{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Week 12: Proving NP-Completeness" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from tock import *\n", "settings.display_direction_as = \"alpha\"\n", "from cooklevin import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tuesday\n", "\n", "Last time, we showed that the language $\\mathit{TIME}_{\\mathsf{NTM}}$ was NP-complete:\n", "\n", "$$\\mathit{TIME}_{\\mathsf{NTM}} = \\{ \\langle N, w, \\texttt{1}^t\\rangle \\mid \\text{NTM N accepts w within t steps} \\}.$$\n", "\n", "Today, we start to consider other NP-complete languages." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "### Proving NP-completeness using reductions\n", "\n", "
\n", " \n", "
\n", "\n", "Now, we take the next step towards more real-world problems by showing that a simpler problem called 3SAT is NP-complete.\n", "\n", "If we wanted to prove that 3SAT is NP-hard \"from scratch\", we'd have to give a polynomial-time reduction from *any* NP language $A$ to 3SAT:\n", "\n", "![image.png](attachment:image.png)" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "But now that we've proven that $\\mathit{TIME}_{\\mathsf{NTM}}$ is NP-complete, our task becomes slightly easier. We no longer have to show a reduction from *every* NP language $A$ to 3SAT; we know that every NP language reduces to $\\mathit{TIME}_{\\mathsf{NTM}}$, so it's enough to show a reduction from $\\mathit{TIME}_{\\mathsf{NTM}}$ to 3SAT, and we automatically get a reduction from every NP language $A$ to 3SAT:\n", "\n", "![image.png](attachment:image.png)" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "This is possible because polynomial-time reducibility is transitive. Here's a pictorial proof of this fact:\n", "\n", "![image.png](attachment:image.png)" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "Once we've proven 3SAT NP-complete, we can prove that (say) CLIQUE is NP-complete by giving a reduction from 3SAT to CLIQUE, and so on.\n", "\n", "Here's a picture of the reductions proven in the book (with the addition of $\\mathit{TIME}_{\\mathsf{NTM}}$):\n", "\n", "![image.png](attachment:image.png)\n", "\n", "So we can revise our skeleton NP-completeness proof. To prove that a language $B$ is NP-complete by reduction from another NP-complete language $A$, you must do the following:\n", "\n", "- To prove that $B$ is in NP, you either:\n", " - Give a polynomial-time deterministic verifier for it, or \n", " - Give a polynomial-time NTM for it.\n", "- To prove that $B$ is NP-hard, assume that $B$ can be decided in polynomial time by $R$, and construct a polynomial-time decider for $A$: $S={}$\"On input $w$, 1. Compute $f(w)$. 2. Run $R$ on $f(w)$. 3. If $R$ accepts, *accept*; else, *reject*.\"\n", "You fill in:\n", " - Define a mapping $f$ from instances of $A$ to instances of $B$.\n", " - Prove that $w \\in A$ iff $f(w) \\in B$.\n", " - Prove that $f$ runs in polynomial time." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Cook-Levin Theorem\n", "\n", "
\n", "

Read Section 7.4, \"The Cook-Levin Theorem.\"

\n", " \n", "
\n", "\n", "A Boolean formula is made out of variables, negation ($\\neg x$ or $\\bar x$), conjunction ($\\land$), and disjunction ($\\lor$). A formula $\\phi$ is *satisfiable* iff there is a way to assign true or false values to variables such that $\\phi$ is true.\n", "\n", "The Boolean satisfiability problem (SAT) is\n", "\n", "$$\\{ \\phi \\mid \\text{\\phi is satisfiable} \\}.$$\n", "\n", "Now we want to show that SAT is NP-complete.\n", "\n", "#### The big picture\n", "\n", "This is a really long proof. I think it's helpful to first look at how it lines up with our skeleton proof.\n", "\n", "First, we have to show that SAT is in NP, which is easy. Let's get that out of the way: it's enough to say that we can check a truth-assignment for $\\phi$ in time linear in the length of $\\phi$.\n", "\n", "To show that SAT is NP-hard, we need to show that if SAT was decidable in polynomial time by a TM $R$, we would be able to decide $\\mathit{TIME}_{\\mathsf{NTM}}$ in polynomial time, in three steps: On input $\\langle N, w, \\texttt{1}^t\\rangle$,\n", "\n", "1. Convert $\\langle N, w, \\texttt{1}^t\\rangle$ to a Boolean formula $\\phi$.\n", "2. Run $R$ on $\\phi$.\n", "3. If $R$ accepts, *accept*; else, *reject*.\n", "\n", "So all the work is in defining a function $f$ that converts $\\langle N, w, \\texttt{1}^t\\rangle$ to a formula $\\phi$, showing that that $\\phi$ is satisfiable iff $N$ accepts $w$ within $t$ steps, and showing that $f$ runs in polynomial time." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "#### The medium picture\n", "\n", "Given $N$ and $w$, can can construct a *tableau*, which is a two-dimensional representation of a computation history for $N$ on $w$. The first row is the start configuration, and the following rows are the steps of the run. Each row is delimited by # on the left and right. Finally, if a row is an accepting configuration, the same configuration is repeated in the rows below it (this detail is missing from the book, but something like it seems necessary).\n", "\n", "![image.png](attachment:image.png)\n", "\n", "Because we only need to simulate $N$ up to $t$ steps, we can fix the size of the tableau in terms of $t$. There are $t+1$ rows: one row for the start configuration, plus one row for each step. And there are $t+4$ columns, because in $t$ steps, the head could move as far right as the $(t+1)th$ cell, plus one for the state, plus two for the #'s.\n", "\n", "Now we need to write a giant formula $\\phi$ that checks whether the tableau is an accepting computation history for $N$ on $w$. The variables of this formula are $x_{i,j,s}$, where $i$ is a row number, $j$ is a column number, and $s$ is either a tape symbol or a state. If $x_{i,j,s}$ is true, that means that cell $i,j$ contains symbol $s$. It's $\\phi$'s job to check that a truth-assignment encodes a well-formed, accepting tableau.\n", "\n", "The formula $\\phi$ has four parts: $\\phi = \\phi_{\\mathrm{cell}} \\land \\phi_{\\mathrm{start}} \\land \\phi_{\\mathrm{move}} \\land \\phi_{\\mathrm{accept}}$. The purpose of these four parts is:\n", "\n", "- $\\phi_{\\mathrm{cell}}$: Each cell contains exactly one symbol.\n", "- $\\phi_{\\mathrm{start}}$: The first row of the tableau is the initial configuration of $N$.\n", "- $\\phi_{\\mathrm{move}}$: Each row (except the first) is a configuration that legally follows the row above it according to $N$'s rules.\n", "- $\\phi_{\\mathrm{accept}}$: The last row is an accepting configuration." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Every cell has exactly one symbol\n", "\n", "Let $C = Q \\cup \\Gamma \\cup \\{\\#\\}$, the set of all possible symbols in a tableau cell. We ensure that every cell has exactly one symbol with the subformula:\n", "\n", "\\begin{align*}\n", "\\phi_{\\text{cell}} = \\bigwedge_{1 \\leq i \\leq t+1} \\bigwedge_{1 \\leq j \\leq t+4} &\\bigg[ && \\text{for each cell,} \\\\\n", "& \\bigvee_{s \\in C} x_{i,j,s} \\land {} && \\text{each cell has at least one symbol} \\\\\n", "& \\bigwedge_{s,s' \\in C, s \\neq s'} \\neg (x_{i,j,s} \\land x_{i,j,s'}) && \\text{and no cell has two symbols} \\\\\n", "&\\bigg]\n", "\\end{align*}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### The first row is a start configuration\n", "\n", "\\begin{align*}\n", "\\phi_{\\text{start}} = & x_{1,1,\\#} \\land {} && \\text{left boundary} \\\\\n", " & x_{1,2,q_0} \\land{} && \\text{start state} \\\\\n", " & \\bigwedge_{1 \\leq i \\leq n} x_{1,i+2,w_i} \\land{} && \\text{input string} \\\\\n", " & \\bigwedge_{n+1 \\leq i \\leq t+1} x_{1,i+2,\\_} \\land{} && \\text{blank symbols} \\\\\n", " & x_{1,t+4,\\#} && \\text{right boundary}\n", "\\end{align*}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Each row (except the first) follows from the previous row\n", "\n", "This is the most complicated part of the formula.\n", "\n", "\\begin{align*}\n", "\\phi_{\\text{move}} = \\bigwedge_{1 \\leq i \\leq t} \\bigwedge_{2 \\leq j \\leq t+1} &\\bigg[ && \\text{for each $2\\times3$ window} \\\\\n", "& \\bigvee_{\\text{$a_1, \\ldots, a_6$ is a legal window}} x_{i,j-1,a_1} \\land x_{i,j,a_2} \\land x_{i,j+1,a_3} \\land x_{i+1,j-1,a_4} \\land x_{i+1,j,a_5} \\land x_{i+1,j+1,a_6} && \\text{the window is legal} \\\\\n", "&\\bigg]\n", "\\end{align*}\n", "\n", "The book just gives a few examples of legal windows (Figure 7.39) but doesn't list them all out. If you like details to be completely worked out, here they are.\n", "\n", "This is a legal window:\n", "\n", "\n", "abc\n", "abc\n", "\n", "\n", "where a, b, and c are tape symbols, #, or $q_{\\text{accept}}$.\n", "\n", "Recall that if there is a transition $q \\xrightarrow{b \\rightarrow c, \\text{L}} r$, then the configuration $uaqbv$ yields configuration $uracv$, where $u$ and $v$ are strings of tape symbols. So the following are all legal windows:\n", "\n", "\n", "xya yaq aqb qbx bxy\n", "xyr yra rac acx cxy\n", "\n", "\n", "where $x$ and $y$ are any tape symbols or #.\n", "\n", "A special case is when the head is at the left end of the tape and tries to move left ($qbv$ becomes $rcv$).\n", "\n", "\n", "#qb qbx\n", "#rc rcx \n", "\n", "\n", "Similarly, if there is a transition $q \\xrightarrow{b \\rightarrow c, \\text{R}} r$, then the configuration $uaqbv$ yields configuration $uacrv$. So the following are all legal windows:\n", "\n", "\n", "yaq aqb qbx bxy\n", "yac acr crx rxy\n", "\n", "\n", "where $x$ and $y$ are any tape symbols or #.\n", "\n", "These 12 cases cover all possibilities -- nothing else is a legal window." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### The last row is an accepting configuration\n", "\n", "$$\\phi_{\\text{accept}} = \\bigvee_{2 \\leq j \\leq t+2} x_{t+1,j,q_{\\text{accept}}}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Demo\n", "\n", "Here's an NTM for $\\{\\texttt{1}^n \\mid \\text{$n$is composite}\\}$:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m = read_csv(\"primes.csv\")\n", "m" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run(m, [\"1\"]*4)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
 q1 [1] 1 1 1 q2 $[1] 1 1 q3$ x [1] 1 q4 $[x] 1 1 q4 [$] x 1 1 q5s _ [x] 1 1 q5s _ x [1] 1 q6 _ [x] $1 q6 [_] x$ 1 q7 _ [x] $1 q5x _ _ [$] 1 q5x _ _ $[1] q6 _ _ [$] x q6 _ [_] $x q7 _ _ [$] x q5s _ _ _ [x] q5s _ _ _ x [_] accept _ _ _ [x] _
\n" ], "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "run(m, [\"1\"]*4).shortest_path()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The running time of this NTM actually isn't bad -- bounded above by $3n^{3/2}$:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4 18 24.0\n", "6 28 44.090815370097204\n", "8 38 67.88225099390857\n", "9 53 81.0\n", "10 48 94.86832980505137\n", "12 58 124.70765814495917\n", "14 68 157.14961024450554\n", "15 95 174.28425057933376\n", "16 78 192.0\n", "18 88 229.10259710444143\n" ] } ], "source": [ "# Print n, actual running time, upper bound on running time\n", "for n in range(20):\n", " r = run(m, [\"1\"] * n)\n", " if r.has_path():\n", " print(n, len(r.shortest_path().configs), 3*n**1.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we construct the formula corresponding to the run of this machine on 0000:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "9116869\n" ] } ], "source": [ "phi = make_phi(m, [\"1\"]*4, 24)\n", "print(phi.size()) # number of variables and operators in phi" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's too big to print, but we can look at the beginning:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(x[1,1,q3] | x[1,1,q7] | x[1,1,x] | x[1,1,q4] | x[1,1,q6] | x[1,1,q5x] | x[1,1,q1] | x[1,1,q2] | x[1,1,q5s] | x[1,1,1] | x[1,1,accept] | x[1,1,#] | x[1,1,_] | x[1,1,$]) & (~x[1,1,q3] | ~x[1,1,q7]) & (~x[1,1,q3] | ~x[1,1,x]) & (~x[1,1,q3] | ~x[1,1,q4]) & (~x[1,1,q3] | ~x[1,1,q6]) & (~x[1,1,q3] | ~x[1,1,q5x]) & (~x[1,1,q3] | ~x[1,1,q1]) & (~x[1,1,q3] | ~x[1,1,q2]) & (~x[1,1,q3] | ~x[1,1,q5s]) & (~x[1,1,q3] | ~x[1,1,1]) & (~x[1,1,q3] | ~x[1,1,accept]) & (~x[1,1,q3] | ~x[1,1,#]) & (~x[1,1,q3] | ~x[1,1,_]) & (~x[1,1,q3] | ~x[1,1,$]) & (~x[1,1,q7] | ~x[1,1,q3]) & (~x[1,1,q7] | ~x[1,1,x]) & (~x[1,1,q7] | ~x[1,1,q4]) & (~x[1,1,q7] | ~x[1,1,q6]) & (~x[1,1,q7] | ~x[1,1,q5x]) & (~x[1,1,q7] | ~x[1,1,q1]) & (~x[1,1,q7] | ~x[1,1,q2]) & (~x[1,1,q7] | ~x[1,1,q5s]) & (~x[1,1,q7] | ~x[1,1,1]) & (~x[1,1,q7] | ~x[1,1,accept]) & (~x[1,1,q7] | ~x[1,1,#]) & (~x[1,1,q7] | ~x[1,1,_]) & (~x[1,1,q7] | ~x[1,1,$]) & (~x[1,1,x] | ~x[1,1,q3]) & (~x[1,1,x] | ~x[1,1,q7]) & (~x[1,1,x] | ~x[1,1,q4]) & (~x[1,1,x] | ~x[1, ...\n" ] } ], "source": [ "print(str(phi)[:1000], '...')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The last step is to modify the above proof so that$\\phiis in 3CNF, that is, of the form\n", "\n", "\\begin{align*}\n", "\\phi &= (a_1 \\lor b_1 \\lor c_1) \\land \\ldots \\land (a_m \\lor b_m \\lor c_m). \\\\\n", "\\end{align*}\n", "\n", "There arel$variables, named$x_1, \\ldots, x_l$. Each of the conjuncts$(a_j \\lor b_j \\lor c_j)$is called a *clause* and there are$m$of them. (Sipser sometimes uses$k$for the number of clauses, except when he needs$k$for something else. I'll try to stick to$m$.) Each clause has exactly three disjuncts, called *literals*. Each literal is either a variable$x_i$or a negated variable$\\neg x_i$. We'll be using 3CNF a lot, so remember this terminology and notation well.\n", "\n", "For example, this formula gets used a lot as an example:\n", "\n", "$$\\phi = (x_1 \\lor x_1 \\lor x_2) \\land (\\neg x_1 \\lor \\neg x_2 \\lor \\neg x_2) \\land (\\neg x_1 \\lor x_2 \\lor x_2).$$\n", "\n", "It has$l = 2$variables and$m = 3$clauses. It has one satisfying assignment:$x_1 = 0, x_2 = 1$.\n", "\n", "After modifyiing the proof (which I omit here), we have shown not only that SAT is NP-complete, but 3SAT. This will make future reductions easier." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Thursday\n", "\n", " \n", " Read page 311. \n", " \n", " \n", "\n", "Last time, we showed that SAT and 3SAT are NP-complete. Section 7.5 shows that four more problems (clique, vertex cover, Hamiltonian path, subset sum) are NP-complete by reduction from 3SAT. \n", "\n", "I personally find all four of these reductions difficult. It's not too hard to understand them, but difficult to imagine yourself coming up with them. Below, I try to complement the book's presentations of the reductions with a sketch of the thought process one might go through to arrive at each reduction.\n", "\n", "As a reminder, each of these proofs has the following parts (assuming reduction from 3SAT to a problem$B$):\n", "\n", "- To prove that$B$is in NP, you either:\n", " - Give a polynomial-time deterministic verifier for it, or \n", " - Give a polynomial-time NTM for it.\n", "- To prove that$B$is NP-hard, assume that$B$can be decided in polynomial time by$R$, and construct a polynomial-time decider for 3SAT,$S={}$\"On input$\\phi$, 1. Compute$f(\\phi)$. 2. Run$R$on$f(\\phi)$. 3. If$R$accepts, *accept*; else, *reject*.\"\n", "You fill in:\n", " - Define a mapping$f$from 3CNF formulas$\\phi$to instances of$B$.\n", " - Prove that$\\phi$is satisfiable iff$f(\\phi) \\in B$.\n", " - Prove that$f$runs in polynomial time." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Some tips on inventing reductions\n", "\n", "One general fact about 3SAT is that because a satisfying truth-assignment just needs to make at least one literal in each clause true, another way of thinking about the problem is that we need to find a way to choose one literal from each clause -- let's call it the \"lucky\" literal (I have no idea if there's a standard term for it) -- such that no lucky literals are contradictory (that is,$x$and$\\neg x$can't both be lucky). In our example formula, there are several ways of choosing the lucky literals:\n", "\n", "\\begin{gather*}\n", "(x_1 \\lor x_1 \\lor \\underline{x_2}) \\land (\\underline{\\neg x_1} \\lor \\neg x_2 \\lor \\neg x_2) \\land (\\underline{\\neg x_1} \\lor x_2 \\lor x_2) \\\\\n", "(x_1 \\lor x_1 \\lor \\underline{x_2}) \\land (\\underline{\\neg x_1} \\lor \\neg x_2 \\lor \\neg x_2) \\land (\\neg x_1 \\lor \\underline{x_2} \\lor x_2) \\\\\n", "(x_1 \\lor x_1 \\lor \\underline{x_2}) \\land (\\underline{\\neg x_1} \\lor \\neg x_2 \\lor \\neg x_2) \\land (\\neg x_1 \\lor x_2 \\lor \\underline{x_2})\n", "\\end{gather*}\n", "\n", "Most of the reductions in Section 7.5 use this alternative view.\n", "\n", "When you start to look for a reduction, here are some questions to think about. They won't necessarily all have answers, but they may help you to come up with ideas.\n", "\n", "- The formula$\\phi$becomes the input to the problem.\n", " - How do you represent the variables? Sometimes there is one \"gadget\" for each of the$l$variables.\n", " - How do you represent the clauses? Usually there is one \"gadget\" for each clause, encoding which literals appear in each clause.\n", "- Truth-assignments and/or the choice of lucky literals become certificates.\n", " - How do you represent that a variable is true/false? How do you ensure that a variable isn't true and false at the same time, or neither true nor false?\n", " - How do you represent that a literal is lucky/unlucky? How do you ensure that each clause has exactly one lucky literal?\n", " - If you have both of the above, how do you ensure they are consistent with each other?\n", " - How do you ensure that all clauses are true, or that no lucky literals are contradictory?" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "### The clique problem\n", "\n", " \n", " \n", " Re-read the pages on the clique problem, which is scattered across several sections: definition (295-296), membership in NP (296-297), reduction from 3SAT (302-303), and finally NP-completeness (bottom of 311). \n", " \n", "\n", "In a graph, a *clique* is a subset of nodes in which each pair of nodes is connected by an edge. For example, in this graph:\n", "\n", "![image.png](attachment:image.png)\n", "\n", "set {1,3,4} is a clique, but {1,2,3} is not. The clique problem is to decide whether a graph has a clique of size$k$. More formally, CLIQUE is the set of pairs$\\langle G, k\\rangle$where$G$is a graph and there is a subset of$k$nodes that are pairwise connected by an edge." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "Proof that CLIQUE is in NP: If$G$is stored as an adjacency matrix, we can check whether a subset of nodes has size$k$and is fully connected in$O(k^2)$time.\n", "\n", "Proof that CLIQUE is NP-hard: By reduction from 3SAT. We need to show how to convert a 3CNF formula$\\phi$into a graph and a number$k$.\n", "\n", "To try to give some idea of the thought process needed to find a reduction (which is different from the way you'd actually write it), I present an\n", "\n", "> Interior monologue:\n", ">\n", "> The input to CLIQUE is a graph, which has nodes and edges, and$k$. So maybe the variables will become nodes and the clauses edges? Or the variables will become edges and the clauses will become nodes? It's hard to say, so (not just here but in general) I think we will get more traction by thinking about certificates.\n", "> \n", "> The certificates are subsets of$k$nodes; in other words, a certificate says whether each node is in the subset or not, and there are exactly$k$in it.\n", ">\n", "> - So maybe nodes could be variables, and a node belongs to the clique iff the variable is true? But it's not clear why we would want exactly$k$variables to be true.\n", ">\n", "> - Another idea is to create a node for each variable and its negation. A node$x$belongs to the clique if$x$is true, and node$\\neg x$belongs to the clique if$x$is false. Now we want exactly$l$nodes to be in the clique. This idea works, but is not enough; we still need a way to represent clauses, and it will turn out that this idea will become unnecessary.\n", ">\n", "> - Maybe nodes could be literals, and a node belongs to the clique iff the literal is true? As in the first idea, it's not clear why we would want exactly$k$literals to be true.\n", ">\n", "> - How about if a node belongs to the clique iff the literal is lucky? This is promising, because we want exactly$m$literals to be lucky. \n", "\n", "For each literal in$\\phi$, create a node in the graph$G$, and set$k = m$. \n", "\n", "> Here's what our example formula looks like so far. The blue nodes correspond to one possible set of lucky literals.\n", ">\n", "> ![image.png](attachment:image.png)\n", ">\n", "> This graph doesn't have any$k$-cliques, however, because it doesn't have any edges. Imagine adding all possible edges to this graph; now we have too many$k$-cliques.\n", ">\n", "> First, we must ensure that no clause has two lucky literals. We can do this by removing edges between nodes belonging to the same clause.\n", ">\n", "> Second, we must ensure that no two lucky literals are contradictory. We can do this by removing edges between nodes that are contradictory.\n", "\n", "Add an edge between all pairs of nodes$u$and$v$, except if$u$and$v$correpond to literals in the same clause or$u$and$v$correspond to contradictory literals." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "For our example formula, here is the resulting graph:\n", "\n", "![image.png](attachment:image.png)" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "It may be easier to visualize the edges that are *not* added:\n", "\n", "![image.png](attachment:image.png)" ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "Here are the three cliques of this graph, corresponding to the three possible sets of lucky literals:\n", "\n", "![image.png](attachment:image.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we need to show that$\\phi$is satisfiable iff$G$has a$k$-clique. Although we already thought this through, the order was backwards (as is often the case!) from the logical order. Please see the book for how this part of the proof should be written.\n", "\n", "Finally, we need to show that constructing$G$takes polynomial time. In this case, it's if you simply say this is obvious or (like the book) say nothing." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "### The vertex cover problem\n", "\n", " \n", " Read pages 312-313. \n", " \n", "\n", "If$G$is a graph, a *vertex cover* of$G$is a subset$C$of nodes such that every edge in$G$touches a node in$C$. For example, in the graph\n", "\n", "![image.png](attachment:image.png)\n", "\n", "{1,3} and {3,4} are both vertex covers of size 2.\n", "\n", "The vertex cover problem is to decide, given$G$and a number$k$, whether$G$has a vertex cover of size$k$. More formally, VERTEX-COVER is the set of pairs$\\langle G, k\\rangle$where$G$is a graph and there is a subset$C$of$k$nodes such that every edge in$G$touches a node in$C$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Proof that VERTEX-COVER is in NP: If$G$has$|V|$nodes and is stored as an adjacency matrix, the size of the input is$n \\in O(|V|^2 + \\log k)$. We can check whether a subset$C$is a vertex cover by looping over all$(u, v)$, and if$(u, v)$is an edge of$G$, check that either$u$or$v$belongs to$C$. This takes$O(|V|^2) \\leq O(n)$time." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Proof that VERTEX-COVER is NP-hard: By reduction from 3SAT. We need to show how to convert a formula$\\phi$into a pair$\\langle G, k\\rangle$.\n", "\n", "> Interior monologue:\n", "> \n", "> Initially VERTEX-COVER seems very similar to CLIQUE; they have the same type of input (a graph$G$and number$k$) and same type of certificate (a set of$k$nodes). We can brainstorm possible reductions as before, and discard some of them immediately for the same reasons as before. The two viable ideas are:\n", ">\n", "> - For each variable$x$, create a node for$x$and its negation$\\neg x$. If$x$is true, put node$x$in$C$; if$x$is false, put node$\\neg x$in$C$.\n", ">\n", "> - For each literal, create a node. If a literal is lucky, put its node in$C$." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "> Let's think about the first idea. If we put an edge between$x$and$\\neg x$, we can ensure that, for each variable$x$, at least one node ($x$or$\\neg x$) belongs to$C$. And we can make it exactly one if we set$k = l$.\n", ">\n", "> ![image.png](attachment:image.png)\n", "\n", "For each variable$x_i$, create a variable gadget containing a node for$x_i$and a node for$\\neg x_i$, and connect the two nodes with an edge." ] }, { "attachments": { "clauses.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "> Now let's think about the second idea. We need to ensure that each clause has exactly one lucky literal.\n", ">\n", "> - If we could, we would draw an edge like this:\n", ">\n", "> ![image.png](attachment:image.png)\n", "> \n", "> that would ensure that each clause has at least one lucky literal. But edges like this aren't allowed.\n", ">\n", "> - But if we connect all three literals in a clause by edges, then the vertex cover will have to contain at least two of them. We can make it exactly two by setting$k = l+2m$($l$for the variable gadgets and$2m$for the clause gadgets). So let's make the *unlucky* literals to be nodes in$C$.\n", ">\n", "> ![clauses.png](attachment:clauses.png)\n", "\n", "For each clause in$\\phi$, create a clause gadget consisting of three nodes in$G$labeled with its three literals, all connected by edges. Set$k = l+2m$." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "> We still need to ensure that$\\phi$is true.\n", ">\n", "> For CLIQUE, we were able to ensure that no lucky literals are contradictory, by adding edges between nodes in the clause gadgets. You can try this for yourself and see that it won't work.\n", ">\n", "> Instead, can we ensure that every lucky literal is true? Consider a single clause, and imagine connecting each literal to another node like this:\n", ">\n", ">![image.png](attachment:image.png)\n", ">\n", "> The nodes connected to the unlucky literals could be in or out, but the node connected to the lucky literal ($x_2$) must be in. And in the variable gadgets, true nodes are in. So if we connect each literal$a$in a clause gadget to node$a$in the variable gadgets, we've encoded the constraint that lucky literals must be true." ] }, { "attachments": { "image.png": { "image/png": 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nTqnL6T7YwrBWoggoAopADgTyWUw5julPRUARUATSRmDt2rVUtWrVUD1HHHEE/frrr3T88ceHjiXz5dChQ1ShQgXatGlTqPiyZcuoZs2aod9ufjnnnHPoq6++kiZbtWpFkyZNcqz55s2b08yZM6X+Cy64gD7++GNb2urUqRONHTtW6nK6D7YwrJUoAoqAIpADATUhyAGI/lQEFAF7EKhSpQo1adIkVBkU0bwoYNOmTYtQXk866aSMKa+hzrj0BavYTtCBAwecqFbrVAQUAUXANQRUgXUNam1IEQgeApdddllEpz/88MOI38n8yHlNzjqTqUPLKAKKgCKgCGQXAqrAZpc8tTeKgKcQ6N69O8Fm1dDUqVMJNqTJElZtP/roo4jil19+ecTvTP4oWLBgJpvXthUBRUARCCwCqsAGVvTacUXAeQRg79q2bdtQQ3///Td98sknod+JvsB8INwRrGnTplS9evVElzl6fsyYMbR79275w3clRUARUAQUAfcRUAXWfcy1RUUgUAjk3PLPaRIQD4ycZb2w+nrMMccQIgLg7+ijj47Hvp5TBBQBRUARcAgBDaPlELBarSKgCBxGAN7zt9xyC+3bt08OTJ48mbZt20bHHntsXIhymg8cddRRBJOEaPTHH3/Q4sWLJcoBIh3ky5ePSpUqJSGuWrZsSfG2+v/6669QlVBIES3B0Jw5c2j58uW0YcMGuuKKK6S+gwcPElaSQSibSIlNhzfDR7TPX375hebOnUurVq0iOLY1atTItjBb0dpDv3/66SdpEyvQCIl24okn0sknnxyteNRjwOLHH3+kNWvW0NatW6lkyZISlaJy5cop1RO1cj2oCCgCwUIAYbSUFAFFQBFwEoGLLroI4fpCf6+99lrC5qZMmRIqj2vPPffcXNewMmT17NnT4limEWXD2ypcuLDVo0cPa/PmzbmuZ6Us4rovvvhCyuCzfv36EedYWZRzXbp0CR3nEFS56jQH0uUN9TRs2DDUFr8IWBw9wOrTp4/F8WBDx8P7Wq1aNeuOO+6wOGauYSPq59lnnx26Pl4fcDH6gTKxMAaP48aNi9qOOfjzzz9b1113ncUvEqF2w/nGd1aErf/+97/SR3OdfioCioAiEAsBinVCjysCioAiYBcC7IgVobhAgUpEt99+e8Q17777bsQlUDJ5VTaiTE6lKPx37dq1LV5JjagjmgL71ltvWex4lqteo8Amo/zZwRsYDVdgzzzzTKtNmza5+Arvo/l++umnW+vWrYvoa/iPZPqA8i+++GJMxdW0hU/IYeTIkeFNhL7PmjXLKlasWFJ8o66rr77a4tX30PX6RRFQBBSBaAj8/14ZjxxKioAioAg4gUDHjh2pePHioaonTpxI27dvD/3O+SWn+QCvolLXrl1DxebNm0cXX3wxYVs7nGAqAJOBs846K5eJAkwMHnnkkfDiub5jS55XdEMmArkKJHHAKd54RZqAmyGYSbBSTg0aNCCYV4QTTB9YiaWVK1eGH07p+1133UW33XZbyPQDFxcpUoTgSFevXr2INiEH2DqzEhvRBswEkPjBZP3CSZhdsGJOSKYAWcGWOJyGDRtGTzzxRPgh/a4IKAKKQG4Eomm1ekwRUAQUAbsRuOaaayJW4d58882YTeQ0H2DlKKLslVdeGVEXVu1mz55tceD/UDmsrmIFkRWmUFlsU4dTzhVYHiFDZWF6cNVVV1mPP/64NXr0aIvtPuXSRKuXdvGGxsJXYA1vWB1+9tlnLU4zG+oKeMMKNSuDIf5RPidu5oJEffjhhx8iVqH55cNixdJi219ThfXnn39avXr1sliRDrUJ3lasWBEqM2LEiNA58IN2OapE6Dy+7Nixw+rfv39EuZxyirhAfygCioAiwAioCYHeBoqAIuAKApx+NUJJ4VXZmO3CjtMobPjktKcRZdnpJ3S+devWEYpVREH+cemll4bKQtni1cBQkVgKbOPGjS1OVxsqF/4lkfJnF29oM6cCyxEQRJkO5yf8+/fff2+xc1yov1De2fEqvIh8j9cHbN/zymioDtitLlmyJFcd5sDrr78eKgtZ3XfffeaUdf3110ecY4e40LmcX2DLbGQOOXG84JxF9LcioAgoAiEE1ISAR0wlRUARcB4BxINFXFhDEyZMIHil56Sc5gPssESscIWKbdq0idi+M/S7c+fOEZEDQif++QJPeUM88tGePXvMz6ifp5xyCk2fPj1P6Wqd5u3aa68ldiKLyjcOwmzg/vvvD50Hlo899ljodzJfvvnmG0L8XUMPP/ywRDkwv3N+wuQCJiKG2IY4ZNrBq7TmsHzCvCIW8Qo98YuD/CGiQjrmD7Ha0OOKgCKQPQioAps9stSeKAKeRgAZucLDYPF2P0VLBDBjxgwJW2U6g2vCbTyhBMOedf78+fLHq3ymaK5P3mZPKXECKhgwYEBEe7kqjXPASd5g89q7d+84rR8+deONN0oIMVOQV2XN16Q+2XwgVA5tQkFNRDfccEOoCJT48ePHy+8aNWqEjuMLFHA2ySA2G4g4jh+wh/3uu+9Cf7C1VVIEFAFFIBYCkZb/sUrpcUVAEVAEbEAAjj7PPfdcqKZRo0YR25mGfuNLTkegaMkLatWqFXGN+YEYsLzdLfFKoYghDe2uXbvM6YSfVatWJQ75lbBcvAJO8QaHrVh1h/MDhzesdgNbEGKuwskq/CUgvHzO7xzyKnQIK9Yc2ir0O9YXOGuFE5tfyE8OnUVDhgwhvKyAsPqNFeIHH3xQFFaOqkDNmzenZs2aEfhWUgQUAUUgWQRUgU0WKS2nCCgCaSPQpEkTSQVrtofZLlY81DnMktQNhQlKp6ETTjhBlBvzO+cngvgPHz5ctryxehdtZS/nNfF+Q0HEqqMdZDdvVapUSZot4GaIY8eKEptzNdScz/m5aNGiiEOJIjdEFP7nB9uvyjfwwfbLBPMAvFwYgkI9adIk+cOx/Pnzi5y7desmK77xEk+YOvRTEVAEgo2AmhAEW/7ae0XAdQTYqSrUJrJgffbZZ6HfsD1F1itDWLGNRrCdxcos7FuxmgdFOJryihBNyBiVLFWqVCnZojHLOcVbosxl4QyFK4Aw3TBZ0MLLxPqODF/pUviKbPv27WnhwoV000035QptZtrBCi0ytLHzHnEyhqimJaasfioCioAiAAR0BVbvA0VAEXAVASiwgwYNCrWJrW5jJvDhhx+GjuOLOR5+ECuK2Ob/9ttvww9TuXLlCFvSWEXFamOdOnXE+YhDOSVlx4nKUlF2Ixr/54eTvHEmsWhNRj2GVK+GkPY2UbpbUxafMKPgUFdyCCvjiLebKiHOazghZezLL79MQ4cOFRtXTvQQWjXP6VSHfsLuGWUgTyVFQBFQBKIhoApsNFT0mCKgCDiGABRLBN+HExYIDj+wU4UNpLHbxPHTTjstqs3nq6++GqG8wnEKwe/DIxXg+rwQh6nKy2Wha5zkDbasyVJ4lAYkDsCqZrIEW9uZM2dKcazkcpisZC9NWA68wN4VfyAo/FOnThW7aKzEI2oCCCvzAwcOVAVW0NB/ioAiEA0BVWCjoaLHFAFFwFEEYBpgFFhsb3/++eey+hluPhBt9RVMGeXKMIiVOijEsQhe8W6Rk7xxDFVxTuMg/3G7gxVNmFQYglkEbEyTJSiwhrAaCnMAhDKLR3v37pUVU1MGEQVKlChBCMllCKGxcppBYGUYDmf4QxY0fJqsXbBpTsX5zLSjn4qAIhAMBNQGNhhy1l4qAp5CoEePHhHOUlh5DTcfwEpduK1sOPNIk2qobNmycZVXOIXBicgtcpI39OWpp55K2JX3338/Ir5uPOU+WmU5t/+TiSML+cGsw/wtXboUSXLoggsukBixiBPL2baiNRc6hnY7dOgQ+g1F3DiDhQ7qF0VAEVAE/kFAFVi9FRQBRcB1BLAqeMYZZ4TahZL59ttvh35jJQ42rdEIipEh2HpiGzoWIYQT4sqGkwnpFH7Mru9O84aIC7DpjUWIIIA4tuHEmbHCfyb8DrtTs8WPwrBb5dS+Ma9DsoLBgweHznMmMgmRBXMMRJ0whJi/iVbDEd/XUIUKFah8+fLmp34qAoqAIhCBgCqwEXDoD0VAEXALgfAIAzAjCM/KFct8ALyFrxDCdhZxZMOvRRlst1944YXUt29f/IwgO7zsIyoM++E0b1DWr7jiCom8EN4PKPIww2jVqlXIAQtsnXfeeZSXhADhCikUfrxQIJwWEkOEE7b9sWrK6WpDhyE7E4rszDPPDB2H8tq6dWtCBjZj62pObtu2jRAzFtEKDKEvSoqAIqAIxESAVwyUFAFFQBFwHQFWWiy2gcRyasRfgQIFLA6JFZOfV155JaI8rmdnI4tXDS1e8bPY9jLX+fA2ihYtarE9ptTPNpYRZZ944omY7ZoT7CwWuoaVLHNYPu3kDRWyQhxqK7wP5juvUlr169e3OElBrnLFixe3FixYEMGf+RGvD6YMv2DkqhPt8uq5xeHLrOrVq+c6D1xZmTZVWBz71eIV2Vzl2PRD5MUhtqx69epZbDISUQb3BSu6oXr0iyKgCCgCORGAnZKSIqAIKAIZQaBTp04RigsUJA7bFJcXXr2zunbtmus6o9SFf0JZ/eCDD6KWRSN2K7B28gb+whXYc8891+IVzKh9Ce8zvkOpXbFiBaqISskosBx+y+K0r1GV45zt4TeUWl5lzdUeZ/ayOIxWUnyjHnY4s9jcIFc9ekARUAQUgXAE1ISAR0wlRUARyAwC4WYEhoN45gMog+3pd999V7a0jzvuOHNZxCdimd58882ElKaIKYoA+Qjob8h8R13hQf+LFCliiiT1mTP9qZ285WSgdOnS9PXXX9Pzzz9PsDPNSXB8Qwzc3r1706xZsyTjWc4y0X7n7IMpg/pgP4swV+3ataNSpUqZUxGfiJ0LO1ls/8OpLichbBpsc//9738TQp7FIsSKvfHGGyXKROfOnWMV0+OKgCKgCAgC+aDNKhaKgCKgCPgRAcQLXbJkCa1du1bsM5HAgFcfibfPc3UHNphQAKH8wVY1VWU1V4UJDjjNG/qNv+3bt4uyiri5vOKcgKv0Tq9fv57YLEGwRmpbNiMgOFtB2U2GEBZr9erVBPtdpJbF9AOlFn8nnXRSSuG+kmlPyygCikD2IqAKbPbKVnumCCgCioAioAgoAopAViKQ3GtzVnZdO6UIKAKKgCKgCCgCioAi4EcEVIH1o9SUZ0VAEVAEFAFFQBFQBAKMgCqwARa+dl0RUAQUAUVAEVAEFAE/IqAKrB+lpjwrAoqAIqAIKAKKgCIQYARUgQ2w8LXrioAioAgoAoqAIqAI+BEBVWD9KDXlWRFQBBQBRUARUAQUgQAjoApsgIWvXVcEFAFFQBFQBBQBRcCPCKgC60epKc+KgCKgCCgCioAioAgEGAFVYAMsfO26IqAIKAKKgCKgCCgCfkRAFVg/Sk15VgQUAUVAEVAEFAFFIMAIqAIbYOFr1xUBRUARUAQUAUVAEfAjAqrA+lFqyrMioAgoAoqAIqAIKAIBRkAV2AALX7uuCCgCioAioAgoAoqAHxFQBdaPUlOeFQFFQBFQBBQBRUARCDACqsAGWPjadUVAEVAEFAFFQBFQBPyIgCqwfpSa8qwIKAKKgCKgCCgCikCAEVAFNsDC164rAoqAIqAIKAKKgCLgRwRUgfWj1JRnRUARUAQUAUVAEVAEAoyAKrABFr52XRFQBBQBRUARUAQUAT8ioAqsH6WmPCsCioAioAgoAoqAIhBgBI4KcN8z0vWDBw/S3Llzaf78+bR8+XL5W716Ne3YsYN27dolf2CsSJEi8le8eHGqVq0a1axZU/4aNGhADRs2pKOOUtG5IUCVlxsoaxuKgCIQDQEdf6Kh4t1jKi93ZZPPYnK3yeC1tnLlSho5ciRNnDiRZsyYQbt3704LhMKFC1Pz5s2pTZs21L17d6pevXpa9enFkQiEy2v69Om0Z8+eyAIp/ipUqBC1aNFC5ZUiblpcEQgiAjr++Evq4fLS+d1d2akC6xDev//+Ow0bNozee+89mj17dkQrtWrVombNmtGJJ54oq6o1atSgkiVLhlZdUdisxqKeFStWyErtsmXLaObMmbRkyZKI+ho3bkyXXnopXX311VJPxEn9kRQC8eRVrFwNKlOjERU7vjoVK3sCFS1bjfIXLkFHH1OYjipQWOo/uG83HfhrN+3f/Qf9uXk17dy8inZuWklbV3xPOzeuiOBB5RUBh/5QBAKPgI4//roF4slL53f3ZKkKrM1Yr1+/np5++ml6/fXXQ+YAxYoVo65du1Lnzp3pzDPPpOOOOy6tVrds2UJTpkyhzz77jEaPHk07d+6U+mB2cP3119O//vUvqlSpUlptBOViI6/XXnsttDJ+dIEiVKlhR6rU4Bw6rlYzKlisTFpw7N25lbYsmUnr539J6+eOowP7dkl9WEm/4YYbVF5poasXKwL+RUDHH3/JzshL53dvyE0VWJvk8Ntvv9GAAQPojTfeoAMHDkitHTp0oJ49e1KnTp2oQIECNrUUWc2+ffvo888/l3bHjx8vJ48++mhpd9CgQVS6dOnIC/SXIGDkhYEIdkug8vXaUs0zL6eKDc6mI/M7I6+/9++jX+Z/RcunDKcNC7+VdmHPjBcPlZfAof8UgaxHQMcff4nYyEvnd2/JTRXYNOVx6NAheuWVV0R53b59uzhXXXLJJXTvvfdS/fr106w9tct//PFHGjx4MH3wwQeilJUqVUqUoptuuomOOEIDTgBNI6/+/fsTtoHyHXEkVW3SlU7ueAeVrFw3NcDTLP37up/pp3HP05rvRpN16G8x/3j00UdJ5ZUmsHq5IuBRBHT88ahgYrBl5IXFKZ3fY4CUwcOqwKYB/po1a8T2dNasWVLLWWedRc899xzBBiaTBBvZXr160ddffy1sNG3aVGxxq1atmkm2Mt52TnmVq9uKGl/xOBUvXzOjvO3YsJxmv9uPNv48WfhQeWVUHNq4IuAIAjr+OAKrY5XmlJfO745BneeKVYHNI3SjRo2SbV+Ev6pcuTI9++yzdMEFF+SxNmcu++STT6h3794Eux2E48J2ebdu3ZxpzOO1Ql4w54C9cOFSFajR5Y9S5dPP8xTX6+aMpdnD76c92zcQ7KaxXRVUeXlKMMqMIpAmAjr+pAmgy5fr/O4y4HlsThXYFIFD1DE4SUFhBV144YWiaJQoUSLFmtwp/scff4ji9vHHH0uDffr0ESezfPnyucNAhlvJKa/KDc+j5j3/y1EEimeYs+jN79+9g2a80ZvWzR0rBYImr+io6FFFwJ8I6PjjL7nllJfO796WnyqwKchn//79dNVVV4mN6THHHCOK4K233ppCDZkrOnToUFG8//rrL4KN7ttvv0358+fPHEMutBwuryOOyk+nXzaQarW7zoWW029iyTdv0pwRD9Chg/sDI6/0UdMaFAHvIKDjj3dkkQwn4fLS+T0ZxDJfRhXYJGXw559/ionAN998I9vxn376KbVq1SrJq71RbPLkydSlSxfJ+tWuXTsJwYXQW9lI4fI6umBRatPnHTq+VgtfdXXTkuk08dkr6cDePynb5eUrwSizikACBHT8SQCQx06Hywvmdjq/e0xAMdhRBTYGMOGH8WbWsWNHgvJarlw5QrgqtyMMhPOTzndEKkB4r40bN4pSNG7cuKxbiQ2XV8HiZan93R+4HmEgHRmFX4tIBROevIT27tictfIK769+VwT8joCOP/6SYLi8dH73l+w0tlICecEmBmYDRnmdNm2ab5VXdBWKN/qABxV9Qt/Qx2yhcHlBee0w4HPfKq+QCUJ7oQ/oSzbKK1vuO+2HIgAEdPzx130QLi/MiTq/+0t+qsAmkBccthBXFdsKWHk94YQTElzh/dPoA/qCPqFv6GO2kJEXzAaw8lr0uKq+7xr6gL6gT9kmL98LRzugCIQhoONPGBg++GrkpfO7D4QVhUU1IYgCijmEUBoXX3wxwaD7yy+/9J3Nq+lHrE/YxJ5zzjkEx64PP/zQ9yGbjLzgsNX+npG+s3mNJSdzHDaxE4Z0F8eubJCX6Zd+KgLZgICOP/6SopGXzu/+kls4t6rAhqMR9h1BjBs0aCAOT/Dgv+WWW8LOZs9X9O22226T1dj58+eTX5MdQF6nnHKKxHltctVgOqndtdkjpLCeIDrB7Lf7SpzYBQsW+FZeYV3Sr4qA7xHQ8cdfItT53V/yisWtmhBEQQbp4y699FJRXhEHLluVV3QdYcDQRyRkQJ/Rd7+RkReSFCDOa7Yqr5ALwoChj+irX+Xlt/tL+VUE4iGg4088dLx3zsgLc57O796TTyocqQIbBa1XXnmFkB4WGbaQDSnbCX2sVKmS9Bl99xsZeSHDFpIUZDuhj4VKlfetvLJdPtq/YCGg44+/5G3kpfO7v+QWjVs1IciBym+//UYnnngibd++nZC9ymvpYXOwa9tPpJ3F22ipUqVo2bJlVLp0advqdrIiyKtmzZr0+++/U+s73vJcelin+o60s5Oev4ZKlixJy5cv9428nMJD61UEMoGAjj/+Gn90fvfX/J7omdYV2BwIDRgwQJTXs846KzDKKyCAoo4+Q3EHBn4h8ArltVzdVoFRXiGbyqefJ31G3/0kL7/cV8qnIpAMAjr++Gv8gbwwx+n8nszd7f0yugIbJqP169dT9erVJZbfwoULqVatWmFns//rkiVLqF69epQvXz5auXKlmBV4udeQF0KC/X3IovMfnUrFy9f0Mru287Zjw3Ia0/8MOvKIfLRq1SrPy8t2ALRCRSCDCOj446/xR+d3f83vyTzaugIbhtLTTz9NBw4ckNzzQVNeAQP6fMkllwgGwMLrBB4PHjxIVZt0DZzyCtlAYUffgYEf5OX1+0n5UwRSQUDHH3+NP5CXzu/+md+TeRZ1BfYflLAVC6PuXbt2EcIT+TVVbDJCj1cGqWYRjqpIkSK0bt06sbGMVz5T5yAvOJ7t3r2bOg+c5OtsW+lgiFSznz3QmgoXLkxYYYBNrJIioAg4i4COP4fx9cv4o/P7YXn5ZX5P9unVFdh/kBo2bJgorx06dAis8goooLgDAyjywMSrBN6gvJav1zawyitkg1SzwABYeFleXr2PlC9FIC8I6PhzGDW/jD+QF+Y0nd/9Mb8n+0yqAvsPUiNGjJBv119/fbLYZW05g4HBxIsdNbzVbHWFF9lzlSeDgcHE1ca1MUUggAiYZ808ewGEINRlg4HBJHTCQ18Mb2Zu8xBrrrNiMDCYuM6AjQ2qCQGDCYelGjVqSHajzZs3U4ECBWyE2H9V7du3j8qWLSvB8lesWCGObV7qhZHX0QWKUPfnF9OR+YMtr7/376ORd9SmA/t2kRfl5aV7R3lRBNJFQMefSAS9Pv4YeRUrVox0fify+vweeXfF/6UrsIzPyJEjBSWEkgq68goggIGJf2uwEYA88s/whIxUQVdeIRJgACxABhv5of8UAUXAdgTMM6bjz2FovT7+GHnp/H5YXl6f31N5YFWBZbQmTpwomHXu3DkV7LK6rMHCYOOlzhqeKp56jpfYyigvBguDTUaZ0cYVgSxGwDxj5pnL4q4m3TWDhcEm6QtdKGh4MnOaC016vgmDhcHG8wzHYDDwJgQIQVSiRAlxgsH2wnHHHRcDqmAd3rJli5gRwLv9jz/+oKOOOsoTAEBexYsXpz179tDFzy+igsXKeIKvTDOxd+dW+vCOOlSoUCFCjm+vyCvTuGj7ioCdCOj4Ex1Nr44/Or9Hl5dX5/fo3MY+GvgV2Llz54ryWrt2bVVew+4TKPKICwvvdmDkFQIvUF6Ll6upymuYUKDIFytXQ7DxkrzCWNSvioDvEdDxJ7oIvTr+QF6Yw3R+j5SbV+f3SC4T/wq8Ajt//nxBqWnTponRCliJZs2aSY8NRl7ovuHl2Bqne4EdT/FQpkYjz8nLUwApM4pAmgjo+BMbQC+OP0ZeOr/nlpsX5/fcXMY/4o194fg8Onp2+fLlUv+JJ57oaDuoHHHorrrqKklVe/bZZ9Mtt9wS0ebbb79Nn3zyiRy77bbbqH379hHn3f5hMDEYud1+tPYML8WOrx7ttGvH4PE/7dXbiIVJ5U9uQye1uzai7ZXTPqB1c8fKsZPa96TydVtFnHfih8HEYOREG1qnIhBkBMyzZZ41J7Hw4hgTr78GE4NRvLJunTO8mLnMrXZztuPFud9gYjDKybMffgd+BdYIr2bNmo7LC9mtYE86evRoevDBB+mvv/4KtTl58mRCfDacO+KII6ht27ahc5n6YjAxGGWKj/B2DS/Fyp4Qftj17wjhtX/PDlo/7wua//ET9PeB/5flpiXTacabfeRcvnxHULnaZ7jCn8HEYORKo9qIIhAgBMyzZZ41J7vuxTEmXn8NJgajeGXdOmd4MXOZW+3mbMeLc7/BxGCUk2c//A68Art69WqRE+LAukH9+vWTZrZt20YffvihfF+zZg1169ZN8jS3aNGChg8fLkqsG/zEa8NgYjCKV9atc4aXomWrudVkzHbqdeoj5/7atZ3Wzh4j33dtXUeTn7+OrL8PUpmajemMm1+mfPxC4gYZTAxGbrSpbSgCQULAPFvmWXO6714bY+L112BiMIpX1q1zhhczl7nVbrR2vDb3G0wMRtF49vqxwJsQwGMb5FYO+bPOOosaNmwojlFDhw6VeKtdunQhKLRwmhozZoxnYtEaTAxGXriZDS/5C5ewhZ1fF0yg9T+MT7outHvaxQOkfPmTW1OpqqfQ9jULaOk3b1Kl0zvSt/+9kqDQwqGqbZ93XY1TazAxGCXdKS2oCCgCSSFgni3zrCV1URqFvDbGxOuKwcRgFK+sW+cML2YuS7fdL774QuboZOtBu4899pgU99rcbzAxGCXbJy+VC7wCC9sUEJb43SK8iWHFdebMmdSyZUv68ccfqVy5cjR+/HgqVaqUW2wkbMdgYjBKeIELBQwvRx9T2JbWfmPlc9nEYUnXVahkuZACi4vqdepNk1+4jraunEPjB3WiP9ZzaK/iZan93SPpmCIlk67XjoIGE4ORHXVqHYqAIvD/CJhnyzxr/3/GuW9eGmPi9dJgYjCKV9atc4YXM5el2y6iGrz88stJV1OxYsWQAouLvDT3G0wMRkl3ykMFVYHNgAKLjCAnnXQSLV26lOAlWbRoURo3bhxVqVLFQ7fG/yv1v//+O+XLl88TvBk+jipgjwJbpXEXKlGhVsK+/f33fpo69MZc5ZCNB84LOzetpN/X/UTgq91d71GRYyvlKuv0AYOJnwckpzHS+hWBdBAwz5Z51tKpK9lrvTTGxOPZYOLF+cIoa/H4T+bcxRdfTHXr1k1YdP/+/dSjR49c5bw09xtMzD2di1kfHAi8ApsJGR06dIjKlCkjCizaf+SRR6hBgwaZYCXwbRbnrX78JaJDBw/Q1CiFLOsQFSh6rCiwON3gwvuoVJV6UUrqIUVAEVAEUkdAx5jUMXPqCiw84S8RHThwIGoRnfujwpLng+54l+SZPecvzMRbCMJnTZs2LdQ5RB7wIpk3M9jKWBwuygt/xm7n4L7dnoBs1rB7aMvy70K8rJ/7Rei7218MJuaedrt9bU8RyHYEzLNlnjU3+uulMSZefw0mXpwvzFwWj383znlp7jeYmHvajf7b3YYqsP/Yvhph2g1wzvoGDRpEr7/+Oh155JF09913y2mE0MJfPILxOJy+3CSDiZducMPLgb8yr8D++OlTtGLyu2xecQTVOfdWEc3mpTMIYbTi0e7tG2jeyIG0f/dhB8J4ZVM5ZzAxGKVyrZZVBBSBxAiYZ8s8a4mvSK9EqmPMrm3rafmU4bTgk8G0asYocotP9NK0ZTBKr+f2XG14MXOZPbXmrZZU5/69e/fSxx9/LDu0mPtXrFiRt4ZjXGUwMRjFKObpw4FXYIsXLy4Cgt2O04REBQ888IA08/TTT9OQIUOoXr3D280PP/xwzObBW69eveitt96KWcaJE9u3b5dqDUZOtJFqnYaX/bv/SPVSW8sjUQHiv4JOv2wgnd7jYSpRsbb8XjB6iHzG+rdwzNP009jnaP/enbGK5On4/l2H72GDUZ4q0YsUAUUgJgLm2XJj/El1jFkz+1P6tF8LmvlGH1r89Ws07ZVbaPQ9TWjHJnsVn1jgeHH8MfJyY36PhQuOpzr3r127VqIVXXTRRfTMM8/QHXfcQXXq1KFXX301XjMpnfPi/J5SB7hw4BXYatWqCWZ2v93kFMSECRMkUQGO33DDDaKQ4vudd96JD5o4cWKEWQGOffbZZ9S3b1+xj3WaP7SXk1auXCmHDEY5z2fit+Hlz82H4/e6xcMRRx1NLW54gRpd8Rht+HmyJCpA2zVbXUm1zz7s3FXnnJuFnc2Lp9PmZbMiWNuxcQUtHPMMjX/s/JSiHkRUkuDHn1vWSAmDUYLieloRUARSRMA8W06PP6mOMX/xC/2s/91FhUuVp4uenk89hi6n1r2G0b6dW+n7d+5PsZd5K+7F8cfIy+358+ijj6Zhw4bRf//7X8rL3H/PPfcQEgx8+umnBOV71apVVL16dVFkEXLTDvLi/J5qvwKvwLqRjQJhsvAmBcPuVq1a0YsvvhiS02WXXUZly5aV3zlXYXHzjhw5UpIaHHPMMa5HAjAZOgxGIaYz+MXwsnPzKte5qN7yEip2XDWa/Nw1kqig7EnNqclV/wnxUa3ZRVSgWBn5/eMnkauwf/y6hJZNfod2//YLmXiJoQtt+mIwMRjZVK1WowgoAv8gYJ4t86w5Aczv635OeYzZtmqeZAY8pes9VLh0BWGrcsOOdHzdM2nriu+dYDNXnQYTg1GuAhk4YHgxc5mbLCBtPJIFpDr3w9fk888/p86dO9P5558vLCNCEUwOEd1g3rx5tnTDYGIwsqVSlytRBfafFLLLli1zBHoECe7YsSPt3LmTTjjhBProo48Ib2eGoJjeeuth+0m8qS1YsMCcEltZZMnAX5MmTULH3fpiMPHSDW54Qdgqt2n/np004ekehBzlRcpUoVa9/kdYmTV05NHH0EntrpWfGxdNoe0cVstQldM70UVPzZO/Bhf0NYdt/TSYGIxsrVwrUwQUATLPlnnW7IYkr2PMUfkLUmUeY8rUaBTB0gEes0x4q4gTDvwwmBiMHGgi5SoNL2YuS7mCNC7I69wP21foDIgVH04m4YBdNqsGE4NReFt++R74MFomfNWsWZFbvnYJEDY4v/zyS9zqHnzwQcKf18hgYjDyAn+Gl20r5rjOTv5CxejiZxfGbRcrIPjLBBlMDEaZ4EHbVASyGQHzbJlnze6+5nWMKXtSM8JfOK3+7hPCyizMnNwgg4nByI02E7VheDFzWaLydp7P69xfqFAhGjVqVAQr0CGefPJJKl++PJ166qkR5/L6w2BiMMprPZm8LvArsEjrWrhwYVq8eDFt2bIlk7LwVNvAApgAG2DkFQIveMB3bFxOe9m+S+kwAsACmAAbL8lL5aMIZBMCfhh/ELN6PkchmPrSTVSiUh06tfvh1NdOysGr4w/k5ff5/csvv6TGjRvTH3/8IXa1BQsWTFuUXp3fU+1Y4BXYo446ipo3by64TZ0aLVR9qpBmR/kpU6ZIR4ANMPIKgZcWLVoIO1uWOrNq7pW+psLHliUzpTiw8ZK8UumDllUEvI6A18cfpMb+/N/t6UeOhHJC84upw/2fUYEizqcn9+r4A3n5dX6HwnrttddShw4dqHTp0jR9+nRq3769LY+IV+f3VDsXeAUWgLVp00Zwg9e/0mEEDBYGGy/hYnj65YcvvcRWRnlZP/8wFgabjDKjjSsCWYyAeca8Nv78suBr+mLQeYSEAmf3/YRa3vgiwSTBDfLy+GPkZeY0N/BIt41NmzZRy5Yt6b333qMnnnhCHLfsMh0AbwYLg026/GbqelVgGfnu3bsL/p988gnt27cvU7LwTLvAwGQHM9h4hjlmxPC0bu5Y+nu/ygsYrJ87TkRksPGSvJQXRSCbEDDPmJfGn327ttO0l2+hUpXqUqeBE+n4Oi1dg9zr44+Rl5/m99tvv50QC3bSpEkSSjPc8TtdwXp9fk+lf6rAMlqIrwYbE0QKGDt2bCr4ZWVZhPAAFsAE2HiNjLwQDQCrDkGnX+Z/JZERvCqvoMtH+59dCHhx/FnNWbf279lBx55wGq39foxk40JGLvytnfO5owLw+vhj5OWX+X3jxo0Srahu3bq0aNEievPNNyP+tm5Nz/fD6/N7Kjerd4wbU+HagbKXXnopzZ49W0JXIW6bF+mII9x533jjjTek+8DEq2TktXzyu1SlUWevshmdL5vliEkK5GV5RQdCjyoC/kTAa+MPbF9BSya8ngvQQpzcAGH8nCI/jD9GXkjj7tX53chn7ty58vW7774j/OUk6CllyhyON57zXDK//TC/J9MPlMnHQXOtZAtnczlku6hcuTIhPzBisdavXz+buxuzb0i6cMoppxBiza1bt45KliwZs2wmT0BelSpVot27d1PngZOoZOW6mWQnY20j6PlnD7QWT9v169d7Vl4ZA0gbVgQcQEDHn8Og+mX80fn9sLz8Mr8n+8i6s6SXLDcZLAdF7frrrxcOBg8enEFOMtu06Tuw8KryCoTAG1Lygn4a97x8BvGf6Tu8Vb0sryDKRvucvQjo+HNYtmb8wVjs5fEHvOn8TuSX+T3ZkUNXYMOQwgoW7GWwKL1w4UKqVatW2Nns/7pkyRKqV6+epKxFnmSscHqZIC9kN/v7kEXnPzqVipev6WV2bedtxwbOlX0/O2tYh6hEiRLUv39/uummm6ho0aK2t6UVKgKKQCQCOv4spzH9z6Ajj8hHq1at8sV8ofO7f+b3yKct+i9dgQ3DBQpbz5496eDBg9SrV6+wM8H4ij6j78DA68orJAIe8VZtHfqbZr/bLxhCCuul9JmVV5i+IGbgPffcIy9gTz/9NP31119hJfWrIqAI2I2Ajj/9ZOzFGOyX+ULnd//M78k8r7oCmwOl3377jU488UTavn07ffzxx3TBBRfkKJGdPxFi5MILL6RSpUoRciQjcLIfCPJCLmfYOLW+4y3OB36eH9hOm8d1c8bSpOevkW275cuX05w5c+iBBx6g77//XuquUKECDRo0iC6//HKyMwRL2oxrBYpAFiGg409Jwvjjp/lC53f/zO+Jhgpdgc2BEB5ETPygPn36yMpWjiJZ9xOrd71795Z+oe9+GYzAMHh99NFHhffvh/en/bt3yPds/oc+zh5+v3QRfQcG55xzjkTRGDlyJCG39a+//ipZXKDcjxgxQlbWsxkT7ZsikAkEgj7+INRT/vz5MwF9ntqEvHR+98fiVDIC1hXYKCgdOnRI0pXOmjVLViU/+uijKKWy5xDCimC1uWnTppKuzq1wXXYhGC6vyg3Po9a93rKrak/WM+m5awhB1OPJa/jw4fT444/Tzz//LH2oUaOG/MYqu9/k60khKFOKwD8IBHX8wc7OgQMHCGPLhx9+KC/OfrgpwuWF8VDndz9ILTqPugIbBRdM8EjhVrx4cVHshg4dGqVUdhxC36C8oq/osx+VGyOvYsWKiWK35Js3s0M4UXqBvkF5RV/jyQumA3BERBBsbJmtWLGCLr74YsKKyZgxY8RRMUr1ekgRUARSRCCo489XX30lSivGFrxMv/zyyykil5niRl46v2cGfztbVQU2BppVq1aVpAY4/a9//YsmT54co6R/D6NP6BsIAZ7RZ78SeDcBmueMeIA2LZnu167E5Bt9Qt9A6GsieeXLl0/MCJDNBZMLIjYg0kSXLl0k1u8XX3wRsy09oQgoAskjgGfx4Ycflgu+Hz4gEONP69atCbuUN998sziN3nLLLdSjRw/6888/kwcuQyUhL8x5IJ3fMyQEG5pVBTYOiN26dRM7WHh0Y9JHEOBsIfQFfULfYOuLvvqdjLwOHdxPE5+9khBkO1sIfUGf0LdU5XXkkUdKeK2lS5fSc889J1ELsDrbsWNHatiwIX3zzTfZApP2QxHICAKfffYZPfjgg9K29feBwIw/xxxzDL300kv0/vvvS/i+Dz74QMaU+fPnZ0QOqTRq5gud31NBzVtl1QY2gTwQExZp6PBglitXjqZNmyYrWQku8/RpxOxr2bIlIefyJZdcIlvRWK3LBgqXV8HiZanDgM+p6HFVfd21P7esofGDOtHeHZttkdf+/fvp+eefJ4Tb2rBhg2DTpEkTGjJkCJ1xxhm+xkqZVwTcRuCZZ56hu+++m2BbeeWVV9LevXtp1KhRFLTxB9EIunfvTlBeCxQoQMAFq7NepvD5Qud3L0sqOm+qwEbHJeIoJnysVmGlCjf5+PHjfZtqFiuvHTp0EOW1Xbt2NG7cOF95kUYIJsaPcHlhEml/9we+TTWLldcJT14iyqvd8tq3b59MMs8++yxt2bJF0IQCC0UWCq2SIqAIxEYA4wwSh7z11ltS6M4775SXwiCPP2ZHz9jDXnXVVWK+VLBgwdhAZvhMuLx0fs+wMFJsXhXYJAHbtWsXde3aVZRYGH9/+umn1KpVqySv9kYx2LzCbGDHjh0EZWj06NFUpEgRbzBnMxfh8jq6YFFq0+cdOr5WC5tbcbY62LzCbODA3j8dldeePXvoySefFPMCxLUE4f4YOHAgNWvWzNlOau2KgA8R2Lx5s8QInzlzJhUqVIjefvttQjQXQ0Eff2BSgAQHu3fvFkcvOApXq1bNwOO5z3B56fzuOfHEZEhtYGNCE3kCih5WK7HlDgUQcTf9FJ0AvIJn8I4+oC/ZqrxCcuHyggI4YUh38lN0AvAKnsG70/LCBAz7vdWrV0s6WqSlxW5D8+bNJYwckiQoKQKKwGEE5s2bR6effjpBeUUWvBkzZkQorygV9PEHzlzfffedJJmBSQHwws6lVylcXjq/e1VKufk68t9MuQ/rkWgIwBkGceN27twp8VKhBMIZBoohbH68SEhSgJBKTz31FP3999/iAPTaa6/RUUcd5UV2beUpXF4zZ0ynXxdMoN/XL6LyJ7ehI/N7U15IUjD15Ztp0fihkqYRDltuyQsOGW3bthW7Ndjz4d5esGCBtI/oBQjHVbZsWVtlpJUpAn5CAL4Q2MVCpkb4EeBFD9E9olHQx5/jjjuOYEKAKChQYhH2D5jATMmLPhfh8po+fbos8uj8Hu3O9s4xNSHIoyxgpI8tEryt4S0cdoReSzuL9LDIsLV+/XqJ84qwIdkQbSAvIoO8kAcbLx+FS1WgRpc/6rm0s0gPiwxbe7ZvoMKFC4ttXSblBXMCmBFAgYaZASadK664gvr160e1a9fOixj0GkXAlwjA2Wfw4MF03333Cf/YFXnnnXeSTtPst/EHcaYRqs+O8QfYIWPgQw89JI5unTt3FuywVe9V0vndq5KJ5EsV2Eg8Uvq1Zs0acYhCeCLQWWedJXaEtWrVSqkeuwtjtaxXr1709ddfS9UIMo23X8S+CzJBXogogdiFoHJ1W1HjKx6n4uVrZhSWHRuW0+x3+9HGnyeH+MDgDjkef/zxoWOZ+gIHL2zU/O9//yM4fiEQ+LXXXkt9+/aVLcJM8aXtKgJuIAD7SOxiIQEIVumwWHH77ben3LRfxh+n5osvv/ySLrvsMlm9Ropr+JF4+UUYq68wo4L8QTq/p3zLO36BKrBpQAwDdWwfYYLHGytW97A1j7fze++91/VIBYgwgFUCbHMdPHiQSpUqJXmf4SkLpUOJZAXglVdeEVvP33//nfIdcSRVbdKVTu54h+uRChBh4Kdxz9Oa70aLuUDJkiVlpQIxJZFkACsVmDS9Qgi5BVtZrDzBcxeT+Q033CCKbNBfjrwiI+XDXgRgF47nECmZ8XwiZSocHPNKMM3x6vgDW3g4czo5X0CJhxneDz/8EMomiAg/XqSrr75anPNgOrV161bCfIExD/a9Or97Q2KqwKYhh8cee0wUIbyxfv755zRgwADZdkF+aBDCVcHM4LzzznPMRhYrYmPHjpWsIsZIHjmqsV0+aNAgKl26dBo9zN5LsT0OecGsAso+qHy9tlSz1RVU8ZSzHLOR/Xv/Pvplwde0fPK7tGHht9IuXnpwnxh5/frrr3TyyScT7JexfY9zXiKYpPTv319W9YEd7jdk4bnnnnuoYsWKXmJVeVEE8ozApEmTZAsdY0WdOnXkZbJ69ep5ri/8Qi+NP1DKoFjjEwq7088w4uRiBwcLLVhYeeKJJ2TsCMcn099HjhwpC1FQ6uG0BydoJIEBv8AKpPN7pqVEpApsHmUA5QJhQfD57bffUps2baQmTO4IEA/FyGw9YHUW9rF4k4cBO4zb0yGs+E6ZMkWUZti5YuUXBE9KKDtIjVepUqV0mgjMtUZeUBSxog46ukARqtzwPKp46jl03ElNqWCxMmnhsXfnVtqyZCb9Mv8rWjd3LB3Yd3hLCnauWMGMJi+EoYG5A+4dbGXBztprhIQY999/vwRth4MgnMDuuOMO6Q/iKSopAn5FALsM1113nbzcdurUiUaMGCGZpuzuj1fGH5gDwczMxLK1u5/R6sMLO3Z0YCMLZ69XX31VxpBoZd089ssvv8juKVZcEc8WTtowC8SuE3bHJkyYoPO7mwKJ05YqsHHAiXcKK1BYgW3fvn3I1jS8PG7+YcOGyaAwe/bs8FNi94NVW2xNwBaoRo0asj0FBRR/ICi/+EM9K1asIGQ5WbZsmdhvLl68OKK+xo0bi7KDLQ9scymljkA8eRUvV5OOrXE6FTu+OhUrewIVLVuN8hcuQUcfU5iOKlBYGju4bzcd+Gs37d/9B/25eTXt3LyKdm5aSdtWzKEdG5dHMJSsvBBXEvETsWUJe2Yveu6iY7gv4diFuMJYnUDQckyEiKBQpkx6yn8EcPpDEXAYAewowL4V2/yg2267TbLWOf3sZXr8QbSRBg0aiPPounXrxPzMYaileizAIHsZFg8wJ+J3Ju3+oUxjTseilDHhgkkgVmShZGNOB8WTF+x6dX4XmJz/xwJTShGBTZs2Wbx6ZrF0LI51l/BqVkAtVnYtNgIPXYdr8/qHtlEX6kTdSvYiEC4v3kLKs5yMfFFHXuTFK+0Wr9ZL+5yW0d5OOlDbTz/9ZPFqlcWTvfCM+5SdvyzeLnWgNa1SEbAXAbZztM4880y5dzksosWrrvY2kGRtmRp/zj33XOk7nlk3iZVnq0qVKtI2my9Yc+fOdbP5iLbYBlj44HCBFiersDiclvzGGM4rsxFlzY9weRm9wIz9efnU+d0gm/hTV2D5DkuVsOWLPM+IB4hVp1QIb/j8gEpcPKyq4g92R3jrRUgu2BPibd+sxsIbHaYKWKnFH96SGzZsGIg4rqng6lTZWPKCrMwqOdp2Sl64v2B+AlssxFLEPeB1Ap/Ykvzqq6+EVZhBIPzQrbfeKuHcvM6/8hc8BGCmgxW3tWvXUvny5cVDHsH3M01ujj9Tp04lVuDFbwI4sCLlWvfhJIUdJ/CAse7dd991PSwlVqGxOwZTAfi0wLkMK6nYQYWpw8MPP5wQDzfllZCZIBRIrONqiXAENm7caPEWqawy8UQdfiqt7+btlx2y0qpHL84+BNjhQVYBOK2rxQOkbzrIA7/VunVr4Z3HUovNWyyscPz555++6YMymv0IsJlOaGesSZMmFsb4oBKHjZLnNRM7Pn/99ZfFzsfSPjtLWexL4poY2LHMqlu3rrTNL9rSLivR8ptfaCxerHCNF20oeQRgQK2UAgJs2yc3NYcCSeGqxEXN1tXkyZMTF9YSgUKA7a0sbK1BCWTHB9/1HdtwZmJEH4499liLPXottnvzXV+U4exCAEqSMXnhnQ6Lo7pkVwdT7A07Kck4g/GGVyJTvNqe4o8//nhIJmyP7MpLO8dNl36zs5bFSVvkjx2h5RjHv7anY1qL7QioApsCpE6tvoKF0047TR4WzjufAkdaNCgIcBBwuT/y589vcbxfX3Z74sSJFm/LSj+gyMLO7KWXXgq80uBLYfqcabw8cZYpuRex2oedASXLYidMi0P4CS5vvvlmxiDhKCwWRzURPmBX7+QKKJsLSDtsvheyv8VCAcaoU0891eIIKxnDQRuOj4AqsPHxiTjr1OorGjnppJPkgeHsSxFt6g9FwCDAIarkHmE76Iytjhhe0vmEMs62ZtIXTBIVKlSwOG2lr/uUDh56rbsIsH2nhWcI9x77GFicNMRdBjzeGocQE2ywGgmFNlM0bdo0i+OYCy9Y4OFEKrazgjo5Uoq0MWTIEKkfC1Xs0yDHOBaw7W1qhfYhoApskljCI9HYvsJr0m7CJI4BNZano93taX3+QwCrEBxIXe4TdoryXwdycMxZjWSFA/c9/uCJjMmTE4HkKKk/FQF7EIBSZBQWDmNo6YJBblzx/HFmPXkmYR+cSeIQfRaHmRReOBa2xc52trED5ZxDZkndZ599dkhZN3a4Xbt2ta0trcgZBFSBTRJXKAyYZJ26qbESgPph76ikCMRCgL10LWx5ctYcC05S2UAIV2S2LfEMQEnnLD26dZcNwvVQH7AtjW1i3GNQWHSsjS2cF154QXBq1KhR7EIundm2bZvVokUL4QfzpF2ropwBTOpEqEKExgTBMRvjK+4TjhDkUg+1mbwioApsEshhoONQQHKzO6U0cDpRqT9ThvNJwKBFPIKAeZnCFh+8Z7OBsBry1ltvhUxpoGSgfxzYPLQykg391D64jwAidxjzG9xXnP1OX44SiAGOTCYG9TfffJOgtPOnMc5dfPHFMkciRm+6K8OI3w4lFQ584SYkbdu2lTZgLqjkfQRUgU1CRgMHDpSbGsHonSB4vmJghYOOkiKQCAHcLybkCybmbCIoG5xS0jrhhBPkmcBzUa9ePUvDy2WTlN3ry/bt2y3OZBcaX/GSpJQcAo8++qjghm12LxCcqTgzmvCEHSiME3khTr0eGl84pnuoijFjxkjdpUqVsnDfKHkfAVVgE8gIdofGkBxe1E4QtkgwUePBUVIEkkEA2Wqwao8VBLu21JJp160ysMPDNibs3vBs4A+OHJxS1y0WtB2fI7Bo0aKQzTgiXsycOdPnPXKXfew8Fi1aVJ69H374wd3G47T2yCOPhMYELC6lSpdffnloPEHsWRB2Po0jNUL8KfkDAVVgE8gJcQIxeSKOpVMEr1i0gclaSRFIFgET6gUOF9maHAATDJ5BBBM3iiyCzWu85GTvkmCWQ2gko3zhxWf9+vXBBCLNXpvIO1dffXWaNdl7+SuvvCK2qhgTECs22VBXw4YNk3EEUQaWLl0aYuq///2vHIcSq06kIVg8/0UV2Dgiwo1sghkjwLNT9PPPP8vD+oEDQAAAQABJREFUU7t2baea0HqzEAHcn5xWWO4dZOvKZoINHJwusJJmFNkzzjjDmjFjRjZ3W/uWBwSwcm+SE1xyySUSlD4P1egljMCqVavEYRTmbV7LUPbRRx+FYsVCzmY1NZbgFi9eHMq4Fp6cAOYC2P3EuAIzAiX/IKAKbBxZmXh4derUcdSRBI5heHi84PEZBw495UEE8PJjAn6PGzfOgxzayxIC0GML0Zj14LmB4wWyfSkFGwG85Fx22WUylkKB7devX7ABsan3yDqJ5+yBBx6wqUb7qoFZn3GwRmQJOJ9FIxyHLT36ccUVV0QUMVm4YCut5C8EVIGNI69TTjlFbninM5J8++230k6bNm3icKOnFIHoCCBvOQZmbLMHxfkAjhgDBgywSpQoIX1H/7t06WJ9//330UHSo1mNwK+//hrK8obt4U8//TSr++tm5xC6D88X4ud6MeoJ7HPNzgxSsmNsyEmIPIE+wEQg3NwKCwDwJYBTmBPx3XPyob/tRUAV2Bh4mtSd5cqVS7g1EaOKpA8b70ekzFNSBFJFAPZfLVu2lAH60ksvTfVyX5f/448/rL59+4bsHTFJIdwO4jkqBQOBWbNmWRinIXtEr/jpp5+C0XEXe2lSQL/++usutpp8U0hIUbFiRbkHYCMf/iKPONO4NxB+K6eSilVbnLv11luTb0xLegYBVWBjiMJk6IDdndP03nvvyUPUo0cPp5vS+rMUgZUrV4bsu3A/BY1+++03Cw4nhQsXlmcJW8jwNsYKi1L2IoB4oMaEBjtYuA+U7Efg3XfflecKCUe8SrDXrVatmvCJVMFbtmyxkMnLOPPB8SucRo8eLWVLlixpIRKQkv8QUAU2iszwloa3Mtz4WOFxml577TVpDynslBSBvCJg7qNjjz02lFkmr3X59TqkfEasSKy24BlGVh04uGEiU8oeBLDrcPfdd4uMIWd4yav3uHPyRZgpEwnEqXCSdnCPVOwmHBY+TbzsnItDiKVt0nI///zzdjStdWQAgSP44VfKgQCH1JAjPPERp67Lcdb+nxxrVipl2y37K9caA4PA9ddfT7wlRryaQDfeeGNg+h3eUc4eROyFTrwaQ2z3RmzfRuxxTBzhg26++WZavXp1eHH97kMEduzYQeeddx49+eSTxNmUiFfWiBMUiKx92B1fsAyczZiC58urVKFCBZoyZQqxwxZxmCziHRjiMIPESQ8iWGa/AeJdK2IFl2655ZaIc/rDPwioAptDVlu3biW2mSFeuSH2Tsxx1pmf7FktFasC6wy+QaqVHQ6JHZuI7arpjTfeCFLXI/rKNpEyaa1YsYJ4dY7YpEAUHV6Vkeea44JGlNcf/kCA89MT2zjS+PHjiXcaiNOchhQrf/TAv1xCgYUiyw5yxE5znu0IXmL79OkT4o8dzwjzuiEOB0acZUx+YrGKHbjMKf30GQKqwOYQ2Msvv0y8vUDsUEW8xZDjrDM/zQos2+8504DWGhgEsAIxdOhQ6S+nSaSgK2ocx1lW59iEgNjBjQ4dOkS8ZUg1atSgu+66izCZKfkDga+++ooaN24sK2v169enOXPmEMcC9gfzWcAlXgovuugi4nTPhHnSq4SXHLaHF/Ywh7NZEbVu3Tq0+3LfffcR5twLLriAOHSWV7uhfCWDQAbMFjzbJAIhG29WhLZyi5DPnmVlaQo7txDP/nZ4cJZ7CrENWWnL/g4n2UNk3+FJOJTFp2DBghZPaOLwkWQVWiwDCCDvPUIdYZxEXFKk+FZyHwETUgthqxIlDnCfO0viwJp4r0hugJBZJkJLlSpVLDj9wcETjn9w+lLyNwLqxBUmP+NpyW/3YUed/wonEwzMTsebdb4n2oJXEIAHLuI24r569tlnvcKWZ/hAdILOnTuHMjYhesGDDz6oXuyekdBhRqAkXXPNNXIf417mVXN9IcuwjEx89OHDh2eYk9zNw5kP90mtWrVC8V6hxCIVPI4joxg++/fvn/tiPeI7BFSBDRNZ06ZN5eZ2O9Yd4lbiofrggw/CuNGvikB6CGC1AfdVoUKF1As/BpSIF9uhQwfBCVgh8sigQYNciT4SgyU9/A8CmzZtspo1axa6h0eNGqXYeAABrIbjWYFS6CUyfOFlNGcsYCQ3MFEHsJKPtLJK/kdAFdh/ZDhv3jx5KBETDukq3aSOHTtK22PHjnWzWW0rAAiY1SsoAgg9pBQdAaRzRkpaTMz4Q4avwYMHh1Zxol+lR51CYO7cuaHA9JUrV9bEFE4BnYd6MT9ydB55ThYuXJiHGuy/BPeLCZ2HndScBAWWnbtCzzcSXrB/QM5i+ttnCKgTF89WoBdffFE+ecInXrGS7279Uycut5AOXjsIF8MZamjmzJnESTmCB0CSPW7UqJF4tE+fPp3YZo44/jPde++9xIHRCZ7KnEs9yZq0WLoI8E6UyIBjesonnLV42zrdavV6mxDA/HjFFVdIbTnDU9nURErV4FnlXUxxvkZILE5gkut63lUhNqsSJ0A86wizB8cuL0dTyNUJPZAbAZ8p3I6w+/vvv8s2K4y7MxHw/LTTTpM3Qx6oHemfVhpsBExaZNh/eWXFxOsSQbB29ngPrdjAaYWjO3gyF7zXsUyWPzgbPvbYYyHMkRYZAfSVvIeASfaDnQp+ucsYg7hnzj//fLlnkO4WCQpyEkclENtXzO/ff/+9hfnepMaFrSz8BZT8iYCaELDcnn76aXkAkBc5E2QyhyCfs5Ii4AQCt99+u9zjSLGoSkHyCEP5D1dkOUyZBRt5L3pgJ98r75WEo41RRGCjqNmRvCejnBxxPF4ZUziJRM5Trv1GqndelrNKlSplrV69Omq7cNZEmeuuuy50fvv27RactXEcC0icHCN0Tr/4BwFVYFlWRoHkAM0ZkRwmRTxIapOTEfgD0SjCDhknhn79+gWiz3Z28qOPPrJOPfVUeU7xrCIkz7BhwzR9qQ0gI5yRSfkJRWTChAk21KpVOI0AoubgWciUMxdCXeJlByursfxHOOGF8FisWLFc6bXhJFizZk05j1BbmVxJdlpW2Vp/4BXYSZMmyQ0MJZIDNGdEztiGwUCArQ0lRcApBBDDkTPMWZxe1YLTklLqCLz33nvWySefLM8rnlm8FOCYOsiljiWugBJSunRpwbNOnToWZ07LW0V6lesIZNKZa926daEwgQMGDIjad+w0wUQAzymnHY5aZu3atRYnO5EyiEaiu1NRYfLswcArsGzwLTcvYkBmijg9n/CgD0+mJBCcdvv27Sv3GgZ2TrEYnI7b2FPY3WH11ezcYILEd6zSatKI5IHG1jNepoAfZz604Cmu5C8EbrvtNpEfp113jXHYubIjlrQLpTPWy+N//vMfKYNnM97cCtM9E6EAIS1j1edaB7WhpBEItAL722+/SegNrEqtWbMmadDsLIiHEQM4HGyUFAGnEcD9hpUu3HNuTjpO9ysT9WOie+2110KmGcAUq7OfffZZJtjxTZtQJm688Ua5B4EZMhGq4u8b8UUwasJPYhXdLbvwnj17yr3DEUIs2LJGI45gYRUpUkTKcQriaEUijv3www+h0GCoX+/HCHg8+yPQCiwyFGEAxVtcpghKNHiA7ZeSIuAGAoh2gZUv2I7BhEYpPQQOHDggEQpgF4tnGX+wl4UDmFIkAlu3brXOPPNMwQhxO0eMGBFZQH/5DgGTmcuNRBOvvPKK3DtIAY0kJLEIaWTxHCJtdLI0bdo0iUaE6+6+++5kL9NyGUQg0AqscRzA1l+mCDY4eGBgh6OkCLiFwMCBA+W+wyoGPMCV0kcAK1B4KTZOmXiuEcEAIbmULAuhl4ySD4wQ0kjJ/whwnGQZS5CQx0maNWtWKBXsO++8E7Mp2FXj2UMGQtjKpkJ46TTpZjUFdyrIZaZsYBVYPAy4yRHfESsomSLkZAcftWvXzhQL2m4AEcA937BhQ7n3wsPLBBAK27sM22Jk8cLYgmcbf/By5iQJtrfllwqR1hgpPoEFwi9t3LjRL6wrnwkQ2LZtmyh9iAiwYcOGBKXzdnrz5s2hzGzxTJ9gnmJMpBBTOC+ETF7YnYJp4ciRI/NShV7jEgKBVWBvvvlmGUwzvVUAb3AM6jBKV1IE3EQAL0/HHHOM3H/jxo1zs+lAtAUvbc4AZB177LGCMZ5zpKsNmiILD3AoBOg/tnSjBZsPxA2RxZ2EXCFfxGW1m/Cy3apVK6n/jDPOiLvgNGTIECl34oknpmWTaxzAMD5OnjzZ7i5pfTYhEEgFFiskJnTVTz/9ZBOUeavGbHdwWru8VaBXKQJpIGCSeJQvXz6mQ0Qa1euljABMNBDlxIw5mOgRtD/bQ5lBge/WrZsoFFjNihXKSG8S/yPw+eefi5zh8W839e7dW+rGGBVv5Z7TwlpFixaVsoj/mi6Z5C8lS5a08LKv5D0EAqnAvv/++3KTI51cpgkey5jQEEZGSRFwGwF40mN7G/cgHB+UnEOAc7Zb9913n4Wg6sAbf1i5iueM4hw3ztYM235kfUMfixcvbn3xxRfONqi1ZxQBxFAvV66cyBvmeXYRQq3hHoJd6owZM+JWi9TDKHvhhRfGLZfsSYyNqAt1Vq5c2YKCrOQtBAKpwJ5zzjlyU7744osZlwaCoOMB6dGjR8Z5UQaCicDKlStD9okffvhhMEFwsdeIPPKvf/0rhDm21zH5ZssqDxJmlClTRsY1bOVqimwXb64MNnXXXXeJzLFyaQd99913IRMnhKuLR3CUxDwKxy28PNlF2K1t0aKF1I3Us5py1i5k7akncAos4sNhOwu2LbFiyNkDbXK14MHEg4fYc0qKQKYQePXVV+U+hL0mUiwqOY/Ali1bLEz2CAmEMQDj0tVXX20tXbrU+cYdagFhsUxiFiwUaHZBh4D2YLWIpYr7GC8v6TpGwxkMJgOoD8kS4hHaMhGFYHNuN+GF02T0OvvsszOWsdPufmVDfYFTYOEdjIcCGTe8QCYWLex8lBSBTCKAwRnPBuwzldxDAJP1TTfdFArfA2/uG264wVq1apV7TKTZEraQkZAA9w/+0B/NaJQmqD683CiSsInNK8HJr2nTpnIfwXkrkTL81FNPSdkaNWo45iCIREcmW1cihTqv/dbrUkcgcAqsCbr86aefpo6WA1fgjRED/v333+9A7VqlIpA8AtidMI5Gb7zxRvIXaklbEEDMymuvvTa0golkE5gsU41laQszKVSCnax27drJOAZbRdgtKgUTgccff1zug3RM4vAMYE5EzGAkvohHePkzjltO21nDBtdEbfGC+WE8XIJyLlAKLCIO4MFA1iu30t4lupHg1AGe8hqzLlH9el4RSAWB4cOHy/0IxxuvK06p9MtPZbHyevnll1tYicXYAKXwzjvvdCzGZjrYLFq0KJRKF3FvZ86cmU51eq3PEcCYAZtumMXs3Lkz5d6YpAiwZYVJQiK67LLL5Bnp2rVroqK2nEeMWDyTeLlMJkWtLY1qJTEROIKFERjim0/6yuYDxJOCJ/rNoWaED87b7Al+lIlgI8ATAl1wwQXEzgrECQ7wghtsQDLQe86ORhirFi9eTBireHuennnmGTrhhBOIX3iJbWczwFXuJnmbmDgpAbETIHFSDOIUxcRbv7kL6pHAIMAZJYlTBRM7PxEnr0ip3xxSktgRTK753//+RxzFIu71U6ZMIba5JlaWiU3x4pa16yS/WFL//v3lmezevTuxvbpdVWs9eUEgpmqbZScOHTokoTAYIwtesl4hs12iW7ZekYjyAeci40WOFRGlzCKA6ARdunQJJQNARqsHHnjAgnNJpui5554TpzOMp9gu3rNnT6ZY0XY9hoBxTIZNfbKEXYfSpUvL6mYy5nSwiz355JOl/COPPJJsM7aUgy5hEjfA7jaTz6EtHfJxJYExIeC3NbnZYVeDG9ArxG9xwtcHH3zgFZaUD0XAQupPKCfYylu+fLki4gEEEC/23HPPFblANrD9w+SN+LJuEcIKmW1bbBXzapRbTWs7PkEACh0iUWCbPZENK7qE0FTG+Qvx0JNx/jMJWKpXr+6Y41Y8uJGk47TTTpNnEUmIkMJWyX0EAmNCwPFWecwn4niLxAOvfPfCv127dgkbakLgBWkoDwYBmBFwSCfilTX55Jc+c0o/M4QAO6ASp/yl77//nthpijjDF3GGL6patSpx6kv57SRr7DBDnMpTtm1ZeSZ2hCV2QnWySa3bhwiwjwmdddZZss3+0Ucfxe0BxhXMybzLQKzEEtvgE4eTi3sNJxSghx56SMrwTgCxY1Xc8k6c5Bd7GjNmDHGoL5o0aRKxjboTzWidiRBwX2d2v0WEeDEhMJIxDHeTQ7YXkrc4fgjcbFbbUgQSIoAYnhUqVJD7U50ME8LleoHp06dbyA3PY7z8YQsWK1NYHbKbkF3JZFpiW1wr0ym47e6f1mcvAsOGDZN7sm3btnErRkIP3L+IP51s2DizfW9Xxq24DCY4GZ5sAX1WcheBQJgQfPPNN/KQICuM14idH4Q3doDwGmvKjyJgffnll3J/InzMwoULFREPIoCXXxM3E8oAogG88MILFrb77aC33347FD6oTZs2avNnB6hZXgfMWjBmIJJGrMQor7/+uowtiLIBE79kaOzYsXIN71ha69evT+YSx8sYm19EXvDaApnjnc9wA/HX6hMt3/rkPNuXCqfwGvQaGRMCdszwGmvKjyJA7IhBHIuUOOwcXXXVVcTOE4qKxxDgYO/E4auIw/pIVIDNmzcTZ/gitg8knlyJ7fPyxDG2d7FVC7lD/uxwKm1gi1hJEYiHAIfhI87ERmzPSqNGjcpVFBEEbrnlFjn+0ksviWlKrkI5DiCyAe5rENt+U8WKFXOUyMzP66+/njjxiERegOkVx0XODCNBbDXDCrTjzcNbEdsTLFtPriCZLVqvvE06LhBtwHcI8EuWhW1jPEPJeAj7roNZxvAnn3wScjCBzCpXrizJBRJlNAqHAStoHTp0EJnDIeeVV14JP63fFYGECJiY0jBzCScOuxaKOMBhs8JPxf3er18/uR85vJbn0rkie1jjxo2FP6RQTsYRLW5n9WRSCGS9CQGCDWMQr127dlKAuF3IZD7SnOFuI6/tpYIAQs+xc4V4Fs+ePTuVS7VshhBAZJN69erJ+IcxEC8hHDcz4eS/bNky66STTpLr8PKf7PZuhrqpzXoUAXYytAoUKCDjxsaNG4VLRByoU6eO3FvnnXde0ooeQsnhRQpjEOyxvUhYhDLhB/VF3x0JZb0Jgdm+8KL5AE8qZBIZqAkB0FDyKgItW7aku+++WzyLsaXMKw5eZVX5+gcBjHkLFiygd955h2rVqkXsJENIVAFvb3iH8xSTCyuYIfBKkgRor1+/viQnQOQBJUUgVQQQWQcmSDBFQcQKmBNwzGDi7G3EMVwJkYESRRwwbcLcAOZLN954o5jJmONe+oRJA8wV2e6XOKUujR492kvsZScv7ujJmWkFy/hwaGDJWTyQZ4aJOK0inS14gxG7kiLgdQSwTWZWT3r37u11dpW/MAQwFiJZCuJmYszBHwLBs2IRiov98ssvh9LXwsMbpiNKikA6CLz11ltyryGpAduvynesUq5evTrpajkrl1yHudwPO5VPPvmk8It03MlGVkgaDC0YgUA+/OLBLCtp2rRpYhwOZ4YVK1Z4ro8w9ubQNwSnCA7+7Dn+lCFFICcCc+fOlXShWE1B/EOkjVTyDwJIS8ve3/TEE0/Q2rVrhXHEl2WlgiZMmCC/77nnHokr66V42f5BWDkNRwBzHCuesgqLlVjEbOWoQNSiRYvwYjG/Y17E7sG2bdskRix2EPxA3bp1k12ORo0aEYe7IzZ/8APbvuMxq00I2JlBBALPQC+SRiDwolSUp3gIIOc9gufjvfeaa64hcw/Hu0bPeQcBzo5EN998M3F2NeI0wXT88ceLmQGUV2znIurA4MGDPZXsxTvoKSepIoDFGd61EQUW1/KKbNLKK8r37dtXlFck7vCL8gq+8ZKIBCNIOnLffffhkJIDCGS1AsvpMAUy3g5zALr0qzT2r5qFK30stQb3EGBvYIIiy9uA1KdPH/ca1pZsQwArQrBrhr0eCMorVsgefvhh2bXC7pWSIpAuAvPmzaMlS5ZINVBkYQObLOEefPPNN2XVdujQocle5oly7JxN77//vqy8PvPMM8Txaz3BV7YxkbUKLAcUpjVr1hBnj5EtTy8KzqxeqQOXF6WjPMVCAKt4HNxeJha2q6QvvvgiVlE97lEE4GwCBRZpOfEJBy/OtkYcdYCM6RVnUZLtT492QdnyOAK//PILde7cORSHGPMxYrkmQ3DYguMWdnqwgslJiJK5zFNlmjRpIs8U+oC03MBDyV4EslaBhdcjqGvXrp7dDjMKrK7A2ntTa23OI4DVFCg8IATyZucK5xvVFtJGAJPpo48+KithUCYuv/xy+vbbb6lKlSqElXWsqv/73/+mkiVL0sSJE0W5hRKCrVAlRSBZBDC3derUiTZs2ECtW7em008/nfbs2UNff/11UlVg1ZLTFVPNmjXlvkzqIg8W4ji3dO6554qPC0wg4DugZCMCPKBlJZ122mniCcirQ57t32effSY88oPuWR6VMUUgFgLwbOfVO7mHeWswVjE97hEEEJfz/PPPF3khxefzzz8fkzMkMkAsy2LFikl5nnIsRCbQVJkxIdMT/yDAjoJWx44d5b5BPGF25LIGDRokvzljVUKceKXWKlSokJRHHHe/09atW63y5ctLfwYMGOD37niK/6xMZMBL9XKz8Na8hdA/XiWOgyd8XnLJJV5lUflSBOIiwNE9LDxnUHA+/PDDuGX1ZOYQQPYjjv8qcmLHGoudtpJihr3ALY7/G5IxRyaw8LLCq2NJXa+FgofArbfeKvcZwmXhvgPNnz9fjkGRY1vruKBgQQfjyaWXXhq3nJ9OcsQWCVGHRAz4rmQPAlmpwCKeIR4ANh+wByWHamFPReGzZ8+eDrWg1SoCziOANKN43pC1adOmTc43qC2khACbCIRSdyKOL146UqUtW7ZYvXr1sgoWLCiyxkR85ZVXWkuXLk21Ki2fxQiYGKjIwMXhoyJ6WqlSJbl3OBRfxPHwH+x4LWUQQ9Vk7wo/7+fvHL1F+sbmOhYykimlj0BW2sB+/vnnPJ+SGJDLF4/+UxtYjwpG2UoJAWTHQcYdxGq86aabUrpWCzuLAAeBF9kgniZsEjkNJyEudqqEOLEIu8UrahKGC1EMkOELttCwgYYTmFKwERg5ciQhhjDiBw8bNoyaN28eAQinjpXfbDoXcdz8YBMX4pck+Qn7eoR4yyZ64IEHCHFhEX+ZE8FkU9cy15f0dWBv1cCG4rJKgK0ur68GGbsgzZvsrXtIuUkdAeQB59AxssLAoW9Sr0CvsBWB/fv3W/xiIfLg2cVC5rREW7epMLBu3Trruuuuk/z0qJ8jU1jsNW7x5JxKNVo2SxCYPHmyxUkK5H7DKmw04oUlOc8OXdFOW8b0oGnTphbs67OROKRYaBeD49RnYxdd7VPWmRAYxyjO5+0qkHlpjL1+5YHmt828XK7XKAKeQuDdd9+V+xnbf1BwlDKDAJxGOEOayAJbuSNGjHCMEaTKhCkBnMKgyCItNpRlDs/lWJtasbcQWLRokcVRK0T+d9xxR0zmsLgE5ywsLuU0D5gxY4YFsxRe2bcWLlwYs45sOAHnSTwrsBH2+iKb1/HOOhMCE5PSbFfwjeJZMiYEGgfWsyJSxlJAACGZkPWO7buIV+fwcpzC1VrUDgR+/PFHCVk0ZcoUqlChAk2dOpXYGcaOqqPWUa1aNYkJvHjxYmJnVEKqWpgawEzh3nvvJbadjXqdHswOBFgRlTBRCKOHhEHPPvtszI6x/TQhtjDGBTNPozDvFhBHJ5BEGsi8dfLJJ8esIxtO3HbbbXTWWWcRv2hKv7OhT5nqQ9YpsOPHjxcsO3TokClMk27XKLAaBzZpyLSgxxFghy6CvSRSk77wwgse5za72EPqbNgdwsYOQdTnzJkjyqwbvUS8TmQe4tUzeYn566+/aMiQIQQFl0MHSRxMN/jQNtxDADarHC5L7jfcd8OHD5eMbvE4QExU0Jdffhkq9sQTT9DPP/8syQpwr2Q7wUYYtumItQx7YKSdVcojAl5fIk6Fv2XLlsnSfOnSpX1hQ9O9e3fhl7PipNJNLasIeBoB40mM7cLly5d7mtdsYW7w4MGyNcvTgHXVVVdlPHzgggULLN4Fk/ENPBUtWtTiNLUWr9RlC+SB7gdnyrLYcVPky1myLHbgTAoPjAe4H8wczSv3YjsLs4KghZeCaQ+w4AUsC6Y4SqkjkFUrsGb1FR7RyO3tdTIrsGpC4HVJKX+pIAAzAlaiJPMOUiiy81Aql2vZFBBAdqOLL75YtuuxsjNw4EDxAGeHmhRqsb9o/fr1CdFgkMEL26VYrXvooYdkRRYrbvit5F8EsOXPSQaobNmyhHmXFdKkOlOjRg064YQTZEUe9wYimGC1HpEsWrVqlVQd2VIIpj0wu4EeoNFb8ijV1HVe715hsn9wCA/vMhnGGT+w8gYWtDfPMAj0a5YigJU2tsGU+/vxxx/P0l5mtlvw+G/QoIFgDMc5L2cdhJOOGe94qpIVOHir7969O7MgauspI4BsUpAhEpiwEpry9YhWges5RbF8criswK7MI74y4mcDDzYrSBnLoF+QNVEIkHHLeDj6xbOvYcOGcuOyrVrQ70PtfxYiwCszcn8jvE62exa7LT52zhIvZkx82MJFeB4/EF7WmzVrJvcFeD/uuOOs5557ztq7d68f2A88j2zXLrJD2LSxY8fmCY/Ro0dLHSZyRdAz+JnoLYjk4BfdJU+Cd+CirFFgv/nmG3kosCLhF0KeaAzisANSUgSyEQET2/HUU0+1EJtUKX0EMOEh3BDGjnPOOceXq1fIcY94n+gD/pBiFBkUeTs5fYC0BkcQ4EQFEuoK8kpntXDnzp0he2126nKEV79VanaPu3Xr5jfWM8qv9w1F+WlJhuD1DGrfvn0yxT1RhrfPhA+NQuAJcSgTDiDAzkVi8/bDDz8QO/E40EJwquTg7pKp6IorriB2oiHeiiVeBSNOIOE7EGAXO3PmTOLVODrttNNow4YNkuEL0QxYOZJwXL7rVBYzzOmICfcd7Nlhw3zNNdfkubeYq1nrkesvuuiiPNeTTRfyyxuxoyONGjVKnols6pujfcmo+mxj40hcwEB52g4sZ3dN5qLt27fnPKW/FYGsQYBjksrKDbYdZ8+enTX9crMjGCPatWsnYxxMMt566y03m3e8LWwj16tXT/qHcZwdfSysNHNcWcfb1gbiIzBv3jyJIgG59OnTJ37hBGc5RrSstqMu/HHq2ARXBOe0Mc/AbsQff/wRnI6n0dOsMCGAsGFPgywwfnIKMNuAurWaxh2sl/oCAc6RLhNW7dq11d4xRYlxjEyLEwMIfnB44ZXLFGvwR3GkuuVYolatWrVCiizMrLB1na2pRb0umRUrVlgcaUDkcdlll6Wdjvjmm2+WujhZgXzipUXpMAK4/1u0aCG4cFQGhSUJBLJCgUVOYbzNIX2iXwi2XuAZSreSIpDtCMBJp06dOnLPp7uKk+1YhfcPqbERQxVjBZw+169fH346K79DWYWNJYdckn6j73Xr1rXg/INJXskdBOBQZF6cEPM13YUWOB4i3ivmPDYpCjldwxNf6TAC4XFxp02bprAkQCArbGDZgYvHOH/Zv2oMWBGZ/gsIAgUKFJCUo2xGQOx1Tkh1qhQfAaRk7dKli8RM7dGjh6SFrVixYvyLsuAsYnjDxhLpaZHZrWrVqpKpqWvXrmIvG56GNAu668kusKOVpIhduXIlNWrUiD766CPiHcM884p0sYj5yvoI3XfffcTO1sSrjfKbI1Pkud5su5B3HwQf4ISUs7B7V4qDQAIF1xensS3JXbSmT5/uC37B5Lp164TnSpUq+YZnZVQRSBcBZGPCs8opRi0OZp9udVl5PVarsV0LnLBi9cADD2RlP5PtFFb+nn/++VBcYeACn4evv/462Sq0XAoIICRlmzZt5P5DiLatW7emcHX0og8++KDUB/MQ1A967LHH5Bjiwir9PwJ4/jE+4j5HiDml2Aj43oQA2w8QNIIqp7vFERsm+88sWrRI+IbyraQIBAUBpKBkr3O599XOK7fUf/nlF+v0008XfGA6MGbMmNyFAnoEis9TTz1lwQ4YYz7+YDM4efLkgCJif7fhNMcr3YItnIlWr16ddiM//fSTmA3gZQxmBIZgyw0Zws5ZKRIBPPfABglKNm/eHHlSf4UQ8L0Cy2EnRNAcliXUKT98gTc2blBMVkqKQJAQwIQGT3rc/17OHuW2TGbNmmWVK1dOcIEXPnBSyo0Ap8+1kN3NZDDCfYQVQ7UZzI1VKkdgX8ypn+X+K1WqlC3JR6AQswmC1JlzpRUvs8a+m8OopcJqIMqed955ghtkohQdAd/bwPLbN49fROzAJZ9++acxYP0iKeXTbgTYIYceffRRqbZnz57EaWftbsJ39b399tuSC37jxo3Utm1bQp544KSUG4GCBQuKnSCvDkpsYc5gRBMnTqSWLVsST/rEiwO5L9IjCRG48847idOwE+KSjxs3jjhSQMJrEhXgFXO5lytXrkz/+c9/IorDHr558+ZyjF8+Is7pDxJfAeM7wOaRCkkUBLJGgeU821G6591D6sTlXdkoZ84jgMkSCgcC2MNZIajEq17ENq7EqyzEkUkICv2XX35JvAIWVEiS7jcULbatJCiyAwYMoGLFioni1aRJE7rgggto/vz5SdcV9IL//ve/CU6DvDMigfSBYbq0dOlSeuihh6Sa1157TQL156wTYwBIFdicyJAkgLn33nvF0U0dunLjI0eiL8z64+hvv/0mTg78lhIyDPcH55b13nvvyfbAJZdc4heWlU9FwFYEEGMStus8EFkwBQoaIX51hw4dpP+ICc0e90GDwNb+Yj7gCT90T8Hmsnv37mqKkQBlVlzlHkQs9Y8//jhB6eROIxQar65Kvdddd13Mi3jlXMrALl4pNwLhDl1wZFSKRMDXNrCIC4jJr3Xr1pG98sGv119/XXjnFRcfcKssKgLOIMApFOU5gD1jkJwVeHVKnFcwfpUpU8ZCtjIlexCAYy9iDbOpgdxbHJbL4jSo1pIlS+xpIItqQUY3KPr4szO72zPPPCPYJ8oqhcRDeHmD8qxRSaLfWJ9++qlgWbp0aYvNraIXCuhRX5sQsEejrCL7zf4VTKsJgYhO/wUcgZtuuok4SDpt27ZN4kQGAY6vvvqKsEWLLdb69euLjeAZZ5wRhK670kd+ISBWoGjVqlV06623SvxSTksrNsUw0cBxJRJTAeDBuo/gBTMWOwixY/v37y9VIY4ve9LHrLZQoUJ06qmnSrxTdmKMWS7IJ84//3xiJ0XiHYaQ70CQ8Qjvu68V2BkzZkhfEBDZb6ROXH6TmPLrFAJvvPEGlShRgnilgXgVyKlmPFHvSy+9RB07diQ2H6ALL7yQMIZVqVLFE7xlGxMcbotefPFFYlMV4pBthAQJb775JnHYJmKPeOJY3NnW5aT7g+Q/SI6BQPmwU+3du3fS18YrCGUYWHOkCOJVb+rUqVO84nJO7WATQkRPPvkk8So5sRkBrVmzJvEFQSnh15VnxAREKB5sD+3YscN33ejXr59sCyCYs5IiEHQE3nnnHXkeEPcQST6yjZA6mrNLSR+xXdu3b19Ni+qykBHT9KqrrpLtap7fJTbpHXfcYf36668uc5LZ5pDwx9ie9+rVy1Zmhg4dKvd42bJlLdgkJ0Owu4U82rVrl0zxwJa58sorBadLL700sBjk7LhvbWDxEOKmr1evXs4++eI3Bk7wDwN6JUVAEbBCAdTbt2+fVcodcso3a9ZMnnfeMg2kw5qX7u9ly5ZZvPooix8Yg+EEfNddd1mQU7bTnDlzLI7WIPciXqgQ+9Uu4pVBiyNDSN2cejbpaoE75ICYsHD+UoqOAF7sca/iBRhx5JUsy7cmBCYumokjxw+Ar0hNCHwlLmXWBQRgLwf7xQkTJsjWrwtNOt7EvHnziJOVEGcdIsTChMnARRdd5Hi72kBsBGrWrEkcBYY4UYSYcSB8GeKVcvIIuv/++8XWMPbV/j2zcOFCsTffuXMncfQbgukOtqXtohtuuEF8Ozjyg+CabL28WitmNOzERexol+xlgSvHaeeJnRPFZvnuu+8OXP+jddi3Cqyf7V8hCHXiinY76rEgI3DccccRRyUQCHiLXWwX/YzHBx98ILFuOT2sfPLqF51yyil+7lJW8c5pvIlXCiVebOfOncVukzN8EeehJ8RFhZ1ythAcBjlbJW3fvp26dOlCcGqDTbBdBGX466+/Jo4mQi+88ELK1TZu3Fiu+e6771K+NkgXsOmhvORz1BLxGQhS36P11b47OFrtDh4zCqxfV2CNAotg3EqKgCJwGAE4NrGtlygT8IpGoH+/EW/t0cCBA8VJhuM4Sn++/fZbmXj81pcg8ItIEJx7nvCCcc455xBWAh9++GFRZNlHQX77GQckemD7UuIwddK/kSNHErJg2UVsQ0xsgiHVwckIuyipklFgNYtafOSQrMMkh8BLPpzwAk1+tKOAMT4LTeIn+pF/8MyZw6QPkyZN8msXlG9FwBEEEOuwQoUK8nw88cQTjrThVKWIZclhb4R3VhIsDT7uFNLO1cuLIxaHLRIZYp5B/M0hQ4ZYvOjgXKMO1bx+/XqratWq0hfMORwdwPaWOH2v1M8ru3muG3GQgbUmNEgM4YEDByw2gxG8/ve//yW+IItL+NKJi7fmRHh4cPxKDRs2lD5wznO/dkH5VgQcQ2D8+PHyfCDSCNvuOdaOnRVz/Eurbt26wjengrU4VJGd1WtdLiMwefJki2OMizyhXLGJizjdIjuSHwjOUSeeeKLw37RpU0cSBbz99ttSf8mSJS1OC51nWPBygGQGSGrgF3zz3FkbLmQTEMGd7bat/fv321CjP6vwpQkBK308nhA1atRIPv34T524/Cg15dktBLCVi1idcLDh0EfEqw5uNZ2ndjglJmEb9Oeff6Y6deoQtkLbtm2bp7r0Im8ggAQ5rMQSv0wRK4DEGb4kXmr16tXFVpsVB28wGoULBL3naB7EERckUcAXX3xBdpursYIsTkVoHokjypUrF4WT5A5xWC9JNIHn/IcffkjuogCX4lBaBBtuJOXI9tjZ8cTsSwXW2MkYu5l4HfTqObWB9apklC+vIDB48GDxDMeE9sgjj3iFrVx8wIEF2cSgNCBwOzIKQclRyg4E8DKFKBKwk+WdM+KVRnm5QjQDyP7gwYOe6iib4IjDFqIs8I4AIfMbEoXYTXjBhFPYueeeS3Zk8TLzuVmgspvfbKoPDnhwNAQNGjSIvPwyJUw69c9vC8eIE2dizW3dutVv7If45QFFtgB4AAgd0y+KgCIQiQBs45CsBPakXjO3wdbdjTfeKM8xj8/WnXfeqXEsI8WXlb9GjRplseNXSO7YxsVWOiuyGe8v7MdhR4r7EeYDGzdudIQnYzqAxCOws7WDOGua8H3ttdfaUV3W14EYvoiDD1kDuyCS72xgYQ8HgXGoE1/LC7Y+6EeQ7Vd8LUBl3jUEOOahPCu8ZeYZ+zi8PBv7SAQXHzFihGt4aEOZRwDKA2SOexLjOP6gML7//vsZe4nhsF8Wm9UJL3DycSrDGIeFs8wCjJ1ORHCeA44NGjTIvIB9woHJYgan1yDaDvtOgeVc1nKTc7Bkn9xiudlEWkk8qFBilRQBRSA+AhiY2a5UnhmscmaaFixYYFWpUkX4wcThtZXhTOMTpPaxIzhs2DCrRo0acj9gXIcjHxQLO7NcJcIU6dSbNGkiPLD5igUl0ylikwppB9E27CQ4cmG3JX/+/LqwkySwuMdOPfVUkcezzz6b5FXZU8x3NrDGPsbPDlxq/8rDvJIikCQCvMJJvGUpsSs59TIhiHemiBUTQuzptWvXimMPYoci05ZSMBGALSKcDBcvXkyvvfYaccgqceRDPGPeyqexY8c6Dgzi1nbo0IGQBABJGOBQyC9WjrSLRCNffvmlJCx49dVXbW0DjlywK4Y9J5whlRIjgExqxj/gP//5jzi9Jr4qe0r4ToE1HoowpvcraQQCv0pO+c4UAnjeBwwYIIkNOId7KJOdW/zwmgVhgujWrRvh+YXSwjGc6fjjj3eLBW3HwwggMcD1118vXv9sj0gVK1aUDF9w6oNzErJUOUFYDIETFZzMoDzjnkTKUScIHu/33HOPVD106FBCCli7ic0HpEozz9tdfzbWh3uMV2GJ7Z2JdwOysYux++SnxWRs1xQqVEiWy/3s/LRo0SLpQ61atfwEv/KqCGQUAQTwNg4qnHfdNV5YYbVYcZVnFlucjz76qGtta0P+RGDfvn0Wh5ay+AVH7huega0WLVpYrGDa1iFsuZ9xxhlSf+XKla3VnODHKcLca9riEE5ONWMhcQmw6tWrl2NtZGPFJjY+TFkgq6CQr2xgeZtGbm7Yn/mZYDOHh5S3Hv3cDeVdEXAdAQ4NZCG5AZ4fjm3pePtsKiBOJWgPHtdutOl4p7QB1xBA5iteuZeskbiH8Ne6dWtr6tSpafGAlyqTzZFXXC0k0XCSnnzySeGdY71aHC7OsaZMAhM4SColjwAiYMD2GfcXlNmgkK9MCMy2ApbL/UxqA+tn6SnvmUQAcS0R9xDUs2dPQsxLp2jatGli3zp//nxiD3OxMYStoZIikCwCBQsWpHvvvVcCzg8cOJA4Y5Vs8/Nqpmz9m5jmydaHcjBh4SyUkmTh/9g7DzgpiubvlyTJqIQTFBDJCiaCYgJBURHMWfAxx8ecFYyoz6OPEcPfxGNCxRwAUREERRFBQR4lK5JBBAERJLhvf/vePvbu9vY2zMz2zHZ9PnC7OzPd1b/q6q7prq7C1xWfVxXKK50i0roX/17cd6Bnn31WVJa5tJ5P52YVFkrf7nxg00FNRGUxK3LvwNUpX8gZsDmQtDFgcVp35BBwCKSHwNVXXy1qO1YHlP/nP/+Z3sMp3v3SSy/pTFoqXJYQyJ4DMq1bt07xaXebQ6A4AmTBwgicN2+eDBgwQGrXrq0zfKnIAXLMMceknH3K+Lzi62qMVz+TZpCkAX9v5RKhfXx79epVvGEef2vUqJFOukBSkGXLlnlcerSL42wAPvnffvutbz7XtiEYSgPWOHrbBmaq/PAGDXmd2i/V+t19DoEwI8DJbw4r8AKoYnHKW2+95VlzlP+YKP+7ovS1l156qT5J7kcmI8+YdgWFBgEMV06NY8jecMMNeg4wGb5OOukkIXtWWWSiDSj3A31QCyOWU/t+0j333CNE2uCA2IMPPuhnVUVls8sCuVXYIkhS+qBcq4pS+ypf4pSeCftNoTJg2cqDouJC4FZgw64+jv9cIcCqk/LL09VfdNFFOk99tryQFpPV1kGDBgmTATnGH3vsMb09l23Z7nmHQDwCuBJgZHCynx0FQsWpDF+y5557yhlnnCEzZ86Mv11UnFedrnj8+PGizoBoNwR1YKfYPV5/wWUPdx1CNamEBVKrVi2vq0hYnjNgE8KS0o+MhbwkjR49WkzI0ZQeDOlNoTFgyT+9YsUKqVu3rm9hQoKSoXEhcCuwQSHu6okiAgzWhx12mB4XVErXrJqoIoPocEeffvqp3oZjdcuL/O5ZMeUejjwC9evXlwceeEAbsrjDqOQ2elcBI06lVBV1OEtUhi3dzydMmKDjvI4dO9ZXn1dAV8l2inYh2JFQB88Ck4UzYDOHWh00lYsvvlgXoKJgZF5QSJ4MjQGrUshqSNu1axcSaMtm07kQlI2Nu+IQSAcBlZlPGLTfe++9jGMgDhs2TCclwFgg3iwrF/vtt186bLh7HQJZIYDvIiv/c+bMEV7GcJNhBwC/a9wE6JPsOmC8sgLrN916663anYH67733Xr+rK1a+M2CLwZH2F9yeiEvMij6xYaNMoTFgjW9QFAxYswLrXAiirFqubUEgQMB4Jn7oiiuukAULFqRVLasUHKLBv/DUU08V/Asp05FDIBcI0PeeeuopnRCB/ohPNjuPEJELMGz9pi+//FK753CyHV9zIikESSpttK6OXRFH6SNAIotjjz1WVNxsIXNalMl/bfAIvSgZsG4F1qNO4YpxCCgE+vXrpwds/AQJraViIJaLC6eq8TXE/5D7b7vtNnn11VcDn6zLZdTdkJcIsLhhDjHhe4ofKiuy+L1ec801vp3QV3FrtevM33//rQ+ZESUhaFKxZnUkAnzSiQLiKH0ELrvsMv0QL0Ok5o0qOQM2B5I1K7DOBzYH4LsqI4kAAzX+hKTsJM1lMlq0aJFezSKCAcYB7ge33357skfcNYdAYAiw7YvPKW5zrEbOmjVLG7OkMcY3lWgAxH298cYbhXBTXhKpYnFj4DAZL3W5IhNdYfbs2bliIdT1qkQQWoaEInv99ddD3ZZkzIfCgOVt0GwnOBeCZOJ01xwC+YlAgwYNirbLCE/EJJyIiOfaqVMnHRoII4Ac8n369El0q/vNIRA4AvPnzxeMD+Y7gvqTpAD/2LZt28obb7whROI5+uijhZVSAtY3a9ZM8FfloFe2NGLECP3yV6VKFXnxxReFv7kiZ8Bmj7xZhTUuVtmXaF8JoTBgVY5nrbD4B0UhHqNzIbBPERxH4Ufg+OOPl759++pMRQT15sU3npiUVfpNfbChe/fu+mCMOTASf5/77BDIBQK8dOHnyl+VZlyHyuLFLJ722GMPvWNAbFaywuG7TYYv4rQS8orvmRBb9eecc45+9O677xbqySUZA5bVZ0eZIYCLFFGbyPbGi3sUKRQGbJT8X+lExoXAHeKKokq5NuUSAVYbyFBEvEwTJxZD9pZbbtG+fWzBnn/++fLRRx/5mhIzlxi4usOHAP6urLyyAkuWOcK5JUvZSrSMDz/8UO8g9OjRQ8eJJcMXhux9992nX+LSQQHfcbabDznkEO1jm86zftxrDFjnQpA5usQWPu+883QBUV2FDYUBa9wHzOnEzEVqx5PGgHU+sHbIw3ERHQTYoXnuued0g9haxUWAvPFkFCLGJr6yTz/9tA4zE51Wu5aEGQFSf+Lziu8rxigvVwSjT4UI9zZq1CgdXgsDmINPuNDgHvPwww/L+vXryy0Gnfjggw+E5ArsUnBgLNfUqlUrzYIzYLOTBDFhiVxBtsJVq1ZlV5iFT4fCgDVZSdq0aWMhhOmz5FwI0sfMPeEQSBUBsmmR5IDVVlaURo4cqQ94saqVbcKDVHlw9zkEUkGAFyzcWQiV1bt3b522OJOdOYxXYsR+/PHH0qVLF52Z7qqrrtKxYznUWNZJdLboicQBEXLJlhByZgW2LF/2VLB194iOGUyyF6KuvPzyy5GDJBQG7IwZMzTwUTFgzQpsJgNV5Hqga5BDwAcEMGJZecCILSgo0P6u+Bc6cgjYggAHtHr27Km3/0866SR5++23dQrjbPjDWCGOK8k5cDNgVZfA9oTfevbZZ3VsUFM+cULxk+RA2Jlnniknn3yyuZTzv+yk4ELBXLl8+fKc8xNmBowbgdmZCnNbSvIeCgPWrMCSFSQK5FZgoyBF1wZbEXj88ceFkEPmEBerWy6epK3Syk++OPHfq1cvbaCRspgYxLi4eEW4zXDQC6OYA1kk+MD3mzkUNwESJBA6jnvwm7XRRxK+oHnz5um/7r/MECBqBSEGp06dquWdWSl2PmW9AYtjOSFC8M8peSLTTkjL58qswDof2PKxcnc4BFJFgNVW8seTUx7j9aabbtLbo0zWrDCxjebIIZBrBAiHRaYk+uMll1wi//3vf4WsV37Qcccdp0NvvfbaazoUFxF9MJgJv0WKWHYpXnrppZR9bv3gsawynQFbFjLp/U44NJK9QFFbhbXegI2a+wC+SGzd8Lbt5Rt3el3a3e0QiBYCS5cu1f6uZCvCNQcjgYNbhAQihub06dN1JIJotdq1JmwIPPPMMzplMXMASQPYLfD70BTln3LKKUI0H1ZfOeDFiiwZ6NimZ5Eolex1QWNtDNhffvkl6KojVx9RJiCSt+AyEhVyBmzAknTuAwED7qqLPAKTJ0/WyQk4ENO0aVMdQuuEE07Q7SaUDJN2pUqV9KnscePGRR4P10A7ESDxAIcI2R3gxYpwV0ESq62sxBG5AGJlDvca3G323ntvHYkgSH7KqwtdhpwLQXlIlX+dCE4c7luzZo1+uS//iXDcYb0BGzX/V+M+4A5whUNBHJd2I8DWKIezFi5cqP9+8803OoViPNcEhScOLIYDCQ6MDsbf4z47BPxE4Prrr9epXzEin3zySbn55pv9rK7MsocOHapX4Zh/CN9FhAIiD+Afia9k586ddRivMgsI8IJZgXUGrDegm8NcuKxEhtTWgdWk0jzGFNgxFcfMaj5TZU7FtNXtUREVUn3E3ecQcAiUQEAZozF1CEXrEuOD8uuLKfecEndt/cq1ffbZR9+vVsG2XnCfHAI+IrB58+aYMhx0v1MuYzH1wuVjbcmLVkkSYup0v+ZFxX4tuln54sYeeeSRmEpZW6RP+++/f2z06NFF9+TigzKqNT8qW14uqo9cnWr1NVatWrWYcimJ0ReiQPi+WE3Kf013YjpzFEitEOn2qFWhKDTHtcEhEDgCDMRqtUjrkXINiKkT1CnxoHwAY9tuu61+TmUxSukZd5NDIFME1KHCmHJl0f2tevXqsVz2OXWQMaZiImte0J1EpHwjY/fff39MnVjX9/Fi2K1bt9jnn3+e6Hbff1OB9zUftWrV8r2ufKlAhUrTmCr3lUg02WoDllUW5cOmAVfbfpEAXMX+0+1ROdkj0R7XCIdAkAjMnTs3xooMk6s6gBJTyQnSqp6Bm2dVutmYylqU1rPuZodAqggwX6mYrLqvseqpUhun+qgv95l+zyqriquatA54Vz66Wr/QFf6puMqxCRMmJH3Oj4usGFL/2rVr/Sg+78p89913NZ577bVXJNputQHLMjedF6WLCqkA07pNKk5fVJrk2uEQCAQBtjTr1q2r9UcdSoipLD1p18tKlMo1r8tQQdzTft494BAoD4Hffvsttu+++xbNXbnePfzuu+9i6sCW5kfFny2P/aLrq1evjt12222xOnXq6GeZi3HpU76zRff4/aF58+a6bnUWxu+q8qJ8dgVUSFKNKe6MYadtaIDqmFbSZ599pkPjqAlHvvjiCyt5jGdK+TsJJ6KnTJki5HDmH3H31ECgD45weAS4CaGiBgVp0qSJjsdH2jz+qbcinT2FE9OOHAIOga0IEH6ImJnomJpEZciQIaK2FrfekMYntYqrD3oREeTNN98UE7EgjSL0ranoOzcS75l/6DzxN52+p4t0eO7nMOERRxwhP/zwg5b1J598otO55qoF69ev13MKYeSIj5xJwgK1lS/KtUA/yxxGWK7jjz9elA+6tGvXztemqZ1KIXIIWcuUO4OvdZVXeFT0nUgYjKf9+/eXu+66q7xm233dZgtcpb7TbwoqCLm1bLIKpOJN6u0i/JyUtLP6RxlsPVFmJitM1gLlGHMIZIAAh684dGX06pprromxipotqdPXukz8/VQczJSLi9d3dZK7iC/DX7p/KcPpe8rwW32jMlpjjRs31n1CGXaxRYsW5ZxfozvsWODjmg2pbHYx9M/McxwGOvXUU2PKOM6m2KTPUj469fLLLye9z6+L8fpu2p2ujsffb8P8btwYVTxgv2ALrFyrV2DJpPOvf/1L7rzzThkwYIDqB3YQb6QvvPCCTv83ceLEYkzVbthC6rfoJLV3bC61C3aVWgXNpEqN7aTytjWkUtUa+t7NG9bJpr/WycZ1v8vaZT/LmmU/yZqlc+XXOd/ImiVzipVHWJPTTjtNZ08hG5kjh0C+IED6V2JUsgKjfOF0Fhl0wQtSI7dmsN0AAEAASURBVKwovz5hhYysSO+8806ZxSbTdxVNRMdXbNWqlV5ZJec8empWXSmUVSv+UY6aEPXOzKxZs4S4tSZRi6nc6btBIlx/v/zyS+ndu7eW8YEHHijvv/++7ge5bAVpZNldIBYy81T79u09YYekISQJefrpp4Xsd2QRU+44cuutt3q+2qwMZnnwwQd1zFwSPwRByfQ9CvM74QTZ/VUvWHoMMnGBg8DW6zqsNmDViTkddJftwtNPP93rtqddHtlLUCaW301CgspVa0rjDr2k8V6HS4M2XaRa7fpplxv/wPo1v8ryGV/JgikfyYLJI2TThj/0ZeL2kcv66quvFvWWH/+I++wQiBwC33//vY5LSRYedeBK1OEDIZ6rl8R2L1uguPjwQkq62Xgy+q52gopix9auXVsbvLgxHHzwwVmnt1YHarSB/sEHH+g2EmgcwgAmbqPT93iJ2PkZY1WtFArb9bwMvfrqq9pozCW39N0999xTG9S4DeA+4DVhALEFPXjwYO0Wh+sbcZbZmjZJCLKt84EHHpBrr71WrrzySnnooYeyLS7p80bf82F+B1OwDQLXpKBnedFqA1Y5wus3R3WCU1RcuiybmvnjyilfKyUTGX4wUKP23aXlwWfIznv1lIpVqmZeeJInt2zcIAunfCyzxw2RxdNG6zsZJJjYBg4cKOpAS5Kn3SWHQDgRYOUIY5KXRFYHWB1VBzl9aQxZulQMWe2fSqpNgrobfSdvOP7qEH6NpGNklY0VLT9IxeMUdchTrzSPHDlSV0G6aep1+u4H4tmXyZxw0UUXiXJrkQsvvFCnhmVFMpcELypklqjwV/ol8L333vOVHRINYMiiS8yPZPhijiJZAy+f2RCpT1nd5QWBFwM/yOh7Ps3vKqKE3jkiWQTndMJKVhuwTFrkaeZNr1GjRoFjzFK7Cviss/iwrbBNhYqyy77HSrtel8n2TXYPlJ9V83+Q/40YJPO+fldif2/R21OkI2TQJLuLI4dA2BFgWx+XIbJm8RnDEv1TsVt9bdpxxx2nVz8PPfRQfTiFFSQVYkunnyWHPFmU9thjD195KFk4K9CkGiVzEkYBOesxYp2+l0Qqd98x2tg2hzjQpE7s546ZuJrvuOMOzQ9zJv0oqIUO3GOoG6OTuZMXPYz7G2+8UQoKCuI4TP0jLj49e/aUHj16yKhRo1J/MIU783l+Z3zl5WLJkiU6IxuphMNI1hqwbMcoh2f9NsfnoI003irxt+NNBWq4e1fp3PdeqdOoZU7lvHrxbJn48k2y5Iexmg9WqHgzNWn3csqcq9whkCEC6oCJNliJCoCu83LGxBcEsY2vEqZoo9XUpw5WyaOPPir4uOaS8JG9/PLLta8ufDh9z6U0CuvG8Ln00kvl//7v/7T/J+lYOdltAxGth9P6GCgYfKzEBk30WYz5N954Q/PBPI4LAz6s9erVS4sdIvpgXPECSbpbr8jN7yIXX3yx7sOcL+KcURjJ2qU7FQNW44m/Z9DGK5Mo/kMYrzV22Em6Xfa8HHb9mzk3XgEEAxpe4Kn6Do00j/AKz44cAmFEAF3HRYg+TKip4cOHB2a8gheHxFS0Aw0dhxtwYfj4449zbrzCEAY0vMATYyFjEuH2nL5rcQX+H24eJ510kp74WWFUKc6tMV7ZJWS7HRcCXv5yYbyaPsvOAQYnPsG8nLKbQAg5jCX4TJVUlBB9Kwc6vSI3vxciyc4TxPmCsJK1K7AM2pwS7t69u6hsO4Hgy1srhyYefvhhXV+TDkfJ/uc+oqII1Amk/nQr2bhutXz53BUyf/Jw/SgO2RwyI06fI4dAGBBgxYiYkkxQnOTnQEzr1q0DYb2kvsMHfq8qc1Ig9adbye+//679YTFmIafv6SKY3f0YXsccc4z2LSXSBH2ViAO2EP0Xf3FW6fF/tSWeuEp8oA1XlURBQ8VLKtEFrrjiCuFQZDIiygEvCviCm5fMZPcnu1ZS3/N9fse/v0GDBsK4gvuHShqRDD4rr1m7AssSPxTU1jjKgcsAxmuFSlWk85n/lm6XP2+t8Qo2GNbwCK/wDO+0IVtFp2xHDgG/EeDkPy+oGK+8rH799deBGa/x+o6P7eOPP65X02w1XpEFvLHiB6/w7PTd7x66tXwOurBLgGHIQT/+2mS80icwXukjuJTZYryC4D777KN3VQgbh585UT/wHWZFFp93E9FnK9pbP9HPMXIxtnguU4rXdze/F6LIS4HKCKq/JAsjmCnmQTxnrQFL+BzIq3AcycBUeZalV69e+sBE5Wq15NDrXpc2Pc5J9ohV1+AVnuGdrRvaQtxJRw4BGxHgUBJ+nYTcYWK67LLL9AQXlPEYr++sBn300Uc6y5eNWCXiiYxk8AzvTt8TIeTtb5MmTdIntvHtNK5lu+++u7eVZFEafqKsaEKcpA9q0SddllkZ5lAWLjtk2OKgJLHeMWTZOeSsSyIyfrOZuhHE67ub34sjbNwInAFbHJesvxkfWL8NWN7MECJuCtXqFMgRN38gO7Y5IGv+gy4AnuGdNtAWfI/cSmzQUnD1lYcAkxYhqYhNyerK888/rw9LBRV6KF7fGzZsWDSZlse3bddNik3a4PTdP+kQnxesiYbDaXhWXrMNDeUltyxUECmDrXYO5WSaFtlLnsor66CDDhLSxGPMdunSRe/AYICzhf3YY4/ptsSXYQxYwl2lS/H67ub30ugxFuOigW/9ihUrSt9g+S/WrsASZBxiu8YvwieGeJNFxmv/YYGHx/KybYT2OkK1wRixtI02OnII2IDAjz/+KGSaQt8IkcckRqisoChe3zH88L8NOjyWl22Fd9pgjFin716iK0J0ARY3OIR0zjnn6F2CWrVqeVtJlqWxGk9WN/oCq5hhItwJyGCGbyxJSgjpxG5My5YtdZYvE4OZnQYoXReCeH3Xxqub30t1DxIkkZCFyBqcOwobWWvAEvsV8vNtlwNbbMHpbYVrh0qtBrvoOsP8H204VLXFuBPQRkcOgVwjQIB+thDnzp0rHTp0ELZl+R4kGX1nQiRRgMoFHmT1vtRFG2iLcSdw+p49zBg+xP4lVBYn+oltyuE+m/xKaSWJA1566SXBCGEeYyUtjHTkkUfKN998o0/D46JBRiziHXOYkx0aY8By2CgdMvru5vfkqLEKC+GWFDayNgoBSsmbL6kV/XjrJZQG4VBw6MZ/NIxuA8k629IZ42XU/SfL35s36nh85JR35BDIBQKkLMQg4C2fjDqknqxWrVqgrBh9x22BgZpt4SjR2LFj9UE4tpKJv+n0PTPpgh8r2a+/rs4UVK6sfUr5bhvNnDlTvwhyAOq///2v9ie3jcdM+OHlAV0lMQQ7NhCHuLADiLuLYZsKGX1383v5aE2fPl122203nWyCVfAwRTGy0oAlXAmZZ+i46W4blC8ukXkqwgFveijFvmfeJ617nJ3KY6G7Z8ang2XiizdoHInJZ6tzf+iAdQynhAAxM0mDSmYeBkUmJZO5KKUCPLoJfSd2KmMJ28L4CkaRaBurhqxYcbDH6Xt6UsY/mzBZuGWAIREfyABlG3HYiTTr06ZNk759++pVWNt4zJYfXnaJpsDq9+zZs3VxhHwi2gJ+vsmMLDe/p48+Z404d0TIszBl5bLShcBP9wEUg1BTGK/EgYuq8UoXJjoBbaSttJm2O3IIBIEAOsxhDYxXdlDIx54L49XoO8YrcTKjarwiU/whaSNtdfqeXi8nDiYHijBeSRjBXxuNV1pFBA+MV7bYn3zyyfQaGpK7SV5EUgZWB81JeTLmsWuKgUUM3kRk9N3N74nQKfs3whhCuCOFifLOgCW3usmwRZKCqBNtNBm7aLsjh4DfCBDPtVOnTtrPFR9N4j/26dPH72oTlm/0nQxb+DFGnWijydjl9D01aRPWCX9sDkOxUs/80K5du9QeDviuIUOGaLcGXHBwFalZs2bAHARbHdFJiBUN4fZD32Y3kZVyxpgPP/ywGENG38mg6eb3YtAk/WL8YJ0BmxSm1C6aFVivIxAQhuOWW27RTHQ6426rkxSkhlT5d5HsoPMZ9+gbaXsmoUjKr8Xd4RAoRICDJUw0+FIx8XA4I1cxM+nr/fv314wR9D+oOLO57Au08ZFHCl/MabvT9+TSIJnGYYcdpnHiJYuV10aNGiV/KEdX8Xu96KKLdO2PPvqotG/fPkecBFutydbFNjfuBLSdyBscBCXmOQkmiGzi5vfM53ciQnBIkagQrF6HhaxcgV28eLHGz+uBhAEd/9qGu3eVJh0LM1CERVDZ8ElbaTNtNxN6NuW5Zx0CJRFg646g5ITF4iAMhy04LIUve66Ivo5fIwaK2YbMFS9B1ktbaTNtd/qeGHkOC/FCTzINYoVeddVV+hQ8h4dtJPxe2T4n7itb6+edd56NbPrCU/Xq1XW5HFjjECahtohm8p///Efq16+vd3gwwMj45eb3whf2dAXBSwK7ECSZYUciLGSlAbt06VKNH7EivSJCc5ClZJsKFaVz33u9KjY05dBm2g4GYOHIIeAVAvhckpKQtJCc3H766af1ieFchh2ij5vQR6zY5BvRZvAHA6fvxaWPMUjw/3vuuUdjxOl2Yqjid2krxfu9wm8+kTFgiUpkCBcKkh+Q4vfee+/Vh+508qNtKrj5PcP5vVu3bhpeIpqEhazUWLKeQAUFBZ7hyADF28Uu+x4rdRq19KzcsBREm2k7GIQt4HVYMM5HPvEb5EQ0vlOshrCVd/755+ccCvo4gdAxVNq0aZNzfoJmgDbTdjBw+r4VfeYWJmr8R4k0QBD9VEMzbS0l2E/55vdaEl2zKh5vwJp7uHbjjTdKv3799E/N9jvOze8ZJrQwoQVJMBMWstKANSuwXhmwbCs888wzWibtel0WFtl4zqdpO1iAiSOHQDYI4CKA8YpvHmHp8Hcl8kCuib7NTgNE/Nl8JdN2sHD6LvrkPpngJk6cKM2aNdNbz7ha2EycwjcGdj75vcbLJNEKbPx1+jaxcCEzx8Vfz5fPpu2Zzu/4ErOD9t1334XGD9ZKA9aswHrlQoCjPv4zjdp3D3Wq2GwVkVSzYAAWYOLIIZApAoMGDdJuA2THIS7j+PHjhUMWNhB9G19BTtaGOVVstljSdjAAi3zXd1ZaDzjgAB3rkomaSBlt27bNFmJfn2ecJiEFf1lhzCe/13hgjQELDonIze+FqGQ7v4MzkR3IPsd4Hgay0oD1egWWWJRQy659wyATX3k0GBhMfK3MFR45BDigdfbZZ+tYlBzc4iAM27Fmm8+GBpu+na8TfrwMDAYGk/hr+fIZF4qjjz5a1q5dK6effrqMHj1au7vY3n5WXslGRRSPfPN7jZeNMWATuRBwn+nbZm6LfzbfPhsMDCbptj9sbgTWGbA42DPQcNrQi7A3nFZka7Ny1Zqy8552bxel29kyuR8MwAJMwMaRQyBVBHixPOSQQ+T555/XBiuG68CBA5NmxUm1bK/uM/rOqVoOluU7gQFY5KO+E12Aly0O+/CyRVYn/EmZW2wnDFZ4Jc4raVGNEWc7337wV7VqVV0sL88lyei7m98Lkcl2fjcGbFgOcllnwBr3Aa/8X8lpDZGRqmKVQkUoFHV+/g8GYAEZbPITCdfqdBCYPHmy3l4iKQGuAmwx4TpgG5k+TSgpM/HZxmOQ/ICBCSFmsAmy/lzVxTxS8mUrF5ngMmk/6TyvvPJK/Sj+jPl4CDEeN/wyIQ4kliTTp938XohMtvM7bjZEL2G8x/XIdrLOgCVdHETeYy9ozJgxupid9y5MleZFmWEvw2BhsAl7exz//iLw2muv6cNZCxcu1H9ZzePQlo1k+nSuMn/ZiInBwmBjI49e8jRlyhT9skVQdjKwkZzAxpetRG3Gpxy/V1YbSQ186qmnJrotr34zBiwr6iXJ9Gkzp5W8no/fDRYGm3QwYMWfVL1EK2Kct52sM2BXrFihMatXr17W2CEE44zcoPV+WZcXlQIMFmADRo4cAokQINj7bbfdJqeddprg2sN2LGGyCJdlI9GXMVogG6Ih2IKRwQJsoq7vbLezikTsW/4yCZMeNgyEvpEIhNimHTt2lIceeigMbPvOozFgS67Auvk9MfTZzu9EloE46Gg7WWfAmtSHXhiwLIPj+F2nYUupVtvOSTcXHQQsajdsobEBI0cOgZII4Id+7LHHyp133qm3lIg6MHjwYB1mpeS9tnynL3NSmdPlXu3g2NK2bPgAC7ahwSaq+o7xh4/rySefrMc1XrY4rBWmfkAikPfff1+23357fTCySpUq2Yg9Ms+WZcC6+T2xiLOd350BmxjXlH71cgWWrSSoXouOKdWdTzfVb9FJN9dglE9td21NjsBPP/0kXbp00ZMpqWCJ9/rPf/4z+UMWXDV9mZSIjoojgDwhg1Hxq+H+xiIFhuvtt9+us2kRdYCXrTAZgBjbAwYM0AciX375Zdlll13CLRQPuTcGbMndA9OX3fxeGuxs5vcwGbCVSjc9t78YA7Zu3bpZMzJ79mxdRu0dm2ddVnkFbNrwh3zx9KUiaiWgUbtDpHWPs4s9MveLoTJ/8nD9W+tDz5VGu3ctdj3oLwYTg1HQ9bv67EQAvyl88FauXCm77babNmKbN/dff7xAw/TlVq1aeVFcxmVw+OHMM89UQ0FMevbsKRdffHGxsl588UV555139G+XXnqpkMfdbzKYGIz8ri+o8n/55Rd9SI3g62TWwl+b2LdhokWLFmlfV+JvctCsV69eYWI/EF45WIQBixuBMWhNXzZzWSCMJKjExrnfYGIwSsB2mT+1bNlSWLhYsmSJdsVp3Lhxmffm+oJ1LgTGgPXChcAIr3bBrr7jTBiPjX+ulgXffihT3v6XbNm0NeTH0hnj5cvBV+pr26hczQ3b5j5bkcHEYOQ7QK4C6xF46qmntMGF8crBnwkTJkhYjFfANX2ZATiXxEEIDuO8++672iCJD/9DeBpis3KtQoUK0r1790BYNZgYjAKp1OdKeNnCVxTjlfbhsxc24xWD7KSTTpJff/1VDj/8cO1z7jNsoSweXYF4KTRk+rKZy8zvQf+1ce43mBiM0sWEjHWQ7X6w1hmwXvrA4gwP1Spopv/6/V/73oWhT/76Y6X8MvF9Xd0fv86XsYPOkdiWzVK/ZWc56KL/k23+vzL6zU+y8g0mBqNk97pr0UaASZSg6RdddJFe5bjuuuu0gVWrVq1QNdz05RYtWuSc75tuuknzwAs58XKhefPm6dVt8OaAEXE+zcSsb/DxP4OJwcjHqgIp+pFHHtEvW+B75JFH6vSwrVu3DqRuLyu5+uqrdUpboiUE2R+8bEOuyjJ92cxlueKDem2b+w0mBqN0sQmLG0GkXQhWr16t5Valxnbpyi+j+xu16yY77LKnrJw3VWZ+Olgad+wlox/pJxi0HJrqfuXL1sSiNZgYjDJqsHso9Aiw8oPLwLhx46RatWry3HPP6agDYWyY6cscgvGCPvzwQ+1CkWpZ1HvPPffo2w877DDp0KGDPjT1xBNP6G3uY445RjC4OFDFYZ0g49QaTAxGqbbJtvs2bNggF1xwgbz00kuatZtvvlnuuuuuwF4EvMSDbEmPPfaYTqxA9AQv3Oa85M/2skxfNnNZtvwumjpKFnw3MuViqHefk/rr+22b+w0mBqOUG/X/bzQG7MSJE9N9NND7rTNgV61apQHAByNbMoF4K29bI9uiUn6+fe8rZOxj58ivcyfJyIG95fcFP0q1OgVy6LWvy7Y1vZlYU2YmyY0GE4NRklvdpYgi8P333+sUm/gR7rTTTvLee+9poyuszTV9mS18L4hTzumk8Nx5552LDFjqZxWWlwOSPxx44IEC3g0bNpSRI0dqHzMveEy1DIOJwSjV52y6b/78+XL88cfrlwLaQ0a4sMR3LYnjtGnTtCHO76wmk4PeUXoImL5s5rL0ni59929q4WnWmBdKXyjjl+rbNywyYLnFprnfYGIwKqMJZf6Maw7EQTncNrbZZpsy783lBesMWHzHIC/SyBrhVaoanAFLRhAcqNcsnSur5v9PqLvHNa9KzXp2OUIbTAxGueyEru7gEXj77bf1QSNCK3Fqn0NFO+64Y/CMeFij6cvGWMu2aHwTyUNfHhFgPVHAeTJgsa09c+ZMPRHgkjFixAidyay8Mr2+bjAxGHldvt/l4TtsfEXxy8aHuF27dn5X60v5zHEY4ujeWWedpd13fKko4oWavmzmsmyb27TzMbLdTm3KLWbLlo3y+RMXlLrPprnfYGIwKsVsOT8Q65uXbQ5y4frUrFkwbpjlsFXqsnUGrFmB9cKALdXaAH6Ixf6WqrXqaQOW6vY6/kbZoWn7AGp2VTgEykeAt2m2uQnZw2cCp3N4Kwz54ctvnbd3YHym4leJT2si+vvvv3XSBwxYiJi6YQmqn6g9ufqNGMT4inIKnUNabL0bl4hc8ZRpvehc3759Zc6cObLPPvvIk08+mWlR7jmPEaij3Pz4Vx79vXmTfJ7gpqjN/WRbxICdOnWqtQasVYe4CCPCGwMHG2rXrp2gi6T3k1l12LxhXXoPZnH3hBeuk+Wzt2awWDD5wyxK8+9Rg4nByL+aXMm2IMCKD6tY/fv31zr273//W2/DRsV4NX0501UHr+VE+CzSmBpi1TBXZDAxGOWKj3Tqxd+VFcrLL79cG6833nijDB8+PLTGK20n2QJtwN+VXZAg/aDTwd62ezH8S5Lpy2YuK3k96O82zf0GE4NRJljsscce+jEMWFvJKgMWh2M6KvH8vPC5MMLb9FcwBuz37z0gc8a+rHivILsdeYmW+bKZXwphtJIRzuMz1KGvIMlgYjAKsm5XV/AI4D/Iyfe33npL69ewYcPk+uuvD54RH2s0fdkYaz5WVW7RAwcOlGeffVYqVqwo1157rb6fbXD+JaOFCxdq31njSpXs3nSuGUwMRuk8m4t7OT29//77ywsvvCA1atSQ119/Xe69995QHtYy+GG4sgrPAs2rr76aE1cSw0vY/pokBiYGLPybvmzmsly2KdO5f93KxfLt63fJxnWFB869aoPBxGCUSbmswELOgE0RPTNoe+U+gCEMbVxX6FebIhsZ3UaiAuK/Qh1Pv0s6nnqHbLdzW/196rv367+J/vtL8Tbx5Ztl7uevJrrs228b/yg8LGcw8q0iV3DOEWAVEKd8BiIC2ocxXmYqIJq+bNyQUnnGj3tIVICLBkRWqPvvv1/aty90I2IFLhndfffdQkrRTE8Pl1U2sX0hg1FZ99nwO9EfiOBAfFfCf3EIjp2DMBMuA7gOsECDjIlS4Sg1BNiZBTdeBuMXtkxfDmJ+T8ZppnM/ZU57/0H53/BHZeP6NcmqSPuaF/O7MWA5fGorWbUC67UBaxyP1y4rjAfrlxAW/zBWJyqg/JZd+0nbnoUO3rsdfpGuctn08bJs1oRi1S/47iOZPPQOGda/m6xd7i9/xSr+/1/WLp+nPxmMEt3jfgs/AqwCEizfBErHeE3FrzOMLTd9GWMhSGJViJVCTpOPGjVKJyqg/vPPP19vf/P5qquu4o8QfD/erYDf8JHFL7lr165pRT3g2VRp7ty5+laDUarPBXkfPsOkgz3qqKOEl5Cjjz5aJk2aVGT8B8mLl3XhusOhLXN4C1cIR6kjYHzM41dfedr0Zb/n95KcVqhUWQ44/zHp1PceyWTuX71kjjJcH5KR9xydVtSDknwk++7F/M48gXsZqcXXrl2brLqcXYu0AWuyz6xZ9pNvAK+a/4OMffQsnaigoPX+su+Z/y6qq1mXE6Rq7fr6+/fvFF+FJWPXvInvidpPkgqVqoh6tSx6LogPBhODURB1ujqCQ4AtN4wmjCgmgCuuuEL73nm1uxFcS1KvyfTlTLPPpF5T6TtJHctqIWGdwBtj9PHHHy+68fTTT5eCggL9veQq7A8//CDPPPOM4ObhRfjAokrjPhhMDEZxl6z4yApx7969tY8oq2ysUuIzbFbZrGAyQybOPvtsIWxW27Zttc95hsXk7WNlGbCmL5u5LEiAmh94itRu0Cyjuf/3RTNk1tiXZN1vC8XEa/Wad4OJwSiT8knfSzpxVr/pvzaSVQbsmjWFy+heHOACbCM8Qlr5QRv/XCOjHjxVyIVcs35T6Xr5f5UxWrmoqoqVt5XWPc7W35f8OE5WqrBahvY/92E54YFv9b96zTuYnwP7azAxGAVWsavIdwQwBjit/fDDD+s3aOJl8pktuCiT6cuzZs0KvJls+ZPDnjFs11131b7G8StGrGRcckmhXzyrtPF+ZazO4fPJv5LGrVcNMZgYjLwq14tyvv32W+0ygOsAKcQ/+ugjIUFB/HaxF/XkogzcQcjExpxGqLqwZbfLBWYl6yRMHRSvT3w3fdnMZfwWFGUz9zft2Lto7t/ruBt8YdlgYjDKtBITRnDGjBmZFuHrc1aF0fL6oIEJWbNiziRfQKxSvbac9HDyN5M9j71O+GcbGUwMRrbx5/jJDIEff/xRb72yZUxcVyZN4rzmA5m+PGFCcXedINrOSiEHsJLRrbfeKvzLBRlMDEa54CFRnYMHD5ZLL71UiDhA/nUyUjVubFfM7ER8p/IbCStuueUWbYiTJjaqrjupYJHNPWYFtkoVtVMZR6Yvm7ks7pLvH22f+w0mBqNMATF91oQCzLQcv56zagXW+Fl49ZbKQYDq1avL6iWzZf2aX/3CMHTlggWYgA0YOYoGAkQWwFjFeEWu+A/mi/GKBGkzJ9anT58uy5cvj4ZQPWgFWIAJ2Nii73/99ZfORHXuuedq4/XCCy+Uzz//PDLGK37YuI3g18uqOu4RjjJDwKzAljRg6ctufi+NqZfzuzNgS+Nb5i9er8Diw0HoIGj5zOBXZcpsaI4vLJ/xleYAbMDIUfgR4KT7Mccco53tTzvtNG0MkB42n4i+TOglCGPIUSEC48aN0x/AxgZ951AIvOD3W61aNe0XSsrekgZKWOXHPHbsscfqg2hkYyPusqPMEfjzzz/1wxir8eTm93g0tn72cn53BuxWXMv95PUKLBUecsghut6F6tS/o0IEFkwpxMJg43AJLwLr16/XKz0mputdd92lMxVhGOQjmT79wQcf5GPzE7bZYGGwSXhTQD/i0kIGKvxeSQn75Zdf6mxwAVXvezUceDlLJV/gYB4HYIhOEQVfXt+BS1JBWQYsj5g+7eb3rQB6Ob/jQ0v/ZVfPxOLdWlPuP1nlQuD1CizwnnzyyRrl+ZOHy5aNG3KPeI45AIMFk0doLgw2OWbJVZ8hAosWLZKDDz5YB0XH7YZT2/m+2mP6NIYSfpX5TmBgMoAZbHKBCX6MpIPlwBoH3vg7efLkyKXWJXoCyUKI9gHuXrnD5UJmttRJGDKo5Aosv5k+7eZ30BBt43g5v7MQ0qRJEx1ZhUOmtpFVBqwfK7C85XM4gEgBC6d+Yhv+gfOzcMrHGgswARtH4USAQzkkJ8DPFTkS7L1Pnz7hbIyHXBt9JxoAmY/ynfCLBotc6vuCBQv0i9ZDDz2kT5ITEcNkhIuSfN577z19SI9MW6+88krRKfkotTEXbUm2Amv03c3vhZLxY3632Y3AKgPWjxVYxIpPIDR77Mv6r43/kX42CJo9boiuxmASRJ2uDm8RINNTt27dZOnSpTpJwcSJE8WEO/G2pnCWZvo2SRzCRhg/XtJzzz2nizOYeFl2KmWNGDFC9t57b+GFi5UcfJOJSRw1wmWgX79+OmYmKW+PPPLIqDUxZ+1JZsDClOnbNs/vZYLnsb77Mb+TvREyofjKbEsOLng7WmbZANNROS3rJf3jH//QJ3AXTxstJB6wjY64+X3pdetI39mi7WAAvmDiKFwIcKL5hhtu0LLjFPfFF1+sY2b6Ffw+XOhs5Za+TQ5wwhjZnAZxK8dbPxErFj/Kpk2bbv0xw0+0HQzAImh9J/0nsVw5ff/bb7/p7Fqkht13330zbI29jxF32RygPOOMM8T4o9vLcbg4K88usH1+T4Z2mx7nyJkv/Co162UfOs6v+d3s1DoXgmSSVNc4kAJ5fQBl++231xmJKPt/IwbxJy/JtJ3sTGDiKDwI4DdIis377rtPb8M+/fTT8sQTT1hxqtw2FOnb5513nmYLvPKVTNvBIkh9X7JkifTo0UNYiWRFmWD+HCSL4osWB1vww+SQCy49YVz1t10/jGshL2KJyM3vhaj4Nb+bl+lffvklEfw5/c2qFVi/DFgQ5gABYTfmff2urF48O6eg56Jy2kzbwQAsHIUHAbZuWLliNa1+/fry6aefFr2QhacVwXJKHydzz9ChQ8XWLDJ+IkKbaTsYBKnvZNEiePrYsWOlUaNGMmbMGL1rENWT+Ndcc43WR5KGcGiratWqfoo1L8vm5R1Klgbbze/+ze/OgE1R7fw0YMnuwkpE7O8tMvHlm1LkKDq30WbaDgZRyXQTHemU3RIMAoxXMqHsueee8s0338hBBx1U9gPuikaAPk6QfFbILr/88rxDhTbTdjAIQt+pC/cWfD9JnHDYYYcJLgNR7qv4Fz/66KM6fu3bb78t+RZ3OSil+v3333VVZLsri9z87t/87gzYsnpdid/9NGCpauDAgXorbckPY2X+pPw5oUxbaTNbLWDgKBwIPPLII9ptgAH8hBNOkPHjx3viGxmO1mfPJX2dbetPPvlEp9TNvsRwlEAIMdpM24PQ93nz5mlDFZeFihUryj333KN9sxs0aBAOwDLgksNo+CtDJGHo0qVLBqW4R1JBwKzAJjNgKcfN7/7M73Xr1tV+9MjByCIVuQVxT964EAAmgiBOH/TNkFtk47rCrQn9Q0T/o40Th9ysW0fbwcCR3QhwQOvss8+WK6+8UqeiHDBggLzxxhv68J3dnNvFHX3dGHBgaVZy7OLSW25ooznlT9v91nfCYcVHGcB14Kabbop08H4Mdl4oSXHK1jW66sg/BIzRVJ4B6+Z3/+Z3swpL37eJ8sqABXhybpMfft3KRfLlc9EL51Kyc9HGP1cu1m2m7Y7sRoDQWGSXef7557XBiuF65513Rtog8FMiRt/nz5+vt9P9rMuGsnEZIO4qY5yf+k6CBFYgTzzxRP1iQOrUKVOmFKXytQELP3gg1OPRRx8tv/76q3aXIIWzI38RSNWAhQuj725+91YmxoC17SBX3hmwnIp99dVXpXbt2kL2jhmfDvZW0haVRttoI22lzV7HmLSoqZFghcxEnTp10kkJGDBwGWClx1HmCBh9Z/UGP0UiN0SVaBttpK1+6jsHxPDLfvLJJ2XbbbeVQYMGaReNICMd5EKGhLE7/fTTZdq0adK2bVt57bXX3JgagCDMzkmyQ1yGDaPvbn43iHjz1xiwLATYRFYZsGydQlWqVPEVo1122UVMgO9JrwyQpTPG+1pfLgqnTbQNoq202ZG9CDAZcuBl4cKF+i+HtTi05Sh7BOj7JrwRW75sc0eNaJOJNkBb/dJ3dgYIF0WMWQKck6Dgn//8Z9TgTNge4tqacGD8xUhy5D8CxBGGUnWHoe+7+d1buRBRBCJEnk1klQFLvmzIbwOWOtj60j6GmzfKmIf7WZngAD4zIQIa06a/VdtoI211ZCcCBK3Hx5VsMhxiJEYvYbIIl+XIOwSMvvOSTND5sCU4SIYEbaFNtM0vfWcblz6Kvye56ck6xY4BIbPygch+9+9//1uHJcPv1wR3z4e257qNK1as0CzUq1cvZVaMvjMHuvk9ZdjKvJEwcRAubjaRNQYs2zNkb2ELgJOsQdCDDz4op5xyimxav1ZG/ecUWbt8XhDV+loHbaAttIm20UZHdiJAgG58BzlsQ3xeog6QoIDYnY68R8DoO8bYEUccIT/99JP3lQRcIm2gLbTJL33HlYXdAHYJCCb/wgsvCAZdWYHlA4bA9+q++OKLorjLuEt069bN9zpdBYUIYBeQ6Yw4wukmwjD67ub37HtTQUGBLsQZsGVgyYlOKIjVV8MCSsFATNaY9auXyciBvUO9EsvKK22gLbSJtkU1gLiRYVj/YngQeuf999/XAzPxXvMxXmmQ8ovXd7bCDjzwwFCvxLLyShtM5iuv9Z0Fhdtvv126du0qHN7o3Lmzju165plnBim2nNZF+szjjjtORxwguoOfB+Ny2lBLK8d4xYjFvzrdha14fXfze3YCNiuwy5Yty64gj5+2ZgXWGLBBrz5hMJNBpciIvadPKH1i8XkdqXg3xittCvJlwON+GeniRo8erQ9r/fDDD7L77rvLxIkTpXv37pFusy2Ni9d3DL+DDz44lD6x+LzCuzFevdZ3wuVQ/h133CG4uRAai5XYFi1a2CJK3/lgVbt3797CFnavXr3kgQce8L1OV0FxBIz7QKYuVfH6ro1YN78XBzjFb24FthyggvR/LckKW2EjRozY6k5w/8mhik5AtIFRimfjNkBb8mV7r6Qsbf/Oye3DDz9cb4v16dNHRxxw/nTBSi1e3zFSkEeYohPAKzwbtwGv9Z0IBvi2fvnll7Lzzjtrn2ySE+Dmki/E6vPJJ58sP/74o7Rr1067T6S7ApgvWPnZTmPApuP/WpKfeH3X7gRufi8JUbnfjQFLlj1eaG0h61Zgc7VqSL2vvPJK0cGuiS/eIJ89epbVyQ5IUgCP8GoObDH55ApDWzq1jXzwgsb2I7EzTdpNVs1q1aplI7uR5yle3zn8dOmll+qQZSZkj40AwBth1eDVHNjyUt/xycY9gFBRGMfUNXXq1Lz0+cSd5+OPPxayiQ0bNszpaY4UAoMJynQF1rAdr+/MlW5+N8ik9pdwebhxMI/h1mELWWPAmhXYoF0I4gXBAbKHHnpIZz0yceQ+6N/VyrSzpId9v//BRXFeCXgP787nNV6idnwm6Pmhhx6qD2hVq1ZNvyj961//cjEkcyyeeH03cWI5rEQqVtsInvbYY4+iOK9e6/tXX32lV11feuklqV69ujzzzDPy5ptvpn1wxjbcMuGHg1qscletWlXee+89l745ExA9embx4sW6pIYNG2ZdYry+u/k9fTjNKqxNfrDWGLBs2UA2bNMQgoOVB5Ox67NBZ8kn950oqxfPTl/qHj8BD/ACTybDFry6UFkeA+1RcRy0ITnBuHHjZKeddhJyqBOOyJE9CKA7ZJFC3wnUffzxx0vPnj2FgP25JniAF3gyGbbg1St9Zzfg1ltv1bGHOVi4zz77yLfffivnnXderpuek/qHDx8uV111la578ODBuk/khBFXqUYAH2/ICwNWF6T+c/O7QSK9vyYKxKpVq9J70Me7nQFbBrgEQyZsDEvnvLkt+WGsvH/LQfL5/12Uk0gFRBigbniAF3iCN3iEV0f2IUBWpP3331+f4MY4mjRpknTo0ME+Rh1HWofi9f2TTz6R9u3bS9++fXMSqYAXH+qGB3jxQ99nzpypI2Hcdddd2q/thhtu0D7ZrVu3zssewYvBqaeeqsM5cnjNvWjmvhv4YcDSKubMeH1383v5sjaZ0Gxys7LGgCVUBsRAbQtde+212teMIOEXXXSRVKywjfz81VvywYBuOtbqL998IFs2bvCNXcqmDuK6Uid1wwO8mMDl8OjILgRwcsco4E2foO//+Mc/5LPPPhMTisQubh03BoGS+o47zpAhQ3QM1COPPFIIYL9hg3/6TtnUQV24MlA3PPih72yRs9rKSxWTOf0Tt5Z89Z9ftGiRjjjwxx9/6CQNrEo7yj0CxoA1maC85Kikvrv5PTm6Nhqw26jJ1oojZdOnT5fddttN55jm5GeuadSoUXLYYYdJjRo19FYip3HZwiM4Mv5hGCZQ5ao1pUmHo2TnvQ+XBq33k2q1s8ugtH7Nr7J8xleycMrH2r9104Y/dD3wQZYm0kU2btxYpxxt06aN5oMVGnwsHeUeAWOwYojgDoNR4F4yci+X8jhIpu+kZsWwgfCdIy4oESRI/cshn2yIQyq4l3BQCD/XNWvW6OI4Oc02vtf6jkFwzjnnyMiRI3U9vFw9+uijeZ0WFdkiS1ZgiXnL4a18NeSz6ct+PEs0DFzkcGvZe++9Pasimb67+T0xzKSMfvzxxwUfcVvSR1tjwBITk3AlxMX83//+lxjBgH7lQBlbd2yxkT7w+uuvL1YzPiBko+EEMDE846lOw5ZSr0VHqb1jc6ldsKvUKmgmVWpsJ5W3rSGVqtbQt27esE42/bVORTj4XdYu+1nWLPtJ1iydKyvmTJLVS4r72RI8nK0sJhpOAcbTfffdJ2z7Yciy5ZjLA3DxfOXrZ4K9szLOgMvbKltUhDtyZDcC2eh727ZttZ9kq1atpGXLljpOKnqKAco/CAOJf4wbc+bMkdmzZ8usWbNkwoQJwot7PPmp77i0XHDBBUJuefLKP/XUUzrSQHz9+faZsxfoLL6vyBCZlBxn8w0Tm9rLCyKHYHnx8moHKxt9z8X8jkvPtGnTcj6/9+/fX+6++269u8hnK4gVWBtIGWCsBMeU4Zhzdu69917NizIMYyrBQlJ+1IQUUzESY2q1NqZO7+rnaEem/yiDsiiTspMRvMEjdcGzo9whoFbRYirUi5aFGnBi6uUnd8y4mtNCIFN9V7siGeu5GR8ow299V6u6MfUCXMSrSj0bU6e708IoqjerlSSNi4ozWu54G1UMbG3X+vXrtWzUwkxMvWh4xmam+p7v8/v999+v5XHNNdd4JotsC7JmBZbtG7YI2DL47rvv1PieG1q4cKFe0WQrON2teU70Tp48WW9FscrCP1IRElPRrMLQKrM6Q+ieZs2a6ZUbVm9oO4d80gkYnmgrJDfI5W+tbDkRm5M3e/LSs/KKbB3Zj0DU9X3MmDFy9tln64OEhHBTk5Duq/ZLxn8OcQdTk7E+DPvpp5/KAQcc4H+lroaUEWD+ZFV81113lblz56b8XLIbo67vydqe7bXnnntOuzXhgsRnKyhbC9ir55WPi7bulRHrVZEZlaMO3mg+VBaWjJ7PxUPwqjpTDN4dBYeAMlhjKuC5xh78VfidmHqJCY4BV1PWCERV39ULeOyyyy6LqUNgun+qUG4xFZIra7yiUoCKo6uxAZ+hQ4dGpVmRaodanNF9t1u3bp61K6r67hlASQpCZ5jnVIKTJHcFe4nwKVaQWoHV4KjTtznjR624ah7Y1lMHtnLGR7oVw6vZzqQNjvxHQPkRxnr06KH7iwpnFnv++ef9r9TV4CkCUdV3lQI2pnZ0dN9k+/XOO++M8bLlqBCB8ePHx1SSAo2POkfgYLEUARWHV8tIZYfzhMOo6rsn4KRQiPIT1/JQUVJSuDuYW6yJWWXCZ5lwWkEvT7P9q1YsdLWEUCHqQFgIXk3YF9pAWxz5hwBRMjhsw7YjBwsIQaR8DP2r0JXsOQJR1HfSy9544436RD3brxxE5ZDpgAED0nJL8hxsiwoEl6OPPlqHQ7v44ovluuuus4g7x0o8AhyKhZo0aRL/c0afo6jvGQGRxUO4IEHKNzmLUjx+NBg7ufxaVOQBbd2rKATl3+zDHSrcka4/lYNbPlSfdZHxB7poiyN/EHj//fdjtWrV0n1F+SvHlE+VPxW5Un1FIGr6rnzvYyqKi+6XKnxb7Kabboopg9ZXDMNWuDrNHmvRooXGqHfv3s7dx3IBKt9tLaunn346a06jpu9ZA5JBASrdtJbHvvvum8HT/jxijQuBCiejwcGADJqisgUf1i2SoOWdaX0MgmqnQPdTFdos9ueff2ZalHsuhwhETd9xE1AHP3W/JAKGCgWVQ3TtrBpdVdnwNEa8eKpDtXYy6rgqQuCQQw7R8vroo4+KfsvkQ9T0PVcujio8pJbHHnvskYkYfHnGuRCoFW1yXxN1QB2GCnVCAJIZ0AbaYvJ5e7xgn5fFsWVy+umn6+1ZACAW3iuvvCJmSyUvQQlxo6Oi7wUFBTpmKdujREC54oordAQXtUISYul4zzqxXkkRS4xXso6RNEIZAd5X5Er0FAETeaB58+ZZlRsVfc/1/G7mO+dCkMAWV75J2rpniydIitqqZVTeNoPsA8nqwkWgY8eOum/iOoALgaPwIhAFfcddiINZKluU7pcm0gBtc1QaAZWKV+O0ww47uEgMpeGx8hfcX9jtYmdBvaBlzGMU9D2+8bmc36lbvUnE1JmbeJZy+tkaF4KffvpJg6PiogYGSLzfqMq4FVi9fldEW+hoYfXn9RufVMvH50cd0tJYqlWAGH7ajsKLQBT0XcXIjql40bpPYrhecskl2ph1+p64Xw4cOFBjRdQBog84CgcChHyjT6sYsBkzHAV9T9T4XM3vK1as0DJRWfwSsZWT36wxYOfNm6fBadq0aWBAhN2xuyyg4hWXNjpKHwGVKjhGeCwG0e7du8cIm+Uo3AiEWd9ZkVLRBGL4u5qJXSUp0AJx+p64XxLaDqxYyVNpdBPf5H61EgETsoksdZlSmPU9WZtzpe9r167V+oQPri1kjQE7f/58DU7jxo0DwSaXS/FBNDBqWydBYEYdJCK49tprdV9k8lMZtrLawgqKb1dPcgTCrO+TJk3SKbaNMUbyDBIVxJPT93g0YjEO/hhj/7HHHit+0X2zHoFHH31Uj8Eq1FlGvIZZ31NpcC70nYOQjEHKFzYVFgO5xxoDdtGiRRqcRo0aBdLwk046SdfH36hSPrTRS9n9/vvvMfLEo6RMfl6Eb/GSP1dW5giEURc2bNigw2ERFos+SXKCzz//vEwQwtjGMhuTxQUMfpWuW2Om4uJmUZJ7NFcImAyH//nPfzJiIR90Ieg2Mh4xDrEzaQtZY8AuWbJEg4PPod+Ui7cXv9uUqPyov4UmanOmv82cOTNGCCIUtH79+rFx48ZlWpR7zjIEwqjvZNNq27at7o9sgV9zzTXlhm1z+h6LcRi4QYMGGrd+/frFVGIcy3qjYycVBHr27KllmMmh2TDqeyqYlLwnaH3HdcEs7pTkJVffrTFgly1bpsFh8PGT4v1HonRwqyzMouoHVFZ7M/l95MiRse222073P1IZ44/tKBoIhE3f8TNj9cnEG+YgJocJU6V81velS5fqQz9MsuykIHtH4URAZd/S4/GsWbPSakDY9D2txiW4OUh9x70O3WJHyBayxoA1J9zq1avnKzZBCtzXhqRYeLxC03ZHxRF48MEHtUKimCeccIILcF4cntB/C5O+jxgxImYmbsIH3XzzzTG27dKhfNX3NWvWxPbee289wao0z06P0+k0lt2LfzcRNggTh9GUDoVJ39NpV1n3Bq3vzJPIxhayxoBduXKlHny2335737AJesndt4akWXC+bKmkAwuGwT/+8Q/d51DI2267zW03pgNgCO4Ni76T4vSMM87QfZEJgrjDU6ZMyRjhfNN3IjQQKQTsWrVqFQNPR+FF4Ntvv9Wy3G233dJqRFj0Pa1GpXBzkPrOXIme2eKaY40BywEagKlTp04KIsvslqCdnjPj0p+n8rntJRHF39qklSQkyJtvvlnyFvc9AgiEoc8PGTIkxq4TY1/16tVjHFpJd9UpkajC0PZEfKf7m8qyFVPZBzV+DRs2jP3888/pFuHutwwBleVQy/P4449Pi7N86fOJQAmq7eZAqRdjVKJ2pPubXgtWg2egpBovkydPFrXKIMrpXv9TiQxEBS/WfCj/L/1XnSQV/imjVlSCA1GncPU/FchbVD5rUdtsKfM9atQoUTHldApB6lHZJFJ+Ngo3qoxSovzpdJpZ9caWVsrcRPJSE4WsXr1aVE5x/Q+MvJSXX5jT74499lgBj6ZNm8p7770nyu/Vr+pcuQqBXPQf2/VdhQ0UFSJIlNuA7iM9evQQFfVCVOB2T/pMvui7SuQgTz75pJ4j1MFLUXnaPcHPFZI5Atnq+zfffCPPPfecKBcanbY7FU5s1/dU2pDNPUHpu3LVEbUKK0ceeWRW9lg2bS32bLoWb6b3z5kzJ3bPPffECEzMSoNiIqt/lEFZlEnZyShoP5FkvOTyWjr+QfHyYpUyW3lRRqry8gujV199Vcewoy0HHXRQbPny5X5Vlfflxvcfp+9buwMrhsS4NGGecJkaPHjw1hs8/JSpvgctr0ybTGIHdJksW2PHjs20GPecBwjE67sX8wVy7dSpk5vf05BN1PU9ERS+rsCuWrVKVEYjUYaDTJw4UfXJrVS7YQup36KT1N6xudQu2FVqFTSTKjW2k8rb1pBKVWvoGzdvWCeb/lonG9f9LmuX/Sxrlv0ka5bOlV/nfCNrlszZWpj6pBz35bTTThPl1yhqUih2TUUbEBUPUK9Afv/996JifBa7ni9fVE5pvULBCrTq7HLDDTcUa3oyebF626VLF1E+ZvrNq0WLFhpns+pKQWY1lnLUgKZX1tUpUlGnqItW102FyeRl7vHqr/LXETXZiXrZ0UWef/758vjjj+dtP/AK15LlJOs/Tt9F7zhdcMEFwgoTpLb9ZNCgQVJQUFASSk++Z6PvQcork8aCm4rWoHfh3nrrLTn66KMzKcY9kwUCyfQ9yPnCze+FQoyyvpfVTX0xYJUztajT3fLMM8/oLWsqr1y1pjTu0Esa73W4NGjTRarVrl8WTyn9vn7Nr7J8xleyYMpHsmDyCNm04Q/9nHr7EwyUq6++WlRWL71VnOnWeUqMhOymRFstRl7PPvtskTtA7dq19VZ7nz595OCDDxYV3iyrlqrVTmGL74MPPpB3331X2IqAMIDPO++8InllVUmCh1VYIlEHZHS9uJw89NBD8s9//jPBne6nTBEw/cfpe2IE1alqufXWW+WRRx4RtQKrxyWVHSoQoyuZvtsgr8SIJf9V+UhK37599U1q9VrOOuus5A+4q54iYPTdhvkim61zT0GxpLAo6nsyaD01YFW+eOnfv7/QsfGDgRq17y4tDz5Ddt6rp1SsUjUZLxlf27Jxgyyc8rHMHjdEFk8brcvBWMEwUrEBtcHEasfrr7+ecR1RelAdepA33nhDG6gqcYT2N+LtDVLxE+Xcc8+V3r17i9qa86XZKgKADBs2TNerYrDqOlgVp96BAwdK3bp1PakXv2pWZn744QfZYYcddJvVaWVPynaFiDh9L78X0M9VOmLB51UdgNCrhnfeead+cSv/aW/uKKnvNo3P6er7hx9+KMccc4wwXqkDb6ISPHgDkiulXASMvuOfast84eb30mKLkr6Xbl3xXzwxYNmifeqpp+SWW24RthW2qVBRdtn3WGnX6zLZvsnuxWv0+duq+T/I/0YMknlfv6tiPWwRDoRhHLGVrWIs+lx7OIpnMsUVgEEI2WHsn3LKKXL99dcHfggCl4777rtPhg4dql96MDSZ1C688EItu0wRHT16tN6iVeHZZPfddxeV0cWzAzKZ8hSV55y+ly/JxYsXa2OV7W2IQ6cc0tpnn33Kf9jjO0rqu03jM+5ed999d0r6Pn78eFEZmkTlZNfuT7hBOfIfAaPvLE4xnto0X7j5vbT8o6LvpVtW+pesDViVtUj7nk6YMEGX3nD3rtK5771Sp1HL0rUF+MvqxbNl4ss3yZIfxupaVdgk7Yu7yy67BMiFfVWVlBeRGdShEu0fnEtu8cvFp40ICVA28sK/9corr9QGMS4QKlSR1KpVK5fNi0zdJfuP0/fiomWy51Q8J6hxk6Hf3XXXXdpthRXYoCkq8iJiTbdu3XTkE3bWcH9w5D8CJftPFOcL/1EMroaS8or6+JyVAaviZ+ptXwbqGjvsJJ3OuFuadDwqOGmlUNP8ScNl4pCb5c+ViwW/TrY/TjzxxBSejN4tyIvBn/BXrEY//PDDctxxx1nV0HfeeUeuuOIKwc+K8Glsd6YqL1aU8W9lpQu66aab9GquCctmVUNDyIzT9+RCUwHYdWgsc2CVcG0cNspVyL6oyIvdMxU1RPCjZ3uUQ8FOp5P3RS+uRn2+8AIjm8qIir6ng2lGBqwKZ6AP3WAAQU06HCX7n/uIiiJQJ526A7t347rV8uVzV8j8ycN1nazOcciMeGb5QCXlpQJEa0N+u+22s7L5KqmFfjHtfpa5AAA0bElEQVR6++23U5aXyr4jKhWsfP7551KtWjXdPqJSOMoegZL9x+l7cUx5IWR79YknntAuORisHNLCVzMXFCV58SJ74IEHah9i/PNxBcrXKDJB9aWS/SeK80VQWAZRT0l55dP4nLYBq2Kqyplnnql9FitUqiIdT79L2vQ4Jwg5ZV3HjE8Hy6RXBsjfmzdqn88XX3xRVL7lrMu1uYB4eW277bbacCf4dxgIg4BoEipVZFJ5TZ06VRsLv/zyi17tIsoBPoeOskcgvv84fS+NJ+4pHCRatmyZ9g1k9+D2228P9JBWPFdRkheHtEjwwAosRuxHH30kKkZtfHPdZ48RiO8/UZ0vPIYsp8XFyysfx+e0DFhCErHl/Omnn0rlarXkkCtfkh3bHJBTAaZb+dIZ42XMw/1k0/q1enDE2CGUUxQpXl5sx5N1qmvXrqFqqgpQro1TVrmYzErKi1VaXqgIVYTfLC4IRFZwlD0C8f3H6XtxPKdPny68CH722Wf6AlvcvHC1a9eu+I0BfouavIhGwsn3vffeW8aMGaNdigKEM++qiu8/UZ0voiTUeHnl6/icsgGLpd+rVy9tvFarUyCHXjs08AgDXnU+IhWM+s8psn71Mm0Ukc4xaiux8fJSOcKFcFVhTbNIpAK2D5csWVIkL7YRCUd0xx13CFsoJLAgEgarBo6yRyC+/zh934onJ+Dpd7gg4XNdv359uf/++/VLVC5dkqIqL6KSsMOSKz/irZKP9qf4/hPF+SLK83s+j88pGbAYCPgTEuoIsI7oP0xqNdgl1Bq9dvk8GTmwtzZiCSHFwYBcTkBeghkvLwajL774IvQhpIjpyjYiRiyHujjtzeorJ7sJw4WrgSNvEIjvP07ft2LK6j8uAoSp4RARWbXI7lYy89/WJ4L55OQVDM5RrSW+/0Rxvojy/J7v43NF5a91e3mKiXHA6X2WqXve8LYKkdWqvEesv76tSlvbSIX8+nnCW/L9lG/1yXxW+aJARl5sA+HuQSaysBNGAiFceNH47rvvhC1cDqHhMtCvX7+wN88q/k3/cfpeKJbZs2frzE/EK8WVBf9qjFkMWA4M5pqcvHItgXDXb/pPVOeLyZMnR3J+d+OzSLkrsIRmIIsVDsKHXvd66Hxeyxta8Ikddf/J+mAX2alSDdlUXrm5um7kxVY6hx7C5vNaHm74xBLMnC0v4tdedtll5T3irqeBgOk/Tt9F+1WTVAN3AfobL0x8v/jii60J4+TklUbndreWQsD0nyjPF4cffrg+CByl+d2Nz4VdOakBS1DcPffcUwfk3vfM+6R1j7NLKUAUfiA6wcQXb9BxYvG3CmuyA+S111576bdNDpQw0UaRaBvpOVkxIMB5WOVlm2ycvm+VyGuvvSbXXnutLFq0SLsWnXPOOXLvvfdqn9etd+X2k5NXbvEPe+1uvgiXBJ2+l5ZXhdI/Ff6CjyF+ryQpIK5YVI1XWksYMNpIW2kzbQ8bGXmxxUncvqgar8iF09+0kbaGVV629S/Tf/Jd36dNm6YzPtGvMF47d+4sX3/9tU6owYEtW8jJyxZJhJMP03/cfBEO+Rl55fv4XFJaZRqwnOgmPSwZtkhSEHWijdV3aKTbTNvDRkZeZNjCXznqRBsbN24cWnnZJh/Tf/JV30mewQEtQjbhpoKxShY4xsBOnTrZJi4dccONz9aJJTQMGX1380U4RGbkla/jc1lSSuhCQOy9li1byqpVq6TbZc9blx62rMZk+ztpZz8bdJY+VczBDeIQhoGQV6tWrWTlypX6ZL5t6WH9wpADXKzEEmqHYOdhkZdfeGRabr7re61atXT4tRUrVuioFqzwEyrL1kx1+S4vDnSGaXzOVC/9es7NF+GaL5y+l63vCVdgSYuI8dpQndJv0vEov/TIunJpK22m7WAQFoJXjFdO6eeL8YpsaCttpu1hkpdt/Srf9Z2A4BivHHgkwgWHA201Xuk7+S6vsI3PNuq7my/CNb87eyyxvEqtwJJ7etddd5Utf8fk6Ls/VyGzWtqmf77ys3rxbHn/loOkYoVthNijbFPbTMirefPmOpg//ntRCJmVDt4zZsyQ9u3b64M2c+fOtV5e6bQtiHudvs+W924+UOv7zz//bH3/cfIK1/gchA6nU4ebL8I1Xzh9T67vpVZgCRmzefNm2WXfY/POeGUgwGCn7WAAFraTyQhEsOZ8M16RDW2m7WRFCoO8bOtPTt9bSrP9jpMtW7aEov84eYVrfLZR3xkr3XwRjvnC6XtyfS+2AssyNSuO5JXvc9dnoU0Vm+2gQarZDwZ0kxo1aghvQLnOtFNWe5AXTvh//PGHTrcY1lSxZbUv1d9JNUu4t5o1a+osSbbKK9X2BHWf0/dCpMOk7258FgmLvILS41TrcfNFIVJhmS/c+Fz++FxsBfaFF17Qxmuj9t3z1ngFsu2b7C5ggCEPJrYSvGG8kkEsX41XZEPbwQAsbJaXbf3I6XuhRMKk74xJbnwOx/hso767+SI884Ubn8sfn4sZsK+88op+omXXvrbpXuD8GAwMJoEzkEKFhrfzzjsvhbujfYvBwGAS7dZ60zqDlenr3pQazlIMBgYTG1theDO82shjUDwZDAwmQdUb5noMVmasDHNbsuXdYGAwybY8P543vJm+7kcdYSnTYGAwMXwXuRBwAKZFixZSuWpNOXnQdKlYpaq5Jy//btm4QV6/rK1s2vCHzJkzRx+UsgkII6/atWvLsmXLpGrV/JbXhg0bpKCgQCejsFFeNvUdeDH9x+l7oWTCou9OXuGQVyGX9vxv9N3NF4UysX2+MPJy+p5c34tWYF9//XV9Jxmp8t14BQgwAAvIYKO/WPKf4YlQUvluvCISMDAhxAw2lojKSjYMRk7fC8UTFn138gqHvGxTeqPvbr4olIzt84WRl9P35PpeZMCOGTNG37nz3ofbpns548dgYbDJGSMJKjY89enTJ8HV/PzJYGGwyU8UUmu1wcj08dSeivZdBguDjU2tNTwZHm3iLVe8GCwMNrniIwz1GozMGBkGnv3m0WBhsPG7vnTKNzyZPp7Os1G912BhsKGd2oWAkFF16tSRP//8U04a9KNUq21Pzu9cCmP9ml/ljct2k+rVqws5oytVqpRLdorqRl4EWudAB+4DDRo0KLqWzx+WL1+u3QiIHkFqUFvkZZtMnL4nlojN+u7G59Iys1VepTnN7S9uvkiMv63zhRufE8srkb7rFdjJkydr47VOw5bOeI3DDkO+dsMWGhswsoXgBeO1bdu2zniNEwqGPHFhwcYmecWxaMVHp++JxWCzvrO44Mbn4nKzVV7Fucz9NzdfJJaBrfOFG58TyyuRvmsDdsqUKfqJei06Jn4yj3+t36KTbr3ByAYoDC/77befDexYxUOXLl2sk5dVAClmTP9x+l5aMjbru5NXOORVmsvc/mL03c0XpeVg43xh5OX0vbS8So7Pek989uzZ+s7aOzYv/YTHv3Cq/4unLxWV+1QatTtEWvc4u1gNc78YKvMnD9e/tT70XGm0e9di14P+YjAxGAVdf6L6DC+tWrVKdNnT34gbeOaZZ+pUtT179pSLL764WPkvvviivPPOO/q3Sy+9VA499NBi14P+YjAxGAVdfxjqM9iYvp0rnm0cCwwmBqNcYRNfr+HF8BZ/LcjPTl5Bou1dXab/mLHRu5JLl+Tmi9KYpPuLkVcQ+m6jTifDy2BiMNIrsOZL7YJdkz3ryTXCQmz8c7Us+PZDmfL2v2TLpr+Kyl06Y7x8OfhKfW2bbSpIw7YHFV3L1QeDicEoV3zE12t4admyZfzPvnwmuxX+pO+++67ceuut8tdfW+U1duxYIZ4e1ypUqCDdu3f3hYd0CjWYGIzSeTZf7jXYmL6dq3bbOBYYTAxGucImvl7Di+Et/lqQn528gkTbu7pM/zFjo3clly7JzRelMUn3FyOvIPTdRp1OhpfBxGCkDdiff/5ZP1OroFmyZz271r73lbqsv/5YKb9MfF9//uPX+TJ20DkS27JZ6rfsLAdd9H+yjTKKck0GE4NRrvmhfsMLcXuDoJtuuklXs2LFCnnjjTf053nz5smJJ54o5NU+4IADZMiQIdqIDYKfZHUYTAxGye7N12sGG9O3c4mDbWOBwcRglEtsTN2GF8Ob+T0Xf528coF6dnWa/mPGxuxKK/9pN1+Uj1GyO4y8gtJ323Q6GTYGE4ORdiHghD1UpcZ2yZ717Fqjdt1kh132lJXzpsrMTwdL4469ZPQj/QSDlkNT3a982ZpYtAYTg5FnIGRRkOFl++23z6KU1B897LDDpEOHDvpg1BNPPKHjrR5zzDGCQcuhqffff9+aWLQGE4NR6q3MnzsNNqZvZ9vyRVNHyYLvRqZcDPXuc1J/fb9tY4HBxGCUcqN8vNHwYnjLtionr2wRDNfzpv+YsdFv7t18kR3CRl5e6Xt53Ng2Bifj12BiMNIGLH4rUOVtayR71tNr7XtfIWMfO0d+nTtJRg7sLb8vUOG76hTIode+LtvWDMYwS6VBBhODUSrP+H2P4YXtmqCIt2pWXL/66is58MAD5fvvv5eGDRvKyJEjZYcddgiKjXLrMZgYjMp9IA9vMNiYvp0tBL+pF9FZY15IuZjq2zcsMmB5yKaxwGBiMEq5UT7eaHgxvGVblZNXtgiG63nTf8zYGAT3br7IHGUjL6/0PRVObBqDk/FrMDEYFTNgK1UNzoAlwwQOuWuWzpVV8/8n1N3jmlelZr3GyfgP/JrBZNWqVbLNNtsEXn+iCg0fQQ5IZHBp3bq1zJw5U59ir1WrlowYMUKaNm2aiMWc/WYwMR08Z4xYXLHBxvTtbFlt2vkY2W6nNuUWs2XLRvn8iQtK3WfTWGAwsVHfDW+lAEzzhyjKy/TpNKHIi9sNNmZsDKLRYZsvoqzvqcjbpjE4Gb9mDDR9WhuwyR7w61os9rdUrVVPG7DUsdfxN8oOTdv7VZ0rN0sE/v77b6lfv742YCnqzjvvlL322ivLUt3jUUCgjnL74V959PfmTfJ5gpvcWJAAFB9/cvLyEVxXtEbAzRfh6ghhHYP1KSnzZrZ5w7rAUJ/wwnWyfPbXRfUtmPxh0WebPhhM8B+KqdBfNvwzvkzmLSQIvAif9cUXXxRVReQBG8lgYvq0jTzmmieDjenbuebHprHAYGKjvhvenLy2ImAwMX166xX3ySBgsDFjo/ndz79hmy/yXd9tGoOT9cuS+l7MgN30VzAG7PfvPSBzxr6stuQryG5HXqL5XTbzSyGMVjLi8MEMdegrSDKYmEEgyLrLqsvwEtSANHDgQHn22WelYsWKcu2112q2CKHFv0T0yy+/yODBg+WOO+7Q0QnIjBUUGUwMRkHVG6Z6DDamb+eS93THgs0b18svk4bJ1Hfv12PBmmU/ecq+wcRg5GnhGRZmeDG8ZViMJ485eXkCY6CFmP5jxka/K3fzRXYIG3kFpe/p6vQfKxbI7HFDZOo798lPX74pQfEJqqYug5F2ISDPNrRx3e8idXfWn/36j0QFxH+FOp5+l7TteYEsnjZGfl84XU9KO954QMKq/1K8TXz5ZhUpoY606XFOwnv8+HHjH6t0sQYjP+pIt0zDC347TZo0SffxtO4nUcGAAQP0Mw8++KBcfvnl8tFHH8m0adO0gTp69Ohi5RFm66yzzpL169cLb7UrV67Uh70+++wzCSKQNvVBBqNizLkvGgGDTRD6ngzydMcCBs5P/3OKrF4yWypXry2b1q9VofYqyr79/i2tDjkzWVUpX7NZ3528SovRRnmV5jK3vxh9d/NFaTnYOF8YeQWh7+mOwfMmvifjn7lMtqiFBCICwCOH73ve/K7U2bF8N7LSEkjvl5L6rldgmzUrjP+6dllhPNj0ikz97sU/jNWJCniiZdd+2njl826HX8QfWTZ9vCybNUF/Nv8t+O4jmTz0DhnWv5usXe4vf6bO+L9rl8/TXw1G8ddy9dnwMmfOHF9ZGDVqlE5UQCXnn3++Nl75fNVVV/FHxowZU8ytgAHywgsvlMaNGwursL/99pvO0rV8+fKiZ/WDPv43d+5cXbrByMeqQlu0wcZvfS8JUIVKleWA8x+TTn3vkUzGgsmv3S6suB5yxUty2pNz5fj/TJZaDXaRiS/dKBvW/layuoy+26zvTl6lRWqjvEpzmdtfjL67+aK0HGycL4y8/Nb3dMdgFhEn/PcaqbFDIznhwSly6hOzpdvlL8iGNb/KNy/dXBpcH34pqe/agDUZOrzejovnf9X8H2Tso2fpRAUFrfeXfc/8d9HlZl1OkKq16+vv379zf9HvfCBjF1a/ipIvFSpVEeV3UOy6318MJgYjv+tLpXzDi8lGkcoz6d5DmKwTTjhBJyro2rWrPP7440VFnH766VJQUKC/4yZgaOLEiYIRe9ttt2kjlt+PPfZY6dGjhw6/Ze7z86/BxGDkZ11hLdtgY/p2kO1ofuApUrtBs7THAnzPF075WHbe+3BpvM8RmmUilux+5KXy95ZNKqb09540w2BiMPKk0CwLMbwY3rIsLq3HnbzSgsvKm03/MWOjH0y6+cI7VI28/NT3TOyxFT99q7Oo7nnsdVKj7k66wU069JIddz9Yfp3zjXcAJCnJYGIwKm7AqpBWftDGP9fIqAdPFfLu1qzfVLpe/l9ljFYuqqpi5W2ldY+z9fclP46TlSqslqH9z31YTnjgW/2vXvMO5ufA/hLmCzKABVZxkooML7NmzUpyV+aXCBLcq1cvWbNmjey6667y1ltvSeXKW+W17bbbyiWXFPous0o7depUXVn16tW10dulS5dilVOe8VkpdsGHLwYTg5EPVYS+SION6dtBNijTsYAtq532PFSadjq6GLsb16/R3014lWIXM/hiMDEYZVCE548YXgxvnleQpEAnryTghOSS6T9mbPSabTdfeIuokZdf+p6pTleqUk2adOwt9Vt0KtbgTcq+82r8LVZwgi8GE4OR9oE14ZBWzJmU4JHsf6qi/NVOenha0oKw6vlnGxlMDEY28Gd4mTChuLuFV7zhg7Nw4cKkxd16663Cv3g66KCDhH/xNHToUPn666+1C0L87359NpgYjPyqJ8zlGmxM3w6yLZmOBZW2rS7dLvtvMVbXrVwsP454QqptV+BZCD6DicGoWIU5+mJ4MbwFyYaTV5Bo+1OX6T9mbPS6FjdfeIuokZdf+p6pThe07iL8i6efv35HWJnFJTQIMpgYjPQKLGlCWT3jcMR65c/gqBABsAATsAEjWwheatSoIdOnTxf8S22kTZs2ye233y64G+yxxx5y7733+s4mWIAJ2NgkL98bnmYFUdD3RdNGy4jbe+otrQMueFxYHciWbNb3sI/P+SSvbPuh18+7+SIxorbOF2EYn4npPUVFIfj8yQtlu8a7yd4nF6YGT4y0N78mGp+1AVupUiU54IDC0//LZ/qzqudNE4ItZfmMr3SFYANGthC87L///pqdzz9PFBo+t5x+++230rFjRx2loG/fvjJu3DipW7eu70xRDwQ2NsnL94anWUGY9X3jutX6FCzRCEg5fcSA4dJo965pIpD4dpv1Pazjcz7KK3Hvyt2vbr5IjL2t84Xt4zOpqIfdfqh8r0IZ7rr/SXLEzR9I1Zr+p5NPND5rAxbxHnLIIVrKC9Wpf0eFCCyYUoiFwcYmXAxPH3zwgU1s6fSyTLbEHCTE1gsvvBBYSCuDhcHGKmAsY8ZgFCZ9X//7Mvnw7qPk5wlvyz4nDZDed46Wuk338AzZMOi7k9dWcdssr61c2vHJ6LsZI+3gStx8UYYgjLxs0/eFUz+RDwceJSQU6HnDO3Kg2v3CJSEISqTv26jTvTEqJ5xEixYtpHLVmnLyoOlSsUrVIHhKq46R9xwtWzZtkKNu+zit5zK5ecvGDfL6ZW31wTPCjzRv3jyTYnx7xsirdu3asmzZMqlaNffyImwWztXEe/34448F3oKiDRs26MgIHDyzUV5B4ZBqPab/2KzvJdvy2aCzdczow65/Ux0k6Fjyclbfw6LvTl6FYrZdXll1Rh8eNvru5otCcG2fL4y8bNL3DX+slHev6yy1d2wuh6oxuEq1Wj701MRFlqXvRfviGGidO3cWQiFhZTft1CdxSXnyKyF7iJoAJrYZr4ggXl7Dhw/Xp/9zLZohQ4boMFpg9uabbxZjZ7vttpPjjz++2G9efhk2bJiOmmCrvLxsqxdlxfefMOj7n78vlfkqA1e9XfeR3xfP1P/icWi81+EqFF+9+J/S+hwmfXfyEh1SzebxOa3OF8DN8fru5gsR2+eLeHnZou8/q6xbG/9crcfgX755v1ivrVK9jjRVEQr8orLG5yIDlopPO+00bcDOHvuytQYs6WeDIFKlQWBiKxl5keaVmK25psmTJ2sWBg0aVIoVkhv4acA+99xzuk6b5VUKlBz/YPqPzfpuIMLvCuLEK/9K0vZqVyYbAzZM+u7kJTqVJX3A6XtJTSj7u9F3N1+IhGG+MPKyRd/NGDxj1LOlOll1ldzATwO2rPG5yIUAjghCj6FB7vo+d30m2zfZvRSj+fADQX4/GNBNn2ZfsGCBTolqY7tNakD8TYnFymn/fCSCaO+555461uz8+fOtlZdtsnH6XiiRMOm7G5/VPBWS8dlGfSf1uJsvwjFfuPG5/PG52HImuetJGQr9b0TpVbTC4qL/v2k7WICJrQRv5513nmbvvvvus5VN3/kybQcLm+XlOxBpVuD0vRCwMOm7G5+3zk22j89pqqPvt7v5ohDisMwXbnwuf3wutgLL7aw4kn1py98xOfruz6VOo5aFpeTJ/6sXz5b3bzlIKlbYRn766aeilKi2Nh954S/DWbxp06ZJmzZtbGXVF75mzJgh7du3VxmGt9EHEVmhcpQ6Ak7fw6fvbnwOz/icuiYGc6ebL8I1X7jxOfn4XGwFFhXCAGAlK/b3Fpn48k3BaJVFtdBm2g4GYTCG4PHcc8+VzZs3y+WXX24RksGwQptpOxiEQV7BoJJ6LU7fw6fvbnwOz/icuiYGc6ebL8I1X7jxOfn4XGoFFjUy4ZDwweh22fMq/+1RwWhXjmuZP2m4fDboLL0NPXv27ECC73vRZORF6KqVK1fK22+/Lccdd5wXxVpfxjvvvKMPhu2www5Cnu8gkiVYD0oGDDp9317Cpu+Eq3Pjc90Mert7xM0X4Zov3Phc9vhcagUW9cYQuPvuu7WmfzPkFiGbStSJNk4ccrNuJm0PkzEErwMHDtS8X3nllfL7779HXVy6jVdccYVuJ20Pk7xsE47T9/DpuxufnfGa6Tji5otwzRdufC57fE64Aoti/P333zq97IQJE6RJh6Ok2+XPZ6ovoXjus0fPkvmTh8t+++0n48ePlwoVEtr21rYlXl6Eq3rrrbes5dULxggbxmpzWOXlBQZelhHff5y+e4msP2U5eYVrfPanF2Reanz/cfNF5jgG9WS8vNz4vBX1MkcBDLhXX31VZ1PCsJvx6eCtT0XsE22jjWQpoc1hM14Rh5FXnTp1tGH3xBNPRExKW5tD2zBeaWtY5bW1NXZ8Mv0HHXD6bodMknHh5JUMHXetPARM/3HzRXlI2XHdyMuNz8XlUaYBy2277LJLUcDfSa8MkKUzxhd/OgLfaBNtgwhuTJvDSvBOkGro6quvlrFjx4a1KWXyTZtoG0RbwyyvMhuZowtgaQJ8O33PkRDSqNbJKw2w3K2lEKD/uPmiFCzW/uD0vbRoKt6uqPTPW3/ZbbfdZPXq1fLVl+P1yszOexwq1eo02HpDiD8REHvU/SfJlo3rBd9RYxiFuEli5IUbBIecevXqJQUFBWFuUhHvJCw4/PDDdaKNqMirqHGWfDD9x+m7JQIphw0nr3IAcpeTImD6j5svksJkzUUjLzc+F4qkTB/YeIkRY5S0ZkOHDlXGa4Ec0X+Y1GqwS/wtofu8dvk8GTmwt6xfvUxOOeUUvRVNLNEoULy8GjZsKF988YWO7RvmthGT98ADD5QlS5ZETl62ySW+/zh9t006pflx8iqNifsldQTi+4+bL1LHLVd3xssr38fnlAxYBLVx40a9mvfpp59qI/bQa4eGNtWsXnn9zynaeO3Ro4eMGDFCqlSpkqv+6Eu98fJiUBo5cmRoU82y8nrEEUdo4zWq8vKlE2RRaHz/YZB0+p4FmAE86uQVAMgRriK+/7j5wn5Bx8srn8fnpD6w8WLEwHv33XcFA4JVy5H39AmlTyw+r/BOG2gLbYqa8Yrc4uXFquXBBx8cSp9YfF7hnTZEWV7xumbD5/j+4/TdBokk58HJKzk+7mpyBOL7j5svkmNlw9V4eeXz+FyuD2y8sADt1FNP1UG/v5/yrfw84W2pUnN7qbfr3vG3WfuZaANfPHWJ9nnFbeDNN9+UatWqWctvtozFy2vy5MnaTYKg/506dcq26ECeJ9pAv379tM9rPsgrEFDTqCS+/zh9TwO4HN3q5JUj4CNSbXz/cfOF/UKNl1e+js9pGbCItGLFijr70Zo1a/TBrkVTR8mqBT9Ko3aHSMUqVa2UOkkKPv+/i+THkU/oNLEcAHrmmWekUqVKVvLrJVPx8sJRH3eJadOm6cNQVavaKS8SMZxxxhnywAMPyJYtW/QBu3yRl5ey96Ks+P7DwQGn716g6l8ZTl7+YZsPJcf3Hzdf2C/xeHnl4/icsg9sIlGygkkOeozZGjvsJJ3OuNu6tLOkhyXD1p8rF+s4r4QJOvHEExM1J/K/IS/yqBNVokmTJvLwww9bl3aWyAlk2FqwYIGO80qYl3yVl20d0um7bRJJzo+TV3J83NXkCLj5Ijk+tl3NR33PyoBFgPPmzdMRCsjYBTXcvat07nuv1GnUUn/P1X+rF8+WiS/fJEt+KIyFSsYmgt4TSy2fqaS8DjvsMHn00UelTZs2OYVlxowZcvnll8snn3yi+XDyyqk4yqy8ZP9x+l4mVFZccPKyQgyhZaJk/3Hzhd2iLCmvqI/PWRuwiJM0Z0899ZTccsstsmrVKtmmQkXZZd9jpV2vywKPVECEgf+NGCTzvn5Xuwtsv/32Qt7wCy+8MJQZtvxQFyOv/v37y8qVK7UrBT6m119/feCRCogwcN999+kQbZs3bxZ8dAcOHOjk5YfgPSrT9B+n7x4B6nMxTl4+Axzx4k3/cfNFOARt5JUP47MnBqwR62+//SZ0crZ9MUagRu27S8uufWXnPQ/zzUd2y8YNsnDqJzJ77MuyeNpoXS/+rWyXYwzVrVtX/+b+K46AkRduFZs2bdIXCVcFbkcddZT45SO7YcMGGT58uO4nhPeCKleurN1RnLw0HKH4z/Qfp++hEJc4eYVDTrZyafqPmy9slVBxvoy8ojw+e2rAGvjwX3zwwQf1Qal169bpnytXrSlNOhwlO+99uDRovZ9Uq13f3J7R3/VrfpXlM76ShVM+1hnCNm34Q5dTo0YNOf/883VWrcaNG2dUdr49ZORFR//jj0Icybl83HHHSZ8+feSggw6SBg2yy762fPlyGTdunAwbNkxnCMNvGqpZs6Y2mMmC5uQVzp5n+g8H7Zy+2y9DJy/7ZWQzh6b/uPnCZilt5c3IK4rjsy8GrIEOd4IXXnhB+55OnDjR/Kz/1mnYUuq16Ci1d2wutQt2lVoFzaRKje2k8rY1pFLVGvqezRvWyaa/1snGdb/L2mU/y5plP8mapXNlxZxJsnrJ7GLlde7cWfvi/uMf/xDcBhylj0AyebVt21bwS23VqpW0bNlSWrRooXHGAOUfhPHLP8qZM2eODrc2a9YswT96+vTpxRhy8ioGRyS+JOs/Tt/tE7GTl30yCRNHyfqPmy/sk2QyeYV1fPbVgI0X4dy5c+X111+XMWPGCOE5/vzzz/jLaX+uXr26HHDAAXLIIYfIySefLM2bN0+7DPdA2QjEy+vLL78sWlkr+4nkV1gZ33///Z28ksMUmavx/cfpu/1idfKyX0Y2cxjff9x8YbOkCnmLl1eYx+fADNh4keIfS6DkKVOm6FW62bNny88//6zDO5lVPO43q3t16tSRZs2a6ZU/Vv/22msv6dChQ17EcY3HLVefnbxyhXw06nX9J1xydPIKl7xs49b1H9skkpyfMMsrJwZscjjdVYeAQ8Ah4BBwCDgEHAIOAYdA2QhUKPuSu+IQcAg4BBwCDgGHgEPAIeAQsA8BZ8DaJxPHkUPAIeAQcAg4BBwCDgGHQBIEnAGbBBx3ySHgEHAIOAQcAg4Bh4BDwD4EnAFrn0wcRw4Bh4BDwCHgEHAIOAQcAkkQcAZsEnDcJYeAQ8Ah4BBwCDgEHAIOAfsQcAasfTJxHDkEHAIOAYeAQ8Ah4BBwCCRBwBmwScBxlxwCDgGHgEPAIeAQcAg4BOxDwBmw9snEceQQcAg4BBwCDgGHgEPAIfD/2jsTWD2mKI7fUmqppVVqq6LLs1eIWiJqr6CJVi0hse9bQlEhhBIVNKFFmxIhUUmboilFaLW2opaq2ve19qDUUmrc/417e2e+75vv63vz3pu2v5N8Zu5+5jfJ63Hn3HNyCGDA5sChCQIQgAAEIAABCECgfAQwYMv3TtAIAhCAAAQgAAEIQCCHAAZsDhyaIAABCEAAAhCAAATKRwADtnzvBI0gAAEIQAACEIAABHIIYMDmwKEJAhCAAAQgAAEIQKB8BDBgy/dO0AgCEIAABCAAAQhAIIcABmwOHJogAAEIQAACEIAABMpHAAO2fO8EjSAAAQhAAAIQgAAEcghgwObAoQkCEIAABCAAAQhAoHwEMGDL907QCAIQgAAEIAABCEAghwAGbA4cmiAAAQhAAAIQgAAEykcAA7Z87wSNIAABCEAAAhCAAARyCGDA5sChCQIQgAAEIAABCECgfAQwYMv3TtAIAhCAAAQgAAEIQCCHAAZsDhyaIAABCEAAAhCAAATKR6Bj+VRCIwhAYGUh8P3335upU6ea9957z3z99ddG5S5dupg+ffqY3r17m6amJtO/f3/ToUOHukh++ukns3DhQtdvjTXWMN27d687hg4QgAAEILB8EuiQWFk+VUdrCEBgeSXw4YcfmrPPPtvMnDnTLFmyJPcx+vXrZ6688kozZMiQXEP28MMPN9OmTXNzDRgwwMyaNSt3XhohAAEIQGD5JYALwfL77tAcAsslgcmTJ5tdd93VTJ8+va7xqgecN2+eGTp0qJEh+/HHH9d85r///rtmGw0QgAAEILBiEcCFYMV6nzwNBEpLYPHixeaSSy4xo0ePrtCxZ8+eZocddjAbbrihcyOQoSq3gn///Tf0nT9/vhk4cKCZPXu26xcauIEABCAAgZWOAAbsSvfKeWAItA+B4447zjzwwAOpxffYYw8zatQos9dee6XqVXj33XfNyJEjzYQJE8JOrVwPDjvsMOd6sPbaa1eMoQICEIAABFYOArgQrBzvmaeEQLsSeO655yqM16OOOsoZotWMVym7zTbbmHvvvdcZsKussvRP1csvv2zGjh3brs/D4hCAAAQg0L4Elv6r0L56sDoEILACExg+fHjq6S666CIzceJEo2gB9eSYY46pcDuYNGlSvWG0QwACEIDACkyAKAQr8Mvl0SBQBgJTpkwxgwcPDqrI31WuAB07Nu7B9M8//5gePXqYb775JswjP9mtttoqlOUf+8QTT7hyI1EIfv75Z/POO++Yr776yv0Uqqtr164u/Nbee+9t1lxzzTB3tRtFT5BeklVXXbXu86hvHHGhU6dO1aZ1ddLtjTfeMJ9++mkILbbxxhubLbbYwvkK1xxYo0Frv/nmm+bVV181ixYtMptvvrnp27fvMs1VtE41VKUaAhCAQGMEFEYLgQAEINBaBHbeeWeF6gu/MWPGNGupSy+9NMyh+e65557UPAcffHBotwZsqi0uWMMwOfXUUxO7+xv6x/rp3vrXJscee2zy7bffxkNT99tvv30Yf/7556faqhUuvPDC0L9bt27VuiRvvfVWcsoppyTWeA59s7rZw27JrbfemtioC1XniCv1rGJR61ltNIjk0UcfjYdU3BetU8UCVEAAAhBoBgHTjDEMgQAEINAQgb/++iuxu5PBGLNRBpLff/+9obHZTnYX0Y3VeP1shIJUl0YM2MceeyyxO79Bn6xxmC1vu+22yYIFC1Lr+ILdEQ3zFGHAvvjii8m6664b5szqki2feOKJFQy8brrefvvtNQ3XeC7xsC4Z8dBwX7ROYWJuIAABCLSQAD6w9i85AgEItA4BuQrEn80PPfTQup/ma2miz/T6rO9/jWTniud67bXXjA6O+c/+vk3zyWXgoIMOMnZn1Fe7q1wMRowYkaprjYIykMkFwmcS0xo6uKZ4uUrQIP3WWmut1NI64HbDDTek6nxh2LBh5txzzzV//vmnrzKdO3c2ivqw4447ptwdxEMRIrJ+xUXrFBThBgIQgEABBDBgC4DIFBCAQHUC77//fqoh9llNNbRB4ZZbbjG//fZbWMnuYJo5c+aYX375xTz77LPOf1Y+tnbn0hmPvqMiKLS2KKmD9PBid5OdX+4rr7xiHn74YaefUu1eccUVvou73n///amyCq+//rqxLgahfr311nPRHDT/Cy+84HxrlXb3ggsuCJnNvBH70UcfhXFF6hQm5QYCEIBAQQQwYAsCyTQQgEAlASUjiKU9Ddinn346qLLvvvuau+++2+y2225mtdVWC/Xa5T3nnHOMIh94sT6g5tdff/XFVrk+9dRTqXllROvQVizWvcBcd911xvrvhmrppp1SL/aLnLHuDGHXW7vLL730kjnhhBNSRrl2Y2Xk3nnnnX6oG3PXXXeFclE6hQm5gQAEIFAgAQzYAmEyFQQgkCbwwQcfpCp0ir49RDurn3/+eVh60KBBKYMuNPx/oxP6XmQUWp9bX2yVa9ZAlrtDLTnppJNM//793U8GeLxrOmPGDBPvGF9zzTWmqamp1lTOGJZbhxd7MC64WBSlk5+bKwQgAIEiCTQex6bIVZkLAhBYKQjEqWD1wK1tCNaCqt1M+bPaQ2WuS95O8I8//mgeeuihWlO1Sn3v3r1T85588snOMNVusFwAYpE/rHZVq8ncuXNDtXyE493a0JC5Of30042NROBqZeg//vjjzu+2KJ0yy1GEAAQgUAgBDNhCMDIJBCBQjUCvXr1S1Z999lmq3JYFZfaqJooDq7S1ipMqA1DpbmNf2Wpjiq6zobPMTTfdZBYvXuymlqF/+eWXm6uuusod4Npvv/1cut0999zT5KXQlUuBF+0cx76wvj57jV0Q1Ob9lovSKbseZQhAAAJFEMCALYIic0AAAlUJZHfxWmLAajc3TmSw/vrrV5zMr6pEplIJECZMmOA+tWsnMz48lenaZsWtt97aTJs2zcg9QAa1Fx2umjVrlvupbvXVVzcyYocOHep2V+XjGsvbb78dF5sVQeG7775zcxSlU0ohChCAAAQKIoAPbEEgmQYCEKgkkDVgY3/Nyt75Ncoitdlmm4Xfaaedlj8g06pMUscff7zLQKWdTWXtqma8KlyVMlW1tRx44IFm/vz55swzz6wI5+V10Q6tDqPpoJbcIKZOneqb3PXLL79MlZtTiHdki9CpOTowBgIQgEA9AuzA1iNEOwQg0GwCWQNWu4w//PBDTQMtbyEbVD/VbDN8pcp5BZu1yhx55JEme7J+k002Mfo8L/cC6brddtu5Q08KT9WI/2jemtk26VBPunTpYsaNG2fuuOMO5+dqEy+EneKs/7DNEmaOPvpooz56BsmWW25pFG5LoqgFinu7rKLYs7G0VKd4Lu4hAAEIFEUAA7YokswDAQhUENABJO0UfvLJJ67tjz/+MLfddpu5+uqrK/rWq5g9e3aqizfaUpU1CuPHj08ZrzrUpUQAirfaVuIZNLKekhjIVUA/iYxfxaodPXq0iwvrD8fpUNq1114bDFibOczFetUYuRfEYbFU1xJprk4tWZOxEIAABGoRwIWgFhnqIQCBQghkg+8rxqkM2WURRRB48MEHwxDtLu6yyy6hXO9GAfxj0a5lnvEa+9rG4+J7GXRestm9fH181UGxaiK3AOnjf9qhzopi1e6///5mypQpLvmCnt+L/Hj9+jJgvWiHNnYH8PXZq96F2PqffGCL1Cm7HmUIQAACRRBY+he4iNmYAwIQgECGgDJe9enTJ9TKQFOYKB/SKjTUuNFp+jPOOCOc0Fc3+WYq6UCjooxWXrp3727y3A+0nlwd6onm8VLPt1ehqWr10XqDBw82iseqX9bg92v4qz7xH3LIIb7oQpP5g1fZz//XX3996FfrZvLkyc69Qi4W+in5RJE61VqXeghAAAItIYAB2xJ6jIUABOoS6NixY8Vp+IkTJ7odxWq7jfGECmelw1pxcH7tPo4aNSruVvdeBpmXRYsWuU/yvpy9KpxV1l3Bh7eK+8YHvZ5//nnzxRdfxM3hfuHChebiiy8O5exNp06dzO677x6qdTCr3g6wdqS96GDbpptu6opyq/BuB6qQL+0zzzzju1ZclazgxhtvDPVKNKE4s0XqFCbnBgIQgECBBDBgC4TJVBCAQHUCSs2q7FGxyEiU4aaQVjIqY1F0gEceecTstNNOLuVr3CY/UB1WWhaJdyZlFCu1qqISxKKsYUOGDDHDhw+Pq919tdP9/fr1C/2kv0JbxZnH5KeqEFjqF8dnDYOim3322SeUZLwq1e306dON93X1jTL4FZ9V0Qq8DBgwwN+6a2yQyvCW68GIESOMEjTEoqgO2slV/FsvitKgBAiSInXy83OFAAQgUBSBDnZnYunWRFGzMg8EIACBDAEZeXIF0An/rOjAkeKOduvWzaV8rXXgSafqJ02alB3uygMHDnShsVSQUSfj0YsOcSk8VSxaU64EMhL12Txr0MZ911lnHRepYM6cOaFan+11QC2ODiBfVUU00A6mdkljw1yGof9zq+eM/VMXLFjgdk7jdLdaSG4K4qLkBfJplSEcG7VaT76zBxxwQNBLNzJEq3Hu0aOHO9y1ZMmSCpcGpaUVM4URkxStk5uU/0AAAhAoioAMWAQCEIBAWxEYO3ZsYg08/Y9zwz8bzSAZM2ZMYg8r1VTTHsoK81kDNtXPGn3JEUccEdrz1rbGamJdHKr2TU1qCzfffHNiDdOqfeM17O6z09/XWQM2O1VijdPEhqyqO5efwyY1SKy7QcU8qrAGajJy5MjEum80NF/fvn0Tu/NbMVeROlVMTgUEIACBFhDAhcD+a4BAAAJtR+Css84y8hnVgSXtVOaJ2nUITOlNzzvvvIYPbmXTrWr387777nOf0jfaaKOqS8otQbppLcVXVbKA+KBYfO8nGDZsmJkxY4bR2GqywQYbmMsuu8yFwOrcuXO1LqFOMWiVSUshxhTmq5YoLqt2shVZYdCgQVW7KUKCX1e7s127dq3aT3688pOVS0J8KM13LlInPydXCEAAAkUQwIWgCIrMAQEINIuADhHNnDnTHYDSJ3IdeOrZs6dLJtDU1OQMw2qGY7MW+3+Qoh8opJXS2sovVAkM5GurmLVZkT/qk08+aXS4SX60eUao5ps7d65L1KC5ZBxqjNK/LqsoLJbcKOR7q9SydpPCGbUybMWlOXPqkNm8efPcM4txr169XFazOBxYnp6toVPeerRBAAIQyCOAAZtHhzYIQAACEIAABCAAgdIRwIWgdK8EhSAAAQhAAAIQgAAE8ghgwObRoQ0CEIAABCAAAQhAoHQEMGBL90pQCAIQgAAEIAABCEAgjwAGbB4d2iAAAQhAAAIQgAAESkcAA7Z0rwSFIAABCEAAAhCAAATyCGDA5tGhDQIQgAAEIAABCECgdAQwYEv3SlAIAhCAAAQgAAEIQCCPAAZsHh3aIAABCEAAAhCAAARKRwADtnSvBIUgAAEIQAACEIAABPIIYMDm0aENAhCAAAQgAAEIQKB0BDBgS/dKUAgCEIAABCAAAQhAII8ABmweHdogAAEIQAACEIAABEpH4D+rbrlyoERWPAAAAABJRU5ErkJggg==" } }, "cell_type": "markdown", "metadata": {}, "source": [ "For each variable-gadget node$u$and each clause-gadget node$v$with the same label, connect$u$and$v$with an edge. For our example formula, here's what the resulting graph looks like, with one possible$C$marked in blue (but we emphasize, the coloring is only for illustration and *not* part of the reduction).\n", "\n", "![image.png](attachment:image.png)\n", "\n", "Now we need to show that$\\phi$is satisfiable iff$G$has a$k$-vertex cover. Again, please see the book for how to write this, and again, it's okay to say that's obvious that the conversion runs in polynomial time." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "### The subset-sum problem\n", "\n", " \n", " Read from the bottom of page 319 to the top of page 322. \n", " \n", "\n", "SUBSET-SUM is the set of pairs$\\langle S, t\\rangle$where$S$is a set of$n$natural numbers and$t$is a natural number, and there is a subset$C \\subseteq S$such that$\\sum C = t$. For example,$\\langle \\{4,11,16,21,27\\}, 25 \\rangle$belongs to SUBSET-SUM because$4+21=25$.\n", "\n", "SUBSET-SUM is in NP because we can check whether a subset$C$adds up to$t$in$O(n)$time.\n", "\n", "We prove that SUBSET-SUM is NP-hard by reduction from 3SAT. We need to define a mapping from formulas$\\phi$to pairs$\\langle S, t\\rangle$.\n", "\n", "> Interior monologue\n", ">\n", "> A certificate is a subset$C \\subseteq S$; in other words, a certificate says for each$c \\in C$whether$c$is \"in\" or \"out\".\n", ">\n", "> - We could create a number in$S$for each literal, and$C$contains the numbers corresponding to lucky literals.\n", ">\n", "> - We could create a number in$S$for each variable and its negation, and$C$contains the numbers corresponding to true variables and negations of false variables.\n", ">\n", "> Let's think about the first of these options. We can ensure that exactly one literal in each clause is lucky like so:\n", ">\n", "> ![image.png](attachment:image.png)\n", ">\n", "> But it's not clear how to ensure that no lucky literals are contradictory." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "> So let's think more about the second option. We need to ensure that every variable is either true or false, and we need to ensure that each clause is true.\n", "> \n", "> To ensure that every variable is true or false, we can do this:\n", ">\n", "> ![image.png](attachment:image.png)\n", "\n", "For each variable$x_i$, we will add two numbers,$p_i$and$q_i$, to$S$, corresponding to$x_i$and$\\neg x_i$.\n", "\n", "The first$l$digits of each number are used to ensure that$p_i$and$q_i$are not both included in$C$. Let the$i$'th digit of$p_i$and$q_i$be 1; let the rest of the first$l$digits be 0. Let the first$l$digits of$t$be 1's." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "> To ensure that every clause is true, we can add a new digit for each clause, like this:\n", "> \n", "> ![image.png](attachment:image.png)\n", "\n", "The next$m$digits (that is, digits$l+1$through$l+m$) are used to ensure that all clauses are true. Let the$(l+j)$th digit of$p_i$be the number of times that$x_i$occurs in the$j$th clause, and let the$(l+j)$th digit of$q_i$be the number of times that$\\neg x_i$occurs in the$j\$th clause." ] }, { "attachments": { "image.png": { "image/png": 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