{ "metadata": { "name": "Clustering Agreement" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": "Clustering Agreements and Distances" }, { "cell_type": "markdown", "metadata": {}, "source": "Consider a graph represented with adjacency matrix $A$ where its nodes . Here, $A$ is a $d\\times d$ matrix where $a_{ij}$ represents the association between node $i$ and $j$, e.g. the existance of an edge.\nAnd $U$ is a $d \\times k$ matrix, where $u_{ik}$ denotes the memberships of node $i$ in the $k^{th}$ cluster of $U$, for example it is $1$ if node $i$ belongs to cluster $k$ in $U$ and $0$ otherwise. With this representation, a simple matrix outer product and transepose can give us interesting information. More specifically, two matrices of \n$$ M= (UU^T)_{d\\times d}\\quad \\quad N = (U^TU)_{k \\times k}$$\ndenote respectively the co-memberships of pairs of nodes in clusters of $U$, and overlaps of pairs of clusters in $U$.\nSo that $M_{ij}$ denotes in how many clusters node $i$ and $j$ appeared together.\nAnd $N_{ij}$ denotes how many nodes clusters $i$ and $j$ have in common.\n\nWe can also compute $A A^T$ or $A^TA$, which compute the number of common (in/out-)neighbors for every pair of nodes in A: a.k.a. co-citaion and biblographic coupling matrices in case of directed graphs. For undirected graphs, $A$ is symmetric and $AA^T = A^TA = A^2$. \n\nWe use these to define network clustering distances. But first lets visualize a clustered network for having illustrated examples. " }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Visualizing a Clustered Graph" }, { "cell_type": "code", "collapsed": false, "input": "import math\nimport logging\nimport numpy as np\nimport numpy.linalg as LA\nimport networkx as nx\nimport igraph as ig\nimport networkx.linalg.graphmatrix as gm\nfrom sympy.printing import latex\nfrom sympy.matrices import *\nimport sympy as sy\nimport matplotlib \nimport matplotlib.pyplot as plt\nfrom pylab import *\n\nFORMAT = \"[%(lineno)s:%(funcName)20s()]\\n %(message)s\"\nlogging.basicConfig(format=FORMAT, level=logging.ERROR)\n\ninit_printing() \n%matplotlib inline\n\ndef printlatex(A):\n print latex(Matrix(A),mode='inline')\n\ndef draw_clustered_graph(G,U, pos, draw_edge_wights = False, draw_graph = True):\n \"\"\"\n Visualizes the given clustering of a graph.\n \n Parameters\n ----------\n G: A networkx graph \n U: numpy matrix\n A nxk matrix representing a clustering, where n is the number of data points and k is the number of clusters in U, \n so that U_{ik} shows if the ith data-point belongs to the kth cluster in U. \n \n pos: A Python dictionary (optional)\n A dictionary of positions for graph nodes keyed by node\n\n \n Returns\n -------\n None\n \n Examples\n -------\n >>> import numpy as np\n >>> import networkx as nx\n >>> from pylab import *\n \n >>> np.matrix( [[0,1,1,0,0,0,0,0,0,0],\n [1,0,0,1,0,0,0,0,0,0],\n [1,0,0,1,0,0,0,1,0,0],\n [0,1,1,0,1,1,0,0,0,0],\n [0,0,0,1,0,1,1,0,0,0],\n [0,0,0,1,1,0,1,0,0,0],\n [0,0,0,0,1,1,0,0,0,0],\n [0,0,1,0,0,0,0,0,1,1],\n [0,0,0,0,0,0,0,1,0,1],\n [0,0,0,0,0,0,0,1,1,0]])\n \n >>> G = nx.from_numpy_matrix(A)\n >>> U = np.matrix([[1,0],[1,0],[1,0],[0,1],[0,1],[0,1],[0,1],[1,0],[1,0],[1,0]])\n >>> figure(figsize=(10, 4))\n >>> draw_clustered_graph(G,U, nx.spring_layout(G))\n >>> show()\n \n \"\"\"\n \n color_list = ['b','g','r','m','y','c']\n color_list =['#9999FF', '#FF9999', '#66FF99','#FF99FF', '#FFFF99', '#E0E0E0','#FF9933','#FF3333','#33FF99','#33FFFF','#3333FF']\n\n if pos==None:\n pos = nx.spring_layout(G)#, nlist, dim, scale)spring_layout(G) \n print '----- positions to repeat the layout:: \\n ',pos\n \n maxW = 0.0\n for (i,j, w) in G.edges(data=True):\n maxW = max(maxW,w['weight'] )\n if U is not None:\n UG = nx.from_numpy_matrix( U.dot(U.T))\n maxU = U.max()\n # draw clusters\n t =6.2\n for c in range(U.shape[1]):\n nsizes = [ int(t**4 * U[i,c]/maxU) for i in range(U.shape[0])]\n esizes = [ ((U[i,c]*U[j,c])*t**2.0/maxU**2) for (i,j, w) in UG.edges(data=True)]\n \n try:\n nx.draw(UG, pos = pos, node_size=nsizes, style ='solid' ,\\\n #labels ='.',\\\n node_color = color_list[c],edge_color =color_list[c],\\\n linewidths=0, width= esizes, alpha =.5)#, alpha =1\n except:\n pass\n # draw graph\n# if draw_graph:\n try:\n f= lambda w: np.log(w/maxW +1)*w*3/maxW +1 if draw_graph else 0 \n nx.draw(G, pos = pos, node_color = 'w', alpha =1 , linewidths=1, width= [f(w['weight']) for (i,j, w) in G.edges(data=True)])\n except:\n pass\n \n if draw_edge_wights:\n edge_lbls = dict([((u,v,),d['weight']) for u,v,d in G.edges(data=True)])\n nx.draw_networkx_edge_labels(G, pos = pos, label_pos=0.5 ,edge_labels =edge_lbls)\n \n return pos\n ", "language": "python", "metadata": {}, "outputs": [], "prompt_number": 141 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": "Example: A visualized clustered network" }, { "cell_type": "code", "collapsed": false, "input": "A = np.array([[0,1,1,0,0,0,0,0,0,0],\n [1,0,0,1,0,0,0,0,0,0],\n [1,0,0,1,0,0,0,1,0,0],\n [0,1,1,0,1,1,0,0,0,0],\n [0,0,0,1,0,1,1,0,0,0],\n [0,0,0,1,1,0,1,0,0,0],\n [0,0,0,0,1,1,0,0,0,0],\n [0,0,1,0,0,0,0,0,1,1],\n [0,0,0,0,0,0,0,1,0,1],\n [0,0,0,0,0,0,0,1,1,0]])\n \nG = nx.from_numpy_matrix(A)\nU = np.array([[1,0],[1,0],[1,0],[0,1],[0,1],[0,1],[0,1],[1,0],[1,0],[1,0]])\nfigure(figsize=(4, 2))\nfix_pos = draw_clustered_graph(G,U, nx.spring_layout(G))\nshow()\n", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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CSFcJv5/1R+zqighfZ2fqTkZWKxuXwPMsOt/by0rixOcNdZ/StUyqtnIiWq0WRUVFaG5u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\nv9XVJRTP119/HRzHwSxJeSo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"text": "" } ], "prompt_number": 142 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Computing the Agreement of Two Clusters" }, { "cell_type": "markdown", "metadata": {}, "source": "Consider two alternative clustering of $d$ data-points, called $U$ and $V$. Where, $U$ is a $d \\times k$ matrix, where $u_{ik}$ denotes the memberships of node $i$ in the $k^{th}$ cluster of $U$, for example it is $1$ if node $i$ belongs to cluster $k$ in $U$ and $0$ otherwise. With this representation, a simple matrix outer product and transepose can give us interesting information. \nMore specifically, two matrices of $ M= (UU^T)_{d\\times d}$ and $ N = (U^TU)_{k \\times k}$\ndenote respectively the co-memberships of pairs of nodes in clusters of $U$, and overlaps of pairs of clusters in $U$.\nIn other words, $M_{ij}$ denotes in how many clusters node $i$ and $j$ appeared together; and $N_{ij}$ denotes how many nodes clusters $i$ and $j$ have in common." }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": "Agreement from Cluster Overlaps i.e. Contingency Table" }, { "cell_type": "markdown", "metadata": {}, "source": " Now for computing the overlaps between two different clustering $U$ and $V$, we can simply compute: $N= (U^TV)_{k \\times r} $ which we write $N$ for short. The original rand index, is then defined in terms of this contingency matrix. More specifically assume $\\varphi(x)= x(x-1)/2$, then consider these four terms:\n$$\\sum_{ij} \\varphi(n_{ij}) = sum(\\varphi(N)) = \\mathbb{1}_{1\\times k} \\times \\varphi(N) \\times \\mathbb{1}_{r \\times 1} ,\\; and \\quad \\sum_{i} \\varphi(\\sum_{j} n_{ij}) = sum(\\varphi(sum(N,1))) = \\mathbb{1}_{1\\times k} \\times \\varphi(N \\times \\mathbb{1}_{r \\times 1} )$$ \n$$\\sum_{j} \\varphi(\\sum_{i} n_{ij}) = sum(\\varphi(sum(N,0))) = \\varphi(\\mathbb{1}_{1\\times k} \\times N) \\times \\mathbb{1}_{r \\times 1} ,\\; and \\quad \\varphi(\\sum_{ij} n_{ij}) = \\varphi(sum(N)) = \\varphi(\\mathbb{1}_{1\\times k} \\times N \\times \\mathbb{1}_{r \\times 1}) $$\nwhere $\\mathbb{1}$ is a identity vector with appropiate shape, written afterward simply as $\\mathbb{1}$.\nThe rand index which is originally defined as:\n$RI =1 + [2\\sum_{i=1}^k\\sum_{j=1}^r n_{ij}(n_{ij}-1) - \\sum_{i=1}^k n_{i.}(n_{i.}-1)- \\sum_{j=1}^r n_{.j}(n_{.j}-1))]/[n(n-1)]$; can be re-written as:\n$RI =1 + \n[\\mathbb{1} \\varphi(N) \\mathbb{1} - \\mathbb{1} \\varphi(N \\mathbb{1} ) ]/[\\varphi(\\mathbb{1} N \\mathbb{1}) ] + [\\mathbb{1} \\varphi(N) \\mathbb{1} - \\varphi(\\mathbb{1} N) \\mathbb{1} ]/[\\varphi(\\mathbb{1} N \\mathbb{1}) ] $.\nWe can similarly derive the adjusted for chance version of rand index. The generalized forms are:\n $$ \\mathcal{G}_{\\varphi} = \\frac{\\mathbf{1} \\varphi(N) \\mathbf{1}^T - \\mathbf{1} \\varphi(N \\mathbf{1}^T ) } {\\varphi(\\mathbf{1} N \\mathbf{1}^T) } + \\frac{\\mathbf{1} \\varphi(N) \\mathbf{1}^T - \\varphi(\\mathbf{1} N) \\mathbf{1}^T } {\\varphi(\\mathbf{1} N \\mathbf{1}^T) } $$$$ A\\mathcal{G}_{\\varphi} =\\frac{\\mathbf{1} \\varphi(N) \\mathbf{1}^T - E}{M-E} ,\\quad M = \\frac{ \\mathbf{1} \\varphi(N \\mathbf{1}^T ) + \\varphi(\\mathbf{1} N) \\mathbf{1}^T }{2 } ,\\; E = \\frac{ (\\mathbf{1} \\varphi(N \\mathbf{1}^T )) ( \\varphi(\\mathbf{1} N ) \\mathbf{1}^T )}{\\varphi(\\mathbf{1} N \\mathbf{1}^T) } $$\n" }, { "cell_type": "code", "collapsed": false, "input": "def agreement_from_overlaps(U,V, f = lambda x: x*(x-1)*0.5, exact=False):\n \"\"\" \n Computes the agreement between two disjoint clusterings based on the overlap of their clusters.\n Parameters\n ----------\n U: numpy matrix\n A nxk matrix representing a clustering, \n where n is the number of data points and k is the number of clusters in U, \n so that U_{ik} shows if the ith data-point belongs to the kth cluster in U. \n V: numpy matrix\n A nxr matrix representing a clustering similar to U\n f: function\n A Python function (non-linear) to apply on the overlap sizes to compute the divergence,\n f = lambda x: x*(x-1)*0.5 (default) will result in Rand Index and Adjusted Rand Index, \n f = lambda x: 0 if x==0 else (x * math.log(x)) derives normalized VI.\n \n Returns\n -------\n G: float\n agreement between input clusterings from \n $$\\GAM_{\\varphi} = \\frac{\\mathbf{1} \\varphi(N) \\mathbf{1}^T - \\mathbf{1} \\varphi(N \\mathbf{1}^T ) } {\\varphi(\\mathbf{1} N \\mathbf{1}^T) } + \\frac{\\mathbf{1} \\varphi(N) \\mathbf{1}^T - \\varphi(\\mathbf{1} N) \\mathbf{1}^T } {\\varphi(\\mathbf{1} N \\mathbf{1}^T) } $$ \n AG: float\n agreement between input clusterings from \n $$\\AG_{\\varphi} =\\frac{\\mathbf{1} \\varphi(N) \\mathbf{1}^T - E}{M-E} ,\\quad M = \\frac{ \\mathbf{1} \\varphi(N \\mathbf{1}^T ) + \\varphi(\\mathbf{1} N) \\mathbf{1}^T }{2 } ,\\; E = \\frac{ (\\mathbf{1} \\varphi(N \\mathbf{1}^T )) ( \\varphi(\\mathbf{1} N ) \\mathbf{1}^T )}{\\varphi(\\mathbf{1} N \\mathbf{1}^T) } $$\n \"\"\"\n return 1- distance_from_overlaps(U, V, f, exact)\n\ndef distance_from_overlaps(U,V, f = lambda x: x*(x-1)*0.5, exact=False):\n f = np.vectorize(f, otypes=[np.float])\n N = np.dot(U.T,V) # the overlaps, a.k.a contingency table\n \n b2 = np.ones((N.shape[1],1),dtype='float')\n b1 = np.ones((1, N.shape[0]),dtype='float')\n \n m1=b1.dot(N)\n m2=N.dot(b2)\n m = b1.dot(N).dot(b2)\n s1 = (b1.dot(f(m2))) \n s2 = (f(m1).dot(b2)) \n n = f(m)\n I = (b1.dot(f(N)).dot(b2))\n \n # or \n # s1 = f(N.sum(axis=1)).sum()\n # s2 = f(N.sum(axis=0)).sum()\n # n = f(N.sum())\n # I = f(N).sum()\n \n G = float ((s1+s2- 2* I )/( n ) )\n if exact:\n E = (b1.dot(f(m2).dot(f(m1))/f(m))).dot(b2)\n else:\n E = (b1.dot(f(m2.dot(m1)/m))).dot(b2)\n AG = float ((s1+s2- 2* I )/( (s1+s2) - 2 *E ))\n return np.array([G, AG])", "language": "python", "metadata": {}, "outputs": [], "prompt_number": 143 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": "Example" }, { "cell_type": "code", "collapsed": false, "input": "V = np.array([[1,0],[1,0],[1,0],[0,1],[0,1],[0,1],[0,1],[1,0],[1,0],[1,0]])\nU = np.array([[1,0,0],[1,0,0],[1,0,0],[1,0,0],[0,1,0],[0,1,0],[0,1,0],[0,0,1],[0,0,1],[0,0,1]])\nfigure(figsize=(9, 9))\nnr = 2 \nnf = 2\nsubplot(nr,nf,1)#.set_title('$U$')\ndraw_clustered_graph(G,V, fix_pos)\nsubplot(nr,nf,2)#.set_title('$V1$')\ndraw_clustered_graph(G,U, fix_pos)\n\nprint 'RI = %0.3f, ARI = %0.3f'% tuple(agreement_from_overlaps(U,V, exact=True))\nprint 'VI = %0.3f, NMI (_sum, VM in sklearn) = %0.3f'% tuple(agreement_from_overlaps(U,V, f = lambda x: 0 if x==0 else x*log(x), exact=False))\nprint 'RI\\' = %0.3f, ARI\\' = %0.3f'% tuple(agreement_from_overlaps(U,V,f = lambda x: x**2, exact=False))\n", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "RI = 0.667, ARI = 0.312\nVI = 0.624, NMI (_sum, VM in sklearn) = 0.509\nRI' = 0.700, ARI' = 0.408\n" }, { "metadata": {}, "output_type": "display_data", "png": 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S2P0SiKJEL0odCKFC5FL952ze/AIffLCK9etf0+R4ePvtSykouJEvf/n/YrEU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"text": "" } ], "prompt_number": 144 }, { "cell_type": "heading", "level": 5, "metadata": {}, "source": "Compare it with scikit\n" }, { "cell_type": "code", "collapsed": false, "input": "\ndef convert_cluster_to_labels(U):\n return np.nonzero(U)[1]\ndef sklearn_measures(U, V):\n # http://scikit-learn.org/stable/modules/classes.html#clustering-metrics\n import sklearn.metrics.cluster as sym\n U_labels = np.nonzero(U)[1]\n V_labels = np.nonzero(V)[1]\n # print U_labels, V_labels\n\n print 'From sklean:: ARI = %0.3f'% sym.adjusted_rand_score(U_labels, V_labels),\n print 'NMI = %0.3f'% sym.normalized_mutual_info_score(U_labels, V_labels),\n print 'AMI = %0.3f'% sym.adjusted_mutual_info_score(U_labels, V_labels),\n print 'VM = %0.3f'% sym.v_measure_score(U_labels, V_labels)\n \nsklearn_measures(U,V)", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "From sklean:: ARI = 0.312 NMI = 0.523 AMI = 0.327 VM = 0.509\n" } ], "prompt_number": 145 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": "NMI" }, { "cell_type": "markdown", "metadata": {}, "source": "We can also derive NMI directly from our matrix representation" }, { "cell_type": "code", "collapsed": false, "input": "def nmi(U,V):\n N = np.dot(U.T,V) # the overlaps, a.k.a contingency table\n \n b2 = np.ones((N.shape[1],1),dtype='float')\n b1 = np.ones((1, N.shape[0]),dtype='float')\n \n n = b1.dot(N).dot(b2)\n nv= b1.dot(N)\n nu= N.dot(b2)\n \n f = np.vectorize(lambda x: x*math.log(x) if x >0 else 0, otypes=[np.float])\n Hu = -(b1.dot(f(nu/n))) \n Hv = -(f(nv/n).dot(b2)) \n Huv = -(b1.dot(f(N/n)).dot(b2))\n Iuv = Hu+Hv-Huv\n\n vi = float((2*Huv-(Hu+Hv) )/math.log(n))\n nmi_sum = float(2*Iuv/(Hu+Hv)) # VM in sklearn\n nmi_sqrt = float(Iuv/math.sqrt(Hu*Hv)) # NMI in sklearn\n # 1-VI to make it into a agreement measure\n return np.array([1-vi, nmi_sum, nmi_sqrt])", "language": "python", "metadata": {}, "outputs": [], "prompt_number": 146 }, { "cell_type": "code", "collapsed": false, "input": "print '1-VI = %0.3f, NMI_sum = %0.3f, NMI_sqrt = %0.3f'% tuple(nmi(U,V))\n", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "1-VI = 0.624, NMI_sum = 0.509, NMI_sqrt = 0.523\n" } ], "prompt_number": 147 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": "Overlap from Co-memberships" }, { "cell_type": "markdown", "metadata": {}, "source": "The two square matrices of $UU^T$ and $VV^T$ show the co-membership of pair of nodes in clusterings $U$ and $V$ respectively. Therefore the difference of these two will give us the disagreement between $U$ and $V$, i.e. $\\Delta = UU^T - VV^T $. We can show that the $RI$ and $ARI$, can be derived from $\\Delta$ as:\n$$(A)RI = 1 - \\frac{|| UU^T - VV^T ||^2_F}{MAX}\\quad where$$\n$$ MAX_{RI}= max(max(UU^T),max(VV^T)) n^2 \\;\\quad and \\quad\\; \n MAX_{ARI}=||UU^T||^2_F+||VV^T||^2_F-2 |UU^T||VV^T| / (n^2)$$ \n \n" }, { "cell_type": "code", "collapsed": false, "input": "\ndef agreement_from_co_memberships(U, V, same_nodes = True):\n return 1-distance_from_co_memberships(U, V, same_nodes)\n\ndef distance_from_co_memberships(U, V, same_nodes = True):\n\n \"\"\" \n Computes the agreement between two clusterings based on the co_memberships of data points in their clusters.\n Parameters\n ----------\n U: Matrix\n A nxk matrix representing a clustering, \n where upper is the number of data points and k is the number of clusters in U, \n so that U_{ik} shows if the ith data-point belongs to the kth cluster in U. \n V: Matrix\n A nxr matrix representing a clustering similar to U\n \n same_nodes: Boolean\n determines whether the formula should be exact same as the original RI formula or the approximate forms\n \n Returns\n -------\n G: float\n agreement between input clusterings from \n $$\\GAM_{\\varphi} = 1 - \\frac{|| UU^T - VV^T ||}{MAX}$$\n where MAX is $$MAX= \\mathfrak{m} upper^2$$ and $$ \\mathfrak{m} = max(max(UU^T),max(VV^T))$$\n AG: float\n agreement between input clusterings from same formula as G but where MAX is \n $$MAX=||UU^T||+||VV^T||-2 ||UU^T||||VV^T|| / (\\mathfrak{m} upper^2)$$.\n \"\"\"\n \n CU = U.dot(U.T).astype('float')\n CV = V.dot(V.T).astype('float')\n #print CU\n sf = lambda A: np.multiply(A, A).sum() #squared frob norm\n norm = sf\n if not same_nodes:\n np.fill_diagonal(CU,0)\n np.fill_diagonal(CV,0)\n \n pairCount = CU.shape[0]**2 - (0 if same_nodes else CU.shape[0])\n\n sUV = norm( CU-CV )\n sU = norm(CU)\n sV = norm(CV)\n m = max(np.max(CU),np.max(CV))\n\n GI = sUV /(pairCount*m**2)\n AGI = sUV / ((sU+sV) - 2*(np.sum(CU)*np.sum(CV))/(pairCount))\n return np.array([GI, AGI])\n", "language": "python", "metadata": {}, "outputs": [], "prompt_number": 148 }, { "cell_type": "code", "collapsed": false, "input": "print 'RI = %0.3f, ARI = %0.3f'% tuple(agreement_from_co_memberships(U,V, False))\nprint 'RI\\' = %0.3f, ARI\\' = %0.3f'% tuple(agreement_from_co_memberships(U,V, True))\n", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "RI = 0.667, ARI = 0.312\nRI' = 0.700, ARI' = 0.408\n" } ], "prompt_number": 149 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": "The advantage to this formulation is that it extends to overlapping clusters. " }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "OMEGA" }, { "cell_type": "markdown", "metadata": {}, "source": "Collins and Dent (1988) proposed the Omega index as a generalization of the (adjusted) rand index for overlapping clusters with crisp memberships. The Omega Index($\\omega$) derives from our formulation if we define $\\Delta = [UU^T == VV^T]$. Since in $\\omega$, each pair of datapoints is considered as an agreement if they appear in exactly the same number of clusters in the two clusterings,\n i.e. $\\Delta_{ij} =1$ if $(UU^T)_{ij} == (VV^T)_{ij}$ and zero otherwise." }, { "cell_type": "code", "collapsed": false, "input": "def agreement_from_omega(U, V, same_nodes = False):\n CU = U.dot(U.T).astype('float')\n CV = V.dot(V.T).astype('float')\n if not same_nodes:\n np.fill_diagonal(CU,0)\n np.fill_diagonal(CV,0)\n pairCount = CU.shape[0]**2 - (0 if same_nodes else CU.shape[0])\n pair_counts = np.zeros((int(np.max(CU))+1,int(np.max(CV))+1))\n for i in range(0, int(np.max(CU)+1)):\n for j in range(0, int(np.max(CV)+1)): \n tmp = (CU==i)*(CV==j)\n tmp = np.tril(tmp) if same_nodes else np.tril(tmp,-1)\n pair_counts[i,j] = np.sum(tmp) \n \n w= np.array( CU==CV, dtype='float')\n w = np.sum(w)- w.trace()\n w = w*1.0/ pairCount\n\n tU = np.histogram(CU, bins=np.max(CU)+1)[0]\n tV = np.histogram(CV, bins=np.max(CV)+1)[0]\n \n tU[0]= tU[0] - (0 if same_nodes else CU.shape[0])\n tV[0]= tV[0] - (0 if same_nodes else CU.shape[0])\n\n m = min(tU.shape[0], tV.shape[0])\n ew = [tU[j]*tV[j] for j in range(0 ,m)] \n ew = np.sum(ew)*1.0 / (pairCount**2)\n\n aw = (w-ew)/(1-ew)\n\n return np.array([w, aw])\n", "language": "python", "metadata": {}, "outputs": [], "prompt_number": 150 }, { "cell_type": "code", "collapsed": false, "input": "print 'w = %0.3f, Aw = %0.3f'% tuple(agreement_from_omega(U,V, False))\n", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "w = 0.667, Aw = 0.312\n" } ], "prompt_number": 151 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": "Alternative Forms:" }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": "Alternative Formulation From Matrix Norm:" }, { "cell_type": "code", "collapsed": false, "input": "def agreement_from_matrix_norms(U,V, norm = lambda A: math.sqrt(np.multiply(A, A).sum()) ):\n return 1-distance_from_matrix_norms(U, V, norm)\n \ndef distance_from_matrix_norms(U,V, norm = lambda A: math.sqrt(np.multiply(A, A).sum()) ):\n# L21_norm = lambda A: np.sqrt(np.multiply(A, A).sum(axis=1)).sum() \n# frobenius_norm = lambda A: math.sqrt(np.multiply(A, A).sum()) \n# log_norm = lambda A: np.multiply(A, np.log(A.clip(1)).sum(axis=1)).sum() \n CU = U.dot(U.T).astype('float')\n CV = V.dot(V.T).astype('float')\n return np.array([norm(CU-CV)/(norm(CU)+norm(CV)) ])\n\nprint 'I_norm = %0.3f'% tuple(agreement_from_matrix_norms(U,V))", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "I_norm = 0.580\n" } ], "prompt_number": 153 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": "Alternative Formulation From Matrix Trace:" }, { "cell_type": "code", "collapsed": false, "input": "def distance_alternative_forms(U,V):\n return 1-agreement_alternative_forms(U, V)\n\ndef agreement_alternative_forms(U, V):\n CU = U.dot(U.T).astype('float')\n CV = V.dot(V.T).astype('float')\n \n CU2 = CU.dot(CU)\n CV2 = CV.dot(CV)\n\n Q = CU.dot(CV)\n # Cauchy-Schwarz inequality ==> alt1<1\n alt1 = float(Q.trace()) / math.sqrt( (CU2).trace() * (CV2).trace() )\n alt2 = float(Q.trace() / (CU.trace() * CV.trace()))\n return np.array([alt1, alt2])\n\nprint 'I_sqrt(tr) = %0.3f, I_tr = %0.3f'% tuple(agreement_alternative_forms(U,V))\n\n", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "I_sqrt(tr) = 0.666, I_tr = 0.280\n" } ], "prompt_number": 154 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": "Summary of all measures up to here" }, { "cell_type": "code", "collapsed": false, "input": "def get_all_overlapping_agreement_variations(U, V):\n dists= get_all_overlapping_distance_variations(U,V)\n return [dists[0], 1-dists[1]]\n\ndef get_all_overlapping_distance_variations(U, V):\n res= [\"RI\",\"ARI\",\"RI'\",\"ARI'\", \"nF\", \"sqtr\",\"tr\" ] ,\\\n np.hstack((distance_from_co_memberships(U,V, False),\\\n distance_from_co_memberships(U,V),\\\n distance_from_matrix_norms(U,V) ,\\\n distance_alternative_forms(U, V) \n )) \n return res\n\nfrom tabulate import tabulate\nRes = get_all_overlapping_agreement_variations(U, V)\nheadrs = np.hstack( ([\" - \"], Res[0]))\nvals = [ tuple([\"(V,U)\"]+Res[1].tolist()) ]\nvals = np.asarray(vals, dtype=dict(names = headrs, formats=[\"a18\"]+[\"float32\"]*len(Res[1]) ))\nprint tabulate(vals, headers = \"keys\", floatfmt=\".3f\")\n", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": " - RI ARI RI' ARI' nF sqtr tr\n----- ----- ----- ----- ------ ----- ------ -----\n(V,U) 0.667 0.312 0.700 0.408 0.580 0.666 0.280\n" } ], "prompt_number": 157 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Structure Based Measures" }, { "cell_type": "markdown", "metadata": {}, "source": "All the agreement measures presented so far only consider memberships of datapoints, and ignore any relations between them. Here we define structure dependent clustering distances which incorporate the\nunderlying structure of the graph." }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": "Incident Matrix of the Graph to Represent Underlying Structure " }, { "cell_type": "code", "collapsed": false, "input": "def get_incident_matrix(n, edges, directed =False):\n N = np.zeros((n, len(edges)), dtype =np.float)\n for j,e in enumerate(edges):\n w = 1 if len(e)<3 else np.sqrt(e[2])\n N[e[0]][j] = w\n N[e[1]][j] = w * (-1 if directed else 1)\n return N\n\ndef get_incident_matrix_from_graph(G, directed =False):\n #N = gm.incidence_matrix(G) \n edges = [(i,j, w['weight']) for (i,j, w) in G.edges(data=True)]\n return get_incident_matrix(G.number_of_nodes(), edges,directed)\n \ndef get_incident_matrix_from_adjecency(A, directed =False):\n edges = np.nonzero(A if directed else np.tril(A))\n weighted_edges = np.vstack((edges, A[edges]))\n return get_incident_matrix(A.shape[0], np.transpose(weighted_edges), directed)\n", "language": "python", "metadata": {}, "outputs": [], "prompt_number": 158 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": "Distance of a Clustering From Structure" }, { "cell_type": "code", "collapsed": false, "input": "\ndef distance_with_structure(G,U):\n N = get_incident_matrix_from_graph(G)\n return get_all_distance_variations(N, U)\n\ndef agreement_with_structure(G,U):\n dists= distance_with_structure(G,U)\n return [dists[0], 1-dists[1]]\n", "language": "python", "metadata": {}, "outputs": [], "prompt_number": 162 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": "Distance of Two Clustering Given the Structure" }, { "cell_type": "code", "collapsed": false, "input": "def agreement_based_on_structure(G, U, V, method = \"trans\"):\n dists= distance_based_on_structure(G, U, V, method)\n return [dists[0], 1-dists[1]]\n\ndef distance_based_on_structure(G, U, V, method = \"trans\"):\n# A = gm.adj_matrix(G) \n N = get_incident_matrix_from_graph(G)\n # avg dis\n if method==\"trans\":\n return get_all_distance_variations(N.T.dot(U), N.T.dot(V))\n else:\n names, d = get_all_distance_variations(U,V)\n d1 = get_all_distance_variations(U,N)[1]\n d2 = get_all_distance_variations(V,N)[1]\n if method == \"sum\":\n alpha =0.5\n return [d1[0], alpha*d+ (1-alpha)*np.absolute(d1-d2) ]\n elif method == \"prod\":\n return [d1[0], 1./3*(np.sqrt(d*d1)+np.sqrt(d*d2)+np.sqrt(d1*d2))]\n \n return float( (U.dot(U.T).dot(N.dot(N.T)).dot(V.dot(V.T))).trace() /\\\n math.sqrt( (U.dot(U.T).dot(N.dot(N.T)).dot(U.dot(U.T))).trace() *\\\n (V.dot(V.T).dot(N.dot(N.T)).dot(V.dot(V.T))).trace() )\\\n )\n", "language": "python", "metadata": {}, "outputs": [], "prompt_number": 160 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": "The trans method for structured based meaures, in picture" }, { "cell_type": "code", "collapsed": false, "input": "def transformation():\n figure(figsize=(10, 5))\n A = np.zeros((9,9),dtype='float')\n edges = [(0,1),(0,5),(0,6),\n (1,0),(1,2),(1,5),\n (2,1),(2,3),(2,5),\n (3,2),(3,5),(3,4),\n (4,3),(4,5),\n (5,0),(5,1),(5,2),(5,3),(5,4),(5,6),(5,8),\n (6,0),(6,5),(6,7),(6,8),\n (7,6),(7,8),\n (8,6),(8,7),(8,5),\n ]\n for e in edges:\n A[e]=1\n\n fix_pos = {0: np.array([ 0.20385061-0.1, 0.23977043-0.1]), \n 1: np.array([ 0.43693314, 0. ]), \n 2: np.array([ 0.75900616, 0.01462725]), \n 3: np.array([ 0.97478493, 0.24577521-0.1]), \n 4: np.array([ 1. , 0.53455287-0.1-0.1]), \n 5: np.array([ 0.56256428+0.05, 0.38383768 +0.1]), \n 6: np.array([ 0.16250501-0.1, 0.59711573]), \n 7: np.array([ 0. , 0.96007752]), \n 8: np.array([ 0.32060991, 0.8106598 ])}\n\n edges = transpose(np.nonzero(np.tril(A)))\n edg_pos ={}\n for j,e in enumerate(edges):\n edg_pos[j]= 0.5*(fix_pos[e[0]]+fix_pos[e[1]])\n # print edg_pos\n U = np.array([[1,0],[1,0],[1,0],[1,0],[1,0],[1,0],[0,1],[0,1],[0,1]])\n V1 = np.array([[0,1],[1,0],[1,0],[1,0],[1,0],[1,0],[0,1],[0,1],[0,1]])\n V2 = np.array([[1,0],[1,0],[1,0],[1,0],[1,0],[0,1],[0,1],[0,1],[0,1]])\n \n N = get_incident_matrix(A.shape[0],edges)\n \n G=nx.from_numpy_matrix(A)#=N.dot(N.T)\n LG=nx.from_numpy_matrix(N.T.dot(N)) #Line graph\n\n T = N.T.dot(U)\n TRA = T.dot(T.T)\n# nx.write_dot(LG,'graph.dot')\n \n subplot(2,4,1)\n draw_clustered_graph(G ,U, pos= fix_pos,draw_graph = True)\n subplot(2,4,2) \n draw_clustered_graph(G ,V1, pos= fix_pos,draw_graph = True)\n subplot(2,4,3)\n draw_clustered_graph(G ,V2, pos= fix_pos,draw_graph = True)\n\n subplot(2,4,6) \n draw_clustered_graph(nx.from_numpy_matrix((N.T.dot(U)).dot(U.T.dot(N))) ,N.T.dot(U), pos= edg_pos,draw_graph = False)\n subplot(2,4,7)\n draw_clustered_graph(nx.from_numpy_matrix((N.T.dot(V1)).dot(V1.T.dot(N))) ,N.T.dot(V1), pos= edg_pos,draw_graph = False)\n subplot(2,4,8)\n draw_clustered_graph(nx.from_numpy_matrix((N.T.dot(V2)).dot(V2.T.dot(N))) ,N.T.dot(V2), pos= edg_pos,draw_graph = False)\n show()\n \ntransformation()", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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DBw+yf//+UY95vd6cRq61tZVDhw5x/fTpAPT7fOw/dYp3zpzhZ3v2sPnVV9nz5ptjGjiI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\n/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lssTMzN7bMtCuo030vsmGkldoO2NnsHhxuOc7jhG9o62gMjD0INjsNJ8/YvcbQ5+nRO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\nFsXbxiMaA6mjm29e5u/xptogVUehesnM7P9CHtmRX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"text": "" } ], "prompt_number": 172 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": "Examples" }, { "cell_type": "code", "collapsed": false, "input": "def experiment(A,V,U,U2=None, fix_pos=None): \n G = nx.from_numpy_matrix(A)\n plotTable = False\n nr = 2 if plotTable else 1\n nf = 2 #numFigs\n if not U2==None:\n nf =3\n if fix_pos==None:\n fix_pos = nx.spring_layout(G)#, nlist, dim, scale)spring_layout(G) \n print '----- positions to repeat the layout:: \\n ',fix_pos\n \n figure(figsize=(9, 4))\n subplot(nr,nf,1)#.set_title('$U$')\n draw_clustered_graph(G,V, fix_pos)\n subplot(nr,nf,2)#.set_title('$V1$')\n draw_clustered_graph(G,U, fix_pos)\n if not U2 == None:\n subplot(nr,nf,3)#.set_title('$V2$')\n draw_clustered_graph(G,U2, fix_pos)\n show()\n \n Res = get_all_agreement_variations(V, U)\n headrs = np.hstack( ([\" - \"], Res[0]))\n vals = [ tuple([\"(V,U_1)\"]+Res[1].tolist()) ] \n if U2 is not None:\n vals = vals + [ tuple([\"(V,U_2)\"]+get_all_agreement_variations(V, U2)[1].tolist()) ] \n \n vals = vals + [ tuple([\"(N,V)\"]+agreement_with_structure(G, V)[1].tolist()) ] \n vals = vals + [ tuple([\"(N,U_1)\"]+agreement_with_structure(G, U)[1].tolist()) ] \n if not U2==None:\n vals = vals + [ tuple([\"(N,U_2)\"]+agreement_with_structure(G, U2)[1].tolist()) ] \n\n for m in [\"trans\",\"sum\"]:\n vals = vals + [ tuple([\"(V,U_1|G)\"+m[0]]+agreement_based_on_structure(G, V,U, method=m)[1].tolist()) ] \n if not U2==None:\n vals = vals + [ tuple([\"(V,U_2|G)\"+m[0]]+agreement_based_on_structure(G, V,U2, method=m)[1].tolist()) ] \n \n vals = np.asarray(vals, dtype=dict(names = headrs, formats=[\"a18\"]+[\"float32\"]*len(Res[1]) ))\n print tabulate(vals, headers = \"keys\", tablefmt=\"grid\", floatfmt=\".3f\")\n \n if plotTable:\n args = { \"tablefmt\":\"plain\", \"floatfmt\":\".3f\", \"numalign\":\"right\"}\n ax = plt.subplot2grid((2,nf), (1,0), colspan=nf)\n plt.axis('off')\n plt.text(0,0, tabulate(vals, headers = \"keys\", **args))#,backgroundcolor = 'y',alpha=1)\n show()", "language": "python", "metadata": {}, "outputs": [], "prompt_number": 189 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": "Disjoint Example" }, { "cell_type": "code", "collapsed": false, "input": "\ndef basic_example():\n A = np.array([[0,1,1,0,0,0,0,0,0,0],\n [1,0,0,1,0,0,0,0,0,0],\n [1,0,0,1,0,0,0,1,0,0],\n [0,1,1,0,1,1,0,0,0,0],\n [0,0,0,1,0,1,1,0,0,0],\n [0,0,0,1,1,0,1,0,0,0],\n [0,0,0,0,1,1,0,0,0,0],\n [0,0,1,0,0,0,0,0,1,1],\n [0,0,0,0,0,0,0,1,0,1],\n [0,0,0,0,0,0,0,1,1,0]])\n fix_pos_GraphExample = {0: array([ 0.05, .35]), \n 1: array([ 0.02, 0.62]), \n 2: array([ 0.25, 0.4]), \n 3: array([ 0.25, 0.73]), \n 4: array([ .5, 0.9]), \n 5: array([ 0, 0.9]), \n 6: array([ 0.25, 1 ]), \n 7: array([ 0.25, 0.1]), \n 8: array([ 0, 0. ]), \n 9: array([ .5, 0])}\n\n return A, fix_pos_GraphExample\n\nA, fix_pos_GraphExample = basic_example()\nV = np.array([[1,0],[1,0],[1,0],[0,1],[0,1],[0,1],[0,1],[1,0],[1,0],[1,0]])\nU = np.array([[1,0,0],[1,0,0],[1,0,0],[1,0,0],[0,1,0],[0,1,0],[0,1,0],[0,0,1],[0,0,1],[0,0,1]])\nexperiment(A,U,V, fix_pos=fix_pos_GraphExample)", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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NGzj64x9DrVKhs6+PeGmGwkUPenrAi767+0NVCg6nE9UNDahuaPA8plapUJqX5yNWHi8q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\n6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"text": "" }, { "output_type": "stream", "stream": "stdout", "text": "+------------+-------+-------+-------+--------+-------+--------+-------+\n| - | RI | ARI | RI' | ARI' | nF | sqtr | tr |\n+============+=======+=======+=======+========+=======+========+=======+\n| (V,U_1) | 0.667 | 0.312 | 0.700 | 0.408 | 0.580 | 0.666 | 0.280 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (N,V) | 0.889 | 0.723 | 0.975 | 0.586 | 0.598 | 0.797 | 0.177 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (N,U_1) | 0.733 | 0.451 | 0.966 | 0.437 | 0.571 | 0.672 | 0.185 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_1|G)t | 0.816 | 0.455 | 0.822 | 0.501 | 0.643 | 0.768 | 0.322 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_1|G)s | 0.756 | 0.520 | 0.846 | 0.629 | 0.776 | 0.771 | 0.636 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n" } ], "prompt_number": 190 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": "Overlap Example" }, { "cell_type": "code", "collapsed": false, "input": "A, fix_pos_GraphExample = basic_example()\nU = np.array([[1,0,0],[1,0,0],[1,0,0],[1,1,0],[0,1,0],[0,1,0],[0,1,0],[0,0,1],[0,0,1],[0,0,1]])\nV = np.array([[1,0,0],[1,0,0],[1,0,0],[.6,.4,0],[0,1,0],[0,1,0],[0,1,0],[0,0,1],[0,0,1],[0,0,1]])\nV2 = np.array([[2,0,0],[2,0,0],[1,0,0],[1,1,0],[0,2,0],[0,2,0],[0,3,0],[0,0,2],[0,0,2],[0,0,2]])\nexperiment(A,U,V,V2, fix_pos=fix_pos_GraphExample)", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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kNdX3Owtmf3q9ul4zavc8ap4nTUUOhOzzMgAGm81YNHkynly8GIsmT0aWrHFf\nWUMDnghix8FsGAjTjsP4fvsNQf7m3rThuKgozBg9GitvvRUPzJ6NiUOGIEpt5ZRGo35OFMuS5/sL\naMljrdGoP45KUQIAWYmJmDN2LJ5YuBD3zpyJUYMHd1UPXda1WOprdQW5uj0m5eUhT6DVZsOgW25B\nq9WqOMqaZVnk5eXhdJBELY7jYIqPx/vf/z6mDRsGU4hsbjfLQgzkMfGgAXyrc/zFQzjCRK5spVwW\nkN2GAEDxSLJdqUYQwAYxA1EUcezCBdzw4ouwtrcrnkcAGD9+PCoqKhAXF4f29vZuKp3jOCQmJODC\nxx/DpGbA1eDB/X/AX3U1KQUMQW/ZcUJ8PL762c8wYtAgMEG8UYJGAz6YEBBFsG43NErVAtLgvEht\nWK/3uRYEjQZ8iIRYluOUP4sEz6OxtRX7Kitx/1//irYAdhzKhoEw7TghgcTsBxLHjytuKnpzLd75\nk59gQk5OtzJft14PMYyiAIbnoXG5upe8S/jPWWJZ8iNLiPU9IKMooEWGgTvMgZkapxOs3zVkcziw\n/+RJ3LFuXUAbBnphLb7CXbivbj+5iqTX5tZWpCQnB/wCAaCqqqpLVd5+++3Y6KckdTodEkwm7Kio\nQOnZsyHfc9vx49hXVRX0OVqWxa3jxmH8ZZoP4+A4/PvYMVSo6I3x+OzZMIdoZtTS0YGEhISA5/HQ\noUMoKyvDu+++i+XLlys+R6fTIdlshsVqVSdMBsJQNJU3796yY5PJhD/v2oXEEBVPlfX1WO83NVWJ\nqXl5mJOfD+1lcPsKooh9VVXYoSLUtXDcOBSqSABs6ehAYgA7VmPDQJh2HEws9VcCbMZ6cy1+74sv\n8B8FG/5PeTkOBmvopsDQlBTcNmECYi9TLlBlfT02HTkCR5hzm5bPmoUUBfsKZsNAL63FkQ5L7CWu\n7lBOLzh7HnzwQZSXl6OxsREjR47Epk2b8Nprr/XomGr6lLgFAZuPHMH6Q4e6SnZ7i1MNDVi3e7cq\nUQJAsZQyXG644QakpKTgnnvuCegCD5ur2Jmnmp6E7GT0th2rtYn9Z87gT19+iQt+s596SpPNhrf3\n7lUlSgBqw32KCP/m3rDhSOygqrERv9+1C2Uq8hXDwcFx2ORZ48MVJQCgidAGL4sdf8tc3cJExUk3\nJySgsakJXADDePvttzFmzBgkJyfjxIkTYBgGL7/8ss9zOI5Dq9WqOn7Jh3Gzqayvx7rdu3Hg7NmI\njFdOfVukw5gnAAAgAElEQVQbNh4+jPcOHgxL7Kj5vFF6PVpaWxXP46pVq+BwOPCNp9FdoOggx3Fo\nam5GktrZOQNhSqvKv/HbtmOlBmuBaGxvx1t79+LTigq0+k+ODROb04mdJ0/ij198EZbYUft5A9mx\nWhsGwrTjgWDD/gRYl78NGw7HbuU4OA6bPGvn+VCTvUPA8TxKa2uJ2FE7v02BQH/Lt7IWX2FBc3WH\ncqSW8UEwxcZiYn4+iouLscQzwyBctmzZgkl5efjfpUtVPf/Z224LmWMSCEYUIUVIGSBw4qonl0QE\nqUIQQOKYqgkjx0RiT22t4nn84IMPAAApfj0kGIbxuTC2bNmCwlGj1IVxgD45jrvXUfk3fit2LCXz\nabUQNBq8FckwRVEEw3FgbTYwoqhqxyaKIkSGgcCyEFmWdP4N84belWMiVZgFsWclO1Zrw0CYdjwQ\nbNgfvV4xFNDrNixNOpfZ2LP33htWjgkA7wDL6Gjvushx0DgcYJqbwagUOyLDQNDpIGRmEvuVkkjt\n9rDvA4BCjokgkNCgKF7+tfgKD1K9uoVJVBQp+QrB8iVLsG7t2m5f4v79+/GLX/wCf/7zn5GQkIDp\n06dDFEWsWrXK53lrXnkFj0yd6m00FQKdVutNkIpkxyQfqufflE2W3Nr1+0jeQ55M6HarCik8NmMG\nfvfaa93O4xdffIGKigoApOHVd7/7XTgcDnz66ac+z1u3di2Wh7MgDYTOr2H8jT2149+/9hoemzEj\ntB0LAlmoI425S4uaVHUWTChI1Q7ym4nBEL5NM4z3ZhjixvTg5Ml4/ZVXfM6jWhsGwrTjgWDD/kRH\nkzJ4BXpqw7/zt2FR9BEnOqNRve3o9eSzKr3GaCQTpnmerI887012la+/UjKs9Bk0Gt/vPDqatHjn\nOHKvUts/RUKyaeka8tj2D6+/Hmv8bBjoxbX4Ctvt1e1nVDnxc8ns2SgvL0dpaanP761WK7Zv344h\nQ4YgMTERFRUVuPnmm/H00093PaekpARlx47hosWCb9TGIHvqBpOXofmXoknGL/30hqtYxed1chyi\ntFocPnKk23kcNmwYFi9ejMWLF2PJkiXQ6/VgWRZFRUVdzykpKUFFRQWWzJ6t/jMNhEU9jL+xp3Z8\n+OhRJMfGhg7diSLpU6Km/XwwpInbUkMpSbBrNN6eJDpdz70KUl+VEF4/URRxsKoKFy0WlJWV+ZxH\nNTYMRGDHA8GG/QnyN/fUho8cPQpREGCXbtiSV9rtVrdJY1ly30hJIVUnUkv5QEjH1OmIvRqNZEMc\nFUX+Ldl1qDVUpyOT09PSSF8bNRU6Go3375MVApxpaEB9SwuO+tkw0EtrsUZD/rYryNVdLtzeTtp5\nqyDSNsjXXXstrh88GAWZmQCAMYMG4eYJExATaDcpb7ATQSgnIJG0tA+GX+fXYNUDVQ0NKC4tRavd\njvKLF7H3/Hl8dejQ5W1JP1DaeQsCcOSI6l1Ub9hxekICbps0CenBciQk+2BZ8l2EIx4EoXu5qCRS\nNBryuNTqW4mYGPWdkZ1O724yyLVmsdnwUWlp11yrb82Ox4/vM6PkvzU4jgylDPD99oYNxxgMuGXC\nBIyWN1rTaontKHkEDQavdySc9bO+PrzqQI1G/Xwkt9vrRVF6D4fD5zpychy2lpejxFMZetlsOCmJ\nDPO7gmiee+65567oJ+gJOl3IcdASBUOHQsMweGT1atwwcyYyPUIjECUlJZh/4424t7AQecnJXbvM\nxvZ2HKmthSk6Gilxcd1j6P5ejJ5UXciPIwkSKXelp7tMf0+Mgj51cBw+OXoUn5WVdSXmpsbFIV6v\nx//89reYOWuWuvNYVISn7r4bDy9erP7zJSeTHUZ/h2HI4qMyWTkSO553442YlpWFgowMAKQXQmlN\nDQRBQLbZ3L2KTPLKAb5dXNU2kpJewzBej4nB4OsxkTwlkj3L8etjoojk0ZGuL+k4fscSRBEHqqrw\nwVdfdQ1fA4ChqakYnZGBVc8/jxsulx3HxAzMIX4aDbnhBgizR7oW3zh0KEampgIgCaYVFy6goa0N\nuSkpZLKvRtOVgwGNhthbbCzpJRMbG3o4pBIdHeFVGUk5UmqfazAQO5HCn1KOlDSTymPTp+vr8Y+9\ne1EtG1ibmZCAocnJePqFF3rXhrOzr/gYhatbmDAMMcQA8Ux/risoQGZSEr77+OP49JNPEBsfj+HD\nh3c16eE4Dps3b8aKRx/Fa6+8gleWLsXqefMwPjsbTTYbLJ734Xge30gXRXKy78h2f7deuMJEWswD\nLLRdz5HyV9TeLPyRv06ev+LhVH093t27F9Wy5l9ajQZFBQVYWVSEwXFx+O5PfkLOo8mkfB5/9CNy\nHlesCE+UMAxp8NPf29FLaDRkwrBKwrXjV5cuxc9vvRW8IHRVHIiiiJqmJpy8dAmDkpIQJ3fdKrmm\nJa+amvCh9LgUwlEamyBLtPW5YYhicGEiLdqBPHyy662pvR3vHziA0upqCDLbnpibi7unTsW8MWOQ\nqcaOly/Ha6++ildWrgzPjgcNGpihHMC7aQyAjw3/5z+q1uKf33orEmJiUN3U5LtRrKmBVqvFoORk\nMJKtabVEkKj1vgXicgoTCenzGo1eL4o0zbizE58eOYKtx47BKbP5bLMZ911/PW4vLOxdG46OJo0t\nrzBXdygHCDowShGeh+viRWzcuxfrtm1D6enTSE5KAkQRTRYLCocOxfLp07GksNBHcIiiiKO1tfhU\n5j0ASOnWTePGYWxWFhhJpXtfpC6UI0+i8ogt3i2iE0a4RD04aAAwXZEcFgJ0DAcDXDDCCUYvm80T\nahKmhP/uwfNZOzkOn5WV4YjfrItssxmLJ03qms4KAC63GxtLSrBu716UVlWR88gw5DwOG4blRUVY\nMnUq9PHx4c0LiY8HRoxQ//yrHVEkNhxmToeL47Bx506s+/BDlJ444WvHeXnEjidN8rHj8xYLNpeU\noEk2zZhlGFw/YgRm5ueTpk2hYuZSvN0/9ykqynsjVtHNVhGeJ8dQCvU4nV7vTSA4DgLPY//p09h5\n/DjcMhe5KToaCydOxDA/L4bL7cbGw4ex7ssvu9vxqFFYvmQJlsyerW5on4RWC4wbNzDLhSXOnAkp\nuLtseONGlB4/jmSz2WvDw4Zh+YwZWDJxIvSy89jW2Yniw4dxqq4OAPGK/fnLL3HdyJH4w6OPIkPe\nsTQqigyli/R7uJyhHDlOJ9Da6n0vUcS/Dx7ED//wB0wcPBjXeCat6zQa3DhmDCYPHerj6XQB2Hjk\nCNbt2uW9pwHh2TDDkHXXf8TKFeDqFyYAUFUFqK09b272uQFYOzqIJ8RmQ1JsLEzR0UEFRbvDgX8f\nPoyTly75/H54ejpuHDcO6R6DABBamMjFCMNAcAuwuqPhEPQQwZA64FAwgIYREKvpRIyO6y5QAn29\nCm7Ng5WV+PKbb3x6oOi0WswdMwaT8/KUSz89OTVWu52cx9hYch79E5OTktQnVI0YMTDCOHIaGoDa\n2ohfbm1rg+XCBaCpyWvHAbo3unkeu06cwN7KSp8SwpS4OMwqKMAYzyIYFMkNHR3dvbKB48ggt0hJ\nSSE3dikcYLeTUJcKwX360iXsLCvDBb/14JohQ1BUUABDoIXZ40q32u2wOBzA4MFISkxUX9ruT0YG\n8ZgMZNxuoKJCdZ6d1WaDxWoFRBFJJhM59xYL+e7dbp8EZ1EUUVZTg/+UlmJrRQV2enINE+Pj8frq\n1bjvppu865VWS8ITCQnhe5fLysLLE9TpiCBVi9tNBtHKhLzFasWqV17BPzyVNDqNBstnzcKE3Fws\nuvZaJMltUkpUZVmy+TMavecRQFJCgnobTk0l56kP0D+EicsFfPNN6PbPdjtRpUrIdpAAgu7MRFFE\n+fnz+OToUXR6Fv+D1dXYd+YMXr33Xjx4ww3kolASJv7eEQAcz8DijIEbGjA9+TYYIEbrgknfKX3Q\nwF4UmTBpbm/Hqr//HR8eOoTHZs3qas2cm5KCRYWFSApW/SRVB0kEUtsaDbnhhNq5mM3AkCHBn9Mf\nEUWSyK0yLBmQ2lpv7oVsarQSF1tasLmkBA1tbQCAS1Yr3tq7F6sXLMDzd9yBqEC9DKQEbymG778j\n7Q1hotORc9LWRq5NqfIigDjh3G689PHH+H+bNmHZpEkY6unjkBATg8WFhRji19fBBymkJPWz0GqB\nEPH6oBiNwOjRA9tbImG1AqdPR94B1+Hwel2kajFB6LK/Vo7D937/e2zatcvnZbdMn443fvpTDPLk\npAAgN+7s7PCSkY8eDV+YjB+v7rlWK5nCLNtAbNq5Ez/69a9RL/M0xURFYd3q1bjvuutIXxPpWtDr\nvX9LpJ4aiehoYOTIPtN35+rOMZGQkumCdYrkeeJVCXSBKO0uAzyXYRikmUyYkJODFrsdp+rr8c+v\nv4bd5cJHpaX4qqoKM/PzybA/aSGVl/96RIkgAi2uKFhd0RA8lds9rbfhBA06eCMMGjc0rKgohAB0\n5ZhsPHQIt7z8MvafPg23IMDS0YHCnBwsGDcON48fj+hQjXb8L/JASVPSxONgAxD1ejLwbCAu6AxD\nbvJNTT1rY97R4b2phwjrxUVFYWJODsAwqG5sxD+++go2pxP7Tp3CB199hcLcXGSbzd4XaLXkO5Ju\n3izrjYlLISCAvGdPpurGxJDjWizkRiTF4OWlxbJzVFZbi4W//S3e3bcPvCCgurkZhdnZmDZ8OO68\n7jokh3JNS+XLUVHe40fqzmYYYsNXOHmwz2A0kp9IRxZIibTS9ZGcTP7L84BWC2NGBpbNm4eROTnY\nVVKCTo83/FRtLd786COkJiZi4siRZKPocBCPuU6nfspvfX14eYIaTejBo2432UCcP9+1cWhsacHD\n//u/+MUbb6BDljR847XX4j+vv45ZkyeD0enI9RATQ95D8u7zPPldpDYXFUW81H0op69/eEwkgoV0\nJJdgIPw9JoCqQUYigI+PHcNDb77pE7ePMxrx8r334vszZpDcE89FIMLrSGnmTRAEBoxfzKbHxcCe\n0FCMzgmTVuEGIYpotNvx+Ntv459ffeXz0NyCArz7gx8gVY37T9ppygm1oAcK6TAMMHQocbcOZHoY\n0oF8PhLPE4+DioW1srERy37/exyVvTfDMFg5fz5+ec89iImLCy0YpXg+z/t4TAQRcAgGOEUdRJEB\nw4jQM25EsU6wSi5CgyF0vo0gwNXZiV99+CH+b/Nmn1ySoamp2PDYY5iUlRXy7wbDEJv1F9iRekzS\n0/tE8mCfo7WVTNKOZKghx3XPe5KqbGTrfX1zMx5/6SX8a8cOn5fPmzIFf/6v/0K2XDAkJBDvSaiN\nV297TFpbyfUtu7d8sH07HnvxRTTK/pa4mBi8vHIlvn/77b4hqcRE8jfLzyPPR95oMzaWCOk+JEqA\n/iZMBAE4daq7yOjsDJ2DoiRM1HRE9ewcG9vasOKdd7DhwAGfh28cMwZvPvIIclJSurzrbp6BRTD5\n5JDIxUmPhAnDyA7AwKjlkKTzhgdEUcQ/v/oKj7/zDpo8LnwAiI+Kwm/vuQcPz5pFXi51OgyGtGuW\no2Z3qhTSyckhv6eQnZQnsS9s/Ac3chzxogRL4PMITJfbjV8XF+P/Nm8GJ7/Rp6fjrRUrMFNNXxlP\nAyt3WweaORNa3HGwCwYIYvdFk2VEGFknErXtSNZaoRNdZPMQFRVykS2tqsJDa9agTDZJlmEYPDF/\nPv7vO99BtMEQMpQFliW7TqWdZiTCxGwm1WRXeM5In8XlIqELT/5DRGg0RPhJa4XCjf5fO3Zg+W9+\n0+1G/9LKlfiB/41+8GDyvQX6znpLmEheElmIpr65GY+9+CI+/Pxzn6fOnzIFfwompDiOHKsnM31Y\nluRApab2SXvtX8IEIAtRVRXZKUr/39gY+iarJExCNB7zuTF7XNmbvv4aP/rjH1Evc13GGAz45Xfu\nwg9m3QiARbOQoJjYKomTHpkJ2/3VRJx0oK61Fcv/+lds+vprn8dvmjQJbzz6KLJMJq8Yk1yEgc6b\nvJGcHDUu8Ohor2eEYcgFR0WJL5GKE39hIopEmMjmbPggLzn3dLg8duECHlq7FiVVVT5Pfezmm/Hr\n++9HbJBwHC+yuOBIQpMzDoJGB3XWLILl3UgSmzFIcwm62MBtxZ0ch//dsAG//vBDnw62IwcNwtsr\nVmDasGG+nTKVxIm8e3Kgzp/hChMqStTT0kJCJOHkU2m1xNuant7dy+F2k+tFlkDa1NqKlS+/jPWf\nfebz1DnXXIM3f/5zDJEnJptMZGOk5D3pDWHS0kKEhOc4oihi/WefYcXLL3clqQJkltCrq1fjwYUL\nuyfuJiZ2t63WVuJhlW0wQ6LRkPOYlnbFu7sGo/8JE4AswufOEUESKoQjoSRMAOUkWGlhk+LqOp3P\n4tbc1oYn3nwL/9i9y+dlM0bm44/Ln0e8Ubm3QY+9Jj7eEi8igEOnSvHwuhe7erEAJDHw1YcfxgNz\n5ngvBEmQSAlWgbxG/kmvEmpj80lJ5Lk5OTR8E4iGBrLghhPj9hcmALF/aXGV36iVbNhjB26ex0ub\nNuG59evhkonz3NRUvPn447hRYVfY5o5GtTMdLl4LcC6QkjENdIwbOtEJnciBgQgRDNyMDhyjh0vU\nAYJ3lo4ObmTHtSBR39Ht+IdOncJDa9agQhZuYlkWT912G5676y5EyT0f0owTyY6lv1keftRqA+c8\nqRUmLEtulhkZVJSEi91ObtodHeTf8k2glIgcHU3WicTE0ImZCsmkm3ftwqO/+lW3ZNJfP/44lt9x\nR1e/D2g0QFZWd+9JT4QJx5H7kOy9LzU14dFf/QpbvvjC52W3Tp+OP0aarCslCEvnUf55GcbbxC02\nlqy7fSTBNRj9U5hINDcDhw6pyhUJKEz8d1xSopxer9jcTBDJmuzigE9LvsITb/8BF1uJy61o0mw8\nPHshclOSMSghCUpE7DUJIEqcbjdO1dXhbGMjnv7ri2i3k79z4TXX4I/LlyNTntzoj7TLVuofEaiL\nolphkpoKTJo08Np1h4vDQRbbQPbpj5Iw4XnfZFR/YR3khvpNbS2+t3Ytvqqs9Pn9D+bPx0sPPoh4\nT9+SelcizrtSIIqkGo11dSJGtCFatEPD8B7hLn8fERBECCIDOxMNGxMLgfEIBp0e6QYLBhvIDtjh\ncuG59evx0ubNEGQibXRWFt5esQLXjRwZ+HyIoldg+w8TjIoKHFtXI0yio4mXZKA2UettpE2QZJ+R\n5ExI5beyHCeL1YonXnkFf//kE5+n3jBxIt767//GMHkuUnw82SxJItcjTNxuEZ0dIpxOEaJAbEir\nY2AwsiSPVvJUS+XCkpfEI7ZEUcQ7H3+MJ155Ba2yazkxPh5rnnwS98rLm3U6r5ckEuSbSaVw+1VA\n/xYmAFnYjx0ju89g8eZAC7+UqarReFtrK3zRgkD0D+dGV5iGEXl0WBvxzPvv4uOyCvzmgScRpSPu\nQlNUFEZkZHT9v5yIxIl/CEcE6tqsOF1fDzdPjPTrs6fwt23vYs13v4t75s4FozbhSfKiOBzkj5Sq\nJJQIJUyMRpJsNWQI3WGqRRSJm7qhIfQ0bSVhApDdlJTomZhIFr/2dlWdLXmex6tbtuDn774Lp2w3\nlpWcjD8/9hgmFNyIc07vTs/I22ByNYIVedlXzBAbZVhvxZDMQyiARRtrgp2JBXSk82u6vhnnzu7B\n99auxYnz57ueq2FZPLtkCX5x112B+5LIiY4mNxxBIDeM9nayeAdL8A4mTAwGIqzVlL9TrgxtbUTQ\ny5KoP96zBz944QVclImWKIMBLyxfjhV33gmN5EnQaEj+RUoK7PsOo73RAd7uCjohWx+nR4JZA61e\nQ0JDsvyP8/X1+OGvfoVP9u71edlts2bhD88+i3R5Q7ikJCJK+lgy6rdN/xcmEhYL6RPR1kZurv5/\ntpIwkdy+8j4HfvA88Y64ZYJEghF56DiyUy2p43DJaoWT87orWZZBbnIKBiUm+YgQf2HS1tmBFhv5\nfImxcYiP8usr4uctcbrdqLxUh2a/GG5KfBxGJBuQk6Ali3UkLj3JiyJ5kvzPo5IwkQbBpaWRsjRa\nShk5bW1EpFitykLbX5iwrHeSr1JSqctFYtUqqiVOnj+P761di30nTnT9Ljl5CB69+38wf2IhjDod\nYjkLYvg2MAL5bPKZk212jx0zQGJMHOKju/fH6WSi0aJPBycK2HnsGP7w/q9w/nxZ1+Njc3Lwl5Ur\nMWnYsJCfFxoNCRP625soEg+SNJVYKVTmL0xYloib5GRy46Giuu/D88R70tDQ9avW9nY8+dpreHvL\nFp+nThs3Dm//939jZG4uAGISza0acE1WnzWuzW5Di43kdCTGxiM+WiZuGSDO6EZcNvF0iKKIt7ds\nwY9ffRVtsjlNZpMJv3vmGdxZVOTrJaFh7S4GjjABvJnRzc3ECyLFnyV3L+A7vyPAjVsE4HQB9o7g\nUSKW5xDdaYGTZ2HjDOB5HtWN9ahr9c2mjouKwoiMQYjWexdQl8uBT4/sw9/3foby6tNITiIhlyZL\nMwpyh+H+6+fj5sJp0Ov0PjebS60tqKqr6/KSAIBOq8HwjAykxpvAahmkx9mJMu9pGEXuJpfOo6T0\npVHhUvtypfgtJXKkZlMdHd7ZMdLvWNY7ml3NeHVRJIm2Knqo8DyPtf/6F372xhvgeBEzZ/4IUVEJ\niIuOxoNTxmGESQ+IIjQC8aw43S5sPbIP7+z5FOVnT/na8ZDhuH/6Atw86XrotV5bPOdksG5PBSxt\nbeC4Tuza9Xvwbgf+64EH8LP771fXGt5sJrkfocS3KJKLWOoyK4ltqaeJ1GZfbd8LSt+jvZ2UKsu8\nJ5/t34/v//KXOFdf3/U7o8GA53/4Q6xcdjcsl9wQneQe4RTc+E/JPryz+2OUn6kkbfMBNDU3oyBv\nBO6feQtZi1kS2jemm9DONeAHL7yArX5Vmt+ZOxe/e/pppMo7hJvNZH0c4F4SOQNLmEi0thI3XzhJ\nTSCCpLMT6LCpeynLuxBjb4LFYQR472lutdtQVXfBZ+YOyzDITknF4KRkFH/9BZ7/4E8oGDcWj69a\niYULF5IZJiBDmYqLi/G719egorwczy37PhZPngUH58LJCxfR4uclSTXFY3hGJnSS0TOAOd4NQ3pi\n6Br+3iBYxjulb2GzkesiVLgIwOlz5/Bff9kBu0jc0FmxWkzPjEJKQhKGpA+CgRGx5dBuPP+vP6Fg\nrBo7/gFuvWYGztbX4YLFgkP1DpxqJdeHAS34+V2TMSFYLomEwUDsbaCNNKAEh+eJN7GhoUt8t9ls\neGbtWryxcWPX01iWxR8e/z/MHjcBMUYjPtqzDc/9U70NL5o8E5farHh+w19RvP8/XcdNTUrCumef\nxdI5c7yfSa/3tsqn+DAwhQlAdpjnzhHvSQgEEei0A7YOgA+jPxDLu2Boa4TVFQXG7zTzIo+axnpc\navEdcrW74it8UrYXm4u3YNKkSUGPX1JSgtsWLsJdU4pwzdDxPuWTeq0WwzMzkBJv6vY6nYFBSm7s\n5RULWi3ZBXgGolGuEgQBuHSJeFACLA0cB1jbGZQ3peJI5QkcOHYQ87L0MGqI506v1eHQ6SN4b/9n\nYdnxgrHTMLtgCgDALYj4rLYT14wvxPTx4zA+vQl6TYhhaqmpJDfgKqg6oFwhbDbiPZFVau44eBCP\n/PKXqL54EctuuB2Lr7keLMvgYFUZPjiwLSwbvnXCDMwYdS2cbg4/eedVNLQ24J758/H6U08hWS5A\nkpNJDxXqJVFk4AoTCYUGPRKCQDzlUhuIcGF5F4SWVnDuwAultdOG03UX4XC5sP/kEWws2YH9Xx1A\ntsphSrW1tZh63RQsmXQjpo6cAABISzBhWHqG10vij4ZB5rDLKEzUdlWk9F06Ooj3xFPNIwJwOcm6\n7nQCLa4YNDiJ6NV21KLtfBmsHSQPqjfsOC4mGum5BWCShwIAMmLbMSg+QII69ZJQwkEQiPekvr5L\nfNvsdjz/57+iIDkfWlbTKzZc1ViH8ePTsWjmTO+T9Hpiq6buG0aKF5pSnpBABm7JMqPdPMktrK8n\n4clIRAkAuDnALQTfvZmiYjEhdxiS4+Lx3p6PUfzxv7tdCFqtFgzDdP2YZSW+2dnZ2PLvYry352Ow\nLFCQk41Rg7MCixKAlGlG+DcFRasF8vJIa3kqSq5uYmKA/HyIGZmwOxg0NfoO5m53e5oziSLSdG6M\nzBqOIRnZEESxx3aclZaKwhEjkWEUwYjEUC0OhX4jDEO8JKNHU1FCUQ/LEm/FyJFdTcZio6PxzF0/\nwDX5+dBq2B7bsNkUjweK5mPB1Bu8L05JAcaMoaJEBVSYAOSGmpuLzqzhaLbp0dCgqooyKCJItY6g\nouhXw7A4cb4K48eNQ2FhYbfHn3nmGZw9exaiKOL555+HxWLB3Llzux6fNGkSxo4tQJO1AclxKhZo\nUVUaQXgkJpKLjoZu+gWCADQ0sSi3ZKJSMwp2eHt1iCLgFIjw1ItOsDwHMEBKQjIutTZh7NixEdvx\nuHFjUV5zEgzDgBV56HnisXG6tXALMrsyGsmNJTubhm4okREbS0RtejrAMHDZXEiIjUODrQnjxvXM\nhs801ELLatBuFYhHb8QI4imhtqqKAS9MRJF4RU6dAo7VmFBlGINWQxo4QQNejPwGy7kAUVAvbt7d\n9ykef2Kl4mMvvPACcj1lbBIjRozw+f8VT6zCu/u2qv58oWakqUbuJaHN0q44Uj8dh8PbFy8c3G6S\nYnLsGIlwOp2AWxeNxuR8tMUNgsiwcAlaCJ5rQ8v7dlX+4KvPsHL1KsVjq7Hjx1etxDtfeBth6WXH\nt3OkvwnS08kNRc2gSQolGB7viTt3WNdi/Y8vPsGKJ3pow7s/BgC4NQbq0YuAAZtjIookVFNTQ1pD\nSOM1pLOh4Z0wOlphgAtG1gWDhkOMxgmjJvRKL40n0fAuaBy2bomv/rR1dmDqT7+L1jZrV8a3P0aj\nEbhfVpgAACAASURBVE6PmsjOzkZNTY3P4xzHIdGUgK9f+rtifwh/DOZYmDN72E8kKYkkuFJBcsXg\nOJImJXWjdji6hx61nrY1Unfv+PjuTi2Xi1wPTU3B+xBquU7omi6ioY2EVuIdDTCJpPy93W7DjJ/c\n1Tt2/Pr7iI+ORacuDi1G0lMkJ9WOlIJ0KkgovY6trh1tB0+iraUZ1/xoSe/Y8J+2wJSejoy5Yy77\n5+9vDDiPiSiS8SM7dwIHD5LFWN4GQoLXGGCPToFdG492dxSanPGosaegxp4MKxcFIYjWUOrfFoxW\nWxuSk8wBLwQAcDgc4DgOt912G2pra/G9733P53GdTgdzUhJaO9S1Lu+RHNXpiIckL4+KkiuEzQac\nPUs8GzU1RFDY7cr5UG43Ed91dcQzWF5OvCIcR2y/upr8rr4+uCgBALcuChZTHpyGeLh5xme+U0tH\nG8y9ZceehoKMKJLmgbGxEHPzqCihXBZ4lwCOAy60dMJsTu65DZvNaO20QbwsyXz9nwElTNrayAJ8\n/jzZYYZCZFg4DCbYo80QWGKoDl6POkciztrTvAmAMgSR5JYAgIvRwwEjnNAH/XFBpzRsuBtarRab\nNm2CXq/H+++/r/gcF3Qh388JPXgmwlin2UxySSKd40DpEU4nUFkJnDhBklEjWfecTiJqdu0CDhxQ\nN3xbDsMycOpiYWGTwTFEmIqierGrxo55gYgkp6gFzMlAfDwYzYBarijfAlLo8mwNC4ejd20YAM23\ni5ABUUQtdSZubPQ2JzUa1SeAEu9JMvSudui5DkAk1TYXO5MQp+tEmsEKDUNWdpcTPq3pRRXJrwmx\n8WiyNIPjOOhUeCBEUeym6DmOQ7PFAlOMuiF6jP9snVDQZkBXFFEk9nvhQmivRjAcDuJtkVfHOxzk\na1Xr/NJoPLknjA4WbSriuDZoBRfio2N7zY5jjXFwQg+LJhV6nR4MaKFXf0cUiS1KzYzlQ7ClBrxG\nY++MJ3K5SK+1xkZPCF9jRBQAU2wCmpqbesGGm5EQawIbE2B6NSUo/X4L4nQCx4/7NPwDQKohw0Fk\nWDgNJtijkru8JwDQzkWh2p4CB68FL3iG+MkI5ZlwuBxotjZjSEYWiouLuz3+73//G+PHj0dFRQVs\nNhuKiorAcRyWLVvm87wtW7agIG+k7+yGIOgNYXz1yckkgYuKkiuCIABVVSQZNRJRIo2GaWwkI6P8\nW/ZwnDcUpPZ40gSHTiYaToFBjaURZy9W95odR5nSwGsMcGq8Fyod4ts/cTiIbR89ClRUkNCilO/U\n1ET+XV0NfPMNeU51tXpbVXovKXRZV+e9njgION94Ceeqj/eKDY8dNgrxMbHQmcK80VAA9PPkV4eD\nuL0DzbOR92UIBwYi9M526Dlbl3eEdwtI0zZDD29yrCACLgePKKH7VdTh6ECdpQ4t7VYAwL4Th3Gs\nrRa7v/zC53mffvopbrrpJp/fTZs2DXv9JlXOvmEWbh89Awuvm4OQMEB6XiyiokN4TWgzoCuOIJC8\nkEDDr4MhCRKbTZ2gcTpJYqysNYMiFgv5aWtrReXJfRgjnICBJRdCb9jxwnHzcMvUeRAYFlUx45CW\nqYXBQKbJU/oPLhcRJK2tkb0+Pp44cY3dI+rdsNmIELH6zuSDzdaGTZvewPr1r+HWiTMxt2BSz214\n5iwsu3YeFs+cD/OsAhji6NDScOm3wsTlIsOEgwkPp1NVR/qAaHgXjI5W8C43BB6AICBD3wSjhmwn\nBRFwOUVE8d75NdYOK+os9Wi3+8604dxuPPm332Dr59sV6+eDUVJSgpvmzceuX74Ho04HJoQzRGA1\nyBoeHdw1npJC2nvTlslXDMlTYrWG/7pwOxZLg3YZhhRbySexy3E6gZKSMuzevREcx0IUBYw161Fg\nJouvIAJP/OUFbN2xLUI7XoCtL26B0aiDVZeMemMuMjKAjAzSE4vSP2huJhNBVAy1DorUKy0lpXs6\nhyh6k779hX1TUx3ef/91fPjhH2CzkQssPSkNLz3wJARBxI//9puIbfjm+Qvw1RtbYExLQfp0FVOw\nKd3ol3cdUSTJfaG8IQYDiauH2+tBgtfo0cymQMe0wyDaIIJFgysRmfpGaGURHB4MWtuaUWepR6ez\ne2JLTFQMMpLS8PPvPIbFty7C3gP7wmqDfNvCxfivO5ZDr9WRaiGeXLAB866CxU5pe+8+g7TDUwvP\nk52h3R5e1ZUkSgDyOouF2I98AKooiigt3Y0///k3KCn5FDqdEUVFT4JltTjVymFMajzSkwcjISED\nTy17EotuXYR9Ydrx4oWL8dSy1WBZHXiBRYs+HQCx40BCiXL1cf48se3eQBCI18VuJ8sWw5DftbSQ\nEJB/yKe29hT+8Y+X8fHHf4PL5XuDaHN0wKKLw8yRY/HMXZHZ8G2LFuO5h1ZDbzAgYSxV0pHSL4VJ\nY6N613dsLDHiSHA4AM7NwMnEw8YYES8Sn6SFi4OZaYfdacc/d2wG5+zEtUO6K2dTTDzSzWmIiyIJ\nqzdfOwfNtlZcP2UaNhd/pHJw1GI8OOt23HLtbJ/HBIFUWTL+AoUBdMYAXzsdgtZnsNtJtYBaWltJ\nwmC4/k+O6y7gJXECACaTgN27N+Odd36DioqDstc5cP78UYwbdxPy869HdFoGklALAJh/7TxY2lsw\nbco0fKTSjhcvXIz75tyNBZPngWGAlqhMuFij5zOoc9dT+j69KUrkSP13YmOJIPEP31dUHMLf//4i\nPv/8Q/gHCZKSUnHXXauwdOmPEBdrAld5EgsmExu+fuo0bN6ici1etBg/uOVuLJ4xD8bhg2E0UaON\nlH4nTJxOUrmgFqOR3IelGHxHhxXt7SS+ExdnRkyMcn6FvKsmzwMio4eFTUGMaEOnoxMbPnsf//jk\nTVg7rMg0Z+CaIT8GAzJfISkuAelJ6YgydM/Y/u7sJTDHJuKmogUYM7YAK1atwKJFi3xGbW/ZsgVr\nX1+Lbyoq8JM7VmDRtTMUP6MI0n2WgSeTnQEEjR4GrZ8rxWAAcnNJ9y3KFUcQSIJeOCJDXq6r1obd\n7sBeRY5zY/v2T7B+/dM4f76y2+OjR8/A4sXLkZ+/AKLIoNUFWAQ7ksQmAMDdc+5EUlwiFsxbgIKC\n0Hb81LLVWDB5HgDAoTfBoksDQOw2K0v9eaD0XZqb1YsSm82K1lZiwwkJZsTGBs5zk0KXdXVEmEit\nbkRRxIEDW/HOO7/B11/v7Pa6wYOH4r77nsIttzwAo5GsxXY70BY7DIM6TuHBBXciLTERN3ls+PEA\nNvy7NcSGn3toNRbPmAf9kEwkjUwN48xQ/Ol3OSbV1UQ9h0NLixOffbYR27atw+nTh2E2pwAAmpsb\nMWzYRBQVLcfUqUuh05GkDLnrWxC8cdKOjhacPr0f1dWHUV9fiQMH3ul6j1/csxo3jJqAtKQ06LXB\n6x6djBGdPPB56U58uHcjvjl7HImeihhLSwtG543GHdcvwdxJs6HX62Dk7WAROruRYQAmPgZGA4vk\nZEBv8AxBy8ykXpI+RFMTseNw6OhworhYvQ3zvLKHheMcqKoqwcmTB9DW1ojt218Bz3tjndddtxhL\nljyL/PypAIjtd3Z6dqiiiGyxGkmiN3GLc3PB7Xj6EhRdMxs6LQkvdmgT0BSfB9GTKJWQAEyf3jsl\nopQrh8tFqmqC5ZS4XE7s3LkRGzeuw4kTh5GcTGy4qakR+fkTsWTJcsyZ42vD/qFLhgESE93YvfsD\nvPPOi6isPNLtffLzC3H//c9izpyl0MjWPYYhAsdgAJnTVH8ORlsTXG4O2w7txPu7N6KiyteGxw0f\njQfmLcFNU2dDHx2FmPxsmIYkdXtPSnj0K2HidgNlZeE1i9q6dQNefXUVCgrGYuXK5Vi4cKGPIi4u\nLsaaNetQXl6Ohx56HVOm3AmHbDwIaQleh8rKvTh/vgKi6H3znTt/By3cuGvOMtwz906kRWlCtqfn\nGS0ciIK8/UlbRxsOH9sOAIg1RmPiuHlgWZZ4QjQAKwowCnYgRJs2t8aAeDO5qM2DjDCMzKWdNPsg\nx4+rawAoEa4NT5t2ZzdR0tnZjsrKr3D69CFwnNeNUlZWjIsXj2H69O9i6dKnkJ09qtv7O53kBiFh\nFpuQKZyDxk8sB7JjDUvK8es1meiITYPG49GLiSFhnMJCKkyudk6fDl59I9nw2LFjsWKFsg2vXUts\neOVK7zost2G3m0Nl5WHs2bMRH3/8m27vMXnyXNx//7OYPPlGMLL4tlZL9meCoODRaW+D3lIPg7MN\noiCiqaUNXx/12nDRnHnQGfXQZSQjYWQadNG0E3Zv0K+ESV0diWGqZcOGNVi//mV89NEmVTHERYtu\nx9y5T2HevJUARNTVVeP48b2orz/d7fnR0SakpeVh4qhpGKFvQgw6wIjKpcNeGNiZGIh+WauCIODk\nyS+7/n/kyBlgPSu1lOSqE1zQiYGzfQWw0CdGQ6dn0RGThsxrMhEbT1f7vkZHBxEmaonEhouKnkJR\nERkY2d7ejBMn9uLs2aMQBF8hodXqkZU1EmPGTEFs7CCwLGl05S8SRJEk6cpLknWiCyliPcxiMzTw\nVKn52XH+yBlgtDpYNUlo1KRB0BkR5YluxsR4Z/pQYXJ109lJ+pMEIhIbvuWWp3DrrcSGnc5OfPPN\nQZSXfwWHg6yv+/f/Dc3N1WBZFnPm3IH7738Go0b5HttgANLSSGK1IJDeJgE9Oi4XxHYb7M2t+HDD\nryCIAhqszXj1jT8hY1gyWC010N6kX+WYhBPC2bp1A9avfxn79u1RlXU9adIk7N+/B1OnTgfHcdDr\n49Hc3D2ZxWRKw/Dh12Pw4DFgGA1EAJVIRqpYjwzxAjhGD52o3FjFxRi6iZJQiALAaP4/e28eH1d9\n33u/z+waLaPNkizJsi0bL3gBy2ExGAMGDAQwweTWJE3SEtKmj9OYOiG3TdLcpEna3CZ53QSSx5f2\nCaF93edJStoowSRNAbMYDDaLZMALXmVbqy2NlpFGs885zx8/Hc12ZubMSF40Ou++psEzZ2aOpM/5\nne/vu0LYZMMcjaQN6ciOIqSiItzlCwjbSqg3rqPLkoulYUmyUlRUSXf30ZRkQIejhKVLr2PRomuw\n2RyTu1JZFjcZLePEbBZGhLqwhyUbvdI8+pQGSvDiVMax4qXLG0ZWYDQkU2RrJmCpQJbMSBI47eJz\ny8qMZmqFxMBA+temomG7vZTS0rkcPdpOOJy4pi5efAO33HIXn/rUYzQ2Lkp4zekUA6orKmKFAb29\nWUqXbTbk8kpkm4Of7PrZ5NNP1vzCMEouAAVjmEQiJIRYMhEKBfnRjx7l+ef/M+FiaGxspGcic9Zi\nsRBOqiNuampi167fcOutt3PTTX+JyRSLT1ZXL2Dp0hupqVk86SacXO8liX6pDo/koil6hkrJjUVJ\nvAqiWAiTuxtQmfgeSYKQyaEZ0glZnFBbz0B5PVmbnBhcUvSGcC6EhktKKlm+/AYWLLgas1ksDfFt\nwUEYJz6fME6S05JMJlGJHo3GwqmKZGKMMsakMmTC7O2NXaTLTS7ME52RrVZxw3C5jHSnQkKW0/eK\nuhAattsdXHnltaxY8RgLF5YkGNBlZcJDkjxdOxgUncGzUVmZf2sJg9woGMMklxbFr7zSysqVK1Oa\n5zQ0NNDU1ER7ezvRNK0y165dy8qVK+nr+5DGxlXMnbuMJUtupLIye816UCrihHkZtXIPCziDRVFV\nLhGU7OgYq6OJ6jWRJdOERyYW0vFZXXjqllJUYbRGvtxRPRJ6mC4NNzSspLKynuXLb6SxcTlSnOGq\nKMLI0ArdqJ6TZCNCkkTMXlHEzyPL4v0mk3bul2rMzJ0rXOsGhUUgkL7r8HRquLi4jFWr1rFsWQtW\nqxBSKCQ0Wl4uPCTpxpD09mbPSzSZxGecP5/5OIPpYVYaJq2tO/n613ekPP/WW28B4HK58GX4wC9/\n+a/4yle+zZ/+6ZOUlmbu/KR6MyaRJM6bGxmVK1gqH6FY8U6EcPL3ZCjq/5NiIR1JUhi2z6W/bDFz\nyg0vyUwgl8Zo06Hhxx77Jp/61PeprV2IllWs3hO0zkk1TtRy+2RMplgDQ0mamBQcjHDw4O+Q5Sh+\n/yif/vR/x+GwUlJiGCWFSqZ1eTo0/KUvfYNPfvJvWbx4VYLnRJKEIbJ8eeYeOD5frGdPJmpq9A+5\nNJg6BXPH0hvG8Xo9HD16gM2bN6c9Jls+8ObNmzl37hRms3Wyf0T8DjEajT3SWeJ+UzHvWz5Cp6UZ\nvzT1CZRy3Cl7bFWcLlvNubIlFJeaDNf4DEHv3Kbp0vD582coLa1CUaRJ/UajIiwaDouH+m/t75ho\nMhjn3pYkMWKpuHii7NIU86JYLApnz7bR1fUebncHkiReNwrDCpd0dsV0adjt7qShYeGkUaLqSQ3Z\nZGvM19OTfTNgsQhvicHFo2A8JnpLhEdGBqmunpMyqjoeKUsCqtVqpbKymtHRIez2/AfcKUh0SfMZ\nsNVTG+nBJQ9hIoda5/jPUiAkOfAU1eK1VyOZJGPRn2FcCg0PDw9hsaRqONmDnuL5i3te3RQ4HDEP\niV5KSoyKm0ImnaanS8MVFdV4vUOUlbkoLhYGsfq2bIMrR0f1jXyoqxPGyVTn+hjop2AMk+nkYldQ\nB6JWeqwLOE8jruggldEB7Io+F5CChNfswuuYQ7ioDMkkTTrlS0tzu0kYFA5T0XC60I2WltQcEdXb\nk4veTKb0cX8DA70aLisToZZctKco+jqE22zisw0uLgVjmMTvutQQSnxIRX2EQlW43QOEw2GsaYKG\n2Sz1cDjM0JCb4uLp6/AXiQAWC8PWWoattZjlEEWyD4fsw6KMcfxcDybJRDgaoXpZBWGLi7DFiexw\nYrGJHz7+rC0Wo+RyphGvYS39qs+FwxdWw3o8N2azWLTVMGEwKB6Koj9fxDCcC5903rDy8unR8PCw\nm9raSk0dZQphDw/rq4Crrzc8epeCgjFM/H5R8hWNZo4ZOhwuFi9ew3PPPceWLVsSXvN6vbjdbuSJ\nlbm7u5vy8nJKkuIhu3btYuHCFpxOfWGcdLvNZCIRYVCYTBA12fCabHgpJ6j4+Ltf/GjyuH+9+x8o\nLXViNqdPEjIW/ZlHNCo0rOYqpcNunx4NNzenalhPvN1mS5xeHf+eUEj8W8/QPcNwLnzS6aCkxMXS\npVPX8KJFLRQVaa/D6b5blvV5S4qKoKoq+3EG00/B2IJ2u7ix6/H+3XHHNp54YmfK842NjSxcuBCv\n10skEmHevHnM05gg9vjjO7nxxm3TcdopRCLZY6NaZZrx2GxMdtA0mDkUF2dOmI5nOjS8fn2qhrW+\nW01SdTpj2stk9IbD+sueDQqbTMbnxz42dQ1v2LANt1s7/yNdmNDt1pdo3tBgbO4uFQVjmJSV6T92\n3botHDp0iPb29oTnR0ZGUBQl4TE8PJxwTFtbG4cPH6alJdHKn05U1z3EqhxywRgSPDPJZnDGMx0a\nXrs2UcPpjBKLReSR5FLdpQ73K5yBFwb54HSmD4XcdtvUNXzNNVsIh0UTt+TqMC2jKBoVfUuyUVoq\nmv0ZXBoKxjApLta/cFqtdh5++HHuu+9jdHZ26v6Ozs5O7rvvAT7+8cexZJkQDNqubr1Eo7Fa/Fx6\nPDgcRk+ImYrJpC8EAlPX8B/9UaqG43WqekkyNUfLhmGcGJhMovW7Fna7nUceyU/Dmzc/wCc/KTSs\nNgIcHJyYco0wLLQ2dOfP66uuMbwll5aCMUzUltZ6uemmrdx992OsW7eetra2rMe3tbVx/fXrueWW\nx7jmmq26vydXcUtSLLEwvhRT73sNb8nMZmKiui5uumkrH/1o7hreuPExrr02UcOq4RFvkEhS7JGv\ncRGN5tY4zqDwmDMn/Wu33LKVe+7JTcPr1q3n9tsf4/rrhYZV7art74NB7UqaUEhjerAGFRVGm4VL\nTcEYJhaLEJNeQyAchltv3c6WLT9g06Z7uPnm22ltbSUSZ06Hw2F+/etfs2HDbWzadA/33fcDNm7c\nrvuccjFK0rnM1V2nHoqKjO6EM53SUqEDPchy7hq+//4fcNttiRpWjY94g0RF/fdUDAt1vo5hnMxO\nSkrS3+jNZrj33u188pM/4M477+GWW7JrWOg9puF4XSmK6E+ilafX15fd8ydJwlticGmRlIvdtOMC\ncviwyLbO5mVQB/6pP3kkEuKdd1rZs2cnp061UzaRsOLxjNDc3ML69X/JmjVbdIVvVNTFXr0Q0oWZ\n4t3l6QgGfTzySCyT61e/GsduT3QPSZLYJegNZy1bZuwKLkc6O+H06eyNn9S5Oqq+kjXscpWjKDIe\nzwhNTSu5/fYvcfXViRqOD9OkW7DjG6alM/wVBbxePT+dj099Kqbj118fx+HI7uZsaTFKNmc6fj98\n+GGqzjyeWNluOBxi375WXnxxJydPtuNyVSDLUTyeERoalnD33X/DRz6Sug5brbEQqCSJShq7HZqa\nYt6aQEDcH7Ld7WpqxPu0CATg3Xd93HRTTMODg+NUVhrlZdNNwZQLgwh/lJbG+iloEY0mGiUAFouN\ndeseYt26h/D5PLS2fo9QyI/VWsRdd/0VZWV1OcfYs3lLTKbs1Q25kEuOjcHli1pRNT6euRV8vFEC\nqRres+f/0Nd3Aqu1iOuue4AlS64jHBbvjdee2opei2R9ynL+GlM9ggazk6Ii0ROkuzvx+Xg9Wa02\nNmx4iA0bHmJ83EN7+8u0t7+K1VrEkiVr2Lhxa4ruIXEtdzpjYfCzZ8U1VFenr/W82SyGSRpcegpq\nH2KzCes5nScgGs2ejOd0upgzZyFOZwVWqwO/f3TS+6GXTMernTItlvyNkuQL02g9XzioPULSVQRo\nGSXJOJ0u6uoWT2rY5xPuFzVUGK+9dKXpamgn+bvzxWYzkglnO7W1UJnUzy+doVtc7KKpafmkhr1e\nDyaTMHCSdaleC3Z7anVmTw+cPKlvUF9trREKv1woOMMExE06WWCq61vP4hrfdEpd1HM1TJKZDoNE\nJfnGZMwbKRxU3drtqcncqlGSrc8NpNdwvPZy8ZZAfpU56vdqVUgYvU5mF5IECxYkGieZPHDFxTEN\ne72jQKyfTvz71G7DFRXaa2tHhwgZZVr7rVZhmBhcHhTU7Uxd1CVJVDeoN2t1Qde743M4Yma336+9\nqKcjPnkwU1LhVFCTCaNRcYEa80YKh/gbeFlZooEdCOgzSiDZMBnVPCZdqMhs1jZ08/WYpCtfHxnR\n1xbcoHAwmWDhwlir90yGSUlJ/DrsJRoVgpWkxEZ/Vmvieh9PICBC+z6faEOfTsNz5xqh8MuJgjJM\n4hd1qzVmmft8+nd7skxCi+P4RV1P3ohqjJjNsQX+QriwVWPLbjdc5IVEfLKpySQ0bLGIBTaX6aZO\nZ2xRVz0m8ciy9iKt6laLfDwmqqcwHR4PjI3l/rkGMxdJEoaJmoCfbv1yOJwJ04fHx2NCUVsjuFxi\nDUynzXhtBQIipJN8rMMB1dX5/jQGF4KCNUzUf+favS8ahaKiVI8JZDYAVK+IxSIeya7wC1H7ZDIJ\n48RwiRcOyTdys1kYJ7kan/EeE79/DEVJXI21PC+ZjBLIT8N6mv2NjekbP29QWDidcOWVohLG4dDS\nuJQQzhkfFyJRwzY1NeJRVKStZ58vsRssCO9JsnFiDOq7/CioPHmtOHZxMcybJ2rY1a6A6VB3kYmL\neuKKmdwFM947kincMxXDRFHAbLYiSSZkObZtVrPPR0bEORkhncLAZkvUqsUiShh7e/WHJB2OEkwm\nM7IcRVEU/P6xSV0ne0tUDWdbnHPVsNkcq8RRFPGwWh3IcpRoNPGOMT4uXne5DA/gbEKSRMjSbFYn\nZ8ceIgfKz/nzxxkb68ftbuHqqxekGM/l5eKaiTdCFCW9Jy4UEo3YKivFd6frTGtw6Sgow0TdbSZb\nyQ6HME7Oncvc6Em1uuNDOWK3qWiO4FYXXj3Wdi6LenxfCbGgW7j77q/FvW5BlmOTlC2WWHKXUZ0z\n89EysM1maGwU04dHR/U0ipIoKiplfHwEEOEc1TCJDwnlUraeSyhHlsVnBoOxwYSRiJU77/zridej\nBIOWCaNbPNSQa7okRoPCxGYThqmqg/ixDKOjR3jnnV8C0Nu7EbN5c8r7JSnmVVQ7u46PZ87HUufr\nLFpkaO1ypKAME9A2TEDcvOfOFZMl/X5xTPxCq97kARyOUiRJQlGUiQXUi8Mher2rIRs9O0y9qLMe\nVINEPQ91Z6AoUtLxEpIU21WrPSLUz8hloKHB5Ue6nAy1iZ7VKnaD4XDmxdfpdCUYJhA7Xk9jPy1k\nOX1irKrj+O9QDZRkhDdHmtwdq16bSES8p6rKuGHMFjINKa2ri3U7O3cu/TydSEQk1VosokmhnoZ/\nFosoJ3Y6cxtnYnDhKbjIWiaRm82iE2BJSWyEu9WaGp4xmUyThoiiyHi97oT8EfU9uZDcNll1W4ZC\n4qHeZJKPS/dzJOevhMNixzkwIHYCBjOXTBqWJOFRKC+PLag2m3YZenx83uM5P3mMWraej2GtajIa\nFbr1+8VNIBQS3pFIRByjnoteL4uixMYvDA+LYWv5licbzCwy6b22dt7kf58/35X2OHWTVlcnrols\nHmo1eTYchuPH9XYuNrhYFJzHJJPIIVbpMDwsFlKLJeZuhpigOzr2cuLEPrzeARYtWk19/cK8z0nd\nTapx0+Tn011E8Qt8PJkSFCOR2AjwmhojqWsmkk3DalxeksSCGvOsJT5GRk6yd+/PGB8fRFEGaWm5\nPW89qD1P1ERrVbPx3r7485vKZG1ZFuGqYFAkJhoUNtNpmASD4r/Ly0XuXTr9xc8Vi0SEcbJoUe7F\nEgYXhoK7bWVb1CFmnBQViUVQdSXH9xyxWKyMjp5DlqMMDqa/ILRQ8z8ikdiindzMSv13Pgt3Nhe3\nooick64uY9c5E9GjYdU4iQ/bqfpVc5+Ki0sYGekhHA7Q39+ZU7mxqmHVq6d69FSPCMS8HMnhxiCD\nawAAIABJREFUpOQ29vmgTtbu7DQqdgqdTOXkekM56qavt1dt+ZA+V0lrCrssw6lT+jrEGlx4ZqVh\nArEmbKBtHFRVxSz1TIaJamBEIrFFXF2sM3lC9CzYUy0xDoVETo1hnMws9GoYRFiyvFx7Aa6ujml4\nYKAro56SDRE9Go43UlS0KtOmouNoFI4dM0riCxm9HhOv15PQyyQeWRYGbLxh4XCIXKVkL2G6uWKy\nLAZoDgzkcvYGF4JZa5hAzFOi9Z6qqpilPjgYs9STDZFwOJawl20BVl3suRgK+S7q6lyJSCRzx0OD\ny49c8z+cTm3jZM6ceA0nGte5GiIqqoa1jBLQPu+ptLJ3OMRN5MQJ4aY3KDwy5ewVF5dSUhKLr2QK\n53R3p2rSZhPGiWqIZJsrpg7/U6t7DC4Ns9YwUevcJUk07EluBFVZKSx1STLh8fQnJKrqNUS0vjPX\nRTrfUE/8sKtgUMTsDWYGaoJqLhQVifBk/AIf7zHx+8cYH/cnJKnqMUSSUXNKtN433T187PZYH5RQ\nSMw8MQzswiOb3vXkmQSDIqdEC6tVGCcWi/65Yt3d2oaOwcWh4JJf1Zbe2QQVDCbuwNTpp+o8krq6\nVdx88/9FSUk1RUWulPh88jycy4Vko0TF5xPP5+JRMrh02Gy5ewjsdmGcuN2qN7CCDRv+guLiSsxm\nKz6fj5KSosnj89FwuvJfSL/g5+MxcThSb1bj42Ina4ymLzwy6b2urolTpw4B2nkm6iazqCjlpUks\nFlGxY7OJNV4P584JA76hQYSIhodhcNDCnXf+NYoi4/MN09trwmyOJaMbTA8FZ5io1nemLq/JXQHV\nXaDqCYlGobS0jtLSGgCCQS+yHMVkMie8R/3f+IU9065RUfIrM/b7PYyPDwNgs6W/+uKHW2l9zsiI\nKJc2LqDLn3wMyFAo1kBQePYk6utX4PW6AaGjkpKqyePjNQwxbWbSsCxr60tP11ifT5+O7fb0O+i+\nPhG2ynQTMph5TKUyJxAQes92zTQ1Ce2cOKFveKSaEHvypKjWiUZhdHSUUEgkPBUXVzE8bCYQEJpt\naEicnGyQPwVnmEBqS+9k1AZrIIyRYDC2q1P7ldjtxZhMFmQ5gqIoBAKjOJ3avYvjS361hvbl4w4M\nh4O0t7fy5ps7OX36AK6JOraRkWG6u/dy881f4NprH8RiEVdjfDw+HZGIuCCN7rCXP7kYJpGISPxT\nd5yqgRoOiyZrMcMkczwv/hrQMk6SjXEVkym9xsPhIG1trbzxxk46OrLr2GbL/LPLsmiKtXhxxh/F\nYIaRbygnfpOZudlgrGnfkiXC4MgU3g6FhIdE5GEF2b27lRde2MmxYwcoK4tpuL9/Lw8++AU2bnyQ\njg4bw8OwYIExqXiqFFyOCWRe2FQhq+WIgUCqq9lkAptNShrmpy9JI7l7a/z36uWdd57hb/92PidO\n/JzvfvdLjI6O0NfXQ19fD6OjHr797S9x6NBTfOlLTezf/wyQGI/PRKaW/AaXD3oME0URhqbbneoG\nV8uG0w2kzISWhjP120m3CL/99jN89avzOXbs53znO9l1bLXqG/oXb4QZFAbp9K4oMHfuYurrV7B0\n6a1YLLWTE6n9fvG/apg9k2HS0BAzps1mYdimm5ETDIpeUNEovP76M3z+8/N5662f841vfAmPJ1HD\nf/u3X2L37qfYvLmJF154huFh4ZHJdC4G2SlYj0k6xsfFTtLvzxz7NpvF6PjxcVF/pndRh9ginm7X\nmSmU8vLLT/Dqqz/khRd+z9q1a1Net1qtbNmyhS1bttDW1sbmzQ/g853n/vu36zo31UNkcHmTLflV\nUcSOLl28XPUYZhpIme3z1dBjppwttXdKMi+99AQvv5ybjoPB89x7b3YdK4oo6Wxs1P3jGFzmJK/Z\nkYjYRPl8UFNzHS0tHwdE+EQNw6iGuTqSI926WlqaOqbDZILmZlGB43bHno9GY1WMv/vdE/z+9z/k\n+ef1afj++x9gePg8W7du5+xZ8fkG+TGrDBO11j2bUaKS76Kuosbk9eZ0vPPOM7z66g/Zv38vTU1N\nWY9fu3Yt+/btZd269VRW1nLTTVt1fY/Pp+98DC4d2cIZQ0Ppw5VqjgkktqXX6/VL/q7kUE28ca3l\npXv77Wd4+eX8dOxy6dPx4GDiLthgZqPqPRqNecRUzRUXx6yK8XEPoADSZFM1Ve/hsAhnq9OKVRob\n0zdamz9fHHv+vHhOndT++uvP8Pvf/5B9+/Rr+M0393LDDeupqKhl06atVFQYk4vzZVaFcjye2ART\nPSQaJrkv6snJhZkIh4P8x388yu9+99uUC+HcuXPYbDYkSZp83H777QA0NTWxa9dvePrpRwmHMyTW\nJHxXTj+GwSUgk2t7eDhzDlUopL2o52NcQ3q3tFYuSjgc5Fe/StVxJg1D7joOhw3PXyFhs8VmfQUC\niWtmvIYjkQiBgD/B+FYRCdaxQa0gklGLi9N/ryQJw6WhIVapGQ4HefrpR3nuudw1/Oyzv+FHPxIa\n7u2d0q9kVlOQhomWGzwcFrvMXEoXp2NR10t7eysrV66kpaUl5TWPx0NxcTH/9E//hKIobNiwgZde\neoknn3wSENb6ihUr2LevVdd3qY21DC5f1BHwyYyNZb4hqyMWVBI9JupuM3e08qa0zq+tTVvH2TQM\nuevY8PwVBmoreY9He302my0UFcUy9r1eT4LxHY9aVTk8LK4VPbOWJEmUoDud4r/37Zu6hl95pRW/\n3+gflS8FaZho7TYHB8lpVgikekwu5EC8N9/cyaOPbtN8benSpQwPD/Pnf/7nAOzZsweAp59+evKY\n7du38eKLO3V/n9Hi+/JGqyNxKJS9zDF5wXY643ebIaLR4JTDH4qSOuFaZe9ebR3r0TDkpmM9JZ8G\nlz9dXdDfn7mSpaQkpmOv15N2YxWvfVnWP2ldfZ/LBS+8sJPt2/PX8Be/uI3WVqFhwzDJj4I0TJJb\neudruRYXuwiHA4yPD+N2d+D3e9KWUk4Fn8/D6dMH2Lx5s67jW1vFjjL++M2bN3PyZPtEDDY7hhv8\n8ifeMFH70GSbd5O8YFssNmy2okkdd3d/QCDgyUvD8ZU5WjeRXHSspWH133p1bGh45tPfLx6Q2TCJ\nX4s7Oj5Mq4/4kvfSUtH3JpNxInqTwJkz4jx6ez2cOjV1DX/4YTter8fw6uVJQSa/qrtNtWLB74/1\nNtGb7/HOO628+upP6eg4QHm5yGB67bWdLFy4hvXrt9HS8iBmc+5dsLSqcsbHB6msnINFR72v2+3m\n4x//ODabja9//euTz1utViorq/F6hxLc9+kwBvtd/sSHJH2+7B6/5Bu1quN33/1X+vvPUF5ewbFj\nv2V4eJCFC9dw441Cx2oPET1kahLo9Q5SVZVdx+k0DLnp2NDwzCYYFD1pVLQMk3A4yL59rfzhD/9I\nT8/xCQ3/hn/+5yGam9dw883bEvrgxHKrYjrt6hIJsVaruIa83thjfFy8R80vGR2dHg1XVVXj8QxR\nVZV9LTZIpSA9JpCY5R0Min8XF8daz6dj//5n+PKX53P48M/57ncfY2xsdLJu3eMZ5jvf2cHRo0/x\nta818c47z2Q8B61W35IUyx9QH9FoAEXJvsoGAgHq6uoAGNTYBkgS1NSIuGq2h9E58/JH1bBaFpkJ\ntXOxSryOf/zjv5/UcU/P2UkdHzv2FF//enYdJ6NdPhzB4+lGljM3cMimYZXiYrHjLS2d/hk8BpcH\nZ88mJlYnGyZqD5G2tp/zgx98M07DnXg8w3z72ztS+jmpnYnVJpKyLAyQ9nY4cgTef190cj13Tjwf\nX6CgKDLDwwNEo5nXYr0aNsifgvSYQGxRj28opg7sU+cyJE9IfeGFJ9i9W3/vhfvue4CxsfNs3Kiv\nh4hKIOBlcPAsbnfsMTQ0QDgcxpqmgUUkEqG0tBRZluns7KQkqX1rOBxmcNCNy6WvJ7JRZnn5o2pY\nHRyZiXhvyYXUsWqUhMNBhoa6GRg4S3//WQYHuwkGxxkacqfVcTYNg9Dx0JCb+vrKrB2KL2TOl8GF\nxetNDa/HGya59hDZvPkBRkfPc9dd27FaxWera7yKLCd6ISORMEePtnPgwGt8+OEhysqW4/WOZFyL\n9WpYXYv1NL00SKVgf22qprRifGr7dlmOiXf//mfYvTu3uvX9+/dy/fXrKS2t5Zpr0vdeiEQC+Hwj\n+P0ePJ7zHDv2ctK5OqiqauC5555jy5Ytmp9RXFxMJBLh0KFDNGp0ltq1axfLl7ckjAjPhDHM7/In\n3rjORDQaC2tcKB3Lchi/34Pf78HnG+HIkd2Ew4kZ1Nl0nE3DkJuOc53AbHD5MDCQ+pxqmOTTQ2Tf\nPqFhp7OWu+/W1rDHE6Kzcz8HDrxGe/sePvjgTQIBcXGZTGbuuuur065hpzPr6RtoULB7DpstNto9\nHSaTCGlYrUF+8YvUunWAl19+GbPZPFm3vnr16snXmpqaeO653/Af//EosiyK6hVFwesd5OzZdtrb\nf0N7eyunTu2nr+8oIyN9KIqM2Zy6os6bt47/9b+e0DzPJ598ktBE0f7KlSs1z+UnP9nJli3aVT1a\nGBfM5U+8xyQToksxwNR1HImILwsGvfT2Hubgwf/krbd+ycmTb9DdfYjBwS78/jEcjtSdot3uZNmy\nu/nRj36S8poeDUNuOjY0PDNRy3mTMZvT9xABfRr+1a9ifXDC4RA9Pad4992X+d3vnuanP/02f/EX\nt/Lkk9/g7bd3TxolALIcZWSkB4vFwtKlt0+bho25ZPkhKUphRmo9HvjgA+0LIJnXXvsl7777FK++\nujvlNTUJ6vDhw3zrW9/i3/7t3/ja177G3//9308ec9NNG6mu3kht7VLc7rMEg97J10pLa5k7d3nC\nZ/b0fIDJZKa6ev7kw+Gw85WvzOfFF/9Ts5dJJtra2rjrrnvYtasTqzW7K8RshquvNsI5lzuyDO+8\nE+tKmY2p6/hWnM61VFbOx+sdjHuvnebmdQmfNzzcidc7QE3NfObMmU9NzXxKS+cQiYT48pcvjo6X\nL8/cPMvg8mR0FI4fT31eUeCZZ6au4aqqdVRVLcTt7kNOypB+/fV/xuPpm/x3cXEpV121njVrNnD1\n1XdRXb2KaDTC5z8/nxdemJqGi4psrF5thBzzoWANE78f9u0TscxsfOMbN/HNb+5Icd0dPnyYlStX\n8v3vf5+vfOUrgIhtOhwOxtSRlsCvf/1rHn30q6xZ88mUz7Zai2huvg67vYSionKcThdFRSU4HLHs\nU3Wi8f79z9Da+hXdLkyAzs5ObrhhPdu2/YBNm/S1pC8thaVLdR1qcInZvz9WTpmNC6nj5uYbcDrL\ncDqFhp3OUsrKioFU6/Zi6NhkEsa1sejPPM6dg+5u7dceeeTCaRigo+M1ampcrFmzgTVrNnDFFVdN\nGjzqDKZIRISTfvGLqWlYLTQwyJ2CNUyiUXjppfRDzlTGxz187nMNeDwjKSViX/ziF/npT39K/K+o\nrq6O/v7+BEs8HA5TVubi5pu3Y7U6MJlMlJfXU1UlvCFVVQsxmUT4Rq3UiV9QrdaY90JNXNy16zea\nSV/xqIOjPvGJx9i6VX8C7vz5MGeO7sMNLiFvvaXPY3IhdFxaOoeqKuERqa1txmoV7glVw5lyPF56\n6Qmef/7C6biy0hiSNlM5fVq7t4jX6+Gee6ZXw05nKXPnzmfu3PnU1c2nvr6aigpta1Zdl4eHRRj1\nt799gn/7tx/y7LO5a9jphGXLDMM5Xwo2+TVdZ8pkxsbS162fO3cu5TmnRmDbarVSXl7JggWrWbLk\neqqqGjGbbZNVP+owPy2SG7bdd992ampqufPOe1i5ciXbt29j8+bNk+cXDofZtWsXP/nJTg4fPsyO\nHY/r9pSA+L1U6ivcMbgMyNR0Kp7p0nFFRRVXXbWRJUtuxOEoJhKJnUN887ZM2xmLBT72se1UVV04\nHdfU6D7U4DIjXd7fyMj0abilZT1XXnkDZWUVaHn1QKy9TqfwIJeUiIfZLNrj9/bCQw9tp7Kylrvu\nEhr+4hf1adhigYULDaNkKhSsYQLak09zQa1Vj8ebJjZkNltYunQdNTULE74/uSQ59X2x/7bZxOOm\nm7Zy/fUPsG9fK3/3dz/m05/+DKWloiWzxzPC8uVr+fjHv8D3vrdFVyw+nqoq/Tc7g0vPdJQb5qJj\nk8lMXd0VOBzCO6L2uwmH0/UvScRiib0nm46vvHItDz6Yu46dTiOpcLaR21psZuHCFZSVJe7AJElo\np75eGCPxTdjiUcMvfX2wadNWbr31AV55pZV/+IfsGrbZYPFio0/UVCnYUA7A3r1icB8IASY3NjOb\nRRvtLVsaGBkZTqlb14prWiwWioqKEuKa4XAYl6uCxx/vSZivE3td7BLi+6nEnw8It7jDof1zeDxu\n/uVfvjNxXBE7dnyHqqrcayXNZrjyStHLxWBmcOSIaAgF2s351Iff7+H++6dXx+pCbjKJkGh8Xwit\nUI7ZLBbkdJ7KZB1/85vfSdu3JxOLFhnj5GcyHR2xdTkeNZQzVQ2Xl1fws5/1UFrqmtzs2WxCr3Pm\nwIIF+s5zbEw0gYtPBxgedvM//6e2hqurxaRio3fJ1CloZ1NdnXD5zp0r/nvOHBHGcLnEjquoCKqq\nXCxbtobnnnsu5f0rVqzAbDbz1a9+lWPHjrF161ai0Sg7duxIOG7Xrl0sWtSiaZSAuCC0Qkt6jBIQ\ncyKczgqczgqsVkfW8tF0NDQYRslMo7pa6LauTui4pkZ4vcrLxa7P6RR/0/Ly6dex1RrbUToc4pHO\nPa2W3mcKnybrOJ+W8pWVhlEy00m31pWUTI+Gly5tYcECF3V1Qi8lJbGO37l4MkpLYcUKYQi7XGpH\n2UQN22wKNTXiuAULDKNkuihoj4nbLYYzZeP553/J7t1P8corqSVqr732GrfeeutkgtXq1at5//33\nE47ZsOE2Vq/+M9ateyjj94TDYsepVuGYzYmu73REImGefjpWEvfZz36dhgZrTjHMsjK44gqjRHim\nEQzCwYP6jp1OHUuScHUn6yUYFO3xVY8fxGL12bSVrOMvfenrlJbq95hYrcLjZzRWm9mMjMS8gMlM\nVcO33HIbmzb9GZs2aa/FS5cKgyMfxCBNH83NSwCF8fFhRkbcmrkuBlOjoD0mevVy661bOHToEO3t\n7SmvbdiwgWg0iqIoKIqSciG0tbVx5MhhbrxxS9aFOd5zorrgM3lK0qEo2ZtuxWOziUocwyiZedjt\n+ndh06Hj664TZZrpZkrZ7bHwDsR2ofloKxcNS5LYkRpGycxHy+BVmaqGDx8+zK23anfPVkOT+aKO\nNBkZ6WFkpDel87HB9FHQhklRkb5ET5vNzo4dj7N588fo7OzU/fmdnZ1s3vwADz/8OMXFNl1DAu32\nmFsw3wUd9C/qFovwlBghnJmL3iZi06Fjl8uGw5F5ZIHDIcJLqqck3+oDvRpWjRKXMai1ILBa03st\npqLh++9/gB07Hk+bSF1ebiT+zxQK2jCRJP3x6E2btvKJTzzGDTesp62tLevxbW1trFu3nnvueYyb\nbto6+X12u7iRxPcmicduFwlSNTVT82DoWdRtNuG6NDLEZza5lHdPh46zeSWsVpHnMtVEv2wVayCM\nnoULxfcZFA6Zyr3z0fANN6znE594LGPJudG7aeZQ8Kk6NTUi10QPW7dup6Iie936E0+IuvWHH358\ncjGPR2tIoPp8ZaVYbMvKhOHg8WSe55OOcFgs6umMm/JyaGoyhvUVAhUV0NWVfcKwynTpOB2qB0fM\nmRI5A/kkZKshyXTevKIi4Skx2s4XHi6XWCPTNcDUq2G9fXCcTrHmGswMCjr5VeXoUX2t6VXC4RCv\nvNJKa+tOPvywnaqqagAGB90sXdrCxo3bWLdOf++FaFQYKBZLaq6HLIvZEZkmyCYnDT788NexWKxU\nVaUu6hYLzJtn7DALje5u0co7FzLpePHiFu64IzcdgzCqa2oSwzeKIhJix8Yye0C0dFxRYU1x60sS\n1NaKfhJGk6rCZWxMzMzJpJlMGl6+vIUtW7Zx662ZNSxJYq7SdOSo+nw+iuMs5fHxcSP59QJQ8B4T\nEGWWJ07oP95qtbFp00Ns2vQQXq8Hj0cU3btcldhsLt0eGBV1+mtFRaqHw2QS3g2nUyzugUB297ZK\n/G7TZhOuyupqI0GwEFE9f3q9JpBex2VllXi9Lt06i0erKZUkiZJMh0MY2D5f+k7HyQSDsXwDs1kY\n1HPmGOHH2UBpqfhbZ5oFlWktLinRl3RUV2dMop5pzArDxOUSN+xcDQoQdevxF4AaPsl1US8uzrzY\nqk2AolExgFANAaUL86jzSqqqhMHjchlVN4WMzSZyOvSUv2uRrONQSGgsF6zWzB1XLRbhLi8tjWlY\nLZHPhMsljPPKSiM5cbbR2Ci0EtcjLS3JGtaDyyU2pgYzi1kRygGxOB45kl8sPJnBwdwWdYtF7Azy\nMRyiUfB6/Xz60x9BkkzIcoRXX22nsbFIV+8Ig8Li5EmR0zFVxsb03QxUJCl/b5wsCwMlEPDzmc9c\ni6JECYeDfPDBQerqnIaGZznRqNB1LnrUg8slmqNNZzjQCOVcHGaFxwSYHKx04oR+N3M6bDb9hokk\nid1gPouvwyF2nyaTQl/fkcnn581TDNfkLGX+/Jg3YirkmhRdVpafUaKWhpaUCB339h6afM3w8hmA\n8JJdcYVI8B4YmPrnSZIIfTY0GDlKM5VZY5iAWCCbm8WshqkYJ3oXdbVcWc/xaqOqkpLYQq7eCDIl\nxhrMLqxWsYgfPz4175/ab0ePv1QdeKYHuz1Rw3Z7zPgwdGyQDpNJGN0VFWI+Tb6Gt8MhKrmMIY8z\nm1llmIDwXkzVONGzqJtM4iJLVwqpdiGMH7ltzFkw0IPDAUuWCO9fvgu4OoQvm3FTVpZ5kXc4Ug0R\nA4N8KSsTc2eGh4X3RG81pZpIW15ueEkKgVl5KywvF+VjZ86ISphcybao22ziO+INDZNJ7DrVRby4\n2Ej0M8gfh0NouLNTe1KrHmy29Bo2m2O9JuJxOmOGdGmpUQFmMP2YTCKpv6pKVCmOj8cqFtViALVz\nttMp1tJ8RnsYXL7MSsMEhKiXLRO9Ifr6cveeaC3qkpRodMQv4FpllgYGU8FiEd6/igphoITDub0/\nXYhRbUallrkbXj2DS4U61droyzS7mNXLjCSJUrLKSuE2zKVPRPyirhohtbXCU1JSMrUZIgYGuVBR\nIYyHwUGh43TdNJOJD0mqocXqavFQDRHDq2dgYHCxmdWGiYo6v6a+XsQ2PR6RqBcMaueRSFJsR1ld\nLYybTBMzDQwuNBaLMIxrakTZ5fCw0LDfn94bqA7jKy0V2ne5DGPawMDg0mMYJnHExzYh1uxMHTYm\nSeIGoHdqsYHBxUY1mtW5ILIsPCjhsPhvSRI6V+fcGBgYGFxuGIZJBtQQzaVERmaMAMUN5WCSUCIy\nfkI4MRqZGGTHZLr07bgVFHwE8Ug+SpoqUaIykUAYmVnR29HAwCBHDMPkMiOKzDlGcDOGh3HGCBC0\nBln2ufWTx+yxfkgxRbhw4qKYeipwGYaKwWWEm1HO48GDDw8+IkQJW8IsffiGyWNeshyiChflOJlD\nGTW4kDDioQYGsx3DMLkMUFDoZZgDnMaDjzKyTzALEWGAUQYY5QR9DOFlCXO5ivkUY9TOGVx8Rhin\nndN04aaS7K7GqCQzjJdhvJymnxHGqaWcFhZSjTGj3sBgtmIYJpeQAGE6cdNOBz0MoaBgwUwpRTnt\nG8cJ4GYUN6O8yylWMI8VzKMGFyZjB2pwAYki08cw73OG4/QRRWTaluDAlsPyEkGmf8LLcoguFlLD\nGhbQQBVWjIQuA4PZhGGYXGRkFAbw0MkgZ+mnjxGCxBpQRIgyTpAS9LfQ9BDr9R0iwnuc4TT9zKOK\nJubQRJXhRTGYVjz46MTNWQboYZAxAimvz8nB6zGKH2Ui50RG5hTn6GOYBiqYTw1NVFNBsRHqMbjo\n+Akxwjgj+Bgyj7L4k9eiKApRf5gzpgFqqcSFE4thQE8bhmFykRgnSBduuhgkQIhRfJzDM7kYx+PB\np9swUQ2ZeBQURhjHT4hxgpykjypKaaKauVRgxqgJNcidEBF6GKILNx58BAjTwxARoinHevBTTaku\nQ0IBRkkdpOMjSAf9BAjThZsSHDRRTSNV2DFKigwuHDIyvQxzhgGGifXFD5vCuK6omfz3UXMvpxjA\njJkGKlnAHCPfbxowDJMLiJrI2okbN6OTz3vwcT6NUQIiNBNBxqLDgIjfaSYTJEwXg8yjikHGGGSM\nQ3TRQCVNVBsXkEFWFBQG8dKJmz6GkSdCNQFCdDM0GbpJJkoUL0FKdXjqAoQSvIaJnyPTwxD1VAJw\nhG4+pIdaymmimjmUGeFKg2nlPCN8QCcB9E/JjBKlkwE6GaCOclbRhIMcR3gbTGIYJhcADz66cNPN\nEGESW8mO4c9olIC4GYziy5pAqJAYxtEiTIRuBmmiGjMmwkQ4Qz9n6MeFkyaqaaASqyEFgzgChOhi\nkC4GGU8K04SIZDRKVEbx6TJMsmlYRqGXIRqpoggbCgrnGOYcwziwMY8q5lFNcQ7hTwODZMJEOEQX\n3QxO6XPOMcIgXlbRRMOEQW2QG8bdaJoIE6GHYTpx40F7MmCYSFajRMWDjwpKMu4F/YQIkb2Hfmji\ne+upSPmOg3RymG7mUkET1VRRYsTxZynyRAJqJ2760+hUQaGP4axGCYCXIGGiGZNXZZSU/JR0x/Ux\nwgKqMcV5EgOEOEEfJ+ijmjKaqKaOciNcaZATQcLs54RmSDEfwkRop4NxAiyhflo+czZhGCZTQEFh\nCC9dDNKrYwd5Ho+uBR2EMREgRFEGd2C2nWY8Y/gZxaFZiiwj08MgPQxSjGNiB1pluCJnCV4Ck/lP\n6UIqKkN4CWQ5JobCKH6qMnj+xvBPhoeyESbCAGPU4tJ8Xa1Ms2KhcSJcWWaEKw2yECIg+7D6AAAg\nAElEQVQyrUZJPMfoRULiCuZO+2cXMoZhkgcBwnQzSCfuFDd3OkbwpSSpZsODjyJsjHu8BIeFF8ZS\nJIyFKDJe/Dl9Xj8enNgyZo+PE+AoPRyjlxpcNFFtlB0XINGJ5L5O3Awxpus9QcIMxiUC6sEzEZKU\nQFPHuRjX6vGlOHBmCNuEiXCafk7TTznFzJsMVxpVEwapvM8Z3UaJloazcZQeXDipSWNQG6QiKYrW\nmDqDZGJlvm7d4RgVBYUO+jWrF9IRCYY51LqPD3a+wqkDRylxidJLz/AIS1qWs/4L99L04FVYbLlV\nJ1RRknPzKjvWyTh+iVF2PGNRUCbynwbpZjAnPQL0MqQr7BJPJBimt/Uge3Y+x8kkHS9uWc5VX9jI\nqgfX5aTjImw0UZ3TeZgxUT/hRTHKjg1UuhnkAKczHhMOhniz9RVe3NmaouElLcvZ9IUHueHBjVgz\naNiBjVu40sjl04lhmGQhucw3H8bw08uw7uPfe+Z1/vPRp1m1ahV/tW079913HxaLEHQ4HOa5557j\nxzuf4NChQ3z08Ye5eutNuj/bgplmavJemKsoZR7V1BtlxzMGtcy3E3fe7uowUU7Tn5NBrup49apV\nPDrNOp7PHBx5lgyX4GDeRNlxvp9hMPMJEeFlDqUUKMTzyjP/xb8++mNWZlmLDx86zGcf38GGrZvS\nftZ85rCa+dP+cxQihmGiQboy33zpYhCfzjDOG0/8jrd++Hue+80u1q5dm/HYtrY27ntgM9c9dg83\nbr9X9/nMpUJX2/tMWLEYZceXMaLMd2yizHdEdx5HOtwT5eZ6udA6LsdJLeW6z0cLCWmi7LiKOUa4\nctZxknN8SHfK82pC9q4nfsneHz6bk4ZveewBHtj+x9ixpqjJhIk7WJ1TR+TZivEbikPtZtmjUeab\nL2Eiuo2S9555nbd++Hv2791HU1NT1uPXrl3L/r37uH79OoprXbp3nKM65/FkIr7suCyu7Ni46C4t\nfkKT+U96daeH0RzymS6GjkcJUIMypZCMUXY8e1FQOMtAwnMBwnjwMYaftmf2sPeHz+alYVNtEddt\n3YgLJ2UUTXqWZWQ6cbOYugvyMxUSs95joqfMdyroDeNEgmG+P//z7P7PF2hpaZl8XpJSF16Hw4Hf\nH7tRtLW1ccc9d/LfO/9JV6zejIlF1E57nN2EaaLsuIoqnV0/DaZOfJnveTyQQ7hFDxGinOK8vmMv\noo6nEs7JhFF2XPgMMsabHCOKzCh+PPgmK9KmU8MSEqU4cOGkCDulFHErKy78DzjDmZXbW7XMt4Pz\nnGWACFEChJGQMGPCinnabqoe/LqSDN9rfYOVK1cmXAgA8Xbj4cOHWblyJZs3b044Zu3ataxYsYL3\nW9/kqofWZ/2uCFHG8E9bIlYUmTAR5InGcMfppYwiFlNHE9VG2fEFwkuAM/RzivP4CaGgECSMCRM2\nLNMWmvAR1J0oezF17MGHMkXPn4qMMqnhQcY4ywB2rDRTwwJqjHBlAaGgcGZiTtmYRufsg637pqzh\nQ637uPqhDRPNMv2MTqy3LpyM4ad0mnRbqMwqj8kYft7jDB2cZwRfQrgmPn6uGigWzNiwTKnMcBS/\nrrDQv9/0Pb6/49ts2bIl7TFLly7l+PHjaP3Jfv3rX/PXj3+L//ba3+g6rxIcec8bETfACGGiE/+n\noO7SqyidPM6EhA0rdZRzJY0sZS5mo2RzSoSJcpBOjtGLm1FCRBIW1piOVQ0LQ9uGJW9j20cIv86w\n0MXUsQNr3sMpFRTCRAkRIYpMBJl4T5OqYwkJGxYqKGEJc1lttBqfscR3Mz5BH2NpwpP/z03f4Hs7\nvjklDX/98W/zude+o/neeVSzgDk0UU0troSGgQaCWWGYePBxhgHe5wz9eDSPyZTYZ8aMAyv2PBb3\nYcazJh4GPD7+qeFRRkdGJzO+tTCZTLhcLoaHU0ND4XAYV4WLz/c8jsOVfXfnxJ6xeZsWEWSChAkS\nTludEW+YJCKxmiYWU8c8qoyyuRwJEOIsbj6km5OcS3tcOh2bMGHHgh1rzuEJL4Gsjdfg4uvYiiXn\nXCkZmSARAoQzXpfpdNzEHFYyj/nMMXJRZgDpwpxnGNDUtN8zzvcaPsfoiGeKGi7nqz0/o8hVnPJ6\nDS4qEM/bJloxNBmtGBIo6LtDmCgf0j2Z5FSCg35GyTUGHyXKOFH8mCjGPu0JnoFBLxVzqjJeCE8+\n+SSKovC9731P83Wr1Up5dSWBIa8uwyTXPiw+QhMdP/OzY4uxEyTMYbo4wTlW0ZTSIt8gFeF2HuBD\nuokiT4Zp9IwiiEdGxj/xNyzChgOrbiNb71/84us4Ny0GCOMjmJP24zFPGHenOMdp+rmCOhYz16jm\nuQzJ1s04nVHqGxyjcho0XFFdiX/Iq2mYxOsvRJhTnOMU56ikZHICfKYmmLOBgjVMBhjlfc4muKCt\nmCnGrrtbazIyMmP4sWPFif2iLkhf+9rXkCSJv/iLv7ho3wnCuBsnoLuVfjriY/QhwrRxij4qWUWT\nUcmThnECvMfZhM6sElCGM+8ydmFkBgkRoQTHRU/uvBQ6jiIzTnDKlXZlFE1e8zIyx+jlHCNczQKj\n9X2ejOJjBB8efHgJTBgMInzmoggXTioo0bVG5NPNOB8ulIaH8DKEl0N0TTYDLMepawMhEnjHJzqM\nq+u1hBUzLpwTv8fivMP3F5uCvCN0cJ7DdKO1o3JRlLdhoiKWuCilcaVgU8FRWczQwCDhcBirVVs4\nw8PDLFmyJO1nhMNhhgeGwKzvfPSIPUB4oo3+1KJ9ZsyUaLi9exliGC/Xs8RwYyYxyBhvc1Iz6dRF\nEW7GmMrfJUIUDz5KcGRd9PWa31FZZqjfPXUdu4dwVGSerK33zCJEGdVIcMwHrQRYDz5e5yhraaZu\nin1VZgthonQzyBkGMo7VODdRzSiq/cpZQE3KxHW1m7Ha5kFvkrbI60g91my3MDgNGh5yD+Io1zZW\ns629EaJ0MkAnAxlbMUSI0s0QZxnI2DjxPCOT31tHOQuYk3P374uN+Vvf+ta3LvVJTCcnOccRjaY5\nKlYsE9n8iQuVP8eurgoKIaJZqx/CRNO6DQOjPjr3H+fof7Uz/uEAVzQtYvny5SnH/fEf/zEHDx5k\nz5491NTUaH7Wb3/7W3a/vQdvNICny43JYsZZWYpk0j43+8SZpyNfo0RrhkkFxWmTFCNE6WWYWlwz\nxpq/0LgZ5W1OpvVSmTARJKwZzslVxyGiWDBlNLBF1ZX2gh8Jhun74CxHf/8uZ/Z+SPCMZ1p0HCkx\nocgyzqpSzFZtt7YNS0ajKjxRfZaPUZKsYwe2tHkn6sTlEhxGtUUWunDzFic5x7DucKSCwhh+unAz\njJcqSlFQ6MTNB3Rygj48+JBz+Dv7CRGc+H5Fluk70c37L77Ngd1vEzg9Mi0a9pj9hPxBnOWl2Iti\neqqkRHeOXZAw/Xg4Tf9EJaUZJzb6GGY/J+ljSFf+l4qXAN0M4maMKp2eqEtBQSW/nmGAg5zNelw/\nowwnDSPLpatlPGZMEy5e7YXdRzDhZiFHZdzHe+lp78B9sg8mfv1DB3uo7S9i3+tvpHyG3W5HlmXC\n4fQCvH79DfTXBahc2TD5nNVpZ+5VC2hYs4iSmkQLuZzitDejIGG8eXpKtBbvhdRkvQAc2FjPspwT\ncguNEcZ5k+NEs+z8vAToYSjl+Xx0LHotFKWtPgsRSahgUBTwdA/S036K84c7iYZiN5jp1rHJYqZm\nWSMNLc1ULKxJ6CWRqbIsgsyoxgZEL8k6rqWc8izhGhMmrmUxcy7z3eilIEA4Y/GBHhTATxAvARzY\nptQkcggvp4e7OX3gOB0HjuMfi/WwuhBrcc2CeppbljJv+UKWWRvyrsSJIjPM+GRIdyoVo2ZMLKeR\nhWgbWJeSgjFMRvHzOh/qar0dnOhaGk++hgmInVu6nVKQCF78jLvH6Gk/Re/7ZwiPp4aSFEXhxE/3\n8uqLL6fUz2ejra2NjXfdztXf/Cjjbu3cA1djNQ0tzdSumIfVbktxiapEkTU9SnpJXtBzGbhWTRnX\nc8WsbcwWRWYPR3SFGtMNhsxXxyZMuHBqev9kFIbxEhoP0vf+GXoOnGJ8II3OGqp49+vP8sp/vZSX\njm/dtJHF227CZE49j6KKEurXNFN/9QIcZSJurpUkKNz7/qzGXSaSy96bqcOsQ5c2rNzKist2J3op\n8BFkPyfyDqGHJ8JxnqQWD/kMJA0FguxrfYVXn90Ny7U9YMWuUt77hz/wyvN5avjO21j6xZtRlNR7\nUXQ0SH3QxR2f+xiL1izN6bPV0E3MQyJRjB0XTkqw571uLqCGlcy7rNbdgjBMZBTe4CgjOXRu7cSd\n4MmYimEC2ru30HiA93/zJu6gB0+XW/t9teU0tDRTt2o+p547wFtfaeUtnW2QATo7O7lu/Tqu+8EW\nlm+9ntG+YXraOzh38CyRQKpb32yzUF5dyRWrljL/+qUJO1BlYkbEVJIEkw2TOspzak61ivksYE7e\n3z+TOUwXHTo7rIJI8B6aJs8fiCnSybk+cjTK8Rffp7O3i+EeN0o0dbG1lRRRf/VC6tc0U1xVwofP\n7J+SjhfetZre907Tc6CDwIjGNS1JVM6vYW7ZHJbf+5GULrHJXsp8iNexC2dO+SP1VLKW5il9f6EQ\nIMQbHMt5PIKCgpcgo/gyem+rKKU6bYuCGB3vHePFp3bx6v/7B8ZHxDWy4gu34KgWGzSz1ULTimaa\nW5YyZ14d7/3qdV7+yi90t6QHoeHr169j4w8+yYqPXUfnoQ46DhxjsDu2Ce76r8P0vyWmGTevWcqm\nz93Phk/eRUl55p8hipy2wghEHp+aLJyPUbyQWlYyL+f3XSgKwjBJN4wpEx58nGMEv2cc3+AYI4zj\nqCrRVWqrhYQkMqgVia53TvD2z17kvX97neCYnys+dR1li2I3W7PdytxV86lf00xZfSXxnY7bn3iB\nD364m9/pHBx17wObWf3Y7bRsT5xqGQ1H6T/SRc+BDobPJHqHOv69jeEjfdQsb+Taz21i7advoWSO\nayKvJL9dTcDjIzDopZxinFWlFLmKMU20vs+lesmMmVu4UjNXpZAZwssbHCOX8FmICKcnPH/TpeMy\nirBiYejMed55+iXeffolRrrc1N10BQ0bYzs8ySRRfUU9DS3NVF1Rjykpl2k6dKwoCkOn++lpP0X/\nh90JRlH/22fo+sMhSmpcrP3MrVz7yB3ULGucSOr1k29isJaOm6jOOcT4ERYxd5aXwyso7OO4bmN5\n3ONlaHCQMfxEq2zYXPoS4huo1EyeH/d42fOL/2L3U7s42fZhyus11y3kqkduobllGfNXNmO1J/6N\np2sQpad/iI7245xqO8q733mOaDBx42dz2Lnh4xu545H7WXlzi2br+x6G8Opdmz1hTINhinHgqiqn\n2KUnkRxaaKaBSn3fcYGZ8YZJFJkX+SCnXX44GOKN1pf5/c5/p/PASSrnVKGgMDwwSP2aZlZsu5ml\nD16L2abf8gz5gnT+1yH2frOVc4cS81xcS2tZ/NA1lDfNoaFlEbVXNmb87A+f2c+rj/6CVStXsmPb\no2zevDlh1PauXbv40c7HOXT4MLc8/kmWb70+47mND3rpPdBB73un8fYNc/BHL03mtoDYLaz42LVc\n++2PUbVkbtqE2WQiwTDHW9/h8M499B7ooGJOFRISQwODzFuzmA3b7uXuB+/FqmPuSTwLqGEV+nYp\nhcJ+jjOQYwlwOBjiudZdvLnzD3RNg47liMz59jO8+betnNz9fkJXS0uxnVU7bqNkjov6lmbqr1qA\nvTRzjH86dRzyBTl38Cw97R14z49w+P9+lYA70Vu04Mbl3PjdB6m/YXFO124mHc9fs5h7tv0RNzy4\nMScdl+HkZq7UfXwhcpp+DtGZ8Rh1LX5+56/pOHCcyjlVABNryCLWbruDVQ+uyzg7yYKZ+VRjxoSi\nKBx5/T1e/NmzvPkfLxPyp3pqSivLuPlTd7Hxc/fBqvKMlTzvPbOXPzz6NCtXruSvtm3X1PCPdz7B\n4cOHufvxh7l6a/pRCqUhO6d+287up3bx/otva3aNnbu4kds+ex8b/+QeKuvFZnYUP+cmKmvSEQmG\nOdi6j7adL9J14BSVcyphQsOL1izlzm0PZtWwDQs3s+KCzJ/KlRlvmHTi5n3O6D7+9Wde4OeP/ohV\nq1axfdsXue+++xKE9txzz/GjnY9z8NChrIuloigMdfTTc0Ds6EIePwd/tBtFjv1KS2pcrP3TjVz1\npTtw1uqPh0ZDEY62vsPhna/S295BebWwZEfcQ9S3LGTZtg2s2HJ9TguwLCsM7Ovgre//nqO/fxc5\nbgdaceVcmv/bWhwuJ/VXN1O/ZiFF5anNgVTUm87qVavYse1Rzd/jEzt/wqFDh/js4zu4aeumtJ+V\njAUzd7B61jQZ8hLgFQ6Tyy5f1fHKVat4dIo6HjvvofdAB30fnCHsC3Lkf+/B3x/b5VocNlZ//Aau\n+Zt7KL9yLhoburREQxEOte7n2M7XNXTczMptt7B0yzW6dawoMHbaTds//oH3fvkawbFYUq61xM6q\nHbdjKbJRt3I+DS2pHslkLqSOb2Bphk7IhU2AEC9zOGOez3SuxfJwkEP/vIe3n9qN+0Sv5jFX3H4V\n1z5yOys+dj1Wh/COJCd2axENRTg2Ybj2tJ+iYkLDw+4hGloWiQ1AFg2bMCX0JBk+2887T7/EOz/f\nzYhGmN9kNrHso2u59s83UXf3cjIthdOp4QYqabkMwpAz3jB5jSN4MtRwx/O7J57hdz/8Jbt+8+yU\nwiQBjy9tDLzj1+2MHDnHsrtbuOaR27ny3mswWy0TlS65hUkiyISIEPT4CAyJ73FUFmN3OZEQlSy5\npCvFJziO9g3x7r++zNs/e5HBU+dY8ifrKF1QFTtYkqhsrqWxZRFzljZgssSyyHN1029+4H7ufewT\n3Lt9q+5znU25Jofo4nQOuSXToeNIMMz5Q110t59itGcw4T0D756l8/cHaWhZxLWfu4M1n7iJovKS\nvBKjZZSJjsFo6tg+MTJTP9JEuMkscrj+/Q3eeWo3p/ceYe7NS6i/JbG/REltOQ1rmqlbPR+bMzE8\neKF1PJtzTY7Ry3G0DQSYHg3LssLgiT56DnTQf6SL93/wAtFAYg6Gq7GKax6+jWsevp3KhbWanz9G\ngJCuklsJxRMiMiRK0E2VDiwuPSFniTIcmiXCcjTKid3v8/bPXuTws28TDSd6/mvXNdO8ZW1CDlc8\n061hCYnbWHXJqyNntGEyhp9XOazr2NefeYH/7ys72bf3zbwS8pZ+/FoGjvXQ097B4KlzCaEQlaKK\nEmrmz2X5R1ZS3phaiaJ3oJ+KmOeR/s9jw5KxF0kypRSlJEYpisKpN47Q09/L+SNdyJHUHY7VaWfu\n6gU0tDTT9cqHeSU2rlt/A3/8g226d5wVlLCeZbqOnek8z3u6ezpMRcfXfn8Lc29YTO+BDs4d6kQO\np36nxWGj9sp5LJy3gMY1qTdVP6GcEhnDRNP2QAGwTLTY14sDm+aMmv6j3Rw/doL+492ENKreJLOJ\nmuWNNLQsonJhDUd/9dYF17EJE3dx9UXvrnupkZF5iUME0iQgT3Utnn/HysnQdLzHrPuFI5zf14HJ\nYmbF/ddy7SN3sGTT1ZjMmT2v6gTgdCEdC2bsaWal6ZkfVoxd1+BH74CHtv/zKu889SLnj3QBsOKL\nt+KojHmuKxbU0LCmmZor53G89Z0LouErmMsyGjRfu1jMaMNEbxgnHAzx5/Pv54X/fD6l/Otf/uVf\n+OxnPzsZ73M4HAwMDFBSIixTtfxr+ZdvIxpMvdBMFvPkglexYA4myZS2FFdGZkTnjjN+p5kOE5Lu\neKBWxYWK6s4MB0KcO9hJT3sHY32pPTLkSJQT//sN9rz4Ssrv8X/8j//Bd7/73cnf4/XXX8++ffsm\nX29ra+POe+7inzt36YrVmzBxN2sKfg7JOEFe5qCuY6eq41vu2MgVX1iPSaM7cMXCWrHgLW/EbDVn\nLMXNtIgn48+wYKsU6fT8mSc8flpljWpJ82SfoAMduE/0aW4gbCUODv/jbs1y0OnW8Y0sS7seFCrn\n8fA2JzRfm7KGN23kim3aGjZLZmpKKkUyf01uXXjliSZuqq4lpAljxKpr86cg1tEg4bjNp0Qxtpyn\nUSuKQudbxznw69cJV5gT+gSpmCxmjv74VV59IbW9xFQ1XISN21md0zlPNzPaMDlIZ0o/Ei32/PJ5\n3n1qN6/ufiXlNbPZjMlkoqurizfffJMHH3yQ+vp6enp6Jo9Zd9MNnK9NbJhTUldBw5pm5q6ej7Uo\nUXiZmpcJIyBAtnyCEFFdi78Da9abtxlzwpyPZLTKK0f7Rug9cIq+D2Jlx+kaD42MjFBRUUFdXR1d\nXV08+OCD7Nq1i+9973v8zd/ExtfffNstXPtnm9jwkD6vyc1cWfAzSHoZoo0OXcdOt47tpbEyX2dl\n4s0zU/OyKDKj+LP2DIpOTPLNhh7PnzQRwkmXd6SVKxAY9dH33hl6DnTgH44lyl5MHa+k6bJsYHUh\nyRTGmW4Nm6wW6lY20dDSTHljNZVSSd79OBQUoijIyFix5L0liiITQc7aUTkbfkKMBr2cPyyqK+Nb\nTlxoDd/BVZc0CXZG+xj15pa8uLOV7du+qPmaLMvcfPPN1NXVsWXLFoqLi3G7E5ORHvurLzP+QT8W\nu5XGjyzmuj+/k+s/fydN112RYpQAGQfe2bBMzI1JL3sFdDeHimS5OYjOtI6MxovWZ5TNLWfZR9ey\n4cv3s3LLOioW1DD+QT9f2fHllGPVKZt9fX1YLBaeffZZJElKmb65fdsXeWFnq54fC4ARnX/fmYxe\nDcP06Nj3wQBzljVy9Sc3sH7HZhbftjrFKIHMujJjohRH1u6V2bQZOy6z1tXOtJmSobWuOUeZk4Ub\nruTG7few9k82UrdqPiaL+aLqOJe/b6GQ6WeerrXY1VjFlZuv5ebH7mfF/ddSPq8aJP2ai8eCmUpK\naaaWFTSyiFrseTbIk5CopIQVNLKcxslS5nyMpSgyFruVhpZmrn3kdtZ94aPMX7cMq9N+wTXsyaEn\n2IVgRrcn1NNEadzj5eSBo2zevFnzdYfDwZ49ezh58iRvvvkm4+PjrFu3LuGYzZs386nPfJqP/OlG\nnNWiskYrF0MlGA2CnP51CXBIJsbNIU37JIJMVGfOQYgopjSucLNswhE1E8kSEgpbQkSl9B6cmuWN\nuOor2fuXv0z7e9TC600s59y8eTOf+ZPPMO7x6qqtn2qTrJmA3p9x2nT8J59mye1XYXc5UaIy0TQy\nDckhrFlsYwcmxi0R/v/27ixIjvo+4Pi3e+57j1ldrLQr0CIhhJDlWEKysEFCoCpzWQ8hhiKhTMWV\ngO3CsYifUkXih6SACMgD5apUkuIh5YdUYUWYIxaQghiwZS8REhEIC3SCVuw5uzOzc3bnYQ7tjubo\nme0Z9cz+PlU8UOqVent+2/v7X7+fViZ2dHTSpDFy0kgD0ihlk2dFV/Blneh6puo+nKSaImurfMOh\n/l5C/b2s2jLEsb//VcvieDHEcKlKp1zMjOEN996EK1+rJ5u+9Lknsgl0rfavNSW/zBLEiw83CqCT\nIUkGG7CcAHElxbSaIK6koMr7EcCmqwQ0N0EttzE7k//cHUAYL124mSbONHFSBgedSXuKrHIp0fJ0\n+bhm5w2s2DTIkb99pakxPEOC8luFW6OtE5NqMxMFM+NT9PaFi8enSr388svs2rWLoaEhABwOB+++\n++68axwOB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"text": "" }, { "output_type": "stream", "stream": "stdout", "text": "+------------+-------+-------+-------+--------+-------+--------+-------+\n| - | RI | ARI | RI' | ARI' | nF | sqtr | tr |\n+============+=======+=======+=======+========+=======+========+=======+\n| (V,U_1) | 0.965 | 0.911 | 0.987 | 0.884 | 0.809 | 0.942 | 0.325 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_2) | 0.935 | 0.379 | 0.958 | 0.328 | 0.397 | 0.881 | 0.314 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (N,V) | 0.911 | 0.793 | 0.979 | 0.664 | 0.651 | 0.832 | 0.189 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (N,U_1) | 0.921 | 0.786 | 0.975 | 0.570 | 0.588 | 0.808 | 0.178 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (N,U_2) | 0.928 | 0.317 | 0.962 | 0.411 | 0.479 | 0.757 | 0.172 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_1|G)t | 0.969 | 0.852 | 0.966 | 0.850 | 0.799 | 0.953 | 0.351 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_2|G)t | 0.951 | 0.371 | 0.939 | 0.341 | 0.440 | 0.904 | 0.347 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_1|G)s | 0.978 | 0.952 | 0.991 | 0.895 | 0.873 | 0.959 | 0.657 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_2|G)s | 0.959 | 0.451 | 0.970 | 0.537 | 0.612 | 0.903 | 0.648 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n" } ], "prompt_number": 191 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": "Matching Example" }, { "cell_type": "code", "collapsed": false, "input": "A = np.zeros((11,11),dtype='float')\nfor e in [(0,1),(0,3),(0,4),\n (1,2),(1,3),(1,4),\n (2,3),\n (3,4),\n (5,6),(5,7),\n (6,7),\n (7,8),\n (8,9),(8,10),\n (9,10)\n ]:\n A[e]=A[(e[1],e[0])]=1\n\nfix_pos_GraphExample = {0: array([ 0.5/2 , 0.95]), \n 1: array([ 1./2 , 0.59]), \n 2: array([ 0.81/2, 0. ]), \n 3: array([ 0.19/2, 0. ]), \n 4: array([ 0. , 0.59]), \n 5: array([ 0.74, 1. ]), \n 6: array([ 1, 1. ]), \n 7: array([ 0.88, 0.69]), \n 8: array([ 0.88, 0.35]), \n 9: array([ 0.74, 0]), \n 10: array([ 1, 0])}\n\nnp.set_printoptions(precision=3,suppress=True)\n\nU = np.array([[1,0,0],[1,0,0],[1,0,0],[1,0,0],[1,0,0],\\\n [0,1,0],[0,1,0],[0,1,0],[0,0,1],[0,0,1],[0,0,1]])\nV1 = np.array([[1,0],[1,0],[1,0],[1,0],[1,0],\\\n [0,1],[0,1],[0,1],[0,1],[0,1],[0,1]])\nV2 = np.array([[1,0,0],[0,0,1],[0,0,1],[1,0,0],[1,0,0],\\\n [0,1,0],[0,1,0],[0,1,0],[0,0,1],[0,0,1],[0,0,1]])\nsklearn_measures(U, V1)\nsklearn_measures(U, V2)\n\nprint '---', nmi(U,V1)\nprint '---', nmi(U,V2)\n\nexperiment(A,U,V1,V2, fix_pos=fix_pos_GraphExample)\n", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "From sklean:: ARI = 0.660 NMI = 0.804 AMI = 0.600 VM = 0.785\nFrom sklean:: ARI = 0.471 NMI = 0.713 AMI = 0.621 VM = 0.713\n--- [ 0.842 0.785 0.804]\n--- [ 0.745 0.713 0.713]\n" }, { "metadata": {}, "output_type": "display_data", "png": 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cBnS43vv6iKekqUn7oaMO9Dvf+Q6uX78Oj8eDpUuX4mc/+xlee+01Q9erhEOHDgEArl69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\nsLCwsLCwKAssUWJhYWFhYWFRFvz/Nt9+LdTI4EcAAAAASUVORK5CYII=\n", "text": "" }, { "output_type": "stream", "stream": "stdout", "text": "+------------+-------+-------+-------+--------+-------+--------+-------+\n| - | RI | ARI | RI' | ARI' | nF | sqtr | tr |\n+============+=======+=======+=======+========+=======+========+=======+\n| (V,U_1) | 0.836 | 0.660 | 0.851 | 0.703 | 0.705 | 0.840 | 0.355 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_2) | 0.782 | 0.471 | 0.802 | 0.567 | 0.626 | 0.721 | 0.256 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (N,V) | 0.945 | 0.865 | 0.977 | 0.620 | 0.615 | 0.814 | 0.176 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (N,U_1) | 0.818 | 0.621 | 0.970 | 0.502 | 0.589 | 0.707 | 0.182 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (N,U_2) | 0.800 | 0.506 | 0.968 | 0.485 | 0.552 | 0.702 | 0.152 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_1|G)t | 0.900 | 0.790 | 0.906 | 0.806 | 0.768 | 0.902 | 0.407 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_2|G)t | 0.857 | 0.564 | 0.862 | 0.607 | 0.667 | 0.798 | 0.305 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_1|G)s | 0.855 | 0.708 | 0.922 | 0.793 | 0.839 | 0.866 | 0.675 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_2|G)s | 0.818 | 0.556 | 0.897 | 0.716 | 0.782 | 0.804 | 0.616 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n" } ], "prompt_number": 195 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": "Graph Example" }, { "cell_type": "code", "collapsed": false, "input": "A = np.zeros((9,9),dtype='float')\nfor e in [(0,1),(0,5),(0,6),\n (1,0),(1,2),(1,5),\n (2,1),(2,3),(2,5),\n (3,2),(3,5),(3,4),\n (4,3),(4,5),\n (5,0),(5,1),(5,2),(5,3),(5,4),(5,6),(5,8),\n (6,0),(6,5),(6,7),(6,8),\n (7,6),(7,8),\n (8,6),(8,7),(8,5),\n ]:\n A[e]=1\n\nfix_pos_GraphExample = {0: np.array([ 0.20385061-0.1, 0.23977043-0.1]), \n 1: np.array([ 0.43693314, 0. ]), \n 2: np.array([ 0.75900616, 0.01462725]), \n 3: np.array([ 0.97478493, 0.24577521-0.1]), \n 4: np.array([ 1. , 0.53455287-0.1-0.1]), \n 5: np.array([ 0.56256428+0.05, 0.38383768 +0.1]), \n 6: np.array([ 0.16250501-0.1, 0.59711573]), \n 7: np.array([ 0. , 0.96007752]), \n 8: np.array([ 0.32060991, 0.8106598 ])}\n\n\nU = np.array([[1,0],[1,0],[1,0],[1,0],[1,0],[1,0],[0,1],[0,1],[0,1]])\nV1 = np.array([[0,1],[1,0],[1,0],[1,0],[1,0],[1,0],[0,1],[0,1],[0,1]])\nV2 = np.array([[1,0],[1,0],[1,0],[1,0],[1,0],[0,1],[0,1],[0,1],[0,1]])\n\nexperiment(A,U,V1,V2, fix_pos=fix_pos_GraphExample)", "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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kiXeZra1EQfZFu/gA3G43pkyZguLiYpjNZhw+fBh2ux3Z2dm9O7HSnhCM/odc\nrxIliJS6pKdEKmzTS5gMM4JQWnQAkPySwPEKnorHLCkZ7kHYJhy9kmG5+Tj+H0DCOIyQMKNECo4D\nTCZkZ2Z6f3WttZXU1AcuBIWLLsVoRFNLC5wSXpb9+/eD53ls3LgRJpMJJSUlWLx4MeoDBNjpdKK5\npQXJJpOy79GTEACjf9BTbx/Fo9SzRH0+rpnNvVLmKUYjmlpb+0aGAZIvEqI/CgDW32EgE6nHT2pI\no0aD7Kws79NrZjMEt7vH1SwpcXF9I8OtrX7zoULml4jvEY2NLCQZhuhc8b01SgDiNhQthrrm5l6V\ndZkMBkwsLMSGDRuCXps2bRoAEqvs6urCiRMnsHHjRhgCZoSsX78ek0aOhEluEJQYjab3NzbGN0dv\nPCUiskVGSV1bm7QMKzRSTLGxmFhQ0HsZHjoUJo4jfUiam8nusbGR9H6wWn2l9oCy0QqM/kskulil\nIomvARu9TE/bdwBwuFxobW/v8eX0mR4uLoYpcIaTXH6J+G/A88C1az2+/sEAM0pCkCVaDNfEia5i\naEdMBayYNQur3ngj6PdqtRo///nPceHCBRgMBoz3DJHavHmz33Grfv97rCgtVXbx4YaeMfo3tPdI\nL/HLi+qDZmQrZszonQy/+SZWLFrk/2aa49LVBbS3k06uDQ3EUGGG9cAmUl2s1wdN39VrtUgR5Zxc\nkyoLBpTr4d7K8BtvYMXcudInd7mCPSGBf4PmZlbqHgJmlITAb5dpscifV+FiKC0pQUVFBY4cORL0\n2q9//Wu4XC4IggBBEGCz2TBz5kzv6+Xl5Th16hRK589XdvHMKBnY9LQCJwBxPL61sxPdgZ6SCEM5\npRMn9l6GRX0fQqLT9aySjtF/6Ikujo8P8hSKjes6cXuGSBEEIsMnT/ZOhidPlv8MsaePjiURw/Nk\nEjZDkug0SiJJsApBVmqq9+drbW1+GeF+KNzR6rVavHHnnfjOkiWo8cxfUEJNTQ2WLV2KN374Q+iU\nZm+Ls9kZA4+e9CqRIMlohF50Y6i3WuVv9ArWjF6rxRvf/W7PZfiuu6BTWhUWyRBKRv+kpxtEcf8S\n+BvX1+gGMVBeQ8mvqLRdr9HgjeXLeybDt96KN+64g0wMljPoxfkldJxDIC0tiqd9Dzai0yjpTUml\niGyRUrzW1gYB8M3ACeieqdQIumPKFCwcOhRTJ09GeXl52OPLy8sxc9o0PLl4Me6cOZPE3encBTn0\neqbQBzp5Gu2nAAAgAElEQVR9ZJRwCOjz0NZGzkuVOlWsERjxd06ejO+OGxeRDM+YOhVP3nQT7pw2\njbiuaY8H2QvnyJh7xsCmp+E3tZoYJh6yRcn9dWazzwMRuEak5FiiU/GdkyfjR1OnRiTD06dMwZML\nFuDOKVOI7Dqd8jLM88RjIpcTJQgst0SG6DRKgN4bJTyPTJGl7nS5fF1dNRoSHqGv02mVCjh66RLy\nTSbMzMnBTfPnY/6cOSgrK4NL5AFxOp34+OOPMWvGDNw0fz6WjByJR5Ys8Z2kq4u0LZYrT05LY6WU\nA50+Ct+gu9tvZLs3r4Qq9R7ISWN7O5JjYrwyPG/WrLAyPCcvDz+eN893ErebGCZylQh6vd9NiTFA\n6U34jeaXOBzIEm8QxTIcuE7E8kw7E0t4NBxuN5JEMjxn5sywMjx9yBDcOm6c/4lcLvneI+EGXdKK\nToYf0Ruw7a1RYrFAp1IhNSEBzZ5s77rWVl+XV9qkqrubCJ9KFbY6p9VqxabjxwEAY7KzUTptGrjY\nWLz+q1/h/vvuQ6onbtrc2oqxBQUYotdj/uzZUKtUqKqtRfGQIb6Tud3EBWg0+gZb0esShZ0YAxQl\nk4LD4XQCLpd8R0wqM4EekxCK1MXz+Li8HC63G2OyszGtqAgZqal4/bnncP+99/rJ8MSiIuQbjV4Z\n3nvmDBaKlTp1c7tcwd5Hg4FV3kQDvU1Ujo0F3G75zsTUMKHTrqkMhQkRbjl1Ci1WK8ZkZ2N0djYy\nk5Lw+rPPBsnwpMJCTMzM9MrwjtOnUTBnDrjAoZZOZ7CRr9WSgX10mGsggkByS4qLI/6zRDPRa5T0\nZjHYbF4LNispyc8oGVdQ4DuODkNzOolLWq2WNUx4nkfZ4cNweKzqeIMB35k7F4aYGNw1Zw4snZ3e\nDoHJRiNMcXFYs3UrKi9dAgBsP3QIRUOGIGhfS0soExOJ4A8ZwpIDo4Hehm+o+xghWs0Lgi/0KN5V\nhjBMdpw9iwbPeuA4DnfMmoW81FTcN2sWLDabvwwbDNh/7hw2eRIKD5w7h2nDhyOODmGjuFxkInBM\nDPneMTHE2GaVNwOf3mwOBYGEqgMbqElVkdGQJN0ghhgsea6hAYdF82wWjR6NWTfcgIfnzycy7JlO\nnRwXB5PBgGtmM/6yfTsAoKalBRcaGzEsIyP4Wp1On+dGpSLyS79Daqr0em5rI/cbVpjghYVvAnG7\nSVmiB7+SSqmyYFHnwaCx8CJ2nTuHq6L33+YxSCimuDgUZmSgMCMDprg4AMD8khKvRV7b1IRzAYOh\nvDidpMwMYHH4aKG3RomokZPsUD6x0qYhyBDhnEstLdh78aL3+ayRI5En8sqZDAYUpqejMD3d28Ph\nxuJiJHh+drhc2F1ZKX1yQSAbAYeDDMeMjWUhyGigN0UH7e1e70e2yAiQLW2nIckQerjT4cA6j7ca\nAPJTUzFj+HDvc5PBgMK0NBSmpXllOCsxEaNEXurtp055pxYH4XYTfazT+a7B5QIsFnkPZG2t9O8H\nKcwoCSQgiTSo1bwcGg0Z6ifxubVtbdgpUsZTRo3C0JycsJeSnpyMMSLX3vbycvnFwHHEDcgUeXTQ\nm/CNuCQR8MspCfKUiBEbJgFy1O1yYe3Ro175y0pKwrwxY8JeikatxtzRo73PD124gPZQcfSEBPK9\n2c4xOuhp0YHdTrxnHsSVkHVtbaH1oFrtbxR4EACsP34cnR4Pol6jwbIbb4RKgc6cP2qUd4N4zWzG\nmVBJqlpt8Hfu6pLPH7FYiMebAYAZJf5YrUFNbSSH8smhUgXNcHC4XCg7fBi8ZxGlJiRgUUmJ4kua\nN2kSVJ4dc0NLC05VVwcfxHHAiBGkTTMjOlCpehaGozs1EVlyA83kWmJLGCafnTwJi0epatRqlE6Z\nArVCT86EwkIkeRpiudxufHXqlPSBRqNPhlk+SfQQqS7medLtV0SWSA87XC60iQyWIKhhEuClOVpT\ng7OilvHfGjcOiQqN37T4eIzLzfU+33H6tFen+6FWk82pFBaLfGI361vihRklFKeTJCUFIF4MIT0l\nFI4jQukJzWytqPBW7ahUKiyfPh3aCNzyKSYTJojcizsOHwYvTuLiOJJHwpKloo9Iu7rKzN/Ilkt0\nlUsGpErdY5xU1NXhxNWr3pcXjR6NtAj64KhVKj+vypGqquCbSkwMkJnpu4kwT0n0EKkutliCcvP0\nWi2SRTJXF26DCPjWD8eh1WbDJpExPCo7G+MVeKvFzB050rtBbGxvR4VoTQDw6X65NSsIxNiSWnft\n7X5pA4MZZpQAPmGRsHxzU1IwND2dVBkYDMST4nD4atTldptxcdh56RJ2nT3r/fX8sWPJrjXCLppz\nJk707kpbLBacuHCBvKBSkfLfMWNY2CYaiTSvxG6XVHjZSUnIS07G5IICjMrMhIOGdyT6N/ihUqGu\nvR1/37fP+6uh6emYUlgYsQyPzc9Hmqdyjed57KyoIC/QicYZGb5wlUrlNeoZUUAkulhUZOCHIGBc\nbi4m5OZiZnExuru7iQy73fJ62PPZLkHA69u2+YoMYmKwZPx4Eo6JQI6T4+IwMT/f+/zLykq46XpT\nqYghHe67Op3yxkddXZ9PPh6IqJ9//vnnv+mLuC6oVMrHRLe3+7rrCQIRdIcDsNsRp1LBZbdjaFoa\nhiQmYnpxMXmdzjhwOn1WvShRsMliwYLnn8feixeRajRiYkEBlk6eTBZChK75GJ0Ond3dqG1qAgDU\nt7bixokToUpNBYYNY91bo5XWViKbSgZBulz+fWuoHLvdiFGr0dnVheK0NBSlpqKkoAAxarVPmVNF\nGNBIjed5lP7xj/jg0CFoVCoMy8jAfTNmQE+NpQhyXjiOgzEmBqeuXAEANFgsGJGXB2NSEklsFc87\niY1lCdvRhM0m6YUOwu0mOX1UDmmprd0OOBxQu91INxpRlJaGUTk5yIyP91WN0UdgM0CVCi+tX49f\nbdgAS1cXClJScM+0acigrR0iaHwJAJmJiThUVQVBENDlcMAYE4MhaWnSTTXloFU6gQaMw+HnZR+s\nRK+nRGmCFU2oEgRfp8muLq8nJF4kINauLgTZsXSYWHc3OY/dDsHtxo//+Ec0mM3o6O7GhpMnccu0\naVBRJd4Da3j2hAnQajRos9nwzs6deHvnTuIlEYWXGFGGUk8JDdsAPkUu8uRxAIwiOe6QGrFOjROR\ncn9z2zZ84dkNbq2sxLi8PMTTXI8eyPDInBxkJiWh2+nEjrNn8dgHH0h3H2ahm+hCqaeEFhm43USe\nbTZf0rYg+GQPgNXhCDYAqCFut5P3O504eOECXli/HgBw7MoV8ACKA8t5I8AUG4vJRUVw8zyOX72K\n+995B3aelx4/EgqLRbrpGvOWRLFRAoRfDDShinaXlHB/G0ULwc3z6JLrogp4DZvDJ0/iqshL8+aP\nf4whmZm+hlBhSi+D4DjEJydDm5aGN7dvx6m6Orz03nvoYp1boxulFTjd3URuaXdJCaUmNq47wnWR\nFAQ0mM3Yfvo0NB6j6PszZ+Lb48cT2aWPCOE0GoweNgy/27oVO8+dw4e7duF4U1PwuViSa3ShxCih\n/Zbsdt+mMECOxbq4o6tL2tss8vo57Hb8c+9exHn63YzMysKvli3zyW9PdCfHYcqwYfjLrl345Ngx\nnK2vx9tffRV5pRztXxK4Vm22oCTfwcbgNkrMZp9nRCbpT6NSwSCqpukIM0Sp1WrF1qNHsWTsWNw3\nbRrunTMH31+wgLxI6+ipezo5mYReYmLItWo05KHVkt/Fx5NjPMf+8I47YPTsIuuamvCnt99W/rdg\nDDxosmkoqHs71BwO+BslVilPiQgXz2PtkSOYlJeHh+fOxYziYrx5992+A8RyHBvr61hJr5c+aGlm\nTAxxSxsMmDVuHG4cNsx7qmffey/4ApinJLoI1wTP6fTpYodDVjbjA40SqQm8ovduqahAnE6HFfPm\nYXJBAf7x4IOI1Wh8DQKpjFLjX1x1Jn6Ij9NokGwy4UHRyIRfr10LW6jNaqjvbbEE/36Qe0sGr1Fi\nsxFLNcQioARZ6DLwgoC1+/d7E6rG5ebizw88AC7w/Dzv6wZLDY+0NGJ8pKf7wjLUYPFY4amJiXjs\nrru8p/nNb34DK6tvj17CeUp4noQMFeScBIVvQrCjshL1HmWZYjRi9Y9/jAS5OLdG4zM8DAZifNCH\nweAzWDzGFcdxeOmee7xvX//VVzhAk14pzFMSXYTSw4IANDaGH9AIGW+fOLdJpGfP1dfjsKcbtl6j\nwe/uuAOT8vJ8IUpxgqzY6KA9RsSPQKMFwFOLFyPBI6f1bW3448aNEf5RPEgl9nZ1kXyyQcrgNEpc\nLpIEKzdIKYDAvBI5dldW4grtrArgO1OnEteh1IJTOr49gMcffBBJnl4Ozc3NePPNN3t0HsYAIFxO\nidWqLAkWAQo9hFES1LV12DAUpKQEVziEqtoJw8IJEzBf1Kvnl3/+s+9FvZ6NSYg2QnV1bW725fSF\nwS+nRCzDtIOr5xyddjvWHTvmfTkvJQUzhw4lTwJlmBY1hBueF0Cy0YjHb73V+/y3ZWVot9kUv98P\nqfySuroe3yMGOtFtlMi5DWtr5ZvYSBDkNpSgrrUVX4p2fFOGD8fQzEzyhLbQFguZwpuJHyoVEseP\nx1NPPeX91csvvwzzII9BRi2hPCWdnZHJsIKckm6nE2uPHPF1bU1MxLwbbvAdIGWY9ISEBLz08MPe\np1sPHMBOOj6eeUmiD7mig44O6bwKGQL1sN+7PGEZQRCw/tgxv66tpZMmka6t1HCR+jxxgjgtlw+F\nVovHli3z9k5p6ejA656E2ojh+eC/g91OBq4OQqLbKJFaCK2tvkoFhfgtBon3OlwufLxvn7epWWpC\nAhaNH+9/kGhAmvd5pGRnAwYDHn30UaR7SibNZjN+97vfRX4uRv9HzlMSWP6rANldpojPTp6ExbPb\n06jVKJ00Kbhrq7iMuCcy7AnzzBg/Ht+eOdP761/8+c/EGGL5JNFJoC6mYZsIDFtxCNLldqNb3H3b\nE4YJ27WVemwCy+DF56FdkeUMFJUK0OuRYDDgP0pLvb/+3bp1aFVS+iyFVP+Sa9cGpbdkcBkl1FUX\nYflWOE/J1uPHg7u2Su1waW8Tei2REB9PGkwBiIuLw3/91395X3r99dfR5OlhwogixImjFFq6HmLo\nmBThckpO1dbihKeHCAAsGjVKvmurnEIPh1pNepJ4rvuFn/7U+9LuY8ewZf9+5imJVgJ1cXs70cMR\nVK1o1GrEyhUd8DxaOzuxSeStluzaKm6YFk5+Aw0UaiCI7h//vngxMjwdk9ttNry8dq3i7xNEZ6d/\nfonDAQxCvT64jBKLhQiWTkd2ZAoXhDE2Ft1OJ9o6O1Hd2OjdTQLA+WvXcOj8ee/z+WPG+M0aCcJu\nj3yXqdEAhYV+N6GHHnoIQzyTK61WK377298qPx9jYEBzK8RGCd290VHtCktz42NivDJc29aGFlGb\n9/auLnx64oT3eTHt2ioHVdaRGiUmk9+aKxk5EqXz53uf/+JPf4LAjJLoRKyLaT8o2gU1gk2iWI5P\nX73q1cW8242yw4elu7YGEtjJVYkc035UYiNFEGDQ6/HM7bd7D3vz00/R0JtwemB+SX19z0L9AxhO\nkB23GAUIAnDkCPnX6ZS2Oj3dAqWwO50oO3QIb2zfjhOXLiEpMREcALPFgolFRfjhzJloaG72uhHz\n0tLwwIIF4adO6vVEQSsdoFdYCKSkBP36L3/5Cx566CEAQExMDC5evIjs7Gxl52T0fwQBKC8nsWVq\nzMolTcskbdudTpSVl2PV7t0or6pCkmdXZ7FYMLGgAA/PnIluhwM1nmz/WJ0OK+bP98tBkUSt9pX6\nKsFgAEQzeCinLl7E2Lvu8uaxrC0rw3eWLVN2TsbAoa7ON3ROKoROG6bJbNaoLv71xo2oamhAUmIi\nNCoVWtraMLGoCPMLCyHwvDfceO/06RgaqiswrYAElHsdaQkyPdbz3C4IGPbv/+4tclh56614/Uc/\nCn8+OXQ6ou/p5+TkkLlQg4To9pSIE6zkpkrq9URhBuw41+zfj/wnnsB7p07hP/77v9He0YHaa9dw\n9do1tFkseOyFF/DXU6fw261bUVFXB71Wi2XTpikag+3Xmj4cycmyXVt/8IMfoNCzo+3u7savf/1r\nZedkDAyoEqSy6XJJK23qNQmQvTUHDyL/v/4L7509i8dfeskrw7VUhl96CW+fOYMn1q5FheeGcev4\n8eENEiC4rXcoNJrgrq0eRhcX4+5bbvE+/+Wzz/oPnGREB1QP046rgdDpuhJ5gGJd/OJrr3nl+HJt\nrVcX72htxR927UJFXR2mFhf7igzkiHDuDYDgKiLPZlfvcuFZkSH9p88/x5XehF0cDv/8kggqRaOB\n6DZKACLkPB86uVWt9hum9OaWLXiqrAwbt2zB1i+/xLJly6ARlSlqtVqUlpZi5+7d2LZjB/ZcvQqz\n04kkpbvGwKRXOXQ6IC9P1orX6XQQjy56++23cclTm8+IEtRqX8gjVLUNNcA9x775xRd4at26sDK8\nY9curwzXtrdjVCSeNiVllBxHPCQhwkzP/+QnUHuuu6KiAmvWrFF+DYyBgXhzGEpmYmJIXpFH5ynV\nxbv27MG2HTuwt7YWZxobw8+0ibSbaxhvyvdnzkSxxzPjcLnw6zVrepek2tnpu2e5XCQpeJAwOIwS\nmempfniama05cgSvbNuG3fv2oUTUS0GOkpISHDh0CB8cOYI1+/crvy6ZkJEfBQVhezbcc889GDFi\nBADA6XTihRdeUH4NjP4P9ZTQhk/hUKuxprwcr2zfjt3790ckw5vPn8eaQ4eUX5uSXiVGY9iOnkNz\nc/GDJUu8z5977jm4BtHOcFBAjRIllY8aDRAXhzUHD0asi/cfPIjXvvwSaw4eDJ9vRb0lSu4NYc6l\n1Wjwq+XLvc/f3b4dVdXVYbvUhsRs9nlIGhoGjbdkcBglCvs52J1OrPzb3/DJhg3Iy8sLev3f/u3f\nwHGc9/H4448DAPLy8rB2/XqsfP99b6JVWORc8ZSMDFmXtxi1Wu1niPztb3/DuXPnlF0Do/9De5Uo\n3HXZnU6s/OADfPLpp5HL8IYNWPmvfymTYSVlwTqd//TfEPzyRz+CzmO8nD9/Hn//+98VvY8xQKAe\na4Vha7vLhZWrV/dMF2/YgJUffUTkOJQxoXRCcKjmbyK+N306RnmKD1xuN35VVuYLV9HKGomZPrLQ\n2Ww0sVzp1PsBDjNKRJTt24cxY8Zg0qRJQa89+OCD2Lx5M37xi19AEARs2bIFt4hi4SUlJRg9ejTK\nlO40aTa3FLGxgEe4lbB8+XKM9/RF4Xkezz33nOL3Mvo5tCxYoTIvO3So9zJ85Ijy65O7Lhq2Uegm\nz8vKwk9/8hPv81/96lew92SeCKN/otVG1DW1T3RxebkiL0dIFBokAKBWqfCCyFvyjz17UFlbS54E\nTpPv7lbm+XA4SJM5gIRwlHjYBzjRb5TodIqNklVbt2LFo49KvvbXv/4Vs2bNwosvvggAWLRokd9C\nAIAVK1di1c6d4T+IWuhS16VSkWqbCBaSSqXyXhcAfPjhhzghKvFkDGAi9JSs2rkTK1aulHxNsQzv\n2aPs2jhO/roSEiJrFx8bi58/8wxiPSXBNTU1eOedd5S/n9G/iTCxtE908e7dvs+WMyxCGRw9mIZd\nOnkyJubnAyCz0J77+OPgg2g1aFcXGRXR3R1600GP4flB4S2JfqOExuPDYOnsxNELF7B06dKg17q6\nusDzPBobG73uwtTUVNQHCMjSpUtx5OJFWOx236Ayvd6XvBUXR9zZRiP5WUrgPV1bI2XJkiWYOnWq\n9/mzzz4bdIzLRZK6m5uJ0d3YSH7u6Bh0pfADB5pTokChW2w2HK2q6r0MV1eT/g9S01IDpwBLKXU6\nnC8SYmORmZmJRx55xPurl156CbaAeSI8T3S0WIabmkh7hwi67jP6MX2mi6uqYOnuJrJK15GUDEv1\nq+K4iBq7+d7G4SVR35J/HjyIo4HFB+LQJ/WedHQQ5dzVJa2MzWby++bmqPeWRL9REmpCpYiWjg6k\npaT4ZXZTvvrqKwDAhQsXsGPHDhw4cABmsxmTJ08O+CgtUlNS0Op2+0a663S+SZOiKZOSiLq2RgrH\ncXjppZe8z9etW4eDBw/BbAaqqoCTJ4Fjx4Bz54BLl4CaGvK4dAk4e5a8VlFBnrPBw/0IJXLjocVq\n7RsZTk5GK62SED9oGTB9OJ3BLuiArq2K8RgxTz/9NOI9nWTr6+vxpz/9CTYbkdXTp4GjR4EzZ/xl\n+PJl4Px54Phx4MQJ4MIF0gqDVRb3MxR6zvpMFycno7W7m3wu3SQGGtqAdIgnwo7JYr41fjxmDBvm\nff7sxx8Hd4ela8ft9j2cTpIYazaTh83m24zQ+Thut6/fS5QyuI0Sag3T0esyZHgMhblz52LevHmY\nMmUKlixZgloaL+wL1GpSbdPDhQAACxcuxLx586DR6FFcPBN/+1u5V0GHC88LAjHYm5uJ0j99muxA\nmWL/hhErZmoMiBUZfdDXZIhIhiOpFAg8NqBrq2I8YZuUlBQ8/vjj4DgOOTnjsG3bVRw7ZvdOtw93\naQ4HvIZ4RQXR38yD0k8IZZTQXjt6fchRA73SxbTvjxRime1B2Mb/Y3zekvyUFBjUalxpaIisCzId\niULzT+jzjg7STDHC+W0DieifEU4rAMTuOvG/HlJiYtDU0gKn0wltgCEzYcIERR/ldDrR2NyMgxUV\nUAkC8jIypNscU8Sv5eWRBdkLOI7DL3/5Cn7zm/cRExOPmpp61NRcRl5efsTnstnIDrSxEcjNVVQI\nxLgeUGVJvRVSuzwPKQkJfSPDra3YcfYsupxODM/MhEapgjYYQhr3Yd/r4eGHH8e+fW3Q6UjH4wMH\nDmD27DkRn9LhIEZJYyPJG09N7ZXNz+gt8fFEF9OQiVgPi+VYr+8bOW5pwaXGRmSYTDBQ3UrvA4EG\nPPWWCELPjOoA5o8ciV/eeitUHiNkx+nTuH/WrMhOQq+HelXo30KvJ8P6Qo2CGMBEv6dEpSIhEaPR\nN2dBYmaIyWjExBEjsGHDBsnT5OXlYefOndizZw+OHTuGTz/9FLm5uX7HrF+/HjkpKaisqsL/btiA\n1z/8ENsOHUKjp4V3ENRqD9G1VSkuF1BdDSQklGDsWF/G+vbt2wFEsPMNwGYDdu8m3c6jPJTZP6Ey\nEhPjP6BPInnPZDBgYlFRn8hwTUsLPjp0CC9v2oR1R4+iurkZvNQuj15DiK6tYdHpAI0GgkDy+Gpr\nE/Dtb/vi8nv37kV3d/AgTKW4XCQ8uWuXr5CB8Q2QmkpkJC6OyLNOJxkm6UtdvLOiAq+sW4f3v/oK\nJ2tqSJlwYEWNWIYjqLaRxZMr8uO5c72/qmpsRHUkXV4D1zcdxGmzEU9JU5P/8L4oIrpn31Cqq8l/\nZBg+2LwZ727bhm07dgS9ZrVakZ+fj1aPgZGamoqzZ88iWWRMzJ4xAxnd3RgjUc6bkZKCcUOHYkxR\nEUzUc5OZSRbmqFGRVSoE4HCQmDqV0WvX6vDWW295X7/33vtQXFzco3NbLL4O/XFxwMSJvbafGJFg\nt5OEoPp68p8Rhg/27sW7FRXYJlEF1lsZjo+JwdicHIzNyUFmQgI4Ov8mPp7M6gjTJE2WxETwRUNx\n6RIJNQKA0+nAG2+8gU6P8M2ePRsLFizs0em7ukg4HiDLbOxYMk6EeU2+Zrq7SUxNAb3VxbNmzECm\nhBzrNBqMyMnBuLw8FKWkkLEg1HOj1/typXoKDad6eH/vXpzzJOHmpqTgh3PmhPaeU+QScAEiuAkJ\nwIgRwNChPb/Wfkr0e0oAxUPDSufPR0VFBY5I9GkwGo1oaWmBIAgQBAFNTU1+i6C8vBznz53DL+69\nFyMLCrxtsykNLS3YeuAAXv/wQ/z100+x48QJtLW3K+raGgqnkySvio3mrKxsjBw50vt8x46eeUto\nSJPS2QkcPEji9YOkueA3D5UjhTJSOnly72T47Fn8v+XLcWNBAWIDjIyO7m7svXABf/nyS6zasQNf\nVlaS3Z+Crq2hEGINqKryGSQAoNXqMHv2bO/zAwcOeA2USOB5/zEiLhdJhq2oiOqwfP8kJka5HPdW\nF585g5/cdBOSA5r3OVwunLh0Cf/46iv87vPP8fnx4zh6+TIEcU5LT63VAIMEAOaPGuX9+UpLCy4o\nbRcfKmQqCESoL16Un+k2gFE/Lx6eEq1wnPSE4AA0ajVy09Px4OOPY/l3vwuTyaTo9DU1Nbhl0SK8\n+uijuOnGGzEmNxdTRo1CiskEu9MJS0A5i9lqxXvbtuGxVatw5NQpaDQaFBUVSWabh8LhIGEVKV9X\nWlo6yssPAwA6OjqQlZWF1NRUxecWBOkKBrebrAebjeSj9TSFgKEQjiNeEpqZH8axqVGrkZuUhAef\nfRbLb789MhleuBCvlpZizg03YHhGBqYXF2OIZ5J1q83mF76xORzYVlmJH737LrYePQq7w4HCIUNg\n6IFAXHYNQas12KjJzMzE8ePHYLfb4Xa7IQgCiosj2xmazcFhR0EgFWZWq7ejOfOafF3Qnhth6JUu\nvukmvHbffbitpARThg3DsKwsaDUamDs74RTtppwuFy42NuIH772Hf+zZg5aODgxJSUFKfHzkPRIk\nDBKAeBcb29vR5IkbNnd0oKSgIHyuoZK8lq4uoqAjaLQ5EBgcRolWS+6kCpIixhQXQ81x+NFjj2HO\n3LnIDjOgrLy8HLcsWoQn77oLD952m7cMWOt2Iys5GROGD8ekG26A0WCArbsb1q4uuHkea48dQ7fD\ngTNnzuCf//wnfv/73+P8+fMwGo3Iz8+HKkxyoSAAhw8TW8vpJMaBWM7j4uLQ0tKCRo9l3tTUhJKS\nG5W5DkH+XHIVO3Rdd3SQPymNRjGuA9Sg7u4O32TJw5icHKgFAT965hnMmTdPmQwvXIgnFyzAg7Nn\ne7vD3VEAACAASURBVOPZKgCpRiNGZWdjalER0uLj4XS7Yfb0DtlaWYlmqxVXGhrw2Z49eO3993Hw\n1ClwHIeiIUOgU1CO39YVg1o+U1KAVCoV9Hqdd2xCfX09Jk6cAL3ChHDa/kEKWsRECxqMxl45LBlK\nUav9XWIh6JEuvukmPLl4MR68+WZAqwUnCEjQ6zEsKwvTb7gBuWlpAIA2qxVunsfhmhqcb2xEq9WK\nnadO4Q8bN2Lj0aOwdXejIDUVRiVGdqju3ADSTSYcrq4GAFi7u5GZmIg0T9m7JJHktXR1kd5WUbQ7\nHBxGCUD+k81mRYdOHTMG2cnJuO/f/x2bPv8cxoQEDBs2zGsoOJ1OfPLJJ3hkxQq8/tprePXRR4lB\nQtFoSFKt2w24XNDrdMjLyMCNI0diVFEROnge+y5fhkWUI2C323Hs2DH8/e9/xzvvvIO6ujqkpaUh\nMzMzyJAQBNJb5MoV8tzlIgZETIy/bs/IyMDhw4chCAI6OzuRlpaGdM8ky1A4HOHTFxwO4rF3OIiO\niYmJqnXRv2hu9s3NUBg3m1pcjOz4eNz39NPY9NlnMJpM0jL80EN4/dVX8ery5cQgoQQk2mlUKmSa\nTBifm4sbCwoQo9Vi5/nzqBOtKV4QcL6mBh9v3443PvwQldXVMOj1KMjKkjSyXbwKF8yp4ONNAKSV\ncEZGBk6ePInu7m7wPA+n04nhw4eH/f48T+QylGPJ5fJ9xeZm8jPzmlxn9HryH6PQE6FYFz/8MJHj\n++/Hg4sWkTfTEmC1GnC7wQFINhoxMicHU4cPJ8ZCXR3OXL3q5wWsa23F5hMn8Nrnn2PPuXMQBAFF\n6enQSxnZYQwSAIjT69HW2YkGj1Jtam9HSWGh/AZRiXXMccRVrdEQD2pAou9AZnAkugJES508GVES\nk8PpRNmOHVhVVoYjlZUwxcdDAGC2WDBhxAg8evvtKJ0/P/SOsKuL3OHFcZAxY8AXFGDv3r1YvXo1\nPvroI2/SViAjRozAvffei7vvvhuFnhKwa9dIEympvlXJyf6tWTZsWO+Ny6akpGDFip/BZuuA2UwS\nfxMTU2A0+lyjgkA25qHWmdtNdqFaLUmJoaSmkgRCtuPsY86cIXWtZjORpwgSehwuF8oOHsSqnTtx\npKoKiSYTeEGA2WLBqJwcPLlwIUpLSqAL9Z8mNXjPk+R6zmzG6vJyrN68GRevXpV8e3pyMu5ctAj3\n/Nu/Ycro0V5lXNWWiFZ3IhGcEJw4cRxr164FQLwnjzzyCDQalawMAySxNVRxAs/7hocXFPjWjNFI\nnjMD+zpSXw/IyIocDqcTZZ99hlXr16P8/HmYPJVeFosFJcOHY8WiRSidPl1eF9NGTOK1o9MB+flo\nsljwz40bsXrzZuw9c0by7bE6HZZOmoR7ZszALePG+daLTNgmkNbOTvxh61bwnnVUOnky8lNS0OIJ\n7acYjTAZDL7us6FQq4lBIm4LUFJCPCZRwOAxSgBioVdV9eitFqsV//Paa7BarYjVavHoz36G7Kws\nZW92u8kNxW4nVsPMmX7bMYfDgc2bN2P16tVYt24dumVirjNmzMCyZfdg1Ki74HIlSR7DcUBSkk+p\nWiwW/P73b8LhsKO+vhJ2+2VcunQGqanEjdnc3IQRIyaitHQFFixYDptNJ5s7JQjkK4jtuowMMneN\n4lnnUBgCZijhwgViiba1kbuoki5iYjyK02Kz4f19+3Dm2jXEarW4bdIkTBd1ngyJuLMrQHa8NCEj\nPR2CWo2Dp05h9aZNWLN1q2wZ/NDcXNx9yy244+Zb0R1TAsFgDCssgsDjT3/6E+rrr6G+vhIdHedR\nV1clK8Nuty5khMDh8J8mn5AAiJeySkX0e0YG85pcF3geqKyMvKS1sRFwubDz6FGUeTq7jisqwoO3\n3qr8HE6nLy49ZIivCEIQgLY2VF++jPd37sTqnTtRKWM4JRuNuGPqVNwzYwZmFBYqrhbZcPQoDly4\ngMr6epxubsaV5makpaQAAJpaWjCxsBAr5s7F8qlT5TcJdHQJRaUilnRWFnDDDQqvpH8zuDIBkpP9\n76ARYDIakZ2SgiSDATFaLRyRTDBVq0nJZHIyqakN0HQ6nQ633norPvzwQzQ0NOCvf/0rFi1aFOTy\n3rt3L5566mf47W9/js2b38fFiyfhcvnnyXjWltewMJlM0Ok6sXv3H2EwNOGll56BxWLG5cvVuHy5\nGmZzG5555jFs2/Yuli7Nw6ZNayS/gtNJzhnoaKL3SQotT750iVXo9BniGLNKFXmli+fuazIYkCeS\nYXsk/0Hi2Te0z4+oBTbHcZg6ZgzefPJJ1G7ciM/feAP3futbiAvoznnhyhW88M47uP25P+CttZ/g\nwInjsIaZa8BxKsTGdntl+H/+51chZXjDBmkZdruJDNvt/jZdYO4lz5ON/NmzrELnuqBSRd69WhS6\nTDGZkGQwIMlggDrSZDatloTWk5L8qzI9U60Ls7PxzB134NQf/oAjr76KJ779bWQn+W8AW61W/PmL\nL/DgW2/hzU2b8MWpU2gUl3jJ0NzZiT/u3o0mgwH//cYbMLe3o/rKFVRfuYI2iwWPvfgi3j11CnmP\nP441+/f7v1ml8o0uoc/pWBKjUXEC8UBgcHlKACLcp0716I75zrvv4qrHer7re9/DDZFapkOHRmQU\n1dfX48MPP8Tq1atx+DCppElMzMasWT/2HqPV6lBQMAJDh45DdnaRnyETFwds2vQmPvjgFaxbtxYl\nJSUhP6+8vBxLly7D4sVPYskSMqGT50PnV3Icsbc8Br8fOh1pVNtDO5BBuXqVDHlpbibPBUF+cJcU\nTqf3Lry1ogJ7PImj04cNwy1jx0Z2LWL3Mk3CSE2V7Ubc2dWF9V99hdWbNmHzvn1wud1QqdRYtOgJ\naLWxntNwKCoqwtix4zBy5AjodP7nWrOmdzIs5eELxGgk3pHA+yTzmlxHamuJB1AJ7e3eoVznr1zB\n6k2bAABZqan46bJlkX2uTkcUltR/qN3un4zkcMDd1YWdlZX4x549+PjQIbR7PDx3T5mCYaIcvUyT\nCWNzczE2NxcJAcb4m198gVe2b8faDRsUyfCypUvx5E034dGbbybrjVYy0DUnVV2QkREVuSWDzygB\niHCfOxfxYJe//9//ocoT/iktLcW4SBT6kCH+PuIIcLuBzZvPYe3a1Th37jISEgokj4uNjUNx8RgU\nF49FevoQ7Nr1Ed5//yns27cbeXl5ij6rpqYG06fPwt13v4wpU+4U389kiYkhfeDkiiJSUshaYbkm\nPeTaNeJ6Epe187yvJDAcoqqzr86cwfbTpwEAJYWFuHXiROXXITUZ2Ggk/8EKkjCazWZ8tHUrNuyv\nhCZhkuQxWq0WN9xwA8aOHYvi4qH44ot/YdWqp7B3b89keNq0O4M8I9KfC6Slkc2nFCzX5DogCKTX\nhpICBDo7BkBNfT3e83R7TTGZ8Mgddyj/TI2GyGuoktuODv+yrc5O7zrrdjjw6bFj+Gj/fozJzPTm\niIjhOA75qakYl5uLUUOGYN3Ro3hq3Trs3r8/IhmeNX06Xr7jDtw5f35oY4Si0wHjxik6f39mcBol\nALG8L1yIyDBZ89FHqKysBAAsXrwYk2+8Udkbs7J6XEsuCOQyaTVMU5OA2tpaXLx4EhcvVqCrSzoB\nxGhMwKZN/40vvtiCSZP8bwAajQbugF22WAzKy8tx882L8eqrNdBowocKtFqyVtLS5HeTzGvSC5qa\niPIObLykxDChszM8HLh4EZ8fPw6AlA5/d8oUZddAKxkC/4Pj4khYUjS7JhxXLfGorBdQUV2Nk1VV\naJLpIaTTabF9+2tfiwzT0HxamrzxzLwm1wGeJ3l+oQwTu92vI3d9Swv+XFYGADDGxuLJe+9V9lka\nDZHVcLsj2qSJhuidzuDQCM+jq6sLp2trcbKmBpeoFzPoVAL+sGsXtu7YESTD5JLk5bi8vByLb7kF\nNf/4B3RJScp6l4wb16tGhv2BwZVTIiYhARg+PKL/QHF/BIeSQTAqFXER9KK5zZUrPoOE5MtyiIvL\nwYQJ38Lttz+Bm2++F0OHjoNW6/89zp7dg1GjRkouBI7jMHPmTG9HxEC7tKSkBKNHj8ahQ2Uhr40W\nZTgcJBoWKjXA4SDGVXU1yzWJGI1GendE48yhlFWAwSJOoFOcU0JDNlJ3YnHyq0IazVpouQRMGD0N\n9967Ag888FNMmzYD8QFuiurqI1+bDDudZH2FKoUX55pE6diRrx+VCiguDl2BFfDHFpfm2pVWU2q1\nxEOitNw2MdG3riRmpUEQEKvVoqSgAA/MmYPHvvUtLBozBhkBSdsVdXUYNWaMpAyTj5KX45KSEowe\nMwZlR44oHxLo6SE0kBm8RglAtkajRkknREggNkrs4RJdDQYym8AzarsnNDb6b467u30T6l0uwOFQ\nITl5KCZPLkVp6ZOYPXs5cnKGQ6VSobHxBJ544jHZc4dzkK1cuQI7d67yHOtrNuVyEQXucPhyz2iI\nx2oNb3C0tACnTytuGcMAJIeWeREnwMkZDSL0YqNEiUIPN6QsQqNEEACbQ0vyPNxaWK0ctNosjB17\nM+6++zEsW/Z9jBkzEXq9vk9lmH62nAzT39vt4fW61UqKR+rrI7bHGFJwHImNDR3q388A8JXyitCL\nNpJOl0t6UKT43PHxxOiJZPqvWk0MEyr3gZvXgM80xcZi5vDheHjhQqy46SbMuuEGmAwGnGhsxGNP\nPBHyo0LJ8YpHHsGqstCGtR/MKIkCNBoyAnro0LABY51IMGWNErWa+HhHjIjIpR2I2exrjkaRc86Q\nifY6DBkyFrNm3Y1Fi36M1tY6LF26VPb8e/fuBcdx0Gg0eOSRR4JeX7p0KS5ePAKz2eKnuHleWhG7\nXOT3CmbGMa9JpFCjQM4w4DiiNKW8JoFGiUjpO0L98cVVNqGI0ChxOAEnT67Rrfa/AfG8CqmphZg+\n/TZ85zs/QWvrtT6RYYvF4jVAwskwQCK74aK61Gty5gzzmvQZiYnA6NHEgKByR3diIgJ7kTjkjGud\njpwrPr5n8Ta9nmxcgeC1EELm0xMScNPo0fjB7Nm41toaUoaB0HK8dOlSHKmsDBpVIktvhgn2E5hR\nQqELYtgwfwtZRMjwjcFAGnSMG0eMkl70XbfZyA07UO6VypvT2YWUlHTZWTr/+Z//iaqqKpjNZsya\nNQt/+MMf8P777/sdo9VqkZycis5OZS2hqd5QstOktLSQQijmNQmDuNolFGo1kUODgShRjgsSopDh\nGzpzQ6tV3upaqrFaCMTLhlfJNx202SxITU3rExm2WiOT4cAhfqHo7GRekz5FoyFekzFjiB6VqDDT\nqNV+A0/tYqHiOCL/aWnEIFEw6iAkRqMvg1/heANKa2cn0lJSQs40CyfHWq0WqSkpaFWy2wOiQghZ\nPYQYjiONnEwm34hcm408uruh0ulgczjg4nnUWSxAejpZAHFxZJfaB1AvglS1Z195FV588UXvz19+\n+SV0Oh1efvll3H333T0+p3gttLcHt7yXw+kk35dV6ISA/lFUKmUGAB17Tt1bosZnWrUaNocDbp5H\np8NBzkm9MKG8MXJE6CmhhrWgUkPgem64X28ZttnI0laScka9Jm1t5H7aR6pgcKPT+bKKGxuJ1dfa\nShQkz4MXBFjtdthdLrS73aTDq0ZD3teXg7hofglNZFW6BhVyPeR4oMNuAXLodOQhapxz8dgxvLxl\nCwDgZpUKDyss71KK201u0FJhGiXdjOn9ITY2BS0tTXA6ndD2cKfgdDrR2toMgyE5/MHwvza604yk\n0qalhbwnP59V6ARBm5b1xGAIUNAOjvPKsF6rxcv339+7a4vQU0LmzQhwyXhJaN6HXv/1y3CgbWWx\nkM220j879ZpkZZESeVah0weo1eQPmpXl64zd2oq/Hj6MS3V1AIB77rsPuTTMcr2uITGRKCm9XnG8\nLsVoRFNLS69luLmlBclKW2RHwWTUgf8NvkYSPPMWAKBDbvxoDxEEErKRC304nf7yFirxVK83obBw\nIjZ4avnFVFRU4IEHHkB9fT2sVituuukmOJ1OPPaYf0Lh+vXrUVg4CTExJq9BRGPxUhvjwN/ZbIqG\nMgd9xwsXSIUgyzUJIJLJoRQJY0Hc1MnudIbOK1GKQk8J75ldplO54FZp4Hb7un53dZEEUquV/KzR\nfP0yDPj/yWgX40jgedITjOWaXAdoZ+xhw5AgKk7o+DqSO2l+CR3wp2AtmgwGTCwslJRh4P+z993x\nUdR5/+/tyab3kB5IIPQSAoFApKuUiBEB8c67x7P8xFNAfU591Dvr6d2JinpYntM7K2KhRwRRpCdA\ngiEJJYEkpPfsJrubbJ3fH9/M7Mzs7O7sJvAoyfv1ijKz0+fz/cz7+6ni5HjXrl2YMno0gsSSruvA\nTDdESjwAO2WxS6zTWSRqa13HVpjNZByQrBv3gaezZq3Fpk2bHdbrdDp88sknGDZsGAICAnDw4EHc\ne++9uIs3Y9648Q2kpS3hRIbTk2KaENH/pkMXhGaa3rg4OzqGYk0c4Cwt2BUETGv8Vuzd/f1yeuC+\nMZsAUIDUaoauV0F7RRl55h/mhhv6K8OvIylpNmw2O/HiyzB/DPEfWXe3dwSZtpo0Nl4Xbv5fHAJY\nE8Su0FDi6rnale0CAuwWdJEThLWzZmHzpk2Cv4mR49c3bsTE6Gjxk+B+JFf8UjBESjwAm5QMpKWE\nn/orBNoXL/a7NGVKLkpLS5kOwTQyMzNhtVqZnHir1Yr333+fs01hYSFKS0vR26vDyZNb0NsrfK/8\nHm18he5qpmm1kplkdzchH/SfVmsP46moGLKaMBggS4lcJoMvK1Ciu7/9MjwhJX0y7CMzwyJxb87O\nyOivDJcBkOKnn95FZ6fzrrT0LUgkjo/MVUYZ3WlYpyPbsGWYtvjU1g5ZTa4GOFZro5GQkrFjgdGj\nSRxKfwNchUB3O1UqRdc7yZ0+XVCGAfdyXFhYiLLSUgRTFP65eTOKi4vhcqTR5QE8gM1GZLWlhXSy\nqK4mFvsrV4CGBiLP1zqhZyimxAOwB8JAWUqEUn/5oCi7K0Qud/2RphWsTKZCTs7LWLx4KU6e9Ky8\n8eLFy5CaOh9SqQxNTeVob/8nxo+/CXFxE5m282zQREkotKC7256pajDYiyOKadsikRCrSXMzaYAZ\nKi404PqESJMxA2cmNBAXTk+fQHUNhKVEZEyJqU+5+SossFpd14wgl67CihWvY/HiZTh58oRHMrxk\niV2Gu7vbcOTIB0hJmYm0tLmQSh3VnisZpt1Lvr5Ebg0GsiyGLEskJBShtRUYPrzfiXlD6IOg1Zou\nxe7nB8TFEeXT0UEikMX2iXIHOr7EZLJXfOWDzmKTSqECsOk3v0HOkiU4XlDgkQznLF2K+ampkEml\n6O3txfYdO1B27hyWLV3qUGgQALGSiBAuo5GQEL2e/ImZUyiVRP9GRHichOQxhoaHB+BbSvpbod9Z\n6i8ftIkZcD0BoL8PFAVYLEaYzUZERk5GRsZ0FBYWur2ewsJCTJuWidmz12HqVHs/CbO5F0VFO1BQ\nsAW9vY5kzJVCt1pJZkJlJSFfXV3i9QPdSK21FThxAjh92vM4lesGnrpvXBCFAJaZ+5paSmhi7auA\nTOacYNFxUjYbBaVSjcjISR7JcEbGdMyY8QDmzn2QaVBJURQqKo45tZrQGabOZLOzk3zfWlo8c+nQ\nVf41GuDMGeDYsSG35EDAbXyfREKqdiclARMnEkYYHDwwjNDHhxxLKDWLTqmnA9N9fDAqPh4TIyIw\nPSNDtAxPz8jAHTfcgGcffhhqlkumvLzcudUkIsLpMW02okcLCoADB4h7XKcT71o0mUgCVGkpsWCL\nLZviDYZIiQdgDwSr1Yrefih0V6m/fLDNZ30EnAO2nxwAbDYbTp/+GlptExITMxAXl4UFC25GdvY8\nbNu2DRaWRjWbzfjmm28wc+ZszJ27ALGxM5GQkI709JWYOvV2KJX2AdHcXI4ff9yMmpqfGUJGd7QH\nuPdiNhPSpdUSIsJuI+ENrFZiTjx4kNMGY/DAU/eNC8FiB7sOmKXEjXZjZ49ZlWpBfU63LKDluLz8\nKKqrzzAyPH/+jcjOXuBWhuPishAYGINRo+YgO/teBAVFM9vSVpOysu9htRJhZMswn2PRVkraRdOf\neQhFEXJz7Bgh6UPwHh650qVSMs1PSSF1pBITnXdeFH8B3GPIZISk0OxWKgXUalS3tWH3kSPISExE\nVlwcFs6bhwVz5jiV4eysLCyYOxdZcXEIt1qRlJSEB9euxZgxY5htaavJli1b0EXfu1zOyRQF+qon\nG4hbpqAAOHnS3teQjuPyFLQ78+JFctwBzI5mMHgb8nkBiqIgk8mYD3JTUxOivCgjb7WSlyo2aJzV\ntRsURWZqTL0HAet5Scm3qKw8ySynpc1DcnIm9u59CWfObEF7ex2Cg0NBUTZotRqEhcVh4sSVACSQ\nSmWQSqXIzv5/CAiIhMmkR2npt6ivL+OcIyoqFRMnLkNAQCBjvaEoMi7pIFy6RAZAFD9dz8vPz/t0\nSZWKBOBHRhIL7aAxhTc3k8hJsW5DF/6FOS++iEMXLgAAtv7xj1iZmdm/a/Pzc+uX6O0llgYA0AQn\n4Yo+HBqNnc+wrYEAUFdXhpMnv2KWo6JSMGXKChw9+i8cPvwm2tvrEBQUAokE0Gg6ERYWh8mT18Bm\ns0IqJR+GSZOWITExHTabFRUVR1BefpjT1dXfPxxTpixHWFgcxyStVpNvi83GdTXSdbn6K3MyGZnU\nBgeTifyvvH/a/wn+8pe/4PnnnwcAPPDAA9i82TEg2i2MRsIS29u9C/qxWIipm6+AFQpApUKbVosP\ndu1CT9+MLMjfH3ctWYJ9Z87guS+/RG1bG4KDgiCVStHR2Ym4sDAsz8xEiEQCY9+Ed/z48bgtNxcA\nUHbuHPLy8mBgfTh8fHxw0003YeKiRZDExwMg34aODnJbNJkWuj1/f2JM6g98fIgMD2RG9lBMiQeQ\nSCTw9/dnmHl3d7fHpMRd6q8Q+AUL+XWx2KisLOAQkvj4SUhNnQ1AgujoNEyevAZmcy8SE6eiru5n\nWK0WKBQ+mDHjLpSW7kV3dytsNhvOnt2DrKz/glLphylTbkdMzFicPZsHo5FErjY3V+Ddd2/HjBmr\nMXv270FREuZa6MwG/n1brfZr9yYOTSq11zBpaSE6ZcSIQUJMhExkruDKfTOQlhJAlAvHxLKQmeW+\nUCiIDBgMjrLS0VGHwsLtzHJQUBSmTr0dcrkKiYnpjAwHB0dDLlehre0KFAofpKXNhcGgQU3NGQDA\nuXMHEB2dBpXKD6NGzUF0dBrOnNkBrbYJAKDTteGbb55ESEg0Vq58HkoleS709fT0OFpNenv7n+AQ\nFEReZVcXmZykpl79xJHrDQNSnkGlIgVloqOJIHZ02Au0iYFcTuqnNDTYI6VVKkChgKG3F5/v28cQ\nEpVSiTU33oiwwEDMGTcO5eXl6DWbYZVIMHv2bBw/fBg+CgWSY2IwadIkbN9O5L+kpASTJk3CiOHD\nMXbMGCQlJiLv229x7tw5AMRq8vEXX+Dy9h3469/ehUoVy1j0bDbXt9PT039S0tsLlJcTPSy2lIo7\nDAZ1PqDob7BrXZ1nPmXaJ82GVEq+UfzvQFNTOUpLv2OWw8OTMHHiMgASABQ6O+sBAAqFD5KSpmLY\nsDFQKIg27O5uxYQJS5l9OzpqGOUOANHRYzB37lrExo4FAHR21uH8+e/xwQd3Y+PGJWhvJ356ulaK\nEGgS5a0LJzCQ29pFqyUusKthQvzFwRP3jZvgU7b7pt8xJfT53JASOp6EkkhgUdhJCf+W9PpOnDix\nBVYrESIfH39Mn74GcjkxZbBlOD5+MuLiJjAy3NXVjLFjFzIuR5OpB2Vl+5hjBwVFIzv7XqSlzYFU\nKoXZ3Ivi4p347rtX8dRTk1FRcaJvP+f+drq2irdQq7kExGgkSn3Qxkp5iQEvz6BWE9Pr+PEkqj4i\nQlyGjb+/nWX2tXewWK344vvv0dF3XVKpFLfPn4+ovkj9+r4PgI9CgXGpqUgfNw4+fbO05uZmTBg/\nHsnJycwp8vLyGFePn58fVt5+O26//XYm1mT32bPYlbcHmZlj8ckn/4HNRsFsJt8aV3JltTqP1fUE\nNhtw+bJ4I647DJESD9GftOCWFmKF9wRC9RvoSTN7zGi1jSgs/JpxLfn7h2Hq1FWQSMhXvLe3C0Yj\n8QFJJBIEB8cgMNBu5enqakZoaCISEiYz686d+x4mkz2nV6EgVpP09BW4fPkYc66Skr145pmxKCj4\nChYL5TLEgF1fxROoVMIz1K4ukr523cMTUuLm4Q5ooKuIc1Kwf8gtch9QEilzO2q1/bbM5l4cP/45\nY42TyRTIzFwDX1/7FEyjqWf+HRISy5FhrbYJSqUa48YtYtbV1p5Fa6s9gEMqlfXFmtyHjo4qJt29\nsfEinn8+C1u3PgWdzszIqRCMRu9iS2Qy4ZmpyUSIyUAliAwGXLVClnRXYbqPWUoKidVwZaWkfXFS\nKSgAOw8fRk1TE/PzzTNnIiUujlluoEvWA4iNjUVkRAST1WgwGKDT6bBkyRKmv09HRweOHD3K7GO1\nAYmJY7B61YOgQhNwqa+ehE6nxfPP/xfWr1+KCxc60dPjaO3jY6DqztlsZII4EMcbIiUewtvBoNW6\nT/0VgtCsjB4fdEJGT08X8vM/h8VCaLFSqcb06XdCobDPiOkZJgAEBERAJlM6kBIAGD3aPtM0m3tQ\nVrbf4fwxMePwpz8dQUbGKtZ19uLSpePIz/8MPT1ap8SEnsR7Mttku22E0N5OXMPXNTzJvnHzdRvQ\nQFfAraXEarFzFrOcnJt23ykUxHJgs1lRUPAlurtbARDiPHVqLoKCYpjjmEwG6PX2F80n1gZDJywW\nE+LiJiI8PIlZf/ZsHqeAGtk3Gvfe+ymWL38OMpm87zYoNDVV4uDBd9HeXuu0tQPtxvEU9IRarZvJ\nBQAAIABJREFUCL29pBLsEMThatWM4oBWPCNGEIKSlERYJX9yQAfSyuX4qbAQJZcuMT/NGD8eGaNH\n27eVyVDPIiyxsbF9jSPt9Q6am5sRHhaG2bNnM+uOHj2K+vo2pkRClxawqiOR88e38MorXyEkxJ55\n09TUiT173kNV1RlYLJRLYiLQhNlr2Gykzkl/o1SHSImH8MZsaDCQaHtvXpaQ+Y1WbBIJYLXq8NVX\njzIzPqlUhmnTVjv0+2DPMIODYwGAo9C7u1sA2KBUqjFmjH2mWVdXjLa2KofzBwSE4/77v8DatV8j\nMDASY8bcCF/fILS0XMLBg5tx5UoRrFbKaYt4T0gJ320jhJqa67zI2tWylFwDUsKOJ7EoCOGlXZAA\n4ONDYceOZ9DUVM5sN27cQkRHj2YfhkOs/fxCoVSqoVL5Q6Xy67sMCt3dLZBIJJg4cSkT8KrTtaO8\n3D7TpPsOyuUK5OT8Gc8/fxqJicQVFBU1CjpdOw4f/hAlJftgNJqdNsf0RN74bhshtLaSIPYhuMfV\nrK4tCLmcNEIaOZK4eOLiuKZbmQxfnD6NnceOMatGJSZi4fTpnMMYZTK0trYyy7GxRBdHR9szxJr7\nLB+zsrIQGkrK6VutVuR9m4eeXgAUYFL6oSM0BZREivnzV2Dr1jIsWLASfn5hSEubB5OpFwUFO3Ho\n0Gfo7u5ySky8JdjOYDCQKsb9wRAp8RCeMnRPUn+FIPTxppWqzWbFO+/cgSNH/oVz5/aBomyYPHk5\nQkIcC/QIkRI/vzCmkJTVamZmoXFxExEWlshsX1Kyh/Hx82d66em34bnnzmPGDHtpZLPZiJ9/3oX8\n/M+g12sFB4PZbH8mer0WTU2VaGqqhF7PLZ/pzG0jdDxvLFG/GnhSPM0dKbkalhIX52TLsFlhf5m0\ntWT79r9jz56XUVDwGUwmA5KTp2L48BkOx+G7bgBiURGy+Pn7hyM1dRazvqLiCHS6Nib9l36UUimQ\nkDARTz1VgJUrX2OIDKlrcgI//vguWlpqBAkI2x/vSoaduW34oCjiihzKh3SPq9mHzC2UShIcO2YM\nqSI7bBgOlZTgrhdewIfHjqG5qwvDwsNx27x5kPLGbKNGw7i9AwICENj3PWEnTDQ1NUOnBzo75cjM\nXMysb2ioRkVFMXpVQWgPHQmKVQQwKCgCjz66FU88sRdqtd3d2dh4CXv3/hOXLp2BwSA8SaRdLjqd\nFnV1lairq4RO56SMsQg0NfWP6Axl33gITwJdXXX9FQOKEp6N0Yr1o48ewZkzewAAlZX5yMhYidjY\n8QKCZ4NG08As0aREIpEiICACWi2htlptE/z8wiCRSDB+/FIcPvwubDYrqqtPw2TaiJtvftzhWmw2\nMmudMmVFX4bOHiYmoKXlEn78cTPGjbsRSUmTIZXaB6jRaMSPP27D4cObcenSGYSFEfNje3srUlIm\nY+HCtcjKug3BweLzJTs7gdjY6zTFks6pFgM3pORaB7qaWfJPu28AMvk8duxrfPzxEwCA9vZqtLVd\nxMqVfwVFORIwtqUkONju1gkMjGLiRrRae9DWyJGzUVdXAr2+AzpdG7744mHcd99nIIHfdlgsgFSq\nwOjR8xEbOw5FRTuYMUGsJv/GiBGZGD9+HlQq+zswGo3Iz9+Gn35yLsMzZtyG0FClaM9bby8JhOeV\nnBgCD9fcUuIMvr4o1+tx66OPwmyxwGyx4Nvycrywfj2Ucjl3XCgUqGcFFdJWEgCIjIhk/l1f34Su\nPk4QFzscKSkTcOnSWZisVjz/n7fwP6/dgmCp3XRM178xGIDk5AzExIxFYeG3qKkpBUAmiQUFO1FT\nU4bp05chPDyIFcdlxOHD23Dw4GZcuHAG4eFEhtvaWpGWNhm5uWsxb95tUCjEK1WbjcRPiixe64Ah\nS4mHEGsp8Sb1lw+z2bmu37//bezf/yaznJV1FxYtWi/Y5V6na2fiTaRSOQID7QNAaJYJkLiTpKRp\nKCnJQ37+x9i16y9obq7g3B+/blZ09GjMmfMgYmPHM9tZLMRqcvz4p8wM8uTJrXjyyUSUlHyIZ599\nBFqtBjU1VaipqYJG04m//GUDTp/+APfdl4Afftgq+nnZbAArhuz6gxhSIqKQ2YAHurogJexsK6tM\nCZvMfg8VFQV4443fMsvx8WPxwAMfQ6WSOyQ+UBTFISW0pQRwLsNSqRwTJixGVVUBDh16BwUFW5Cf\n/xnnuHTRQfqxBQREITv7HowePY9jNbl06QS+//5dNDfXAADy87fi0UcTUVzsWobvvz8Bhw+Ll2GA\nuHGG4BrsyaFer+fUn7mWaGtrw5IlS9DZF9Tm7++P3Xv3InzuXBIkyy6A4+uL+gb75DA2NhZmM6Dt\nAmQyuwxrNG2wskzrmZmLUN+tx+affsLB0mK8/c8nmN8oiqT9Go3kW0PKLagxc+YKzJq1Ej4+fsy2\njY2XkJe3GaWlRbDZKBw5shX335+IwsIP8fTTRIavXKnClStEhp96agMOHPgAOTkJ2L/fMxlub/fe\nOzBkKfEQYs2Gnqb+CsGZheX06Tx89NE6ZjktLRt/+MP7kEolrKqu9gkzW5kHBQ1jMnIAIDCQXe2S\nmxqUmpoNg4EMNovFiM8+ewAbNnwPQMKk5fOhVKoxZcptiI0dg+LiPCbjp6XlMn74YTN6eztQXLwV\n+/fnIT093WF/hUKB3Nxc5ObmorCwELfccis6O5uxatXDTp8TG21tpI7XdQk6h9YV6RChCa5loCs7\ne8zMCrxuaKjGk0/mwGQipCg4OAp//nMegoODYDSSW5XJ7MTcYNDCZCIMXyKRIihoGHOsoCAuKaEo\nChKJBBIJEB2dAn//EKZ66xdfPILx4xfD3z+UqZvDv3yJRIbU1GzExo7C6dM7oNHYrSY//fRv6PVN\nuHAh76rJ8P/lxP/XAn7vF51Ox9HN1wJGoxG33norLvUFtkqlUmzduhUTJk0iGwQHkxiUhgYS9KZQ\noL6eHRcVwxBQtV8wlEoVTCYjbDYbNJo2hETEoMc3DPqICETMXA3toYMAgJ07P8CSJb/DpEmz0dlJ\nCInVah9rdOf2mJgxuPnmJBQVfYsrV+xWk/z8Xdi79w1UVf2EffuujgxbrYQsuah87xRDlhIPIcZs\n6E3qrxCE4kkqK3/GP/6xipkZREenYt26bVAqVZxgUDqQUCoFTp/eitLSb1Fb+zN8fLgD198/Alpt\nA65cOY2CAu4sUqn0xZo19kqJ58//gIKCLQwhcfVtjI4ejXnz1iIuzm41qakpRFHRp8jPPyo4EPhI\nT0/H8eNHsWXLq6KZ+nVd70FMsKuIGeNVCXR1cl5u0TQST9LdrcH69UvQ2UkC+pRKXzz11C5ERiYy\nZAQgsqtUEoJSXv4Tfv55B6qrTwKgIGNZXAICwqHXd6C+/iyKi3dCq63nWAxXr36NSSvu7m7F118/\nweFuQp2BKQrw84vCDTfcg7Fj7VaT+voSlJbuwIkTV0+Gh+AeKpUKCpbl8Fq7cCiKwj333IOjrFTd\nN998E4sXL+ZuKJMB8fGwzchCuX8M/vfHH3Hk0iVcbm1FYFgCKIkUlEQCSiqD0j8UF5ubcfDiRfxU\n34rmyAnQBiXAovDF8uX3YMKEmcxhX3nlAbS0mJjYDX6aOu36l0jUmDZtBbKyVjFWk4aGUlRUfH/V\nZdhZd213GCIlHsKd+8bb1F8h8ElJe3s9XnxxKXp7ScyGv38oHnssDwEBJEKbrvYK2BUrRQHnz3+P\n6upTKC7eCZuNe1Bf30AcOfK/KCnJQ0lJHnp67JIkkQDjxi1CRsZqZt2XX25gAmJdkRKKAuRyNSZP\nvg3Tpq2GXO6DioofsHdvntNOmf/5z3+Yqrk0EhISsHPndrz++jqYzdcz4xABMaREhKWEE+g6UKH3\nToSBE0+i8IXFYsYTT9yOqipSkVIikWDDhk8wcuS0vmVi8aZvk5bpysqjqKsrRmnpXnR1NUAmA/On\nUChw8eIPOHNmOyor81Fbe4bzmIKCorFixSvM8uHD/4tLl465JdbkNxlSUrIxZ859CAgIH5LhXwgk\nEsm1SQt2gueffx6ffvops7xu3To8+OCDDtsZDOR7UFIC7PnuDM43NuLHCxdwuLETmoRMNA6bgsZh\n6WiKnowCgwJfnDqFwxUVKLhQCooVNyKVSvHkk+8ytUsqK8uwdetrALhd5IVgtQJRUaOxcOGDiItL\nu2YyrNe730YIQ6TEQ7gKdO1P6i8fNhs3yLWnR4cXX1yG9nZi/pPLlXjkkR2Ijk5ltqEnrHRxMuLP\n70VdXTGzTVLSNM55AgIiOKbw+voSAPYMHwBYufI1xsLS3d2CHTue9OheoqLSEBwcjQkTJmLKlClO\nt7v33nshk8mYQkI00tPTMXbsWBw8uM2j8153EFNqXoSlhBPoeg0tJSa5L/72twdx8uQBZt099/wN\nM2fextlHJnMspslunZCczJVhAIiLm8D8u7b2rMPvN9xwH0aMsPf4+fTT/weLxSy6RkNAQBTU6hBM\nnDhpSIZ/Ifi/Cnb99NNP8eyzzzLLy5Ytw8aNG5lli4VYy8+dI3/NzWSCWVZml+GxYx1lODXVLsOX\nLjnKcErKeNxxxyPM8tatz6O5uaqvo7b761Yo1LDZKEyaNPmayLC3lY+HSImHcMbO+5v6yweb+Vqt\nVmzcuAaVlfay7w899CHGjJnd9zsRANr/zv5u1dYWM+m8anUIIiNHOEy24+ImMv+uqzvLISQAiUO5\n9daXmeXDh9/D5csnPLqfgoIP8Mgjzv2RN910ExQKBeLj4yHUI/Khh9Zi2zYvmm5dT3BnKRER5Apw\n3Te9ZjPM/S3w4oSU2FjZYzapDB9teQs7dvwv8/vy5fdizZrHBA+pUrG7T1tQXW1v+Z6amuHwGOLj\nuTLMh1QqxZ13vstyw5TiwIHXxVTIZ3DixLvYsOEhp78PyfC1xf9FWvCRI0fwhz/8gVmePHkyPv/8\nc0gkMmg0pNz62bMkhISf5HDunDtSYpfhigpHGaYoYOXKvyAykpRrMJl68O67D8JkEk71FcLRo5ux\nfv0fnf7+S5DhIVLiIYQGgtVKhHEg4xnYLPPf/34Mp07tZpbvuONZzJp1JywWck5+Yz42qaiqsg+E\npKQMJi2XrdRjY+0Mva6umPMbrbSzs+/nWFk+/fR+huy4Q0+PFtXVZ5CTkyP4+/nz57Fv3z5s375d\ncCAAQE5ODs6fL+pX/vyvHmJIiQgE8Kp4DUgGjsC5zWaQGvMA9hQcwVtv27MGpk9fiMcf/ycUCuH7\nkUjsqd0NDedhNBINr1KpERc3BnI5t6BefDzbUlIMPqxWQlwWLFjPrNu161l0dDj3tbJdoHq9FlVV\nQzL8S8K1dt9UVFRg+fLlMPUp+tjYWHz55W50dvqjpIRMSjs7hYchRVE4d+4UsyxESkaMGMf8u6Oj\nGe3t9sBEikJfoz0/3Hff28z6oqK9OHHia46FnP/3a5PhIVLiIfgmQ4oipXW99Z85A01K8vL+id27\n32DWz579GyxZ8mf09Lj+BtHfLhIYSECbvWnSQv+xTd/19XaGzp5FSqUy/OY373EC/oqKvhF1Lzpd\nO0JDIyB30uAqOzsbaWlpuPHGGx1MhjQUCgXCwsKh1XaIOud1CXel5kWSEoVczjQAA64iKekj6WfK\ny7DhH48zii45eQxeeeUryOUKl1nOcjn5u3yZTazTIZPJmVgTOiGJLcPNzRUMiQG41stly55FaChp\n8W4y9WD37uecKmDAPgaGZPiXh/42R/UE7e3tWLJkCTo6yLtTq/2wadMeaDSxjHvGFerqLqOri8Ti\nyeUKjlWEhlrtj7i4Ecwy7cKhKJKRRVteMjKWYsaMXGa7zz7bwGSxsYk0u2yDzQZ0d/86ZHiIlHgI\nPjuvrx/4vit0bYfTp7/Fv/5ld3mMGjUbd9/9L9DFn1xNmukCa2xLCd8XT+/PNn3X15fAZrMJmrXj\n4ydh3jx7KvLx4/+GwdC/vOe//e1vaG9vR35+PgC4/UBoteSvu5sQwZ4eEnlOV4i9rqthurOUeOA7\nHPCqrgLnNpuBupZG/NdLj6DXSJRmaGgk3ngjD/7+JBuGXW6eDzrolR1PMmKEowyTCuCx8PMjrRUo\nyoaGBhJIy+dKPj7+uOMO+0zzwoUDaGo679m98uCNDGs05EOj05GPTW8vsXpaLKK55aDHtbKUGI1G\n5ObmoqKC1GmSSqV46aWtSEycJPoY7HiS1NQJUKmEew7wXTgUZdd1bNxzzyb4+JBA1M7Oely4cFD0\ntQjhlyTDQ6TEQ/DZeWPjwH8FLRbg4sViTupvVFQK1q/fDoVC5WZvOwwGDZqb7f1EkpIyHLYhtRxG\nMSmWRqMera1VTj/uy5Y9h5AQ0vGyp0eD0tK9LgUYIB2LOzpaYRaYTnz22WegKArBwcGQSCS4cuUK\n9Ho9E2VOw2w2o6OjDQpFKPR6MlC1WkII29tJwanm5v73XfhFw12peQ80QeBApwULnLtNo8NdL6xH\nq4bMqlQqH2zcuAsxMUmc7Vx1iJdKuaRk+HBHszchJhIkJLDdkGedhthMmpSDSZOWAyB1G0pL98Js\ndt3DfaBl2GAgyryriyj3jg5SY6elhZTpHoJ7XItAV72ewpo19+Lw4cPMukceeQOzZi3x6DhsUjJm\njKMM02AHu1ZUnEV3N5ETPsLD47Bq1YvMcnn5EU7VbiH4+V1bGW5wfTlOMURKPAR7IFgsFphMrpWZ\nJzCZyMs9d64BL720FL29RBr5qb80+AGpfFRXn2b+HRoaj6CgaMHtlEoFYmLGMMtCPnkaPj7+WL36\nLQCkUFVz80U0NV1weV++vkFISpqM3bt3O/y2d+9eHDp0CIcOHcLBgwcRFRUFHx8fnDjBDaTdtWsX\nUlKmwM8vyOEYgwau3Ddu+s/wMeCWEh4D6DVZcO9fn8TFmkpm3XPPfYJx46Y77OrKhWM0GlBTU8Is\nDx/uSKxpsONKamqKnRJrigJWr34TKpU/dLpWGAwaXLzoeqY5JMO/PFytQFd29syjj76Ibds+YX5b\nteohrFrlPNjZGdxl3tBISbHL8MWLxYKEBCDDbf78B5GYOBkA0NXVhOLi3S4r26rVQUhO/uXL8BAp\n8RDs3G0AMBj6NxisVsI2W1oIy+zo0OOll5aho6MOACCTKbB+/XYMGzZScH9XpIQb5Co8EJzFlbg6\n7qRJyzFxYg7TH6S0dC8sFtfkbObMtdi0yTFqOzY2FtnZ2cjOzsacOXPg6+sLuVyOadO417tp02bM\nnbt2cJu2XblvPHwwV6X/DfNPCg/9/R849HM+s+6Pf3wF8+evENzVFSmprPwZNhtxDQUEhCMiIsnp\ntnxLiSsZDguLxy23PA+bzQqdrhXV1QWMPDvDQMjwnDlrByxDb7BjIN03Nhscsme2bfsc7733Z2ab\nWbOWYsOG1z0+tsViRnm5PXPSFSlhW0quXDkHi0U4WMVsJm0U7r77PUgkEmi1DdBoGjkxhEIYCBm+\n4Ya1ojpki+335LCfd7sNXlitUqjVdmKi13tuNqQoEgvR3k7ISFcXYedWqxWvvXYnqqqKmG3vvfdD\npKVlOz2WWFIiVNuBjjsB+HElZ90ee/XqtyCTyaHXd6C3t8vtTHPy5FyUlJSiqKjI5XZVVVUOCqaw\nsBBlZWWYPDmXiSMZlIrdVQCGhw/kqvS/6SNGr332Gf61017L4PabVuKuu/7kdFdX7puKCrsMp6RM\ncxqAB5BuvzRIWjDlIMPsWKl58x5CfPwkaDQNoCgKZ8/uBkU5J3cDIcNTpuTCYCA+eG/rOAyBYCAC\nXXt6SEsQfvbMzz8fxfPP/xez3ciRk/DSS1sc3BlicPlyKYx9MVV+fgFITBzldNuYmGT4+pLvi8Vi\nRn39RYdt2I1aR4zIwPz5DzKE+vz5H9HT4/xZTJmSi9LS/slwenouenpInIvJ5DyOT2z/UD6GSIkH\nsNmI4KrVdoau14tn6LR7prkZTM8C9gv96KM/oaBgJ7N8661/xqxZv3F5TGc6mqIoVFYWMMt8Xzyb\nkAD8tGB7rRJnLqLQ0AQsW/YcWlsvAwCqqlzPNBUKFW67bROWLl2Ompoal/fERk1NDXJybsWaNZsg\nl5McUYsFThW7t+z8VwE6qlMIHlpK2KRkIPvfbD94EP/9pr1R5KwJGXjm0VddkglXBiA2KRk1appL\nohwVNQYSCREAvb4DWm2DYINK+t8ymRx33vke2tqIi0mjaUB19Sn+YRkMpAxbrSQw0J1iH4JzeGsp\nod0z588DZWUk/oGtR2prL+Gxx5YzlUsjImLw2mu7OZNRT8B23aSlpbskNj09UiQk2FtzVFc71ivh\nB5Lm5r4Ik8kAirLBYjGhtPQ7p8dXKFRYsWJgZNhmI98wvZ7IMl8FqcSHP3JwPavwAQXd9VevB/z8\n2B0qXTN0vnvGYBD+fuzd+w527nyNWZ45cw1yc591e13OlHRnZz202qa+bSRISkrnbMv+eFutXPdN\na+tl9PZ2uzw+AMybtw5mM/mgkZnmHpczzYyMVbjhhseQmTkLhYWFTrejUVhYiMzMWZg37zFkZq5y\n+J1W7DqdneCp1W4P++vGAJGSq1HV9VRZGe585hkm8Dk1LhnvP/43gNdviQ9XXKu83K7QR46c5lTR\n0d1Ro6LsFY7p2ChX5Do5eRpGjpzDNI68cMH1TNNbGZ479zFMn+4ow0KK3dsZ5mCDJ4GuFOXonhEq\n46DVdmD9+iXQatsBAL6+fnj99T2Iiorz+jrFxpPo9SR4PynJrourq7nxfeyu2zTU6iDcdttf0dxM\nrCoNDec4CQ58ZGSswpw53snwtGmOMkxfE23FJj13AF7PRNEYIiUiwU79ZVtKhGJKnLlnnKGo6Du8\n/749eGrkyCzcc88HLmeXNJwp26oq+4xv2LDR8PUNYLbjExKAtH8PCIhk1tfXl3LOIfRvmUyOW299\nGZ2dpACVRlPPCa4Vwty5D2PJkn9g4cIluOGGBdi2bRssrIdjNpvxzTffIDt7PhYtWoJly/6BuXMf\ndmnqpns/6PXes/NfDeiKYnx4aikZ4EDXmtZW5Dz+OHqMJLYoLCgEH//5dQT5B8CscM8UhT7EXV3t\naGq6zCynpmY4FE0DuDNHZ+XmnckwACxf/hLa2qr7jmVEWZnzmSZAZHjp0n9g0SLPZJjdMZkPtmL3\nwkMwKCEm0JV2z5w967q4GQCYzSY8/vhtqKkhH3SpVIoXX9yCUaMm9+s6xZASg8HewI5LSriWErpI\nGh9Tp66ASuXHLJ89+y2sVufVPOfNexjLlomX4Vtu+Qfmz3/YbbqvxQKmhpa3utiFN3cINFpbuWl6\nbEsJm5SYTOSFuCtsxkZ1dQn+/veVTDBfVNQIbNiwA0qlcB67EIQaiwnFk9BVMmmh5gt3fPxEnDv3\nPQDiwhkxYgYA+7HZTdLodcnJ0/vMhWTFhQs/YNiw0fDxcU6TMzJWYfLkW3HmzDb893+/gDvv/A2C\ngoIhlcqg0XQiOXkKsrLWYs2aXMjlSuZZms2uZ5Eq1SAgJUImBZHl5dkYyEDXLoMBS/7+dzS1k9ml\nj1KFfz+1EQlRsbDKFLDJ3E/9hW7r0iU7sY6KSkZgYDgA8o57esgt01UsacTHT8Tp018BcCw3T3e3\npkk5vZ+vbxAyMu5AXd0ZSKVyNDaeQ3NzBcfqwkdGxipMmXIrioq24ckn/8bIMAk61DrIMB1yY7G4\ndldJpUDQUHKOKDhz31gsJD21vV18UUuKovDSS/ehsPAnZt369a8hO3tZv67RYNAxzScB4XRgNiEB\ngORke2wUn5QIVQ0nci3BsmVPY//+TVCrQ/oyyg5hzJiFTq+N1sNFRdvw9NOvMzIMEMtTcvIUzJq1\nFr/9bS7jsgHsMuzMVS6REBl2FSvmCkOkxA26uoipjw0/P/Zg6GKKx3jaQqSjoxEvvLAEPT1kQPn7\nh+BPf8pDQEC4R8cRtpQ41naglSG/2R+NuLgJLFIinBZMn4v9DZw/fx127PgfBAREMjPN9PTbXV6z\nXK5ERsZqKBQ+qKzMh9ncgxEjsjB27I3w9Q1ysADRAYrOiIlEAoSFOa6/7iB0815E/Q5UoKvFasWq\nt99GKas19rtPPIv0UcQvbpaL86cJ3VZFhZ2UpKbalTldyVUo4NlZuXk2sWaTa5pgT5mSi8rK4wyZ\nLi3NQ3j4g0z9Hjbo/eRyJaZNW41hw9JQUPAFzOYehIUlYtasP0CtdmQWNDGhZVho3AYFDVlKxIIf\n6KrRECKi1XpevOvDD19CXt5HzPLKlX/E6tXOe3WJxYULRUyablhYtIMbqKeHLh9vX5eQwC4334Cu\nrjYEBoY7tZLQiIwcjujoVHR1tQKQ4PLlE4iLm4DAwCin+9AyPG7cTfj221dgNvdAKpVj2bI/MzIs\nJI+uiImPD+Dv7z0pGXLfuEBPD/FB8iehbPdNc3O3W/eMEHp79XjppRy0tRFlLpcr8MQT2xEd7Twy\n2xn4ys1ms3HcN8nJ0zgNZun74ZcjZge71tae5fxGg15mn1OtDsbIkXNhNpOPW0NDGVpaLom6dh+f\nQERHpyEmZlyfmymIc4388wr5VAHA15cMhOseQu4bL/KkByLQlaIoPPzxx/jurH0299e1a7FkxgJm\n2azwFdrVAUIKjB3kOnIkd4bprCwL233T1HSRkUmhbdnkRCqVYM6ctejubgFACg+Wlx9yug9bHqVS\nBYYNG424uAmIiRnLyDAfbJmmm2eyIZcDoaGCuw5BAGxLiVbb7dY94wz79m3Bu+8+wyxnZS3Ghg2v\ni3KfOwMtG9yiaRmgKAmsVkIu9Hpi0eH3rPH1DUJkZBKzX2XlWVitJPZIqLcNu7/NDTfcxyQc2Gw2\nFBfvgc1GOS09T/9ZrRYMGzYa8fGTEBc3gSPDzoywQq4cqdQ+ORyylAwwzGbHrr9GIwmqDAkZh9Gj\nF0AqlUOpjER3t90szJ6JOXuZNpsVr7/+W1y6ZI+/uPfefyE5+QaXTf1c+aPZwtHYeJGRqiTFAAAg\nAElEQVQJVJXLVYiJGc8MBLYA848XG8tNC7bZKM7AdOUhSE9fgYsXf4BCQQq0lZTkYc6ctYIzTTbU\n6mAmYyIoaJjDffGtJTTYFhOZDAgOdnma6wf9tZT0PcT4kBDMS0uDQibDmKgoe3Saq6hQHt747ju8\n88MPzPLdN92Ex3/3ezTb+4iJiicByDuUyey3QlEUJ8iVbSkxmcj7l8kcJwNhYQnw9Q1CT48WNpsV\nDQ3nkZBgjwng3xZ7rEZGjkBkZCp0ujbIZApcvnwcsbETEBhoj7USGgMKhS9CQxMBACEhcQ7EnX1O\nm82uJ9gWE9pt460iH0ywWEgG45UrIRg58gbI5SpIpTLU19sglUohkzm6yPgTKxplZcfx3HP21N/h\nwydiw4Yv0Nkpd7qPq+PxtysstMtwQsI0JgzAYiGBzc50anz8RLS0VAMglV2HD58nOBnj636pVIkZ\nM36Hkye3wN8/HB0dtaipKUJCQrrwiex7MjLs4+PPkWG2zPLBtphIJGRySCcbDFlKBhB06i/NTNvb\ngcpK4MoVkkETG5uOESOykJw8Hb6+kTCZyLY9PfZUVTpd1WJx/Pv008dx6tR25ny33PI0srLuYgLh\nnP2JBdtKkpAwGUqlPYWLfRy+kEVHp0EqJZLU29uN9vYros8pkUiwcOFjqKwkBbMMhk7U1Jxxsxdg\ntdpHGp/A8O+dP/hJASEyCPz6Yryu65RgQNju725qyA5oMJsBsxnDw8IwOyUFmcnJGB4ebo+gY23j\nqpnQjtOn8ejnnzPL88aMwTsPPwyrVcLZxSKSlABcJdbaWgOtllgtpFIZhg8nxIIea2S94/uWSCQc\nF05d3VmXMs9fP3fug6ipKYLNZgVF2VBe/hPctVFgy7BcbpdhZ2OYT64BYvL2NlthsKCzE8jPB/bv\nBwoLAa02ECNHzsHw4TOQlDQNnZ1mdHWR7Vpbia5uayMu+N5e+5/RSP6qqy/jueduYVoMhIQMw1NP\n7YFCEeCgu+lJHXtyx7dSCIkJ29pHE2t3hATgVyc+65H1JzU1CxKJhJmYVlQcZSyGzuBMD/OtKkLX\nTD8flYoQa3osDZGSAQKd+ks3HGppIX1W2OZWdv8ZoUqmtP6nBwA76v6HH97Dt99uZLbNzFyNFSue\nZ87tDfgTW25n4AzmmtwpZ4VChejoNGbZWVyJM0RGpiAlJQt1dcWIj58Ms7kHRqPrSDNXpARwVOrs\n+5BIiDL387N/nK77mSaflLgKcqUjQWnNytJsKtaDMgr5Hul9ae3M2rewqgp3vvMO87FOi4nB1+vW\nQSmVwsSazVESKSwy8ZHHbCMQW5knJIyFj48fh5DQEPJ3s1047srNsyGRAAqFEjff/CSKi3ciIiIF\nAQGR6Opy3YxGrAyz/82WYZWKyPF1H6TtBSiKEItz58hEsa3Nbh2Ty+WQslipxcI1M9Pp1jRR0evt\n++p0nXjhhSXo6moDAKhUajz99G6Eh3uf+suHRtOClhb7xC4lZaooQgJwqxPX1BR77JLKyXkWJSV7\noFaHIDZ2HNraqlxuL1aGnakbpZL8sUsyDJGSAUJdHflj1xThfwcUCnYksiMpYb80OrDNZAKKivbh\no48eZH5LTZ2J++77N+Mi8ZaU8MEPcnUmSEJWen65eU9x442PIzU1G93drbDZrGhuLnc606QoClar\n/YPoytXDJycymT0o0M+eCXf9kxK+XdqZtqKZsRNrB4eUuCstyjpWbXs7lm3cCEMfO4gIDETeY48h\nxM8PsFphZn0XzAq1KDcQ+9Zo8INczWZHQgKQw/OJCVuG2Rk4Yi6FooDU1GzcfPOT0OnaYLEY0dp6\n2eGDx4Y7hc4+Nlu507UclEquDA+BwGgEysuB6mqii2n3gB0SlxNENvmz2QgZ6O4GOjtN+Otfb2Oq\npUokEjz66OdISXHn4vAM7OyxmJhUqNWhoggJwLWU1NeXcdJ13YGiALU6DHfd9SFMJgOMRj26upqh\n1ztvZy+GlNDgW01ol42PD3csDpGSAUBjI2Hk/OhtvuKTy9kDwVFZCQmdRtOC/PytzL4REcPx8MM7\noFD4MPsMBCkxm42orf2ZWU5MnOb2uGxlHRfHL9XtGeRyJSZNuhUaTR2uXDmNzs5apzNN9kAgz1i8\nFPv7E+uIjw9X+AcFKWH7LPikhKLslhEXL17JelAmkQrP2NuLT376CVTfOVUKBXZu2IDhkZHMtbD5\njdggVxrOLCXDh0+DqwQhvr+b3TKhtrbYrfsFcJwFTpx4C6xWE6qrT6Gzs56pXCwErkIXL4A+PuSe\npVLux7Yf8ZXXDVpbiS7mlx/x5YkUe4LI7/QsxNetVgonTuxEZ2cLs+63v92I9PRb+n3NfLBjokaM\nyGDS2MUgKmoEVCpidjCbjWhurnC7D1+GR4yYiaCgYaipOYO2tko0N1+As+KWYog1331OUYRM09YR\nfqLBECnpJ1pbgTNnhGdjAFdhstk5fyAICZ3RqEN+/mcIDU1AVtbdCA1NwPr1efDzi2Dc926+IW5B\nK7K6umJGwNTqYEREpIjajwY7A8cbSwkAhIcnIT5+EkwmA2pqzuDChR8EyRt7IJBYFufamG3VkUrt\ndSr4M8zrnpTIZNyXxg5ypQmJCFuviiXQZqvVZXdRgETyf33qFExmM/4rKwvJ4eH46P77MSM1lbON\nmcVvxKYD06CNQFarlRMEnpDgvAom4DhpiI0dy1gfdbo2dHU1M9vx4cwkrVSqMWbMIthsFjQ1ncf5\n8weg07UJnl+spYR9DVIpsZ7abESps6/tupdhN6irI/F7QvHbSiX3+SiVznWxkEhfvHgU9fVlmDJl\nBUaMyMKCBWuxcOF69PSQJIbeXs8zKZ2BTayTktxPDtmQSmWIi7OnBjubILpyq0gkEkyYsBRSqRQd\nHTWoqDjitKO7JzJMro98E+nzKpWOMfhDpKQf0GiA06ddCyPbau7KfcMXDKvVjPz8LejpIdVxAgIi\nsGHDAURGpnH2oYOn2Bky3oDduyMpKYPjc3UF+t7Ypu+Wlgq3MSHOMGbMIiiVvgAotLRcQmnptw7b\neDoQ2B8fk4m8L74f/rpX6M7cNzQhESk4Kt6DMrrI4KEoCnvPnkVFX+qAUibDv+++G6t4HURtZhvA\nDuL00FJCl5uvqzuP3l4id0qlL+Lixrrdlx306uPjj4iIEcxv7HLz5H5cB+7RiIubiLCwJACAXt+O\nU6e2ALDw3J6UWznmJzXRvNJqJW6JQUesXaC2lluoUgjsuAWu+8Y+8RGyPNfVleLcOXu22Jw5D2DV\nqk2gJ0N08PxAEBSKohysfZ7CWc0dGmJk2N8/HCkpswAAJpMBRUXfQK/vcNhOjAwD9nFGV1amW30I\ntfcYIiVewmIBKirEZVXSTNCV+4Zr4qJQWLgNGk09s27ChBxERqa6/IbQStMTgkIrPHaQa1JShvsd\nwU1dDAoaBj+/MOb6GxrKRB2DD6VSjdGjFzHLtbU/o729mrONwaBBd3cLDAaN05LI7FRrvpm+t9ex\nZsl1r9BpjQBw8wFdZMoIQSaVQs4yL5hcxJUUXL6MU5WVzPKkxERkjxrlIMA2i31qSkkksMg9IyUA\nuTXuDHOKaJcI24gkFBvFJyPu3ZoSjB+/BFIpeU46XTsqKo5xxovFYoRW2wSDoRO9vV2QyRSCmdX0\nv/kyTDeX5D+DwYimJnDSyZ3B11d4gsi2lPCtJB0dtTh9egezHBgYhalTVwCQw2Ry1P/9JShNTZXo\n7iYff5lMjsTESeJ37gOXlHBl2JPhnpIyG35+pACOzWbF2bO7wZk9ANBo6mAwdKKnRwuJRMKRX7o5\nOT0f4rd6oMcUG0KxXmIx6ElJbS15gOHh7pUB/bsz9w1fSM6dO4DGxvPMcmrqbMTHT+Js647tiiUo\ntBBUVjqWlxcDu/KUcOJKvHXhAEB8/CSEhiYwy2fP7uEEtur17WhsPIe6up/R2VnHXAfNxtkK3Fme\nfAeP9A8KhU7fJJuQeFFAjR1XIpiBA+BiYyP2lZQwy8kREVg2ebK9fg2LmFBW+zVYZCpQUs+1kkIB\nXLxot/Z5MsNkK0JuXMlZl5kDrhAQEIERI7KY5fLyI9Dr2xmFbTbr0dR0AXV1xWhsLINUKnUgJa5k\nWColJQfY1zUoZJiHnh6goUHctjKZvYagM/cNezjo9Z04ceIL2GxExn18/JGZuYaZXNJx3M5IB5+g\n0E3nXMlSebldhuPjJ/RZjT0DP75PjGVECDKZHOPHL2GW29qqUFdXwtmmqeki6uqKUVt7BhRl5RAR\nNtmn17OhUJDYH/bz43uZPcGgJiV0WWKAPPzwcOf9zgAwVVG5fQCEScmVK4W4dOkYsxwbOw5pafMc\njumJsnRGUGj2qtdrOT7DpCTPTYaA8+wFT0H7NOniaDpdGy5fPg4A6OnRoqXlEvT6TpjNvVAq1U6J\nh9B6uZzMmOhKh+z11z1orUBPl7woMw+4Twtu1Gjw9alTTKBoeEAAVmZmQsZ2CbKsNWxLiSf1Sdiw\n2fgBgp7JME0CBiI2ikZqKnumaUFxcR7zTDSaJuj1ndDrO0FRzrWwM0Li60t0jk5nXz8oZJgFiiIZ\nNp7watpdIOS+YVvBzOZeHD/+GeOGlskUmD59jUPVXVqM6TgfV9dKN52ju+Lyq/PabMD582zXjTiL\nNf88sbHjmeWOjlrodI7ZM2IJSkTECM7xzp3bx3R47+nRoLOzjtHFvr6+TuWVL5skjZ5cB7t/T39k\neJCJvx1Wq2NPG7pErkZDhE0ICgUZCGZzL0wmslF3dzsCAsIYAWltvYzi4jxmn5CQOEyadAv4gZwU\nRV4qu4aBUJquENgDT6Eg91NVZQ8ODAmJQ3DwMCd7uwZboXtaq4SPgIBIjBiRhUuXjsBqteDgwbex\nZ88TqKk5i+DgUFCUFRpNJ8rLv4PJZEB6+m0c0ic0OGQykkpJfxvZ3YEHhUKn/YjummG4gc1mQ2df\nx7J2nQ7xrBrnXT09+PzECZj7yIpapcKamTPh66SiLCWVApSNEWKxlVzZ6O0F2tp6ON19vSElRKHb\nZbix8TwsFhPH1O/JbFMmU2D8+CXIz/8EANDUVI7vvvs7LlzYg6qqMwjq66Cn0XTi4sU8ZGWt5cix\nMwXv52d/lXo9yV6gJxiDCc3N4hvn0fDxIc/QarUwqa46HZlh0qTCZrMiP38rurtJgLJEIkF6+m0I\nDo5xOB6tT4lLzl5h2BXYiW60lU4qJSTl8mXviTVAFyMLQWhoPDo6SCuSurqzGDXqBs75PcGYMTei\npaUCZnMvDAYtdu58BnV1Baiu5spwTc1RzJ79IKZO5cqwkFyyy2UYjYTU8YORPcUgE387OjqEOy5K\nJEBICBEw9uwFIObBEye2Yd++zbh8uRDBwSEAgPz8D5CcPBkzZ67FyJGzcerUl0zqlVodgmnT7oBU\n6j7Nir0s1vQlldpNiZWV3H43YsEmRYCjP56iuOXmPcXIkdnIz/8YZWW7MGHCeDz99H9j2bJlkPdJ\nrtlsxu7du7Fp02Zs27YBK1ZsQkbGKgdlTitspZKbFUsXqJPLB4lCp79kIjNt2DCazdhWWIjNR4+i\nsLISIX31+T/Iz8fk5GSsnTULSydOxOfHj6O7j5nLpFKszsxEqItiGpTVCgll1+JmD+NJjEZS4Kqq\n6mfGxefvH4aIiGTRx2BX3AwLS4JK5Q+jUQer1Yzm5guMXHuTfk9mmuNw6tQXqKj4ARMmTMCLLz7i\nVo6nT1/lIMO0WZxtlbXZyERIrR4kMtwHiiIFKj2ByWTEwYPb8NVXm1FeXsR0tj1x4l84cIB0tp0y\nJRclJd+htdVeNGzs2EUYNizN2WFhs3GNkDab647O/PugsyjNZjOqq4uY3zxxQdLzDHquERs7QZCU\neCPDPj7+SEtbgH37XumT4fF46SXnMvz11xuwcuUmZGauciqT/DmKwdB/UjJo3Tetra5/Dwwk/VRo\ngTxyZCvuvz8RRUUf4oUXHkF3dxcaG+vR2FgPrbYTL7ywARcv/gsvvjgBV64UAgAUCh9Mn74GSqVn\nlZHY8YuuQM8KaeFkB7nS9UlcCS67mBN7u5iYsYzLxWDQMPEe3uLw4XdQXf0jDh48gKNHD+PWW29l\nBgEAKBQK5Obm4tChA9i/Pw+7d/83Dh580yFNkmbl/IFAUfZgwUGh0Omb9DA1YOvJk0h88kl8ePEi\nHnnxRXR1d6O+sRH1jY3o1Gqx4YUX8MGFC0h68kkcOG+PhVqeno4ENy2YKasNEpsNkj4y7omlxGgk\nkwSKAi5d4s4wxZBhqxVMsCI9bqRSqaAbsj/1gNrbq1BXd6xPjg+JkuMff3yT+Z3ubkynU/IxqGS4\nDxqN8OTQGfbv34pbbknEDz98iL/85RF0dWkZPdzVpcHzz2/A+fMf4E9/isPx458w+yUlTcXw4Zlu\nj8+vxWE2i9PF7MSFhoYyxoquUvkhKmq022PQRTbpeQZ9HezYKHbAtreorDyG+vrjonXxzp1cGWZD\nqEtwT4+dzHmLQST+duh0jhHvQlCriSL55JM3sXv3q9i3Lw/p6Y5V/+gXmZubi8LCQixevBQWSy9W\nrXoL/v4RXl8nXfVRSC+z0xtpsCu5JiVlOLiF6P34lhHH+/FBdPQoJki3rq4YoaHxXt3DqVNbcejQ\nqygoOIaEhAS326enpyM//ygyM2chMDDKgaU7M6v29hIiOSgUOu2v88B18+YPP+DVH39E3v79omR4\n6eLF6DGb8fjNN2N8vIh3TwESWAHKBqvMBzYRKd4A+SDRhATgxpO488XzHwGbcEgkxOJHxzDV1hZj\n+vTfeK3QT53aimPH3sKpUwUey3FAQBSyslZxxqAQKaGJ1aCQ4T64mxyysXXrm9iy5VV89514PWw2\n9yAj4w6MH79YFMFl60oaFotz9wW9DzvwlZ1skJQ0FYCMmT+wg/gB4QQG9r/ZxJoUAnTcRixOndqK\nw4c34uTJfI9keMYMuy5mQyj+kqKILh6ylHgIjUb8tocObcWePa/ixImjggOBj/T0dJw6VYCWlp85\nJMFbCM3shAhJZ2c9k3oskUiQmMi9Vn6RHXdCzY0r8S5Q0Gw24ptv1mHPnh0Og8Df378v9Yz8paTY\ni7wlJCRg9+7t+PLLdQC40yhngcjsQX/dQ6FwzIV2ga0nT+LVH3/E0fx80TJccOoUfm5pQQM7es0J\nqL7/SEBBarOKdt3wCQnALc0tZPamPwBCaZx88C0l3hKSgZBjdsq7UE9F+7kGDymxWh0rtjrD/v1b\nsWXLqzh+3FM9fKYvo0+cYnCmG2lLhpC7nZ+Jw64VRfce4x+Hbg7I35d/fq4rvbSvUaSoW+GgPzK8\na9d2fP75Ok75C6EsHBq0K91bDAYV7gAxVhKA+C5ff30ddu1yfJGFhYXw8fFhXuSNN97I/JaQkIA9\ne3bim2+4L9JbCGXo8AWTPRCio9Mcoss9xUCkBZ85sw3jx4/DlClTHH57+eWX0djYCIqi8P777+Py\n5cv43e9+x/yenp6OsWPH4tSpbcw6V7MVwKus2F8nFArRrhuj2Yx1X36JHXv2eCzDu/LysP6rr0SV\noacASCgbpLCKyrwxmwkhYb+z7u4ONDTYy2mzLSW08ndlTuev72/LBBoDLcdCVhIag4mUGAziZvz9\n0cN5ebuxfftjA6aH6ebZ9LJQarCzsgxCdXLYMSRChCgyMpVpRWI296ClxXm7A1cYaBl2laXaXxke\ndKSEHX/gDgcPbsO4ccIvMjs7GzKZDFeuXMGjjz6K/fv34+2332Z+T09Px7hxY3HmzDaHfb2FK9Md\nt5Krd6nAbPS3MR8AHD++GevWrRX87aGHHkJ0dDRnXSqrZDkArFu3FocObWaWXSlzYBCREjrSly4i\n4CyXGsC2wsJ+yfDYsWOxrbDQ5eWw5VFiNbmNJzGbSSo+/32xS8tHRCQhKCiSmVm68+0LjYnYWHuZ\n7q6uJnR1eRhR2YeBlGMhPzwbg4mUiM246a8eHjt2LIqKBk4P0zFMQoTEaNSjvr6UWU5OnuZARlwd\nl7+dTCZHTIy9orG35HogZdiZ+5HGECnxELQwicG2bZvx0EOOL7KqqgoGgwHvvPMOEhIS8Oqrr8Lf\n3x8vv/wyZ7t169bi+PHNDvt7C4nEuWBz40n6T0rY7pumpotM4JZY9PRoUV19Bjk5OU63CQ0NhUQi\nwX333YepU6fi6aef5vyek5ODy5eLYDBo3Q6EQQWlkggBu8KRQmFvQEF/+SQSbD56FGvXrXM4hFgZ\nXrtuHTYfPer6eljyKLOYXbpvLBZhQgI4NuHzpCeU0DY+PoEID7dn73hDrgdajt3JMP1aBwOclV3g\nYyD08LFj4vWwO3mjSYaQbF65UsRkXgYGRiI4OMGjgmfsiSdNUIRKNHiSDHmtZdhm658MDxLxt0Os\nK16n0+LCBeEX+cUXXwAA7rrrLmZdYmIi2tq4DbtycnJQVVXE9L3pD/gBqmxBt9lsDj1v+ouQkDio\n1cF957OhsfGcR/vrdO0IDY3gRHbz0dHRAYvFggcffBCnT5/GM888w/ldoVAgNDQcOl2HqNS8waLM\nmWpFQqBL4srl0JrNOFNV1W8ZLqqshJbuHc+vO61QwCJTwipTwSLzgU2ugEXuI3hprggJwA1yZQdq\nu4OQ2Zte198iagMpxwZDh9sZpNg6RdcDxOjigdTDBkP/9TA/W5FfYp0b5Coue4w+rjPwZZhfKdgd\nBlKG9foOl64bGt6WmAcGISkRq+g0mnaEhwu/yGaBBg0BAQEOnVYVCgVCQsIFGyB5AjYhYYMeHM3N\nFQzxkcuVHCH2/pySAfPJu4JMJsPbb7+NkJAQvPfee4LbqFRAaCgpLqVWk8JJdC4823PRn4HwqwK/\nC6ETtOt0iAgL67cMh4eGokMuJwV8QkPJ/4ODgaAgUIGBMCoDYFL6w6z0g1EVJKgtaUIiFJxKUYDR\nSPEybzyvsyO0zE6pvFoyDIiT46AgUvTPz49UclWpCL9kl+QeNDIMcbp4oPQw/UHtD4TKJ9DraddL\nVZX3k0Nnz4Mvw0IxhgMBMTLs70+yHF3JMDCUEuwRBmIWEhUV5bBOo9GIjvD2FO5qjbBdN3Fxkzil\nl/uD2NgJaGgoQ3BwjEM3ZHfw9w9DR0crzGYzFCL8LlarFX684lxmsxmdnW2Ijg5FX40vp7DZgMhI\njy7x1wtSVphbRpK2XrD/72I65ZEM09YRgWPZbOC4b4SsJFarMCGhKOJONZuBtrY6aLXNfaeTIjnZ\nMX5ACPyPBD/uKjZ2Anx8AhEUNAwymYgpHg8DKceJiaEICHC+L0UJd1u9XtFfXXwt9bArQsL+P1sX\ne1LA0hViY8dDofBBUNAwBAXFwGjUQ6USX/tqIGU4IcG9DFNU/1ztg85SInYmEhwchrY28iL5WL16\nNQDg448/ZtbV1tYiIoJbk4R+kXTfjKuFgQ5ypZGZ+VvMmfMgJk261eOGUr6+QUhKmozdu3c7/Hbs\n2DHcdNNNqKqqQk9PD37/+9+jq6sLd999N2e7Xbt2ISVlCiIj3WcSSaWExQ8KSKVAaiqQlATExwOx\nscCwYYSVhYcTS0ZQEMJiYtDa3t5vGW7r6EBoXBx5wCoVx09m4xENfpCrECGx2Ug6pF5PSAlFccty\nx8WNha8v92WyPwpsfzs9Y3TW/Tc1NRsLFmxARsZqhIbGw8a/YDcYKDkeNWoKAgJcy7FEApcK/3qD\nGF08UHq4o8N7PSxESPjyCADd3a1oa6titqEtJfxthWTZ1cTT3z8ct9zyIjIz78Lo0Qug17d7dP0D\nJcOpqVMQGupehv38hmJKPAJPpzqFv38Q0tKEX2RycjLUajUeeOAB1NTU4JFHHoFer8dTTz3F2W7X\nrl1ITp7S7/Rcd6it/Zl1bQNHSoKC7D0iurqaQbkaOQKYOXMtNm1yDDCTyWQ4cOAAhg8fDrVajU8+\n+QQrVqzAc889x9nuzTc346ab1sJHOETBAYNplglf9yQxyN8fk9PS+i3DU0aPRlBEBLHbhoUB0dFA\nVBQQGgqjKgBmuS9sUmJ07fWxm7RoQkIHllut3Fbw9rLcQHW1vcdSUtI0JvWS/mOTECEi4gz+/mGQ\n9RVys9msHit0YGDkODdXOPOBj8EkwyJEeED1sFrtuR7mEw8hMkKjttYuwxERI6BWh3GIsrM/MQgM\ntFuFuroc3VbuMBAyvHy5OBl20Y1CFAad+4buzCkmHS03dy3eemszcnNzHX47duwYMjMzkZiYCAC4\n8cYb8cADD3C22bhxE9LT73LYdyBhs1kxZsxCJCRMhkbTgJSU2QN27MDASEgkElAUBZPJAKNRBx8f\n8VO5yZNzsW3bBhQVFXHS+TIzM2FxkwJVWFiIsrIyPPOM47MXglwuOtTi+oBaLary1NrcXGx+6y2v\nZfiNjRuxIivL8cB9pXV7ZD4w931cKIkEPT6kH5TNZickdLEodvEpPpkIDR2ORYseg0bTgIkTc0BR\nzmOpPIFEIkVgYBTTKqGrqxkBAZ75+Ygcr++XHL/yijg5HkykROy99l8Pv4GUlIUQ28OLXZySbc1w\nB5lMjptvfhJabRMiI0eKOgcNd3IeGBiNlpZLALwjJQOhi19++drI8KCzlADiH9rcubkoLS1FUVGR\nw2+TJk1Cb28vKIoCRVH47rvvOL8XFhaitLQEWm1DvzvtukJXVzNsNivU6hAkJExBWFjigB1bJlNw\nTJ6eDgaFQoVFi/4HN9+8BDX8lswuUFNTg5ycW/GHP2xCUJC4OIDBZPYGIHo6kjt3bj9luBRtly7h\n+wMHYOUFhVAUYGbpM5PCD5DKYLMBbW2EiGg0QFeX3U1Dg62UKcoGjaYBSqUfIiNTkZSU4dQd4w0C\nAvo3y7RYepGautBrOX744U2cDsXOoFCIsx5cL7h2ergUFosZ+fmfwWjUORxDCHw3oRhoNPWQyZQI\nDU3gdPNlgx2eJVSZ2xn6aymRyWSYMCHXaxleu3YTlGLSbtB/XTwoSYnYh6ZUqq6B8swAACAASURB\nVLBhwybk5Cz3+EUuXrwUqanzYbPZcObMdpw5s83jYFExoEvLA0BwcGy/uvkKgavQmzzaV6drR1zc\nRAwfPh8ZGdNR6KYIF0CUyIwZs7BgwWOYPXuV6GC4CO9bDP06Qfe5dwOVUolNGzZgeU6OxzK8dPFi\nzE9NhUwqxbFjx/DBhx+ivcOewWA2gxPkalIFwmYjXV+7uoirRozC1enamYqbMpmcY8lwVjDwWpm+\nzeYeNDSUYfLkWxEdne6xHN9002O46aZVbrcHSDjQYEkHBkgGnRjXbH/08JIly5CaOh9SqQwtLZdw\n8OC7Lqui0s9fjGuQDYqiHHSxq+OTfcQdG+Dq4e5uz1zpFGVFfX0pJkxYhpiYaR7L8MKF4mXY37//\nxHpQkpLgYPHRwYsWrcIddzyGmTNniX6RmZmzMH36PUhOns6sr6s7i8OH3+MI7kBAzEDoD7xV6AZD\nJxoaykBRFGbOvAfjxq3EwoWLccMNC7Bt2zaOydBsNuObb75BdvZ8LFq0BLm5/8CNNz4MiwUQ0XoF\nPj6D0FKiVMJtSlIfVi1ahMfuuAOzZs4ULcOzZs7Ew7fdhkVTpzLrGxoa8N5776H4LEmtNbFiDymJ\nBN2qcDQ0EEJCG1XEBDN2dtplOChoGKRS7k58f76n8FaGLRYjamuLYbGY4OcXhqysezBnzp+waNES\n0XK8ePHDDuX0hSCRDEJiDfH37K0enjPnMUyfvoZZbzTqcOLEJygr2+806NkbC11PjwYmEykVLpFI\nERQ0zOWxaYg9h79/GDMuLBYTDIZOUftRlA0NDedgMGigUPgiO/sBZGTci4ULPZPhzk5xRUcHIgNS\nQnkavXidoL4eaGwUv/22bVvx/vvrMG7cODz88Frk5OQwufNmsxm7du3Cpk2bUVZWhhUrNiEjYxWM\nRh2KinYwvkCANIYaNWoeRozIGhCrxk8//RPd3aTVZkbG/2/v3IOjuq88/723H1K/1FJLQgiE0AMM\nApmnwZiHeRhsJxhlLTvGEw9O7aR2K8Ns7PXGtbXjODvZiT2VmTjlBVcxW5lKapLJ2MXEYBuMPXgc\n29jmYWMJjBEPAxIPIV5CqKWW1Orn/nH49b19+97u25KAxjqfKpVxq9Wtbn3v6e/v/M7vnMcxduzU\nYT+mmosXj2P//tcAAB7PGCxblrnYaWDAj/b2Q4mL3mKxobJyFmTZhgMHtmLPnk1oa2uGz1cCAOjq\n6kR19RwsWbIe8+c3Ii/PDqtVcdxOZ/rP38rKUXQcWE1PD/D116bvvvm99/D0yy+jvr4e63/0I10N\nb3rlFbS0tGDDM89g7f33IxqN4oMPP8Tu3buTHmvGjBlYuPDbiEWpkKc/rxBfBiYhGEx9XqNBZuKD\n+tChHYn+DrW1C1Bf/2DiPtqfG0qdSTgcxL//+y8S///gg/8Ttgyt8KPREM6ePaj6oAHKy6ehoGAM\notEQmpu3YvdufR3fe+96LFjQCLvdnthls9moRtioyL6oCKitze51fROIRIBDh8xvkbzzzmZs3Jhd\nHAaoCPXQoR1JM3AKC8fhrrsegctVnLhtqMb3/PnDaG5+HQDg9Y7Fvff+0PC+2WzbqPn44/8Hv5+y\n1XfdtRbl5XVp7x+Px3HhwpHE5wMAFBWNx5gxkxCNhnHggLGGlyxZj3vuaYTVak+cppFl0rDRgt5u\nB+rrh9/EctSaklAIOHzY3MUQCFD8D4dD2Lt3K3bu3IRTp1L/kIsXr8fs2fSHFMTjcZw6tQ9Hj76f\n5MxLS2swa9bDWRWOagmHB7Fz5y8SqbxVq348rMfTo7+/G3/60/8FQCuAb33rOVgsxvXRwWAv2tu/\nRDRKttpisaKiYmbK7zUw4Ed/f9f1Y5C+pMp4u52MiHqV7XCQMdH6OKcTmDp1FHVzVROPA0eOmO/X\nDSAUDmPrhx9i09ataD56FCXFFJA7r17FnLo6rG9sROPy5bBrIs+pU6fwxptvIhBQ9uQLCoqwYvkj\nKB0zHi3hO3AlWKD7nKIltxaRTdm169fo7u4AAMyd+wgqKu5M+tmR4P33X040GFy48PsoLq42vG80\nGsa5cwcxOKhUw5eXT0FBAa1+1Y1tBwb8iaZcLpeiY5tNafInsNmo95w2e2SxANOmjbJCbRVnzgBX\nrmS+XyxG9wsGKQ6/994mnDxpLg4DQF9fF5qatiRl5qxWO2bM+Pb1RpHSkOuXWlp2orV1LwBg4sS5\nmDFjzdAeKA0HDryRqE+8445lmDJlWZp7x3Hx4vGEiQHILI0dOwWAlFTT0t9PGrZYkjVssZAm1dsx\nskwa1isvqa0lcz1cRq0pAShTcj7DbkooRKcIxLsUidBnQH+/H4FAF8Jh5Q+Zrkq7u/sCmppeRyCg\nHEl0OLyYObMBpaVDWyJ1drZh797fAQDy8z1YterHQ3qcdFDx2C8S9TD33vtDeL1jde87ONiHc+cO\nIhqlvL4sW1BRMUP3SLS6VbLWUNjt+tsx+fkkenExyTIZktF0YiGF3l7KlgzhMvYHAui6vj/m83rh\nzdDopa+vD2++9RZOnFAm+cqyjEnzn4Cr/rsIBiXDFK9etoSO+kawY8ffJbpwrlz5VFJx9UgUugLA\n55+/ikuXKKtUX/8gqqsX6N4vFougvf1LDAwoJ5vKyiahsLAi6X5Ct0ZmWJb1TbTVSqtNtTEZtZm+\n60QiQEtL5rbzXV1IysT19wO9vRSHYzEgPz9zHI7Fojh27AOcOJGc+aupWYCpU5fDas0bkt527/4t\nurqo3mXmzAZUVppr/pcNp07twZEj7wEAxo6tS2SBUonj0qUTCaMP0ElKyqwogtT2VtSaZUmiLgDa\n7qySRMZEbaJ9PqCmZggvSgfLz372s5+NzEPdfrjdIgOi//14PHW8eihE/2+z5cPlKoLDUZQYLS1+\nRo/8fA8qK2djcDCQcK8OhxetrXsRiQRRUlIFScpuud/R0YLOzlYAQElJTdJU1JFCkiRcvnwCPT2X\nEAz2wm53oqCgLOk1A0AoNID2dsWQSJKMioo7E/NzUh83+UuNLOuvGsXxUodDpNPpYhjV5OXRG2N2\n5KqKfLsdRQUFKCooQL6Jynq73Y476+vhcDjQ1taGeDwOu6sMH5wJoePiWUycWAOLJU/3A0EMk1QT\njwPd3R04fbrp+uM7UFe3csSLtQFqbNXVdQbhcBCRyCCcTh9kWU7ScSxGBYEDAz2J20pLa1BUNEH3\n9aSbPyJJ9KfRfl80jsvPJ50XFFD/u9FU4KpFXO/X0pRJ9PUlSzwWAwYHlTjsdBbBYqG/Zbr3UpJk\nlJbWorh4Aq5caUUkEkJ+vge9vZ04c6YZPl8FHA79jJ8RsVgMLS3vQgzimzp1BfLyRr6TYzQaRnv7\nlwiHg+jv74LPNzFFw0AcV660JmWD3O5ijBs3DUYlpOpFnvZ2u12/LiwYVGZ/2mzUy3GkstWj2pRI\nEhkTdSZETXc3mRA12j1zdaDNPDDOgvLyqXC7aQ7DwEA3YrEorl1rx6VLX6OkZCLsdvOdZ1pb9yEQ\noLxnRcXMET0ODND2UFPTH7Fr169w+PC7CATacOzYO9ix40UcO/YuZNmBsrIpGBwM4MyZ/YnVriRJ\nGD++Pm0HRSNTIjqni07pWsTY8PJyYOLE0R3ME3g8MF2JNkxoJlIFKsbfgY6OSzgRKse1ENDbew0n\nTnyJ0tJSeDzFKQbEyJRcuHA0UXNVXFyVNOdjpAiHB3Hw4Jv44ot/xtGj7+PChf1oavoD3n775wkd\nl5bWoq3t86Rp2MXFE1FcXGX4uHpZPoFYXerNAInHKY4UFgJTpoyueTdGOBz0nujtRIbDqYZFNNcT\n6GVH0mU8XC4fJkyYid7eTsRiEfT3X0M4HMS5cwchyzJ8vgkQWQWjjK6gt/cy2to+A0D1c9OmPTDi\nxjocHsRXX72NPXs24ejR93Ht2lE0Nf1rkobLyqbg/Pmv0NNzWfU6i1BRUY90hsTIlAhdGq1XgkEy\nk9OmmTtFZZbRuBOfhMNBaSethgYGUi8QM2PUM2kxHgfGjavHvHmPw+NRSs97ei7i449/jbNnm5F0\nzlKHgQE/rlxpRXv7IYTD5JJG+uTN/v2b8dOfTsTJk7/Fr371M/T29uDChfPo6DgLv/8aXnjhGZw4\n8Rs8/3wl/u3f/jtaW/chFOq/nsGoSyoe08PofRQXhtYMqvF4gOpqNiQJZBmYNGl4AyeypLBoLGat\n/l9wT5iduC0Y7MfOna/iwIF3IcupBkkd9Pr7ScNnzzYlNFxUNPKnx4SOOzt34pVX/uG6jtvR3t6W\n0PHXX/8GP/nJBHzwwUYEAp2J36WkpCrtYxttLYlAny5e2O20uhzO4LJvGlVVqaMiKJuW+j5m8t9m\npujm5blw991/hqqquYmTLbFYDEeO/An79v0LQqHetBkxEYfb2j5LaNjrHTfis3eEhk+fflWl4fNJ\nGj5x4jd47rnxeOedFxPZc4ej4Hr2fGi/j8ViXA8G0PVcXT38Dq5aRnVNiZquLuD0aeWP0NmZ6rxF\nV0o12r1yM93/xPfj8SiOH9+Fkyc/STp3Pm7cdMycuQZW1XCzcHgwcXLl9OkD8PlKEY2G0N19DcXF\n47Fq1fOYN+/PUoq7hsKHH27Erl0vYfv2NzB37ty0921qasK3v/0QysrmoKZmIRYsWAefr9LU84gm\nQuprWMyZA8gwaoN2SQlw9928utRlYAA4cSK9oxsB4gCO+sfhZB+NIWhtPYxPPtmOUEjpw+PzlWHx\n4kfhdCrGOxwexN69W/Hpp5vQ1nYAxcWliETC6O7uQnHxeCxc+JdYseK/aQrFh15TMlQdr179v6+P\na8jseq1W/boRoWm7PXUr0ukEFiwYRbOasiAaJQmLemq/P3VnMhbTv0374Wm2Eys9z0V88cXrCVMK\nAHa7E3PmfAdlZVMSt1H2ODkOU7a7E8XF43HnnY9izZr/MyJxGBi6hhct+gvMnNkAWc68UBGmSx1T\nRbZa/Ftbt2e1ArNnU8Z6pBn1mRKBz0fVwxYLOXM9MZvJjptx6Eo60IK6uhVYuPDJpNMpHR0t+Oij\nf8S1a1Q4pc5avPji/0BPTzfa29tw4cJ59PT4sXHj36O19V/w/POV2L9/czYvO4X9+zdj166XsG/f\npxkvAgCYO3cu9u//DJcuNQOQTBsSIPXDRjuIVv3ZarHQ3jsbkjQ4HMAdd9zYyl9ZRrh8Itqjylyk\nmpp6NDb+JcrKlNqLrq5LeOedX+PMmSYAcezbtxk//vFEHD/+W7zwAmn43Lk2XLjQntDwxYs78JOf\nJGvYzPWkx1B1fPnyQVy92gpJkkw9r96RZbXJVi9aRIHgwoVsSIywWEjCRUXK0EYtI7FLqdaVJAFF\nRWOxYsV/RVWVUqAaCvVj377XcPjwu4jFIti/fzOefz41Dnd0nE1oOBD4bETiMDAcDR9AKNQHi8U2\n5GyyWsNi/pTA5QLmzbsxhgTgTEkK/f3AF1+QMVETjdL3tGTqwSAQwSoep8fSiiUU6seBA2/h4sXj\nqp+R0N9/FUeOvGnaKa9Z8zCWLn0Wy5c/leml6ryWQfz0pxPx/vvvJM1HAICuri5UV1ejp6cn8but\nW7cOv/vd7xLPvWrVarzwwlnTqwTtCQZ1lkTgctF2TVkZnbThdLcJYjHg4kU6XjaSl7fbDVRV4WJ3\nPvbvT33oWCyG5uaPcPBgcuavt/csvv76/aw0vGzZs1ixgjScbbbESMeZNCye//77V+PFF8/CYknO\n2Oghy8YrTEFeHhW0+ny0/z6qT4tlwalTwLFjyR+IAMVh7W1G2wx6XVlFzBG60sac8+db0Ny8PbEl\nAwCXLx/FuXN7sH37mzc8DgM3V8PaTIksp8ZZq5U0XFBAdVAlJUN6WabgTIkGpxNYsoTcunqLPtNx\nNTV6R63sdno8vYsAoFTh/PmPY8aM1ZCvT1w9f/4rfPXVH7Nyyvv2fYpdu14aklM/cGAr7ryzPsWQ\nAEAgEIDP58PWrVsRj8fx+OOP4/e//z22bNmSeO76+uk4cGBr1s8L6L9nhYVkRsrK6EJgQ2ISWQbG\njQPq6kam1a3NRmmqKVOA/Hxcvqwf4GRZxl13rcDq1d+Hy0UnGDo6DuPo0Xez1vBHHw1NwwBw8KC+\njjNpWDz/9OnT0dy8NWU1rS3I1ruO1YZElsnHlZVR59JRf3w9S2prKRZ7vckNx7SGJB3qv5Esk5TV\nJ0r0/objx0/Hfff9EMXFlPnr6DiM06c/xr59u29KHAaMY/FIaligZ9oEkkQJ2NJS+po8+cYaEoBN\niS6SRAFk0SKa0p6fn92FAJDo1Q2U1M7c+HklVFfPw9Kl/wVOZyFOnPgT3n13ByorlS2R2bNnw2Kx\nQJIkFBSkHl2rrKzE9u1vYMuWp5O6F5phz55NePpp/Y6tlZWVaGtrw8MPPwwAePXVVyFJEv7whz8k\n7vP00+uxZ8+m668l9XSN9jb1l92uNE0bM4YKqMrKKKhrDSJjEqeTjMT06fSmZrvv5fFQFfidd9If\n4/ofMlPr//LyKjQ2/hATJtQOS8Ovv569hiXJWMdmNAyQjnfvVnQssiFiBSlqRtSD1SSJNCqu+eJi\nKtwcP56yfbW1vGUzFAoKgMWLKcPk8WTfTE+SlAnieXlKDVCmzJvTWYglS/4zJk++R1fDQHodDycO\nAyOrYSB97FXHZ7GAzsujReGECdRHp6AAqKi4Of10eO2ZhoICYM4cKoD1eJSz8oODysURjZLA1UWb\neqsqgH5G3B8wNilebxk8nmLMmDEzxSlXVVWhtrYWH3zwgeHIaXXWYt68x9O+xlgshnA4iGvX2nH6\n9AE0NDSYeWvw0UcfIR6P46GHHkrc1tDQgHXrvo9QyA+XK7VhmhYR5GWZ3l+Phz5Hxftlt5MhMTmc\nkjHC4aDIUlFBuW/xFQwq+W3hDJ1O5cvgjfd4KHiFQpRBDIdTU+f5+U44nRbMmjVryBoWq71MGo7H\n44hGQwgGe9DTcxFtbeZ0rKdhQNHx4KA/qdOw3jUtzIh0vb2A200mRJ0Kr62lWMIMDYuF3kOfD2hr\noyLYQIDqutUZbL0YrP3QFZjZEpRlGQMDXZg1a7Zu9jiTjtVxeP78xzM8XxyxWATBYC/8/gumY3G2\nGjZCaNjhoOvb7U5eCJaX0wL9ZsCmJANWqxJU2tvJPYoGSAMDqSPZ0xEO6zt9cYGIWpR4HNi799f4\n+c+fSbnvG2+8AYAcc7e28EXF00+vx1//9d9jzJjJyM93Q5IsiEbDKV+xWBQDA904duxDeL3exByJ\ndPj9fqxatQpFRUX4wQ9+kLjdZrPB5ytBf3+XKVMCUMApKqKAow4aNhsZktHaevuGIPYThrFkFwZE\nZLYEsViySQmFgP/4j3/E3/zN8DT83HP/gLFjp0CWbbDZHLoajkYjiMdjOHnyUwQCV03p2EjDgKLj\nvr4uUwFdlsmIjB2bmvqurqbtB2b4FBXR+9zaSp45HietiVicTTY7FjNXQP3JJ5vwt3+bqmHAnI6F\nhseNq0MsFoXDUZhGw3G0tx/ElSttN13DkkSxtrw8NStdVka7wTcLNiUmkCRKW3k8dEEMDCiLSWFQ\ngkHKoKQzKJkKjQD6kO7v92dc7WWqT25oaMCf//k6NDX9EdXVd8PpNB5KoO3Omo5QKITy8nLIsozz\nmXr0p0EszN3u5NbxABnByZNHtiEPMzIYnTaWZfp7ib9ZIODHyZMjo+HPP9+MsWOnZmhkJpsusB5J\nDVut9EGpN2xv4sSRmQXCKNjttCN54QJ9CXPs8SgGJRjMfELHzEKyv9+P1tbMGYt0OhYa/uyz11BQ\nMBYTJsxK+1jqNhDpGCkNA8qR38LCVENSUkIJ1qGe4hkKbEqywOGg2sH2duDy9aZ5sjw0g5KOQOAq\niotL0zrlTB0DbTYbvN5ChMMDhiO6BbJsgcdTgu7uawiHw7AZFHBEo1GUlJQgHA6jo6MDDvWkJtCU\nzq6uzrSdXMX+vAjoDkdyMLdYqA8YFwTmJmb39Lu7r6KkZOQ0LAY8Gj8WYLe74PNVpNVxJg0DmXUs\n9t6FlkXxpJrKyhtfEDhakSRauXs8tJ0TCiXXpWVrUIwwE4fp9zHWcXIczvyL2Gx5KCwsvykaVp8c\n0+tF4vPdmq7ZbEqyRJaVwp/Tp5MFfyMMihFmTnKLOQ9ebzm83nJYLLaUL6vVBlm2YNq0VTh58j1s\n374djY2Nuo9XUlKCvr4+nDx5EqWlpSnf37ZtG2pq5uimC9VmRH2buhugaEzKBYGjA7MaLimpQnHx\nBPh8FboaFl91dcsgy8DRo9sMdZxJw4CxjtNpWH3bzSoIHO14PFQAe+ZMcht6rUERQ1SHY1DSkUnH\nkiQlRhYUFY1Pib/q/5ekZZAk4PjxHTdEw2pDLRCfW+o6+MJCKtS+2YYE4NM3Q6awUKkI10P8oX0+\n2pMrKqKLxMwf2e0uxtWrVxBOcw450yozHA7D7+/GPfd8H5MmLUJpaQ18vgnwesfC7S6Gw1EAu91x\n/fgxPdbCheuxYcMm3cfbsmULuru7EYvFUFNTA2ouJeGBBx5I3GfDhk1YunR9St8Gu12/86W6Y6so\nCByJE6zMjcNsB+3CwmJ0do6Mhhct+gtMn/4ASksnweebCK93HNzuUjgchbDbXdd7MSiPtXixvo7N\naBggHd977/qEXsVRUqPureqF6rhxN68gkKH3v6aGVvR62hSFyAUFyrFWj8ecjs3EYXoOYx2Thv1Y\nvPgHmDu3EWVlk1FcXIXCwvHweMbA4SiC3e6GxZIH9cexUSzORsNLlyoaFplpmy31tYvPKkFBAb2n\nI9wt3zRsSoaBOB0yfnx6syHLFLh8PlpVORz6jcIETqcXNTWzsX379pTvDQwM4OLFi4hGo4jH47hy\n5QoGdKZYbdu2DdXV+lkLPSQJmDOnEYcPH0Zzc3PK9x955BHE4/GUr507dwKghj0tLS2YP78RVitl\nOzwe45MzkqScSOCCwNsHvcm3erjdXkydOnwN19TMgdvtTazu0j23+N7cufo6zqRhQNHxggWNcDpJ\no/n5xs/rdivfKyu7cV0uGWMkicxGXV36bV9hUDweijUuF+nZ6KR8ujgMmNNxtnFYYBSLs9Hw/PmN\nidM02kyImrw8JU57PJStvlWGBGBTMmwkiQLRlCmZT4oII2K1UqBzu40NytKl+k65rq4O5eXl6Ojo\nQCAQwJgxYzBt2rSU+23YsAmLFq1POiKXCZstD48+ugEPPfSfcPbs2cw/cJ2zZ8+ioeFhPPHEBrjd\ndrjditDFdpZ2W1achZckShNyQeDtgej5YIbGxvV45ZXhaXjx4vUpxzv1jnyqi8Vttjw89tgGrFkz\nNB0/+eQGeL125OfTtelw0AeY9jqVZcVYl5be/IJAJhmHg/pLmdk6ExkDEaOMDIpRHAbM6VjE4WwZ\nbixet24DCgrscDjoNebnK69RaziEhl2uW29IADYlI4bbTU7dZ1zjqduC2sigzJun75RPnz6d4pLb\n2tqS7iOc8pw5+rUhWtSBdN68tVi+/FksWLAYTU1NGX+2qakJ99yzGI8++iy++921upkRi0UJ7GIL\nS3RprKykkwvM7YPZIuTly4ev4blzFQ1r+4RojYqahQvXYuXKZ3HPPeZ1vHDhYjz22LNYuXJtirkQ\np4vUgV2Y7eJi0jEbkluPqPmbNCl9B2ht/aiRQTGKw0BmHRvFYTPZPgCYP39osXjt2mfxrW+tTfms\nEbU2LhdpWRRpezwUnydPzo25YmxKRhCrlbYhqqqM3Wa6zqRqg1JQkId164a22luz5mE8+uiGlCOS\nZoKmLAMrVz6F73znl7j//tVYunQltm7dmtQcKBwOY8uWLVi69D48+OBq/NVf/RLr1j2V2KIyeh5Z\nVuaAeL3ULdCgTovJYcwWItvteXjmmQ1oaBiahh97LFnD2qaEarRHymUZuP/+p9DYmFnHy5aRjtev\n/yWeeOIplJQYf6CpA3tpKWX4blVBIGOMqPkzalqXriGj2qAUFubhySdHLg6bNSRC60OJxd/73lPw\n+dK3VLDZ6PWVlipzPHNljAcP5LtBBIPU00Q7xC8YBLq6zD/O229vxI4dL2HbtqENM1Oj18VQHei1\n2zyRSAhNTTRqvrW1GT4fnXG8dq0TU6fOwSOPrMfy5Y2w2ZKv8FCIXqPR8dGCAroIbmZDHmbkiESA\nQ4fMHw/evHkjXnvtJbz1ljkNNzQ8jPvu0x9mZjSOXmhXGJLk3zeE/fu3YteuTTh1inQsSUBXVyfq\n6uagsTFVx9EocPWq8WmNvDwqBqytvfXpbsaYeJxmU3Z0pMa+zk7jvjtahhKHly831rD6vwKj7UhA\nicW7dysaBigWG2k4HqfBsjrlWgBItxMmUIY/l7pmsym5gcRiwPnzwKVLym3xOHDlivmjaZIEHDiw\nGa+88jTq6+vxox+tR0NDQ+LsfDgcxrZt27Bhwya0tLTgscc2YN68tboGRO9i0O7T62GzAcGgH8Fg\nF2w2oLraB58vfeGWkTGx2YD6et5/v91pa6MPbbO8995mvPxyeg1v3LgJhw+34Hvf24AFC9aanvwq\n9KtnSLQMDvoxONiFwkKgvNwHt9tYx7EYvUbt4QtRmD1tGhuS24VAgDQ7OKjc1t+fOg0+Hfv2bcY/\n/ZP5ODx//lpDE62Nz+kMiUBoPBgkDbtcwMSJ6TUM0GvUm3A/Zgwwa1buNalkU3IT8Pupp4kIboEA\ncH3ydEbETJhwOIQPP9yKrVs34ejRZhQXlyAep9VeTc0c3Hvvesya1ZiUKtQb2613MWh7L6iRJKXI\nTwTgTKlBQThMxkS0f5YkKgiePJkNye1OIEBj5bMhnYYnTZqDVavWY8aMxqRx63rGRBvoRbBOtx9u\ntSZPh6Ut0sy/cyxGGlavqMvKgLvuyo39d8Y8kQhw9qySqY7HacFoJuNnsdBWRzSaqmEAuHqV4vDS\npRSH1RrWMybaBaK2gFsPUbAqSgDsdvMN+vx+mtsmcLmAhQuTj7PnCmxKhfIftQAABv5JREFUbhLh\nMDn1nh4SaGdn5mxJXp5+EWgg4Iff34VAAJBlH1wuLyIREp164B+Q3phkMiSiQFV72qKw0HyxYyRC\nq81olI5Oz5nDhuSbwqlTyU2rskFoeHAQiEZ9iVlJg4OpKfV0xkQc89QzCGI7R0zpViPaapuBjBP9\nbh4PTa3lqdW3J/E4xaNz5ygm9fVlnnotSbQQ08ZBoeF4HBgYIA3H40rTTLURyWRM1FOn9Z7faiXt\naWunsmnS19NDiwmbDVi0KHeHRLIpuYkIZ97RQft8XV3GnV5lmZx5utWYNuMiOheKC0AYEq0xEf/W\nMyTa9sMul/4Rsmy6rkaj9Bhz53K6+5tEOAy0tAyvS2YoRAZdEI/TB4WekdZuo8Tj+hkSYVT0GkUJ\n8vPTn5TTEo+TKZk7NzdXl0x2BIPKxGFhOI0wk1W7cCFZs/39FPdEHFbHYjXqCfN6J75EjLbZUrPT\nspx9o77+fvPHpm8VOVJvOzqQJBKRmNkQDCan1NQUFmZOD2sDrthTj8WU48fiQohElAtCiFy9lWPU\nflgvqJstcBSUlqY/kcTcnthsdPyytXXoj6HVhFgV6tVx2GzJt4uGUCKzIu5jpnNythp2OoGZM3Or\nIJAZOvn5tJXc0UHmobNTXxOiVX0mZDl5SrHNpizGhMZjMbpNnc22WEjv6p/VG2egdzJGGB2zmWer\nlTLVuT7Gg03JLcDlUroPfv11arpanCPPhN6HvN1OZkcgzIbFQsYkGlVWkGpTovdYRilqswFdkmj/\nPVPHW+b2xecjY60u5s4GPeNtt6eaEiDZmOTlUcZC6FtkTczqLBtTItpu58qRSWZkkGUquPd4gCNH\nyJiosx2yTItDs60UtKYkFEqtfRL1T0Lfoi+ViMd6GRNh1PUQC9BM5OeThm+HQad8md0iLBYSiccD\nNDcr6UMxp8EMRkZCezGovycamAmHHg7T/QcHU38m3YWQifx8mkfBs2y++VRUKKvNbBFBWPthYLXq\nbwuJwuu8PNKzaDoYiVBtgNkjnmaLGysquJfONx2vlwqXv/qKTksKLXq95o2omQWiQJJIs6KBmTDT\noRDdX2vI05mOTKZEkmirZvz42ydTzabkFlNaCixZAnz+OdDba96ZA+kbtGn3SMWF4HJRIFenocNh\npeBLTDQ22roB0gd0q5UqwseNu30uAmZ4SBIZUItlaBkT7SoTIH1qTYloXOZ2K9lEpbU8FYX39SkF\n3+lIl/oWK+SKCt6uGS3YbMDs2bSIOn6ctJVN7ZBerBNmQ1sfZbUqcdjpTN7eCQaVglSh4XRF1eli\nsdtNGs717RotXOiaI0SjdFzt2jXzqeVYjBoDadEWC1qtFGTNOP/BQWXFaWQq9Kq+nU66zedjMzKa\n6e4mHZvNWADUt0dvu2ZgQDEmYs5MYWHmmhFxAqK/P30BY1lZ8ipTHLEsKWEzMprp6qLCVaOmY3po\nj9wKRBYaIM2KyfFi69GIWIyMid+fPhNSVJRsniwWevzS0ttjq0YPNiU5xsAAcOYMCdIM2qpvweAg\nBXSvl0Q6lP3wSIQ+LMJh+rfY+7TZKBMihu05nRzEGYVIBGhvp6OXZqLL1av65iESIXPhclEWZChN\nnmIxRcPhsJIFtFjIlHg89PhOp/kJyMw3H/VJSTOLxN5e+tJ7nL4+xfC6XNlrTJw8E1+xmJLJLiqi\n+C7isMNx+y8K2ZTkKL29tILs7k5/UVy6lJqqFsfHHA5jMyL2Ms1+aU/mMEwmgkHScLp27QBlB7Wr\nUnWPHKOpxKL2JJsv1jCTDZEI1Up1durXhwj0+p2ILfO8vOStRu19hqLhb7J5ZlOS44TDSpvgvr7U\npjxXrpCTFiZE7FVycGZyhViMNNzXRzoWPRwEfj/pWpyocThoq8ZmG93Bmckd4nFaKAYCSixWbzkO\nDJDGhQFxOikLl5eXebHHGk6GTclthjjrru4vks1RSIa51cTjSmMpgTgayTC3C+reT0aN/JjsYVPC\nMAzDMExOwEl8hmEYhmFyAjYlDMMwDMPkBGxKGIZhGIbJCdiUMAzDMAyTE7ApYRiGYRgmJ2BTwjAM\nwzBMTsCmhGEYhmGYnIBNCcMwDMMwOQGbEoZhGIZhcgI2JQzDMAzD5ARsShiGYRiGyQnYlDAMwzAM\nkxOwKWEYhmEYJidgU8IwDMMwTE7ApoRhGIZhmJyATQnDMAzDMDkBmxKGYRiGYXICNiUMwzAMw+QE\nbEoYhmEYhskJ2JQwDMMwDJMTsClhGIZhGCYnYFPCMAzDMExOwKaEYRiGYZicgE0JwzAMwzA5AZsS\nhmEYhmFyAjYlDMMwDMPkBGxKGIZhGIbJCdiUMAzDMAyTE7ApYRiGYRgmJ2BTwjAMwzBMTsCmhGEY\nhmGYnIBNCcMwDMMwOcH/BzisS05PJ1coAAAAAElFTkSuQmCC\n", "text": "" }, { "output_type": "stream", "stream": "stdout", "text": "+------------+-------+-------+-------+--------+-------+--------+-------+\n| - | RI | ARI | RI' | ARI' | nF | sqtr | tr |\n+============+=======+=======+=======+========+=======+========+=======+\n| (V,U_1) | 0.778 | 0.556 | 0.802 | 0.604 | 0.695 | 0.815 | 0.432 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_2) | 0.778 | 0.556 | 0.802 | 0.604 | 0.695 | 0.815 | 0.432 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (N,V) | 0.750 | 0.500 | 0.979 | 0.327 | 0.512 | 0.662 | 0.200 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (N,U_1) | 0.750 | 0.491 | 0.979 | 0.337 | 0.503 | 0.668 | 0.193 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (N,U_2) | 0.639 | 0.264 | 0.977 | 0.275 | 0.481 | 0.616 | 0.178 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_1|G)t | 0.926 | 0.744 | 0.928 | 0.752 | 0.799 | 0.923 | 0.527 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_2|G)t | 0.857 | 0.417 | 0.859 | 0.435 | 0.708 | 0.844 | 0.480 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_1|G)s | 0.889 | 0.773 | 0.901 | 0.797 | 0.843 | 0.904 | 0.712 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_2|G)s | 0.833 | 0.660 | 0.900 | 0.776 | 0.832 | 0.885 | 0.705 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n" } ], "prompt_number": 197 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": "Omega Example" }, { "cell_type": "code", "collapsed": false, "input": "A = np.zeros((5,5),dtype='float')\nfor e in [(0,1),(0,4),\n (1,0),(1,2),\n (2,1),(2,3),\n (3,2),(3,4),\n (4,3),(4,0),\n ]:\n A[e]=1\n\nfix_pos_GraphExample = {0: array([ 0.49682607, 0.95151713]), \n 1: array([ 1. , 0.59183855]), \n 2: array([ 8.12052312e-01, 3.19389103e-05]), \n 3: array([ 0.19258776, 0. ]), \n 4: array([ 0. , 0.58628989])}\n\n\nU = np.array([[1,0,0],[0,1,0],[0,1,1],[1,1,1],[1,0,1]])\nV1 = np.array([[1,0,0],[0,1,0],[0,0,1],[1,0,0],[1,0,0]])\nV2 = np.array([[1,0,0],[0,1,0],[0,0,1],[1,0,1],[1,0,0]])\nprint 'V_1', agreement_from_omega(U, V1)\nprint 'V_2', agreement_from_omega(U, V2)\nexperiment(A,U,V1,V2, fix_pos=fix_pos_GraphExample)\n", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": "V_1 [ 0.5 0.219]\nV_2 [ 0.5 0.194]\n" }, { "metadata": {}, "output_type": "display_data", "png": 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QW1OY+FdtlcLt7qrYA6lqgFwQe/d+Im737VuEYcMmi9tGYzr69BmMPn0G+1wsmZl9ceGF\nc8Tts2cPoKLisLjN86QOhM1GtjMyyHFQQZJ8nD8vT5AAXdMnGSawfba3m7Fr1weiIElLy8XFFy+C\nIEiAwPYJAMOHT8HgwePF7Z9++g4VFUfgcvkKdYYhM0va76b3YjbLEySAdNNIrVZ6bOM4N3bufE8U\nJGq1BjNmLBMFCRDchrOzB2Dy5AXidn19Ofbv/wwcR2zY+3pKSwMMBlqjJBro7SkMpKq2SiGVM8+y\n0sqZ53ns3r0JDgdRDjqdscugH4zhw4uRnz9U3N6z5xO0t5u7HI+wf4NB1sdSehBNTb7LMaGQa59u\ntws7d74Hu50ET2k0OlxyyTJxiVAeDCZNWoDs7P7iI7t3b4bZXA2OIx4ap5O4vLVaKkp6KzYbSRyQ\ni1RsUiBxvX//52ho8ARaXXzxIqSn54V1fIMHX4Thw6eI26dO7cGZMyXixM9u99ivwUBLLkQDFSUy\nCVS1VYpAwXxCUR1vTp78AbW1nqtx8uRrYDDIz4lkGAZTplwLnY6M5k6nHd9//yF43hMlptEQlyJA\nY0mSDatVvl0KBCo05WufPEpKtqKpyTN1nTp1MVJTw0+NUanUmDFjGQwGkovudjvx7bfvwG5vB8+T\nGa+Qpk5Fc+9DqllkKALZsErl66UoKzuAU6d+FLdHjChGYeEFER3n+PFzkZc3WNzeu/dTNDSQ1GK3\nm9gww1BhHS1UlMhAaGgmNx0s0OsEJS8E8bW01OLQoa/E5wcPHo+CglFhH5/BkIqpUz2xJA0N53D0\n6H8AkH316+fZJxUlyYOQpRDOYC50/pXC2z5Pny7BmTP7xedGj74E/fuPjPhYDYY0TJ++DCxLDLG9\nvQU7d74HlnWjf3+P250O6L0LofOvnEQAb4JVcBXi6MzmauzZ41kW79NnEC688PIIjxRgWRWmTbsO\nJlMGALIs9N1378FqbUFenmdspcI6OqgokUGgqq2BCCZeGEYwWie+/34j3G7yYpMpAxMmXBXxMfbt\nO9zHvXj06A7U1p5Cbq6vEKEXTHIgCGUhXkguUvFO3jAMcO7cbmzb9pL4WH7+UIwdOyuyA/UiJ2cA\nJk2aL26fPLkLGzc+4BOITdfiexd1dWT5MVxClZW32xuxYcPD4vhqNKZh2rSfiaI4UnQ6Iy655Aao\n1cRQW1tr8eKLy6DReFQVHWOjg4qSEASr2hqIUB4VhgE+/PARlJRsBM9zYBgGxcVLwlyr78qFF16B\njAyyVlpWtgfr1s0D4GkPK2TjUHo+NTUkMDBcQg3mZnMt/vrXpdi16/9w5sz3MJnSUVy8FAyjzFAx\nZMgEDBs2GWVle/D996/jgw+exqZN/wBAvCR0Lb730Noa/tgKEGEdrIaJ2+3Gk08ux86dr+Pgwc1w\nu52YPv166PXKlLLOyMjHlCnXoqHhLL799u/Yt+9z/PnPd4LnebAs9UZHCxUlQQhVtVWKUBcMABw+\n/A02bVqHY8e+xM6d/0RR0QTk5BRGd7Aga/fFxdeipORdHD68FTU1Z7B27Z1i5oRU3RJKz6OlRX6W\ngj/BRInL5cS6dcvQ2HgeHOdGaekOTJ16OQwG5dZUWBYoLp4Llm2H200O5q9/XYmDB3fRGWYvwuEg\nY2skBSlCCeu3334UBw58AQA4d+4AhgwZiry8ggiOUhqGAYYNG4PCwgJYraSgyr///Sbefvspmt2o\nAPT0BSFU1VYpQnlJLBYznn76FlEoZGfnYdq0K31iTSKBZYno6N+/LxYtWiU+/tVXH+Djj18DQN2K\nyYDdHvlgDgQf0F9//UEcOfIfcfuXv3wJQ4aMhdEIxezTaARSUjT43/99H337DgRAxNCDDy6F2Xw+\n8h1QegxCs0g5nX2lCDbG/vDDJnzwwZ/F7csvvw1XXLECBgMZ/8Jpq+APw3gybLRaYNWqP2LGDM9y\n5LPP/hYlJdsi+3CKCBUlAWhrI22xwyWUKHn55XvE9DStVo/Vq9+EVqsVW7YbjWRdnWWDXzwM42n3\nbjB4LhSGAa699m7MnLlIfO26dfehrOwEdSv2cEJ1/pVDoPfu2PEOtmx5Sty+6qqVmD37VgCeMt7R\n2KeQ8qtSkarC2dm5WLduE3Q6opQbG2uwYsVi2MINkqH0OM6dC94sMhSBxExl5Qk8/fQt4vbQoRNx\n110vgOk0VLXad6yU0y2dZSEW+jOZPN7mjAxAp2Pxxz++hYEDRwAAOI7DqlXLcPr06ci/HIWKEilc\nLhJEqLRrcceOd7Bjx9vi9i9+8QQGDPDNtlGpPBeAyQRxlur9JwzyJhPZ9lb/KhWQkcHg97//B3Jz\n+wEAbLYOPPLIjWDZEFXfKAmLkKUQrufOG7dbOlOnrOwwnn/+dnF7xIhi3H77U11fiMjtUyAjw7M9\nYsR4PProa+JzJSV7cNddd4EWmU5eGhpI4kA0SI2xHR1tWLt2MaxWUkEwNTUbDz30oU+BNAFvr52/\nDet0XW1YKIYmjLEpKR6vc0pKOp54YjNMpjQAgNncjEWLFqFNbiVDSheoKJFATtXWQASaidbXn8NL\nL/1S3J4wYR6uvnpl0M9iGE/evfdfMBdkerogTHKwZs0b4izhxIn9+OtfH4noO1G6n/p60so9GqRs\n02IxY+3axWKBtIyMPDz44AeyWrSHa5+pqV2DAOfOXYZbb31I3H7jjTfwzDPPhPW9KD2D9nagoiK6\nz+D5rsKa53k899xtqKw8BgBgWRYPPPAO+vQZGPLz/G1Yq/XYsFRsiE5H7NibQYNG4PHHN4hj7dGj\nR3HrrbeKPXYo4aFas2bNmu4+iESiuZmU7I6U1tauHhaO4/DXvy4VL5rU1GysWfM5jEb5RdLkQNbr\nPdv9+w+BzWbFwYM7AQC7d+/CtGnTMHTo0ACfQElELBbgzJnoP0eoPCnAcRzWrbseJ0/uBkACpX//\n+60YODCy4lLBELpTS4mViRNn4dSpPSgvLwUAfPnll5g2bRqGDBmi+HFQugenk/RmimbpUfgcf2/h\nRx89gU8+8QjZm29ei9mzb4HSqFSkYaSUWCksHAa9Xovdu0ndqePHj4NlWVx22WWKH0eyQz0lXoRT\ntVWKQJk3H3/8NA4d2i5u33PPK8jK6hv5jiRQq0nfBX/uvvt/MGrUJHH7lltuQV1dnaL7psQOh4PE\nkSixouHv9n7vvT/5FJdaseJvGDPmkuh35IdaTeJIAnn3VCoVXnnlbQwfPhwASelctmwZziihxCjd\nDs+T4OxQ3avl4C9qDh78Cv/6l8fTVly8FEuW/L/od+QHwxAbDhbsfe+9D2HZsmXi9po1a7Bp0ybF\njyXZoaKkk3Crtkoh9d6yssN4442Hxe05c1aguHhJ5DuRgGHIWr2UgtdotHj88Q0wGk0AgNraWtx2\n22103b4HwHHEQxJploI/3va5d++neOedNeL2zJnLsWDBfcrsyAthMA+VJpmfn4HNmzcjrVNZNzU1\nYdGiRbBYLIofEyW+nD8fXvHJYHhfC/X1FXjiiRvEZZKCgpFYteo1cRlFSdLTQ3f9NZkYvPrqq7jw\nwgvFx26++WYcPXpU8eNJZqgo6STcqq1S+IsSp9OOJ5+8CS4XmSLk5Q3GHXcov16ekhL8ghkwoAiP\nP/6CuL1161Y8//zzih8HRVkqK8nSjRJ4l5evrj6NJ5+8SRSmgwaNwz33vBKzwVxOlVajERg5ciTe\neust8TiOHDlC1+Z7OOE2iwyFIEocDhv+8pelaG0lHVINhlQ8/PBHii+JA54me6EgwbEmbNq0CTk5\npEeUxWLBokWL0BRJ2dpeChUliKxqqxT+ouTNNx9BeflhACT4avXqfyl+0Wi1vnEkgfj5z2/BDTfc\nIG7/9re/xaFDhxQ9FopyNDaSEtxKIbR6t9nasXbtYrGTtMmUgYce2gi93qTczjoRMhtCodV6MnIW\nLFiAP/3pT+JzGzduxOOPP674sVFiTyTNIkMhjLGvvHIfSkv3io/ff//rKCiIvDdTILTawLFQ/gjC\nZdCgQXj//feh6lzrOX36NG644Qa4og2o6SX0elESSdXWQHi7Fg8d+hqbN/9N3F6y5CGMGjU9+p14\nISzbyLlgjEYGL730EgYNGgQAsNvtuPHGG2ENtxMWJeZ0dCg/mDudJEvhhRfuFIUywzD49a/fQt++\nygc+a7XSMU5S+M9CH374YVx33XXi9qOPPorNmzcreHSUWBNJs0g5n8lxwBdf/B3btv1DfHzp0odQ\nXLxYuR11wrLBY6G8Ual8W3hcdtllePrpp8Xtbdu24aGHHpJ4J8WfXi9KIqnaGghBCFssZjzzzK2i\ne3zo0Im44YbHlNmJF+npvjUgAiF0f01PT8dbb70FtnOB/6effsJvfvMbxY+LEjnCYK70ioXTCXzy\nyXM+dXJuuGENJk26WtkdwVMgTe5qkL83hWEYvPbaaxg3bpz42M9//nP89NNPCh4lJVZE2iwyFC4X\ncPLkj3j55XvFxy688HLcdNOfgrwrMuQEtnpjMHS193vuuQe33+6p//O3v/0Nb775poJHmZz0alES\nadVWKTjOcyPxrdpqwK9//aasug/hIBT4kYNW6wk0nDZtGh57zCOQXnzxRToLTRCELIVIa+QEY9++\nHXjtNY8AnTx5Aa6/Xvm6NeEO5oC0HZtMJmzevBnZ2dkAPGvzzc3NXV9MSSgibRYZirq6OvzlL0vF\nGL0+fQbigQc2iMskSpKaGl7zUqllSoZh8MILL6C4uFh87I477sDevXu7vpgi0mtFSTRVW6UQlm52\n7NjgV7V1neJrnSqV/HVOoOug/7vf/Q6XXOJJ/bzttttwPpriLBRFqKoizfaUpr6+Cn/+8/ViG/e+\nfYvwq1/9S/SYKUlaWugsBX8CxZ34r82XlpbixhtvhFvJNQGKorS2Rt4sMhgulwt/+MMyNDaS4D+N\nRoeHHtqItLQcxfclVHMN9z1S6HQ6fPjhh+jXj1TXttvtWLx4MWqVmg0nIb1WlERTtVUKlyuyqq2R\nIFRtlYt/FU2VSoU333wT6enpAEj65S233EIH+27EbAaqq5X/XKfTgQcf/BnMZjII6nRGPPTQRqSk\nZCi+L6GvSDgIJb8DMWvWLDz1lKfk/eeff46HH3448Bso3YbdTlLYY1Ft4PnnH8KhQ9+I27/85UsY\nOnSC4vvRaMKb8AkEs/u+ffvio48+gq7T0CsrK7F06VI4lCjckoT0SlHS1BR9yW5/HA4OzzxzK9rb\nyVQ3NTUb9933T8XTLIU+DeEg9frCwkL8/e9/F7e3b9+OJ554Isqjo0SCzUaWbWLBk0+uxuHD34vb\n9977KgYNGqv4fjQa+UHX3hiNod9z7733YsWKFeL2unXr8Pbbbwd5ByXeKNEsMhDbtr2Ht97yJA1c\nddUvMWfOLxTfjxDYGq4DkWFCL6VffPHFePnll8XtnTt34r77lK8LlAz0OlHicETff0GK999/GocP\nfy1u33PP3+NWtTUUgS6Y6667zicQ65FHHsGePXsiPDpKJLjdymcpCHzyyev44IP14vbChasxc+YN\nQd4RGeFkKfgjJy6KYRi8+OKLmDp1qvjY7bffjpKSkvB3SFEcJZpFBqK09Aj++MfbxO0RI6bi9tuf\nDvKOyJGbOOCP0Dk4FLfeeit+9atfiduvvPIKXnrppfB3mOQwfC8q7cnzwKlTylUXFCgtPYybb54k\nBmDNmbMCq1b9U9F9MAyQnR3+ej0AXHRR4OUei8WCiRMn4uTJkwCAoUOHYv/+/Uj17zpFURwhsDUW\ndZWOH9+HO+6YDrudpEBccMGl+MMftkGtllHJLAyEwNZwvXcChYVAnz7yXltVVYVJkyahunOda8CA\nAdi7dy/6yP0ASkyoq4vNRM9iacGtt05GRcUpAEB6eh889dQ+ZGf3V3xfKSmRTfgA0g9Hbpsml8uF\nefPm4auvSI8ctVqN7du3+8T49XZ6ladEiaqt/tjtNvz+991ftTUQWm3w+JOUlBRs2LABms6ym6dP\nn6ZuxThRWxsbQWI2N+L//b8loiDJzu6P3/72XcUFCUDsMlJBAoQXg9KvXz989NFH0HZeCOfOncPP\nfvYzujbfjVgsJD5PaTiOw2OP3SIKEpZV4cEH34+JIJHq/BsOcrMgASJC3n33XQwePBgAESlLly5F\nRSxUXQ8idJ3gAAAgAElEQVSl14gSpaq2+vPii4+gtDQxqrZKIeeCmTBhAtauXStuv/7669iwYUNk\nO6TIorU1um7UgXC73XjkkRtRXU2qr6nVGjz44AfIyMhTfF96feR2Cchbi/dnypQpPi7vb7/9Fvff\nf3/kB0GJGKczdoGtr732Z+zYsUXcvuOOJzBmzEzF9xOqWaQcwg3uzs7OxubNm2HqTPGpr6/H4sWL\n0RGL9a8eSK8QJUpWbfVm796v8fbbT4rbS5c+3K1VW6WQO+ivXr0aV1xxhbh9991342ysoi97OQ4H\nscdYDOYvv/wodu/eJm6vXv0cRoyYGuQdkaFWR2eXAJmhRlJiYsWKFVi1apW4/dJLL+GVV16J/EAo\nYSM0i4yFk2rnzn/j5ZcfFbfnzr0R8+crLzzlNosMRbjCGgDGjh2L119/Xdzet28f7rjjDtooFb1E\nlChZtVWgtbUZjz12S8JUbQ2EXNc6y7J4/fXXxUZSra2tuOmmm2i/BoURshSU6vzrzTffbMJrr/1Z\n3L7mmhW4+uo7Fd9PpFkK/kQymAs88cQTmD17trh977334rvvvovugCiyOX+eFJ9UmsrKM3j0UU+z\nyKKisXjwwb8D6L5mkcFQqyP/jKVLl+L3v/+9uL1hwwaaAYleEOja1gacPKn8rPSRR5bj88/JEodO\nZ8CTT+5TvEiaXh+9a3HkyPBc7Fu3bsWCBQvE7UcffRR/+MMfpF/McWRdrL2d5LW63eREsyy5Wo1G\n8qfTRfclkojychLbpDRlZSfwi19MRns7uVOMGjURr7zyLWw2g+KCPDMzOkEh0L8/0DeKBLWGhgZM\nnjwZZWVlAIA+ffpg7969GDBgQOA38Tyx2Y4O8q/bTeyYZYnbRqicpddTmw1AY2NsUthttg7cdts0\nnDp1EACQkpKON97Yi5ycIihdyNdkIqIkWtLSgOHDI38/x3FYvHgxtmwhS1Usy2Lr1q2YN29e8Dfa\n7WTc7ejwNAViGGLDer1n7I1BgcRYk9SixOUCfvqpq4uxnbehle1AG9uBDpUNHOMGBx4sWGg5DVLc\nRqRyRqTxRmiYrv7lzz/fgEceWS5u//KXL2DePGWLpKlUQE5OZO5tb8aPD9/TsmrVKjz33HMAyEXy\nzTffeKLDOY5U+qqvJxeFnDUxwdefmxt+qcQkoqGBVBEW4Hlio04n+RM0nYBKRWZhwl+ge2R7extW\nrJiCs2ePAQDS07Pxr3+VoG/fgaivV9YrE02Wgj9FRcQsouHQoUMoLi4W1+MnTpyIb7/9FgZv1cTz\nJIhHiHSXY7MsS+5aubkkCpIKFADkHnj8uO8pdLs9NkwaP5I/hiGn0duGA90jeZ7HmjW34tNP/yU+\n9tRTn2DGjPlobSUBtUqh1ZJMRiV+0vx8oKAgus9obW3F1KlTceyYcP2mY8+ePRg2bJjvCzs6iA03\nN8srCMMwZLzNzVXGtRknklqUnD3rKZJm4504r65Hra4BDpW8hVAGDNLsaejvyEUOnw6WYVBTcw43\n3jgWFgspklZcfBUefHCr4kXSsrKiy2oAyMXn1dNMNjabDRdffDEOHyYBvAMGDMDB/fuRabcj6ruc\nyQTk5ZEv2ItobwdOnCCDucvlO1GXg9BUUXA8CfA8j4ceug7bt38IgIjIZ5/9HFOmXA6AVIlV6grX\n6cjPppSpjxsXWUaZP++//z6uv/56cfvnP/853njjDeLwr6sjf9GUb9brSd5ybm6vFicuF3DsGDmV\n3k7ScFZ4tVppR9R77z2Pdes8WX//9V+P4c471wAgY7hS1beVmuwJDB5MBE60nDp1ChdffDHMnU2D\nRo0ahR9++AFpaWlkElhTE50yU6vJF+/bV7kvHyNUa9asWdPdBxELmppILIkVDhzXlKPUWIEWbSvc\nbHhVquxqO+p1TahRN4FzAY//9ucoKzsOgMxI//a3z8AwymbbGI3RZTUImEyRXTBqtRozZ87EP//5\nT7hcLmRqNMhvbcX4QYPARBst7HQSpW+1khlogl8gSuB0kiVEq5X0tmltJd67cMWCy0U+w2bzzEDf\nfPMJvPPOs+Jr7rlnLebPv0V8fXu7Mt9BpSKCRKnJlloN9OunzD1+zJgxcLlc+PbbbwEQ70mftDRM\nzswk7qloK9O5XOSHa2sjF2Y0QV49FJ4nga1tbcR+W1qIHYY7HLjd5H1WK/lMrRY4ePA7/O53N4Ln\nyYdNn341Hn74ZXGi19qqjLAWAlujjSPxpl8/ZT4vOzsb48ePx4YNG8DzPBoaGlB6/Dh+NnkymKqq\n6COKOY6ImqYmogijnfHGkKQUJQ4HUFoKlKMePxlPo13TATDRWbWbdeNE81G0G9xoOHEWtjYL/vjH\nt1BUNFnRFt1KpKgJZGREvm7ap08f5GRnw11Whvljx6KlqQnp6enoG00QgDc2G5kC6XTKBCgkKDxP\nbLG+nkx4lIgb5jhy+o4fP4y1a28Va+TMnr0Uv/nNM+Jgbrcr0z6eYYggUXIwN5nIxE0pLrvsMuzb\ntw8nT57E9KFDkdvWhsL8fGQp6ZFzOIjIUal63TJkdTUpqdDUROwqWpHA8+R0Nja24NFHr0NzMymI\nV1AwFM8++xn0epJn63Yrt3STnq7sUMOyZOlGKedZUVERDAYDvvzySxT16YMpWVnQOp0YPGiQMjsA\nyAltaiInPy0tIT1/SSdKeB74qdSFH7lSVBvqwEcpRgSs1nacPfsT9BkpGHLZxZhwwWW44ao7YbUq\nlxYnDP5KTcRycqIYOzkOEzMzoW5tRWNDAwDgzJkzGD16NIzhJuYH2QfMZvKFk3SQLysjokTpYFOL\npQX//vc7yM8fDYulAbm5uXjqqa3Qaj1rO0rZZkaG8hOrzExlAg0FGIbB/KuvhvnwYYzr0wcMw+DU\nqVMYPWqUb3xJtPA8cRO43Qk7qCtNUxNw6JByHgsBjnPjs882wGDIBwC0t9fhhRe2oV+/QeJrnE5i\nx9FiMCgfGmQwyK9GLJdp06bBXlWFC9PSoFOrUV5ejj55ecjNzVV2Rx0dRO0lYKxJYh2NApypcuBb\n9wm06JQr3cpxHMrOHgPPkSvSmJqCMcsvxxlVteJBhEqssQtEPBZzHFBaCqalBQuvuUYsOe90OvHh\nhx/CpWSjFp4nNarr6pT7zAShulo60Dpa3G4XvvzyXdhsHdBqjZg27RasXfspTCbfZUQlbFMI4lea\nWDjH0s1m/GnVKug7FZTVasWGd96BPRbFNGprY1ONMcFobwdKSmLT1+aHHz5HTU0FGIbFiBGz8D//\n828UFfkGwSlhw5F2/g1FLK4LpqkJf7jtNvTv1098bNOmTaiNxfjY1kb6rihdwCtKkkqUNLa58HnL\nKVjVCkhrL6qqzsJq7VycZ4CBg0ZBpVKhwngelboaRfYRTdXWQEQ8uy0vF+vxG41GLF68WFwSqK6u\nxvbt2xU6Qi/OnSNekyTBbAYOHIhFoz0eO3duRX19lfjIZZctgck0uMuNI9qlIq1WWW+GN4oP6NXV\nQEMDsrOzsXTpUtFe6+vr8dFHH8WmKFVtLflLUpxOYPduZTwV/pSWHsTRoz+K22PHTsXIkZd2aQMS\nrShRqqaOFIoL69ZWoKwMWrUaNyxbJlZ8dTgceOedd9ARix/CYiHBQglE0ogSl5vHR5Wl6FAp+8O1\ntZlRV+uZEeXnFyIlheRE8jxQk1UJsyG6JPpoq7ZKodFEuAx0/jxZN/diyODBmD7dU6l2165dOH36\ndJRH6IfQajQJirVxHLB/f2wKpB0/vg8nTuwXt8ePn4FBg0aJqwqCU4DjohNE0XT+DYWQSaQYHR0k\nqr2TYUVFmDNnjrh9/Phx/GfHDgV36MX588oE7iQgR44om4or0NhYjW+//Vjc7tt3IC6+mFSTbm/3\n3Wc015AwrsYqLllRYe12k/GvUzynp6fj+uuvB9upppqbm/HBBx+Ai4VXw2z2pKkmAEkjSr6vrYWZ\nVfYKcrlcYqYNABhNqejbd5C4LUy+KvqeglUb+b6jrdoqRUQq3mIBDh4kosRvNJg1axb69/c0w/po\n0ya0K5XaIeB0xqbdaJyprIy+UZ0UdXWV2LXrU3G7f/8hmDTJU9WU58n4wvPRD+aZmbFLjDIYFJy5\nchwJ3PHzhEyfPh0XXHCBuP3NN9/g2PHjUJwA++/pNDeT+6TScRh2uxXbtr0nVoo2mVIxe/Z1YFmP\nsbW1eeqdRCOsY3ENeqOop6Syskve88DCQlx11VXi9pkzZ/DFtm3+71SGc+di0zMgApIi0LXBZsNO\n6xmoNDw4LrzxwdpmQWtdHaytrWBYFhqdJ6ijvPwE2i3En8iyLIqGjYNG43nezfOwa2xwau1oM7Sh\nj7kvmDDLIev1sanNlJ4epuud44A9ezwF0axWclCdQS4sw2DwoEHYf+AA3G43HA4HGhoacMHYsWAA\ntFgsqKqrQ3NrK1iWhT7S4Bir1VPIoAfS1ubpmmowkFMo91pvb29BU1MVLJZmMAwLrdZzDqxWCz79\n9A2x829qagauuupmH3sEPMvDPB95bYe0tNisl3t/fmamQh9WUyPZapkBMGzYMJSWlsLSOfU+deoU\nRowYIbrFFbNZh4O4JpMkWNvlIsHZHEeS47Ra+Rk3wWyY5zls2/YeGhqIV4tlVZg37yZkZnYN4nS5\nyEQt0lgWvT42cSQCWm101Yh9CNJquV+/frBYLKiuJtlJlZWVyMjMRH5+vvgaReyY44gdJ0D9qKQo\nnvZRzUnUcUQ8CKlmwW4ELocDh7/4Gnvf3YhzPx1HVjbJTWxqbMCA0SMxadkSFEy+AOcqS8X3DCgc\nhtxcT/CRi3XBytrg9jp9/eoLUVA/VPZxK13Ix5vCwjAjwysqiJfE3xx0OuID7TzIAwcPYtOmTQAA\nl9sNXX4+vjh4EPuPH0duZ45nfUMDLho5EiuXLMHS2bOhDTeXNNrazd0EzwNHj3b15tvtZOYp5Xl1\nOu34/vuN2LZtPUpL9yM7mwzQjY31KCq6CFdcsRJTpizGl1++g6qqMgCASqXGwoW3IydHelRkGHKP\njGTiYzAov5ToT0EBqYQZNRxH1hiCfFFzSwteeeUVseJraloacoqK8I9PPlHWZnU64IILkiIbR6oV\ngstFbFjKAyfHhouLl+Lgwe+wf79nGW3GjPkYNWpywOPQ6SIT1kKdsFgmlWRkkIrEinD6NILV0Xe7\n3Xj9jTdQ0elFVqvVWH7TTdh94gTWb9yonB0zDLFh7+qM3UCPX76ps1pFQQKQ86rTBS77f+DTL/C/\ncxah8tOv8JeHH0GruQWV5eWoLC9HS7MZax/6Hc5t/RIvLV6B8u8PAADS0rNEQcIDsKvssKqt4OB7\nA6/PqIXVIH8ZJz09ti5y2QjBTlL6VKji2hlkdeGFF2Ls2LE4UlWFF777DttOnsSvH3kE5pYWnC0v\nx9nycjSbzVj9u9/h1S+/ROHChXj3iy/CO/i2th65Tt/aKn3YOh0pBuo/Pnz77bu4666BKCn5J9as\n+TVaWsyoqDiLioqzMJub8dhjq7F376u4884C7N37ifi+GTMWBBQkAPkZI5lhxipLwR/FvDBmc0jl\nleG1Nn+kqgp/+vhjvLZ9u/I2a7ejS5RmD8Tlkg4vEG70/r+dXBv+r/8qwNat68X3DR8+HqNGTQp6\nLJGsDivV+TcUitmwwxEywF+lUuH6664j1V0BHKiowKTbb8erX32lrB3zfGwac4VJj/eUfFVXgVKX\ndLqU4MIW1P3Of72L3a9vwMebNmPixIlBP7ekpATzF16DQVdOx6Jfr4ZGowXHcESMMGTKK7XemWXN\nwuDyMVBxwYNEjMbo+34EQ3bPG7eb5K1WVIRewDUYgPR0/G3DBvxtwwZ8vHWrrPO4eNEiPHDjjVi1\nbJn8L5CXBwRrrJaAlJYGH1+EYNSODuCTT57F1q1PYMuWj2Sdw6uvXoC8vAm46qpfYvr0BUFfD5AB\n3WiULzBYltx04lGsNJJ+TJKcOCG7Ve0DTzyBt77+Gp98+mnsbFbR6XP3UFMTOtO5vZ3or48/jsyG\nJ05ciGuuuQ1qdfBZfEcHWSYJx1aUahYZiqFDFVqCrKryCdIO/tIq3PXoo9hbXR07O9ZogLFju7V2\nSY/2lNjdbpS5AkcNC1H+BgNw8N9fYPfrG/DDzl0hf0yANPb68fsfUP7FLhzd9g0cKic6NB2iIAlE\nh8qKujzp9UEBtVq5pmZShJV5c+4c8ZTIiSizWvHuhx/imfffxw8//ij7PH63axee2LAhPNXe0iL/\ntQlCqEMWsgFKSt7F1q1P4Pvvv5N9Dvfs2Y26uv1wuULPxjmO/IUT7BrLLAVvwr3JBCSMUp/vfvEF\n3vvuO+zesye2Niu32V8C45d4J4nJBOzfH6kN70NKiiakIAHCt+GUlPgVh1ZsP2GUQfj2yBHsr6uL\nrR07ncr1poiQHi1Kzne0w4XQN1Pe7cDWtU/hk81bUFhYKPvzCwsL8cnmLdi69il0uNvAI7RTyaly\noi2tEa1p0mJJuDHFUojKjhE1myUzbQJhdzpx/6uvYtOWruexoKAADMOAYRho/NYpCgsL8dHmzbj/\nqafgkDvK2O2xKPIRU+T4HB0OO9avvx8ff7wpbFvcuvVjvP76r+F0Bl+yEE6b3NMX6ywFbxQbzDs6\nZJ1wu8OB+596Kj42K9T/78HIOXyHw47nnovUhj/Bhg3/HdKGhYQF/87ZgdDpSMJAPFCpFAq7CMNe\nBDve8sknPuc8mA0DEdpxLCrlhUGPFiV1dnmK7sC/v8YFYy7AhAkTAr7mL3/5CxiGgdpvGjdx4kSM\nGTMGxz7/1ufxQBeKW+UGz/Oo61MBp6ZrlJbSVVulkDXwO50klREgM06XK+Qsb+P33+OCC6TPY//+\n/VFcXAxdgKtVOI8bv/5axsEh8sCIBOfrrzcGPIcCoWzx++83Bt2H8DPKGdDjOZgDCq7Fy7SNjV9/\nHT+bBbp9lhkP4mnDPB/a+aRSxT442xshqy5qrFbZnrVAdhzKhoEI7JiKkshpdMk7ebve2Ihf3Xtf\n0Nf893//NwCIlSC9WX3vfTj89taA7+XBg2M4uFk3XKwTdt4JTuVGTf5ZH+9KLKq2ShFy1svzRJAI\nhcra2z19yC0Wz7YQkNM55V6/bRtWrlol+ZG7d+/Grl27gl4cK++7D+s3Bh+MfEhCUbJx43rcd9/K\noK8JZourVq3Etm3ruzzO8+TndDjI5MvpDO1sUrL5o1wU9ZTIYP3GjVh5n/S1HxObjUXVzQQjljbs\ndhPbFWw4VCZlrGvqSKGYsA7DVgLZsRwbBsK0YypKIsfMhf5Rra0WlB05joULFwZ8zYUXXgiWZZGR\nkSFZjnrhwoWoPHIC1tY2cODgYtxwMi64VE441Q441U64VC64WTc4loNTRW72VqMFTdkkvzwWVVsD\nEVKU1Nf7BkB437mEqYn3Ha6jAy21tdh/6lTQ80jeHnhqvnDhQuw7dgwtcstE9rDlm1BYLC04fnx/\n1LZYWroPLS0tsNt9taSgI10uj4ckUIHceGUp+KPYgC7DNlosFuw/HvzaBxS22SSoSBwMpW1YGGIE\nG+7o8AiSUDYMkNi8WHue/VFMWMu0FTl2HCpfJSw77uZxt0eLEqeMeBJLsxlZOTld3IgCe/bswaFD\nh/DGG28E/GE1Gg0ysrPQ0tYMB+uCi3GDYzhwjHSUiZvxHFdTdjWsektMqrYGIuhFY7X6htd738GC\n0GixIDc7O+B5FJCaGQloNBrkZGejSW4Qaw8PGvTHbG5ETk5u1LaYmZmDhoYmOByhV90CPZee3jVF\nOdawrIIlEGTYRqPZjNwg176Aojbbs5MZQ6K0DQvOWP+f0/utgX7qWDWLDIViokSmrcix42A2DIRp\nx9087vZoUeJfJyQSZs6cidzcXCxfvjzkDysXjvX8qDzDo6HwLLTG+KhPtTqI+OE44OxZX6NTeGan\naIZ5EhSiCgclbNF/PJEaX0ym7hnMw0lRDomCtkFtVjmUGk+9fxKe73r/FppFxvt0M4yC1w61YUl6\ntChhZZR0T8nMQFNDA5wSkcf3338/bDYbfvrpJwCBf1in04nmxiYY0j0RgcFMgGM5cJ2fxTAAm2LH\nuYz49HTR64PYVHV11/VCl0uWEWanpKC+sVHyPHoTbCByOp1oaGxEls1Gsn7MZuKzDRT8EM+F4jiQ\nkZGNhob6qG2xqakBKSnS5aD93+Yf7KrVxjYdPRiKpmvKsI3sjAzUB7j2vZFls3J7NiSZzfrTHTbs\nH+zKsvENbPVGp1NwyVOmrcix41ACMCw77mYb7tGiRMv4ugQ4nofd7YbF5USzw44GhxUtOqD/mOH4\n+OOPu7z//fffBwDk5uaCYRi0tLTA7XZ3+YG3bNmC/hcMhy5NXm8LnnGL3hK9nhhxk7ERTfquPTqU\nJuDA39ZGKiP543LJusrSjUZcNGSI5HkEAIvFgrKyMrGLZWVlpdhzRGDLli2YUFSEdIOBxKt0dJDa\nDo2NpAV8dTWJdxHESrzWu2KIy0VWzFpbAbs9HUVFF0Vti0OHToDRKD24SN0HhMdUqvgHtnqjqCiR\nMV1NT0nBRSNHRm+zo0YhXW6EerwKZcQRt5vEeVgsgNMZfxtmGI8oEWKhumtoUNTDKNNWgtmxHBsG\nwrTj7nCjetGjR33GpYKZs8PFc3DxHDhIr4WNWz4fTz3/HJYsWeLz+I4dO3D06FEApL/AzTffDJvN\nhs8++8zndU89/yxG3zRP9nHxajfcLicMrMrn4qnIqICp3gSdO3a9BSSDXF2uwJ1MXS5yt5KRw77y\n0kux/plnupxHgOTLt3itVw4YMAAZGRlo9urpsP7ZZ7HyiisC70BobyscSzf3YAgX4dCFP6l4jyuu\nWIlnn10fsS0+88x6XHpp4MyHQAO6kDbZnZMgRcc6mR+2cskSrH+u67UPyLTZ557DSon3RntciYrL\n1dWG/Z2YsbZh/2vGW5SkpnbvsKC4sGYYWbElgexYjg0DYdpxN9twjy4z/1b5MZzkJGb/frjsDqyf\neRO++uyLoLn1mZmZsFgsPm6ykpISzLnqStyx8/+g0nZGBvIhlm/0NqTZ0tFHk9JlVppiT8XwxuFh\ndxOWy/DhEu75s2elG1oAxHvidMpKA7M7nRj4m9/g023bgp5HKUpKSjB/7lxUvPKKvCZRajUwb163\nljsOly1bQr/G6bTjrrsG4osvPo3IFufOnY8nn6yAWi2dcuCdPik05tNqSXPG7m5ie9FFCooilws4\ncCDky+wOBwYuWoRPP/88MpudNw8VW7bIs1mGIV+yB9msP4lgw96ZNwCxYY2GeEi609MHAMOGhdl9\nPRRHj8pKDY6rHUveROJHz716APTTyav6pNZpMefRX2L+omvETotSNDc3+1xAFRUVWHDtQlz62J0e\nQRIChmPBMgygc0lePBZdG2pSQgupSOniKWlqCixI3G4yBWFZWQOpTqPBM8uX49prgp9HfyoqKrB4\n4UI8s3w5tDKzfZCa2qMH90BoNDqsWPEMrrnm2rBtceHCxVi+/JmAg7mUlwQg+q67J/B6vcJeGrVa\nlsrSabV4ZvVqXLtwYfg2u2gRnlm9Wn6n1SS1WX9iacOAtB3zfPcEtvqj+OqcTIUTNztWqbp99tKj\nr6CilAywfOivwDEchi2cgXF3LMKU6cUoKSkJ+Z6SkhJMmV6McXcswuiFl4JlIMu3wTA8GBZwqwJn\ntVSnVsGikd9NWC4qlV+ap8NBGu0FQsi8YRjZi7TLpk7FA5dfjhnF8s/jjOJiPHD55Vg2dSrZZ3t7\n6Kyf7GxZx5NIyB0wL7lkGebPfwDFxTNkn8Pi4hmYP/8BzJ69LOB9T2owV6mIpyTpBnOAtF6WwbK5\nc/HAjTdixrRp8m122jQ8cOONWDZ3rvzj6Wwf35ORW/MjGhu+/PJlAQWqvw2zrKeHWXf79NXqGKTR\n5+TIvjjjYsfZ2TTQNRryjUaY+OALjC7WBZfKBTDAhNsWYcpDt2LO1VfiktmXYePGjXB53RydTic+\n/PBDzJh1KeZcfSWmPHQrJty2iDzJENthEHjphgHA6exgGcDJusQMHH94hkdZZplPPRMl8Cl/7F+1\nVQrv5zQa2RfHqrlzsW7JEsyfOxeXX3ppwPM4Z+ZMzO987Srvi4LnicvSZpMeabTa2LZQjhHh9I9Z\nsGAVli9fhyuvnI/LLrs84Dm89NI5uPLK+Vi+fB0WLFgFlYp4PaTGDf+1eJWKHJPgEOtOYuKpycqS\nLaZXLVuGdStXYv68ebh81qzANnvZZZg/bx7WrVwZXodgrVahtrHdSzhfQa4NX3LJLB8bFtJqpW7w\nUqJESBbo7rp0iqa0C+j1YS2VeNvx7GBjb6R2LFPox5IeHVMCAK9VHEK5u7GLUOAZHi7WBZ7p+vXc\nDidOfLYTR9/8DFWHTyIjOwu8m4O5qRm5Qwsx9tb5GLN4luSSjZgzLxFXwnIskGYVPSr97H26ZAh5\nk92Rg0HmQeF83aDk5ACDhI+rrSUdgINhNvvGklitYV35DpcLG/fsweNbt+J0TQ0y0tOhZlk0mc2Y\nMHQoVl56KZZMngxtsBuHMOp432UzM4ExY8hNpwexd6/sLuQiTqcD33+/Edu2rUdp6T5kZeXA6XSi\npaUZ2dkFuPLKe3H11XdDo+k6hbXbfWNIvNfiVSrS0kA49dnZ3RsgWFQUI51ZWSmdVRYAh9OJjV9/\njT+9+irOVFURm1WpiM2OGoWVS5ZgyaxZ8pdsBPr3B/r2DfPgE4/Tp4Fjx8ITsVI27Ha70NzchOzs\nAkyZsgzLl/9e0oaFdgiC3brdnsBahiErCYLdpqbGt0+TP/n5QEFBDD64pQU4dSqstzicTvxp/Xq8\n8/XXqGxsRFZmJtRqNRoaGyO347Q0Ek/SzfTo7BsAyNEaUdNugY31NL9zs27ihQigalVaDUYvvAyj\nF14GW2s7bOY21B+vAHgGWqMB2cP7h44hYQDGS5gwAHit08f15GRc0AY5xY3GBqTZ0pBlU+bmK7rI\nrYZMRf4AACAASURBVFbg/PnQb/AXIDqd/LacALRqNW4oLkZdUxOqmppgdTqxZOpUjB80COlyp8Yc\nR45XqyV/Oh35IvFqW6sgGRmk/EqwXh3+aDRazJx5A2bOvAHt7S2wWJrw3Xcfo7a2ChqNHkOGTJIc\nzAFPzQRhUPf+2fR6XyeC09m9oiRmMS19+wLNzeQkyECr0WDZ3LmoOHgQTS0tsDqdWLZsGcYMHy4/\n7dcfgwHIy4vsvQlGSgr5reRW1QekbfjEiX04cmQPNBo98vOHB7RhjYYIaKE3nX9NHW+bldvkNlbE\nLNs7PZ1MxPwyZoKh1WhwQb9+WH7RRbA5nZg4ZQomTZiArPT0yOyYZYEwOj7Hkh69fAMAGWoD0jUa\nsGABhodL5YSbDSxI/NGnmZBRmI/sIf2hNRKrc3YEGeC879deSzoMz4DV+97kHUxor0NFRgUcqjDu\nYkHQ6yFdtTUQ/qIkgjrgTrcbzRYL9BoNMo1GTBg8WL4gEeB5clOx2TzRbD1QlBiN0QXjmUzpyMsb\njMGDx0GjId+/oSG4F0Cj6epW1mq7nr7uHNBjshYvoFIBAweGddLb2trQ0dEBvUaDLJMJk8aOjVyQ\nMAxxTyZJgKvR6OthCxfBhocNmyjacGNjcBtmWbJftdozbEnFWyatKAGIIAjzpNd0egj1Gg0uGj0a\ng/v3j9yO+/dPmDG3x19J2RoDVGoGJmjhYJ3gJJZr5KA2en6QoKJEAgYMeJOty+NOGaLEzbpQluHb\nTThSDAaQ9QM5XR4DBRpoNGFdHI1tbWLlRr1Wi5RorlyhQZCiZRPjh7BOHm0n6OxszzJAqAEd8GhJ\nIYlKKni+O9fjFWv1Hoi0tLDWwmu9lnuysrLCX6rxJj+/27MVlMRgIDYUbaZLdna++P/29lbYbMHH\nJGEeolJ5lm3899+dsVHCKnPM0GiIuJaJw+HwqUWSH42nLiWF1AxIEHreyO9HVqcaT9FpoOUjX43S\nGj0eAmdHV4EBQDKOhAHAatyS91AnI0/atymQJqxSARprK4klkUOwu1QY+Zv1ra3i/3PS0iKvvmIy\neWJIEkSxh4vgIEpJia5zqfeA3tLSAJcrtB1xHBnX0tKk9ZzcTOxYEJd05AEDZAet1HhdI/n5+UFe\nGYKsLKBfv8jfn4AIcwKdLjqtpdXqkZrq+T0aG6tDvkco8peSEtiz1l3eEiHYNqZkZsoOWqmtqxMn\ngyaTCSnRLD0WFXV/ep4XPV6UZOv1YDpLkfVRp0AlI0VYCo2Xp8Rlc4KT0b6ZAcCwAK+TvlJcQTJw\n/KlOrUK7pl3Wa6UwaFxgysvk33mCiRKGIcYqQ5g0eFUTzI204I5OR2IDhAujh4oSwckUbSnslJQ0\n6PXE48RxHJqb60K+h+OCa0mhWG53EJfK6wwDDBkiS5jUeomSvEhnmFlZZNkmgQZzpRBEZGpqdL9d\nuB4/t5sMBcEEfXfZcNzq/OTnk6WUENQqIawNBlINLsHaefR4UaJhWZhAvBxqRoVsjR4qPvyBQqVV\ng9V4fhypJRy/cBKwDA8YAi/18AwPF+Sl/fIMj7OZZyNOE85qrwgvwjKUP18QJiEM1ttTkhtuqUOG\nIaNQXp7v3bSH9g/x7iCqUpGMl8hWBpiwBnTB9R1qbOmuJZy4DegsCwwdSlzRQcRCjdfyTdhub4Yh\nN47Bg3vkEqMchMuPYYjGi/RyzMnx3CzliBIh1j0YSS2sBfr2DRmn5G3DEQnrtDRgxIjoXLoxIimu\nqnTWYzFG3oAUgwrqCBYStCbvJZzAYoPhGTAqDrwxtAiQE+wqYFfbUJkWIo1XAoO1CUZrmM3+5Nyh\nBGESpPVwfaSeEqHghtSo10M9JYDvDVgQJpF8He8lnGCub7Vafunt7hjQ4x6zzDAkaHDYMMmgbafL\nhUavCsd54cwy9XoykBcUJKWHRMDbhgVhkpoa/lf2tuGGhsA2LHT9lTNhT3phLZCTA4weHTAHOmJh\nrVIRwTN8eMJ5SASSQpRkqn1vaunONGhTXdBoeTBheE00XnEljnaJuBIeUPEsGIMd0Msb4R0y40oE\nGkwNaNbLTw1TuR1Ib6kI377CubqFFA+/AmtujkOjV+6gLFEiRGUaDESlS70nSUQJQL5uVhYZdMOZ\nWPsO6F1nmUIwYG6u/JtFd4gSIXAy7qSlkUHdzwtX57UWbzAYkCbHZtVqMnsdPTr6KOYegL8NMwy5\nN4br+fP29rW0NMLl6jqJ0+mIDRsMXRv/SdFdsVHd4rzV64l4KCz0Edg8z6OuzrOkK2v5RhiIxoxJ\n+MrDiSmVwiRLowe87J0Fg0xbJhqMDVDrAN6ig5uDZCE1b7xFicvPU8LyDHiVG7w+vMwcJ+MK3r1P\ngvKMcpjqTNByIVxrPI8M81mwnAvqcJYJOE7eCOCNEH7u1cm3qbVVbJmtVasDpwIL9c6FogQM45mC\n+d+xdLpuL3McDYEGL6ORfDWLxVOTIRjeA3pTUy14ngPDsGAYouVSUz2eV7liQyiuFs9JfreuxKlU\nJAC2Xz/SA6q+3neGmZ8f3J8qqL6srKRdqpFCiI3yn7doteR+1t5O/kINISZTKvR6I2y2DvA8j6am\nOvTpUyDuw2TyCCCHQ57YEIafeK46aLXd6FRgGLIcmZtLiqzV16Pp7Fk4OpfqVSoVsoOJDK2WvDcn\nJ4Z5+cqSFKIkW2sA/GJENZwGqY5UtOpawaTbwHAA36ED52TBMdJ3BO9gV0eHHQzPQMUwYPROMDpX\nWCEbAk7WBYSZxuZmXSjLLMOwxmFBuwmntNdCZ28T7/myicYHKtwVtVrsOnQI7+7di34ZGZhaVARG\no/Hc9RjGk6MqCBGfgw+QotKDvSSAJ0pfSnSoVCTVMjWVCJOOjsAzv/T0bKjVarhcLrhcTrS21qN/\n/zyxnoM3ckUJz5P9xXNsSojwIJWKDMy5uXjrpZfwyY8/om96OgZfdBHxqAhNKYUlReGvhwziSiPE\nRnmFi/k8l5JCBIXdTsRJYEHBIDs7H+fPnwEANDRUYuDAAphMXS/9cIakeIuS7m5mCcAzicvIwH8O\nHMBru3ahX0YGpo8fD1VGBrFh4Uag15OD9i6H24NIClGSpdORWiF+LgmTIwV2lR12tR0MCzApdrAA\neA6AQw3eqQLvFm6WDHQ6Lc5u24vGM+dQe7IUd//4JDQZxF0bqctQyMBhw5yetulaUZtSi3yLtGtO\n7exAahupaa5Wy64V13lQyizMHqqowPGaGhyvqUH//Hz5dyCtNrAbPCHuYpEjDOjBKmIKtURMJjKW\ndDqexGK6RNexsFqrcODAV2hpqcaUKcMxatRyyc8L5+eMtyhJiAHdiz379+NUXR1O1dVhxZAhCVFW\nOxEJJEoEhFghwXnqcnns2GPDgFZrx759H6KlpRpqdRUuv3yq5OeFs7QY72XIRBuS9h86hIqmJlQ0\nNWHkzJlJZ8NJIUrULIsURo823urzOAMgw5aBelO9j3eEYQHoXWD8KrCqABz59+ew1JKYjvoT5zBg\nyigA0axj8nAx7qDl5gNRlXoeqfZUmJy+BQMYnkOm+SwYnnynsJZuAMWu6p+8euuMHjBA3psExR9I\npPVwTwlABjG5ZbqFEBupCY3JxKG29iQA4MSJ/Zg3r6soEW4IcnE64zvIJtKAzvM8Dh06JG5feOGF\n3Xg0iU04YpJhiNCVErt5eSmoqjoCADh58kDAzwhnSIp3sGuiCeuDBw+K/09GG06ahdIMVnr0U/Eq\npNvkdwLLHe2p/19/zHPTjSa4yo7IRECgNOHU1vPQOD0CLKZBrkGISJSkpQU/4CQQJUoNYsOHjxf/\nH2hADzfwL56zTK02sVZAysrK0No5/Ver1Rg9enQ3H1HiEgsbPn36sE9HW2/CFdbxDHZNJGENUFHS\nY8hQBb6ZGVx6GB3yrrI+I71FSYX4fz6K8sZyys0HgqQJV4rbOnsrUtp9q7ZqukGUuNxunPBq+jda\nTjMnYa0z1Gt6OEoN6CNGXCT+/8SJ/ZBq6B2uyIjngJ7Ig/nIkSOh64Hr7fFCqU4PhYXDodeTC8Ju\nt6Gs7HiX17hc4ZWPD9c7GA0qVWKFZTQ3N6OiwnNfoqIkgcnSBB8B0+zpUHOh7965ozw317pj5eL/\noxnIoxElANBgqkezvhks50KGuazL82F5SiLJvJHgbG0t7J13RJ1Gg8GheicIUZ7BYmu6NcxdOZTq\n9VJUNBZs552hpaURtbWVXV4TrijhuPj1D6Fu756LdyHAaFCpVBg2bJy4LeXxi0RgxMvjF/O+TWHi\nvfxYUFCArCxlOswnEkkjSnJ0wUUJCwYZ1syQdUtyR3mWIZRavnGy0cv68vQy6C2noXL7pgAxDKAK\n5z4eg6WbkQUFUIVK/0lPD50ilAReEkC55l16vREDB44Qt6UG9EgG53gO6IkEFSXhEYslnBMn9nd5\nPhJ7jJenhArr+JM0oiRTpwMb4utoO9OEg5HrtXxjqW1GR2Nr1O7ucHrgBILh2lCeUdYlw6i7Mm+8\nRcmoUE2kjEZ5d+kkESWAkgO67xKOP4k8y6QDes9GKVHpbcMnTyojSqiwTl4bThpRomIYpDKhb2om\nRwp0rsCLhPp0E9L6Z4vb9cfPKbAGz8OByMUAw7mht7ei2WRHZaZvQZbuCnI9JjfIVa2WrtoqRaKN\nAFGg1FfxjivxH9AjbeUejwFdyCpKFFpbW3HmzBlxO1kHdCWJV2xUpKIkHrFRiTYkUVHSw0hnQ4sS\nIU2YDdJNONcv2FUJ4484roQH9LZmMf33TG4b2ry6EoedDhzPzJtAVVsDQT0lXfAf0L2JVFzEw/Vt\nNCbWWvzhw4fF/+fl5UXeHbgXoVQ8xdChF4jLu21tZtTUeAI1Iw1xi0dslFJxNUrhcrlw5MgRcZuK\nkh5ApkqerCVpwoE72uaOHij+v7tFidZpgdorjoRneBzr2wx3Z8n87vCUcByHY5WeoMuAoiRQ1dZA\nJNq0JApisR5fXV2O1lZPX6RoREmsB/RE+ym9Z5jjx48P8kqKgHKxUQYMHDhS3PYW19EMR7H2+CmV\ngaQUJ06cgN1O2pwYjUYUFRV18xHFhgQ65dGTpZU/EhpcBhid0neOPl7BrnXHK6JKBxZwhtmYDwBY\ntxNae1uXxzt0LpzuQ+othJUOrFAuXUV9PTo6Lw61SoWivn27vihY1VYphIYbSYJarUwp7IyMbOTl\neezRO9g1mkE51gN6IouSZJ1hxoJYe/wS2YYTyUsC+Nrw2LFjQycX9FCSSpRka8OT9Wk26TRhn+Wb\nnxTylISbgcPzMNiawQTo5leV0Y6GVFv8et544b10M7xfP2j8xYTQizwc328SLd0IxHpAT+RZZiIP\n6FSUyCcWNkyFdWT0FhtOKlGSodNBFcZXCpQmnDvSMzPtaGxFe7056mNzse6wMnB09lawXPC7zqm+\nZthVYSzIxiueJFTVVikSbQRQgFhWduW46H7OWMeVJNLP6Xa7aXn5CFEuA0c6LTiRRQkV1t1DUokS\nFcMgFeHNuLWcBil+acLaFAMyBnqKgTWcqPB/WwTIz8BRuezQOttDvs6t4XAgw9wlTTggCl3F3vEk\nXdKB9frIRjLqKQmIlKckWlERywFdrw+za3WMKS0thdVK2jLodDqMGDEixDsoArEQ1rW152A2N0a9\nmhxp9plcEklYA1SU9FjSZQa7epPiSIHWL03YPwNHCeQEuzIcB71NnmeGZYF6vR1nTKEFDIDYe0pU\nqvCXbQSSUJTEIi24rOwYbDZr1KIi3J454ZDIg/mYMWOgTqLYpVijViuT2p2enoW+fT0JBCdPHlDE\nBmMlrtXqxOrbVFdXh5qaGnF73LhxQV7ds0k6UZKpDn9EZABk+qUJe5ebV8ZTAjhCBbvygN5uBsvL\nW5IRIsOPp7WhRS3j6lRAlPA87ytKvHvepKdHHq6eaHcyBVCqan5+fiHS0jIBkKWIM2eORj0Y83zs\nBvRE+yl7ywwzVsRqCUeJOVKsbDjRUtq9bXjIkCFITQ1eBLQnk3SiJEsT2YzbP024j7coOX5O6i1h\nEyrYVePqgNplk/15bKeLnGN47Ms0i2nCkvC8Ij1vqpqa0NrRQfbPshjerx95wmSK3NuhVidV5o2A\nUnUOGIaJyYAeq7gSuhafXMRqGVIJQRFLUZJI9CYbTjpREqoHTjAMLgMMnWnC/p4SqQ6t4eIKsnzD\ncC7obC1hfR7rpeQtGid+SmsNsnNl/PXeXpKh+fnQC+4AuVVbpdDrE2taoiCxKjdPB3T59KYBPRbE\nwoZPnjygiP3FSlhTb1/3kXSiJF2rhRqRR9mld6YJ5wwvEG+UNrMFltqmqI8tYAYOz8NgMwdM/5WC\nZbvex8tM7ajRBfC0xCqehGGAzMzoREUSxpMIKBdX4uspUSRNPQaiJNHW4puamlDpFZid7AN6LFDO\nU+Kx4fLy42hr64j6M2MVG0VFSfeRdKKEldkDJ+D7wSDDmgGtQY/MQZ5S1Mos4fBwoOudQOuwdOn+\nG4pAoRsHM82wsRLLNDHoeTOqoAD/v703D3KrvPO9P+foHEktqffFe7uxDXglBhKCTVhMwEDYfZNL\nkUmYCanKO68rE0JuKjWT3Kmbl3on994kVRNCyjdTNZNU3UnI8M4bA4bcyQUSwrAYQsxivAHGS7tt\nd7vdi7oltaSz3T/U2rq1HElH3cet51PVZUstnaXP7zzn+/y2h+bm2p9CbhsBHKQes8yjR/djOBCK\nq8f6IW5b6j13MF+xYgXt7e3zeDQXJk71NVy0aAWtrR1Aqiv08ePvlflGeeqRG+VUJ1unSCQSHD58\nOPNaiJILkDa5toec1/QSSoboXpfNFj9/xKlk13xxIBtJvMlIxdspJkqScpEy4Xp4Si66KJVLUitu\nGgEcxu93plV1X99avN5UGUQ8HuPs2Q9r3qZDaUZ5iNDNwsPZ3KisuD5+/J0Sn7aP0yEcp+5Zpzh0\n6BD69Em2tLTQ19c3vwdUZ1z0p3eONqX2h1wo2UzPJX2Z105V4OSVBVcRtklT6qYZ9ic4HpzhGnWo\n8uZgrijZsMGZafEC9pRIkjOnpygKq1dvyrw+dmz2EvDV4PQs022XUogSZ6hHvxK32rCbhfVll12G\n5CZXZB1YkKKks4I1cIohAb0r12deDzvkKcmtwPElwmW7thajnJI/3DLBRLpM2KE1b4bDYUYns2vx\nrF29uuZt4vG4KwmhDtSjesGpWWYjDehiIb7qqYcNu1WUuFlYN4INL0hRUksFTi6LV12c+f/I+6cc\nqcBJixJFj+PVqk/0KidK8sqEDcPxypu+JUsIOnH3LuDKmzSNMqBLkrsicZqmcfDgwcxr4Smpnno0\nAjx5cj+GUftkyencKDeLkkaw4QUpSppVtaYKHEi1L+6+aCXydL/sxGSMyTPnaz42Q9IxDd1219ZC\nFKq8KcRkuky4Hvkkq1Y5sk3XjQB1oB4D+rFjbztTpu5g9UJTk7ti8e+//z7JZCqBPBgMstoJz16D\n4lSexcqVl+KbnjQmk3FOn/6g5m065AjO4CZvn2VZQpQsBGRJolWq7UlgmqB4vXT2Ztd2cardvKyP\nIlnVL9pQyeBwIhhlSLHZhr4Ms5JcncBNU+s64VR3yDVrNmXiyRMT5xkdPVPzNp1cP8Rt+nLmUu+y\nmxTTBYZTya4ej6cuuVFOiRKnujA7xenTpxkdTbWjkGWZjRs3zvMR1Z8Fe5e2yrU97NID9aI1WY/A\n+fdrLwtWLA3TmqppG5WOre90TBD31P7kOXz2bOb/64QosY1TJYZNTUGWL88uJue2EI7bRMk772Tz\nbhphhllvnLq+a9bk5ka5y4bd5CWBfGF9ySWX0OS2m6wOLFhR0q7W7ikBWHxx1uU7drC2mamEiWom\nSMq1CYRKRUlSMnh3ccL+asKFUFUO9Wc9RY55ShrgJgPnTnPVKvfmlbh5QBeipHacur75NuyuhG23\nDUeNaMMLVpR0OiZKsp6SkSOnUHRv1dv0mnHAQqvRa1GxF9o0ORfSOdFW5Z0rSYzKMoMjI5m3HPGU\nyHLKX9oAODGgWxb09bm3pFIM6Asbp0TJypVZGz5+3JncKKeSXYWwnn8WrijxOR++GTx6jEC4Fcmq\n/M+mmsnM6r9JZQ5FiWnCtIfkUHeSCV8V3bKamzmc06p7WU8PraFQ5duZSQNU3qRxYrDT9fxZppua\nT3m97qrsHhwc5Ny5c5nXmzZtKvFpgR2c6ta7fHk2v2dycpTz52sPi5umM7lRQljPPwtWlIRUFS/V\nZSxZVlZ1d63sxaOmtqNNxZkcOEcw2lri27ORLQPFyraR12UTo8pQimSz8iZDzp1qyhZvLUmUXk14\nJj4fBIMcOnYs85ZIcq0cJ0SJpsFFF2VnmUNDx4lEqq/iSqPrtQ/obh7MV69evaCXep8rnMiN0nXw\negMsW7Y2855bQjgeT2q4cwuxWIwPP8x2bhai5AJHliRaqqzAyW29rXhVuvqyKwYPfngMb6IJb8Lu\ntq1M2CaXavNKPFWEbnKZ9Bkc7ra5zo4sQ1sbSBKHjh/PvC3ySSpHUWqPVGkatLZ209m5LPOeW5qo\nCbd3Y1DrdU575XLFtVuSXd22btOBAwcwp8fvzs5Oli5dOs9HNDcsWFEC0OqpTtbPnDUuzgnhDB09\nhgQEo63IZnlPjNdMIDFbgCSrzCupJp9kJsfbkwwFbfjsW1tT0wfgcI4oEZU31eHUgO7GEI7b9KUQ\nJfWh1uucFg5uTNh2u7Be6O3l0yxoUdKhVHcHzXyO5+WVfPgRALIlE5psI9WQvjAeS8djFb5T5kyU\nGIX38+7iBIlSx9DUlDcCCU9J7dQ66KUH3YsuEgN6OYQoqQ9O2bAQ1uVp1JL2BS1Kql0DZ5anJKcs\neOhoNrdC1b00xQonfEqZsE1h5tNTApBQzOJlwh5PyksyzUQkwqmhocxrR0SJLLsrgDsH1DLo5TY5\nW7XKXRU4bruU8XicI0eOZF43wnohc4Vzwjp7Tc6dO8nk5GhtG6b23Ci3iZJGW/MmzcIWJVVW4JTy\nlAx9dAIzJ+mkaaq5YJlwoTySXKotC66s8sYqeQxDhcqEJSmVR5KzoyMnT2b+39PRQWdbWwUHUQSf\nz10B3DmglgE9VzTkzjIHBg6TTBYXv3appd2822Lxhw4dwpi+R9va2ujt7S3zDYFdasmNMs1svl5L\nSyddXSsyv5vv3CinVvN2CtM02b9/f+a18JQsEEKqio/K6hRzK2/SdPYuxzNd76gnEoycOp35nQSE\nJtvyyoQVS0O2SvsSddlEr7ACp5bKm2Ic6k4y4c3J7A0GZ01761J546YRYI6opYV17mDb09NHMJjy\nZBmGTn//wSLfsk8t64e4OXTTCEu9zzXVXu+Z9uWmvBKfL5M+5wpOnDjB5PSK7Kqqsm7dunk+orlj\nQYsSgBapMm9Joee4R1HoWd2XeZ0bwgHwmEqmTFiyUl1b7VBpBU7loZvyPUlM2eLtpdNlwqoKBUon\n65JP0mBJrlDbbCx3sJUkKc/9Pd8Dutv0pcgnqS/VipKZ9pVfgTO/eSVuFtbr1q3D2yBNJqEBREmb\np7IR0yjyHJ9ZgTOTdJmwzyodtsml0rySWsuBizHhMzjSrWXKf2ciRIlzODXLdFOyq5sHdCFKnMcp\nUeImT4kQ1u5hwYuSjgrbzRd7ji9ak012HfxwtiiRgO6wjKrbD8kkPZV1V3UqybUQxxZLDIcKf74u\n5cBuGwXmiGoGdNMs7fqe73i8my5lIy71PtfUQ5QMDBwhkahtoVKoPjdKCGv3sOBFSbtae/gGYNHF\ns8uCc1HNBEEjRseEH6lEmXAulSa71k2UeBRQVd5uGych5wulWDzO8TPZhQgd8ZRIkrvKNeaQaga/\nQi7p3AH9xIl3M4mdtVDNgO73uysWPzAwwNjYGJBa6n3Dhg3zfEQLD1WtPDeqUM5Sd3cvoVA7AKZp\n0N9/oOZjs6zqxLWbhDUIUbKg6fY74ynJLQsePn4SI+cOkyyTkD4OloUv6aE5ai/+V2n4puLKGztP\nGEmaXoMGEh6Dd9vCeWXC7588mVkwq72lhUWdnRUdc0F8vioU1sKgmlMvNMguX74WVU0Ju3g8ytmz\nR2s+ttzqCLu4bTDP7e1w6aWXNsRS73ONJFUurgsJ3nrlRlWaV6Io7lq3aWJiguM53mkhShYYAUXB\njz2RUKjyJk3H8qWo/tRDwNA0RvqzC9QFjXBmsT2AlqgXr1Z++mjIFnqBbq+FkCTnK28A8PlBzm54\nyB/nZCCWeT2z8saRSoYGzSeBlCCp9DlZSJQoikpv78bM6/kK4bjtmd/IM8y5pBpRUgg35JUEAu4q\nac8tBV6yZAnd3d3zeDRzz4IXJWC/AqfUc1yWZXpWZUMXgx+kQjheYwqfkR8LlSzoDPuRrfKWbtdb\nUpfQjaqCOtsPe6h1gkkldWeLTq7Os9AGdDchRMnc4ISwBnfkRrltOGp0G24IUdJus918ued4Xl7J\n0WPIlkHICBf8rGLItE2Wz5uwLUoqjduXO5kSbTgNyeKt9nEMLFF5UwecGtDdUBYsREljUul1t2PD\nJ07sdyQ3StMqy40SNuwuhCjJodxzfGa7+ZA+jmQV/1JwSiUQLx2stNurxNkeJek8kuKenAlV4/2W\nSVF5UwcqGQRLJZ/mzzLfzuT+1EIlya5ui8VHo1GOHs3m1jTigD5X+P2VjUnFRMny5WvxelOTlEQi\nxpkzH9R8bJZVWW6U24ajRl3zJk1DiJIOr72ZeTlDzu1Vcu7DD201SWuf9KEYxf/Mdj0ljvYo8Xpt\nlUwcUcc4OpDNnXGs8kZ4SmzHsEt5Lvr6st1Kw+FhRkfP1nxsuWvslMNt7eXfe++9jDDr6upiyZIl\n83xEC5dKGgGWsimPR2Hlyk2Z13MdwpFldw1HhmFw4EC2CkmIkgVKl801cMqGb3JEyfDJAXQbli+b\nUskyYU0xMW00W6vIU1IqY9fjsb14xZnjZzLu1FAgwPJFiyo4iCJ4vQ1beZPG47FfEV3KxJqazdBM\nKAAAIABJREFUQixZcnHm9fHjcxvCcbPbe/PmzaK9fJ2xe/3LVcPMZxiyUo9Pvfnwww+ZmkrlKPr9\nfi655JJ5PqK5x0WXo340KQpNZSpwSj3H07QtXYxv+k40dIPBE2dKf2GaVJlwYT+3IVmpFu8lcK7y\nJlv+a4dTH5zK/N+xyhu3+UrnCbsDernBdT6TXd12KRs9Fj/XLAQbdrOw3rhxI0q1i2VdwDSEKAFo\nlUuPoHZc1rIss3h1dsXRMx/1295/S9RXtEy4XF5JxUreKLK9Cptk9H+YFSW9F68o8ckKcJOvdB5x\napaZP6DP7fohbh7QhSipP3ZFaaWiZC5zo4Swdh8NI0rKrYFjq4LWTLBi1bLM69MViJJSZcLl8koc\nKQeuIisx11PSsmExEaXK1a5yEaIEsPdAt9PMLH9Rs7mbZbotNaiRl3qfL+z29yhnTytXbsp4YScn\nRxgZOV36CzawmxslRIn7aBhR0q6UHkHLGXC6a+vSHE/J6aP2RQkULxMuK0pqLQeW5FSTtAqjLwNH\ns0muyy5ZwVttY7byX0ritlFgnrDzZ7AjDnJnmYODx4hGC5eoV4Kul78fmprcFYs/fvw4kUgESC31\nvnbt2nk+ooWPnSRRO5Uwfn+QZcsuzbyeyxCO8Pa5DxcNK/Wl01eDp8SCkJ7q2rp8TY4oqcBTkiY4\npRJI5McJy62BU7OnxO/L69pqB0M3OP1Rdsay4uLlhL0aR1omKzyYGbhpej2PqGr5fGM7g2pbWw8d\nHUszr0+ceLfEp+1Tbt9u05a5g/n69esbaqn3+aScHdgNo8xHXonXW/kaPvVkZGSE06ezY+5ll102\nj0czfzSMKClXgVNKzfvMGF4zlRG9NEeUnDs1iJZIVnws7RP+vDJhzVO6AqeicmDLgtzeKdWsngWc\nPXEWXUuFa7x+L93LU62OPwpGOe8tXwpdEJulyI1CuVma3WS9+Vg/xM2ipFFnmPNBPWx4rsqC3ewl\nWblyJW1tbfN4NPNHw4gSn8dDgMJ1mKUqb2TLIGhMZF6393TSFEpZs2WanD0+UPiLJZhZJlyqAqem\nypsSXVvLcSonyXX5muV40mJCsni7fdx207c83PYkm2fszDLtMB+zTDcP6EKUzB1OiZJ62LAQ1hcm\nLnJe1Z9WuYlYgYZnRUM3FoT0sbyurZIksWxNL0ffOcKS5ctIjk0hJyT06bViTI+J6S3vr5QAfxIi\nTSkXzaQ3TpMx24tQcejG0kHRU3vwKSCV9+RYlolsmJmVhZvwEh0dp727lbHhMCsuya+8iXsM3m0d\n5+Nj7UX7rxREhG7yKDWgF1rqvRi5A/qZMx/N+p4sO7MycS7zOaDHSRIhgYEJWMjIHDzxfub3jTyg\nzzX1ECWR5DjnjDP4AkES/ihIoJgKiqEiV9iWQCnRFqk5BIMVbc05dAyiJNAxCOEngI93TxxCkiUs\n02poG24oUdLm8XO2gAApJkqazAiqmfNQ18BjWHzpb/5vdFVHCag0NQdI+GMYnmz8R9IlJFPGlCRi\ngSTJQLE700JTTXQZzksaTfrsu0eSKnygKCb4rFQOiVQ8JqUmTXyahWRamBJYkgXTXpkpM0nX5qV8\n6UdfRoskWNTThTYVRVF9SNOhoMGmOKcSU/TGKpgyC1GSR6kB3W4s3jRh1aotXH31F2ltXYLPFyQa\n1ZHl/Fs7LUw8nlQ0r5xNpfdf6Bng9c5te/k4SQYYZZQIYWLEyRfa8Xic1nvWsPm2PmJnwwQ/vpgJ\nYrTgMnfOAkRRUvaQLDL3sSOsdVknvtTgzke+jdrlx9ca4NjiQwSDbST8MUw5NY5JloRiKMimghcP\nHk95gTLWVDx6PRmcuwegicUkU8RIEEdDw8CaDtkvpo1WApxfB5u/fRtTQ5MsuXUdQ4TpoaWyid8C\noKFESYfaBAX0QSFR4jE1AkYqqVNOSFiSRtKnoQHB3mai4VSmv6HNfvBbsoU1fSMFEjKhaICkajHZ\nEkXKexpIBOIykwGTYp3oq+pXJpGquJl5XJZJMA4e3cSQLUwoGsCLx1IeJTXkI7Sig7AcRzISBDQP\nPtmP7PNxoDVMR8JLyLBpRm7zl84z6US7QgN3qRlmuqJB01LfDQSWsGTJOjQtgWmahMPDtLfnt1g3\nzdSPrqceIB5P6XSjtKemkPiYq8t4nklOcI5BxjMDeCGGhoYA8PgUlm7qY7h1ipc4RDsh+uhmKe3I\njROpnnMCgcKipFwVV1SNMNIyzGRoDFMyWXL5GiYnRgGIxyMEg/k5FZZkoSkaoJEAFF3Fa6ioHrlo\nY8di+5ekuUlvS6IzTpQJpqY9e4UxDINzw8PIHpng0lYCazv5Ix8SwMdKuumlC2+DPK4b6k7t9BYe\nTWcZrmXRrI9B0oKkQcIfI+nLPiU8atY4DBtTAVMxUCyTzpEQvhmdXT2mRFNCKipKKscqOA32Jkya\noyaYBoZcbgpukZjKhrl8Tb7pdy2iss4oEWJTYXRD4632cftlwsJTkkep9UOKiRLDgKmp1E/a9CRJ\nor19ceYzY2Ol18BJC470dooN3MWOod6iJE6SP3KUvbzPWcZKChKAwcGhzP8XLc75OxDhbY7z7xxm\njGjdjrfRKebxKzY06rLOya5jHFt2hHDzCKaUMkC/vznzmampSNn96opGzBcjIk2hG4VtpJhtq2p9\n120ysRhmghMMM0a0pCABOH/+POZ0tYXX66W9vR2AGAkOM8DvOcAAI/U7YBfRUKKky194DZqZhhs0\nJvBO6ehqHM03ewqgKFmJbRiG7Q6EpmLQlPDQNhzAytmpT5PwGBQcfCu+cSSZvIYklkkoaqDoJmaZ\ndvZpkgk9c3ySLOHzz54ux2SdcWOCETPM+802yoSrrAJa6Ngd0C0rNRudmipcKZbrGRkftx8p13WI\nxQoLkGKipJ5JrqcY4Q8cYohx299Je0oAFhVYn2mSKV7lCIcZKPtwEFROMXsoZD/jTWN8uOwgE6HR\nWb/z+0OZ/yfi5UVJGsNjEPFGiBsaMxdtL1ZVWc/w4xRJ+jnPKJGygjpNrrDuWbRoludHQ+dtjvNH\njhIv5O5fQDSUKFFlmeCMChzLyhclih4jEJsk3jSVyrMogCTL2TCMZc9bkv2yBYpB50gIKfM1iaak\nhGTWKN1nlOpIhkkoamJOJwTaJRGLZ/7v8/uKKiMDi3EpxgHlLMPqVOmNitBNQex4SiwL4nFIJIrn\nmbS15XpKKkvfS28/Hs/f/lyKEguL9+jnHY6jUVnn4KHB7PkuzvGUzNz+UQbZywcVb19QGrvevrOt\npzm16CN0T2HDamrKipJ4IoY1U2GUIe6NE5WnMM2sEZtm4XumXvOjCWKcYoREhcIhV1gXs2GAIcb5\ndw4xQazqY3Q7DSVKAFrk/BBCnpfE0GmbGiXhL92HQ0JCUbPeEr0SUZLer2LQPhbICBPJkmiN5V+O\nirwkkpTX0EQyTIIx+96RXPJCN4HyJcUROcnLwVMkSg32InRTkEIP+NwW2ZaVH6opRn74ZrCq9UM0\nLV/4FEq2raHKvCgWFu9ykhOcq/i7pmly7lz2e4sXl17JeowIrwlh4ijFmpDlipIzbac43146rKiq\nfjye6Q1ZFvF45SE33aMXFCaz91XxpssSJsYgYdvekVxyhXUhb18uCTRe4wPCC1SYNJwoaVPyZX3G\nYC3ojA6T9NlrDObJuQsLJbvaIS1M0qESjyXRFq3ykihK1hlimQSnTMyyuSOFieflk9gTE2FPgheb\n+4vfkEKUFKTQ0unpwTztwSjXphugpaUbeXo9Al1PEo3Odo/bIS1MoPDaO01NzsfiDzHAKc5X9d2R\nkdHMpEBRVTo6Ost+Z4IYb3BUhHIcQpJmi+tc2xlsOcNI29DsLxbA7w9m/h+vIISTi+ExiMlxrGlh\nUmwpMCeZZIqhKgUJFgzmeUpKixJIhXNe50OixMt+9kKj4URJp1pYlLRGxtH89pWnJ8dTYujViRKY\nFiajKbdlwmPRHvHg1VKjvu3B3+NJlQBPT2tDMasqD0maRGx2kqsdznqjHPIOF/6lCN8URJZn/2nS\noiRdXWNvOx5aW3syrysN4czcf+4x5OJ06GaIcY5h74FV8PtD2fPs6elBtrmcwhgR3udM1fsV5DPT\nhtN2G/FGON9R2kOSiz83hFOlKIGUxyQ+7Q2bKaztlMRXgoZRvSABopEIsei0V0iS6OkpL0oAkmi8\nzYmq9+tWGlCUzA7feDQdU53EqqAeXMmR2tWEb/KQTXxRlaRiISOxKKxgW1Pk1rZZFt5E6Zb15bAs\nSExl1bffRvgmTcDwcEqdIFnINS48JUUpJEoMo3jvh2JUUoFTjkQidW/MFCVOaksNnf1Uvn5ULrkJ\ngovLuL1ncowhxqj+wSfIMlOsahoYmJzuquyhmVuBE7dRgVOKhBpHM8xZnhKnQzdDhGvyug0PZSdy\nHR0deL32D3CMSE2i3o00nCjpmFGBY5oQSo5hegxMScaUZFu3UDp8E49Ocf7UEMMnh5iarDLGJ1kE\nYyoJKdVQx2tIdE567HlKFCVVbGMBpoFXqyypNZepiSkGPxpk9OxoylsiSXj95Rc281gSrZpKwPCg\nyQbvqTNm6YoiKm9KUGhAL5XUWox0BY6mxTl5cj/nzh0jFqtu1WDLSh3DTL3tpKfkIAOzGqHZJRqO\nMHhsgI/eex8jnlJOi0okCBbCwuIdTogwjgMUsuGhttMkvZWFF9LJrsnYFMMnTzJ66jTxyerFSVyJ\nY+hW3r3k5FAUJlZ1CGUqHGXk2CBH3zqSseFKhTXAEc4QWUBhnIZ7UqQrcCLEsSzwTCXRvdmEKgsp\nVVZrmUX9JlpS4+0X/sjLv3qeUx+epL2zA0mSGB0ZoW/dKq7+jzdw+c1XoXjt/3lNxSA0EUDzGHgN\naInLJJMWUW+JAVPxZFf/tSwCcSoO22gJjXd/+zZ7f/kaJw+eoKOzA9M0GRsZY9maZUS+PMnHb/14\n0XPxmTJBXclTt2f8US5JTtEsTU+r65GIsIDIHdBNMyUG7OSR5KJpCY4de4O33/4lIyOnaWvr4NVX\nH2NkZJhVqy7n+ut3ctVV/wFFsb96rq6nclpyccpTEiXBqQr7LmiJJK/tfpHnd+3m6NtH6OzuIqkl\nGR8dp3VZJ6c61nD55s2oFcw0I8Q5wygr6Kr0FAQ5pHOj0l6JqK4x1lMklFsEPZnkyO9e5vVf/oLh\nj/pp6+zgT7LM2MgIS9dfwqb7b2ftLdfhqeD6GrJBUjexrOwkzylPiYXFSIWeNj2h8d7uvfxp1/Oc\nevsoHd2dGLrB2Mgorcs6WXx/G9o9WkU2bGJylEE201fhGbiThvOUALTJqZHVNKFJm91jw0LClDyY\nBR6kb/72Nf72toc4+tx+/tt/+R4T4QlO9w8wcPIU4bEw/+/fPMLRf3uP/7L9Yf70b3srOi6vLpP0\npESFR5JYHPGgFCsTTvcMzxy0hUevbMa375k3+X8+9bd89PRRvvfXf8fE+AQDJwc4c+oME+EJvv/d\n73Pk6SP89bV/zR+f/WPedyWgWVdoniFI0pxUx7IvROimJLmaTdftrxeS5vXXn+A//aeV9Pc/zWOP\nfZ/JyQnOnh3g1KnjhMNjPPLIwxw48E984xu9vP76ExVtOzfR1u93rgvmSYapxKP38hPP8ZWVd7Pv\nZ7/ju9/4z4THw/QfP8ngwFkmwxP8j//+Y07seYev9N7Fy088V9GxnKCyh6dgNrmNAC0Lhv3np1sR\n2OO93z7Hjz5zN0PP/55HH/mvTE5McPbUAKdP9hMeG+f7f/23nH/mVX56w+c59JsXKzq2hCeRJ/Kd\nEiVREhVVcb3zxMt8f+X/xcDP9vHfvvFdJsbDDBzv5+yp0xkbnnilvyobPsNo4bD5BYhkVVM7eIHz\n6vkzHEieQZsyUGOnMx0FCyFhIU17TV58/Le89M/P8czTe7jyyitL7mPfvn3cec9dXPvFm7nhC9tt\nH5tqWrSZ2TVKoqrJQMsMY5MA1ZvXI02Naahx+67wP/z8RV75p5d45qlnbJ7Lndz44I18+i8+jWpJ\nhHQFj1Xc+6GaMjdFLkKRFFixAqpwSzYSBw6kBMDEBAwO2g/dPPfcj3nhhR+yZ8+Ttq7jXXfdy003\nfZPt279ma/uSBMuXp7w57e2werW94yqFgckL7Lc9iD774yd49oe/Ys+TT9s7x3vv5o5v3s8dX7vP\n9jFdyzraCJb/oKAoJ0/C8DAkkhav+t9DU+yNR68//gR/+sWvePZpe9f3jnvu5mN/cS8f//Mdto+t\n3QwSCsnIcmoocsJxO8Co7dDNqz9+ljd++BueedLes6MaG17PclZTWQjTjTRc+AagQ/VDEryROIan\ntJq3kLAkD2/99hVe+ufneP21vfT29pbdx5VXXsnrr+7l6mu2EOps5uO3bbF3cJoKHi1z0wQ1mfYp\nmbGmnOP0KMyMLfni9iPj+555k1f+6SVef/X1Cs7lda6+5mo6O1r59K1by6YEa7LJkDzJMqtdVN7Y\nIBBIiZJo1L4gef31J3jhhR+yd+8rtq/j3r2vsGXLp2hpWcTVV5cf8Cwr1fE1EHDuMp4jbFuQvPzE\nczz7w1+x95XX7J/jK6+x5VNbaV3UzrX32ZsQDDAqREmNpO1jxIrYFiTv/fY5/vSLX/HGa/av7xuv\nvsYnr9lKoKud9bdvs7WfKdMghOxYe3kDkxj22ke888TLvPHD3/D6K/afHdXa8EIQJQ0ZvkmvgSOZ\n9oxKS2r8+vv/zLN7npllVIqiIElS5qezM9snobe3l2ee2sOT//1x9KS9Qdia7i2Se+N0xTz4jOk3\nZDmvSVoayWb3Qy2h8eQjv+bZp5/NO5fBwUG8Xm/eudx0000zzuUZfvl3/2L7XMbk6VmECN+UJZ1X\nYrfiRtMSPP74QzzzzFMV2+SePU/y+OMPoev2dpbuW+JUkuu4zXVotESSnz309zzz1J6KbXXPk0/z\ns4f+Hi1pLxZm95gExUnbx7hk72+pJ5P87x/+Pb/Zs6diG372qad58e92Ydi8vpqsY1nOJbnGSdqq\nKtITGv/roZ/z7FOznx2l7LgaG54ss+jfhUJDipIOny+1aqhkU+m+8AYbN27iiiuumPW7b33rWxw/\nfhzLsnjkkUcYHR3NGyCvvPJKNm7YwDsvvGlrX6bHxMLKEyUyEksmFWSkgneVZZnY7VD/7m/fLngu\n4XCYYDDIP/zDP2BZFtdddx2/+93v+OlPf5p3Lhs2bGDv8/bOJazkLEcrKEl6lilJ9voovPnmbjZu\n3Fi1TW7YsIE339xddPvpSnOvNyuQnfKU2O1E+druFwueY0W2utte/sEEsZpK6QXZ3KiEP5ZqnSSX\n9koc/N2LbKrJhjdy5LmXSx5TeuUNS9ExTcuxocju+jPv7d5b9D4tZ8eV2rCFtSC6vDakKFFkmYCp\nYqlJZDlVwCLl/sz4/Ov/+ju+/tXCMfjvfe979PX15b13ySWX5L1+6KsPsff/+0Pee5KV+pFNCY8p\noZgSiiEhW2DpntnhGUOiSw/MPjhA1cCSp6uGck+kwIf3/vI1vv7Vh2a9f+mllzI2NsZXvvIVAF56\n6SUAfv7zn+d97mtffYjnnnipwF9iNmE1iVVi7RxBlkAglVCqKKnBPRiEUCj1vt+f0nUeT/ZP+dJL\nu3jooZ0Ft2XLJh/ayUsv7QJSDw9FSQmQmfv2+fIFihOM2xw4n9+1m6/t/KtZ79u21Z1/xXO7iguv\nXAzMBVVWOR94PCl7ifujKErKZr3ebBv6mULlnf9/N1//6uzrC/Zs+OGv/hUHfvWbzOv0sJeuAUjv\nL71Pw3RufmR3bZs/7Xqer+8s/OywY8eV2DDYF/xupiFzSgBaTIVIunx2phBJv7YgNhnlxKFj3HXX\nXUW35ff7SUz7uHt7e9m1a1fe7++66y6++MAXGTk5TCBUfrr56lNv0P/RB/lvemSQPcQUA31GYu6K\n5T187JaPld6oBfFonJMHTpQ8lzS7d+/OHPvMc3ngz79IdDJGsLm0P9+QTDSvgkPPsgWNqs72jqTF\nwExn0+RkmOPH367ZJr/whQd47bVf5LX2LsbJk78lGHTgoe2RUO5cXvZjyWicD9467ICtPkA0HCHY\nGir01TymSNKCyH+qhUAAkjNikLn9HdPEJiIMHD5Suw0/8EVOHziEN1g+tvjOvx9gsv99m2dSmpYb\nVqK0lQ5La9EE/W99YMuGobAdV2PDFzoNK0qa7TwqpVSTpo6ujrwOrjOJx+Pous7nPvc5nnrqKR58\n8EF+9rOfZX6vqirtHe2MnxtDttHf+KP3jvPK86/YOg+A5CfXsmpzX9nPjZ8bp62jreS5AJw/f57P\nfvazeL1evvOd7+T9TlVVOjo6mAxHyooSAKOCXi2Njt2F7qLRETo7u2u2ydbWVo4ceZNAoL3sPn//\n+38lFhsr+7lyeJpUNvfeUvZzibEoLW2ttdtqVyeTo2FbA/pCiMfPN74mC0srHwabCo/T0dlVuw23\ntzNy4jShnvJrHn207z0O/tvz9k6kDOuD19PU01zyMykbLj/eQnE7bkQbbsjwDUCr4uxSp4qi8OST\nT+L1evmXf/mXmraVu8LlXBOPxzNLZ4+MVNbcqhCSqLyxjdN/KidtstouwfXaDNTBVmvegsDptZEc\ntWGXdr9w0o4Xgg037DS2qykI48V/LyEhI9HW1sroyCiapqHaCEhaljVLGWuaxtjoGN3LumgKlb9r\nr7n1Ki69cmnqRToYO4OIojOlpDoC9bS30LmqfB+QYE8L46PjRc9F13Wam5sxTZP+/n5CodnKXNM0\nRkfHaO7uSMUUDHO6jWPhG172OzxKLWDsDOgeD3R3dzIyMlyzTU5MhLnuutvxekMFV1LNZevWDrze\nCru6FToWGUY+Wd5LGY9M8Q//+Hrttnp+hOaOVlvH5mncOZpjhAISkiVjler9JEFzZxujI+drtuHw\n2BhLN6zBFwyU1btbP7udq27aYOc0yiJtakMKlT7uZCTOv5awYShvx41oww0rSpa2tSGfkbGk1CJ4\nMhKylPrxSNnVcQJtLaxav4ZnnnmGHTvym/U8++yzfOc73+Hxxx9n5cqV3HvvvWiaxgMPPJD3uT17\n9nDRhtV0Li7tYkwL+S23bkZRL0v1IwkUnj6bWPQHpkh4DDyaiS9qr5Jo5aaLCp4LQDAYRNd1Dhw4\nwPLlheP+e/bsYc2mNQS7Zrj8TQtMIyVQpn+8uoQ30GLruATQmjPupOPwqpr/k4r+tbJ27eU12+T6\n9Vdy++2pHgimme0mm16dWNNSNinLcNttWx3r5vo8+22tefP7K56o3VavWGfL7Q0QxFnvaSOiqhCw\nfESlKSBrx+nk03TiaSgUom/j2pptuPeytfRuuAhITYssCyxz+t+cH4A161fT1uaML+EsY0wwVfZz\nb1xxcVEbhvJ2XLkNX/jtFy58WVUlHkliqdxByKMS8Cj4PR68sowiSbNcYDfcdzOP/uTHs7ahKAr7\n9+9n48aNNDc388ILL7B161b+8R//Me9zj/7kUa753A1lj0mSUp1QPaqZelGiv4eMxJK4D9mSMFQZ\nqUR31Vy2fGErP/rJo7Pe/+lPf5pJUNu4cWOmbv6yyy7L+9yPf/Jjtj9wc4EDkrIlHH4/BAK0ti4R\nlTcVEAxCV1fqZ/Fi6OlJdVENhVL5JrnpSDt27OSxx3bN2oZdm3zssV3s2JGt3pHl1KULBqGtLXUM\nS5akjmHZMufaywO0Ys97dvPOHfx412Oz3rdtq7seY/tOe10/VZQFMaC7gSWBAE1NKbsNhVJhSZ9v\ndqn71gd28KOfzL6+dm34Rz95jMsfuD3zWiI1DKW7YatqqvG11wteVaKAM61q/Ngr4/n4zpv50a7Z\nzw6wZ8eV2DDYv7fcTMOKEoAO1Z5L7BPbt3DgwAHeeuutvPdvvfVWLMvK+3n11VfzPrNv3z4OHjzI\nFTddZWtfqiGnRJHPn11srwg+00NXIuUKl20+/D926xUcODj7XP7yL/9y1rlYlsX+/fvzz+XQQbbY\n7E7bavPvK0ghSakW2Lm9QYqxbduOmm1y27byg52ipASKk7TZHDi37thW8Bxt2+rBg2zZYa/j50IY\nzN3CiuZgavHyMja8+bZtBcciuzZ84NAB1t92bcl9SEzP72QPiuLcBMlnU5Rs2lH42QHl7bhSG5aR\naV4AwrqhRUl3oHzGNoDqVfn833yJO+++k/7+ftvb7+/v58577uKz3/oCimovUua1pGmJb+/zbZpK\nUFcwbVT1AHi9Kp/7289xx913VHwud91zFw9+90u2V7Ds8HbY3r4gRdBmp3Ov18fDDz/KXXfdU/F1\nvPvue3n44UdRVXvF2k7OMAHasbdB1eflwUcf5s577qrcVu+9mwcffdi2rbaLFvOOscRGiTmkru9/\n+O7D3HF35df3jnvu5pbv7kSxeX0DirMNHP2oyDbSShWfymce/RJ33FP5s6NSG24jkGoKeoFz4Z9B\nDfT1LMVr2RuYt3zmWm7+89vZcs0W9u3bV/bz+/bt4+prtnDDF7fzic9sLd/ekFRyrddn2K8Nnf7O\n4rgP3V/ecD2mhN/wcPXtn+TGB2/k6muutn0uW67Zwh1fuZ1r7y49M0njx0d38zJbnxVk6ews3801\nzfbt93H//d9k69ZP2b6OW7d+ivvv/ybbt9tb6EtV83NdnKCLZgI28zeuvW87d3zzfrZ8aqt9W/3U\nVu745v221wwBiRU47A5qYJYGgrRK9jxPH797O9d95X6uvsb+9f3kNVv5xFfu5bK77XkQADpCzj7q\nZGRCNnvabL7vWj75zdu5+lP2nx2V2zD0LhAbbmhRoigKy9Ultj+//Yt3sOMbn2f7bbdw/Y03sHv3\nbnQ9uw6Mpmn8+te/5rpt17H9tu3c+fXPcuMXbs1uINNptTBNSQW51YbvfuZ5WDJdehMeq8jltMBr\nyHjN7O8//Ref5u5v3c3227Zz/Y3XFz2X67ddzy2fuYU/+/bnuePLd9g+pl7vEmSpoc09deK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"text": "" }, { "output_type": "stream", "stream": "stdout", "text": "+------------+-------+-------+-------+--------+-------+--------+-------+\n| - | RI | ARI | RI' | ARI' | nF | sqtr | tr |\n+============+=======+=======+=======+========+=======+========+=======+\n| (V,U_1) | 0.800 | 0.245 | 0.902 | 0.318 | 0.532 | 0.764 | 0.378 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_2) | 0.875 | 0.490 | 0.942 | 0.577 | 0.663 | 0.894 | 0.444 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (N,V) | 0.850 | 0.333 | 0.933 | 0.528 | 0.682 | 0.816 | 0.333 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (N,U_1) | 0.600 | 0.200 | 0.870 | 0.444 | 0.590 | 0.771 | 0.280 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (N,U_2) | 0.700 | 0.400 | 0.900 | 0.576 | 0.666 | 0.822 | 0.300 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_1|G)t | 0.856 | 0.186 | 0.868 | 0.211 | 0.536 | 0.860 | 0.538 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_2|G)t | 0.913 | 0.427 | 0.924 | 0.483 | 0.672 | 0.961 | 0.581 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_1|G)s | 0.775 | 0.556 | 0.919 | 0.617 | 0.720 | 0.859 | 0.662 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n| (V,U_2|G)s | 0.863 | 0.712 | 0.954 | 0.765 | 0.824 | 0.945 | 0.706 |\n+------------+-------+-------+-------+--------+-------+--------+-------+\n" } ], "prompt_number": 199 } ], "metadata": {} } ] }