYpXgkUhiGJBazJmosIpYUdCsBEHoRJmogqzdPxCAQDo0yYDALD+QCXm/HDg3A4yAcU1iJo1axYGDhyItLQ05OXl4ZprrsHevXsDrrdhwwYMGzYMBoMBJpMJQ4YMgdXq35xxy5YtuOKKK5CRkYHs7Gzce++9qKsTN+MdOXIEY8aMgV6vR15eHh577DG4XKk7u4KQaODLeWFsBhyOX8vO4nStHblpGsy82r+HH3tDsbs8TS6VZkFLONOopUFUqKu5WDnvlFk8PFL4/YVBVLnZ+7rFAqxYrbxqLuledhW1dticbr5vrbk9UQD47XyYdN+qxuhkopIviNLy+wkmfjlPmInq2Uq8lU7vtumYNKwLAODr30+cwxEmprgGUWvWrEFJSQk2btyI0tJSOJ1OFBcXo77eXzvdsGEDRo0aheLiYvz666/YtGkTJk6cCLnc9wnwxAmMGDECXbp0wS+//IIVK1Zg165duPPOO/n7cLvdGDNmDBwOB37++WcsWLAA8+fPx/Tp02P9IxOS1HKiXM6z+PZkOy/fiA6+XgpA3CRuayLwYM3hyjCmtkvLeeFmohj2+wGEe+t5gz6O4/gG9G4FaQAiv81JpLHfNQtCKmrt/AazWpVcVHINhfD3nC/JYvlnRTX/w+0psw2Pfbodvx+rBgCcrUveICrmmShn+B8+GOFtegpKecyIHvkAAqfXp4K4rvtcsWKF6PT8+fORl5eHzZs3Y8iQIQCAKVOmYNKkSZg6dSp/vW7duvH/X7ZsGVQqFd544w0+sHr77bfRp08fHDhwAF26dMH333+P3bt3Y+XKlcjPz0e/fv3w7LPP4oknnsDMmTOhViffE4yQeGB7nUWrIZqNN2isR8nqcAdcLuT0BS2qcDJRGkkmKsTgQPqGI3yzFu5sD3hLYfUONxRyGbrmpflmACV2EMXeWNtn62FxuGBzevDftQcBAIM754S8rQ5jEPyeW2U0EESdQybqpRV78dmWY/h08zHse240an1/T8kYRLHGcpszNn8j59ITpRFmotoEBlHs+VqXgkFUQvVE1dR4B3VlZWUBAE6fPo1ffvkFeXl5GDRoEPLz83HZZZdh3bp1/G3sdjvUajUfQAGATudt7mTX27BhA3r37o38/Hz+OiNHjoTZbMauXbuCHovdbofZbBZ9EdLSRXvEAdvY1iApr8kFG9029cnc5fF9olacSzkvxMZyRSNBFL+zvfd4DvqyUIWZOr6slfBBlO+NVa9WoEueEQDw1XZvSWaMbxuXcAiD34J0cRDFltGfSznvlNk/0JGthJTL0OQS/UQUt56o5pTzRJmo9IDLWfBscbhTrrk8YYIoj8eDyZMnY/DgwejVqxcA4OBB7yeemTNn4u9//ztWrFiB/v37Y/jw4di/fz8AYNiwYSgvL8fLL78Mh8OBqqoqPmt18uRJAEB5ebkogALAny4vLw96PLNmzUJ6ejr/VVhYGPkfmpAkI5zz44rCBrr1vnJesHIaP+agiTcVlvlhfUehMEjLeY1kuoSkgwmFG7SqJY3lbIl3xxwDf7tk6YnSKBU4L89bgvRw3uCRlWjCIXxcW6frRJfxU8stzQ+iOuT4FyMc8JUdM/VqftPoZKKN8eo8RwNzokLBgtR8kyboAFb2uLs8XNJsvB2qhAmiSkpKsHPnTnz88cf8eR7fJ8r77rsPEyZMwAUXXIBXX30V3bp1w/vvvw8A6NmzJxYsWIBXXnkFer0eBQUF6NixI/Lz80XZqXBNmzYNNTU1/NfRo0fP7QckJAUIV+5E48WQrb4LGkSxT+aOxr8vK+cpw8hESQdzNqcnKlvSKC0dcXDQ96beMcfIv1El/uo8f4mna34af/6Q83Kald0RZhilmah0ffD983afMIccSCgE5cV1+88ASL5Bm4xOFdqHhkg5l9V55+UbMePqHvh/N14QtMSrF3y4sER4k+l4S4ggauLEiVi2bBl+/PFHtG3blj+/VStvurhHjx6i63fv3h1Hjvj30LrllltQXl6O48ePo7KyEjNnzkRFRQU6deoEACgoKMCpU6dE98FOFxQUBD0mjUYDk8kk+iKkpROWr6QrtyLB3xMVWFIItbzh5DNRob+8STNPoa7OE35ql/bdSIdtHqpkmSg9XzJJ9HIe68fRqhQ4L9/In9+cUh4A6EPJRAnKect3nMSVc37CE5/9Lrqu1eHGez8dxB8nxW0WwhEY6w54g6hk7IcC/KvzmtMTtW7/GXy9PbyVcCxgDqcMzshkMkwY3BFFnbODXq5UyPnnSqr1RcU1iOI4DhMnTsTSpUuxatUqdOzYUXR5hw4d0Lp164CxB/v27UP79u0D7i8/Px9GoxGLFy+GVqvFFVdcAQAoKirCjh07cPr0af66paWlMJlMAQEaIaRhSoWcX/UWjQCArd4JVk7ThThw098TFXoJRzrdPOTGcsEbTrZBXMaQZqLYzKLcNK2/nBejpuHmEmaiurcyQS7z/q5GdA+/lAeIG5CljeXBeqKmf7kTAPDlNnFAsHzHSTz3zR8Y/Z+fsGZfBX++8G/j92O+HtsknBEF+PdvDHeTao7jcNvcX/DQ/7biWJWl6Rv48KXbMIbUhoNldxN9wGy44ro6r6SkBIsWLcKXX36JtLQ0vj8pPT0dOp13I8/HHnsMM2bMQN++fdGvXz8sWLAAe/bswZIlS/j7ef311zFo0CAYjUaUlpbisccew4svvoiMjAwAQHFxMXr06IHbb78dL730EsrLy/Hkk0+ipKQEGk14c04Iaek0SjlcDndU+nnqQyrnNf5J1tGMcp60BBHynChhOU+S8VArxT1RbOm+Saf0l/MSvD9EmIlqnaHD27cNgEmnEm3JEw5hFkIa3AQbttnQPDI23BQAPtx4GJedl+s73sC/yTxTcr7Ga31/I02N9JCqFfyOqy1OtM0M7XYN7Z0XKQaNAmfr/X2PqSKuQdRbb70FABg6dKjo/Hnz5vFzniZPngybzYYpU6bg7Nmz6Nu3L0pLS9G5c2f++r/++itmzJiBuro6nH/++XjnnXdw++2385crFAosW7YMDzzwAIqKimAwGDB+/Hg888wzUf8ZCUk1aqUc9Q53VDJR9SwTFWR1XKiZqOaU86RCfSMR9lJJh0fymSjf74lt5mvSqvi+k1gNUmwu6bL34p7B2x9CJczwSZu9peU8YRZFuLEzAFQKVocKN0kOluXo3io5WzF0zcxEVQoCT3cTg2mFHOcw4iAULLucaj1RcQ2iQl3qOHXqVNGcKKmFCxc2eR/t27fH8uXLQz42Qkhw3n4ep6gp2uHyQCmXnfMqKJaJCjYHShuksfxkjRWPLN6O2/7Snu/T4SeWh1HOkwp1/tFtf2mPz7ccBxD4Rq+WZJvMVl8mSqvyD+JM8ExUpLMT1/Rrg1/LzuLSrjkBl7Egqs7ugsfDYdnvJ/nLpPO4hEGUMHAKFmAHG/6YDPjG8jA/rJyt989wC6d05m8sj045j/U5plpPVFyDKEJI8uGzKL5PrjanG5f/32p0yDbgf/f+5Zzu298TFVpj+bz1h7DhYCU2HKzEmD5jAABOXyP3uWSiQtW/XSZ+evxy/LT/DK69oI3oMr6x3OWB0+3hj9ukU/JvVIneE8XKY5F6Y1Ur5fi/6/sGvczk2/aF44CzFgfmrz/EXyb9PQkDBeGbcrCszXmCVYXJhG8sDzMTJSyBWkIsnXEcxwdRzWksD4W/J4qCKEJIC6aRNEUfPWvByRobvyntuQhlxIGw70U4C+p0rQ15aVo+ExVOT9S5KMzS45aL2wWcr+Ybyzl+rznA22/FLkv4OVFR7pMR0igV0KrksDk9+HZnOcoFgzOlGTthyapeGEQFyURpo5RZiTY+iArzb+SsIEtXH2IAJvz9NmfEQShYOS/UY0oWCTHigBCSPKTL81kjq8vDnfPco7pQeqIcwiDK/xK23rek3dmMYZvRIFydx7YyMagV3uXeqiQp50V5xZYUK+kd8g0mbe2bJSX9uxKW8+oFPTYsCGerB4OVDZMFWzEafk+U/8NMU4swGGF/Y7QCZra1Un2KlfMoiCKEhEUjmbZdZ2u8nBIOlupvtCdKkG0QviCvP1AJAHD5ynnRKkuEigVxLg/HN0uzVW3SbF6iYlkQbQwyUYA/iDrty2qyFXvCjJ3Hw0myLS6+v5aVvqaO7oY3bumP12/pH5PjjobmDttsKMBsjDBIjVo5j28spyCKENKC+bcs8b7wCgMZi7P5L5De3iHvm2GjIw6EQZQgaGOruRwRWJ0XCcL9xNibPuv70Uh+h4kqXpmo075SHpsdJXyTN9ucolVnHOf/m2D/GjUqjOnTir+/ZNTcYZvCUmeo++4Js7fhbiodKvacpnIeIaRFkwYAwrk05zJITxiMBZ1YrvbNzXEEz0RV+/Zc8/dExbecJ/xEz7IDJj4T5f35En3bl1hnotjvh/XXpflGIng48Hs1ssbpNI0S7P2+zu7y7ufoC650SdoHJcR+BofbE9aoAlGWLsSsD9sqKZofPNhikVRrLKcgihASFmlPVKTKeWwIn1opD/pirvOVAxoq51VZvG8e/hEH4b28BVsReC6EPwPrU2FBgbQkmqjilomSBFGA/++NBQk5aRrR7CHh34V0L8RkJGyIF5b09pSbsXK3eBuz3SfM+NnXE3imLvwRB7HI3rItf+pSbE4UBVGEkLBIB0XWRSgTxa/Ma+ANkH0yF36POlEQ5QTHcXxPlCrM7MkH91yMPm3T8en9RWHdriEKuQxsbBafifIFCfwMqQTPREmHbUabSTArCoBoMrqDD6K8QUKWQc0vQKizu/gAXiGXxX1RQSQIf+fCAHHU//sJ9yz8DTuPe7e1MducGPPaT7jlvV+w71StKBMVataHbZUUk0wU9UQRQloyaTlP1BN1Dql6/7Ty4JNXWJbilGDpuzCgcri8s5ia+6m6f7tMfDXxEgzskBXW7RrDgqUzAZmo5NuAOBakPUx6jQIKXyTKHldWts3Uq/x9NnYXH2joVYqo9fXEklwu459rtiAfWHb4gqjFvx4Fm1v9xdbj4sbyED/UsHLeuQyobYq/J4qCKEJICybNokSuJ4pNKw/+ht27TToAYN+pWv7NRDr9uMri9PdEneP09EhggRxr9jVJVue5PFxY/S6xFss5UYA/E8VolAr/TC1fQMcCCq1KIZg95M9EaVOglMewsiT7mdnoB8BfIl706xH+vHnrD4n+nkLN+vAfPKL4OLOsodnqwie/HcWB07VR+16xREEUISQsjfVEnUsQZRbsLRdMQboWrdO18HDA70erAQQ2zlbVO/gVftKtQuKBBQBnGyjnAYld0mMl21gFUdJMlFYlnKnlm5DPB3YK/o253u6G1bcyNBWayhmtUrxC78+KOv6ygxX14DhOtMegdDVeqM/HSOw32ZR2WXoAwO6TZjy+5Hdc88bPUftesRT/VxlCSFIJmBMl2naj+al6NkupsWXp/dt7t6TfcqQKgD97xY6pyuKIyRtCqPyZqOCN5UBiN5ezQDlW5TyTVlzKFWWiXNJMlBxGYTnPt6diQ5nMZCTddLtMkIk6eKYedsFYkA7Z+oDbJ1IQ1THHKApwU2UPvfi/yhBCkkpAJipC5byQgqh23iBq29EacBzH91ewzX8Trpyn9B7DiRpvH1frDO9xKhVyvtcnUfuiPB6OL/PEKhMl7YfTKOUB5WNhYGfgV3y5+H68ZN3mJRitZOCmKIiqqOOztzIZ0K8wg7+sMMv7dxZq/1EkNu1uikIuw/mtknMfw8bQ3nmEkLD4V+dFtpzHB1H6hoMoFiydqbPD6nTzDbVtM/X4s6Ie1ZbEKudJP9lfIHijUyvksHrcCVnOe+br3aLTsQpMpFkkjVIesJDBJigxssn29YIRB6mUiRJu/bJwwyF8ue0Ef5nZ5sKRSm8pz6hW4rwCf4DSLT8NR89aGxw5wnEcZn27BwDwzyu7wxGDOVHsuLYeqY7q94g1CqIIIWFhb2osS1HXxAawodh5vAaHK72fshvLRLEl77U2J/99ZTKglW+PtbP1Dr6xNhHKecJZVZ1zDcjQq/nTGpUcVqc74cp5h87U4/31ZaLz4paJUimglgwmFWaijBrv/y2CxvJU6onit35xeTDnh/38+XKZdwDp5sPesnaaVonz8vxBVNf8NKz843SDwzYPV1rw7tqDAICHhnWJWQk806AWnfZ4OMgTIGN8LuL/KkMISSr8ti9B50SF3+ew/Wg1rnptHZbvKAfQVBDlfZOttbn4fiiDWsm/OLMhjUD8NyD2HoP/JZaVIhkWYIW7rUe0CX+HgPf3qIxRQBosEyUt5wkzUcJyHgvgU2l1HssAmq1OflL7Zw8MwnDfBsu/lJ0F4P1wcV6+P4jqlGMA0HBmePuxav7/ZpsrZlP+JwzqgHyThj9taeaHrkRCQRQhJCysJ6re4YLbw51zT9Q636RlprEgysRnolyCuVIKZOrZnmvCICr+L2/CQG5Ae3EQ5V91llhB1Mkaq+h0WgOrJaPBINl4WqtSBJTz7ILZVfyIA7v/78EYZPPqZMUyUUfPest2aoUc/dtloGdrEwBg40HvpttpWiVf6gaA7q28l7s8XEC52On24Fdf8AV4s7rNnfIfrjyTFhunDeeH0Ia6LU0iS52/NkJITLA3tfUHKnHtm+tFL9LN2fYlQ9IDFUomyup0w+zroTJolHyZTLjlRSIEURWC4xnWPU90Gd+gn2CZqGNV4iCKjRGIBel2LcKeKDbiQDhFnWWp6uwufl6ZUZs6b2ss0D7kK3XnmTSQyWTo2do7M419aEnTKiGXy/DZA0U4U+dAN0F/lMXhglrpfX54PByufm0d9pT7ZzSZrS443LErgctkMhg0StTaXKi1uZBvivq3jKrU+WsjhMSEsD/m92M1osuak4lSycUv3I0FUcI3yHLf5HKDWslnqNg8JrkM/Oq3eDp61h+Q5KVpRZexT/2JlomSBlFGTewyURqld9Ui62vTKOX+3xNfzvNnolgQVWN18gscjA1MvE9GLBN12NdAXmDy/g2xTBTDsoUD2vun7asVcjjcHtQ73MjwTT+otbtEARTgy0S5oj9sU3S8viAqFTJR8f+oRghJKo1tRtucTJS0j0qamRJSKeT8G8tJ39gAg0bBzxdi85gSIQsFAMPO92af7r+sc8Bl0j0IE8Xxakk5L4ZBiUwmE/VFaZQK/++Jbyz3z4nK8AXc1RYn/4aclkKZKNYTxTJR+b4gqlW6VvQ8CfYz630ZROHstmCzmWptLsHeebH54CHcrifZJcYrDSEkaTTWN9GcfbGkzaXSrT+k2BsGWyqdl6blb8P2CkuUIOrF63rj7dsG4IlR3QIu0wneIFftOQWOS4ztX44LJmADsS+PCfuiNKqGM1EapYJ/3Gus/tWaDe29mIz41Xm+n5kFUTKZDB2yDfz1gvWt6VX+ae4My9ZlG9QY3asAAOuJYnvnxXYVZioM3EyMVxpCSNJgmYFgmpWJsotv01g5D/AHUSv/OAUAGNQ5O+CTeCKszAO8Ad6oXgVBN8RlZacXlu/BXfN/wzc7Tsb68AJwHBeQiYp1UKLXCDNR/r6ngDlRKjn/t1JjdaI2Bct5WslzTbiyjW2jAjSUifKeJyyx1/qGcxq1Sv42ZpuLD1Bj9eHDmEKbEVMQRQgJS7CZQaz9qDk9UdLbsIbrhhgln7ov6ZoTsN9eomSiGiPNHny/6xTcHk7UHB9rNVZnwMiFWAclwnKesO/JLpkTpVEq+MGsdpcHlb5+uFRqLJcOOWWZKABoL9jmRbpdDgAYfL9HYbm8VlDyZH9/ZsHqvFg9b9hiBeGg3mSV+K80hJCEEizIyTF6PyHX2V1hl6XYxrGhEr5hdMwxoG2mPkgmKvFf2qTH7PJ4cN8Hv+HC51bij5PmuBxTtcUZcF6se4yEj513dZ542KZo7zy1kg/gT/gyaLHs4Yo26WrFPEEmqlCUiQrM3rLb1jsCy3lGjVI0LoQPopSxyeCyxQp19sTqB2yOxH+lIYQklGCr3roVpEGtlKPO7hLtNB+KcLNXwjf1C9plAPDuRSfMYCRKOa8x0uyB081h5R+nAQALNxyOxyHxW+8IxToTpRCUPjVKRaN758nlMr4viv0dpVJPlFbygSXXGHo5j/WWCRvL/SVPlb+cZ419T5RRw/q1KBNFCGlhsvTqgPNyjBoM7OAdJrlu/5mAyxvD3vzy0jT4+N6/NHn9NMGSe+GUZmFJLzkyUeLsgUsw6sAZp7EHwYKoWAclwm1AVAqZYBSE9+9EOLEcAL9Cj0mlnihpJkq4r6SwnCe9HuDviRI1ltu9j69J0BNVa3PxYzZiV86jxnJCSAuVrlfhm0mXoGuekT/PqFHiki65AAInkDeFNaNPu/J8/KVTdpPXF37qPi/ffwwmnf/85AiixG/2jjgFUb+WncXPf3ofs2BBVKzLY0pBECWTyUQbXnMcJ8pEAYELEVJrxEHDM9TyBXPHZAjMvLLVecKeKL6cJ+iJEs2JoiAqbKnz10YIiZmerdPRq0069p/2lu6MWiUGdfYGQGxT1FCxF3mdKrSXI2HZrqtg09U0USYq8ct50kyUcMuaWAVRdpcbN7yzAQCw8pEhqA5WzotxUCItFwuHktoF0/FZJko6EiOlynmCxnK9WiHqR5TLZXj0ivOw+6QZF3XMCrgtW+UoLJebhT1ROn8myt9YHqueqNSZE5U6f22EkJgSbgdi1Cj5ptfaMFfcsBd56eazDWGrsACgTYZ/vzBhj1EyZqLYQEUAAfudRUtlnf93Of/nQ2iV7v19GtQKviE51kGJUhJEsWDpy20nRLORgmWiNEp5Ujz2oRIGUdKyJQA8NLxrg7dlPVHCIKqOX52n4svfZsGcqFiPOEiFTFTq/LURQmJK+OZq1Cih92WSgm162hirM7wgSvh9hf0zaUnXExXYWM4EWyUXDcIg6rPNx/nxCq0FwWnMG8sb2a7nPz/s56/DHmNhEJVKpTzAP2wTANKD9CI2elt1YPO2uJxHPVGRkFp/cYSQmBFOljZqlKLmVqvDza+qagr7pBysOTaY+4Z0wsGKelx/YVvR+aKeqBjtAXYugi1LZ4TZtmiqrPeXEK1ON4749mhrk6njS7WxDkykQVRBuj+gU8plcHk40awyYRCVSk3lQNOZqMbwc6IEOwLU+hrL0wQjDiwON9+sH6tyHvubojlRhJAWS5SJ0iqhVsr5UowljNlPrLFcGJQ1JtuowXvjL8TIngWi80Wr8xJg8+GmBBuQyFTGaODmWUmwxqaVJ1Imami3XIzp3QqAN8sJSIILwYq1VBq0CYgzUY3tKRmMnpXzgmWiNErR74r9HYT6wedcCbNgyY6CKEJIsxgFPVFsBZdOHdjM2hiO4/jG8lDLeQ0RZnakk54TUWOZKOFWHNEkLOcBwLEqbxAlnEcU656owky96LRKIccDQ8UbOAszUd1bmfj/J8j2gxEjXJ0XbjDLGsuFwzaFE8uFm3mzICpW5TzhysBkl1phOyEkZoRvruz/erUCtTZXyHvo2V0e+JILIZfzGlKQ7n/jv72o/TndVyxIl69LVVkcom0+okFaNmQ9Kh1y/IFMrDNRDw3vinKzDWP7tubPkwZywiB5cOcc/v+7TsRn0nu0CH/OcJ8f/mGbwr3z/D1RgDeYsjrd/N9B7IIotneeG24P12gfXKKjIIoQ0iyinigtC6KUAOwhZ6KE19OHWM5ryOherWB1eFDUORsdcwxN3yDOgm1KLHSmzh79IKqBsmGHbAPmTRgIrVIR8zc4o0aJ/9x0geg84UpQQJyJkstl+Pd1vfHEZzswaViXmBxjrAh/zmB7VjbGv+1LYDmPDaw16VQ4XWsXbEAc254owBu4N7XpeCKjIIoQ0izC8htfzgsy4K8x7Hpqpfyc36y1KgVuubjdOd1HIpH2K8Xye6TrVLigXWbUv3+opNkwjaRce+PAdrikay7y0zRIJcJAO9wSNT/iwO7GN7+fRJ3dya+ETRNkooRite0L287H4fKg1uakIIoQ0vIIgx5WbmEZg1DLedYwZ0SlKoVcBrdH3NAT7p6CzXFG0FAs7MFKtDc1nUoBmczf86QNkpURzgxLReFmolhPVLnZhpJFW/jzVQoZ//hK+/JiuarVpFXiTJ0j6ZvLqbGcENIswiCKBUG6IAP+GsMP2kyCRvBoGNkzHwDw7LheAZfZnNEPos76Rhx0EOzDJpMlXhAlk8lE5WNpJqolkE5mb0pDH0wK0rX8fDVpJiqW89X8zeXJHURRJooQ0ix92mbg0q45aJup58sOwfbraky4M6JSzZu3DsDZegf0agX+uXSH6DK7M/qr8876Vue1zzZg3ynvXKhsgxrKBBxWatAo+Mb3xsZDpJpJw7pgzf4z+NuAtk1fWaChHsNW6cIp/5JMVAy3S/KPOUjuFXot5y+REBJRCrkMH9x9seg8fZgjDuwu7/WSYSRBNCjkMuQ20Mdjc0U3E+Vwefjl78KxArlp0W1mby5vydibOcsxplbvU2MeKe6GR4q7hX27hjJRrdL9j680GI1VTxQQOCuqvMaGO+f9ituL2uPWixN/dS2TeB83CCFJK9w5UawPJ9x+j1Q0rl9rqBQy9C3MABD9cp5dEKTlpPm3FGkoqIs3YXN5oh5jIlEp5OjeyoQ0jRKdc/2rVYWZqLiW8zTiWVHPL/8De8pr8a+lO2N2DJFAr1yEkIhhn36tIQYAdl8QFatJyYns/93YD5ufugI9WqUBAGxRLucJG8mzDf4gKi9BAxRhZiXHGN4+ci3V0gcHYdOTI3DPpZ3481pn+DNR8WwsZ2NRzHwmyhqz7x1JVM4jhESMv7E8tJ4oO5+JapnlPCGZTAaTVsX/LqKdiWKbzqoVclFvTKIGUcJMVEsq550LViYXrlwsEMweE+43CcR2uyR+/zxfn1uyNpjTxz9CSMQ0tyeKynl+7I0v2pko1riuVspF+6glaqnMQEFUs7XN9AdRwn0RWUmNic/qPG85r85OQRQhpIXjy3mhBlG+N/KWuGS9IWw7mKg3lrsFQZQgQMlL0MZyUTkvQQO9RCUMnIRT8AN6omI8JwrwZ6CSNYiich4hJGL8E8vD64miTJSfPxMV/dV5gLecJ+yNSdRMlEeQmBP2cJGmaVUKvHVrf1idbtHjK509FZ8RB8ldzqMgihASMfogm542xkGN5QHYNO5oz4niS6kqaSYqMYMo4WKFljoS41yM7t0q4DxhJqpTriGmIw5YH15lnR0cx4km9ns8HD8QNNHRKxchJGLYVhMWZ6iN5dQTJRWrTJRdkIkSNhgnaqksFtvgtDSZen9G7/lreje5KXYk9W6bDgDYcbwGhyotostCXd2bCCgTRQiJGH2zy3mUWWD4ICoGwzYBbxZQr1bi3dsHQCaTBWz2S1KXQaPE3PEXQiYDijpnx/R7t83Uo19hBrYdrcbCDYdEl1mdbtFCgkSWHEdJCEkK4ZbzKBMVKGar8yT9aMU9C6L6/c7V1NHdsPVIFe6/rHO8DyWlDO+eH7fvPaZ3K2w7Wo156w+Jzg/19SMR0CsXISRiWDkv1JU2/tV59FLEsNV50X4jSbZ+tC55afjtyRH4+5BOTV+ZJIXrBrRFpj5wY+VkKuclx7OHEJIUWI9Frc0Fp7vpTIpw4CPxin05L3lKqbHs2SHRl2VQ4/lre0MuA9pl+fdvpEwUIaRFStepwN7nqi1N785Oc6ICsSAq+qvzKIAl8Xdl71ZY+/jlKH1kCLrkGQEk1yICevYQQiJGIZfx2agqi6PJ61NPVCB+2GbU50T5RxwQEk9tM/XQKBX8nLlo/+1HEj17CCERxXocKutCCaJo2KaUNsZ752koE0UShC7MDcwTAT17CCERlWVoPBPl8XB4acUe/PDHKRpxEIS/Jyp2e+cRkgjC3fEgEdCIA0JIRLFy3tn64EHUl9uP483VfwIAerUxAaBMlBAr57k9HJxuT9Q2heUzUfS7JwlCT5koQkhLx2eiGgii9pys5f/voHJeAOGWJtEs6SXbiAOS+lgmyupInn306NlDCIkoFkSdbaCcV2P1r9rjy3nU3MwTBpTRHLhppyCKJBgty0Q5olvKjiR69hBCIooPohrIRAlHH7BMC/VE+clkMj6QimYmyj/igH73JDGwbaOonEcIabGa6okSZqLY/6mcJ8bPioriwE0HZQFJguFX51E5jxDSUjW1Oq/aKsxEUUkpGP+sqMiWNd5d+yde/HYPAH+ARsM2SaKgEQdhmjVrFgYOHIi0tDTk5eXhmmuuwd69ewOut2HDBgwbNgwGgwEmkwlDhgyB1WrlL9+3bx/GjRuHnJwcmEwmXHLJJfjxxx9F93HkyBGMGTMGer0eeXl5eOyxx+ByJU+0S0iyyGTlvAbmRJXXWAPOo3KemDYKQwddbg9eWL4Hb6/5EwdO11FjOUk4yTjiIK7PnjVr1qCkpAQbN25EaWkpnE4niouLUV9fz19nw4YNGDVqFIqLi/Hrr79i06ZNmDhxIuRy/6FfddVVcLlcWLVqFTZv3oy+ffviqquuQnl5OQDA7XZjzJgxcDgc+Pnnn7FgwQLMnz8f06dPj/nPTEiqS9d5h23W2gI/pNicblQF2Q6GynlibOBmJD+RC8uotTYnjTggCYeNOEimieVxnRO1YsUK0en58+cjLy8PmzdvxpAhQwAAU6ZMwaRJkzB16lT+et26deP/f+bMGezfvx9z585Fnz59AAAvvvgi3nzzTezcuRMFBQX4/vvvsXv3bqxcuRL5+fno168fnn32WTzxxBOYOXMm1Gp1DH5aQloGg8b7QljvcIHjONGmsSdrbEFvQ305Ykat96W53h65bLkweK22OmnYJkk4WmosPzc1NTUAgKysLADA6dOn8csvvyAvLw+DBg1Cfn4+LrvsMqxbt46/TXZ2Nrp164aFCxeivr4eLpcL77zzDvLy8jBgwAAA3mxW7969kZ+fz99u5MiRMJvN2LVrVwx/QkJSn0HtDQA8nLenZ0+5GSt2nsRpsw2HztQHvQ315YixbJ7ZGrkgqlrQo1ZZ56BMFEk4XfPScM8lHTGmd+t4H0rIEmZiucfjweTJkzF48GD06tULAHDw4EEAwMyZM/F///d/6NevHxYuXIjhw4dj586d6Nq1K2QyGVauXIlrrrkGaWlpkMvlyMvLw4oVK5CZmQkAKC8vFwVQAPjTrOQnZbfbYbfb+dMswDObzZH9wQlJMR4PB4/dAgDYfvAEbv7vL3B7OHTM0WNM79b8ZYxCLoOlvi4eh5qwNB4bPHYLys+chdmcHpH7PHb6LP+7P376DOpra+GxW+C01dPrGkkIbY3ApCFtAUT2vZbdF8dxEbtPHpcg7r//fq59+/bc0aNH+fPWr1/PAeCmTZsmum7v3r25qVOnchzHcR6Phxs7diw3evRobt26ddzmzZu5Bx54gGvTpg134sQJjuM47u9//ztXXFwsuo/6+noOALd8+fKgxzNjxgwOAH3RF33RF33RF32lwNeff/4ZybCF4ziOS4hM1MSJE7Fs2TKsXbsWbdu25c9v1aoVAKBHjx6i63fv3h1HjhwBAKxatQrLli1DVVUVTCbvPlxvvvkmSktLsWDBAkydOhUFBQX49ddfRfdx6tQpAEBBQUHQY5o2bRoeeeQR/nR1dTXat2+PI0eOID09/Rx/YnIuzGYzCgsLcfToUf4xJ/FBj0XioMcicdBjkVhqamrQrl07vlUokuIaRHEch4ceeghLly7F6tWr0bFjR9HlHTp0QOvWrQPGHuzbtw+jR48GAFgs3vS0cLUeO+3xeGv+RUVFeP7553H69Gnk5eUBAEpLS2EymQICNEaj0UCj0QScn56eTk+KBGEymeixSBD0WCQOeiwSBz0WiUUaJ0RCXIOokpISLFq0CF9++SXS0tL4/qT09HTodDrIZDI89thjmDFjBvr27Yt+/fphwYIF2LNnD5YsWQLAGyBlZmZi/PjxmD59OnQ6Hf773/+irKwMY8aMAQAUFxejR48euP322/HSSy+hvLwcTz75JEpKSoIGSoQQQgghTYlrEPXWW28BAIYOHSo6f968ebjzzjsBAJMnT4bNZsOUKVNw9uxZ9O3bF6WlpejcuTMAICcnBytWrMC//vUvDBs2DE6nEz179sSXX36Jvn37AgAUCgWWLVuGBx54AEVFRTAYDBg/fjyeeeaZmP2shBBCCEktcS/nhWLq1KmiOVFSF154Ib777rtG76N9+/ZYvnx5WMcnpNFoMGPGDMpcJQB6LBIHPRaJgx6LxEGPRWKJ5uMh40KNZAghhBBCCI+mrBFCCCGENAMFUYQQQgghzUBBFCGEEEJIM1AQRQghhBDSDBREheCNN95Ahw4doNVqcfHFFwdMPyfnbu3atbj66qvRunVryGQyfPHFF6LLOY7D9OnT0apVK+h0OowYMQL79+8XXefs2bO49dZbYTKZkJGRgbvvvht1dbQnW7hmzZqFgQMHIi0tDXl5ebjmmmsCBt7abDaUlJQgOzsbRqMR1113Hb8LAHPkyBGMGTMGer0eeXl5eOyxx+ByRW5D3ZbgrbfeQp8+ffihjUVFRfj222/5y+lxiJ8XX3wRMpkMkydP5s+jxyM2Zs6cCZlMJvo6//zz+ctj+ThQENWExYsX45FHHsGMGTOwZcsW9O3bFyNHjsTp06fjfWgppb6+Hn379sUbb7wR9PKXXnoJc+bMwdtvv41ffvkFBoMBI0eOhM1m469z6623YteuXSgtLeW3Ebr33ntj9SOkjDVr1qCkpAQbN25EaWkpnE4niouLUV9fz19nypQp+Prrr/Hpp59izZo1OHHiBP7617/yl7vdbowZMwYOhwM///wzFixYgPnz52P69Onx+JGSVtu2bfHiiy9i8+bN+O233zBs2DCMGzcOu3btAkCPQ7xs2rQJ77zzDvr06SM6nx6P2OnZsydOnjzJf61bt46/LKaPQ8R340sxF110EVdSUsKfdrvdXOvWrblZs2bF8ahSGwBu6dKl/GmPx8MVFBRwL7/8Mn9edXU1p9FouP/9738cx3Hc7t27OQDcpk2b+Ot8++23nEwm444fPx6zY09Fp0+f5gBwa9as4TjO+7tXqVTcp59+yl/njz/+4ABwGzZs4DiO45YvX87J5XKuvLycv85bb73FmUwmzm63x/YHSDGZmZnce++9R49DnNTW1nJdu3blSktLucsuu4x7+OGHOY6j50UszZgxg+vbt2/Qy2L9OFAmqhEOhwObN2/GiBEj+PPkcjlGjBiBDRs2xPHIWpaysjKUl5eLHof09HRcfPHF/OOwYcMGZGRk4MILL+SvM2LECMjlcvzyyy8xP+ZUUlNTAwD85p2bN2+G0+kUPR7nn38+2rVrJ3o8evfujfz8fP46I0eOhNls5rMoJDxutxsff/wx6uvrUVRURI9DnJSUlGDMmDGi3ztAz4tY279/P1q3bo1OnTrh1ltvxZEjRwDE/nGI68TyRHfmzBm43W7RLxoA8vPzsWfPnjgdVcvD9lQM9jiwy8rLy/nNpRmlUomsrCz+OiR8Ho8HkydPxuDBg9GrVy8A3t+1Wq1GRkaG6LrSxyPY48UuI6HbsWMHioqKYLPZYDQasXTpUvTo0QPbtm2jxyHGPv74Y2zZsgWbNm0KuIyeF7Fz8cUXY/78+ejWrRtOnjyJp59+Gpdeeil27twZ88eBgihCSINKSkqwc+dOUb8Bia1u3bph27ZtqKmpwZIlSzB+/HisWbMm3ofV4hw9ehQPP/wwSktLodVq4304Ldro0aP5//fp0wcXX3wx2rdvj08++QQ6nS6mx0LlvEbk5ORAoVAEdPWfOnUKBQUFcTqqlof9rht7HAoKCgKa/V0uF86ePUuPVTNNnDgRy5Ytw48//oi2bdvy5xcUFMDhcKC6ulp0fenjEezxYpeR0KnVanTp0gUDBgzArFmz0LdvX/znP/+hxyHGNm/ejNOnT6N///5QKpVQKpVYs2YN5syZA6VSifz8fHo84iQjIwPnnXceDhw4EPPnBQVRjVCr1RgwYAB++OEH/jyPx4MffvgBRUVFcTyylqVjx44oKCgQPQ5msxm//PIL/zgUFRWhuroamzdv5q+zatUqeDweXHzxxTE/5mTGcRwmTpyIpUuXYtWqVejYsaPo8gEDBkClUokej7179+LIkSOix2PHjh2iwLa0tBQmkwk9evSIzQ+SojweD+x2Oz0OMTZ8+HDs2LED27Zt478uvPBC3Hrrrfz/6fGIj7q6Ovz5559o1apV7J8XYbfFtzAff/wxp9FouPnz53O7d+/m7r33Xi4jI0PU1U/OXW1tLbd161Zu69atHABu9uzZ3NatW7nDhw9zHMdxL774IpeRkcF9+eWX3O+//86NGzeO69ixI2e1Wvn7GDVqFHfBBRdwv/zyC7du3Tqua9eu3M033xyvHylpPfDAA1x6ejq3evVq7uTJk/yXxWLhr3P//fdz7dq141atWsX99ttvXFFREVdUVMRf7nK5uF69enHFxcXctm3buBUrVnC5ubnctGnT4vEjJa2pU6dya9as4crKyrjff/+dmzp1KieTybjvv/+e4zh6HOJNuDqP4+jxiJVHH32UW716NVdWVsatX7+eGzFiBJeTk8OdPn2a47jYPg4URIXgtdde49q1a8ep1Wruoosu4jZu3BjvQ0o5P/74Iwcg4Gv8+PEcx3nHHDz11FNcfn4+p9FouOHDh3N79+4V3UdlZSV38803c0ajkTOZTNyECRO42traOPw0yS3Y4wCAmzdvHn8dq9XKPfjgg1xmZian1+u5a6+9ljt58qTofg4dOsSNHj2a0+l0XE5ODvfoo49yTqczxj9Ncrvrrru49u3bc2q1msvNzeWGDx/OB1AcR49DvEmDKHo8YuPGG2/kWrVqxanVaq5NmzbcjTfeyB04cIC/PJaPg4zjOK7ZOTRCCCGEkBaKeqIIIYQQQpqBgihCCCGEkGagIIoQQgghpBkoiCKEEEIIaQYKogghhBBCmoGCKEIIIYSQZqAgihBCCCGkGSiIIoSQcyCTyfDFF1/E+zAIIXFAQRQhJOFVVFTggQceQLt27aDRaFBQUICRI0di/fr18T40QkgLpoz3ARBCSFOuu+46OBwOLFiwAJ06dcKpU6fwww8/oLKyMt6HRghpwSgTRQhJaNXV1fjpp5/w73//G5dffjnat2+Piy66CNOmTcPYsWMBALNnz0bv3r1hMBhQWFiIBx98EHV1dfx9zJ8/HxkZGVi2bBm6desGvV6Pv/3tb7BYLFiwYAE6dOiAzMxMTJo0CW63m79dhw4d8Oyzz+Lmm2+GwWBAmzZt8MYbbzR6vEePHsUNN9yAjIwMZGVlYdy4cTh06FBUfjeEkPiiIIoQktCMRiOMRiO++OIL2O32oNeRy+WYM2cOdu3ahQULFmDVqlV4/PHHRdexWCyYM2cOPv74Y6xYsQKrV6/Gtddei+XLl2P58uX44IMP8M4772DJkiWi27388svo27cvtm7diqlTp+Lhhx9GaWlp0ONwOp0YOXIk0tLS8NNPP2H9+vUwGo0YNWoUHA5HZH4hhJDEcY6bKRNCSNQtWbKEy8zM5LRaLTdo0CBu2rRp3Pbt2xu8/qeffsplZ2fzp+fNm8cBEO30ft9993F6vZ6rra3lzxs5ciR333338afbt2/PjRo1SnTfN954Izd69Gj+NABu6dKlHMdx3AcffMB169aN83g8/OV2u53T6XTcd999F/4PTghJaJSJIoQkvOuuuw4nTpzAV199hVGjRmH16tXo378/5s+fDwBYuXIlhg8fjjZt2iAtLQ233347KisrYbFY+PvQ6/Xo3Lkzfzo/Px8dOnSA0WgUnXf69GnR9y4qKgo4/ccffwQ9zu3bt+PAgQNIS0vjM2hZWVmw2Wz4888/z/XXQAhJMNRYTghJClqtFldccQWuuOIKPPXUU7jnnnswY8YMDB06FFdddRUeeOABPP/888jKysK6detw9913w+FwQK/XAwBUKpXo/mQyWdDzPB5Ps4+xrq4OAwYMwEcffRRwWW5ubrPvlxCSmCiIIoQkpR49euCLL77A5s2b4fF48Morr0Au9ybXP/nkk4h9n40bNwac7t69e9Dr9u/fH4sXL0ZeXh5MJlPEjoEQkpionEcISWiVlZUYNmwYPvzwQ/z+++8oKyvDp59+ipdeegnjxo1Dly5d4HQ68dprr+HgwYP44IMP8Pbbb0fs+69fvx4vvfQS9u3bhzfeeAOffvopHn744aDXvfXWW5GTk4Nx48bhp59+QllZGVavXo1Jkybh2LFjETsmQkhioEwUISShGY1GXHzxxXj11Vfx559/wul0orCwEH//+9/xz3/+EzqdDrNnz8a///1vTJs2DUOGDMGsWbNwxx13ROT7P/roo/jtt9/w9NNPw2QyYfbs2Rg5cmTQ6+r1eqxduxZPPPEE/vrXv6K2thZt2rTB8OHDKTNFSAqScRzHxfsgCCEkEXXo0AGTJ0/G5MmT430ohJAEROU8QgghhJBmoCCKEEIIIaQZqJxHCCGEENIMlIkihBBCCGkGCqIIIYQQQpqBgihCCCGEkGagIIoQQgghpBkoiCKEEEIIaQYKogghhBBCmoGCKEIIIYSQZqAgihBCCCGkGSiIIoQQQghphv8Pv5sGHMZgdAAAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"var = 7\n",
"plt.plot(data_dict['02'][:,var-1])\n",
"plt.xlabel('Sample')\n",
"plt.ylabel('Reactor pressure (kPa)')\n",
"plt.title('Faulty operation')\n",
"plt.ylim(2680, 2730)\n",
"plt.xlim(0,500)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "PYB_QlHG3ezT"
},
"source": [
"The disturbance is apparent! The pressure in the reactor increases and then slowly comes back due to the control system that it has. This univariate method for process monitoring is closely related to the so-called [Shewhart charts](https://en.wikipedia.org/wiki/Shewhart_individuals_control_chart).\n",
"\n",
"\n",
"However, this method ignore the correlation between the process variables. In other words, some faults required the use of multivariate statistics because the fault might not become evident in the univariate cases of all process variables (i.e., all process variables individually might appear to be within normal ranges), but rather in the combination of several of them."
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "jLFU061Vb4GM"
},
"source": [
"### $T^2$ and $Q$ indices\n",
"\n",
"Let's consider the above matrix of observations $X$. The sample covariance matrix is\n",
"\n",
"$$\n",
"S = \\frac{1}{n_d-1}X^TX\n",
"$$\n",
"\n",
"and the eigenvalue decomposition of this matrix is\n",
"\n",
"$$\n",
"S = V \\Lambda V^T \n",
"$$\n",
"\n",
"if we assume that $S$ is invertible and using the definition\n",
"\n",
"$$\n",
"\\bf{z} = \\Lambda^{-1/2}V^T\\bf{x}\n",
"$$\n",
"\n",
"we can define the [Hotelling's $T^2$ index](https://en.wikipedia.org/wiki/Hotelling%27s_T-squared_distribution)\n",
"\n",
"$$\n",
"T^2 = \\bf{z}^T\\bf{z}\n",
"$$\n",
"\n",
"The $T^2$ index is a measure of how different an observation $\\bf{x}$ is from the mean of the multivariate distribution. It takes into account the direction of the data and the variability along different directions. This allows a scalar threshold to characterize the variability of the data in the entire observation space. By comparing the $T^2$ index to a threshold value, we can determine if the observation is significantly different from the expected conditions and in this way use it for detecting faults. This threshold value can be determined automatically based on the level of significance we choose, using probability distributions. One significant threshold can be calculated as\n",
"\n",
"$$\n",
"T^2_\\alpha = \\frac{(n_x)(n_d-1)(n_d+1)}{n_d(n_d-n_x}F_\\alpha (n_x, n_d-n_x)\n",
"$$\n",
"\n",
"with $F_\\alpha$ being the upper 100$\\alpha$% critical point of the [F-distribution](https://en.wikipedia.org/wiki/F-distribution) with the indicated degrees of freedom.\n",
"\n",
"Heuristically, the required number of observations to use $T^2$ as a process monitoring tool is approximately 10 times the dimensionality of the input space. This motivates the use of dimensionality reduction in the context of process monitoring. \n",
"\n",
"Another important reason for employing dimensionality reduction techniques, perhaps the most significant one, is that the $T^2$ index may not accurately represent the behavior of the process in the directions corresponding to smaller singular values. The inaccuracies in these smaller singular values have a substantial impact on the calculated $T^2$ index due to the inversion of their squared values. Moreover, these smaller singular values are susceptible to errors since they often possess low signal-to-noise ratios. Consequently, it is advisable in such cases to retain only the eigenvectors associated with the larger singular values when computing the $T^2$ statistic.\n",
"\n",
"This sensitivity of the $T^2$ statistic to the smaller singular values also motivates the use of the $Q$ index which can be computed as\n",
"\n",
"$$\n",
"Q = R^TR\n",
"$$\n",
"\n",
"where $R=X-\\hat{X}$ is the residual matrix measuring the discrepancy between the observation in the original space and the observation reconstructed from the reduced space (i.e., the observation reconstructed using the reduced number of principal components). If a data point has a large $Q$ value, it suggests that the model is not able to adequately explain that observation, indicating an unusual pattern in the data. The threshold used for $Q$ is given by\n",
"\n",
"$$\n",
"Q_\\alpha = \\theta_1 \\left( \\frac{h_0 c_{\\alpha} (2\\theta_2)^{1/2}}{\\theta_1} + 1 + \\frac{\\theta_2 h_0 (h_0-1)}{\\theta_1^2} \\right)^{1/h_0}\n",
"$$\n",
"\n",
"where $\\theta_i = \\sum_{j=n_x+1}^{n_x}\\lambda_j^{2 i}$ and $h_0=1-\\frac{2\\theta_1 \\theta_3}{3 \\theta_2^2}$\n",
"\n",
"Since $T^2$ and $Q$ detect different types of faults, they are both used together as process monitoring tools!\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "bC8FMNnIVXqG"
},
"source": [
"### Fault detection\n",
"\n",
"Let's now jump into using these two indices for fault detection. We are going to consider here Fault 1 which is caused by an step change in the $A/C$ feed ratio in stream 4. This results in a decrease in the $A$ feed in the recycle stream 5 and the control system reacts to increase the $A$ feed in stream 1."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 507
},
"id": "6ue_-LcOZNHF",
"outputId": "f4dbf6ff-2eca-4ddc-b7c7-924349161b31"
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"var = 1\n",
"\n",
"fig, axs = plt.subplots(1, 2, figsize=(10, 5), sharey=True)\n",
"\n",
"ylabel = 'A Feed (stream 1) [kscmh]'\n",
"ylim = [0, 1]\n",
"\n",
"axs[0].plot(data_dict['00'][:,var-1])\n",
"axs[0].set_xlabel('Sample')\n",
"axs[0].set_ylabel(ylabel)\n",
"axs[0].set_title('Normal operation')\n",
"axs[0].set_ylim(ylim[0], ylim[1])\n",
"axs[0].set_xlim(0,500)\n",
"\n",
"axs[1].plot(data_dict['01'][:,var-1])\n",
"axs[1].set_xlabel('Sample')\n",
"axs[1].set_ylabel(ylabel)\n",
"axs[1].set_title('Faulty operation')\n",
"axs[0].set_ylim(ylim[0], ylim[1])\n",
"axs[1].set_xlim(0,500)\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "x5sciofecH8f"
},
"source": [
"This control response results that the concentration of $A$ in stream 6 reaches steady-state after enough time "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 507
},
"id": "pnr6iH-a2Ncp",
"outputId": "21e6cbf8-9456-4338-a8ae-62d198b031f7"
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"var = 23\n",
"\n",
"fig, axs = plt.subplots(1, 2, figsize=(10, 5), sharey=True)\n",
"\n",
"ylabel = 'Concentration of A in stream 6 (% mol)'\n",
"ylim = [28, 35]\n",
"\n",
"axs[0].plot(data_dict['00'][:,var-1])\n",
"axs[0].set_xlabel('Sample')\n",
"axs[0].set_ylabel(ylabel)\n",
"axs[0].set_title('Normal operation')\n",
"axs[0].set_ylim(ylim[0], ylim[1])\n",
"axs[0].set_xlim(0,500)\n",
"\n",
"axs[1].plot(data_dict['01'][:,var-1])\n",
"axs[1].set_xlabel('Sample')\n",
"axs[1].set_ylabel(ylabel)\n",
"axs[1].set_title('Faulty operation')\n",
"axs[0].set_ylim(ylim[0], ylim[1])\n",
"axs[1].set_xlim(0,500)\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "hN-LZmDgd3cn"
},
"source": [
"Let's see if we can detect this faults automatically using the $T^2$ and $Q$ indices in the reduced space"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "phVA4kKveHDY"
},
"outputs": [],
"source": [
"from sklearn.decomposition import PCA\n",
"from sklearn.preprocessing import StandardScaler"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "j81-V7ajfQZO"
},
"outputs": [],
"source": [
"fault = '01'\n",
"X_train = np.hstack((data_dict['00'][:,:22],data_dict['00'][:,41:]))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "C3v2sHcMeZvS"
},
"outputs": [],
"source": [
"scaler = StandardScaler()\n",
"scaler.fit(X_train)\n",
"X_train_norm = scaler.transform(X_train)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "ZrwVjNmgf1nh"
},
"outputs": [],
"source": [
"pca = PCA()\n",
"X_PCA = pca.fit_transform(X_train_norm) "
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ymEqEbbHgfg_"
},
"source": [
"Let's now visualize the cumulative explained variance by the principal components"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 466
},
"id": "Q5VLc-6_gmN9",
"outputId": "14221010-d2d2-4f52-ccf1-d71fd12526c9"
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 0, 'Number of principal component')"
]
},
"execution_count": 354,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cum_var = np.cumsum(pca.explained_variance_ratio_ * 100)\n",
"plt.plot(cum_var, 'ko')\n",
"plt.ylabel('Cumulative variance explained (%)')\n",
"plt.xlabel('Number of principal component')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "fvjXnIxwha0G"
},
"source": [
"Let's for now select the number of principal components that account for the 90% of the variance"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "Nijq_p6Tht3c",
"outputId": "9ad5f59e-6e81-43c4-9309-f6991af718a7"
},
"outputs": [
{
"data": {
"text/plain": [
"17"
]
},
"execution_count": 355,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n_pcs = np.argmax(cum_var >= 90) +1\n",
"n_pcs"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "uVyFg5S4lYgr"
},
"source": [
"This means that the first 15 principal componets explain 90% of the variance. This translates to a dimensionality reduction from 52 to 15 by only missing 10% of the \"information\". Quite impressive right?\n",
"\n",
"Let's now extract the first 15 principal components"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "cGt7x-uekbEa",
"outputId": "ce4d5a85-bfed-4f79-a679-37e4157baa1e"
},
"outputs": [
{
"data": {
"text/plain": [
"(500, 17)"
]
},
"execution_count": 356,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"T = X_PCA[:, :n_pcs]\n",
"T.shape"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "LXe5Y-WTs0NT"
},
"source": [
"This is equivalent as doing"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "AJo4WE_xriUD",
"outputId": "9351bef2-2fed-4f37-f6de-f47f97d366fb"
},
"outputs": [
{
"data": {
"text/plain": [
"(500, 17)"
]
},
"execution_count": 357,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pca = PCA(n_components=0.9)\n",
"pca.fit(X_train_norm)\n",
"T_train = pca.transform(X_train_norm)\n",
"T_train.shape"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "y60shJhdtiB8"
},
"source": [
"we can reconstruct the observations from the reduced space like this"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "RYHz3Lw87YtE"
},
"outputs": [],
"source": [
"X_test = np.hstack((data_dict[fault+'_te'][:,:22],data_dict[fault+'_te'][:,41:]))\n",
"X_test_norm = scaler.transform(X_test)\n",
"T_test = pca.transform(X_test_norm)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "SS3fshwXtr6w",
"outputId": "355776b6-429d-4d5e-d20c-a14541a1c365"
},
"outputs": [
{
"data": {
"text/plain": [
"(960, 33)"
]
},
"execution_count": 359,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X_test_norm_reconstruct = pca.inverse_transform(T_test)\n",
"X_test_norm_reconstruct.shape"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "aO5gA358h-Bz"
},
"source": [
"\n",
"\n",
"Let's now create functions for the $T^2$ and $Q$ statistics"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "kGG7afMsd-Bw"
},
"outputs": [],
"source": [
"from scipy.stats import f, norm\n",
"\n",
"def compute_T2(T):\n",
" # Calculate the covariance matrix\n",
" S = (1 / (T_train.shape[0] - 1)) * np.dot(T_train.T, T_train)\n",
"\n",
" # Perform eigenvalue decomposition\n",
" eigenvalues, eigenvectors = np.linalg.eig(S)\n",
"\n",
" # Sort eigenvalues in descending order\n",
" sorted_indices = np.argsort(eigenvalues)[::-1]\n",
" eigenvalues = eigenvalues[sorted_indices]\n",
" eigenvectors = eigenvectors[:, sorted_indices]\n",
"\n",
" # Compute z scores\n",
" z = np.dot(np.dot(np.linalg.inv(np.diag(np.sqrt(eigenvalues))), eigenvectors.T), T.T)\n",
"\n",
" # Calculate T^2 statistic\n",
" T2 = np.sum(z ** 2, axis=0)\n",
"\n",
" # Threshold for T2\n",
" n_d, n_x = T_train.shape\n",
" alpha = 0.01\n",
" T2_alpha = n_x*(n_d-1)*(n_d+1)/(n_d*(n_d-n_x))*f.ppf(1-alpha, n_x, n_d-n_x)\n",
"\n",
" return T2, T2_alpha\n",
"\n",
"\n",
"def compute_Q(X_norm, X_reconstruct):\n",
" # Compute the residual matrix\n",
" R = X_norm - X_reconstruct\n",
"\n",
" # Compute Q statistic\n",
" Q = np.sum(R**2,axis=1)\n",
"\n",
" # Threshold for Q\n",
" S = (1 / (X_train_norm.shape[0] - 1)) * np.dot(X_train_norm.T, X_train_norm)\n",
" eigenvalues, eigenvectors = np.linalg.eig(S)\n",
"\n",
" n_x = T_train.shape[1]\n",
" n_d = eigenvalues.shape[0]\n",
" alpha=0.01\n",
"\n",
" theta1 = np.sum(eigenvalues[n_x:n_d+1]**2)\n",
" theta2 = np.sum(eigenvalues[n_x:n_d+1]**4)\n",
" theta3 = np.sum(eigenvalues[n_x:n_d+1]**6)\n",
" h0 = 1 - 2*theta1*theta3/(3*theta2**2)\n",
"\n",
" c_alpha = norm.ppf(1-alpha)\n",
" Q_alpha = theta1*(h0*c_alpha*(2*theta2)**0.5/theta1 + 1 + theta2*h0*(h0-1)/(theta1**2))**(1/h0)\n",
"\n",
" return Q, Q_alpha\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "FZg0i3_DpxMt"
},
"outputs": [],
"source": [
"T2, T2_alpha = compute_T2(T_test)\n",
"Q, Q_alpha = compute_Q(X_test_norm, X_test_norm_reconstruct)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 466
},
"id": "3cQKsgn1qELW",
"outputId": "be4699fc-f33c-4202-dee9-f5631409078f"
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, '$T^2$ index')"
]
},
"execution_count": 405,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(T2)\n",
"plt.axhline(y=T2_alpha, color='red')\n",
"plt.xlabel('Sample')\n",
"plt.ylabel('$T^2$ index')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 466
},
"id": "CK4BXt30uUZ_",
"outputId": "b12e5836-82f4-4d35-9dbf-29f48bdf4f72"
},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Q index')"
]
},
"execution_count": 406,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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"text/plain": [
""
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},
"metadata": {},
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}
],
"source": [
"plt.plot(Q)\n",
"plt.axhline(y=T2_alpha, color='red')\n",
"plt.xlabel('Sample')\n",
"plt.ylabel('Q index')"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "oYs66qvocx14"
},
"source": [
"We can clearly detect the fault happening around the 200 sample!"
]
},
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"source": [
"## References\n",
"\n",
"```{bibliography}\n",
":filter: docname in docnames\n",
"```"
]
}
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