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[(pa)25.1(t)13.5(h)16.3(w)12.4(a)14.5(y.)-240.1(W)13.8(e)-252.9(t)13.5(h)16.3(e)14.5(n)-251.2(s)15.1(h)0(o)26.9(w)-249.4(ho)26.9(w)-255.1(t)19.2(he)-242.3(C)17.3(a)0(y)25.1(l)13.5(e)14.5(y)-251.2(g)16.3(r)14.3(ap)25.1(h)-251.2(a)14.5(d)16.3(d)0(i)24.2(t)13.5(i)19.2(o)0(n)26.9(a)0(l)28.1(l)13.5(y)-251.2(p)0(r)24.9(o)16.3(v)16.3(i)13.5(de)25.1(s)-252.3(a)-247.2(na)25.1(t)13.5(u)16.3(r)14.3(a)14.5(l)-253.9(h)16.3(a)14.5(n)0(d)26.9(l)13.5(e)-252.9(f)14.3(o)16.3(r)-253.1(t)13.5(h)16.3(e)-252.9(a)14.5(n)16.3(a)0(l)28.1(y)0(s)25.7(i)13.5(s)-252.3(o)16.3(f)-247.4(c)0(y)25.1(c)14.5(l)13.5(i)13.5(c)]TJ
T*
-.0142 Tc
[(c)-14.2(h)10.9(emica)-14.2(l)-321.9(sy)-14.2(s)11.5(t)-.7(ems)-334.8(s).9(uch)-333.6(a)-14.2(s)-320.3(t)-.7(h)-14.2(e)-319.1(trica)-14.2(r)9(box)-14.2(y)12.7(lic)-335.4(acid)-333.6(\().1(TCA\))-335.6(cy)-14.2(c)10.9(l)-.7(e)-329.7(\().1(Ha)-14.2(r)9(v)2.1(ey)-333.6(an)-14.2(d)-323(F)2.9(e)-14.2(r)9(rier,)-333.3(2)2.1(0)-14.2(1)12.7(0\).)]TJ
/F2 1 Tf
10.959 0 0 10.959 237.8834 404.6739 Tm
0 Tc
[(2.)-501.9(PRELIMINAR)6.4(IES)]TJ
/F5 1 Tf
-14.9453 -1.6399 TD
[(2.1.)-502(Graphs)]TJ
/F1 1 Tf
9.9626 0 0 9.9626 84.0755 368.7873 Tm
[(In)-299.4(this)-294.3(cont)-7.6(ribution,)-301.3(we)-297.5(consider)-305.8(directed)-303.5(as)-294.7(well)-298.8(as)-300.4(undirected)-305(connec)-9.9(ted)-297.1(graphs)]TJ
/F5 1 Tf
33.2044 0 TD
(G)Tj
/F6 1 Tf
.8877 0 TD
(=)Tj
/F1 1 Tf
.717 0 TD
(\()Tj
/F5 1 Tf
.3357 0 TD
(V)Tj
/F1 1 Tf
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()Tj
/F5 1 Tf
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(E)Tj
/F1 1 Tf
.6317 0 TD
[(\))-298.6(with)-297(vertex)]TJ
-37.9787 -1.2007 TD
(set)Tj
/F5 1 Tf
1.4226 0 TD
(V)Tj
/F1 1 Tf
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(\()Tj
/F5 1 Tf
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(G)Tj
/F1 1 Tf
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(\))Tj
/F6 1 Tf
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(=)Tj
/F5 1 Tf
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(V)Tj
/F1 1 Tf
.9219 0 TD
[(and)-305.7(edge)-313.9(set)]TJ
/F5 1 Tf
5.3776 0 TD
(E)Tj
/F1 1 Tf
.6203 0 TD
(\()Tj
/F5 1 Tf
.3301 0 TD
(G)Tj
/F1 1 Tf
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(\))Tj
/F6 1 Tf
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(=)Tj
/F5 1 Tf
.717 0 TD
(E)Tj
/F1 1 Tf
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[(.)-302(A)-306.3(graph)-309.2(is)-307.1(vertex)-314.5(or)-305.1(edge)-308.2(labe)-9.4(led)-302.7(if)-307.9(its)-310.6(vertices)-310.4(or)-305.1(edges)-315.9(are)-309.4(equipped)]TJ
-14.1239 -1.2007 TD
[(wi)-8.2(th)-237.6(a)-235.9(labeling)-245.6(function)-9.7(,)-233.7(respect)-10.9(ively.)-239.1(If)-238.8(it)-240.4(is)-233.1(b)-6.5(oth)-238.4(vertex)-240.5(and)-243.1(edge)-239.9(labeled)-10.5(,)-233.7(w)0(e)-240.6(simply)-242.4(call)-239.8(the)-240.2(graph)-240.9(labe)-9.4(led.)]TJ
T*
[(We)-341.6(write)]TJ
/F5 1 Tf
4.1313 0 TD
(l)Tj
/F1 1 Tf
.2845 0 TD
(\()Tj
/F5 1 Tf
.3357 0 TD
(x)Tj
/F1 1 Tf
.4439 0 TD
[(\))-338.5(for)-336.3(the)-336.9(vertex)-337.2(labels)-339.2(\()]TJ
/F5 1 Tf
9.6 0 TD
(x)Tj
/F7 1 Tf
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(2)Tj
/F5 1 Tf
1.0983 0 TD
(V)Tj
/F1 1 Tf
.6999 0 TD
(\()Tj
/F5 1 Tf
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(G)Tj
/F1 1 Tf
.717 0 TD
[(\)\))-335.5(and)-334.1(edge)-342.4(labels)-339.2(\()]TJ
/F5 1 Tf
8.0351 0 TD
(x)Tj
/F7 1 Tf
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(2)Tj
/F5 1 Tf
.9389 0 TD
(E)Tj
/F1 1 Tf
.6316 0 TD
(\()Tj
/F5 1 Tf
.3357 0 TD
(G)Tj
/F1 1 Tf
.7227 0 TD
(\)\).)Tj
-28.76 -1.195 TD
[(Given)-365.1(two)-356.1(\(un\))-7(directed)-360.4(graph)-7.6(s)]TJ
/F5 1 Tf
12.9631 0 TD
(G)Tj
/F1 1 Tf
1.0755 0 TD
(and)Tj
/F5 1 Tf
1.8096 0 TD
(G)Tj
/F7 1 Tf
6.9738 0 0 6.9738 249.1086 324.5668 Tm
(0)Tj
/F1 1 Tf
9.9626 0 0 9.9626 255.0613 320.9952 Tm
[(and)-356.9(a)-361.1(bijectio)-9.3(n)]TJ
/F8 1 Tf
6.4929 0 TD
(u)Tj
/F9 1 Tf
1.5023 0 TD
(:)Tj
/F5 1 Tf
1.104 0 TD
(V)Tj
/F1 1 Tf
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(\()Tj
/F5 1 Tf
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(G)Tj
/F1 1 Tf
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(\))Tj
/F7 1 Tf
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(!)Tj
/F5 1 Tf
1.2804 0 TD
(V)Tj
/F1 1 Tf
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(\()Tj
/F5 1 Tf
.33 0 TD
(G)Tj
/F7 1 Tf
6.9738 0 0 6.9738 399.4581 324.5668 Tm
(0)Tj
/F1 1 Tf
9.9626 0 0 9.9626 401.8392 320.9952 Tm
[(\),)-355.9(we)-360.1(say)-358.1(that)]TJ
/F8 1 Tf
6.0263 0 TD
(u)Tj
/F1 1 Tf
1.0243 0 TD
[(is)-352.6(edge-)]TJ
-39.9477 -1.2007 TD
[(pres)-8(erving)-272.9(if)-273.7(\()]TJ
/F5 1 Tf
5.7304 0 TD
(v)Tj
/F1 1 Tf
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()Tj
/F5 1 Tf
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(u)Tj
/F1 1 Tf
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(\))Tj
/F7 1 Tf
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(2)Tj
/F5 1 Tf
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(E)Tj
/F1 1 Tf
.6317 0 TD
(\()Tj
/F5 1 Tf
.3357 0 TD
(G)Tj
/F1 1 Tf
.7227 0 TD
[(\))-270.2(i)0(f)-268(and)-271.5(only)-273.3(if)-273.7(\()]TJ
/F8 1 Tf
6.4815 0 TD
(u)Tj
/F1 1 Tf
.9446 0 TD
(\()Tj
/F5 1 Tf
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(v)Tj
/F1 1 Tf
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(\))Tj
/F8 1 Tf
1.1153 0 TD
(u)Tj
/F1 1 Tf
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(\()Tj
/F5 1 Tf
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(u)Tj
/F1 1 Tf
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(\)\))Tj
/F7 1 Tf
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(2)Tj
/F5 1 Tf
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(E)Tj
/F1 1 Tf
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(\()Tj
/F5 1 Tf
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(G)Tj
/F7 1 Tf
6.9738 0 0 6.9738 324.6235 312.6046 Tm
(0)Tj
/F1 1 Tf
9.9626 0 0 9.9626 327.0046 309.033 Tm
[(\).)-270.6(Additiona)-9.5(lly,)-270(if)]TJ
/F5 1 Tf
7.3408 0 TD
(G)Tj
/F1 1 Tf
.9902 0 TD
(and)Tj
/F5 1 Tf
1.7185 0 TD
(G)Tj
/F7 1 Tf
6.9738 0 0 6.9738 434.3243 312.6046 Tm
(0)Tj
/F1 1 Tf
9.9626 0 0 9.9626 439.3699 309.033 Tm
[(are)-275.3(labeled)-10.5(,)]TJ
/F8 1 Tf
4.9337 0 TD
(u)Tj
/F1 1 Tf
.9389 0 TD
(is)Tj
-42.5369 -1.2007 TD
[(labe)-9.4(l-preservin)-13.2(g)-410.5(i)0(f)]TJ
/F5 1 Tf
7.9838 0 TD
(l)Tj
/F1 1 Tf
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(\()Tj
/F5 1 Tf
.3357 0 TD
(v)Tj
/F1 1 Tf
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(\))Tj
/F6 1 Tf
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(=)Tj
/F5 1 Tf
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(l)Tj
/F1 1 Tf
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(\()Tj
/F8 1 Tf
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(u)Tj
/F1 1 Tf
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(\()Tj
/F5 1 Tf
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(v)Tj
/F1 1 Tf
.4496 0 TD
[(\)\))-415.2(for)-416(any)]TJ
/F5 1 Tf
4.5297 0 TD
(v)Tj
/F7 1 Tf
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(2)Tj
/F5 1 Tf
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(V)Tj
/F1 1 Tf
.6999 0 TD
(\()Tj
/F5 1 Tf
.33 0 TD
(G)Tj
/F1 1 Tf
.7227 0 TD
[(\))-418.2(and)]TJ
/F5 1 Tf
2.612 0 TD
(l)Tj
/F1 1 Tf
.2845 0 TD
(\()Tj
/F5 1 Tf
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(v)Tj
/F1 1 Tf
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()Tj
/F5 1 Tf
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(u)Tj
/F1 1 Tf
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(\))Tj
/F6 1 Tf
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(=)Tj
/F5 1 Tf
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(l)Tj
/F1 1 Tf
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(\()Tj
/F8 1 Tf
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(u)Tj
/F1 1 Tf
.8365 0 TD
(\()Tj
/F5 1 Tf
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(v)Tj
/F1 1 Tf
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(\))Tj
/F8 1 Tf
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(u)Tj
/F1 1 Tf
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(\()Tj
/F5 1 Tf
.33 0 TD
(u)Tj
/F1 1 Tf
.5008 0 TD
[(\)\))-420.9(for)-416(any)-419.5(\()]TJ
/F5 1 Tf
4.8711 0 TD
(v)Tj
/F1 1 Tf
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()Tj
/F5 1 Tf
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(u)Tj
/F1 1 Tf
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(\))Tj
/F7 1 Tf
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(2)Tj
/F5 1 Tf
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(E)Tj
/F1 1 Tf
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(\()Tj
/F5 1 Tf
.3357 0 TD
(G)Tj
/F1 1 Tf
.717 0 TD
[(\).)-418.5(The)]TJ
-40.6362 -1.2007 TD
[(bij)-7.8(ection)]TJ
/F8 1 Tf
3.9037 0 TD
(u)Tj
/F1 1 Tf
1.0357 0 TD
[(is)-375.4(an)-373.2(isomorphi)-7.7(sm)-376.1(if)-370.5(it)-371.2(is)-375.4(edge-pre)-9.7(serving)-377.3(and,)-374.3(in)-374.2(the)-371(case)-379.5(that)]TJ
/F5 1 Tf
26.5862 0 TD
(G)Tj
/F1 1 Tf
1.0926 0 TD
(and)Tj
/F5 1 Tf
1.821 0 TD
(G)Tj
/F7 1 Tf
6.9738 0 0 6.9738 424.403 288.7369 Tm
(0)Tj
/F1 1 Tf
9.9626 0 0 9.9626 430.4692 285.1086 Tm
[(are)-377.7(labeled,)-375.1(labe)-9.4(l-)]TJ
-35.7708 -1.2007 TD
[(pres)-8(erving.)-341.5(If)]TJ
/F5 1 Tf
5.8214 0 TD
(G)Tj
/F6 1 Tf
.8877 0 TD
(=)Tj
/F5 1 Tf
.7227 0 TD
(G)Tj
/F7 1 Tf
6.9738 0 0 6.9738 155.2818 276.7747 Tm
(0)Tj
/F1 1 Tf
9.9626 0 0 9.9626 157.7196 273.1464 Tm
[(,)-330.4(then)]TJ
/F8 1 Tf
2.6461 0 TD
(u)Tj
/F1 1 Tf
1.0015 0 TD
[(is)-335.5(also)-338.8(an)-333.4(automor)-9.7(phism.)]TJ
-11.0397 -1.2007 TD
[(Given)-268.4(a)-264.3(\(di)-7(rected\))-267.8(graph)]TJ
/F5 1 Tf
10.1519 0 TD
(G)Tj
/F1 1 Tf
.7227 0 TD
[(,)-262.1(w)0(e)-269(call)]TJ
/F5 1 Tf
3.6647 0 TD
(G)Tj
/F1 1 Tf
.7227 0 TD
[(\(strong)-7.6(ly\))-263.1(connec)-9.9(ted)-268.6(if)-262.3(there)-268.2(exists)-270.3(a)-264.3(path)-269.4(from)-266.6(any)-265.8(vertex)]TJ
/F5 1 Tf
23.6784 0 TD
(u)Tj
/F1 1 Tf
.7625 0 TD
[(to)-266.1(any)]TJ
-40.7045 -1.2007 TD
[(vert)-9.6(ex)]TJ
/F5 1 Tf
2.9079 0 TD
(v)Tj
/F1 1 Tf
.4496 0 TD
[(.)-393(W)0(e)-398.5(call)-393.4(the)-399.5(subgraph)]TJ
/F5 1 Tf
9.9755 0 TD
(H)Tj
/F1 1 Tf
1.1153 0 TD
(of)Tj
/F5 1 Tf
1.2235 0 TD
(G)Tj
/F1 1 Tf
1.1153 0 TD
[(a)-395.2(\(strongly\))-401.5(connecte)-10.3(d)-393.4(component)-398(if)]TJ
/F5 1 Tf
15.5295 0 TD
(H)Tj
/F1 1 Tf
1.1097 0 TD
[(is)-392.4(a)-395.2(maxim)-9.7(al)-393(\(strong)-7.6(ly\))]TJ
-33.4263 -1.2007 TD
[(connec)-9.9(ted)-336.9(subgr)-7(aph.)]TJ
1.0015 -1.195 TD
[(Since)-322.3(the)-314.1(motiv)-7.2(ation)-318.4(of)-316.5(this)-317.1(work)-316.2(is)-312.8(root)-7.8(ed)-316.3(in)-311.6(chem)-10.2(istry,)-314.5(som)-7(etimes)-320(it)-314.3(is)-318.5(more)-317.6(natural)-318(to)-317.3(talk)-317.7(about)-321.3(the)]TJ
-1.0015 -1.2007 TD
[(un)-7.2(directed)-354.7(labele)-9.8(d)-347.9(graph)-7.6(s)-349.1(a)0(s)-345.9(mol)-8.6(ecules,)-355.7(their)-354.5(vertices)-355.9(as)-351.6(atoms)-354.5(\(with)-351(labe)-9.4(ls)-346.9(deni)-7.6(ng)-348.7(the)-354(atom)-352.6(type\),)-352.2(and)]TJ
T*
[(their)-400.1(edges)-401.2(as)-397.2(bonds)-397.7(\(who)-9(se)-391.5(labe)-9.4(ls)-392.4(disti)-7.6(nguish)-395.5(sing)-7(le,)-393.4(d)-6.5(ouble,)-395.7(tripl)-8.4(e,)-395.6(and)-396.7(aromatic)-403.8(bonds,)-398(for)-398.9(instance\),)]TJ
T*
[(whi)-9(le)-330.4(still)-340.4(using)-337.8(common)-337.8(g)-6.5(raph)-336.9(terminology)-342.6(for)-336.3(mathemat)-12.6(ical)-336.5(precision.)]TJ
/F5 1 Tf
10.959 0 0 10.959 74.0976 165.5433 Tm
[(2.2.)-502(Graph)-330.2(transformatio)8.2(ns)]TJ
/F1 1 Tf
9.9626 0 0 9.9626 84.0755 147.6283 Tm
[(As)-228.6(mo)17.7(le)16.7(cu)13.8(l)13.5(e)0(s)-232.1(a)0(r)17.5(e)-235.9(mo)12(de)19.4(le)16.7(d)-234.1(a)0(s)-232.1(u)0(n)15.5(d)0(i)18.5(r)14.3(ec)12(t)13.5(e)0(d)-230.9(l)0(a)16.7(b)0(e)19.4(l)0(e)16.7(d)-239.8(gr)19.3(ap)13.8(hs)20(,)-233.7(i)0(t)-229(i)0(s)-233.1(n)0(a)19.4(t)0(u)18.5(r)0(a)17.5(l)-236.8(to)-226.2(th)18.5(in)12.8(k)-234.1(o)0(f)-231.1(c)0(h)19.4(e)0(m)15.9(i)0(c)16.7(a)0(l)-228(r)0(e)17.5(a)0(c)17.7(t)0(i)15.7(o)0(n)21.2(s)-241(as)-226.4(gr)13.6(ap)19.4(h)]TJ
-1.0015 -1.2007 TD
[(tr)16.5(an)13.8(sf)18.1(or)19.3(ma)15.9(t)13.5(i)0(o)18.5(n)0(s)14.4(,)-341.8(wh)17.3(er)17.5(e)-349.7(a)-344(se)18.3(t)-345(o)0(f)-333.6(e)0(d)19.4(u)0(c)13.8(t)-345(gr)19.3(ap)19.4(hs)-338.5(ar)17.5(e)-344(t)0(r)16.5(a)0(n)19.4(s)0(f)18.1(o)0(r)19.3(m)0(e)15.9(d)-347.9(i)13.5(n)0(t)18.5(o)-347.9(a)-344(s)0(e)18.3(t)-345(of)-333.6(pr)13.6(od)21.2(uc)13.8(t)-339.3(g)0(r)13.6(a)0(p)19.4(h)0(s)20(.)-347.5(We)-335.9(mo)17.7(de)13.8(l)-339.3(s)0(u)14.4(c)0(h)]TJ
T*
[(tr)16.5(an)13.8(sf)18.1(or)19.3(ma)15.9(t)13.5(i)0(o)18.5(n)0(s)-247.4(u)0(s)20(i)0(n)18.5(g)-251.2(th)18.5(e)-252.9(d)0(o)15.5(u)0(b)21.2(l)0(e)-245.1(p)0(u)21.2(s)0(h)14.3(o)0(u)21.2(t)-253.9(\(D)15.3(P)11.4(O)0(\))-246.4(a)0(p)19.4(p)0(r)19.3(o)0(a)13.8(c)0(h)19.4(.)-250.8(F)11.4(o)0(r)-242.5(a)-252.9(de)13.8(ta)16.7(i)13.5(l)0(e)16.7(d)-251.2(ov)15.5(er)17.5(vi)18.5(ew)-246.3(of)-242.5(t)13.5(h)0(e)-248(D)12.4(PO)-243.7(ap)13.8(pr)19.3(oa)19.4(ch)-248(an)19.4(d)]TJ
T*
[(it)15.7(s)-241(v)0(a)13.8(r)0(i)16.5(a)0(t)22.4(i)0(o)18.5(n)0(s)14.4(,)-245.1(se)18.3(e)-241.6(H)0(a)15.5(b)0(e)13.8(l)-242.5(et)-233.7(al)16.7(.)-245.1(\()14.3(20)15.5(01)15.5(\).)-230.7(He)15.5(re)17.5(,)-245.1(w)0(e)-234.9(w)0(i)14.5(l)13.5(l)-248.2(u)0(s)20(e)-241.6(DP)12.4(O)-243.7(a)0(s)-237.8(d)0(e)19.4()11.4(ne)13.8(d)-239.8(i)0(n)-237.6(t)0(h)18.5(e)-241.6(st)17.3(ud)15.5(y)-245.5(o)0(f)-231.1(A)0(n)17.3(d)0(e)13.8(r)0(s)18.1(e)0(n)-230.9(e)0(t)-239.4(a)0(l)16.7(.)-239.4(\(2)13.6(01)21.2(6\))]TJ
T*
[(th)18.5(at)-319.1(sp)20(ec)17.7(i)13.6(ca)17.7(ll)21.4(y)-325.1(d)0(e)13.8(s)0(c)18.3(r)0(i)16.5(b)0(e)19.4(s)-326.3(ho)21.2(w)-323.4(t)0(o)-317.3(m)0(o)17.7(d)0(e)19.4(l)-327.9(ch)19.4(em)15.9(ic)16.7(al)-313.4(re)17.5(ac)12(t)13.5(i)0(o)18.5(n)0(s)-315.7(a)0(s)-317.5(r)0(u)19.3(l)0(e)16.7(s)-326.3(i)13.5(n)-325.1(a)-326.9(D)0(P)18.1(O)-323.4(fr)17.3(am)15.9(ew)15.5(or)19.3(k.)]TJ
1.0015 -1.2007 TD
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