{"title": "Abstraction based Output Range Analysis for Neural Networks", "book": "Advances in Neural Information Processing Systems", "page_first": 15788, "page_last": 15798, "abstract": "In this paper, we consider the problem of output range analysis for feed-forward neural networks. The current approaches reduce the problem to satisfiability and optimization solving which are NP-hard problems, and whose computational complexity increases with the number of neurons in the network. We present a novel abstraction technique that constructs a simpler neural network with fewer neurons, albeit with interval weights called interval neural network (INN) which over-approximates the output range of the given neural network. We reduce the output range analysis on the INNs to solving a mixed integer linear programming problem. Our experimental results highlight the trade-off between the computation time and the precision of the computed output range.", "full_text": "Abstraction based Output Range Analysis for Neural\n\nNetworks\n\nPavithra Prabhakar\u2217, Zahra Rahimi Afzal\u2217\n\nDepartment of Computer Science\n\nKansas State University\nManhattan, KS 66506\n\n{pprabhakar,zrahimi}@ksu.edu\n\nAbstract\n\nIn this paper, we consider the problem of output range analysis for feed-forward\nneural networks with ReLU activation functions. The existing approaches reduce\nthe output range analysis problem to satis\ufb01ability and optimization solving, which\nare NP-hard problems, and whose computational complexity increases with the\nnumber of neurons in the network. To tackle the computational complexity, we\npresent a novel abstraction technique that constructs a simpler neural network\nwith fewer neurons, albeit with interval weights called interval neural network\n(INN), which over-approximates the output range of the given neural network. We\nreduce the output range analysis on the INNs to solving a mixed integer linear\nprogramming problem. Our experimental results highlight the trade-off between\nthe computation time and the precision of the computed output range.\n\n1\n\nIntroduction\n\nNeural networks are extensively used today in safety critical control systems such as autonomous\nvehicles and airborne collision avoidance systems [1, 16, 17, 18]. Hence, rigorous methods to ensure\ncorrect functioning of neural network controlled systems is imperative. Formal veri\ufb01cation refers to a\nbroad class of techniques that provide strong guarantees of correctness by exhibiting a proof. Formal\nveri\ufb01cation of neural networks has attracted a lot of attention in the recent years [2, 5, 18, 28, 29, 31].\nHowever, verifying neural networks is extremely challenging due to the large state-space, and the\npresence of nonlinear activation functions, and the veri\ufb01cation problem is known to be NP-hard for\neven simple properties [18].\nOur broad objective is to investigate techniques to verify neural network controlled physical systems\nsuch as autonomous vehicles. These systems consist of a physical system and a neural network\ncontroller that are connected in a feedback, that is, the output of the neural network is the control\ninput (actuator values) to the physical system and the output of the physical system (sensor values) is\ninput to the neural network controller. An important veri\ufb01cation problem is that of safety, wherein,\none seeks to ensure that the state of the neural network controlled system never reaches an unsafe set\nof states. This is established by computing the reachable set, the set of states reached by the system,\nand ensuring that the reach set does not intersect the unsafe states. An important primitive towards\ncomputing the reachable set is to compute the output range of a neural network controller given a set\nof input valuations.\nIn this paper, we focus on neural networks with recti\ufb01ed linear unit (ReLU) function as an activation\nfunction, and we investigate the output range computation problem for feed-forward neural net-\nworks [5]. Recently, there have been several efforts to address this problem that rely on satis\ufb01ability\n\n\u2217Both authors contributed equally to this work.\n\n33rd Conference on Neural Information Processing Systems (NeurIPS 2019), Vancouver, Canada.\n\n\fchecking and optimization. Reluplex [18] is a tool that develops a satis\ufb01ability modulo theory for\nverifying neural networks, in particular, it encodes the input/output relations of a neural network as\na satis\ufb01ability checking problem. A mixed integer linear programming (MILP) based approach is\nproposed in [5, 7] to compute the output range. These approaches construct constraints that encode\nthe neural network behavior, and check satis\ufb01ability or compute optimal values over the constraints.\nThe complexity of veri\ufb01cation depends on the size of the constraints which in turn depends on the\nnumber of neurons in the neural network.\nTo increase the veri\ufb01cation ef\ufb01ciency, we present an orthogonal approach that consists of a novel\nabstraction procedure to reduce the state-space (number of neurons) of the neural network. Abstraction\nis a formal veri\ufb01cation technique that refers to methods for reducing the state-space while providing\nformal guarantees of properties that are preserved by the reduction. One of the well-studied abstraction\nprocedures is predicate abstraction [4, 12] that consists of partitioning the state-space of a given\nsystem into a \ufb01nite number of regions, and constructing an abstract system that consists of these\nregions as the states. Predicate abstraction has been employed extensively for safety veri\ufb01cation,\nsince, the safety of the abstract system is sound, that is, it implies the safety of the given system.\nOur main result consists of a sound abstraction that in particular over-approximates the output range\nof a given neural network. Note that an over-approximation can still provide useful safety analysis\nverdicts, since, if a superset of the reachable set does not intersect with the unsafe set, then the actual\nreachable set will also not intersect the unsafe set. The abstraction procedure essentially merges\nsets of neurons within a particular layer, and annotates the edges and biases with interval weights\nto account for the merging. Hence, we obtain a neural network with interval weights, which we\ncall interval neural networks (INNs). While interval neural networks are more general than neural\nnetworks, we show as a proof of concept that the satis\ufb01ability and optimization based veri\ufb01cation\napproaches can be extended to INNs by extending the MILP based encoding in [5] for neural networks\nto interval neural networks and use it to compute the output range of the abstract INN. We believe that\nother methods such as Reluplex can be extended to handle interval neural network, and hence, the\nabstraction procedure presented here can be used to reduce the state-space before applying existing\nor new veri\ufb01cation algorithms for neural networks. An abstract interpretation based method has been\nexplored in [11], wherein an abstract reachable set is propagated. However, our approach has the\n\ufb02avor of predicate abstraction [12] and computes an over-approximate system which can then be\nused to compute an over-approximation of the output range using any of the above methods including\nthe one based on abstract interpretation [11].\nThe crucial part of the abstraction construction consists of appropriately instantiating the weights\nof the abstract edges.\nIn particular, a convex hull of the weights associated with the concrete\nedges corresponding to an abstract edge does not guarantee soundness, which is shown using a\ncounterexample in Section 3.1. We need to multiply the convex hull by a factor equivalent to the\nnumber of merged nodes in the source abstract node. The proof of soundness is rather involved, since,\nthere is no straightforward relation between the concrete and the abstract states. We establish such a\nconnection, by associating a set of abstract valuations with a concrete valuation for a particular layer,\nwherein, the abstract valuation for an abstract node takes values in the range given by the concrete\nvaluations for the related concrete nodes. The crux of the proof lies in the observation (Proposition 1)\nthat the behavior of a concrete valuation is mimicked in the abstract valuation by an average of the\nconcrete valuations at the nodes corresponding to an abstract node. We conclude that the input/output\nrelation associated with a certain layer of the concrete system is over-approximated by input/output\nvaluations of the corresponding layer in the abstract system.\nWe have implemented our algorithm in a Python toolbox. We perform experimental analysis on\nthe ACAS [15] case study, and observe that the veri\ufb01cation time increases with the increase in the\nnumber of abstract nodes, however, the over-approximation in the output range decreases. Further,\nwe notice that the output range can vary non-trivially even for a \ufb01xed number of abstract nodes, but\ndifferent partitioning of the concrete nodes for merging. This suggests that further research needs\nto be done to understand the best strategies for partitioning the state-space of neurons for merging,\nwhich we intend to explore in the future.\n\nRelated work. Recent studies [2, 10, 14, 21, 29, 30] compare several neural network veri\ufb01cation\nalgorithms. Formal veri\ufb01cation of feedforward neural networks with different activation functions\nhave been considered. For instance, [11, 18] consider ReLU, where as [22, 23] consider large class\nof activation functions that can be represented as Lipschitz-continuous functions. We focus on ReLU\n\n2\n\n\ffunctions, but our method can be extended to more general functions. Different veri\ufb01cation problems\nhave been considered including output range analysis [6, 8, 14, 22, 26, 27], and robustness analysis\n[11, 20]. Veri\ufb01cation methods include those based on reduction to satis\ufb01ability solving [10, 14, 18],\noptimizaiton solving [9], abstract interpretation [23, 24], and linearization [10, 21]. There is some\nrecent work on veri\ufb01cation of AI controlled cyber-physical systems [13, 25]\n\n2\n\nInterval Neural Network\n\nvaluations over S. A partition R of the set A is a set R = {R1, ..., Rk} such that(cid:83)k\n\nA neural network (NN) is a computational model that consists of nodes (neurons) that are organized\nin layers and edges which are the connections between the nodes labeled by weights. An NN contains\nan input layer, some hidden layers, and an output layer each composed of neurons. Given values\nto the nodes in the input layer, the values at the nodes in the next layer are computed through a\nweighted sum dictated by the edge weights and the addition of the bias associated with the output\nnode followed by an activation operation which we will assume is the ReLU (recti\ufb01er linear unit)\nfunction. In this section, we introduce interval neural networks INN that generalize neural networks\nwith interval weights on edges and biases and will represent our abstract systems.\nPreliminaries. Let R denote the set of real numbers. Given a non-negative integer k, let [k] denote\nthe set {0, 1,\u00b7\u00b7\u00b7 , k}. Given a set A, |A| represents the number of elements of A. For any two\nfunctions f, g : A \u2192 R, we say f \u2264 g if \u2200s \u2208 A, f (s) \u2264 g(s). We denote the ReLU function by \u03c3,\nwhich is de\ufb01ned as \u03c3(x) = max(0, x). Given two binary relations R1 \u2286 A \u00d7 B and R2 \u2286 B \u00d7 C,\nwe de\ufb01ne their composition, denoted by R1 \u25e6 R2, to be {(u, v) | \u2203w, (u, w) \u2208 R1 and (w, v) \u2208 R2}.\nFor any set S, a valuation over S is a function f : S \u2192 R. We de\ufb01ne Val(S) to be the set of all\ni=1 Ri = A and\nRi \u2229 Rj = \u2205 \u2200i, j \u2208 {1, .., k} and i (cid:54)= j.\nDe\ufb01nition 1 (Interval Neural Network). An interval neural network (INN) is a tuple (k,{Si}i\u2208[k],\n{W l\ni }i\u2208[k]/{0}), where\n- k is a natural number which we refer to as the number of layers;\n- \u2200i \u2208 [k], Si is a set of nodes of i-th layer in the interval neural network such that \u2200i (cid:54)= j, Si\u2229Sj =\n\u2205. S0 is the input layer, Sk is the output layer and Si, \u2200i \u2208 [k]/{0, k} is a hidden layer;\n- \u2200i \u2208 [k \u2212 1], W l\ni + 1-th layer. We assume that \u2200i \u2208 [k \u2212 1], si \u2208 Si, si+1 \u2208 Si+1, W l\n- \u2200i \u2208 [k]/{0}, bl\n\u2200i \u2208 [k]/{0}, si \u2208 Si, bl\nA neural network can be de\ufb01ned as a special kind of INN where the weights and biases are singular\nintervals.\nDe\ufb01nition 2 (Neural Network). An INN T is a neural network (NN) if \u2200i \u2208 [k \u2212 1], s \u2208 Si, s(cid:48) \u2208\nSi+1, W l\n\n: Si \u00d7 Si+1 \u2192 R represent the weights of the edges between the i-th and\ni (si, si+1);\ni : Si \u2192 R are the biases associated with the nodes in the i-th layer, that is,\n\ni (s, s(cid:48)) = W u\n\ni (s, s(cid:48)), and \u2200i \u2208 [k]/{0}, s \u2208 Si, bl\n\ni (si, si+1) \u2264 W u\n\ni(si) \u2264 bu\n\ni (si).\n\ni(s) = bu\n\ni (s).\n\ni }i\u2208[k\u22121],{bl\n\ni , W u\n\ni, bu\n\ni , W u\ni\n\ni, bu\n\nFigure 1 shows a neural network with 3 layers. The input layer has 2 nodes, the output layer has\n\nFigure 1: A neural network\n\nFigure 2: An interval neural network\n\n1 node, and each of the hidden layers has 3 nodes. The weights on the edges are a single number\n\n3\n\n\f\u2200s(cid:48) \u2208 Si+1, v2(s(cid:48)) = \u03c3((cid:80)\n\ni, bu\n\n(singular intervals), hence, it is a neural network. Figure 2 shows an interval neural network again\nwith 3 layers. The input and output layers have the same number of nodes as before, but the hidden\nlayers have 2 nodes each. The weights on the edges are intervals (and non-singular), so this is an\ninterval neural network (rather than just a neural network).\nAn execution of the neural network starts with valuations to the input nodes, and the valuations to\nthe nodes of a certain layer are computed based on the valuations for the nodes in the previous layer.\nMore precisely, to compute the value at a node si,j corresponding to the j-th node in the layer i, we\nchoose a weight from the interval for each of the incoming nodes and compute a weighted sum of the\nvaluations of the nodes in the previous layer. Then a bias is chosen from the bias interval associated\nwith si,j and added to the weighted sum. Finally, the ReLU function is applied on this sum. The\nexecution then proceeds to the next layer. The semantics of the neural network is captured using a set\nof pairs of input-output valuations wherein the output valuation is a possible result starting from the\ninput valuation and executing the neural network. Next, we de\ufb01ne the semantics of an INN as a set of\nvaluations for the input and output layers.\n(k,{Si}i\u2208[k],\nDe\ufb01nition 3 (Semantics of\n{W l\n[|T|]i = {(v1, v2) \u2208 Val(Si) \u00d7 Val(Si+1)|\ni , W u\ni(s(cid:48)) \u2264\nbs(cid:48) \u2264 bu\nThe semantics can be captured alternately using a post operator, that given a valuation of layer i,\nreturns the set of all valuations of layer i + 1 that are consistent with the semantics.\nDe\ufb01nition 4. Given an INN T with k layers, i \u2208 [k \u2212 1] and V \u2286 Val(Si), we de\ufb01ne PostT ,i(V ) =\n{v(cid:48) | \u2203v \u2208 V, (v, v(cid:48)) \u2208 [|T|]i}. Given V \u2286 Val(S0), we de\ufb01ne PostT (V ) = {v(cid:48) | \u2203v \u2208 V, (v, v(cid:48)) \u2208\n[|T|]}.\nFor notational convenience, we will write PostT ,i({v}) and PostT ({v}) as just PostT ,i(v) and\nPostT (v), respectively.\nOur objective is to \ufb01nd an over-approximation of the values the output neurons can take in an interval\nneural network, given a set of valuations for the input layer.\nProblem 1 (Output range analysis). Given an INN T with k layers and a set of input valuations\nI \u2286 Val(S0), compute valuations l, u \u2208 Val(Sk) such that \u2200(v1, v2) \u2208 [|T|] if v1 \u2208 I then l(s) \u2264\nv2(s) \u2264 u(s) for every s \u2208 Sk.\n\ni }i\u2208[k\u22121],{bl\ns\u2208Si ws,s(cid:48) v1(s) + bs(cid:48)), where W l\ni (s(cid:48))}. We de\ufb01ne [|T|] = [|T|]0 \u25e6 [|T|]1 \u25e6 \u00b7\u00b7\u00b7 \u25e6 [|T|]k\u22121.\n\n=\ni (s, s(cid:48)) \u2264 ws,s(cid:48) \u2264 W u\ni (s, s(cid:48)), bl\n\nINN Network). Given an INN T\n\ni }i\u2208[k]/{0}) and i \u2208 [k \u2212 1],\n\n3 Our Approach\n\nIn this section, we present an abstraction based approach for over-approximating the output range of\nan interval neural network. First, in Section 3.1, we describe the construction of an abstract system\nwhose semantics over-approximates the semantics of a given INN and argue the correctness of the\nconstruction. In Section 3.2, we present an encoding of the interval neural network to mixed integer\nlinear programming that enables the computation of the output range.\n\n3.1 Abstraction of an INN\n\nThe motivation for the abstraction of an INN is to reduce the \u201cstate-space\u201d, the number of neurons in\nthe network, so that computation of the output range can scale to larger INNs. Our broad idea consists\nof merging the nodes of a given concrete INN so as to construct a smaller abstract INN. However,\nit is crucial that we instantiate the weights on the edges and the biases appropriately to ensure that\nthe semantics of the abstracted system is an over-approximation of the concrete INN. For instance,\nconsider the neural network in Figure 3 and consider an input value 1. It results in an output value of\n2. Figure 4 abstracts the neural network in Figure 3 by taking the convex hull of the weights on the\nconcrete edges corresponding to the abstract edge. However, given input 1, the output of the abstract\nneural network is 1 and does not contain 2. Hence, we need to be careful in the construction of the\nabstract system.\nGiven two sets of concrete nodes from consecutive layers of the INN, \u02c6s1 and \u02c6s2, which are each\nmerged into one abstract node, we associate an interval with the edge between \u02c6s1 and \u02c6s2 to be the\ninterval [|\u02c6s1|w1,|\u02c6s1|w2], where w1 and w2 are the minimum and maximum weights associated with\nthe edges in the concrete system between nodes in \u02c6s1 and \u02c6s2, respectively, and |\u02c6s1| is the number\n\n4\n\n\fFigure 3: A concrete neural network\n\nFigure 4: An incorrect abstraction\n\n5\n\ni, bu\n\nan\n\nINN T =\n\n- \u2200i \u2208 [k], \u02c6Si = Pi;\n\ni }i\u2208[k]/{0}), where\n\ni, \u02c6bu\n\ni (\u02c6si, \u02c6si+1) = |\u02c6si| min {W l\n\ni(si) | si \u2208 \u02c6si} and \u02c6bu\n\ni (\u02c6si) = max {bu\n\ni (si) | si \u2208 \u02c6si}.\n\n(Abstract Neural Network). Given\n\ni (si, si+1) | si \u2208 \u02c6si, si+1 \u2208 \u02c6si+1}\n\ni (si, si+1) | si \u2208 \u02c6si, si+1 \u2208 \u02c6si+1};\n\nof concrete nodes corresponding to the abstract node \u02c6s1. In other words, [w1, w2] is the convex\nhull of the intervals associated with the edges between nodes in \u02c6s1 and \u02c6s2 multiplied by a factor\ncorresponding to the number of concrete nodes corresponding to the source abstract node. Note that\nthe above abstraction will lead to a weight of 2 on the second edge in Figure 4, thus leading to an\noutput of 2 as in the concrete system.\nNext, we formally de\ufb01ne the abstraction. We say that P = {Pi}i\u2208[k] is a partition of T , if for every i,\nPi is a partition of the Si, the nodes in the i-th layer of T .\n(k,{Si}i\u2208[k],\nDe\ufb01nition\nT /P = (k,{ \u02c6Si}i\u2208[k],{(cid:99)W l\ni ,(cid:99)W u\ni }i\u2208[k]/{0}) and a partition P = {Pi}i\u2208[k] of T , we de\ufb01ne an INN\ni }i\u2208[k\u22121],{bl\n{W l\ni , W u\ni }i\u2208[k\u22121],{\u02c6bl\n- \u2200i \u2208 [k\u22121], \u02c6si \u2208 \u02c6Si, \u02c6si+1 \u2208 \u02c6Si+1,(cid:99)W l\nand(cid:99)W u\ni (\u02c6si, \u02c6si+1) = |\u02c6si| max {W u\ni(\u02c6si) = min {bl\n- \u2200i \u2208 [k]/{0}, \u02c6si \u2208 \u02c6Si, \u02c6bl\nFigure 2 shows the abstraction of the neural network in Figure 1, where the nodes s1,1 and s1,2 are\nmerged and the nodes s2,1 and s2,2 are merged. Note that the edge from {s1,1, s1,2} to {s2,1, s2,2}\nhas weight interval [14, 22], which is obtained by taking the convex hull of the four weights 7, 10, 8\nand 11, and multiplying by 2, the size of the source abstract node.\nThe following theorem states the correctness of the construction of T /P . It states that every in-\nput/output valuation that is admitted by T is also admitted by T /P , thus establishing the soundness\nof the abstraction.\nTheorem 1. Given an INN T = (k,{Si}i\u2208[k], {W l\ni }i\u2208[k]/{0}) and a partition\ni }i\u2208[k\u22121],{bl\nP = {Pi}i\u2208[k] of T such that P0 = S0 and Pk = Sk, [|T|] \u2286 [|T /P|].\nWe devote the rest of the section to sketch a proof of Theorem 1. Broadly, the proof consists of\nrelating the valuations in the i-th layer of the concrete INN with the i-th layer of the abstract INN.\nNote that the nodes in a particular layer of the abstract and the concrete system might not be the same.\nThe following de\ufb01nition relates states in the concrete system to those in the abstract system.\nDe\ufb01nition 6. Given a valuation v \u2208 Val(Si), AV(v) = {\u02c6v \u2208 Val( \u02c6Si)|\u2200\u02c6s \u2208 \u02c6Si, mins\u2208\u02c6s v(s) \u2264\n\u02c6v(\u02c6s) \u2264 maxs\u2208\u02c6s v(s)}.\nGiven a valuation v of the i-th layer of the concrete system, AV(v) consists of the set of all abstract\nvaluations of the i-th layer in the abstract system, where each abstract node gets a value which is\nwithin the range of values of the corresponding concrete nodes. Proof of Theorem 1 relies on the\nfollowing connection between corresponding layers of the concrete and abstract INNs.\nLemma 1. If (v, v(cid:48)) \u2208 [|T|]i, then AV(v(cid:48)) \u2286 PostT /P,i(AV(v)).\nThe proof of Lemma 1 broadly follows the following structure. We \ufb01rst observe that the abstraction\nprocedure corresponding to edges between layer i and layer i + 1 can be decomposed into two steps,\nwherein we \ufb01rst merge the nodes of the i-th layer and then we merge the nodes of the i + 1-st layer.\n\ni , W u\n\ni, bu\n\nNote that(cid:99)W l\n\ni (\u02c6si, \u02c6si+1) = |\u02c6si|\n\nmin\n\nsi\u2208\u02c6si, si+1\u2208\u02c6si+1\n\nW l\n\ni (si, si+1) = min\n\nsi+1\u2208\u02c6si+1\n\n|\u02c6si| min\nsi\u2208\u02c6si\n\nW l\n\ni (si, si+1)\n\n5\n\ns1,1AAAB8HicbVBNSwMxEJ2tX7V+VT16CRbBg5SNCHosevFYwdZKu5Rsmm1Dk+ySZIWy9Fd48aCIV3+ON/+N2XYP2vpg4PHeDDPzwkRwY33/2yutrK6tb5Q3K1vbO7t71f2DtolTTVmLxiLWnZAYJrhiLcutYJ1EMyJDwR7C8U3uPzwxbXis7u0kYYEkQ8UjTol10qPpZ/gMTyuVfrXm1/0Z0DLBBalBgWa/+tUbxDSVTFkqiDFd7Cc2yIi2nAo2rfRSwxJCx2TIuo4qIpkJstnBU3TilAGKYu1KWTRTf09kRBozkaHrlMSOzKKXi/953dRGV0HGVZJapuh8UZQKZGOUf48GXDNqxcQRQjV3tyI6IppQ6zLKQ8CLLy+T9nkd+3V8d1FrXBdxlOEIjuEUMFxCA26hCS2gIOEZXuHN096L9+59zFtLXjFzCH/gff4AD/uPQA==AAAB8HicbVBNSwMxEJ2tX7V+VT16CRbBg5SNCHosevFYwdZKu5Rsmm1Dk+ySZIWy9Fd48aCIV3+ON/+N2XYP2vpg4PHeDDPzwkRwY33/2yutrK6tb5Q3K1vbO7t71f2DtolTTVmLxiLWnZAYJrhiLcutYJ1EMyJDwR7C8U3uPzwxbXis7u0kYYEkQ8UjTol10qPpZ/gMTyuVfrXm1/0Z0DLBBalBgWa/+tUbxDSVTFkqiDFd7Cc2yIi2nAo2rfRSwxJCx2TIuo4qIpkJstnBU3TilAGKYu1KWTRTf09kRBozkaHrlMSOzKKXi/953dRGV0HGVZJapuh8UZQKZGOUf48GXDNqxcQRQjV3tyI6IppQ6zLKQ8CLLy+T9nkd+3V8d1FrXBdxlOEIjuEUMFxCA26hCS2gIOEZXuHN096L9+59zFtLXjFzCH/gff4AD/uPQA==AAAB8HicbVBNSwMxEJ2tX7V+VT16CRbBg5SNCHosevFYwdZKu5Rsmm1Dk+ySZIWy9Fd48aCIV3+ON/+N2XYP2vpg4PHeDDPzwkRwY33/2yutrK6tb5Q3K1vbO7t71f2DtolTTVmLxiLWnZAYJrhiLcutYJ1EMyJDwR7C8U3uPzwxbXis7u0kYYEkQ8UjTol10qPpZ/gMTyuVfrXm1/0Z0DLBBalBgWa/+tUbxDSVTFkqiDFd7Cc2yIi2nAo2rfRSwxJCx2TIuo4qIpkJstnBU3TilAGKYu1KWTRTf09kRBozkaHrlMSOzKKXi/953dRGV0HGVZJapuh8UZQKZGOUf48GXDNqxcQRQjV3tyI6IppQ6zLKQ8CLLy+T9nkd+3V8d1FrXBdxlOEIjuEUMFxCA26hCS2gIOEZXuHN096L9+59zFtLXjFzCH/gff4AD/uPQA==AAAB8HicbVBNSwMxEJ2tX7V+VT16CRbBg5SNCHosevFYwdZKu5Rsmm1Dk+ySZIWy9Fd48aCIV3+ON/+N2XYP2vpg4PHeDDPzwkRwY33/2yutrK6tb5Q3K1vbO7t71f2DtolTTVmLxiLWnZAYJrhiLcutYJ1EMyJDwR7C8U3uPzwxbXis7u0kYYEkQ8UjTol10qPpZ/gMTyuVfrXm1/0Z0DLBBalBgWa/+tUbxDSVTFkqiDFd7Cc2yIi2nAo2rfRSwxJCx2TIuo4qIpkJstnBU3TilAGKYu1KWTRTf09kRBozkaHrlMSOzKKXi/953dRGV0HGVZJapuh8UZQKZGOUf48GXDNqxcQRQjV3tyI6IppQ6zLKQ8CLLy+T9nkd+3V8d1FrXBdxlOEIjuEUMFxCA26hCS2gIOEZXuHN096L9+59zFtLXjFzCH/gff4AD/uPQA==s1,2AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMv+iPnPdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYKPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMv+iPnPdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYKPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMv+iPnPdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYKPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMv+iPnPdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYKPQQ==s0,1AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5RECnosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMu/Cn7nuoFL1at4caJX4BalCgeag8tUfxiQVVBrCsdY930tMkGFlGOF05vZTTRNMJnhEe5ZKLKgOsvnBM3RmlSGKYmVLGjRXf09kWGg9FaHtFNiM9bKXi/95vdRE10HGZJIaKsliUZRyZGKUf4+GTFFi+NQSTBSztyIyxgoTYzPKQ/CXX14l7cua79X8+3q1cVPEUYYTOIVz8OEKGnAHTWgBAQHP8ApvjnJenHfnY9FacoqZY/gD5/MHDnKPPw==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5RECnosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMu/Cn7nuoFL1at4caJX4BalCgeag8tUfxiQVVBrCsdY930tMkGFlGOF05vZTTRNMJnhEe5ZKLKgOsvnBM3RmlSGKYmVLGjRXf09kWGg9FaHtFNiM9bKXi/95vdRE10HGZJIaKsliUZRyZGKUf4+GTFFi+NQSTBSztyIyxgoTYzPKQ/CXX14l7cua79X8+3q1cVPEUYYTOIVz8OEKGnAHTWgBAQHP8ApvjnJenHfnY9FacoqZY/gD5/MHDnKPPw==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5RECnosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMu/Cn7nuoFL1at4caJX4BalCgeag8tUfxiQVVBrCsdY930tMkGFlGOF05vZTTRNMJnhEe5ZKLKgOsvnBM3RmlSGKYmVLGjRXf09kWGg9FaHtFNiM9bKXi/95vdRE10HGZJIaKsliUZRyZGKUf4+GTFFi+NQSTBSztyIyxgoTYzPKQ/CXX14l7cua79X8+3q1cVPEUYYTOIVz8OEKGnAHTWgBAQHP8ApvjnJenHfnY9FacoqZY/gD5/MHDnKPPw==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5RECnosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMu/Cn7nuoFL1at4caJX4BalCgeag8tUfxiQVVBrCsdY930tMkGFlGOF05vZTTRNMJnhEe5ZKLKgOsvnBM3RmlSGKYmVLGjRXf09kWGg9FaHtFNiM9bKXi/95vdRE10HGZJIaKsliUZRyZGKUf4+GTFFi+NQSTBSztyIyxgoTYzPKQ/CXX14l7cua79X8+3q1cVPEUYYTOIVz8OEKGnAHTWgBAQHP8ApvjnJenHfnY9FacoqZY/gD5/MHDnKPPw==s2,1AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvqFP3PdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYSPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvqFP3PdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYSPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvqFP3PdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYSPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvqFP3PdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYSPQQ==1AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==1AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==0AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==0AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==0AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==1AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==1AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==s1,1AAAB8HicbVBNSwMxEJ2tX7V+VT16CRbBg5SNCHosevFYwdZKu5Rsmm1Dk+ySZIWy9Fd48aCIV3+ON/+N2XYP2vpg4PHeDDPzwkRwY33/2yutrK6tb5Q3K1vbO7t71f2DtolTTVmLxiLWnZAYJrhiLcutYJ1EMyJDwR7C8U3uPzwxbXis7u0kYYEkQ8UjTol10qPpZ/gMTyuVfrXm1/0Z0DLBBalBgWa/+tUbxDSVTFkqiDFd7Cc2yIi2nAo2rfRSwxJCx2TIuo4qIpkJstnBU3TilAGKYu1KWTRTf09kRBozkaHrlMSOzKKXi/953dRGV0HGVZJapuh8UZQKZGOUf48GXDNqxcQRQjV3tyI6IppQ6zLKQ8CLLy+T9nkd+3V8d1FrXBdxlOEIjuEUMFxCA26hCS2gIOEZXuHN096L9+59zFtLXjFzCH/gff4AD/uPQA==AAAB8HicbVBNSwMxEJ2tX7V+VT16CRbBg5SNCHosevFYwdZKu5Rsmm1Dk+ySZIWy9Fd48aCIV3+ON/+N2XYP2vpg4PHeDDPzwkRwY33/2yutrK6tb5Q3K1vbO7t71f2DtolTTVmLxiLWnZAYJrhiLcutYJ1EMyJDwR7C8U3uPzwxbXis7u0kYYEkQ8UjTol10qPpZ/gMTyuVfrXm1/0Z0DLBBalBgWa/+tUbxDSVTFkqiDFd7Cc2yIi2nAo2rfRSwxJCx2TIuo4qIpkJstnBU3TilAGKYu1KWTRTf09kRBozkaHrlMSOzKKXi/953dRGV0HGVZJapuh8UZQKZGOUf48GXDNqxcQRQjV3tyI6IppQ6zLKQ8CLLy+T9nkd+3V8d1FrXBdxlOEIjuEUMFxCA26hCS2gIOEZXuHN096L9+59zFtLXjFzCH/gff4AD/uPQA==AAAB8HicbVBNSwMxEJ2tX7V+VT16CRbBg5SNCHosevFYwdZKu5Rsmm1Dk+ySZIWy9Fd48aCIV3+ON/+N2XYP2vpg4PHeDDPzwkRwY33/2yutrK6tb5Q3K1vbO7t71f2DtolTTVmLxiLWnZAYJrhiLcutYJ1EMyJDwR7C8U3uPzwxbXis7u0kYYEkQ8UjTol10qPpZ/gMTyuVfrXm1/0Z0DLBBalBgWa/+tUbxDSVTFkqiDFd7Cc2yIi2nAo2rfRSwxJCx2TIuo4qIpkJstnBU3TilAGKYu1KWTRTf09kRBozkaHrlMSOzKKXi/953dRGV0HGVZJapuh8UZQKZGOUf48GXDNqxcQRQjV3tyI6IppQ6zLKQ8CLLy+T9nkd+3V8d1FrXBdxlOEIjuEUMFxCA26hCS2gIOEZXuHN096L9+59zFtLXjFzCH/gff4AD/uPQA==AAAB8HicbVBNSwMxEJ2tX7V+VT16CRbBg5SNCHosevFYwdZKu5Rsmm1Dk+ySZIWy9Fd48aCIV3+ON/+N2XYP2vpg4PHeDDPzwkRwY33/2yutrK6tb5Q3K1vbO7t71f2DtolTTVmLxiLWnZAYJrhiLcutYJ1EMyJDwR7C8U3uPzwxbXis7u0kYYEkQ8UjTol10qPpZ/gMTyuVfrXm1/0Z0DLBBalBgWa/+tUbxDSVTFkqiDFd7Cc2yIi2nAo2rfRSwxJCx2TIuo4qIpkJstnBU3TilAGKYu1KWTRTf09kRBozkaHrlMSOzKKXi/953dRGV0HGVZJapuh8UZQKZGOUf48GXDNqxcQRQjV3tyI6IppQ6zLKQ8CLLy+T9nkd+3V8d1FrXBdxlOEIjuEUMFxCA26hCS2gIOEZXuHN096L9+59zFtLXjFzCH/gff4AD/uPQA==s0,1AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5RECnosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMu/Cn7nuoFL1at4caJX4BalCgeag8tUfxiQVVBrCsdY930tMkGFlGOF05vZTTRNMJnhEe5ZKLKgOsvnBM3RmlSGKYmVLGjRXf09kWGg9FaHtFNiM9bKXi/95vdRE10HGZJIaKsliUZRyZGKUf4+GTFFi+NQSTBSztyIyxgoTYzPKQ/CXX14l7cua79X8+3q1cVPEUYYTOIVz8OEKGnAHTWgBAQHP8ApvjnJenHfnY9FacoqZY/gD5/MHDnKPPw==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5RECnosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMu/Cn7nuoFL1at4caJX4BalCgeag8tUfxiQVVBrCsdY930tMkGFlGOF05vZTTRNMJnhEe5ZKLKgOsvnBM3RmlSGKYmVLGjRXf09kWGg9FaHtFNiM9bKXi/95vdRE10HGZJIaKsliUZRyZGKUf4+GTFFi+NQSTBSztyIyxgoTYzPKQ/CXX14l7cua79X8+3q1cVPEUYYTOIVz8OEKGnAHTWgBAQHP8ApvjnJenHfnY9FacoqZY/gD5/MHDnKPPw==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5RECnosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMu/Cn7nuoFL1at4caJX4BalCgeag8tUfxiQVVBrCsdY930tMkGFlGOF05vZTTRNMJnhEe5ZKLKgOsvnBM3RmlSGKYmVLGjRXf09kWGg9FaHtFNiM9bKXi/95vdRE10HGZJIaKsliUZRyZGKUf4+GTFFi+NQSTBSztyIyxgoTYzPKQ/CXX14l7cua79X8+3q1cVPEUYYTOIVz8OEKGnAHTWgBAQHP8ApvjnJenHfnY9FacoqZY/gD5/MHDnKPPw==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5RECnosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMu/Cn7nuoFL1at4caJX4BalCgeag8tUfxiQVVBrCsdY930tMkGFlGOF05vZTTRNMJnhEe5ZKLKgOsvnBM3RmlSGKYmVLGjRXf09kWGg9FaHtFNiM9bKXi/95vdRE10HGZJIaKsliUZRyZGKUf4+GTFFi+NQSTBSztyIyxgoTYzPKQ/CXX14l7cua79X8+3q1cVPEUYYTOIVz8OEKGnAHTWgBAQHP8ApvjnJenHfnY9FacoqZY/gD5/MHDnKPPw==s2,1AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvqFP3PdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYSPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvqFP3PdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYSPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvqFP3PdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYSPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvqFP3PdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYSPQQ==0AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==1AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==0AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmltfWNzq7xd2dnd2z+oHh61TZxqxlsslrHuBtRwKRRvoUDJu4nmNAok7wST29zvPHFtRKwecZpwP6IjJULBKFrpwa1UBtWaW3fnIKvEK0gNCjQH1a/+MGZpxBUySY3peW6CfkY1Cib5rNJPDU8om9AR71mqaMSNn81PnZEzqwxJGGtbCslc/T2R0ciYaRTYzoji2Cx7ufif10sxvPYzoZIUuWKLRWEqCcYk/5sMheYM5dQSyrSwtxI2ppoytOnkIXjLL6+S9kXdc+ve/WWtcVPEUYYTOIVz8OAKGnAHTWgBgxE8wyu8OdJ5cd6dj0VrySlmjuEPnM8f4Z2M3A==1AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lEqMeiF48t2A9oQ9lsJ+3azSbsboQS+gu8eFDEqz/Jm//GbZuDtj4YeLw3w8y8IBFcG9f9dgobm1vbO8Xd0t7+weFR+fikreNUMWyxWMSqG1CNgktsGW4EdhOFNAoEdoLJ3dzvPKHSPJYPZpqgH9GR5CFn1Fip6Q3KFbfqLkDWiZeTCuRoDMpf/WHM0gilYYJq3fPcxPgZVYYzgbNSP9WYUDahI+xZKmmE2s8Wh87IhVWGJIyVLWnIQv09kdFI62kU2M6ImrFe9ebif14vNeGNn3GZpAYlWy4KU0FMTOZfkyFXyIyYWkKZ4vZWwsZUUWZsNiUbgrf68jppX1U9t+o1ryv12zyOIpzBOVyCBzWowz00oAUMEJ7hFd6cR+fFeXc+lq0FJ585hT9wPn8Aep2MtQ==s1,2AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMv+iPnPdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYKPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMv+iPnPdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYKPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMv+iPnPdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYKPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMv+iPnPdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYKPQQ==\fA similar observation can be made about the max. Hence, our \ufb01rst step consists of a function labs\nwhich merges the nodes in the \u201cleft\u201d layer and associates an interval with the edges which corresponds\nto computing the convex hull followed by multiplying with an appropriate factor. Next, the function\nrabs merges the nodes in the \u201cright\u201d layer and associates an interval which corresponds to only\ncomputing the convex hull. Next, we de\ufb01ne these abstraction functions, and state their relation with\nthe concrete systems.\nDe\ufb01nition 7. Given an INN T = (k,{Si}i\u2208[k],{W l\nj\nand P which is a partition of jth layer of T , we de\ufb01ne an INN labs(T , j, P ) =\n(1,{ \u02c6Si}i\u2208[1],{ \u02c6W l\n- \u2200\u02c6s0 \u2208 \u02c6S0, \u02c6s1 \u2208 \u02c6S1,(cid:99)W l\n- \u02c6S0 = P, \u02c6S1 = Sj+1;\n0 (s0, \u02c6s1) | s0 \u2208 \u02c6s0};\n{W u\n- \u2200\u02c6s1 \u2208 \u02c6S1, \u02c6bl\n1(\u02c6s1) = bl\nFigure 5 show the left abstraction of the the neural network in Figure 1 with respect to layer 1, where\n\n0(s0, \u02c6s1) | s0 \u2208 \u02c6s0}, and(cid:99)W u\n\n0(\u02c6s0, \u02c6s1) = |\u02c6s0| min {W l\n\n0 (\u02c6s0, \u02c6s1) = |\u02c6s0| max\n\ni }i\u2208{1}), where\n\ni }i\u2208[k\u22121],{bl\n\ni }i\u2208[k]/{0}),\n\ni }i\u2208[0],{\u02c6bl\n\n1(\u02c6s1), and \u02c6bu\n\n1 (\u02c6s1) = bu\n\ni , \u02c6W u\n\n1 (\u02c6s1).\n\ni , W u\n\ni, \u02c6bu\n\ni, bu\n\nFigure 5: A left abstraction illustration\n\nFigure 6: A right abstraction illustration\n\ni, bu\n\ni , W u\n\ni , \u02c6W u\n\ni }i\u2208[0]},{bl\n\n0(\u02c6s0, \u02c6s1) = min {W l\n\n= (1,{Si}i\u2208[1],{W l\n\n1(s1) | s1 \u2208 \u02c6s1}, and \u02c6bu\n\n0(\u02c6s0, s1) | s1 \u2208 \u02c6s1}, and (cid:99)W u\n1 (s1) | s1 \u2208 \u02c6s1}.\n1 (\u02c6s1) = max {bu\n\nthe nodes s1,1 and s1,2 are merged. The edge from {s1,1, s1,2} to s2,1 has weight [14, 20] which is\nobtained by taking the convex hull of the values 7 and 10 and multiplying by 2.\nDe\ufb01nition 8. Given an INN T\ni }i\u2208{1}) and\nthe layer 1 of T , we de\ufb01ne an INN rabs(T , P ) =\nP which is a partition of\n(1,{ \u02c6Si}i\u2208[1],{ \u02c6W l\ni }i\u2208{1}), where\ni }i\u2208[0],{\u02c6bl\ni, \u02c6bu\n- \u2200\u02c6s0 \u2208 \u02c6S0, \u02c6s1 \u2208 \u02c6S1, (cid:99)W l\n- \u02c6S0 = S0, \u02c6S1 = P ;\n0 (\u02c6s0, s1) | s1 \u2208 \u02c6s1};\n1(\u02c6s1) = min {bl\n\n{W u\n- \u2200\u02c6s1 \u2208 \u02c6S1, \u02c6bl\nFigure 6 shows the right abstraction of the interval neural network in Figure 5, where the nodes s2,1\nand s2,2 are merged. The edge from {s1,1, s1,2} to {s2,1, s2,2} has weight [14, 22] which is obtained\nby taking the convex hull of the intervals [14, 20] and [16, 22]. Note that Figure 6 is the same as the\nFigure 2 with restricted 2 layers 1 and 2.\nNote that applying the left abstraction followed by right abstraction to the j-th layer of T gives us the\nj-th layer of T /P . This is stated in the following lemma.\ni+j}i\u2208{1}).\nLemma 2. rabs(labs(T , j, Pj), Pj+1) = (1,{ \u02c6Si+j}i\u2208[1],{ \u02c6W l\nProof of Lemma 1 relies on some crucial properties which we state below. The crux of the proof of\nthe correctness of left abstraction lies in the following proposition. It states that the contribution of\nthe values of a set of left nodes {s1,\u00b7\u00b7\u00b7 , sn} on a right node s, can be simulated in a left abstraction\nwhich merges {s1,\u00b7\u00b7\u00b7 , sn} by the average of the values.\n\nProposition 1. Let v1, v2, . . . , vn and w1, w2, . . . , wn be real numbers. Let \u00afv =(cid:80)\nexists a w such that n mini wi \u2264 w \u2264 n maxi wi and(cid:80)\n\n0 (\u02c6s0, \u02c6s1) = max\n\ni+j}i\u2208[0],{\u02c6bl\n\ni vi/n. There\n\ni+j, \u02c6W u\n\ni+j, \u02c6bu\n\ni wivi = \u00afvw.\n\n6\n\n13AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU0GPRi8eK1hbaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmlldW19o7xZ2dre2d2r7h88mjjVjLdYLGPdCajhUijeQoGSdxLNaRRI3g7GN7nffuLaiFg94CThfkSHSoSCUbTSvXde6Vdrbt2dgSwTryA1KNDsV796g5ilEVfIJDWm67kJ+hnVKJjk00ovNTyhbEyHvGupohE3fjY7dUpOrDIgYaxtKSQz9fdERiNjJlFgOyOKI7Po5eJ/XjfF8MrPhEpS5IrNF4WpJBiT/G8yEJozlBNLKNPC3krYiGrK0KaTh+AtvrxMHs/qnlv37i5qjesijjIcwTGcggeX0IBbaEILGAzhGV7hzZHOi/PufMxbS04xcwh/4Hz+ACF/jQY=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU0GPRi8eK1hbaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmlldW19o7xZ2dre2d2r7h88mjjVjLdYLGPdCajhUijeQoGSdxLNaRRI3g7GN7nffuLaiFg94CThfkSHSoSCUbTSvXde6Vdrbt2dgSwTryA1KNDsV796g5ilEVfIJDWm67kJ+hnVKJjk00ovNTyhbEyHvGupohE3fjY7dUpOrDIgYaxtKSQz9fdERiNjJlFgOyOKI7Po5eJ/XjfF8MrPhEpS5IrNF4WpJBiT/G8yEJozlBNLKNPC3krYiGrK0KaTh+AtvrxMHs/qnlv37i5qjesijjIcwTGcggeX0IBbaEILGAzhGV7hzZHOi/PufMxbS04xcwh/4Hz+ACF/jQY=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU0GPRi8eK1hbaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmlldW19o7xZ2dre2d2r7h88mjjVjLdYLGPdCajhUijeQoGSdxLNaRRI3g7GN7nffuLaiFg94CThfkSHSoSCUbTSvXde6Vdrbt2dgSwTryA1KNDsV796g5ilEVfIJDWm67kJ+hnVKJjk00ovNTyhbEyHvGupohE3fjY7dUpOrDIgYaxtKSQz9fdERiNjJlFgOyOKI7Po5eJ/XjfF8MrPhEpS5IrNF4WpJBiT/G8yEJozlBNLKNPC3krYiGrK0KaTh+AtvrxMHs/qnlv37i5qjesijjIcwTGcggeX0IBbaEILGAzhGV7hzZHOi/PufMxbS04xcwh/4Hz+ACF/jQY=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lU0GPRi8eK1hbaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmlldW19o7xZ2dre2d2r7h88mjjVjLdYLGPdCajhUijeQoGSdxLNaRRI3g7GN7nffuLaiFg94CThfkSHSoSCUbTSvXde6Vdrbt2dgSwTryA1KNDsV796g5ilEVfIJDWm67kJ+hnVKJjk00ovNTyhbEyHvGupohE3fjY7dUpOrDIgYaxtKSQz9fdERiNjJlFgOyOKI7Po5eJ/XjfF8MrPhEpS5IrNF4WpJBiT/G8yEJozlBNLKNPC3krYiGrK0KaTh+AtvrxMHs/qnlv37i5qjesijjIcwTGcggeX0IBbaEILGAzhGV7hzZHOi/PufMxbS04xcwh/4Hz+ACF/jQY=14AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbSbt0swm7G6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSATXxnW/ndLa+sbmVnm7srO7t39QPTxq6zhVDFssFrHqBlSj4BJbhhuB3UQhjQKBnWBym/udJ1Sax/LRTBP0IzqSPOSMGis9eJeVQbXm1t05yCrxClKDAs1B9as/jFkaoTRMUK17npsYP6PKcCZwVumnGhPKJnSEPUsljVD72fzUGTmzypCEsbIlDZmrvycyGmk9jQLbGVEz1steLv7n9VITXvsZl0lqULLFojAVxMQk/5sMuUJmxNQSyhS3txI2pooyY9PJQ/CWX14l7Yu659a9+8ta46aIowwncArn4MEVNOAOmtACBiN4hld4c4Tz4rw7H4vWklPMHMMfOJ8/IwSNBw==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbSbt0swm7G6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSATXxnW/ndLa+sbmVnm7srO7t39QPTxq6zhVDFssFrHqBlSj4BJbhhuB3UQhjQKBnWBym/udJ1Sax/LRTBP0IzqSPOSMGis9eJeVQbXm1t05yCrxClKDAs1B9as/jFkaoTRMUK17npsYP6PKcCZwVumnGhPKJnSEPUsljVD72fzUGTmzypCEsbIlDZmrvycyGmk9jQLbGVEz1steLv7n9VITXvsZl0lqULLFojAVxMQk/5sMuUJmxNQSyhS3txI2pooyY9PJQ/CWX14l7Yu659a9+8ta46aIowwncArn4MEVNOAOmtACBiN4hld4c4Tz4rw7H4vWklPMHMMfOJ8/IwSNBw==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbSbt0swm7G6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSATXxnW/ndLa+sbmVnm7srO7t39QPTxq6zhVDFssFrHqBlSj4BJbhhuB3UQhjQKBnWBym/udJ1Sax/LRTBP0IzqSPOSMGis9eJeVQbXm1t05yCrxClKDAs1B9as/jFkaoTRMUK17npsYP6PKcCZwVumnGhPKJnSEPUsljVD72fzUGTmzypCEsbIlDZmrvycyGmk9jQLbGVEz1steLv7n9VITXvsZl0lqULLFojAVxMQk/5sMuUJmxNQSyhS3txI2pooyY9PJQ/CWX14l7Yu659a9+8ta46aIowwncArn4MEVNOAOmtACBiN4hld4c4Tz4rw7H4vWklPMHMMfOJ8/IwSNBw==AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0GPRi8eK9gPaUDbbSbt0swm7G6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSATXxnW/ndLa+sbmVnm7srO7t39QPTxq6zhVDFssFrHqBlSj4BJbhhuB3UQhjQKBnWBym/udJ1Sax/LRTBP0IzqSPOSMGis9eJeVQbXm1t05yCrxClKDAs1B9as/jFkaoTRMUK17npsYP6PKcCZwVumnGhPKJnSEPUsljVD72fzUGTmzypCEsbIlDZmrvycyGmk9jQLbGVEz1steLv7n9VITXvsZl0lqULLFojAVxMQk/5sMuUJmxNQSyhS3txI2pooyY9PJQ/CWX14l7Yu659a9+8ta46aIowwncArn4MEVNOAOmtACBiN4hld4c4Tz4rw7H4vWklPMHMMfOJ8/IwSNBw==15AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0WPRi8eK1hbaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmlldW19o7xZ2dre2d2r7h88mjjVjLdYLGPdCajhUijeQoGSdxLNaRRI3g7GN7nffuLaiFg94CThfkSHSoSCUbTSvXdR6Vdrbt2dgSwTryA1KNDsV796g5ilEVfIJDWm67kJ+hnVKJjk00ovNTyhbEyHvGupohE3fjY7dUpOrDIgYaxtKSQz9fdERiNjJlFgOyOKI7Po5eJ/XjfF8MrPhEpS5IrNF4WpJBiT/G8yEJozlBNLKNPC3krYiGrK0KaTh+AtvrxMHs/qnlv37s5rjesijjIcwTGcggeX0IBbaEILGAzhGV7hzZHOi/PufMxbS04xcwh/4Hz+ACSJjQg=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0WPRi8eK1hbaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmlldW19o7xZ2dre2d2r7h88mjjVjLdYLGPdCajhUijeQoGSdxLNaRRI3g7GN7nffuLaiFg94CThfkSHSoSCUbTSvXdR6Vdrbt2dgSwTryA1KNDsV796g5ilEVfIJDWm67kJ+hnVKJjk00ovNTyhbEyHvGupohE3fjY7dUpOrDIgYaxtKSQz9fdERiNjJlFgOyOKI7Po5eJ/XjfF8MrPhEpS5IrNF4WpJBiT/G8yEJozlBNLKNPC3krYiGrK0KaTh+AtvrxMHs/qnlv37s5rjesijjIcwTGcggeX0IBbaEILGAzhGV7hzZHOi/PufMxbS04xcwh/4Hz+ACSJjQg=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0WPRi8eK1hbaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmlldW19o7xZ2dre2d2r7h88mjjVjLdYLGPdCajhUijeQoGSdxLNaRRI3g7GN7nffuLaiFg94CThfkSHSoSCUbTSvXdR6Vdrbt2dgSwTryA1KNDsV796g5ilEVfIJDWm67kJ+hnVKJjk00ovNTyhbEyHvGupohE3fjY7dUpOrDIgYaxtKSQz9fdERiNjJlFgOyOKI7Po5eJ/XjfF8MrPhEpS5IrNF4WpJBiT/G8yEJozlBNLKNPC3krYiGrK0KaTh+AtvrxMHs/qnlv37s5rjesijjIcwTGcggeX0IBbaEILGAzhGV7hzZHOi/PufMxbS04xcwh/4Hz+ACSJjQg=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0WPRi8eK1hbaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmlldW19o7xZ2dre2d2r7h88mjjVjLdYLGPdCajhUijeQoGSdxLNaRRI3g7GN7nffuLaiFg94CThfkSHSoSCUbTSvXdR6Vdrbt2dgSwTryA1KNDsV796g5ilEVfIJDWm67kJ+hnVKJjk00ovNTyhbEyHvGupohE3fjY7dUpOrDIgYaxtKSQz9fdERiNjJlFgOyOKI7Po5eJ/XjfF8MrPhEpS5IrNF4WpJBiT/G8yEJozlBNLKNPC3krYiGrK0KaTh+AtvrxMHs/qnlv37s5rjesijjIcwTGcggeX0IBbaEILGAzhGV7hzZHOi/PufMxbS04xcwh/4Hz+ACSJjQg=21AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0mKoMeiF48V7Ae0oWy223bp7ibsToQS+he8eFDEq3/Im//GpM1BWx8MPN6bYWZeGEth0fO+ndLG5tb2TnnX3ds/ODyqHJ+0bZQYxlsskpHphtRyKTRvoUDJu7HhVIWSd8LpXe53nrixItKPOIt5oOhYi5FgFHOp7rvuoFL1at4CZJ34BalCgeag8tUfRixRXCOT1Nqe78UYpNSgYJLP3X5ieUzZlI55L6OaKm6DdHHrnFxkypCMIpOVRrJQf0+kVFk7U2HWqShO7KqXi/95vQRHN0EqdJwg12y5aJRIghHJHydDYThDOcsIZUZktxI2oYYyzOLJQ/BXX14n7XrN92r+w1W1cVvEUYYzOIdL8OEaGnAPTWgBgwk8wyu8Ocp5cd6dj2VrySlmTuEPnM8fVHiNGQ==AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0mKoMeiF48V7Ae0oWy223bp7ibsToQS+he8eFDEq3/Im//GpM1BWx8MPN6bYWZeGEth0fO+ndLG5tb2TnnX3ds/ODyqHJ+0bZQYxlsskpHphtRyKTRvoUDJu7HhVIWSd8LpXe53nrixItKPOIt5oOhYi5FgFHOp7rvuoFL1at4CZJ34BalCgeag8tUfRixRXCOT1Nqe78UYpNSgYJLP3X5ieUzZlI55L6OaKm6DdHHrnFxkypCMIpOVRrJQf0+kVFk7U2HWqShO7KqXi/95vQRHN0EqdJwg12y5aJRIghHJHydDYThDOcsIZUZktxI2oYYyzOLJQ/BXX14n7XrN92r+w1W1cVvEUYYzOIdL8OEaGnAPTWgBgwk8wyu8Ocp5cd6dj2VrySlmTuEPnM8fVHiNGQ==AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0mKoMeiF48V7Ae0oWy223bp7ibsToQS+he8eFDEq3/Im//GpM1BWx8MPN6bYWZeGEth0fO+ndLG5tb2TnnX3ds/ODyqHJ+0bZQYxlsskpHphtRyKTRvoUDJu7HhVIWSd8LpXe53nrixItKPOIt5oOhYi5FgFHOp7rvuoFL1at4CZJ34BalCgeag8tUfRixRXCOT1Nqe78UYpNSgYJLP3X5ieUzZlI55L6OaKm6DdHHrnFxkypCMIpOVRrJQf0+kVFk7U2HWqShO7KqXi/95vQRHN0EqdJwg12y5aJRIghHJHydDYThDOcsIZUZktxI2oYYyzOLJQ/BXX14n7XrN92r+w1W1cVvEUYYzOIdL8OEaGnAPTWgBgwk8wyu8Ocp5cd6dj2VrySlmTuEPnM8fVHiNGQ==AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0mKoMeiF48V7Ae0oWy223bp7ibsToQS+he8eFDEq3/Im//GpM1BWx8MPN6bYWZeGEth0fO+ndLG5tb2TnnX3ds/ODyqHJ+0bZQYxlsskpHphtRyKTRvoUDJu7HhVIWSd8LpXe53nrixItKPOIt5oOhYi5FgFHOp7rvuoFL1at4CZJ34BalCgeag8tUfRixRXCOT1Nqe78UYpNSgYJLP3X5ieUzZlI55L6OaKm6DdHHrnFxkypCMIpOVRrJQf0+kVFk7U2HWqShO7KqXi/95vQRHN0EqdJwg12y5aJRIghHJHydDYThDOcsIZUZktxI2oYYyzOLJQ/BXX14n7XrN92r+w1W1cVvEUYYzOIdL8OEaGnAPTWgBgwk8wyu8Ocp5cd6dj2VrySlmTuEPnM8fVHiNGQ==22AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0mKoMeiF48V7Ae0oWy203bp7ibsboQS+he8eFDEq3/Im//GpM1BWx8MPN6bYWZeGAturOd9O6WNza3tnfKuu7d/cHhUOT5pmyjRDFssEpHuhtSg4ApblluB3VgjlaHATji9y/3OE2rDI/VoZzEGko4VH3FGbS7V6647qFS9mrcAWSd+QapQoDmofPWHEUskKssENabne7ENUqotZwLnbj8xGFM2pWPsZVRRiSZIF7fOyUWmDMko0lkpSxbq74mUSmNmMsw6JbUTs+rl4n9eL7GjmyDlKk4sKrZcNEoEsRHJHydDrpFZMcsIZZpntxI2oZoym8WTh+CvvrxO2vWa79X8h6tq47aIowxncA6X4MM1NOAemtACBhN4hld4c6Tz4rw7H8vWklPMnMIfOJ8/Vf6NGg==AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0mKoMeiF48V7Ae0oWy203bp7ibsboQS+he8eFDEq3/Im//GpM1BWx8MPN6bYWZeGAturOd9O6WNza3tnfKuu7d/cHhUOT5pmyjRDFssEpHuhtSg4ApblluB3VgjlaHATji9y/3OE2rDI/VoZzEGko4VH3FGbS7V6647qFS9mrcAWSd+QapQoDmofPWHEUskKssENabne7ENUqotZwLnbj8xGFM2pWPsZVRRiSZIF7fOyUWmDMko0lkpSxbq74mUSmNmMsw6JbUTs+rl4n9eL7GjmyDlKk4sKrZcNEoEsRHJHydDrpFZMcsIZZpntxI2oZoym8WTh+CvvrxO2vWa79X8h6tq47aIowxncA6X4MM1NOAemtACBhN4hld4c6Tz4rw7H8vWklPMnMIfOJ8/Vf6NGg==AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0mKoMeiF48V7Ae0oWy203bp7ibsboQS+he8eFDEq3/Im//GpM1BWx8MPN6bYWZeGAturOd9O6WNza3tnfKuu7d/cHhUOT5pmyjRDFssEpHuhtSg4ApblluB3VgjlaHATji9y/3OE2rDI/VoZzEGko4VH3FGbS7V6647qFS9mrcAWSd+QapQoDmofPWHEUskKssENabne7ENUqotZwLnbj8xGFM2pWPsZVRRiSZIF7fOyUWmDMko0lkpSxbq74mUSmNmMsw6JbUTs+rl4n9eL7GjmyDlKk4sKrZcNEoEsRHJHydDrpFZMcsIZZpntxI2oZoym8WTh+CvvrxO2vWa79X8h6tq47aIowxncA6X4MM1NOAemtACBhN4hld4c6Tz4rw7H8vWklPMnMIfOJ8/Vf6NGg==AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0mKoMeiF48V7Ae0oWy203bp7ibsboQS+he8eFDEq3/Im//GpM1BWx8MPN6bYWZeGAturOd9O6WNza3tnfKuu7d/cHhUOT5pmyjRDFssEpHuhtSg4ApblluB3VgjlaHATji9y/3OE2rDI/VoZzEGko4VH3FGbS7V6647qFS9mrcAWSd+QapQoDmofPWHEUskKssENabne7ENUqotZwLnbj8xGFM2pWPsZVRRiSZIF7fOyUWmDMko0lkpSxbq74mUSmNmMsw6JbUTs+rl4n9eL7GjmyDlKk4sKrZcNEoEsRHJHydDrpFZMcsIZZpntxI2oZoym8WTh+CvvrxO2vWa79X8h6tq47aIowxncA6X4MM1NOAemtACBhN4hld4c6Tz4rw7H8vWklPMnMIfOJ8/Vf6NGg==23AAAB63icbVBNS8NAEJ34WeNX1aOXxSJ4KkkV9Fj04rGC/YA2lM120i7d3YTdjVBK/4IXD4p49Q9589+YtDlo64OBx3szzMwLE8GN9bxvZ219Y3Nru7Tj7u7tHxyWj45bJk41wyaLRaw7ITUouMKm5VZgJ9FIZSiwHY7vcr/9hNrwWD3aSYKBpEPFI86ozaXapev2yxWv6s1BVolfkAoUaPTLX71BzFKJyjJBjen6XmKDKdWWM4Ezt5caTCgb0yF2M6qoRBNM57fOyHmmDEgU66yUJXP198SUSmMmMsw6JbUjs+zl4n9eN7XRTTDlKkktKrZYFKWC2Jjkj5MB18ismGSEMs2zWwkbUU2ZzeLJQ/CXX14lrVrV96r+w1WlflvEUYJTOIML8OEa6nAPDWgCgxE8wyu8OdJ5cd6dj0XrmlPMnMAfOJ8/V4SNGw==AAAB63icbVBNS8NAEJ34WeNX1aOXxSJ4KkkV9Fj04rGC/YA2lM120i7d3YTdjVBK/4IXD4p49Q9589+YtDlo64OBx3szzMwLE8GN9bxvZ219Y3Nru7Tj7u7tHxyWj45bJk41wyaLRaw7ITUouMKm5VZgJ9FIZSiwHY7vcr/9hNrwWD3aSYKBpEPFI86ozaXapev2yxWv6s1BVolfkAoUaPTLX71BzFKJyjJBjen6XmKDKdWWM4Ezt5caTCgb0yF2M6qoRBNM57fOyHmmDEgU66yUJXP198SUSmMmMsw6JbUjs+zl4n9eN7XRTTDlKkktKrZYFKWC2Jjkj5MB18ismGSEMs2zWwkbUU2ZzeLJQ/CXX14lrVrV96r+w1WlflvEUYJTOIML8OEa6nAPDWgCgxE8wyu8OdJ5cd6dj0XrmlPMnMAfOJ8/V4SNGw==AAAB63icbVBNS8NAEJ34WeNX1aOXxSJ4KkkV9Fj04rGC/YA2lM120i7d3YTdjVBK/4IXD4p49Q9589+YtDlo64OBx3szzMwLE8GN9bxvZ219Y3Nru7Tj7u7tHxyWj45bJk41wyaLRaw7ITUouMKm5VZgJ9FIZSiwHY7vcr/9hNrwWD3aSYKBpEPFI86ozaXapev2yxWv6s1BVolfkAoUaPTLX71BzFKJyjJBjen6XmKDKdWWM4Ezt5caTCgb0yF2M6qoRBNM57fOyHmmDEgU66yUJXP198SUSmMmMsw6JbUjs+zl4n9eN7XRTTDlKkktKrZYFKWC2Jjkj5MB18ismGSEMs2zWwkbUU2ZzeLJQ/CXX14lrVrV96r+w1WlflvEUYJTOIML8OEa6nAPDWgCgxE8wyu8OdJ5cd6dj0XrmlPMnMAfOJ8/V4SNGw==AAAB63icbVBNS8NAEJ34WeNX1aOXxSJ4KkkV9Fj04rGC/YA2lM120i7d3YTdjVBK/4IXD4p49Q9589+YtDlo64OBx3szzMwLE8GN9bxvZ219Y3Nru7Tj7u7tHxyWj45bJk41wyaLRaw7ITUouMKm5VZgJ9FIZSiwHY7vcr/9hNrwWD3aSYKBpEPFI86ozaXapev2yxWv6s1BVolfkAoUaPTLX71BzFKJyjJBjen6XmKDKdWWM4Ezt5caTCgb0yF2M6qoRBNM57fOyHmmDEgU66yUJXP198SUSmMmMsw6JbUjs+zl4n9eN7XRTTDlKkktKrZYFKWC2Jjkj5MB18ismGSEMs2zWwkbUU2ZzeLJQ/CXX14lrVrV96r+w1WlflvEUYJTOIML8OEa6nAPDWgCgxE8wyu8OdJ5cd6dj0XrmlPMnMAfOJ8/V4SNGw==24AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0lKQY9FLx4r2FZoQ9lsp+3S3U3Y3Qgl9C948aCIV/+QN/+NSZuDtj4YeLw3w8y8MBbcWM/7dkobm1vbO+Vdd2//4PCocnzSMVGiGbZZJCL9GFKDgitsW24FPsYaqQwFdsPpbe53n1AbHqkHO4sxkHSs+IgzanOp3nDdQaXq1bwFyDrxC1KFAq1B5as/jFgiUVkmqDE934ttkFJtORM4d/uJwZiyKR1jL6OKSjRBurh1Ti4yZUhGkc5KWbJQf0+kVBozk2HWKamdmFUvF//zeokdXQcpV3FiUbHlolEiiI1I/jgZco3MillGKNM8u5WwCdWU2SyePAR/9eV10qnXfK/m3zeqzZsijjKcwTlcgg9X0IQ7aEEbGEzgGV7hzZHOi/PufCxbS04xcwp/4Hz+AFkKjRw=AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0lKQY9FLx4r2FZoQ9lsp+3S3U3Y3Qgl9C948aCIV/+QN/+NSZuDtj4YeLw3w8y8MBbcWM/7dkobm1vbO+Vdd2//4PCocnzSMVGiGbZZJCL9GFKDgitsW24FPsYaqQwFdsPpbe53n1AbHqkHO4sxkHSs+IgzanOp3nDdQaXq1bwFyDrxC1KFAq1B5as/jFgiUVkmqDE934ttkFJtORM4d/uJwZiyKR1jL6OKSjRBurh1Ti4yZUhGkc5KWbJQf0+kVBozk2HWKamdmFUvF//zeokdXQcpV3FiUbHlolEiiI1I/jgZco3MillGKNM8u5WwCdWU2SyePAR/9eV10qnXfK/m3zeqzZsijjKcwTlcgg9X0IQ7aEEbGEzgGV7hzZHOi/PufCxbS04xcwp/4Hz+AFkKjRw=AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0lKQY9FLx4r2FZoQ9lsp+3S3U3Y3Qgl9C948aCIV/+QN/+NSZuDtj4YeLw3w8y8MBbcWM/7dkobm1vbO+Vdd2//4PCocnzSMVGiGbZZJCL9GFKDgitsW24FPsYaqQwFdsPpbe53n1AbHqkHO4sxkHSs+IgzanOp3nDdQaXq1bwFyDrxC1KFAq1B5as/jFgiUVkmqDE934ttkFJtORM4d/uJwZiyKR1jL6OKSjRBurh1Ti4yZUhGkc5KWbJQf0+kVBozk2HWKamdmFUvF//zeokdXQcpV3FiUbHlolEiiI1I/jgZco3MillGKNM8u5WwCdWU2SyePAR/9eV10qnXfK/m3zeqzZsijjKcwTlcgg9X0IQ7aEEbGEzgGV7hzZHOi/PufCxbS04xcwp/4Hz+AFkKjRw=AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0lKQY9FLx4r2FZoQ9lsp+3S3U3Y3Qgl9C948aCIV/+QN/+NSZuDtj4YeLw3w8y8MBbcWM/7dkobm1vbO+Vdd2//4PCocnzSMVGiGbZZJCL9GFKDgitsW24FPsYaqQwFdsPpbe53n1AbHqkHO4sxkHSs+IgzanOp3nDdQaXq1bwFyDrxC1KFAq1B5as/jFgiUVkmqDE934ttkFJtORM4d/uJwZiyKR1jL6OKSjRBurh1Ti4yZUhGkc5KWbJQf0+kVBozk2HWKamdmFUvF//zeokdXQcpV3FiUbHlolEiiI1I/jgZco3MillGKNM8u5WwCdWU2SyePAR/9eV10qnXfK/m3zeqzZsijjKcwTlcgg9X0IQ7aEEbGEzgGV7hzZHOi/PufCxbS04xcwp/4Hz+AFkKjRw=s1,1AAAB8HicbVBNSwMxEJ2tX7V+VT16CRbBg5SNCHosevFYwdZKu5Rsmm1Dk+ySZIWy9Fd48aCIV3+ON/+N2XYP2vpg4PHeDDPzwkRwY33/2yutrK6tb5Q3K1vbO7t71f2DtolTTVmLxiLWnZAYJrhiLcutYJ1EMyJDwR7C8U3uPzwxbXis7u0kYYEkQ8UjTol10qPpZ/gMTyuVfrXm1/0Z0DLBBalBgWa/+tUbxDSVTFkqiDFd7Cc2yIi2nAo2rfRSwxJCx2TIuo4qIpkJstnBU3TilAGKYu1KWTRTf09kRBozkaHrlMSOzKKXi/953dRGV0HGVZJapuh8UZQKZGOUf48GXDNqxcQRQjV3tyI6IppQ6zLKQ8CLLy+T9nkd+3V8d1FrXBdxlOEIjuEUMFxCA26hCS2gIOEZXuHN096L9+59zFtLXjFzCH/gff4AD/uPQA==AAAB8HicbVBNSwMxEJ2tX7V+VT16CRbBg5SNCHosevFYwdZKu5Rsmm1Dk+ySZIWy9Fd48aCIV3+ON/+N2XYP2vpg4PHeDDPzwkRwY33/2yutrK6tb5Q3K1vbO7t71f2DtolTTVmLxiLWnZAYJrhiLcutYJ1EMyJDwR7C8U3uPzwxbXis7u0kYYEkQ8UjTol10qPpZ/gMTyuVfrXm1/0Z0DLBBalBgWa/+tUbxDSVTFkqiDFd7Cc2yIi2nAo2rfRSwxJCx2TIuo4qIpkJstnBU3TilAGKYu1KWTRTf09kRBozkaHrlMSOzKKXi/953dRGV0HGVZJapuh8UZQKZGOUf48GXDNqxcQRQjV3tyI6IppQ6zLKQ8CLLy+T9nkd+3V8d1FrXBdxlOEIjuEUMFxCA26hCS2gIOEZXuHN096L9+59zFtLXjFzCH/gff4AD/uPQA==AAAB8HicbVBNSwMxEJ2tX7V+VT16CRbBg5SNCHosevFYwdZKu5Rsmm1Dk+ySZIWy9Fd48aCIV3+ON/+N2XYP2vpg4PHeDDPzwkRwY33/2yutrK6tb5Q3K1vbO7t71f2DtolTTVmLxiLWnZAYJrhiLcutYJ1EMyJDwR7C8U3uPzwxbXis7u0kYYEkQ8UjTol10qPpZ/gMTyuVfrXm1/0Z0DLBBalBgWa/+tUbxDSVTFkqiDFd7Cc2yIi2nAo2rfRSwxJCx2TIuo4qIpkJstnBU3TilAGKYu1KWTRTf09kRBozkaHrlMSOzKKXi/953dRGV0HGVZJapuh8UZQKZGOUf48GXDNqxcQRQjV3tyI6IppQ6zLKQ8CLLy+T9nkd+3V8d1FrXBdxlOEIjuEUMFxCA26hCS2gIOEZXuHN096L9+59zFtLXjFzCH/gff4AD/uPQA==AAAB8HicbVBNSwMxEJ2tX7V+VT16CRbBg5SNCHosevFYwdZKu5Rsmm1Dk+ySZIWy9Fd48aCIV3+ON/+N2XYP2vpg4PHeDDPzwkRwY33/2yutrK6tb5Q3K1vbO7t71f2DtolTTVmLxiLWnZAYJrhiLcutYJ1EMyJDwR7C8U3uPzwxbXis7u0kYYEkQ8UjTol10qPpZ/gMTyuVfrXm1/0Z0DLBBalBgWa/+tUbxDSVTFkqiDFd7Cc2yIi2nAo2rfRSwxJCx2TIuo4qIpkJstnBU3TilAGKYu1KWTRTf09kRBozkaHrlMSOzKKXi/953dRGV0HGVZJapuh8UZQKZGOUf48GXDNqxcQRQjV3tyI6IppQ6zLKQ8CLLy+T9nkd+3V8d1FrXBdxlOEIjuEUMFxCA26hCS2gIOEZXuHN096L9+59zFtLXjFzCH/gff4AD/uPQA==s1,2AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMv+iPnPdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYKPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMv+iPnPdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYKPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMv+iPnPdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYKPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMv+iPnPdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYKPQQ==s1,3AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5REBT0WvXisYD+kDWWz3bRLdzdhdyOU0F/hxYMiXv053vw3btoctPXBwOO9GWbmhQln2njet1NaWV1b3yhvulvbO7t7lf2Dlo5TRWiTxDxWnRBrypmkTcMMp51EUSxCTtvh+Db3209UaRbLBzNJaCDwULKIEWys9Kj7mX92MXXdfqXq1bwZ0DLxC1KFAo1+5as3iEkqqDSEY627vpeYIMPKMMLp1O2lmiaYjPGQdi2VWFAdZLODp+jEKgMUxcqWNGim/p7IsNB6IkLbKbAZ6UUvF//zuqmJroOMySQ1VJL5oijlyMQo/x4NmKLE8IklmChmb0VkhBUmxmaUh+AvvrxMWuc136v595fV+k0RRxmO4BhOwYcrqMMdNKAJBAQ8wyu8Ocp5cd6dj3lrySlmDuEPnM8fEwmPQg==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5REBT0WvXisYD+kDWWz3bRLdzdhdyOU0F/hxYMiXv053vw3btoctPXBwOO9GWbmhQln2njet1NaWV1b3yhvulvbO7t7lf2Dlo5TRWiTxDxWnRBrypmkTcMMp51EUSxCTtvh+Db3209UaRbLBzNJaCDwULKIEWys9Kj7mX92MXXdfqXq1bwZ0DLxC1KFAo1+5as3iEkqqDSEY627vpeYIMPKMMLp1O2lmiaYjPGQdi2VWFAdZLODp+jEKgMUxcqWNGim/p7IsNB6IkLbKbAZ6UUvF//zuqmJroOMySQ1VJL5oijlyMQo/x4NmKLE8IklmChmb0VkhBUmxmaUh+AvvrxMWuc136v595fV+k0RRxmO4BhOwYcrqMMdNKAJBAQ8wyu8Ocp5cd6dj3lrySlmDuEPnM8fEwmPQg==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5REBT0WvXisYD+kDWWz3bRLdzdhdyOU0F/hxYMiXv053vw3btoctPXBwOO9GWbmhQln2njet1NaWV1b3yhvulvbO7t7lf2Dlo5TRWiTxDxWnRBrypmkTcMMp51EUSxCTtvh+Db3209UaRbLBzNJaCDwULKIEWys9Kj7mX92MXXdfqXq1bwZ0DLxC1KFAo1+5as3iEkqqDSEY627vpeYIMPKMMLp1O2lmiaYjPGQdi2VWFAdZLODp+jEKgMUxcqWNGim/p7IsNB6IkLbKbAZ6UUvF//zuqmJroOMySQ1VJL5oijlyMQo/x4NmKLE8IklmChmb0VkhBUmxmaUh+AvvrxMWuc136v595fV+k0RRxmO4BhOwYcrqMMdNKAJBAQ8wyu8Ocp5cd6dj3lrySlmDuEPnM8fEwmPQg==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5REBT0WvXisYD+kDWWz3bRLdzdhdyOU0F/hxYMiXv053vw3btoctPXBwOO9GWbmhQln2njet1NaWV1b3yhvulvbO7t7lf2Dlo5TRWiTxDxWnRBrypmkTcMMp51EUSxCTtvh+Db3209UaRbLBzNJaCDwULKIEWys9Kj7mX92MXXdfqXq1bwZ0DLxC1KFAo1+5as3iEkqqDSEY627vpeYIMPKMMLp1O2lmiaYjPGQdi2VWFAdZLODp+jEKgMUxcqWNGim/p7IsNB6IkLbKbAZ6UUvF//zuqmJroOMySQ1VJL5oijlyMQo/x4NmKLE8IklmChmb0VkhBUmxmaUh+AvvrxMWuc136v595fV+k0RRxmO4BhOwYcrqMMdNKAJBAQ8wyu8Ocp5cd6dj3lrySlmDuEPnM8fEwmPQg==s2,2AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvpFfea6g0rVq3lzoFXiF6QKBZqDyld/GJNUUGkIx1r3fC8xQYaVYYTTmdtPNU0wmeAR7VkqsaA6yOYHz9CZVYYoipUtadBc/T2RYaH1VIS2U2Az1steLv7n9VITXQcZk0lqqCSLRVHKkYlR/j0aMkWJ4VNLMFHM3orIGCtMjM0oD8FffnmVtOs136v595fVxk0RRxlO4BTOwYcraMAdNKEFBAQ8wyu8Ocp5cd6dj0VrySlmjuEPnM8fEwuPQg==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvpFfea6g0rVq3lzoFXiF6QKBZqDyld/GJNUUGkIx1r3fC8xQYaVYYTTmdtPNU0wmeAR7VkqsaA6yOYHz9CZVYYoipUtadBc/T2RYaH1VIS2U2Az1steLv7n9VITXQcZk0lqqCSLRVHKkYlR/j0aMkWJ4VNLMFHM3orIGCtMjM0oD8FffnmVtOs136v595fVxk0RRxlO4BTOwYcraMAdNKEFBAQ8wyu8Ocp5cd6dj0VrySlmjuEPnM8fEwuPQg==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvpFfea6g0rVq3lzoFXiF6QKBZqDyld/GJNUUGkIx1r3fC8xQYaVYYTTmdtPNU0wmeAR7VkqsaA6yOYHz9CZVYYoipUtadBc/T2RYaH1VIS2U2Az1steLv7n9VITXQcZk0lqqCSLRVHKkYlR/j0aMkWJ4VNLMFHM3orIGCtMjM0oD8FffnmVtOs136v595fVxk0RRxlO4BTOwYcraMAdNKEFBAQ8wyu8Ocp5cd6dj0VrySlmjuEPnM8fEwuPQg==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvpFfea6g0rVq3lzoFXiF6QKBZqDyld/GJNUUGkIx1r3fC8xQYaVYYTTmdtPNU0wmeAR7VkqsaA6yOYHz9CZVYYoipUtadBc/T2RYaH1VIS2U2Az1steLv7n9VITXQcZk0lqqCSLRVHKkYlR/j0aMkWJ4VNLMFHM3orIGCtMjM0oD8FffnmVtOs136v595fVxk0RRxlO4BTOwYcraMAdNKEFBAQ8wyu8Ocp5cd6dj0VrySlmjuEPnM8fEwuPQg==s2,1AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvqFP3PdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYSPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvqFP3PdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYSPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvqFP3PdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYSPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvqFP3PdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYSPQQ==s2,3AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJJUQY9FLx4r2A9pQ9lsN+3S3U3Y3Qgl9Fd48aCIV3+ON/+NmzYHbX0w8Hhvhpl5YcKZNp737aysrq1vbJa23O2d3b398sFhS8epIrRJYh6rTog15UzSpmGG006iKBYhp+1wfJv77SeqNIvlg5kkNBB4KFnECDZWetT9rHZ+MXXdfrniVb0Z0DLxC1KBAo1++as3iEkqqDSEY627vpeYIMPKMMLp1O2lmiaYjPGQdi2VWFAdZLODp+jUKgMUxcqWNGim/p7IsNB6IkLbKbAZ6UUvF//zuqmJroOMySQ1VJL5oijlyMQo/x4NmKLE8IklmChmb0VkhBUmxmaUh+AvvrxMWrWq71X9+8tK/aaIowTHcAJn4MMV1OEOGtAEAgKe4RXeHOW8OO/Ox7x1xSlmjuAPnM8fFJKPQw==AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJJUQY9FLx4r2A9pQ9lsN+3S3U3Y3Qgl9Fd48aCIV3+ON/+NmzYHbX0w8Hhvhpl5YcKZNp737aysrq1vbJa23O2d3b398sFhS8epIrRJYh6rTog15UzSpmGG006iKBYhp+1wfJv77SeqNIvlg5kkNBB4KFnECDZWetT9rHZ+MXXdfrniVb0Z0DLxC1KBAo1++as3iEkqqDSEY627vpeYIMPKMMLp1O2lmiaYjPGQdi2VWFAdZLODp+jUKgMUxcqWNGim/p7IsNB6IkLbKbAZ6UUvF//zuqmJroOMySQ1VJL5oijlyMQo/x4NmKLE8IklmChmb0VkhBUmxmaUh+AvvrxMWrWq71X9+8tK/aaIowTHcAJn4MMV1OEOGtAEAgKe4RXeHOW8OO/Ox7x1xSlmjuAPnM8fFJKPQw==AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJJUQY9FLx4r2A9pQ9lsN+3S3U3Y3Qgl9Fd48aCIV3+ON/+NmzYHbX0w8Hhvhpl5YcKZNp737aysrq1vbJa23O2d3b398sFhS8epIrRJYh6rTog15UzSpmGG006iKBYhp+1wfJv77SeqNIvlg5kkNBB4KFnECDZWetT9rHZ+MXXdfrniVb0Z0DLxC1KBAo1++as3iEkqqDSEY627vpeYIMPKMMLp1O2lmiaYjPGQdi2VWFAdZLODp+jUKgMUxcqWNGim/p7IsNB6IkLbKbAZ6UUvF//zuqmJroOMySQ1VJL5oijlyMQo/x4NmKLE8IklmChmb0VkhBUmxmaUh+AvvrxMWrWq71X9+8tK/aaIowTHcAJn4MMV1OEOGtAEAgKe4RXeHOW8OO/Ox7x1xSlmjuAPnM8fFJKPQw==AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJJUQY9FLx4r2A9pQ9lsN+3S3U3Y3Qgl9Fd48aCIV3+ON/+NmzYHbX0w8Hhvhpl5YcKZNp737aysrq1vbJa23O2d3b398sFhS8epIrRJYh6rTog15UzSpmGG006iKBYhp+1wfJv77SeqNIvlg5kkNBB4KFnECDZWetT9rHZ+MXXdfrniVb0Z0DLxC1KBAo1++as3iEkqqDSEY627vpeYIMPKMMLp1O2lmiaYjPGQdi2VWFAdZLODp+jUKgMUxcqWNGim/p7IsNB6IkLbKbAZ6UUvF//zuqmJroOMySQ1VJL5oijlyMQo/x4NmKLE8IklmChmb0VkhBUmxmaUh+AvvrxMWrWq71X9+8tK/aaIowTHcAJn4MMV1OEOGtAEAgKe4RXeHOW8OO/Ox7x1xSlmjuAPnM8fFJKPQw==[19,20]AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJIUQb0VvXisYD8kDWWz3bRLdzdhdyOU0l/hxYMiXv053vw3btoctPXBwOO9GWbmRSln2njet7Oyura+sVnacrd3dvf2yweHLZ1kitAmSXiiOhHWlDNJm4YZTjupolhEnLaj0W3ut5+o0iyRD2ac0lDggWQxI9hY6THwr89rXui6vXLFq3ozoGXiF6QCBRq98le3n5BMUGkIx1oHvpeacIKVYYTTqdvNNE0xGeEBDSyVWFAdTmYHT9GpVfooTpQtadBM/T0xwULrsYhsp8BmqBe9XPzPCzITX4UTJtPMUEnmi+KMI5Og/HvUZ4oSw8eWYKKYvRWRIVaYGJtRHoK/+PIyadWqvlf17y8q9ZsijhIcwwmcgQ+XUIc7aEATCAh4hld4c5Tz4rw7H/PWFaeYOYI/cD5/AA16jpg=AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJIUQb0VvXisYD8kDWWz3bRLdzdhdyOU0l/hxYMiXv053vw3btoctPXBwOO9GWbmRSln2njet7Oyura+sVnacrd3dvf2yweHLZ1kitAmSXiiOhHWlDNJm4YZTjupolhEnLaj0W3ut5+o0iyRD2ac0lDggWQxI9hY6THwr89rXui6vXLFq3ozoGXiF6QCBRq98le3n5BMUGkIx1oHvpeacIKVYYTTqdvNNE0xGeEBDSyVWFAdTmYHT9GpVfooTpQtadBM/T0xwULrsYhsp8BmqBe9XPzPCzITX4UTJtPMUEnmi+KMI5Og/HvUZ4oSw8eWYKKYvRWRIVaYGJtRHoK/+PIyadWqvlf17y8q9ZsijhIcwwmcgQ+XUIc7aEATCAh4hld4c5Tz4rw7H/PWFaeYOYI/cD5/AA16jpg=AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJIUQb0VvXisYD8kDWWz3bRLdzdhdyOU0l/hxYMiXv053vw3btoctPXBwOO9GWbmRSln2njet7Oyura+sVnacrd3dvf2yweHLZ1kitAmSXiiOhHWlDNJm4YZTjupolhEnLaj0W3ut5+o0iyRD2ac0lDggWQxI9hY6THwr89rXui6vXLFq3ozoGXiF6QCBRq98le3n5BMUGkIx1oHvpeacIKVYYTTqdvNNE0xGeEBDSyVWFAdTmYHT9GpVfooTpQtadBM/T0xwULrsYhsp8BmqBe9XPzPCzITX4UTJtPMUEnmi+KMI5Og/HvUZ4oSw8eWYKKYvRWRIVaYGJtRHoK/+PIyadWqvlf17y8q9ZsijhIcwwmcgQ+XUIc7aEATCAh4hld4c5Tz4rw7H/PWFaeYOYI/cD5/AA16jpg=AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJIUQb0VvXisYD8kDWWz3bRLdzdhdyOU0l/hxYMiXv053vw3btoctPXBwOO9GWbmRSln2njet7Oyura+sVnacrd3dvf2yweHLZ1kitAmSXiiOhHWlDNJm4YZTjupolhEnLaj0W3ut5+o0iyRD2ac0lDggWQxI9hY6THwr89rXui6vXLFq3ozoGXiF6QCBRq98le3n5BMUGkIx1oHvpeacIKVYYTTqdvNNE0xGeEBDSyVWFAdTmYHT9GpVfooTpQtadBM/T0xwULrs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iVr1cvE/z0911AwyKpJUE4GXi6KUOTp28u+dEZUEazYzBGFJza0OniCJsDYZ5SF4qy+vk2695rk1775Rbd0UcZThDM7hEjy4hhbcQRs6gIHDM7zCmyWtF+vd+li2lqxi5hT+wPr8ARIMjps=AAAB8HicbVBNS8NAEJ3Urxq/qh69BIvgQUpSCvZY9OKxgv2QNJTNdtMu3d2E3Y1QQn+FFw+KePXnePPfuGlz0NYHA4/3ZpiZFyaMKu2631ZpY3Nre6e8a+/tHxweVY5PuipOJSYdHLNY9kOkCKOCdDTVjPQTSRAPGemF09vc7z0RqWgsHvQsIQFHY0EjipE20qPvNa/qjcC2h5WqW3MXcNaJV5AqFGgPK1+DUYxTToTGDCnle26igwxJTTEjc3uQKpIgPEVj4hsqECcqyBYHz50Lo4ycKJamhHYW6u+JDHGlZjw0nRzpiVr1cvE/z0911AwyKpJUE4GXi6KUOTp28u+dEZUEazYzBGFJza0OniCJsDYZ5SF4qy+vk2695rk1775Rbd0UcZThDM7hEjy4hhbcQRs6gIHDM7zCmyWtF+vd+li2lqxi5hT+wPr8ARIMjps=15AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0WPRi8eK1hbaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmlldW19o7xZ2dre2d2r7h88mjjVjLdYLGPdCajhUijeQoGSdxLNaRRI3g7GN7nffuLaiFg94CThfkSHSoSCUbTSvXdR6Vdrbt2dgSwTryA1KNDsV796g5ilEVfIJDWm67kJ+hnVKJjk00ovNTyhbEyHvGupohE3fjY7dUpOrDIgYaxtKSQz9fdERiNjJlFgOyOKI7Po5eJ/XjfF8MrPhEpS5IrNF4WpJBiT/G8yEJozlBNLKNPC3krYiGrK0KaTh+AtvrxMHs/qnlv37s5rjesijjIcwTGcggeX0IBbaEILGAzhGV7hzZHOi/PufMxbS04xcwh/4Hz+ACSJjQg=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0WPRi8eK1hbaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmlldW19o7xZ2dre2d2r7h88mjjVjLdYLGPdCajhUijeQoGSdxLNaRRI3g7GN7nffuLaiFg94CThfkSHSoSCUbTSvXdR6Vdrbt2dgSwTryA1KNDsV796g5ilEVfIJDWm67kJ+hnVKJjk00ovNTyhbEyHvGupohE3fjY7dUpOrDIgYaxtKSQz9fdERiNjJlFgOyOKI7Po5eJ/XjfF8MrPhEpS5IrNF4WpJBiT/G8yEJozlBNLKNPC3krYiGrK0KaTh+AtvrxMHs/qnlv37s5rjesijjIcwTGcggeX0IBbaEILGAzhGV7hzZHOi/PufMxbS04xcwh/4Hz+ACSJjQg=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0WPRi8eK1hbaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmlldW19o7xZ2dre2d2r7h88mjjVjLdYLGPdCajhUijeQoGSdxLNaRRI3g7GN7nffuLaiFg94CThfkSHSoSCUbTSvXdR6Vdrbt2dgSwTryA1KNDsV796g5ilEVfIJDWm67kJ+hnVKJjk00ovNTyhbEyHvGupohE3fjY7dUpOrDIgYaxtKSQz9fdERiNjJlFgOyOKI7Po5eJ/XjfF8MrPhEpS5IrNF4WpJBiT/G8yEJozlBNLKNPC3krYiGrK0KaTh+AtvrxMHs/qnlv37s5rjesijjIcwTGcggeX0IBbaEILGAzhGV7hzZHOi/PufMxbS04xcwh/4Hz+ACSJjQg=AAAB6nicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0WPRi8eK1hbaUDbbTbt0swm7E6GE/gQvHhTx6i/y5r9x0+agrQ8GHu/NMDMvSKQw6LrfTmlldW19o7xZ2dre2d2r7h88mjjVjLdYLGPdCajhUijeQoGSdxLNaRRI3g7GN7nffuLaiFg94CThfkSHSoSCUbTSvXdR6Vdrbt2dgSwTryA1KNDsV796g5ilEVfIJDWm67kJ+hnVKJjk00ovNTyhbEyHvGupohE3fjY7dUpOrDIgYaxtKSQz9fdERiNjJlFgOyOKI7Po5eJ/XjfF8MrPhEpS5IrNF4WpJBiT/G8yEJozlBNLKNPC3krYiGrK0KaTh+AtvrxMHs/qnlv37s5rjesijjIcwTGcggeX0IBbaEILGAzhGV7hzZHOi/PufMxbS04xcwh/4Hz+ACSJjQg=21AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0mKoMeiF48V7Ae0oWy223bp7ibsToQS+he8eFDEq3/Im//GpM1BWx8MPN6bYWZeGEth0fO+ndLG5tb2TnnX3ds/ODyqHJ+0bZQYxlsskpHphtRyKTRvoUDJu7HhVIWSd8LpXe53nrixItKPOIt5oOhYi5FgFHOp7rvuoFL1at4CZJ34BalCgeag8tUfRixRXCOT1Nqe78UYpNSgYJLP3X5ieUzZlI55L6OaKm6DdHHrnFxkypCMIpOVRrJQf0+kVFk7U2HWqShO7KqXi/95vQRHN0EqdJwg12y5aJRIghHJHydDYThDOcsIZUZktxI2oYYyzOLJQ/BXX14n7XrN92r+w1W1cVvEUYYzOIdL8OEaGnAPTWgBgwk8wyu8Ocp5cd6dj2VrySlmTuEPnM8fVHiNGQ==AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0mKoMeiF48V7Ae0oWy223bp7ibsToQS+he8eFDEq3/Im//GpM1BWx8MPN6bYWZeGEth0fO+ndLG5tb2TnnX3ds/ODyqHJ+0bZQYxlsskpHphtRyKTRvoUDJu7HhVIWSd8LpXe53nrixItKPOIt5oOhYi5FgFHOp7rvuoFL1at4CZJ34BalCgeag8tUfRixRXCOT1Nqe78UYpNSgYJLP3X5ieUzZlI55L6OaKm6DdHHrnFxkypCMIpOVRrJQf0+kVFk7U2HWqShO7KqXi/95vQRHN0EqdJwg12y5aJRIghHJHydDYThDOcsIZUZktxI2oYYyzOLJQ/BXX14n7XrN92r+w1W1cVvEUYYzOIdL8OEaGnAPTWgBgwk8wyu8Ocp5cd6dj2VrySlmTuEPnM8fVHiNGQ==AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0mKoMeiF48V7Ae0oWy223bp7ibsToQS+he8eFDEq3/Im//GpM1BWx8MPN6bYWZeGEth0fO+ndLG5tb2TnnX3ds/ODyqHJ+0bZQYxlsskpHphtRyKTRvoUDJu7HhVIWSd8LpXe53nrixItKPOIt5oOhYi5FgFHOp7rvuoFL1at4CZJ34BalCgeag8tUfRixRXCOT1Nqe78UYpNSgYJLP3X5ieUzZlI55L6OaKm6DdHHrnFxkypCMIpOVRrJQf0+kVFk7U2HWqShO7KqXi/95vQRHN0EqdJwg12y5aJRIghHJHydDYThDOcsIZUZktxI2oYYyzOLJQ/BXX14n7XrN92r+w1W1cVvEUYYzOIdL8OEaGnAPTWgBgwk8wyu8Ocp5cd6dj2VrySlmTuEPnM8fVHiNGQ==AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0mKoMeiF48V7Ae0oWy223bp7ibsToQS+he8eFDEq3/Im//GpM1BWx8MPN6bYWZeGEth0fO+ndLG5tb2TnnX3ds/ODyqHJ+0bZQYxlsskpHphtRyKTRvoUDJu7HhVIWSd8LpXe53nrixItKPOIt5oOhYi5FgFHOp7rvuoFL1at4CZJ34BalCgeag8tUfRixRXCOT1Nqe78UYpNSgYJLP3X5ieUzZlI55L6OaKm6DdHHrnFxkypCMIpOVRrJQf0+kVFk7U2HWqShO7KqXi/95vQRHN0EqdJwg12y5aJRIghHJHydDYThDOcsIZUZktxI2oYYyzOLJQ/BXX14n7XrN92r+w1W1cVvEUYYzOIdL8OEaGnAPTWgBgwk8wyu8Ocp5cd6dj2VrySlmTuEPnM8fVHiNGQ==24AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0lKQY9FLx4r2FZoQ9lsp+3S3U3Y3Qgl9C948aCIV/+QN/+NSZuDtj4YeLw3w8y8MBbcWM/7dkobm1vbO+Vdd2//4PCocnzSMVGiGbZZJCL9GFKDgitsW24FPsYaqQwFdsPpbe53n1AbHqkHO4sxkHSs+IgzanOp3nDdQaXq1bwFyDrxC1KFAq1B5as/jFgiUVkmqDE934ttkFJtORM4d/uJwZiyKR1jL6OKSjRBurh1Ti4yZUhGkc5KWbJQf0+kVBozk2HWKamdmFUvF//zeokdXQcpV3FiUbHlolEiiI1I/jgZco3MillGKNM8u5WwCdWU2SyePAR/9eV10qnXfK/m3zeqzZsijjKcwTlcgg9X0IQ7aEEbGEzgGV7hzZHOi/PufCxbS04xcwp/4Hz+AFkKjRw=AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0lKQY9FLx4r2FZoQ9lsp+3S3U3Y3Qgl9C948aCIV/+QN/+NSZuDtj4YeLw3w8y8MBbcWM/7dkobm1vbO+Vdd2//4PCocnzSMVGiGbZZJCL9GFKDgitsW24FPsYaqQwFdsPpbe53n1AbHqkHO4sxkHSs+IgzanOp3nDdQaXq1bwFyDrxC1KFAq1B5as/jFgiUVkmqDE934ttkFJtORM4d/uJwZiyKR1jL6OKSjRBurh1Ti4yZUhGkc5KWbJQf0+kVBozk2HWKamdmFUvF//zeokdXQcpV3FiUbHlolEiiI1I/jgZco3MillGKNM8u5WwCdWU2SyePAR/9eV10qnXfK/m3zeqzZsijjKcwTlcgg9X0IQ7aEEbGEzgGV7hzZHOi/PufCxbS04xcwp/4Hz+AFkKjRw=AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0lKQY9FLx4r2FZoQ9lsp+3S3U3Y3Qgl9C948aCIV/+QN/+NSZuDtj4YeLw3w8y8MBbcWM/7dkobm1vbO+Vdd2//4PCocnzSMVGiGbZZJCL9GFKDgitsW24FPsYaqQwFdsPpbe53n1AbHqkHO4sxkHSs+IgzanOp3nDdQaXq1bwFyDrxC1KFAq1B5as/jFgiUVkmqDE934ttkFJtORM4d/uJwZiyKR1jL6OKSjRBurh1Ti4yZUhGkc5KWbJQf0+kVBozk2HWKamdmFUvF//zeokdXQcpV3FiUbHlolEiiI1I/jgZco3MillGKNM8u5WwCdWU2SyePAR/9eV10qnXfK/m3zeqzZsijjKcwTlcgg9X0IQ7aEEbGEzgGV7hzZHOi/PufCxbS04xcwp/4Hz+AFkKjRw=AAAB63icbVBNS8NAEJ3Urxq/qh69LBbBU0lKQY9FLx4r2FZoQ9lsp+3S3U3Y3Qgl9C948aCIV/+QN/+NSZuDtj4YeLw3w8y8MBbcWM/7dkobm1vbO+Vdd2//4PCocnzSMVGiGbZZJCL9GFKDgitsW24FPsYaqQwFdsPpbe53n1AbHqkHO4sxkHSs+IgzanOp3nDdQaXq1bwFyDrxC1KFAq1B5as/jFgiUVkmqDE934ttkFJtORM4d/uJwZiyKR1jL6OKSjRBurh1Ti4yZUhGkc5KWbJQf0+kVBozk2HWKamdmFUvF//zeokdXQcpV3FiUbHlolEiiI1I/jgZco3MillGKNM8u5WwCdWU2SyePAR/9eV10qnXfK/m3zeqzZsijjKcwTlcgg9X0IQ7aEEbGEzgGV7hzZHOi/PufCxbS04xcwp/4Hz+AFkKjRw=s1,1AAAB8HicbVBNSwMxEJ2tX7V+VT16CRbBg5SNCHosevFYwdZKu5Rsmm1Dk+ySZIWy9Fd48aCIV3+ON/+N2XYP2vpg4PHeDDPzwkRwY33/2yutrK6tb5Q3K1vbO7t71f2DtolTTVmLxiLWnZAYJrhiLcutYJ1EMyJDwR7C8U3uPzwxbXis7u0kYYEkQ8UjTol10qPpZ/gMTyuVfrXm1/0Z0DLBBalBgWa/+tUbxDSVTFkqiDFd7Cc2yIi2nAo2rfRSwxJCx2TIuo4qIpkJstnBU3TilAGKYu1KWTRTf09kRBozkaHrlMSOzKKXi/953dRGV0HGVZJapuh8UZQKZGOUf48GXDNqxcQRQjV3tyI6IppQ6zLKQ8CLLy+T9nkd+3V8d1FrXBdxlOEIjuEUMFxCA26hCS2gIOEZXuHN096L9+59zFtLXjFzCH/gff4AD/uPQA==AAAB8HicbVBNSwMxEJ2tX7V+VT16CRbBg5SNCHosevFYwdZKu5Rsmm1Dk+ySZIWy9Fd48aCIV3+ON/+N2XYP2vpg4PHeDDPzwkRwY33/2yutrK6tb5Q3K1vbO7t71f2DtolTTVmLxiLWnZAYJrhiLcutYJ1EMyJDwR7C8U3uPzwxbXis7u0kYYEkQ8UjTol10qPpZ/gMTyuVfrXm1/0Z0DLBBalBgWa/+tUbxDSVTFkqiDFd7Cc2yIi2nAo2rfRSwxJCx2TIuo4qIpkJstnBU3TilAGKYu1KWTRTf09kRBozkaHrlMSOzKKXi/953dRGV0HGVZJapuh8UZQKZGOUf48GXDNqxcQRQjV3tyI6IppQ6zLKQ8CLLy+T9nkd+3V8d1FrXBdxlOEIjuEUMFxCA26hCS2gIOEZXuHN096L9+59zFtLXjFzCH/gff4AD/uPQA==AAAB8HicbVBNSwMxEJ2tX7V+VT16CRbBg5SNCHosevFYwdZKu5Rsmm1Dk+ySZIWy9Fd48aCIV3+ON/+N2XYP2vpg4PHeDDPzwkRwY33/2yutrK6tb5Q3K1vbO7t71f2DtolTTVmLxiLWnZAYJrhiLcutYJ1EMyJDwR7C8U3uPzwxbXis7u0kYYEkQ8UjTol10qPpZ/gMTyuVfrXm1/0Z0DLBBalBgWa/+tUbxDSVTFkqiDFd7Cc2yIi2nAo2rfRSwxJCx2TIuo4qIpkJstnBU3TilAGKYu1KWTRTf09kRBozkaHrlMSOzKKXi/953dRGV0HGVZJapuh8UZQKZGOUf48GXDNqxcQRQjV3tyI6IppQ6zLKQ8CLLy+T9nkd+3V8d1FrXBdxlOEIjuEUMFxCA26hCS2gIOEZXuHN096L9+59zFtLXjFzCH/gff4AD/uPQA==AAAB8HicbVBNSwMxEJ2tX7V+VT16CRbBg5SNCHosevFYwdZKu5Rsmm1Dk+ySZIWy9Fd48aCIV3+ON/+N2XYP2vpg4PHeDDPzwkRwY33/2yutrK6tb5Q3K1vbO7t71f2DtolTTVmLxiLWnZAYJrhiLcutYJ1EMyJDwR7C8U3uPzwxbXis7u0kYYEkQ8UjTol10qPpZ/gMTyuVfrXm1/0Z0DLBBalBgWa/+tUbxDSVTFkqiDFd7Cc2yIi2nAo2rfRSwxJCx2TIuo4qIpkJstnBU3TilAGKYu1KWTRTf09kRBozkaHrlMSOzKKXi/953dRGV0HGVZJapuh8UZQKZGOUf48GXDNqxcQRQjV3tyI6IppQ6zLKQ8CLLy+T9nkd+3V8d1FrXBdxlOEIjuEUMFxCA26hCS2gIOEZXuHN096L9+59zFtLXjFzCH/gff4AD/uPQA==s1,2AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMv+iPnPdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYKPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMv+iPnPdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYKPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMv+iPnPdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYKPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPMv+iPnPdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYKPQQ==s1,3AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5REBT0WvXisYD+kDWWz3bRLdzdhdyOU0F/hxYMiXv053vw3btoctPXBwOO9GWbmhQln2njet1NaWV1b3yhvulvbO7t7lf2Dlo5TRWiTxDxWnRBrypmkTcMMp51EUSxCTtvh+Db3209UaRbLBzNJaCDwULKIEWys9Kj7mX92MXXdfqXq1bwZ0DLxC1KFAo1+5as3iEkqqDSEY627vpeYIMPKMMLp1O2lmiaYjPGQdi2VWFAdZLODp+jEKgMUxcqWNGim/p7IsNB6IkLbKbAZ6UUvF//zuqmJroOMySQ1VJL5oijlyMQo/x4NmKLE8IklmChmb0VkhBUmxmaUh+AvvrxMWuc136v595fV+k0RRxmO4BhOwYcrqMMdNKAJBAQ8wyu8Ocp5cd6dj3lrySlmDuEPnM8fEwmPQg==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5REBT0WvXisYD+kDWWz3bRLdzdhdyOU0F/hxYMiXv053vw3btoctPXBwOO9GWbmhQln2njet1NaWV1b3yhvulvbO7t7lf2Dlo5TRWiTxDxWnRBrypmkTcMMp51EUSxCTtvh+Db3209UaRbLBzNJaCDwULKIEWys9Kj7mX92MXXdfqXq1bwZ0DLxC1KFAo1+5as3iEkqqDSEY627vpeYIMPKMMLp1O2lmiaYjPGQdi2VWFAdZLODp+jEKgMUxcqWNGim/p7IsNB6IkLbKbAZ6UUvF//zuqmJroOMySQ1VJL5oijlyMQo/x4NmKLE8IklmChmb0VkhBUmxmaUh+AvvrxMWuc136v595fV+k0RRxmO4BhOwYcrqMMdNKAJBAQ8wyu8Ocp5cd6dj3lrySlmDuEPnM8fEwmPQg==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5REBT0WvXisYD+kDWWz3bRLdzdhdyOU0F/hxYMiXv053vw3btoctPXBwOO9GWbmhQln2njet1NaWV1b3yhvulvbO7t7lf2Dlo5TRWiTxDxWnRBrypmkTcMMp51EUSxCTtvh+Db3209UaRbLBzNJaCDwULKIEWys9Kj7mX92MXXdfqXq1bwZ0DLxC1KFAo1+5as3iEkqqDSEY627vpeYIMPKMMLp1O2lmiaYjPGQdi2VWFAdZLODp+jEKgMUxcqWNGim/p7IsNB6IkLbKbAZ6UUvF//zuqmJroOMySQ1VJL5oijlyMQo/x4NmKLE8IklmChmb0VkhBUmxmaUh+AvvrxMWuc136v595fV+k0RRxmO4BhOwYcrqMMdNKAJBAQ8wyu8Ocp5cd6dj3lrySlmDuEPnM8fEwmPQg==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5REBT0WvXisYD+kDWWz3bRLdzdhdyOU0F/hxYMiXv053vw3btoctPXBwOO9GWbmhQln2njet1NaWV1b3yhvulvbO7t7lf2Dlo5TRWiTxDxWnRBrypmkTcMMp51EUSxCTtvh+Db3209UaRbLBzNJaCDwULKIEWys9Kj7mX92MXXdfqXq1bwZ0DLxC1KFAo1+5as3iEkqqDSEY627vpeYIMPKMMLp1O2lmiaYjPGQdi2VWFAdZLODp+jEKgMUxcqWNGim/p7IsNB6IkLbKbAZ6UUvF//zuqmJroOMySQ1VJL5oijlyMQo/x4NmKLE8IklmChmb0VkhBUmxmaUh+AvvrxMWuc136v595fV+k0RRxmO4BhOwYcrqMMdNKAJBAQ8wyu8Ocp5cd6dj3lrySlmDuEPnM8fEwmPQg==s2,2AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvpFfea6g0rVq3lzoFXiF6QKBZqDyld/GJNUUGkIx1r3fC8xQYaVYYTTmdtPNU0wmeAR7VkqsaA6yOYHz9CZVYYoipUtadBc/T2RYaH1VIS2U2Az1steLv7n9VITXQcZk0lqqCSLRVHKkYlR/j0aMkWJ4VNLMFHM3orIGCtMjM0oD8FffnmVtOs136v595fVxk0RRxlO4BTOwYcraMAdNKEFBAQ8wyu8Ocp5cd6dj0VrySlmjuEPnM8fEwuPQg==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvpFfea6g0rVq3lzoFXiF6QKBZqDyld/GJNUUGkIx1r3fC8xQYaVYYTTmdtPNU0wmeAR7VkqsaA6yOYHz9CZVYYoipUtadBc/T2RYaH1VIS2U2Az1steLv7n9VITXQcZk0lqqCSLRVHKkYlR/j0aMkWJ4VNLMFHM3orIGCtMjM0oD8FffnmVtOs136v595fVxk0RRxlO4BTOwYcraMAdNKEFBAQ8wyu8Ocp5cd6dj0VrySlmjuEPnM8fEwuPQg==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvpFfea6g0rVq3lzoFXiF6QKBZqDyld/GJNUUGkIx1r3fC8xQYaVYYTTmdtPNU0wmeAR7VkqsaA6yOYHz9CZVYYoipUtadBc/T2RYaH1VIS2U2Az1steLv7n9VITXQcZk0lqqCSLRVHKkYlR/j0aMkWJ4VNLMFHM3orIGCtMjM0oD8FffnmVtOs136v595fVxk0RRxlO4BTOwYcraMAdNKEFBAQ8wyu8Ocp5cd6dj0VrySlmjuEPnM8fEwuPQg==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvpFfea6g0rVq3lzoFXiF6QKBZqDyld/GJNUUGkIx1r3fC8xQYaVYYTTmdtPNU0wmeAR7VkqsaA6yOYHz9CZVYYoipUtadBc/T2RYaH1VIS2U2Az1steLv7n9VITXQcZk0lqqCSLRVHKkYlR/j0aMkWJ4VNLMFHM3orIGCtMjM0oD8FffnmVtOs136v595fVxk0RRxlO4BTOwYcraMAdNKEFBAQ8wyu8Ocp5cd6dj0VrySlmjuEPnM8fEwuPQg==s2,1AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvqFP3PdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYSPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvqFP3PdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYSPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvqFP3PdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYSPQQ==AAAB8HicbVBNS8NAEJ3Urxq/qh69LBbBg5SkCHosevFYwX5IG8pmu2mX7m7C7kYoob/CiwdFvPpzvPlv3LQ5aOuDgcd7M8zMCxPOtPG8b6e0tr6xuVXednd29/YPKodHbR2nitAWiXmsuiHWlDNJW4YZTruJoliEnHbCyW3ud56o0iyWD2aa0EDgkWQRI9hY6VEPsvqFP3PdQaXq1bw50CrxC1KFAs1B5as/jEkqqDSEY617vpeYIMPKMMLpzO2nmiaYTPCI9iyVWFAdZPODZ+jMKkMUxcqWNGiu/p7IsNB6KkLbKbAZ62UvF//zeqmJroOMySQ1VJLFoijlyMQo/x4NmaLE8KklmChmb0VkjBUmxmaUh+Avv7xK2vWa79X8+8tq46aIowwncArn4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6K15BQzx/AHzucPEYSPQQ==s2,3AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJJUQY9FLx4r2A9pQ9lsN+3S3U3Y3Qgl9Fd48aCIV3+ON/+NmzYHbX0w8Hhvhpl5YcKZNp737aysrq1vbJa23O2d3b398sFhS8epIrRJYh6rTog15UzSpmGG006iKBYhp+1wfJv77SeqNIvlg5kkNBB4KFnECDZWetT9rHZ+MXXdfrniVb0Z0DLxC1KBAo1++as3iEkqqDSEY627vpeYIMPKMMLp1O2lmiaYjPGQdi2VWFAdZLODp+jUKgMUxcqWNGim/p7IsNB6IkLbKbAZ6UUvF//zuqmJroOMySQ1VJL5oijlyMQo/x4NmKLE8IklmChmb0VkhBUmxmaUh+AvvrxMWrWq71X9+8tK/aaIowTHcAJn4MMV1OEOGtAEAgKe4RXeHOW8OO/Ox7x1xSlmjuAPnM8fFJKPQw==AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJJUQY9FLx4r2A9pQ9lsN+3S3U3Y3Qgl9Fd48aCIV3+ON/+NmzYHbX0w8Hhvhpl5YcKZNp737aysrq1vbJa23O2d3b398sFhS8epIrRJYh6rTog15UzSpmGG006iKBYhp+1wfJv77SeqNIvlg5kkNBB4KFnECDZWetT9rHZ+MXXdfrniVb0Z0DLxC1KBAo1++as3iEkqqDSEY627vpeYIMPKMMLp1O2lmiaYjPGQdi2VWFAdZLODp+jUKgMUxcqWNGim/p7IsNB6IkLbKbAZ6UUvF//zuqmJroOMySQ1VJL5oijlyMQo/x4NmKLE8IklmChmb0VkhBUmxmaUh+AvvrxMWrWq71X9+8tK/aaIowTHcAJn4MMV1OEOGtAEAgKe4RXeHOW8OO/Ox7x1xSlmjuAPnM8fFJKPQw==AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJJUQY9FLx4r2A9pQ9lsN+3S3U3Y3Qgl9Fd48aCIV3+ON/+NmzYHbX0w8Hhvhpl5YcKZNp737aysrq1vbJa23O2d3b398sFhS8epIrRJYh6rTog15UzSpmGG006iKBYhp+1wfJv77SeqNIvlg5kkNBB4KFnECDZWetT9rHZ+MXXdfrniVb0Z0DLxC1KBAo1++as3iEkqqDSEY627vpeYIMPKMMLp1O2lmiaYjPGQdi2VWFAdZLODp+jUKgMUxcqWNGim/p7IsNB6IkLbKbAZ6UUvF//zuqmJroOMySQ1VJL5oijlyMQo/x4NmKLE8IklmChmb0VkhBUmxmaUh+AvvrxMWrWq71X9+8tK/aaIowTHcAJn4MMV1OEOGtAEAgKe4RXeHOW8OO/Ox7x1xSlmjuAPnM8fFJKPQw==AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJJUQY9FLx4r2A9pQ9lsN+3S3U3Y3Qgl9Fd48aCIV3+ON/+NmzYHbX0w8Hhvhpl5YcKZNp737aysrq1vbJa23O2d3b398sFhS8epIrRJYh6rTog15UzSpmGG006iKBYhp+1wfJv77SeqNIvlg5kkNBB4KFnECDZWetT9rHZ+MXXdfrniVb0Z0DLxC1KBAo1++as3iEkqqDSEY627vpeYIMPKMMLp1O2lmiaYjPGQdi2VWFAdZLODp+jUKgMUxcqWNGim/p7IsNB6IkLbKbAZ6UUvF//zuqmJroOMySQ1VJL5oijlyMQo/x4NmKLE8IklmChmb0VkhBUmxmaUh+AvvrxMWrWq71X9+8tK/aaIowTHcAJn4MMV1OEOGtAEAgKe4RXeHOW8OO/Ox7x1xSlmjuAPnM8fFJKPQw==[19,20]AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJIUQb0VvXisYD8kDWWz3bRLdzdhdyOU0l/hxYMiXv053vw3btoctPXBwOO9GWbmRSln2njet7Oyura+sVnacrd3dvf2yweHLZ1kitAmSXiiOhHWlDNJm4YZTjupolhEnLaj0W3ut5+o0iyRD2ac0lDggWQxI9hY6THwr89rXui6vXLFq3ozoGXiF6QCBRq98le3n5BMUGkIx1oHvpeacIKVYYTTqdvNNE0xGeEBDSyVWFAdTmYHT9GpVfooTpQtadBM/T0xwULrsYhsp8BmqBe9XPzPCzITX4UTJtPMUEnmi+KMI5Og/HvUZ4oSw8eWYKKYvRWRIVaYGJtRHoK/+PIyadWqvlf17y8q9ZsijhIcwwmcgQ+XUIc7aEATCAh4hld4c5Tz4rw7H/PWFaeYOYI/cD5/AA16jpg=AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJIUQb0VvXisYD8kDWWz3bRLdzdhdyOU0l/hxYMiXv053vw3btoctPXBwOO9GWbmRSln2njet7Oyura+sVnacrd3dvf2yweHLZ1kitAmSXiiOhHWlDNJm4YZTjupolhEnLaj0W3ut5+o0iyRD2ac0lDggWQxI9hY6THwr89rXui6vXLFq3ozoGXiF6QCBRq98le3n5BMUGkIx1oHvpeacIKVYYTTqdvNNE0xGeEBDSyVWFAdTmYHT9GpVfooTpQtadBM/T0xwULrsYhsp8BmqBe9XPzPCzITX4UTJtPMUEnmi+KMI5Og/HvUZ4oSw8eWYKKYvRWRIVaYGJtRHoK/+PIyadWqvlf17y8q9ZsijhIcwwmcgQ+XUIc7aEATCAh4hld4c5Tz4rw7H/PWFaeYOYI/cD5/AA16jpg=AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJIUQb0VvXisYD8kDWWz3bRLdzdhdyOU0l/hxYMiXv053vw3btoctPXBwOO9GWbmRSln2njet7Oyura+sVnacrd3dvf2yweHLZ1kitAmSXiiOhHWlDNJm4YZTjupolhEnLaj0W3ut5+o0iyRD2ac0lDggWQxI9hY6THwr89rXui6vXLFq3ozoGXiF6QCBRq98le3n5BMUGkIx1oHvpeacIKVYYTTqdvNNE0xGeEBDSyVWFAdTmYHT9GpVfooTpQtadBM/T0xwULrsYhsp8BmqBe9XPzPCzITX4UTJtPMUEnmi+KMI5Og/HvUZ4oSw8eWYKKYvRWRIVaYGJtRHoK/+PIyadWqvlf17y8q9ZsijhIcwwmcgQ+XUIc7aEATCAh4hld4c5Tz4rw7H/PWFaeYOYI/cD5/AA16jpg=AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJIUQb0VvXisYD8kDWWz3bRLdzdhdyOU0l/hxYMiXv053vw3btoctPXBwOO9GWbmRSln2njet7Oyura+sVnacrd3dvf2yweHLZ1kitAmSXiiOhHWlDNJm4YZTjupolhEnLaj0W3ut5+o0iyRD2ac0lDggWQxI9hY6THwr89rXui6vXLFq3ozoGXiF6QCBRq98le3n5BMUGkIx1oHvpeacIKVYYTTqdvNNE0xGeEBDSyVWFAdTmYHT9GpVfooTpQtadBM/T0xwULrsYhsp8BmqBe9XPzPCzITX4UTJtPMUEnmi+KMI5Og/HvUZ4oSw8eWYKKYvRWRIVaYGJtRHoK/+PIyadWqvlf17y8q9ZsijhIcwwmcgQ+XUIc7aEATCAh4hld4c5Tz4rw7H/PWFaeYOYI/cD5/AA16jpg=[22,23]AAAB8HicbVBNS8NAEJ34WeNX1aOXYBE8SEmioMeiF48V7IekoWy2m3bp7ibsboQS+iu8eFDEqz/Hm//GTZuDtj4YeLw3w8y8KGVUadf9tlZW19Y3Nitb9vbO7t5+9eCwrZJMYtLCCUtkN0KKMCpIS1PNSDeVBPGIkU40vi38zhORiibiQU9SEnI0FDSmGGkjPQa+f+5fhLbdr9bcujuDs0y8ktSgRLNf/eoNEpxxIjRmSKnAc1Md5khqihmZ2r1MkRThMRqSwFCBOFFhPjt46pwaZeDEiTQltDNTf0/kiCs14ZHp5EiP1KJXiP95Qabj6zCnIs00EXi+KM6YoxOn+N4ZUEmwZhNDEJbU3OrgEZIIa5NREYK3+PIyaft1z61795e1xk0ZRwWO4QTOwIMraMAdNKEFGDg8wyu8WdJ6sd6tj3nrilXOHMEfWJ8/CNSOlQ==AAAB8HicbVBNS8NAEJ34WeNX1aOXYBE8SEmioMeiF48V7IekoWy2m3bp7ibsboQS+iu8eFDEqz/Hm//GTZuDtj4YeLw3w8y8KGVUadf9tlZW19Y3Nitb9vbO7t5+9eCwrZJMYtLCCUtkN0KKMCpIS1PNSDeVBPGIkU40vi38zhORiibiQU9SEnI0FDSmGGkjPQa+f+5fhLbdr9bcujuDs0y8ktSgRLNf/eoNEpxxIjRmSKnAc1Md5khqihmZ2r1MkRThMRqSwFCBOFFhPjt46pwaZeDEiTQltDNTf0/kiCs14ZHp5EiP1KJXiP95Qabj6zCnIs00EXi+KM6YoxOn+N4ZUEmwZhNDEJbU3OrgEZIIa5NREYK3+PIyaft1z61795e1xk0ZRwWO4QTOwIMraMAdNKEFGDg8wyu8WdJ6sd6tj3nrilXOHMEfWJ8/CNSOlQ==AAAB8HicbVBNS8NAEJ34WeNX1aOXYBE8SEmioMeiF48V7IekoWy2m3bp7ibsboQS+iu8eFDEqz/Hm//GTZuDtj4YeLw3w8y8KGVUadf9tlZW19Y3Nitb9vbO7t5+9eCwrZJMYtLCCUtkN0KKMCpIS1PNSDeVBPGIkU40vi38zhORiibiQU9SEnI0FDSmGGkjPQa+f+5fhLbdr9bcujuDs0y8ktSgRLNf/eoNEpxxIjRmSKnAc1Md5khqihmZ2r1MkRThMRqSwFCBOFFhPjt46pwaZeDEiTQltDNTf0/kiCs14ZHp5EiP1KJXiP95Qabj6zCnIs00EXi+KM6YoxOn+N4ZUEmwZhNDEJbU3OrgEZIIa5NREYK3+PIyaft1z61795e1xk0ZRwWO4QTOwIMraMAdNKEFGDg8wyu8WdJ6sd6tj3nrilXOHMEfWJ8/CNSOlQ==AAAB8HicbVBNS8NAEJ34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XxSJ4kJKUgh6LXjxWsB+ShrLZbtqlu5uwuxFK6a/w4kERr/4cb/4bN20O2vpg4PHeDDPzopQzbTzv21lb39jc2i7tuLt7+weH5aPjtk4yRWiLJDxR3QhrypmkLcMMp91UUSwiTjvR+Db3O09UaZbIBzNJaSjwULKYEWys9Bj49ctaLXTdfrniVb050CrxC1KBAs1++as3SEgmqDSEY60D30tNOMXKMMLpzO1lmqaYjPGQBpZKLKgOp/ODZ+jcKgMUJ8qWNGiu/p6YYqH1RES2U2Az0steLv7nBZmJr8Mpk2lmqCSLRXHGkUlQ/j0aMEWJ4RNLMFHM3orICCtMjM0oD8FffnmVtGtV36v69/VK46aIowSncAYX4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6J1zSlmTuAPnM8fCNaOlQ==AAAB8HicbVBNS8NAEJ34WeNX1aOXxSJ4kJKUgh6LXjxWsB+ShrLZbtqlu5uwuxFK6a/w4kERr/4cb/4bN20O2vpg4PHeDDPzopQzbTzv21lb39jc2i7tuLt7+weH5aPjtk4yRWiLJDxR3QhrypmkLcMMp91UUSwiTjvR+Db3O09UaZbIBzNJaSjwULKYEWys9Bj49ctaLXTdfrniVb050CrxC1KBAs1++as3SEgmqDSEY60D30tNOMXKMMLpzO1lmqaYjPGQBpZKLKgOp/ODZ+jcKgMUJ8qWNGiu/p6YYqH1RES2U2Az0steLv7nBZmJr8Mpk2lmqCSLRXHGkUlQ/j0aMEWJ4RNLMFHM3orICCtMjM0oD8FffnmVtGtV36v69/VK46aIowSncAYX4MMVNOAOmtACAgKe4RXeHOW8OO/Ox6J1zSlmTuAPnM8fCNaOlQ==\fProposition 2. If (v1, v2) \u2208 [|T|]i, then v2 \u2208 Postlabs(T ,j,P )(AV(v1)).\nNext, we state the correctness of rabs. Here we show that given any valuation v of the right layer\nin the concrete system, any valuation \u02c6v \u2208 AV(v) can be obtained in the abstraction. It relies on the\nobservation that \u02c6v(\u02c6s) is a convex combination of the mins\u2208\u02c6s v(s) and mins\u2208\u02c6s v(s), and the weight\ninterval of an abstract edge is a convex hull of the intervals of the corresponding concrete edges.\nProposition 3. Given an INN T with one layer, and a partition P of layer 1, if (v1, v2) \u2208 [|T|], then\nAV(v2) \u2286 Postrabs(T ,P )(v1).\nProofs are eliminated due to shortage of space and are provided in the supplementary material.\n\n3.2 Encoding the interval neural network and MILP solver\n\nIn this section, we present a reduction of the range computation problem to solving a mixed integer\nlinear program. The ideas are similar to those in [3, 19] using the big-M method. However, since, our\nweights on the edges are not unique but come from an interval, a direct application of the previous\nencodings where the constant weights are replaced by a variable with additional constraints related to\nthe interval the weight variable is required to lie in, results in non-linear constraints. However, we\nobserve that we can eliminate the weight variable by replacing it appropriately with the minimum\nand maximum values of the interval corresponding to it.\nWe encode the semantics of an INN T as a constraint Enc(T ) over the following variables. For every\nnode s of the INN T , we have a real valued variable xs, and we have a binary variable qs that takes\nvalues in {0, 1}. Let Xi denote the set of variables {xs | s \u2208 Si}, and Qi = {qs | s \u2208 Si}. Given a\nvaluation v \u2208 Val(Si), we will abuse notation and use v to also denote a valuation of Xi, wherein v\nassigns to xs \u2208 Xi, the valuation v(s), and vice versa. Let X = \u222aiXi and Q = \u222aiQi. Enc(T ) is the\nunion of the encodings of the different layers of T , that is, Enc(T ) = \u222aiEnc(T , i), where Enc(T , i)\ndenotes the constraints corresponding to layer i of T . Enc(T , i) in turn is the union of constraints\ncorresponding to the different nodes in layer i + 1, that is, Enc(T , i) = \u222as(cid:48)\u2208Si+1C i+1\n, where the\ns(cid:48)\nconstraints in C i+1\n\nare as below:\n\ns(cid:48)\n\n(cid:26)(cid:80)\n(cid:80)\n\nC i+1\n\ns(cid:48)\n\n:\n\ns\u2208Si W l\ns\u2208Si W u\n\ni (s, s(cid:48))xs + bl\ni (s, s(cid:48))xs + bu\n\ni(s(cid:48)) \u2264 xs(cid:48), 0 \u2264 xs(cid:48)\ni (s(cid:48)) + M qs(cid:48) \u2265 xs(cid:48), M (1 \u2212 qs(cid:48)) \u2265 xs(cid:48)\n\n(1)\n\ni(cid:107) and (cid:107)W u\n\nHere, M is an upper bound on the absolute values any neuron can take (before applying the ReLU\noperation) for a given input set. It can be estimated using the norms of the weights interpreted as\nmatrices, that is, (cid:107)W l\ni (cid:107), an interval box around the input polyhedron, and the norms of\nbiases.\nNext, we state and prove the correctness of the encoding. More precisely, we show that (v, v(cid:48)) \u2208 [|T|]i\nif and only if there are valuations for the variables in Qi such that the constraints Enc(T, i) are satis\ufb01ed\nwhen the values for Xi and Xi+1 are provided by v and v(cid:48).\nTheorem 2. Let v \u2208 Val(Si) and v(cid:48) \u2208 Val(Si). Then (v, v(cid:48)) \u2208 [|T|]i if and only if there is a valuation\nz \u2208 Val(Qi), such that Enc(T, i) is satis\ufb01ed with values v, v(cid:48) and z.\nWe can now compute the output range analysis by solving a maximization and a minimization\nproblem for each output variable. More precisely, for each s \u2208 Sk, the output layer, we solve: max xs\nsuch that Enc(T ) and I hold, where I is a constraint on the input variables encoding the set of input\nvaluations. Similarly, we solve a minimization problem, and thus obtain an output range for the\nvariable xs given the input set of valuations I. The maximization and minimization problems can\nbe solved using mixed integer linear programming (MILP) if I is speci\ufb01ed using linear constraints.\nEven checking satis\ufb01ability of a set of mixed integer linear constraints is NP-hard problems, however,\nthere are commercial software tools that solve MILP such as Gurobi and CPLEX.\n\n4\n\nImplementation\n\nIn this section, we present our experimental analysis using a Python toolbox that implements the\nabstraction procedure and the reduction of the INN output range computation to MILP solving. We\nconsider as a case study ACAS Xu benchmarks, which are neural networks with 6 hidden layer with\n\n7\n\n\feach layer consisting of 50 neurons [2]. We report here the results with one of the benchmarks, we\nobserved similar behavior with several other benchmarks.\nWe consider abstractions of the benchmark with different number of abstract nodes, namely,\n2, 4, 8, 16, 32, which are generated randomly. For a \ufb01xed number of abstract nodes, we perform 30\ndifferent random runs, and measure the average, maximum and minimum time for different parts of\nthe analysis. Similarly, we compute the output range for a \ufb01xed number of abstract nodes, and obtain\nthe average, maximum and minimum on the lower and upper bound of the output ranges. The lower\nbound was unanimously 0, hence, we do not report it here. The results are summarized in Figures\n7, 8, 9, and 10.\nAs shown in Figure 7, the abstraction construction time increases gradually with the number of\nabstract neurons. We observe a similar trend with encoding time. However, the time taken by\nGurobi to solve the MILP problems increases drastically after certain number of abstract nodes.\nAlso, as shown in Figure 9, the MILP solving time by Gurobi is the most expensive part of the\noverall computation. Since, this is directly proportional to the number of abstract nodes, abstraction\nprocedure proposed in the paper, has the potential to reduce the range computation time drastically.\nIn fact, Gurobi did not return when ACAS Xu benchmark was encoded without any abstraction, thus,\ndemonstrating the usefulness of the abstraction.\n\nFigure 7: Abstraction Time\n\nFigure 8: Encoding Time\n\nFigure 9: MILP Solving Time\n\nFigure 10: Output Range\n\nWe compare output ranges (upper bounds) based on different abstractions. The upper bound of the\noutput range decreases as we consider more abstract nodes, since, the system becomes more precise.\nIn fact, it decreases very drastically in the \ufb01rst few abstraction. We compute the average, minimum\nand maximum of the upper bound on the output range. Even for a \ufb01xed number of abstract nodes, the\nmaximum and minimum of the upper bound on the output range among the random runs has a wide\nrange, and depends on the speci\ufb01c partitioning. For instance, as seen in the Figure 10, although we\nhave only 2 partitions, the upper bound on the output range varies by a factor of 2. This suggest that\nthe partitioning strategy can play a crucial role in the precision of output range. Hence, we plan to\nexplore partitioning strategies in the future. To conclude, our method provides a trade-off between\nveri\ufb01cation time and the precision of the output range depending on the size of the abstraction.\n\n8\n\n05101520253035Number of abstract nodes0.040.060.080.10.120.140.160.180.2Abstract TimeminAbstracTimemaxAbstracTimeavgAbstracTime05101520253035Number of abstract nodes0.160.180.20.220.240.260.280.30.32Encoding TimeminEncodingTimemaxEncodingTimeavgEncodingTime05101520253035Number of abstract nodes012345678910Gurobi TimeminGurobiTimemaxGurobiTimeavgGurobiTime05101520253035Number of abstract nodes024681012141618Output range 41011minRangOutputmaxRangOutputavgRangOutput\f5 Conclusions\n\nIn this paper, we investigated a novel abstraction techniques for reducing the state-space of neural\nnetworks by introducing the concept of interval neural networks. Our abstraction technique is\northogonal to existing techniques for analyzing neural networks. Our experimental results demonstrate\nthe usefulness of abstraction procedure in computing the output range of the neural network, and the\ntrade-off between the precision of the output range and the computation time. However, the precision\nof the output range is affected by the speci\ufb01c choice of the partition of the concrete nodes even for\na \ufb01xed number of abstract nodes. Our future direction will consist of exploring different partition\nstrategies for the abstraction with the aim of obtaining precise output ranges. In addition, we will\nconsider more complex activation function. Our abstraction technique will extend in a straightforward\nmanner, however, we will need to investigate methods for analyzing the \u201cinterval\u201d version of the\nneural network for these new activation functions.\n\nAcknowledgments\n\nPavithra Prabhakar was partially supported by NSF CAREER Award No. 1552668 and ONR YIP\nAward No. N000141712577.\n\nBibliography\n\n[1] M. Bojarski, D. D. 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