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[(By)-387.5(defa)-8.6(ult,)-383.8(we)-388.5(assume)-389.6(most)-386.1(genom)-9.1(es)-385.8(are)-383.4(order)-9.6(ed)-384.6(with)-388.1(themselve)-11.1(s,)-383.6(but)-386.3(the)-388.1(challenge)-389.4(of)-384.8(com)-7.6(paring)-386.7(ge-)]TJ
T*
[(no)-7.2(mes)-293.3(with)-297(duplica)-8.7(ted)-297.1(genes)-298.8(comes)-296.6(from)-300.7(nding)-296.8(an)-293.5(order)-9.6(ing)-295.3(between)-301.9(two)-293.5(genom)-9.1(es)-294.7(as)-294.7(different)-300.7(order)-9.6(ings)]TJ
T*
[(change)-317.2(the)-308.4(distanc)-9.9(e.)-310.2(Thus,)-311.7(to)-311.6(compare)-312.1(genom)-9.1(es)-311.8(with)-308.4(duplica)-8.7(ted)-308.4(genes)-8.6(,)-307.7(w)0(e)-308.8(mus)-7(t)-305.1()0(n)-6.4(d)-308.1(an)-304.9(order)-9.6(ing)-306.7(betwee)-10.9(n)]TJ
T*
[(them)-341.2(that)-334.7(minim)-10.7(izes)-334.9(their)-337.5(distanc)-9.9(e.)]TJ
1.0015 -1.2007 TD
[(For)-305.1(most)-306.4(situations,)-307.7(ordered)-308.8(genom)-9.1(es)-300.4(are)-303.7(all)-305.5(that)-306.3(is)-301.4(needed.)-306.2(Howeve)-10.3(r,)-299(o)-6.5(rdered)-302.3(genom)-9.1(es)-300.4(can)-307.5(be)-304.9(difcult)]TJ
-1.0015 -1.2007 TD
[(to)-237.6(use,)-244.6(e.g.,)]TJ
/F7 1 Tf
4.7801 0 TD
(f)Tj
/F6 1 Tf
.5975 .0114 TD
(~)Tj
/F4 1 Tf
-.0967 -.0114 TD
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 131.6976 426.3873 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 126.7086 427.8613 Tm
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 131.6976 426.3873 Tm
(1)Tj
9.9626 0 0 9.9626 135.6661 427.8613 Tm
(,)Tj
/F6 1 Tf
.5178 .2504 TD
(~)Tj
/F4 1 Tf
-.0967 -.2504 TD
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 144.8504 426.3873 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 139.8614 427.8613 Tm
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 144.8504 426.3873 Tm
(1)Tj
/F7 1 Tf
9.9626 0 0 9.9626 148.8188 427.8613 Tm
.2244 Tc
(g\\f)Tj
/F6 1 Tf
2.2022 .0114 TD
0 Tc
(~)Tj
/F4 1 Tf
-.0967 -.0114 TD
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 174.7842 426.3873 Tm
(2)Tj
/F4 1 Tf
9.9626 0 0 9.9626 169.7952 427.8613 Tm
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 174.7842 426.3873 Tm
(2)Tj
9.9626 0 0 9.9626 178.7527 427.8613 Tm
(,)Tj
/F6 1 Tf
.5121 .2504 TD
(~)Tj
/F4 1 Tf
-.091 -.2504 TD
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 187.937 426.3873 Tm
(2)Tj
/F4 1 Tf
9.9626 0 0 9.9626 182.948 427.8613 Tm
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 187.937 426.3873 Tm
(2)Tj
/F7 1 Tf
9.9626 0 0 9.9626 191.9055 427.8613 Tm
.1674 Tc
(g;)Tj
/F1 1 Tf
2.1055 0 TD
0 Tc
[(,)-239.4(and)-237.4(yet,)-240.5(frequent)-10.7(ly,)-238(it)-234.7(is)-238.8(desirab)-9.1(le)-239.4(to)-237.6(perceive)-245.6(them)-238.8(as)-237.8(equal)-10.1(.)-233.7(Since)-242.7(these)]TJ
-13.9305 -1.195 TD
[(probl)-8.5(ems)-253.5(tend)-258(to)-254.7(occur)-259.7(frequent)-10.7(ly)-254.7(in)-254.7(our)-254.6(work,)-254(we)-257.6(introdu)-7.1(ce)-255.5(the)-257.2(conce)-9.2(pt)-249(o)-6.5(f)-253.1(an)]TJ
/F4 1 Tf
31.6964 0 TD
[(unorde)-7.6(red)-255.7(genome)]TJ
/F1 1 Tf
7.8017 0 TD
[(where)-258(no)]TJ
-39.4981 -1.2007 TD
[(eff)-8(ort)-428.1(is)-426.6(mad)-7.6(e)-429.3(t)0(o)-425.4(disti)-7.6(nguish)-429.6(the)-433.6(genes.)-430.1(Let)]TJ
/F8 1 Tf
19.0064 .2333 TD
(~)Tj
/F4 1 Tf
-.2049 -.2333 TD
(G)Tj
0 0 TD
(G)Tj
/F1 1 Tf
1.1438 0 TD
[(be)-430.1(the)-433.6(unordered)-435.5(counterp)-8.7(art)-429.9(of)-430.3(an)-430.1(ordered)-434(genom)-9.1(e)]TJ
/F4 1 Tf
22.2842 0 TD
(G)Tj
/F1 1 Tf
.7227 0 TD
(.)Tj
-42.9523 -1.2007 TD
[(Sim)-7.8(ilarly,)-261.7(if)]TJ
/F9 1 Tf
5.1329 0 TD
(a)Tj
/F1 1 Tf
.7568 0 TD
[(is)-255.9(an)-265.1(element)-264.4(of)]TJ
/F4 1 Tf
6.675 0 TD
(G)Tj
/F1 1 Tf
.7227 0 TD
[(,)-256.5(then)]TJ
/F8 1 Tf
2.4925 .0285 TD
(~)Tj
/F10 1 Tf
0 -.0285 TD
(a)Tj
0 0 TD
(a)Tj
/F1 1 Tf
.7625 0 TD
[(is)-255.9(an)-265.1(element)-264.4(of)]TJ
/F8 1 Tf
6.8799 .2333 TD
(~)Tj
/F4 1 Tf
-.2049 -.2333 TD
(G)Tj
0 0 TD
(G)Tj
/F1 1 Tf
.9788 0 TD
[(and)-260.2(if)]TJ
/F4 1 Tf
2.5778 0 TD
(S)Tj
/F1 1 Tf
.7625 0 TD
[(is)-255.9(a)-258.6(subse)-8(t)-259.6(o)0(f)]TJ
/F4 1 Tf
5.4857 0 TD
(G)Tj
/F1 1 Tf
.9731 0 TD
(then)Tj
/F8 1 Tf
2.0884 .2333 TD
(~)Tj
/F4 1 Tf
-.0967 -.2333 TD
(S)Tj
0 0 TD
(S)Tj
/F1 1 Tf
.7568 0 TD
[(is)-261.6(a)-258.6(subse)-8(t)-259.6(o)0(f)]TJ
/F8 1 Tf
5.6905 .2333 TD
(~)Tj
/F4 1 Tf
-.1992 -.2333 TD
(G)Tj
0 0 TD
(G)Tj
/F1 1 Tf
.717 0 TD
(.)Tj
-42.9523 -1.2007 TD
[(Unor)-9(dered)-316.7(extremiti)-9.9(es)-311.8(are)-315.1(distingui)-7.7(shed)-313.3(from)-317.8(ordered)-314.5(extrem)-10.7(ities)-311(by)-314.5(the)-314.1(absence)-321(or)-310.8(presence)-318(resp)-8(ectively)]TJ
T*
[(of)-327.9(a)-326.9(subscript.)-331.9(Transfor)-9.1(ming)-328(an)-322(order)-9.6(ed)-322(genom)-9.1(e)-326.9(t)0(o)-323(a)0(n)-327.7(unordered)-333.1(genome)-330.3(is)-324.2(trivial)-327.4(but)-329.4(the)-325.5(reverse)-334.5(can)-324.5(be)]TJ
T*
[(very)-342.6(difcult)-336(and)-339.8(is)-335.5(problem)-339.8(specic.)]TJ
1.0015 -1.2007 TD
[(The)-339.6(key)-334.1(conce)-9.2(pt)-334.3(that)-334.7(help)-7.6(s)-332(solv)-7(e)-332.6(the)-336.9(genom)-9.1(e)-332.6(aliquotin)-8.3(g)-336.5(problem)-339.8(is)]TJ
/F4 1 Tf
28.0772 0 TD
[(perfectio)-10.3(n)]TJ
/F1 1 Tf
4.0801 0 TD
(:)Tj
/F2 1 Tf
-32.1573 -2.3957 TD
[(Deni)-10.7(tion)-308.6(1.)]TJ
/F4 1 Tf
6.2881 0 TD
[(We)-313.3(dene)]TJ
/F1 1 Tf
4.3077 0 TD
[(perfectio)-10.3(n)]TJ
/F4 1 Tf
4.3874 0 TD
[(betwe)-9.2(en)-310.6(two)-311.4(ele)-8.6(ments)-315.1(of)-311.6(a)-308.1(genom)-9.5(e)-309.8(t)0(o)-311.6(b)0(e)-310.6(that)-315.9(the)-308.4(two)-317.1(elemen)-10.9(ts)-307.1(are)]TJ
-15.9848 -1.2007 TD
[(the)-257.2(same)-254.7(or)-247.4(are)-255.7(disjoint.)-257.7(For)-248(a)-6.5(djacencies)-260.5(we)-252.7(also)-251.7(have)-251.3(the)-257.2(special)-254.6(requirem)-13.1(ent)-251.5(that)-253.3(they)-254.1(are)-250(not)-255.4(of)-249(the)-251.5(form)]TJ
/F1 1 Tf
T*
({)Tj
/F4 1 Tf
.4837 0 TD
[(x,)-259(x)]TJ
/F1 1 Tf
1.4056 0 TD
(})Tj
/F4 1 Tf
.7398 0 TD
[(for)-262.3(some)-260.3(ext)-8.6(remity)-263.5(x.)-264.7(Since)-260.5(ther)-8.8(e)-258.6(are)-261.3(two)-265.8(types)-261.7(of)-260.4(eleme)-10.2(nts,)-262.7(adjacencies)-272.6(and)-258.4(telom)-9.4(eres,)-265.5(two)-260.2(eleme)-10.2(nts)]TJ
/F9 1 Tf
-2.629 -1.2007 TD
(a)Tj
/F4 1 Tf
.8365 0 TD
(and)Tj
/F9 1 Tf
1.838 0 TD
(b)Tj
/F4 1 Tf
.882 0 TD
[(can)-339.8(be)-333.4(in)-334.3(one)-339.8(of)-334.3(the)-336.9(following)-341.3(three)-335.7(congu)-12.1(rations:)]TJ
/F7 1 Tf
6.9738 0 0 6.9738 84.0755 267.8739 Tm
()Tj
/F4 1 Tf
9.9626 0 0 9.9626 92.5795 266.5133 Tm
(let)Tj
/F9 1 Tf
1.3145 0 TD
(a)Tj
/F4 1 Tf
.8081 0 TD
(and)Tj
/F9 1 Tf
1.8096 0 TD
(b)Tj
/F4 1 Tf
.8593 0 TD
[(be)-304.9(a)-308.1(pair)-308.6(of)-305.9(adjac)-8.4(encies.)-315.9(They)-307.4(are)]TJ
/F1 1 Tf
14.3288 0 TD
(perfect)Tj
/F4 1 Tf
3.1014 0 TD
[(if)-308.7(and)-303.9(only)-309.2(if)-308.7(they)-311(are)-312.6(disjoint)-308.6(or)-310(the)-308.4(same)-311.6(and)]TJ
-22.2216 -1.2007 TD
[(neither)-340(are)-335.3(of)-334.3(the)-336.9(form)]TJ
/F1 1 Tf
9.7536 0 TD
({)Tj
/F4 1 Tf
.478 0 TD
[(x,)-338.7(x)]TJ
/F1 1 Tf
1.4795 0 TD
(})Tj
/F4 1 Tf
.8137 0 TD
[(for)-336.3(som)-7.4(e)-332.6(extrem)-12.1(ity)-334(x;)]TJ
/F7 1 Tf
6.9738 0 0 6.9738 84.0755 243.9495 Tm
()Tj
/F4 1 Tf
9.9626 0 0 9.9626 92.5795 242.5889 Tm
(let)Tj
/F9 1 Tf
1.3999 0 TD
(a)Tj
/F4 1 Tf
.8934 0 TD
(and)Tj
/F9 1 Tf
1.8893 0 TD
(b)Tj
/F4 1 Tf
.9446 0 TD
[(be)-390.3(a)-393.4(pair)-394(of)-391.2(telomere)-10.7(s.)-389.3(Sinc)-7.6(e)-389.5(all)-394.8(telomere)-10.7(s)-388.9(are)-392.2(either)-396.1(the)-393.8(sam)-7.4(e)-389.5(o)0(r)-389.7(d)-6.5(isjoint)-393.2(all)-394.8(pairs)-390.2(of)]TJ
-5.1272 -1.2007 TD
[(telomere)-10.7(s)-332(are)]TJ
/F1 1 Tf
5.9068 0 TD
(perfect)Tj
/F4 1 Tf
2.7941 0 TD
(;)Tj
/F7 1 Tf
6.9738 0 0 6.9738 84.0755 220.0818 Tm
()Tj
/F4 1 Tf
9.9626 0 0 9.9626 92.5795 218.6645 Tm
(let)Tj
/F9 1 Tf
1.2633 0 TD
(a)Tj
/F4 1 Tf
.7512 0 TD
[(be)-253.7(an)-251.9(adjac)-8.4(ency)-253.1(and)]TJ
/F9 1 Tf
8.5358 0 TD
(b)Tj
/F4 1 Tf
.8081 0 TD
[(be)-253.7(a)-251.2(telomere)-10.7(,)-250.8(since)-256(they)-259.8(cannot)-253.8(be)-253.7(the)-257.2(same)-254.7(they)-259.8(must)-255.6(be)-253.7(disjoint)-257.3(in)-249(order)]TJ
-11.3583 -1.2007 TD
[(to)-334.3(be)]TJ
/F1 1 Tf
2.3957 0 TD
[(perf)-8.8(ect)]TJ
/F4 1 Tf
2.7998 0 TD
[(.)-330.4(Also,)]TJ
/F9 1 Tf
2.9534 0 TD
(a)Tj
/F4 1 Tf
.8308 0 TD
[(mus)-7.4(t)-333.6(not)-335.1(be)-333.4(of)-334.3(the)-336.9(form)]TJ
/F1 1 Tf
10.0267 0 TD
({)Tj
/F4 1 Tf
.478 0 TD
[(x,)-333(x)]TJ
/F1 1 Tf
1.4795 0 TD
(})Tj
/F4 1 Tf
.8137 0 TD
[(for)-336.3(some)-340(extremity)-346.1(x;)]TJ
-23.6329 -2.0372 TD
[(A)-251(genom)-9.5(e,)-247.6(or)-247.4(any)-248.8(set)-252.7(of)-249(adjac)-8.4(encies)-252.9(and)-247(telom)-9.4(eres,)-254.1(is)]TJ
/F1 1 Tf
21.772 0 TD
(perfect)Tj
/F4 1 Tf
3.0388 0 TD
[(if)-251.8(and)-247(on)-7.2(ly)-245.1(if)-251.7(all)-246.8(pair)-7(s)-246.7(o)0(f)-249(eleme)-10.2(nts)-245.2(are)-250(p)-6.5(erfect.)]TJ
/F1 1 Tf
-23.8093 -1.3999 TD
[(For)-441.7(exampl)-8.7(e,)-441.1(given)-440.8(a)-440.7(genome)]TJ
/F4 1 Tf
13.1053 0 TD
(G)Tj
/F7 1 Tf
.8877 0 TD
.1689 Tc
[(f)168.9(f)]TJ
/F6 1 Tf
2.0315 .0057 TD
0 Tc
(~)Tj
/F4 1 Tf
-.091 -.0057 TD
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 247.8047 170.9291 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 242.8157 172.4598 Tm
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 247.8047 170.9291 Tm
(1)Tj
/F7 1 Tf
9.9626 0 0 9.9626 251.7731 172.4598 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F4 1 Tf
.5008 0 TD
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 270.8787 170.9291 Tm
(1)Tj
/F7 1 Tf
-.4552 1.0324 TD
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 274.9039 172.4598 Tm
(,)Tj
/F4 1 Tf
.4154 0 TD
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 284.0314 170.9291 Tm
(1)Tj
/F7 1 Tf
-.4552 1.3739 TD
()Tj
9.9626 0 0 9.9626 288.0566 172.4598 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F6 1 Tf
.5975 .2447 TD
(~)Tj
/F4 1 Tf
-.0967 -.2447 TD
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 307.1621 170.9291 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 302.1732 172.4598 Tm
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 307.1621 170.9291 Tm
(1)Tj
9.9626 0 0 9.9626 311.1306 172.4598 Tm
(,)Tj
/F4 1 Tf
.4211 0 TD
(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 320.3148 170.9291 Tm
(1)Tj
/F7 1 Tf
-.4634 1.3739 TD
()Tj
9.9626 0 0 9.9626 324.2834 172.4598 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4211 0 TD
(f)Tj
/F6 1 Tf
.5918 .2447 TD
(~)Tj
/F4 1 Tf
-.0911 -.2447 TD
(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 343.4456 170.9291 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 338.4566 172.4598 Tm
(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 343.4456 170.9291 Tm
(1)Tj
9.9626 0 0 9.9626 347.4141 172.4598 Tm
(,)Tj
/F4 1 Tf
.4154 0 TD
(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 356.0314 170.9291 Tm
(1)Tj
/F7 1 Tf
-.4227 1.0324 TD
()Tj
9.9626 0 0 9.9626 360.0566 172.4598 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F6 1 Tf
.569 .0057 TD
(~)Tj
/F4 1 Tf
-.0683 -.0057 TD
(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 378.6519 170.9291 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 374.1731 172.4598 Tm
(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 378.6519 170.9291 Tm
(1)Tj
9.9626 0 0 9.9626 382.6204 172.4598 Tm
(,)Tj
/F4 1 Tf
.4211 0 TD
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 391.8046 170.9291 Tm
(2)Tj
/F7 1 Tf
-.4634 1.3739 TD
()Tj
9.9626 0 0 9.9626 395.7731 172.4598 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F6 1 Tf
.5975 .2447 TD
(~)Tj
/F4 1 Tf
-.0967 -.2447 TD
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 414.8786 170.9291 Tm
(2)Tj
/F4 1 Tf
9.9626 0 0 9.9626 409.8896 172.4598 Tm
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 414.8786 170.9291 Tm
(2)Tj
/F7 1 Tf
9.9626 0 0 9.9626 418.9038 172.4598 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F6 1 Tf
.5975 .0057 TD
(~)Tj
/F4 1 Tf
-.0967 -.0057 TD
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 438.0093 170.9291 Tm
(2)Tj
/F4 1 Tf
9.9626 0 0 9.9626 433.0204 172.4598 Tm
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 438.0093 170.9291 Tm
(2)Tj
/F7 1 Tf
9.9626 0 0 9.9626 442.0345 172.4598 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F4 1 Tf
.5008 0 TD
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 461.14 170.9291 Tm
(2)Tj
/F7 1 Tf
-.4552 1.0324 TD
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 465.1085 172.4598 Tm
(,)Tj
/F6 1 Tf
.4894 .0057 TD
(~)Tj
/F4 1 Tf
-.0683 -.0057 TD
(c)Tj
/F1 1 Tf
6.9738 0 0 6.9738 473.7825 170.9291 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 469.3038 172.4598 Tm
(c)Tj
/F1 1 Tf
6.9738 0 0 6.9738 473.7825 170.9291 Tm
(1)Tj
/F7 1 Tf
9.9626 0 0 9.9626 477.7511 172.4598 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F4 1 Tf
.5008 0 TD
(c)Tj
/F1 1 Tf
6.9738 0 0 6.9738 496.3463 170.9291 Tm
(1)Tj
/F7 1 Tf
-.4146 1.0324 TD
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 500.3715 172.4598 Tm
(,)Tj
/F4 1 Tf
-42.7872 -1.7356 TD
(c)Tj
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6.9738 0 0 6.9738 434.381 676.1195 Tm
(2)Tj
/F7 1 Tf
-.4552 1.0324 TD
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 438.4062 677.6502 Tm
(,)Tj
/F4 1 Tf
.4154 0 TD
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 447.5338 676.1195 Tm
(2)Tj
/F7 1 Tf
-.4553 1.3739 TD
()Tj
9.9626 0 0 9.9626 451.5589 677.6502 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F6 1 Tf
.5975 .0057 TD
(~)Tj
/F4 1 Tf
-.0967 -.0057 TD
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 470.6644 676.1195 Tm
(2)Tj
/F4 1 Tf
9.9626 0 0 9.9626 465.6755 677.6502 Tm
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 470.6644 676.1195 Tm
(2)Tj
/F7 1 Tf
9.9626 0 0 9.9626 474.6329 677.6502 Tm
(gf)Tj
/F6 1 Tf
1.0755 .0057 TD
(~)Tj
/F4 1 Tf
-.074 -.0057 TD
(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 489.0896 676.1195 Tm
(2)Tj
/F4 1 Tf
9.9626 0 0 9.9626 484.6109 677.6502 Tm
(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 489.0896 676.1195 Tm
(2)Tj
/F7 1 Tf
9.9626 0 0 9.9626 493.1148 677.6502 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F4 1 Tf
.5008 0 TD
(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 512.2203 676.1195 Tm
(2)Tj
/F7 1 Tf
-.4552 1.3739 TD
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 516.2455 677.6502 Tm
(,)Tj
/F4 1 Tf
.4154 0 TD
(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 524.8629 676.1195 Tm
(2)Tj
/F7 1 Tf
-.4227 1.0324 TD
()Tj
9.9626 0 0 9.9626 528.8314 677.6502 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
-42.7815 -1.7356 TD
(f)Tj
/F6 1 Tf
.5691 .0057 TD
(~)Tj
/F4 1 Tf
-.0683 -.0057 TD
(c)Tj
/F1 1 Tf
6.9738 0 0 6.9738 117.0708 658.8849 Tm
(2)Tj
/F4 1 Tf
9.9626 0 0 9.9626 112.5921 660.3589 Tm
(c)Tj
/F1 1 Tf
6.9738 0 0 6.9738 117.0708 658.8849 Tm
(2)Tj
9.9626 0 0 9.9626 121.0393 660.3589 Tm
(,)Tj
/F6 1 Tf
.5122 .2504 TD
(~)Tj
/F4 1 Tf
-.0967 -.2504 TD
(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 130.2236 658.8849 Tm
(2)Tj
/F4 1 Tf
9.9626 0 0 9.9626 125.1779 660.3589 Tm
(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 130.2236 658.8849 Tm
(2)Tj
/F7 1 Tf
9.9626 0 0 9.9626 134.1921 660.3589 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F4 1 Tf
.5008 0 TD
(c)Tj
/F1 1 Tf
6.9738 0 0 6.9738 152.7874 658.8849 Tm
(2)Tj
/F7 1 Tf
-.4227 1.0324 TD
()Tj
9.9626 0 0 9.9626 156.8125 660.3589 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.7967 0 TD
(f)Tj
/F6 1 Tf
.5747 .0057 TD
(~)Tj
/F4 1 Tf
-.074 -.0057 TD
(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 179.2062 658.8849 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 174.7275 660.3589 Tm
(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 179.2062 658.8849 Tm
(1)Tj
/F7 1 Tf
9.9626 0 0 9.9626 183.2314 660.3589 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F4 1 Tf
.5008 0 TD
(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 202.3369 658.8849 Tm
(1)Tj
/F7 1 Tf
-.4552 1.3739 TD
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 206.3055 660.3589 Tm
(,)Tj
/F4 1 Tf
.4211 0 TD
(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 214.9795 658.8849 Tm
(1)Tj
/F7 1 Tf
-.4227 1.0324 TD
()Tj
9.9626 0 0 9.9626 218.948 660.3589 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F6 1 Tf
.5747 .0057 TD
(~)Tj
/F4 1 Tf
-.074 -.0057 TD
(c)Tj
/F1 1 Tf
6.9738 0 0 6.9738 237.5432 658.8849 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 233.0645 660.3589 Tm
(c)Tj
/F1 1 Tf
6.9738 0 0 6.9738 237.5432 658.8849 Tm
(1)Tj
9.9626 0 0 9.9626 241.5684 660.3589 Tm
(,)Tj
/F6 1 Tf
.5121 .2504 TD
(~)Tj
/F4 1 Tf
-.0967 -.2504 TD
(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 250.696 658.8849 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 245.707 660.3589 Tm
(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 250.696 658.8849 Tm
(1)Tj
/F7 1 Tf
9.9626 0 0 9.9626 254.6645 660.3589 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4211 0 TD
(f)Tj
/F6 1 Tf
.5691 .0057 TD
(~)Tj
/F4 1 Tf
-.0683 -.0057 TD
(c)Tj
/F1 1 Tf
6.9738 0 0 6.9738 273.3165 658.8849 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 268.8377 660.3589 Tm
(c)Tj
/F1 1 Tf
6.9738 0 0 6.9738 273.3165 658.8849 Tm
(1)Tj
/F7 1 Tf
9.9626 0 0 9.9626 277.285 660.3589 Tm
(gg)Tj
/F1 1 Tf
1.3885 0 TD
[(is)-381.1(a)-389.5(polyploid)-390.7(becau)-9.2(se)-385.8(its)-384.6(correspo)-9.1(nding)-387.8(unorde)-8.3(red)-387.3(genom)-9.1(e)]TJ
/F8 1 Tf
-18.2155 -1.4966 TD
(~)Tj
/F4 1 Tf
-.2049 -.2333 TD
(G)Tj
0 0 TD
(G)Tj
/F7 1 Tf
.8877 0 TD
.1689 Tc
(f)Tj
/F6 1 Tf
1.3828 .0057 TD
0 Tc
(~)Tj
/F4 1 Tf
.0569 -.0057 TD
(a)Tj
0 0 TD
(a)Tj
/F7 1 Tf
.5008 0 TD
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F4 1 Tf
.5235 0 TD
(a)Tj
/F7 1 Tf
6.9738 0 0 6.9738 149.896 648.7935 Tm
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 155.2818 643.1243 Tm
(,)Tj
/F4 1 Tf
.4382 0 TD
(b)Tj
/F7 1 Tf
6.9738 0 0 6.9738 159.4204 651.1746 Tm
()Tj
9.9626 0 0 9.9626 164.8062 643.1243 Tm
(g)Tj
/F1 1 Tf
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(,)Tj
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(f)Tj
/F6 1 Tf
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(~)Tj
/F4 1 Tf
.0114 -.2447 TD
(b)Tj
0 0 TD
(b)Tj
/F7 1 Tf
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(g)Tj
/F1 1 Tf
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(,)Tj
/F7 1 Tf
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(f)Tj
/F6 1 Tf
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(~)Tj
/F4 1 Tf
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(b)Tj
0 0 TD
(b)Tj
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(g)Tj
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(,)Tj
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(f)Tj
/F4 1 Tf
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(a)Tj
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6.9738 0 0 6.9738 220.2519 648.7935 Tm
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 225.6377 643.1243 Tm
(,)Tj
/F4 1 Tf
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(b)Tj
/F7 1 Tf
6.9738 0 0 6.9738 229.833 651.1746 Tm
()Tj
9.9626 0 0 9.9626 235.2188 643.1243 Tm
(g)Tj
/F1 1 Tf
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(,)Tj
/F7 1 Tf
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(f)Tj
/F6 1 Tf
.4439 .0057 TD
(~)Tj
/F4 1 Tf
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(a)Tj
0 0 TD
(a)Tj
/F7 1 Tf
.5008 0 TD
(gf)Tj
/F6 1 Tf
.9162 .0057 TD
(~)Tj
/F4 1 Tf
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(e)Tj
0 0 TD
(e)Tj
/F7 1 Tf
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(g)Tj
/F1 1 Tf
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(,)Tj
/F7 1 Tf
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(f)Tj
/F4 1 Tf
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(d)Tj
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6.9738 0 0 6.9738 282.8976 651.1746 Tm
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 288.2834 643.1243 Tm
(,)Tj
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(e)Tj
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6.9738 0 0 6.9738 292.4786 648.7935 Tm
()Tj
9.9626 0 0 9.9626 297.8645 643.1243 Tm
(g)Tj
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(,)Tj
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(f)Tj
/F6 1 Tf
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(~)Tj
/F4 1 Tf
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(c)Tj
0 0 TD
(c)Tj
/F1 1 Tf
.4496 0 TD
(,)Tj
/F6 1 Tf
.4268 .2447 TD
(~)Tj
/F4 1 Tf
-.0114 -.2447 TD
(d)Tj
0 0 TD
(d)Tj
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(g)Tj
/F1 1 Tf
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(,)Tj
/F7 1 Tf
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(f)Tj
/F4 1 Tf
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(c)Tj
/F7 1 Tf
6.9738 0 0 6.9738 340.044 648.7935 Tm
()Tj
9.9626 0 0 9.9626 345.4298 643.1243 Tm
(g)Tj
/F1 1 Tf
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(,)Tj
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(f)Tj
/F6 1 Tf
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(~)Tj
/F4 1 Tf
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(e)Tj
0 0 TD
(e)Tj
/F7 1 Tf
.4496 0 TD
(g)Tj
/F1 1 Tf
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(,)Tj
/F7 1 Tf
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(f)Tj
/F4 1 Tf
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(d)Tj
/F7 1 Tf
6.9738 0 0 6.9738 378.1983 651.1746 Tm
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 383.5841 643.1243 Tm
(,)Tj
/F4 1 Tf
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(e)Tj
/F7 1 Tf
6.9738 0 0 6.9738 387.7227 648.7935 Tm
()Tj
9.9626 0 0 9.9626 393.1086 643.1243 Tm
(g)Tj
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(,)Tj
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(f)Tj
/F6 1 Tf
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(~)Tj
/F4 1 Tf
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(c)Tj
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(c)Tj
/F1 1 Tf
.4496 0 TD
(,)Tj
/F6 1 Tf
.4268 .2447 TD
(~)Tj
/F4 1 Tf
-.0114 -.2447 TD
(d)Tj
0 0 TD
(d)Tj
/F7 1 Tf
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(g)Tj
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(,)Tj
/F7 1 Tf
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(f)Tj
/F6 1 Tf
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(~)Tj
/F4 1 Tf
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(c)Tj
0 0 TD
(c)Tj
/F7 1 Tf
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(g)Tj
/F1 1 Tf
.8081 0 TD
[(is)-307.1(perfect)-313.3(and)-311.4(all)-311.2(gene)]TJ
-34.149 -1.2007 TD
[(famili)-8.8(es)-334.6(are)-337.9(of)-333.6(the)-336.9(same)-341.4(size)-334.9(\(there)-339.2(are)-337.9(two)-339(genes)-338.6(in)-334.3(each)-338.5(family)-11.7(\).)]TJ
1.0015 -1.2007 TD
[(Our)-332.6(probl)-8.6(em)-336.9(is)-335.5(as)-334.6(follows:)]TJ
/F2 1 Tf
0 -2.3957 TD
[(Denition)-433.1(2.)]TJ
/F4 1 Tf
6.4019 0 TD
[(Given)-435.2(an)-428.3(order)-8(ed)-424.4(g)-6.5(enome)-432.4(G)-425.8(with)-428.7(a)-6.5(l)0(l)-422.5(gene)-433.4(famili)-8.2(es)-425.6(of)-431.1(size)-431.1(p,)-427.9(the)]TJ
/F1 1 Tf
28.1056 0 TD
[(genome)-432.8(aliquot)-9.7(ing)]TJ
-35.509 -1.2007 TD
(problem)Tj
/F4 1 Tf
3.7273 0 TD
[(is)-381.1(to)-379.9(nd)-377.9(a)-382(polyploid)-386.8(H)-380.3(with)-377.5(all)-383.4(gene)-382.2(famili)-8.2(es)-380.1(of)-379.9(size)-379.9(p)-382(ordered)-386.9(in)-379.9(relation)-381.6(to)-379.9(G)-380.3(such)-381.6(that)-384.2(the)]TJ
-3.7273 -1.2007 TD
[(distanc)-8.1(e)-332.6(betwe)-9.2(en)-333.4(G)-334.8(and)-338(H)-334.8(i)0(s)-335.5(minimal)-10.1(.)]TJ
/F2 1 Tf
10.959 0 0 10.959 249.222 527.981 Tm
[(3.)-496.7(BREAKPOINT)-327.8(DISTANCE)]TJ
/F1 1 Tf
9.9626 0 0 9.9626 117.5811 504.1133 Tm
(A)Tj
/F4 1 Tf
.9902 0 TD
[(breakpoin)-8.7(t)]TJ
/F1 1 Tf
4.6207 0 TD
(\()Tj
/F4 1 Tf
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(BP)Tj
/F1 1 Tf
1.2292 0 TD
[(\))-270.2(i)0(s)-272.9(a)-270(dif)-7(ference)-278.2(in)-271.7(adjacenc)-12.1(ies)-269.8(or)-276.6(telomere)-11.1(s)-269.4(betwee)-10.9(n)-268.2(two)-276.4(genomes,)-275.8(e.g.,)-277.6(in)]TJ
/F4 1 Tf
30.3762 0 TD
(G)Tj
/F7 1 Tf
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.1689 Tc
[(f)168.9(f)]TJ
/F6 1 Tf
2.0315 .0057 TD
0 Tc
(~)Tj
/F4 1 Tf
-.091 -.0057 TD
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 524.8629 502.5826 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 519.8739 504.1133 Tm
(a)Tj
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6.9738 0 0 6.9738 524.8629 502.5826 Tm
(1)Tj
/F7 1 Tf
9.9626 0 0 9.9626 528.8314 504.1133 Tm
(g)Tj
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(,)Tj
/F7 1 Tf
-42.7815 -1.7356 TD
(f)Tj
/F4 1 Tf
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(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 117.5811 485.3479 Tm
(1)Tj
/F7 1 Tf
-.4553 1.0324 TD
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 121.5496 486.8219 Tm
(,)Tj
/F4 1 Tf
.4211 0 TD
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 130.7338 485.3479 Tm
(1)Tj
/F7 1 Tf
-.4634 1.3739 TD
()Tj
9.9626 0 0 9.9626 134.7023 486.8219 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F6 1 Tf
.5975 .2504 TD
(~)Tj
/F4 1 Tf
-.0967 -.2504 TD
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 153.8645 485.3479 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 148.8188 486.8219 Tm
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 153.8645 485.3479 Tm
(1)Tj
9.9626 0 0 9.9626 157.833 486.8219 Tm
(,)Tj
/F4 1 Tf
.4154 0 TD
(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 166.9606 485.3479 Tm
(1)Tj
/F7 1 Tf
-.4552 1.3739 TD
()Tj
9.9626 0 0 9.9626 170.9858 486.8219 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F6 1 Tf
.5975 .2504 TD
(~)Tj
/F4 1 Tf
-.0967 -.2504 TD
(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 190.0913 485.3479 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 185.1023 486.8219 Tm
(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 190.0913 485.3479 Tm
(1)Tj
9.9626 0 0 9.9626 194.0598 486.8219 Tm
(,)Tj
/F4 1 Tf
.4211 0 TD
(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 202.7338 485.3479 Tm
(1)Tj
/F7 1 Tf
-.4227 1.0324 TD
()Tj
9.9626 0 0 9.9626 206.7023 486.8219 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F6 1 Tf
.5747 .0057 TD
(~)Tj
/F4 1 Tf
-.074 -.0057 TD
(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 225.2976 485.3479 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 220.8188 486.8219 Tm
(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 225.2976 485.3479 Tm
(1)Tj
9.9626 0 0 9.9626 229.3228 486.8219 Tm
(,)Tj
/F4 1 Tf
.4154 0 TD
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 238.4503 485.3479 Tm
(2)Tj
/F7 1 Tf
-.4552 1.3739 TD
()Tj
9.9626 0 0 9.9626 242.4188 486.8219 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4211 0 TD
(f)Tj
/F6 1 Tf
.5975 .2504 TD
(~)Tj
/F4 1 Tf
-.0967 -.2504 TD
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 261.581 485.3479 Tm
(2)Tj
/F4 1 Tf
9.9626 0 0 9.9626 256.592 486.8219 Tm
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 261.581 485.3479 Tm
(2)Tj
/F7 1 Tf
9.9626 0 0 9.9626 265.5495 486.8219 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4211 0 TD
(f)Tj
/F6 1 Tf
.5918 .0057 TD
(~)Tj
/F4 1 Tf
-.0911 -.0057 TD
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 284.7117 485.3479 Tm
(2)Tj
/F4 1 Tf
9.9626 0 0 9.9626 279.7227 486.8219 Tm
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 284.7117 485.3479 Tm
(2)Tj
/F7 1 Tf
9.9626 0 0 9.9626 288.6802 486.8219 Tm
(g)Tj
/F1 1 Tf
.5008 0 TD
(,)Tj
/F7 1 Tf
.4154 0 TD
(f)Tj
/F4 1 Tf
.5008 0 TD
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 307.7857 485.3479 Tm
(2)Tj
/F7 1 Tf
-.4552 1.0324 TD
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 311.8109 486.8219 Tm
(,)Tj
/F6 1 Tf
.4837 .0057 TD
(~)Tj
/F4 1 Tf
-.0683 -.0057 TD
(c)Tj
/F1 1 Tf
6.9738 0 0 6.9738 320.4283 485.3479 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 315.9495 486.8219 Tm
(c)Tj
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6.9738 0 0 6.9738 320.4283 485.3479 Tm
(1)Tj
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(g)Tj
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(,)Tj
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(f)Tj
/F4 1 Tf
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(c)Tj
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6.9738 0 0 6.9738 343.0487 485.3479 Tm
(1)Tj
/F7 1 Tf
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()Tj
/F1 1 Tf
9.9626 0 0 9.9626 347.0172 486.8219 Tm
(,)Tj
/F4 1 Tf
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(c)Tj
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6.9738 0 0 6.9738 355.6345 485.3479 Tm
(2)Tj
/F7 1 Tf
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()Tj
9.9626 0 0 9.9626 359.6598 486.8219 Tm
(g)Tj
/F1 1 Tf
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(,)Tj
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(f)Tj
/F6 1 Tf
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(~)Tj
/F4 1 Tf
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(c)Tj
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6.9738 0 0 6.9738 378.255 485.3479 Tm
(2)Tj
/F4 1 Tf
9.9626 0 0 9.9626 373.7763 486.8219 Tm
(c)Tj
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6.9738 0 0 6.9738 378.255 485.3479 Tm
(2)Tj
9.9626 0 0 9.9626 382.2235 486.8219 Tm
(,)Tj
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(~)Tj
/F4 1 Tf
-.091 -.2504 TD
(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 391.4078 485.3479 Tm
(2)Tj
/F4 1 Tf
9.9626 0 0 9.9626 386.4188 486.8219 Tm
(d)Tj
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6.9738 0 0 6.9738 391.4078 485.3479 Tm
(2)Tj
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9.9626 0 0 9.9626 395.3763 486.8219 Tm
(g)Tj
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(,)Tj
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(f)Tj
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(d)Tj
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6.9738 0 0 6.9738 414.4818 485.3479 Tm
(2)Tj
/F7 1 Tf
-.4552 1.3739 TD
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 418.507 486.8219 Tm
(,)Tj
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(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 427.1243 485.3479 Tm
(2)Tj
/F7 1 Tf
-.4227 1.0324 TD
()Tj
9.9626 0 0 9.9626 431.0928 486.8219 Tm
(g)Tj
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(,)Tj
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(f)Tj
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(~)Tj
/F4 1 Tf
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(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 449.7448 485.3479 Tm
(2)Tj
/F4 1 Tf
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(e)Tj
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6.9738 0 0 6.9738 449.7448 485.3479 Tm
(2)Tj
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9.9626 0 0 9.9626 453.7133 486.8219 Tm
(gg)Tj
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1.6559 0 TD
(and)Tj
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(H)Tj
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[(f)168.9(f)]TJ
/F6 1 Tf
2.0315 .0057 TD
0 Tc
(~)Tj
/F4 1 Tf
-.091 -.0057 TD
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 524.8629 485.3479 Tm
(1)Tj
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9.9626 0 0 9.9626 519.8739 486.8219 Tm
(a)Tj
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6.9738 0 0 6.9738 524.8629 485.3479 Tm
(1)Tj
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9.9626 0 0 9.9626 528.8314 486.8219 Tm
(g)Tj
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(,)Tj
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-42.7815 -1.7299 TD
(f)Tj
/F4 1 Tf
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(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 117.5811 468.1133 Tm
(1)Tj
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-.4553 1.0243 TD
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 121.5496 469.5873 Tm
(,)Tj
/F6 1 Tf
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(~)Tj
/F4 1 Tf
-.0967 -.2447 TD
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 130.7338 468.1133 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 125.7448 469.5873 Tm
(b)Tj
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6.9738 0 0 6.9738 130.7338 468.1133 Tm
(1)Tj
/F7 1 Tf
9.9626 0 0 9.9626 134.7023 469.5873 Tm
(g)Tj
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(,)Tj
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(f)Tj
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(b)Tj
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6.9738 0 0 6.9738 153.8645 468.1133 Tm
(1)Tj
/F7 1 Tf
-.4634 1.3657 TD
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 157.833 469.5873 Tm
(,)Tj
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(~)Tj
/F4 1 Tf
-.074 -.0057 TD
(c)Tj
/F1 1 Tf
6.9738 0 0 6.9738 166.4503 468.1133 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 161.9716 469.5873 Tm
(c)Tj
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6.9738 0 0 6.9738 166.4503 468.1133 Tm
(1)Tj
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9.9626 0 0 9.9626 170.4189 469.5873 Tm
(g)Tj
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(,)Tj
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(f)Tj
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(c)Tj
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6.9738 0 0 6.9738 189.0708 468.1133 Tm
(1)Tj
/F7 1 Tf
-.4227 1.0243 TD
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 193.0393 469.5873 Tm
(,)Tj
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(~)Tj
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-.0967 -.2447 TD
(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 202.1669 468.1133 Tm
(1)Tj
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9.9626 0 0 9.9626 197.1779 469.5873 Tm
(d)Tj
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6.9738 0 0 6.9738 202.1669 468.1133 Tm
(1)Tj
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9.9626 0 0 9.9626 206.1921 469.5873 Tm
(g)Tj
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(,)Tj
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(f)Tj
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(d)Tj
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6.9738 0 0 6.9738 225.2976 468.1133 Tm
(1)Tj
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-.4552 1.3657 TD
()Tj
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9.9626 0 0 9.9626 229.3228 469.5873 Tm
(,)Tj
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(~)Tj
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(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 237.9401 468.1133 Tm
(1)Tj
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9.9626 0 0 9.9626 233.4613 469.5873 Tm
(e)Tj
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6.9738 0 0 6.9738 237.9401 468.1133 Tm
(1)Tj
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9.9626 0 0 9.9626 241.9086 469.5873 Tm
(g)Tj
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(,)Tj
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(f)Tj
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(e)Tj
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6.9738 0 0 6.9738 260.5605 468.1133 Tm
(1)Tj
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-.4227 1.0243 TD
()Tj
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9.9626 0 0 9.9626 264.5291 469.5873 Tm
(,)Tj
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(~)Tj
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-.0967 -.0057 TD
(a)Tj
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6.9738 0 0 6.9738 273.6566 468.1133 Tm
(2)Tj
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9.9626 0 0 9.9626 268.6676 469.5873 Tm
(a)Tj
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6.9738 0 0 6.9738 273.6566 468.1133 Tm
(2)Tj
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9.9626 0 0 9.9626 277.6818 469.5873 Tm
(g)Tj
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(,)Tj
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(f)Tj
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6.9738 0 0 6.9738 296.7873 468.1133 Tm
(2)Tj
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()Tj
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9.9626 0 0 9.9626 300.7558 469.5873 Tm
(,)Tj
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(~)Tj
/F4 1 Tf
-.0967 -.2447 TD
(b)Tj
/F1 1 Tf
6.9738 0 0 6.9738 309.9401 468.1133 Tm
(2)Tj
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9.9626 0 0 9.9626 304.9511 469.5873 Tm
(b)Tj
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6.9738 0 0 6.9738 309.9401 468.1133 Tm
(2)Tj
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9.9626 0 0 9.9626 313.9086 469.5873 Tm
(g)Tj
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(f)Tj
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6.9738 0 0 6.9738 333.0708 468.1133 Tm
(2)Tj
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-.4634 1.3657 TD
()Tj
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9.9626 0 0 9.9626 337.0393 469.5873 Tm
(,)Tj
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(~)Tj
/F4 1 Tf
-.074 -.0057 TD
(c)Tj
/F1 1 Tf
6.9738 0 0 6.9738 345.6566 468.1133 Tm
(2)Tj
/F4 1 Tf
9.9626 0 0 9.9626 341.1779 469.5873 Tm
(c)Tj
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(2)Tj
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9.9626 0 0 9.9626 349.6818 469.5873 Tm
(g)Tj
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(,)Tj
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(f)Tj
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(c)Tj
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6.9738 0 0 6.9738 368.2771 468.1133 Tm
(2)Tj
/F7 1 Tf
-.4227 1.0243 TD
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 372.2456 469.5873 Tm
(,)Tj
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(~)Tj
/F4 1 Tf
-.091 -.2447 TD
(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 381.4298 468.1133 Tm
(2)Tj
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9.9626 0 0 9.9626 376.4409 469.5873 Tm
(d)Tj
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6.9738 0 0 6.9738 381.4298 468.1133 Tm
(2)Tj
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9.9626 0 0 9.9626 385.3983 469.5873 Tm
(g)Tj
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(,)Tj
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(f)Tj
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6.9738 0 0 6.9738 404.5038 468.1133 Tm
(2)Tj
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-.4552 1.3657 TD
()Tj
/F1 1 Tf
9.9626 0 0 9.9626 408.529 469.5873 Tm
(,)Tj
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.4837 .0057 TD
(~)Tj
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-.0683 -.0057 TD
(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 417.1463 468.1133 Tm
(2)Tj
/F4 1 Tf
9.9626 0 0 9.9626 412.6676 469.5873 Tm
(e)Tj
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6.9738 0 0 6.9738 417.1463 468.1133 Tm
(2)Tj
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9.9626 0 0 9.9626 421.1148 469.5873 Tm
(g)Tj
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(,)Tj
/F7 1 Tf
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(f)Tj
/F6 1 Tf
.5691 .0057 TD
(~)Tj
/F4 1 Tf
-.0683 -.0057 TD
(e)Tj
/F1 1 Tf
6.9738 0 0 6.9738 439.7668 468.1133 Tm
(2)Tj
/F4 1 Tf
9.9626 0 0 9.9626 435.2881 469.5873 Tm
(e)Tj
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6.9738 0 0 6.9738 439.7668 468.1133 Tm
(2)Tj
/F7 1 Tf
9.9626 0 0 9.9626 443.7353 469.5873 Tm
(gg)Tj
/F1 1 Tf
1.0015 0 TD
(,)Tj
/F7 1 Tf
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(f)Tj
/F6 1 Tf
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(~)Tj
/F4 1 Tf
-.0967 -.2447 TD
(b)Tj
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6.9738 0 0 6.9738 467.8298 468.1133 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 462.8408 469.5873 Tm
(b)Tj
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6.9738 0 0 6.9738 467.8298 468.1133 Tm
(1)Tj
9.9626 0 0 9.9626 471.855 469.5873 Tm
(,)Tj
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.5121 .2447 TD
(~)Tj
/F4 1 Tf
-.0967 -.2447 TD
(d)Tj
/F1 1 Tf
6.9738 0 0 6.9738 480.9825 468.1133 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 475.9936 469.5873 Tm
(d)Tj
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6.9738 0 0 6.9738 480.9825 468.1133 Tm
(1)Tj
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9.9626 0 0 9.9626 485.0078 469.5873 Tm
(g)Tj
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[(is)-381.1(a)-378.1(brea)-8.6(k-)]TJ
-38.7583 -1.2007 TD
[(point)-390.6(in)]TJ
/F4 1 Tf
3.6192 0 TD
(G)Tj
/F1 1 Tf
1.1097 0 TD
[(since)-392.6(there)-393.4(is)-386.7(no)-388.5(equi)-7.6(valent)-389.2(ele)-8.6(ment)-392.4(in)]TJ
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16.6278 0 TD
(H)Tj
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1.1097 0 TD
(but)Tj
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1.6673 0 TD
(f)Tj
/F6 1 Tf
.5975 .0057 TD
(~)Tj
/F4 1 Tf
-.0967 -.0057 TD
(a)Tj
/F1 1 Tf
6.9738 0 0 6.9738 358.0156 456.1511 Tm
(1)Tj
/F4 1 Tf
9.9626 0 0 9.9626 353.0267 457.6251 Tm
(a)Tj
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6.9738 0 0 6.9738 358.0156 456.1511 Tm
(1)Tj
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9.9626 0 0 9.9626 361.9842 457.6251 Tm
(g)Tj
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[(is)-392.4(not)-386.3(a)-389.5(brea)-8.6(kpoint)-391.4(because)-394.9(it)-388.3(is)-386.7(in)-391.2(both)]TJ
-26.4212 -1.2007 TD
[(genomes.)-344.1(Extending)-338.3(thi)-7.8(s)-332(notion)-340.2(to)-334.3(entire)-340(genomes)-338(we)-337.3(arr)-8(ive)-336.9(at)-330.4(the)-336.9(fol)-7(lowing)-338.4(deni)-7.6(tion:)]TJ
/F2 1 Tf
1.0015 -2.3957 TD
[(Denition)-484.3(3.)]TJ
/F4 1 Tf
6.4531 0 TD
(The)Tj
/F1 1 Tf
1.9803 0 TD
[(breakpoi)-8.7(nt)-476.6(distanc)-9.9(e)]TJ
/F4 1 Tf
8.0749 0 TD
[(,)-472.7(introduc)-8.9(ed)-481.3(in)-476.6(Sankoff)-479.3(and)-480.3(Blanc)-8.2(hette)-479.5(\(1997\))-8.5(,)-472.7(betwe)-9.2(en)-475.6(two)]TJ
-17.5098 -1.2007 TD
[(genomes)-344.1(G)-334.8(and)-332.3(H)-334.8(i)0(s)-335.5(the)-336.9(numb)-7(er)-334.6(of)-334.3(break)-8.6(points)-335.7(betwe)-9.2(en)-333.4(G)-340.4(and)-332.3(H.)]TJ
/F1 1 Tf
1.0015 -2.4014 TD
[(The)-254.3(brea)-8.6(kpoint)-254.8(d)-6.5(istance)-262.1(is)-255.9(easy)-258.2(to)-254.7(calcul)-9.8(ate.)-253.7(From)-258.2(Ta)-8.8(nnier)-255(et)-256.5(al.)-256.8(\(2009\))-8.5(,)-250.8(give)-7.6(n)-251.2(two)-259.4(genomes)]TJ
/F4 1 Tf
37.2845 0 TD
(G)Tj
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(and)Tj
/F4 1 Tf
1.7015 0 TD
(H)Tj
/F1 1 Tf
.7227 0 TD
[(,)-256.5(let)]TJ
/F7 1 Tf
-41.6833 -1.2007 TD
(A)Tj
/F1 1 Tf
.791 0 TD
(\()Tj
/F4 1 Tf
.3357 0 TD
(G)Tj
/F1 1 Tf
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(,)Tj
/F4 1 Tf
.4154 0 TD
(H)Tj
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[(\))-270.2(b)0(e)-270.8(the)-268.6(set)-269.8(of)-271(adjacenc)-12.1(ies)-269.8(shared)-273.1(betwee)-10.9(n)]TJ
/F4 1 Tf
17.2196 0 TD
(G)Tj
/F1 1 Tf
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(and)Tj
/F4 1 Tf
1.7185 0 TD
(H)Tj
/F1 1 Tf
.9902 0 TD
[(and)-271.5(let)]TJ
/F7 1 Tf
2.9932 0 TD
(T)Tj
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(\()Tj
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(G)Tj
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(,)Tj
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(H)Tj
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[(\))-270.2(b)0(e)-270.8(the)-268.6(set)-269.8(of)-271(telomere)-11.1(s)-269.4(then)-269.4(the)]TJ
/F4 1 Tf
-29.9835 -1.2007 TD
[(break)-8.6(point)-333.7(distanc)-8.2(e)]TJ
/F1 1 Tf
8.3651 0 TD
[(betwee)-10.9(n)]TJ
/F4 1 Tf
3.6875 0 TD
(G)Tj
/F1 1 Tf
1.0528 0 TD
(and)Tj
/F4 1 Tf
1.7811 0 TD
(H)Tj
/F1 1 Tf
1.0527 0 TD
[(can)-341.6(be)-333.4(calcul)-9.8(ated)-333.7(usin)-7(g)-330.8(the)-336.9(fol)-7(lowing)-338.4(equatio)-8.7(n:)]TJ
/F7 1 Tf
-3.3916 -2.6006 TD
(D)Tj
/F4 1 Tf
6.9738 0 0 6.9738 240.3212 334.6015 Tm
(BP)Tj
/F1 1 Tf
9.9626 0 0 9.9626 249.392 336.0755 Tm
(\()Tj
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(G)Tj
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(,)Tj
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(H)Tj
/F1 1 Tf
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(\))Tj
/F7 1 Tf
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.1689 Tc
[(j)168.9(G)]TJ
/F1 1 Tf
1.8039 0 TD
0 Tc
(\()Tj
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(G)Tj
/F1 1 Tf
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(\))Tj
/F7 1 Tf
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.1686 Tc
[(jj)168.6(A)]TJ
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2.4412 0 TD
0 Tc
(\()Tj
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(G)Tj
/F1 1 Tf
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(,)Tj
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(H)Tj
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(\))Tj
/F7 1 Tf
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.1682 Tc
(j)Tj
ET
373.89 338.4 39.061 .39685 re
f
BT
9.9626 0 0 9.9626 373.8896 342.8787 Tm
0 Tc
(jT)Tj
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1.0755 0 TD
(\()Tj
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(G)Tj
/F1 1 Tf
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(,)Tj
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(H)Tj
/F1 1 Tf
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(\))Tj
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(j)Tj
/F1 1 Tf
-1.9348 -1.3657 TD
(2)Tj
13.589 .6829 TD
(\(1\))Tj
-42.0304 -2.3331 TD
[(For)-282.3(exampl)-8.7(e,)-276.1(give)-7.6(n)-279.6(two)-282.1(duplica)-8.7(ted)-280(genomes)]TJ
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[(f)168.9(f)]TJ
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2.0372 .0057 TD
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6.9738 0 0 6.9738 322.2991 311.3007 Tm
(1)Tj
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()Tj
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(,)Tj
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(~)Tj
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(1)Tj
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ET
371.679 308.863 32.145 .39685 re
f
BT
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()Tj
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(1)Tj
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()Tj
9.9626 0 0 9.9626 398.7778 312.8314 Tm
(g)Tj
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ET
407.962 308.863 31.578 .39685 re
f
BT
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9.9626 0 0 9.9626 407.9621 312.8314 Tm
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(~)Tj
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(1)Tj
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(1)Tj
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()Tj
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(g)Tj
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ET
443.679 308.863 31.578 .39685 re
f
BT
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9.9626 0 0 9.9626 443.6786 312.8314 Tm
(f)Tj
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()Tj
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(g)Tj
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ET
479.452 308.863 18.935 .39685 re
f
BT
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(g)Tj
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ET
502.526 308.863 18.992 .39685 re
f
BT
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9.9626 0 0 9.9626 502.5258 312.8314 Tm
(f)Tj
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ET
521.518 308.863 16.441 .39685 re
f
BT
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(f)Tj
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()Tj
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(,)Tj
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-42.8783 -1.7242 TD
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(1)Tj
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(1)Tj
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(g)Tj
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(,)Tj
ET
125.178 291.572 31.068 .39685 re
f
BT
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9.9626 0 0 9.9626 125.1779 295.5967 Tm
(f)Tj
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6.9738 0 0 6.9738 134.6456 294.066 Tm
(1)Tj
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-.4146 1.0324 TD
()Tj
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9.9626 0 0 9.9626 138.6708 295.5967 Tm
(,)Tj
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-.4227 1.0324 TD
()Tj
9.9626 0 0 9.9626 151.2566 295.5967 Tm
(g)Tj
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(,)Tj
ET
160.441 291.572 31.578 .39685 re
f
BT
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9.9626 0 0 9.9626 160.4409 295.5967 Tm
(f)Tj
/F6 1 Tf
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(~)Tj
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6.9738 0 0 6.9738 169.9086 294.066 Tm
(2)Tj
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(c)Tj
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6.9738 0 0 6.9738 169.9086 294.066 Tm
(2)Tj
9.9626 0 0 9.9626 173.8771 295.5967 Tm
(,)Tj
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(~)Tj
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-.0967 -.2447 TD
(d)Tj
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6.9738 0 0 6.9738 183.0047 294.066 Tm
(2)Tj
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9.9626 0 0 9.9626 178.0157 295.5967 Tm
(d)Tj
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6.9738 0 0 6.9738 183.0047 294.066 Tm
(2)Tj
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(g)Tj
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(,)Tj
ET
196.157 291.572 31.578 .39685 re
f
BT
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9.9626 0 0 9.9626 196.1574 295.5967 Tm
(f)Tj
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(2)Tj
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-.4552 1.3739 TD
()Tj
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9.9626 0 0 9.9626 210.1606 295.5967 Tm
(,)Tj
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(e)Tj
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(2)Tj
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-.4227 1.0324 TD
()Tj
9.9626 0 0 9.9626 222.7464 295.5967 Tm
(g)Tj
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(,)Tj
ET
231.874 291.572 18.482 .39685 re
f
BT
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9.9626 0 0 9.9626 231.874 295.5967 Tm
(f)Tj
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()Tj
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(gg)Tj
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(and)Tj
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(H)Tj
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.1689 Tc
[(f)168.9(f)]TJ
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2.0372 .0057 TD
0 Tc
(~)Tj
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-.0967 -.0057 TD
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(1)Tj
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(1)Tj
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(1)Tj
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-.4552 1.0324 TD
()Tj
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9.9626 0 0 9.9626 338.1164 295.5967 Tm
(,)Tj
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(~)Tj
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-.0967 -.2447 TD
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6.9738 0 0 6.9738 347.3007 294.066 Tm
(1)Tj
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(1)Tj
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(g)Tj
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ET
360.453 291.572 31.578 .39685 re
f
BT
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9.9626 0 0 9.9626 360.4534 295.5967 Tm
(f)Tj
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(1)Tj
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-.4634 1.3739 TD
()Tj
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(,)Tj
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(~)Tj
/F4 1 Tf
-.074 -.0057 TD
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6.9738 0 0 6.9738 383.0172 294.066 Tm
(1)Tj
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(g)Tj
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(,)Tj
ET
396.17 291.572 31.578 .39685 re
f
BT
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9.9626 0 0 9.9626 396.17 295.5967 Tm
(f)Tj
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(1)Tj
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()Tj
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(,)Tj
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(~)Tj
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(d)Tj
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6.9738 0 0 6.9738 418.7904 294.066 Tm
(1)Tj
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(g)Tj
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ET
431.887 291.572 31.578 .39685 re
f
BT
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9.9626 0 0 9.9626 431.8865 295.5967 Tm
(f)Tj
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(1)Tj
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()Tj
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(,)Tj
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(~)Tj
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6.9738 0 0 6.9738 454.507 294.066 Tm
(1)Tj
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(g)Tj
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ET
467.66 291.572 31.578 .39685 re
f
BT
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(f)Tj
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()Tj
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(,)Tj
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6.9738 0 0 6.9738 490.2235 294.066 Tm
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9.9626 0 0 9.9626 485.2345 295.5967 Tm
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6.9738 0 0 6.9738 490.2235 294.066 Tm
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9.9626 0 0 9.9626 494.2487 295.5967 Tm
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ET
503.376 291.572 32.088 .39685 re
f
BT
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9.9626 0 0 9.9626 503.3762 295.5967 Tm
(f)Tj
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()Tj
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(,)Tj
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(~)Tj
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(b)Tj
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6.9738 0 0 6.9738 526.507 294.066 Tm
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9.9626 0 0 9.9626 521.5179 295.5967 Tm
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6.9738 0 0 6.9738 526.507 294.066 Tm
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(g)Tj
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ET
107.603 272.466 31.578 .39688 re
f
BT
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9.9626 0 0 9.9626 107.6031 276.4345 Tm
(f)Tj
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6.9738 0 0 6.9738 117.5811 274.9606 Tm
(2)Tj
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()Tj
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9.9626 0 0 9.9626 121.5496 276.4345 Tm
(,)Tj
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(~)Tj
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(c)Tj
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6.9738 0 0 6.9738 130.2236 274.9606 Tm
(2)Tj
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9.9626 0 0 9.9626 125.7448 276.4345 Tm
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6.9738 0 0 6.9738 130.2236 274.9606 Tm
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9.9626 0 0 9.9626 134.1921 276.4345 Tm
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ET
143.32 272.466 31.578 .39688 re
f
BT
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9.9626 0 0 9.9626 143.3196 276.4345 Tm
(f)Tj
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(2)Tj
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()Tj
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9.9626 0 0 9.9626 156.8125 276.4345 Tm
(,)Tj
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.5121 .2447 TD
(~)Tj
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(d)Tj
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6.9738 0 0 6.9738 165.9401 274.9606 Tm
(2)Tj
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9.9626 0 0 9.9626 160.9511 276.4345 Tm
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6.9738 0 0 6.9738 165.9401 274.9606 Tm
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9.9626 0 0 9.9626 169.9086 276.4345 Tm
(g)Tj
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ET
179.093 272.466 31.578 .39688 re
f
BT
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9.9626 0 0 9.9626 179.0929 276.4345 Tm
(f)Tj
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(2)Tj
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()Tj
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9.9626 0 0 9.9626 193.0393 276.4345 Tm
(,)Tj
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(~)Tj
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(e)Tj
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6.9738 0 0 6.9738 201.6566 274.9606 Tm
(2)Tj
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9.9626 0 0 9.9626 197.1779 276.4345 Tm
(e)Tj
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6.9738 0 0 6.9738 201.6566 274.9606 Tm
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9.9626 0 0 9.9626 205.6818 276.4345 Tm
(g)Tj
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(,)Tj
ET
214.809 272.466 18.425 .39688 re
f
BT
/F7 1 Tf
9.9626 0 0 9.9626 214.8094 276.4345 Tm
(f)Tj
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6.9738 0 0 6.9738 224.2771 274.9606 Tm
(2)Tj
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()Tj
9.9626 0 0 9.9626 228.2456 276.4345 Tm
(gg)Tj
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1.4283 0 TD
[(the)-427.9(breakpoi)-8.7(nt)-425.4(are)-428.9(underlined;)-431.9(sinc)-8.8(e)]TJ
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(A)Tj
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(\()Tj
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(G)Tj
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(\))Tj
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()Tj
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(\()Tj
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(G)Tj
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(,)Tj
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(H)Tj
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(\),)Tj
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(W)Tj
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(~)Tj
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(E)Tj
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(E)Tj
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6.9738 0 0 6.9738 282.0472 309.7133 Tm
(0)Tj
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9.9626 0 0 9.9626 284.4283 306.085 Tm
(\))Tj
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(4)Tj
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(~)Tj
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(E)Tj
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-20.4291 -1.2007 TD
[(By)-194(denition)-10.5(,)-188.2(a)-196(quasi)-197.3(maximum)-202.6(perfect)-199.5(set)-195.8(must)-198.3(have)-194.4(a)-196(maximum)-202.6(perfect)-199.5(set)-195.8(as)-192.3(a)-196(subse)-8(t;)-189.2(let)]TJ
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(M)Tj
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()Tj
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(P)Tj
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[(be)-196.8(such)]TJ
-40.2208 -1.195 TD
[(a)-184.7(maximum)-191.2(perfect)-193.8(set)-184.4(of)]TJ
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10.3966 .2333 TD
(~)Tj
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(G)Tj
0 0 TD
(G)Tj
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[(.)-250.8(Since)]TJ
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(E)Tj
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[(is)-244.5(a)-247.2(subse)-8(t)-242.5(o)-6.5(f)]TJ
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(H)Tj
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[(,)-245.1(i)0(t)-246.1(fol)-7(lows)-249.9(that)]TJ
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(~)Tj
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(E)Tj
0 0 TD
(E)Tj
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[(must)-249.5(be)-248(a)-247.2(subset)-250.5(of)]TJ
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(~)Tj
/F4 1 Tf
-.2219 -.2106 TD
(H)Tj
0 0 TD
(H)Tj
/F1 1 Tf
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[(.)-250.8(Thus,)]TJ
/F4 1 Tf
2.9989 0 TD
(M)Tj
/F1 1 Tf
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(and)Tj
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1.8494 .2106 TD
(~)Tj
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(E)Tj
0 0 TD
(E)Tj
/F1 1 Tf
-42.5653 -1.2007 TD
[(are)-337.9(subsets)-337.8(of)]TJ
/F8 1 Tf
6.1799 .2105 TD
(~)Tj
/F4 1 Tf
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(H)Tj
0 0 TD
(H)Tj
/F1 1 Tf
1.104 0 TD
[(and,)-334.5(in)-334.3(fact,)-341.8(we)-331.6(wi)-8.2(ll)-331.4(prove)-337.6(that)]TJ
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(M)Tj
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()Tj
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1.0926 .2105 TD
(~)Tj
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(E)Tj
0 0 TD
(E)Tj
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[(by)-331.6(assum)-11.5(ing)-335.1(towards)-341.3(contradict)-11.9(ion)-335.1(that)]TJ
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16.4514 0 TD
(M)Tj
/F7 1 Tf
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(6)Tj
T*
()Tj
/F8 1 Tf
1.2064 .2105 TD
(~)Tj
/F4 1 Tf
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(E)Tj
0 0 TD
(E)Tj
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(.)Tj
/F4 1 Tf
-41.4101 -1.2007 TD
(M)Tj
/F7 1 Tf
1.1495 0 TD
(6)Tj
T*
()Tj
/F8 1 Tf
1.2064 .2162 TD
(~)Tj
/F4 1 Tf
-.1536 -.2162 TD
(E)Tj
0 0 TD
(E)Tj
/F1 1 Tf
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[(if)-239.6(and)-180.5(only)-176.5(if)-177(the)-177.6(multiplic)-8.9(ity)-172.8(o)-6.5(f)-173.5(all)-174.6(ele)-8.6(ments)-178.1(in)]TJ
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(M)Tj
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[(is)-176.2(not)-175.8(equal)-180.9(to)-175(the)-177.6(multipl)-8.5(icity)-178.9(of)-174.2(all)-180.3(eleme)-9.8(nts)-177(in)]TJ
/F8 1 Tf
18.9609 .2162 TD
(~)Tj
/F4 1 Tf
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(E)Tj
0 0 TD
(E)Tj
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(.)Tj
-42.9466 -1.2007 TD
(Let)Tj
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(a)Tj
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[(be)-236.6(an)-236.6(eleme)-9.8(nt)-231.9(that)-238(has)-238.6(differ)-9.4(ent)-234.5(multipl)-8.5(icities)-243.1(in)-231.9(both)]TJ
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21.4022 0 TD
(M)Tj
/F1 1 Tf
1.0698 0 TD
(and)Tj
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1.8437 .2162 TD
(~)Tj
/F4 1 Tf
-.1593 -.2162 TD
(E)Tj
0 0 TD
(E)Tj
/F1 1 Tf
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[(.)-233.7(Since)]TJ
/F4 1 Tf
2.9477 0 TD
(M)Tj
/F1 1 Tf
1.0698 0 TD
[(is)-238.8(a)-235.9(maximum)-242.4(perfect)-245(set)-235.7(of)]TJ
/F8 1 Tf
11.5575 .2333 TD
(~)Tj
/F4 1 Tf
-.2049 -.2333 TD
(G)Tj
0 0 TD
(G)Tj
/F1 1 Tf
-42.48 -1.2007 TD
[(all)-265.7(of)-271(its)-265.1(ele)-8.6(ments)-269.2(can)-273.3(have)-268.4(a)-270(multiplic)-8.9(ity)-263.9(of)-271(at)-267.8(most)]TJ
/F4 1 Tf
21.2656 0 TD
(p)Tj
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[(and,)-271.9(because)]TJ
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5.4174 0 TD
(M)Tj
/F1 1 Tf
1.0983 0 TD
[(is)-267.2(max)-7.6(imum,)-269.3(the)-268.6(multipl)-8.5(icity)-270(of)]TJ
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13.0996 0 TD
(a)Tj
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(in)Tj
/F4 1 Tf
-42.4174 -1.2007 TD
(M)Tj
/F1 1 Tf
1.1324 0 TD
[(is)-295.7(equal)-300.4(to)-300.2(the)-297.1(multipl)-8.5(icity)-298.4(of)]TJ
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12.1778 0 TD
(a)Tj
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(in)Tj
/F8 1 Tf
1.2861 .239 TD
(~)Tj
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(G)Tj
0 0 TD
(G)Tj
/F1 1 Tf
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[(.)-290.6(Since)-305.3(R)]TJ
/F3 1 Tf
3.7387 0 TD
[(epli)-7.6(cate)]TJ
/F1 1 Tf
3.7899 0 TD
(\()Tj
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(P)Tj
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(,)Tj
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(p)Tj
/F1 1 Tf
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[(\))-293(crea)-10.4(tes)]TJ
/F8 1 Tf
3.9436 .2162 TD
(~)Tj
/F4 1 Tf
-.2219 -.2162 TD
(H)Tj
9.9626 0 0 9.9626 398.0408 222.4062 Tm
(H)Tj
/F1 1 Tf
1.0641 0 TD
[(by)-297.4(settin)-10.2(g)-291(all)-299.8(the)-302.7(elements)-306.2(of)]TJ
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12.1152 0 TD
(P)Tj
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(,)Tj
-42.9466 -1.2007 TD
[(which)-268.4(include)-8.7(s)-263.7(all)-265.7(o)-6.5(f)-264.5(the)-262.9(ele)-8.6(ments)-269.2(of)]TJ
/F4 1 Tf
15.1426 0 TD
(M)Tj
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[(,)-267.8(t)0(o)-266.1(multiplic)-8.9(ity)]TJ
/F4 1 Tf
6.5327 0 TD
(p)Tj
/F1 1 Tf
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[(,)-267.8(the)-262.9(multipl)-8.5(icity)-270(of)]TJ
/F9 1 Tf
8.0806 0 TD
(a)Tj
/F1 1 Tf
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(in)Tj
/F8 1 Tf
1.269 .2162 TD
(~)Tj
/F4 1 Tf
-.2219 -.2162 TD
(H)Tj
0 0 TD
(H)Tj
/F1 1 Tf
1.0357 0 TD
[(is)-261.6(g)-6.5(reater)-267(than)-269.4(or)-265.3(equal)]TJ
-33.9327 -1.2007 TD
[(to)-294.5(that)-294.9(of)]TJ
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(M)Tj
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[(.)-296.3(I)0(t)-290.8(follows)-296.8(that)-294.9(the)-297.1(multipl)-8.5(icity)-292.7(of)]TJ
/F9 1 Tf
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(a)Tj
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(in)Tj
/F4 1 Tf
1.0698 0 TD
(M)Tj
/F1 1 Tf
1.1267 0 TD
[(is)-295.7(the)-291.4(multip)-10.7(licity)-296.2(of)]TJ
/F9 1 Tf
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(a)Tj
/F1 1 Tf
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(in)Tj
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1.2747 .239 TD
(~)Tj
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-.1992 -.239 TD
(G)Tj
0 0 TD
(G)Tj
/F7 1 Tf
.9389 0 TD
(\\)Tj
/F8 1 Tf
1.104 .2162 TD
(~)Tj
/F4 1 Tf
-.2219 -.2162 TD
(H)Tj
0 0 TD
(H)Tj
/F1 1 Tf
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[(.)-290.6(From)-298(Lines)-299.6(26)-292.5(in)]TJ
-35.0936 -1.195 TD
[(Algorit)-8.1(hm)-414.8(2)-416.2(R)]TJ
/F3 1 Tf
6.1799 0 TD
[(eord)-7.2(er)]TJ
/F1 1 Tf
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(\()Tj
/F8 1 Tf
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(~)Tj
/F4 1 Tf
-.2276 -.2105 TD
(H)Tj
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(H)Tj
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(,)Tj
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(G)Tj
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[(\))-418.2(w)0(e)-417(can)-415.6(concl)-10.1(ude)-413.8(that)]TJ
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10.3227 .2333 TD
(~)Tj
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-.2049 -.2333 TD
(G)Tj
0 0 TD
(G)Tj
/F7 1 Tf
.9389 0 TD
(\\)Tj
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1.104 .2105 TD
(~)Tj
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-.2219 -.2105 TD
(H)Tj
0 0 TD
(H)Tj
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()Tj
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(\()Tj
/F4 1 Tf
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(G)Tj
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(\\)Tj
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(H)Tj
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[(\).)-412.8(By)-421.7(denition,)]TJ
/F4 1 Tf
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(E)Tj
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()Tj
/F4 1 Tf
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(G)Tj
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(\\)Tj
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(H)Tj
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[(,)-415.8(hence,)]TJ
-39.9363 -1.2007 TD
(\()Tj
/F4 1 Tf
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(G)Tj
/F7 1 Tf
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(\\)Tj
/F4 1 Tf
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(H)Tj
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(\))Tj
/F7 1 Tf
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()Tj
/F8 1 Tf
1.0983 .2106 TD
(~)Tj
/F4 1 Tf
-.1593 -.2106 TD
(E)Tj
0 0 TD
(E)Tj
/F1 1 Tf
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[(.)-330.4(T)0(h)-7(erefore,)-341.4(the)-336.9(multiplic)-8.9(ities)-339.4(of)]TJ
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13.5207 0 TD
(a)Tj
/F1 1 Tf
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(in)Tj
/F4 1 Tf
1.121 0 TD
(M)Tj
/F1 1 Tf
1.1666 0 TD
[(and)-334.1(in)]TJ
/F8 1 Tf
3.0558 .2106 TD
(~)Tj
/F4 1 Tf
-.1593 -.2106 TD
(E)Tj
0 0 TD
(E)Tj
/F1 1 Tf
.9674 0 TD
[(are)-337.9(equal)-10.1(;)-333.6(a)-332.6(cont)-7.6(radiction)-9.3(.)-330.4(Thus,)]TJ
/F4 1 Tf
13.6289 0 TD
(M)Tj
/F7 1 Tf
1.0414 0 TD
()Tj
/F8 1 Tf
1.0926 .2106 TD
(~)Tj
/F4 1 Tf
-.1536 -.2106 TD
(E)Tj
0 0 TD
(E)Tj
/F1 1 Tf
.6316 0 TD
(.)Tj
/F7 1 Tf
-40.7443 -1.2007 TD
(W)Tj
/F1 1 Tf
1.0414 0 TD
(\()Tj
/F8 1 Tf
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(~)Tj
/F4 1 Tf
-.1593 -.2162 TD
(E)Tj
0 0 TD
(E)Tj
/F7 1 Tf
6.9738 0 0 6.9738 137.5937 166.2803 Tm
(0)Tj
/F1 1 Tf
9.9626 0 0 9.9626 139.9747 162.6519 Tm
(\))Tj
/F12 1 Tf
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(4)Tj
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(W)Tj
/F1 1 Tf
1.0414 0 TD
(\()Tj
/F4 1 Tf
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(M)Tj
/F1 1 Tf
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[(\))-253.1(fol)-7(lows)-261.3(from)-255.2(the)-262.9(facts)-263.7(that)]TJ
/F4 1 Tf
11.4665 0 TD
(M)Tj
/F7 1 Tf
1.0414 0 TD
()Tj
/F8 1 Tf
1.0983 .2162 TD
(~)Tj
/F4 1 Tf
-.1593 -.2162 TD
(E)Tj
0 0 TD
(E)Tj
/F1 1 Tf
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(and)Tj
/F7 1 Tf
1.7072 0 TD
(W)Tj
/F1 1 Tf
1.0414 0 TD
(\()Tj
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(~)Tj
/F4 1 Tf
-.1536 -.2162 TD
(E)Tj
0 0 TD
(E)Tj
/F7 1 Tf
6.9738 0 0 6.9738 358.9227 166.2803 Tm
(0)Tj
/F1 1 Tf
9.9626 0 0 9.9626 361.3038 162.6519 Tm
(\))Tj
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(4)Tj
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1.1723 0 TD
(W)Tj
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(\()Tj
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(~)Tj
/F4 1 Tf
-.1593 -.2162 TD
(E)Tj
0 0 TD
(E)Tj
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[(\).)-259.2(But)]TJ
/F4 1 Tf
2.5437 0 TD
(M)Tj
/F1 1 Tf
1.0926 0 TD
[(is)-255.9(a)-258.6(max)-7.6(imum)-257.6(perf)-8.8(ect)-259(set;)]TJ
-32.7833 -1.2007 TD
[(a)-332.6(cont)-7.6(radiction)-9.3(.)-330.4(Hen)-8(ce,)]TJ
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9.8276 0 TD
(H)Tj
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1.0528 0 TD
[(mus)-7(t)-333.6(b)0(e)-333.4(minimal)-11.1(.)]TJ
/F5 1 Tf
31.3151 0 TD
(&)Tj
/F2 1 Tf
10.959 0 0 10.959 219.0613 117.8078 Tm
[(6.)-496.7(FULLY)-332.4(MODIFIED)-331.7(CLIQUE)-328.7(GRAPHS)]TJ
/F1 1 Tf
9.9626 0 0 9.9626 117.5811 93.8834 Tm
[(We)-256.2(have)-262.7(reduced)-263.1(the)-257.2(problem)-260.1(of)-259.6(aliquotin)-8.3(g)-256.8(a)-252.9(genom)-9.1(e)-252.9(t)0(o)-254.7(that)-260.7(of)-259.6(nding)-256.9(a)-258.6(maximum)-259.5(p)-6.5(erfect)-261.3(and)-254.5(cover)-9.4(ing)]TJ
-1.0015 -1.2007 TD
[(set)-286.9(in)-288.8(the)-285.7(breakpo)-10.9(int)-286.6(model.)-291.1(To)-285.9(nd)-286(the)-285.7(max)-7.6(imum)-286(perf)-8.8(ect)-287.5(and)-288.6(covering)-293.3(set,)-287.2(we)-286.1(const)-9.6(ruct)-288.4(a)-287.1(graph)-286.4(from)-289.4(the)]TJ
0 -1.195 TD
[(genome)-341.7(that)-334.7(highli)-7.2(ghts)-337.1(its)-333.4(import)-9.9(ant)-336.9(information)-8.9(.)]TJ
ET
107.603 723.798 430.356 .51025 re
f
107.603 391.181 430.356 .51022 re
f
107.603 705.486 430.356 .51025 re
f
BT
/F2 1 Tf
8.9663 0 0 8.9663 107.6031 711.7227 Tm
[(Algorithm)-335.1(2:)]TJ
/F1 1 Tf
5.9435 0 TD
(Reorder)Tj
/F2 1 Tf
-3.9455 -2.0549 TD
(Input:)Tj
/F1 1 Tf
3.0729 0 TD
[(A)-369.5(polyploid)]TJ
/F8 1 Tf
5.5262 .215 TD
(~)Tj
/F4 1 Tf
-.2276 -.215 TD
(H)Tj
0 0 TD
(H)Tj
/F1 1 Tf
1.1381 0 TD
[(with)-369.8(all)-369.4(gene)-363.3(families)-374.4(of)-368.4(size)]TJ
/F4 1 Tf
12.5257 0 TD
(p)Tj
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[(and)-367.7(a)-368.7(genome)]TJ
/F4 1 Tf
6.1712 0 TD
(G)Tj
/F1 1 Tf
1.0875 0 TD
[(with)-369.8(all)-369.4(gene)-369.6(families)-368.1(of)-368.4(size)]TJ
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12.5257 0 TD
(p)Tj
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(where)Tj
/F7 1 Tf
-40.4793 -1.2203 TD
(E)Tj
/F1 1 Tf
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(\()Tj
/F8 1 Tf
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(~)Tj
/F4 1 Tf
-.2023 -.234 TD
(G)Tj
0 0 TD
(G)Tj
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(\))Tj
/F7 1 Tf
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.1721 Tc
(E)Tj
/F1 1 Tf
1.5112 0 TD
0 Tc
(\()Tj
/F8 1 Tf
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(~)Tj
/F4 1 Tf
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(H)Tj
0 0 TD
(H)Tj
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(\).)Tj
/F2 1 Tf
-7.8151 -1.2203 TD
(Output:)Tj
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3.6989 0 TD
[(A)-243.1(p)13.1(o)13.1(l)0(y)22.2(p)13.1(lo)22.2(id)]TJ
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(H)Tj
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[(wi)18.9(t)15.4(h)-246.1(al)19.8(l)-243.8(g)13.1(en)23.9(e)-248.5(f)0(a)21.2(m)15.9(il)24.6(ie)19.8(s)-247.3(o)13.1(f)-248.7(s)0(i)27.4(z)0(e)]TJ
/F4 1 Tf
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(p)Tj
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[(su)25.1(ch)-235.4(th)22.3(at)]TJ
/F7 1 Tf
3.7621 0 TD
(D)Tj
/F4 1 Tf
6.2762 0 0 6.2762 362.8345 670.0533 Tm
-.0178 Tc
(BP)Tj
/F1 1 Tf
8.9663 0 0 8.9663 370.9416 671.414 Tm
0 Tc
(\()Tj
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(G)Tj
/F1 1 Tf
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(,)Tj
/F4 1 Tf
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(H)Tj
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T*
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[(sz)-334.6(and)-339.8(Plummer)-342.5(\(2009\).)]TJ
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T*
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[(perf)-8.8(ect)-333(set)-8(:)]TJ
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[(Lemm)-9.3(a)-256.8(3)0(.)]TJ
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[(Given)-264.5(a)-251.2(g)-6.5(enome)]TJ
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[(Assum)-8(e)-429.3(towards)-432.4(cont)-7.6(radiction)-436.1(that)]TJ
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