%PDF-1.5 % 21 0 obj << /Length 12056 >> stream 1 0 0 1 89.559 671.183 cm /P <> BDC 1 0 0 1 -89.559 -671.183 cm BT /F15 11.9552 Tf 89.559 671.183 Td [(Mathmatics)-326(239)-327(solut)1(ions)-327(to)-326(Homew)27(ork)-326(for)-327(Ch)1(apter)-327(1)]TJ ET 1 0 0 1 89.559 645.283 cm EMC /P <> BDC 1 0 0 1 -89.559 -645.283 cm BT /F15 11.9552 Tf 89.559 645.283 Td [(T)82(o)-396(the)-396(Studen)27(t.1.)-643(Ho)27(w)-396(man)27(y)-395(di\013eren)27(t)-396(times)-396(can)-396(b)-27(e)-396(displa)28(y)27(ed)-396(on)-396(a)-396(digita)1(l)-396(w)27(atc)27(h)-396(that)]TJ -17.559 -14.446 Td [(sho)27(ws)-326(hours,)-326(min)27(utes,)-327(a)1(nd)-327(seconds)-326(and)-326(that)-327(distinguishes)-326(b)-27(et)27(w)27(een)-326(A.M.)-326(and)-327(P)82(.M.?)]TJ ET 1 0 0 1 89.559 616.391 cm EMC /P <> BDC 1 0 0 1 -89.559 -616.391 cm BT /F15 11.9552 Tf 89.559 616.391 Td [(This)-265(is)-266(an)-265(elemen)27(t)1(ary)-266(coun)28(ting)-266(problem.)-414(There)-266(a)1(re)-266(t)27(w)28(elv)27(e)-265(c)27(hoices)-265(for)-266(hours)-265(\0501)-265(-)-265(12\051,)-278(sixt)27(y)]TJ -17.559 -14.446 Td [(c)27(hoices)-300(for)-300(min)27(utes)-300(\0500)-300(-)-300(59\051,)-305(sixt)27(y)-300(c)27(hoices)-300(for)-300(seconds)-300(\0500)-300(-)-300(59\051)-301(and)-300(t)28(w)27(o)-300(c)27(hoices)-300(for)-300(half)-300(of)-300(da)27(y)]TJ 0 -14.445 Td [(\050AM)-286(and)-286(PM\051.)-286(Therefore)-287(t)1(here)-287(are)-286(12)]TJ/F21 11.9552 Tf 194.041 0 Td [(\002)]TJ/F15 11.9552 Tf 10.974 0 Td [(60)]TJ/F21 11.9552 Tf 13.382 0 Td [(\002)]TJ/F15 11.9552 Tf 10.974 0 Td [(60)]TJ/F21 11.9552 Tf 13.381 0 Td [(\002)]TJ/F15 11.9552 Tf 10.974 0 Td [(2)-278(=)-278(8)1(6)]TJ/F18 11.9552 Tf 33.305 0 Td [(;)]TJ/F15 11.9552 Tf 5.245 0 Td [(400)-286(p)-27(ossible)-286(di\013eren)27(t)-286(times)-286(on)-287(this)]TJ -292.276 -14.446 Td [(w)27(atc)27(h)1(.)-497(Another)-347(p)-27(ersp)-27(ectiv)27(e)-347(on)-347(this)-347(question)-347(i)1(s)-347(to)-347(\014nd)-347(the)-347(n)27(um)27(b)-27(er)-347(of)-346(\050di\013eren)27(t\051)-347(seconds)-347(in)]TJ 0 -14.446 Td [(a)-326(da)27(y)82(,)-327(whic)27(h)-326(is)-326(also)-327(86,400.)]TJ ET 1 0 0 1 89.559 532.708 cm EMC /P <> BDC 1 0 0 1 -89.559 -532.708 cm BT /F15 11.9552 Tf 89.559 532.708 Td [(3.2.This)-452(is)-451(the)-452(b)-27(o)-27(ok's)-452(main)-452(de\014)1(nition)-452(of)-452(divisible)-451(\050b)27(y)-452(the)-451(w)27(a)27(y)82(,)-483(the)-452(one)-452(will)-451(b)-27(e)-452(using)]TJ -17.559 -14.446 Td [(regularly\051:)]TJ ET 1 0 0 1 130.205 518.262 cm EMC 1 0 0 1 -28.94 -23.657 cm /Quote <> BDC 1 0 0 1 -101.265 -494.605 cm BT /F15 11.9552 Tf 101.265 494.605 Td [(Let)]TJ/F18 11.9552 Tf 22.141 0 Td [(a)]TJ/F15 11.9552 Tf 11.217 0 Td [(and)]TJ/F18 11.9552 Tf 23.932 0 Td [(b)]TJ/F15 11.9552 Tf 10.049 0 Td [(b)-27(e)-424(in)27(tegers.)-729(W)82(e)-425(sa)28(y)-425(that)]TJ/F18 11.9552 Tf 137.734 0 Td [(a)]TJ/F15 11.9552 Tf 11.217 0 Td [(is)-424(divisible)-424(b)27(y)]TJ/F18 11.9552 Tf 77.453 0 Td [(b)]TJ/F15 11.9552 Tf 10.049 0 Td [(pro)27(vided)-424(there)-424(is)-424(an)]TJ -303.792 -14.446 Td [(in)27(teger)]TJ/F18 11.9552 Tf 38.695 0 Td [(c)]TJ/F15 11.9552 Tf 8.94 0 Td [(so)-326(that)]TJ/F18 11.9552 Tf 39.735 0 Td [(bc)]TJ/F15 11.9552 Tf 13.336 0 Td [(=)]TJ/F18 11.9552 Tf 12.425 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(.)]TJ ET 1 0 0 1 228.996 480.159 cm EMC 1 0 0 1 -156.996 -23.657 cm /P <> BDC 1 0 0 1 -72 -456.502 cm BT /F15 11.9552 Tf 72 456.502 Td [(Here)-326(is)-327(an)-326(alternativ)27(e)-326(de\014nition:)]TJ ET 1 0 0 1 242.773 456.502 cm EMC 1 0 0 1 -141.508 -23.657 cm /Quote <> BDC 1 0 0 1 -101.265 -432.845 cm BT /F15 11.9552 Tf 101.265 432.845 Td [(W)82(e)-327(sa)27(y)-326(that)]TJ/F18 11.9552 Tf 65.744 0 Td [(a)]TJ/F15 11.9552 Tf 10.047 0 Td [(is)-326(divisible)-327(b)28(y)]TJ/F18 11.9552 Tf 73.943 0 Td [(b)]TJ/F15 11.9552 Tf 8.879 0 Td [(pro)27(vided)]TJ/F19 7.9701 Tf 49.32 4.707 Td [(a)]TJ ET q 1 0 0 1 309.198 435.834 cm []0 d 0 J 0.478 w 0 0 m 4.498 0 l S Q BT /F19 7.9701 Tf 309.636 428.722 Td [(b)]TJ/F15 11.9552 Tf 9.158 4.123 Td [(is)-326(an)-327(in)28(teger.)]TJ ET 1 0 0 1 390.07 432.845 cm EMC 1 0 0 1 -318.07 -23.657 cm /P <> BDC 1 0 0 1 -72 -409.188 cm BT /F15 11.9552 Tf 72 409.188 Td [(Explain)-326(wh)27(y)-326(these)-327(t)28(w)27(o)-327(de\014ni)1(tions)-327(are)-326(di\013eren)27(t.)]TJ ET 1 0 0 1 89.559 394.742 cm EMC /P <> BDC 1 0 0 1 -89.559 -394.742 cm BT /F15 11.9552 Tf 89.559 394.742 Td [(According)-276(to)-276(the)-276(\014rst)-276(de\014nition)-276(0)-276(is)-277(divisible)-276(b)28(y)-277(0)-276(\050b)-27(ecause)-276(0)]TJ/F21 11.9552 Tf 308.217 0 Td [(\002)]TJ/F15 11.9552 Tf 10.729 0 Td [(7)-278(=)-277(0)-277(and)-276(7)-276(is)-276(an)-276(in)27(teger\051,)]TJ -336.505 -14.446 Td [(but)-357(according)-357(to)-357(the)-357(alternativ)27(e)-357(de\014nition)-357(zero)-357(is)-357(not)-357(divisible)-357(b)27(y)-357(zero)-357(b)-27(ecause)]TJ/F16 7.9701 Tf 412.627 4.707 Td [(0)]TJ ET q 1 0 0 1 484.627 383.285 cm []0 d 0 J 0.478 w 0 0 m 4.234 0 l S Q BT /F16 7.9701 Tf 484.627 376.174 Td [(0)]TJ/F15 11.9552 Tf 9.7 4.122 Td [(is)-357(not)-357(an)]TJ -422.327 -14.446 Td [(in)27(teger)-326(\050in)-326(fact,)-327(it)-326(is)-326(meaningless\051.)]TJ ET 1 0 0 1 89.559 351.405 cm EMC /P <> BDC 1 0 0 1 -89.559 -351.405 cm BT /F15 11.9552 Tf 89.559 351.405 Td [(Another)-236(example)-237(is)-236(that)-237(accor)1(ding)-237(to)-236(the)-237(alternativ)28(e)-237(de\014nition)]TJ/F16 7.9701 Tf 318.051 4.707 Td [(3)]TJ ET q 1 0 0 1 407.61 354.393 cm []0 d 0 J 0.478 w 0 0 m 4.234 0 l S Q BT /F16 7.9701 Tf 407.61 347.282 Td [(2)]TJ/F15 11.9552 Tf 8.256 4.123 Td [(is)-237(di)1(visible)-237(b)27(y)]TJ/F16 7.9701 Tf 71.915 4.707 Td [(1)]TJ ET q 1 0 0 1 487.781 354.393 cm []0 d 0 J 0.478 w 0 0 m 4.234 0 l S Q BT /F16 7.9701 Tf 487.781 347.282 Td [(2)]TJ/F15 11.9552 Tf 8.257 4.123 Td [(\050b)-27(ecause)]TJ/F17 5.9776 Tf -421.647 -8.972 Td [(3)]TJ ET q 1 0 0 1 74.391 341.168 cm []0 d 0 J 0.359 w 0 0 m 3.653 0 l S Q BT /F17 5.9776 Tf 74.391 336.049 Td [(2)]TJ ET q 1 0 0 1 73.196 335.332 cm []0 d 0 J 0.478 w 0 0 m 6.044 0 l S Q BT /F17 5.9776 Tf 74.391 330.763 Td [(1)]TJ ET q 1 0 0 1 74.391 329.497 cm []0 d 0 J 0.359 w 0 0 m 3.653 0 l S Q BT /F17 5.9776 Tf 74.391 324.379 Td [(2)]TJ/F15 11.9552 Tf 9.514 7.964 Td [(=)-290(3,)-336(an)-333(in)27(teger\051,)-335(but)-334(according)-334(to)-333(the)-334(\014rst)-333(de\014nition)]TJ/F16 7.9701 Tf 275.122 4.707 Td [(3)]TJ ET q 1 0 0 1 359.027 335.332 cm []0 d 0 J 0.478 w 0 0 m 4.234 0 l S Q BT /F16 7.9701 Tf 359.027 328.221 Td [(2)]TJ/F15 11.9552 Tf 9.419 4.122 Td [(is)-334(not)-333(divisible)-334(b)27(y)]TJ/F16 7.9701 Tf 96.299 4.707 Td [(1)]TJ ET q 1 0 0 1 464.745 335.332 cm []0 d 0 J 0.478 w 0 0 m 4.234 0 l S Q BT /F16 7.9701 Tf 464.745 328.221 Td [(2)]TJ/F15 11.9552 Tf 9.419 4.122 Td [(b)-27(ecause)-334(they)]TJ -402.164 -17.263 Td [(are)-447(not)-447(in)27(tegers.)-797(Because)-447(these)-447(de\014ni)1(tions)-447(ha)27(v)27(e)-447(di\013eren)27(t)-447(example)1(s)-1(,)-477(they)-447(de\014ne)-447(di)1(\013eren)27(t)]TJ 0 -14.446 Td [(concepts)-440(and)-441(t)1(hey)-441(are)-440(di\013eren)27(t)-440(de\014nitions.)-777(There)-440(ma)27(y)-440(b)-27(e)-441(other)-440(di\013ering)-440(examples)-440(than)]TJ 0 -14.446 Td [(these.)]TJ ET 1 0 0 1 89.559 260.288 cm EMC /P <> BDC 1 0 0 1 -89.559 -260.288 cm BT /F15 11.9552 Tf 89.559 260.288 Td [(3.6)-326(De\014ne)-327(what)-326(it)-326(means)-327(for)-326(an)-326(in)27(teger)-326(to)-327(b)-27(e)-326(a)-327(squ)1(are.)]TJ ET 1 0 0 1 89.559 245.843 cm EMC /P <> BDC 1 0 0 1 -89.559 -245.843 cm BT /F15 11.9552 Tf 89.559 245.843 Td [(An)-326(in)27(teger)]TJ/F18 11.9552 Tf 57.875 0 Td [(x)]TJ/F15 11.9552 Tf 10.554 0 Td [(is)-326(called)-327(square)-326(pro)27(vided)-326(there)-326(exists)-327(an)-326(in)27(teger)]TJ/F18 11.9552 Tf 247.062 0 Td [(r)]TJ/F15 11.9552 Tf 9.502 0 Td [(suc)27(h)-326(that)]TJ/F18 11.9552 Tf 51.767 0 Td [(r)]TJ/F16 7.9701 Tf 5.6 4.338 Td [(2)]TJ/F15 11.9552 Tf 8.053 -4.338 Td [(=)]TJ/F18 11.9552 Tf 12.426 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(.)]TJ ET 1 0 0 1 89.559 219.942 cm EMC /P <> BDC 1 0 0 1 -89.559 -219.942 cm BT /F15 11.9552 Tf 89.559 219.942 Td [([extra])-384(3.8)-383(This)-384(is)-384(a)-383(little)-384(tric)27(ky)82(,)-398(b)-27(ecause)-384(w)27(e're)-383(not)-384(quite)-384(sure)-383(ho)27(w)-384(a)-384(p)-27(olygon)-383(has)-384(b)-27(een)]TJ -17.559 -14.445 Td [(de\014ned)-424(\050and)-425(de\014ning)-424(a)-425(p)-27(olygon)-424(is)-425(v)27(ery)-424(tric)27(ky)82(,)-449(if)-425(y)27(ou)-424(think)-425(ab)-27(out)-424(it\051.)-730(Here)-425(is)-424(a)-425(p)-27(olygon)]TJ 0 -14.446 Td [(de\014nition)-326(\050the)-325(\014rst)-326(reasonable)-326(one)-326(I)-325(could)-326(\014nd\051)-326(\134A)-326(closed)-325(plane)-326(\014gure)-326(b)-27(ounded)-326(b)28(y)-326(three)-326(or)]TJ 0 -14.446 Td [(more)-385(line)-384(segmen)27(ts.")-385(\050This)-385(de\014nition)-384(still)-385(has)-385(problems,)-399(some)-385(unde\014ned)-385(t)1(erms)-385(and)-385(so)-385(on,)]TJ 0 -14.446 Td [(but)-375(it's)-375(a)-375(w)27(ork)55(able)-376(sta)1(rt.\051)-582(If)-375(that)-375(is)-375(our)-375(de\014nition,)-387(then)-375(the)-375(p)-27(erimeter)-375(of)-375(a)-375(p)-28(oly)1(gon)-376(i)1(s)-376(the)]TJ 0 -14.446 Td [(sum)-295(of)-296(the)-295(lengths)-296(of)-295(its)-296(\050b)-27(ounding\051)-295(line)-296(segmen)27(ts.)-424(Y)81(our)-295(de\014nition)-296(should)-295(b)-27(e)-296(something)-295(lik)27(e)]TJ 0 -14.446 Td [(that,)-372(at)-362(least)]TJ/F27 11.9552 Tf 71.711 0 Td [(not)]TJ/F15 11.9552 Tf 20.774 0 Td [(b)-27(e)-363(the)-362(distance)-363(\134around",)-372(since)-362(that)-363(is)-362(not)-363(de\014ned.)-544(Bey)27(ond)-362(that,)-372(this)-363(is)]TJ -92.485 -14.445 Td [(not)-326(a)-327(particular)1(ly)-327(c)27(hallen)1(ging)-327(question.)-435(Consider)-326(3.10)-326(and)-327(3.6)-326(nearb)27(y)-326(for)-326(others.)]TJ ET 1 0 0 1 89.559 92.922 cm EMC /P <> BDC 1 0 0 1 -89.559 -92.922 cm BT /F15 11.9552 Tf 89.559 92.922 Td [([extra])-232(3.10)-233(A)-232(p)-27(oin)27(t)-232(on)-233(a)-232(line)-233(segm)1(en)27(t)-233(is)-232(the)-232(midp)-28(oin)28(t)-233(if)-232(it)-233(is)-232(equidistan)27(t)-232(to)-232(b)-28(oth)-232(endp)-27(oin)27(ts.)]TJ/F27 11.9552 Tf -17.559 -14.446 Td [(or)]TJ/F15 11.9552 Tf 14.632 0 Td [(The)-311(p)-28(o)1(in)27(t)]TJ/F18 11.9552 Tf 54.27 0 Td [(C)]TJ/F15 11.9552 Tf 12.957 0 Td [(is)-311(the)-312(midp)-27(oin)27(t)-311(of)-311(line)-312(segmen)28(t)]TJ/F18 11.9552 Tf 161.638 0 Td [(AB)]TJ/F15 11.9552 Tf 21.995 0 Td [(if)]TJ/F18 11.9552 Tf 10.551 0 Td [(C)]TJ/F15 11.9552 Tf 12.957 0 Td [(is)-311(on)-312(segmen)28(t)]TJ/F18 11.9552 Tf 72.755 0 Td [(AB)]TJ/F15 11.9552 Tf 21.995 0 Td [(and)-311(the)-312(distance)]TJ -383.75 -14.446 Td [(from)]TJ/F18 11.9552 Tf 27.815 0 Td [(A)]TJ/F15 11.9552 Tf 12.853 0 Td [(to)]TJ/F18 11.9552 Tf 14.483 0 Td [(C)]TJ/F15 11.9552 Tf 13.312 0 Td [(is)-341(equal)-341(to)-341(the)-341(distance)-341(from)]TJ/F18 11.9552 Tf 151.411 0 Td [(B)]TJ/F15 11.9552 Tf 13.574 0 Td [(to)]TJ/F18 11.9552 Tf 14.484 0 Td [(C)]TJ/F15 11.9552 Tf 9.233 0 Td [(.)-479(Most)-341(imp)-28(o)1(rtan)27(tly:)-465(mak)28(e)-342(sur)1(e)-342(tha)1(t)]TJ/F18 11.9552 Tf 189.655 0 Td [(C)]TJ/F15 11.9552 Tf 13.311 0 Td [(is)]TJ/F27 11.9552 Tf -460.131 -14.446 Td [(on)]TJ/F15 11.9552 Tf 16.937 0 Td [(the)-367(segme)1(n)27(t.)-556(Instead)-367(of)-367(e)1(mphasising)]TJ/F27 11.9552 Tf 193.849 0 Td [(on)]TJ/F15 11.9552 Tf 12.553 0 Td [(,)-377(it)-366(do)-28(e)1(s)-367(su\016ce)-367(to)-366(sa)27(y)-367(that)]TJ/F18 11.9552 Tf 143.833 0 Td [(C)]TJ/F15 11.9552 Tf 13.617 0 Td [(is)]TJ/F27 11.9552 Tf 12.253 0 Td [(b)50(etwe)50(en)]TJ/F18 11.9552 Tf 42.939 0 Td [(A)]TJ/F15 11.9552 Tf 13.159 0 Td [(and)]TJ/F18 11.9552 Tf -449.14 -14.446 Td [(B)]TJ/F15 11.9552 Tf 9.496 0 Td [(.)-435(Some)-326(e\013ort)-327(should)-326(also)-326(b)-28(e)-326(mak)27(e)-326(to)-326(k)27(eep)-326(the)-327(writing)-326(clear)-326(and)-327(unclu)1(ttered.)]TJ ET 1 0 0 1 72 35.138 cm EMC endstream endobj 56 0 obj << /Length 13670 >> stream 1 0 0 1 72 683.138 cm /P <> BDC 1 0 0 1 17.559 -11.955 cm EMC /P <> BDC 1 0 0 1 -89.559 -671.183 cm BT /F15 11.9552 Tf 89.559 671.183 Td [(4.3.)-431(Find)-316(t)28(w)27(o)-316(con)1(ditions)-316(A)-315(and)-315(B)-316(suc)28(h)-316(that)-315(\050a\051)-315(If)-316(A)-315(then)-315(B.)-316(is)-315(true)-315(but)-315(\050b\051)-316(if)-315(B)-315(then)-316(A.)]TJ -17.559 -14.446 Td [(is)-326(false.)]TJ ET 1 0 0 1 114.727 656.737 cm EMC 1 0 0 1 -13.462 -24.408 cm /Quote <> BDC 1 0 0 1 -101.265 -632.329 cm BT /F15 11.9552 Tf 101.265 632.329 Td [(Consider)-326(A:)-327(It)-326(is)-326(300)]TJ/F19 7.9701 Tf 106.776 4.338 Td [(o)]TJ/F15 11.9552 Tf 8.493 -4.338 Td [(F)-326(and)-327(B:)-326(W)81(a)1(ter)-327(is)-326(b)-27(oiling.)]TJ ET 1 0 0 1 356.413 632.329 cm EMC 1 0 0 1 -284.413 -24.409 cm /P <> BDC 1 0 0 1 -72 -607.92 cm BT /F15 11.9552 Tf 72 607.92 Td [(It)-295(is)-295(true)-294(that)-295(If)-295(it)-295(is)-295(300)]TJ/F19 7.9701 Tf 124.62 4.339 Td [(o)]TJ/F15 11.9552 Tf 8.116 -4.339 Td [(F)-295(then)-294(w)27(ater)-295(is)-295(b)-27(oiling.)-295(It)-294(is)-295(false)-295(that)-295(If)-295(w)28(ater)-295(is)-295(b)-27(oiling)-295(then)-295(it)-294(is)]TJ -132.736 -14.446 Td [(300)]TJ/F19 7.9701 Tf 17.559 4.339 Td [(o)]TJ/F15 11.9552 Tf 7.882 -4.339 Td [(F)-275(as)-276(it)-275(could)-275(b)-27(e)-275(man)27(y)-275(other)-276(temp)-27(eratures.)-418(Of)-275(course,)-285(there)-276(are)-275(man)27(y)-275(p)-27(ossible)-275(examples)]TJ -25.441 -14.445 Td [(here.)]TJ ET 1 0 0 1 89.559 552.628 cm EMC /P <> BDC 1 0 0 1 -89.559 -552.628 cm BT /F15 11.9552 Tf 89.559 552.628 Td [(4.10.)-428(Is)-306(the)-306(claim)-305(If)-306(y)27(ou)-306(pic)28(k)-306(a)-306(guinea)-305(pig)-306(up)-306(b)27(y)-305(its)-306(tail,)-310(then)-306(its)-305(ey)27(es)-306(will)-306(p)-27(op)-305(out.)-306(true?)]TJ ET 1 0 0 1 89.559 538.182 cm EMC /P <> BDC 1 0 0 1 -89.559 -538.182 cm BT /F15 11.9552 Tf 89.559 538.182 Td [(Based)-294(on)-295(the)-294(photo)-295(in)-294(the)-294(hin)27(ts,)-301(it)-294(lo)-28(oks)-294(as)-295(if)-294(y)27(ou)-294(cannot)-295(pic)28(k)-295(up)-294(a)-295(guinea)-294(pig)-294(b)27(y)-295(its)-294(tail.)]TJ -17.559 -14.446 Td [(Therefore,)-326(the)-327(h)28(yp)-27(othesis)-327(is)-326(v)54(acuous)-326(\050alw)27(a)27(y)1(s)-327(false\051)-326(and)-327(so)-326(the)-326(statemen)27(t)-326(is)-327(true.)]TJ ET 1 0 0 1 89.559 497.335 cm EMC /P <> BDC 1 0 0 1 -89.559 -497.335 cm BT /F15 11.9552 Tf 89.559 497.335 Td [(5.2.)-435(Pro)27(v)27(e)-326(that)-326(the)-327(sum)-326(of)-326(an)-327(o)-27(dd)-326(in)27(teger)-326(and)-327(an)-326(ev)27(en)-326(in)27(teger)-326(is)-326(o)-28(dd.)]TJ ET 1 0 0 1 89.559 482.889 cm EMC /P <> BDC 1 0 0 1 -89.559 -482.889 cm BT /F15 11.9552 Tf 89.559 482.889 Td [(This)-326(can)-327(b)-27(e)-326(restated)-326(as)]TJ ET 1 0 0 1 72 482.889 cm EMC 1 0 0 1 29.265 -27.397 cm /Quote <> BDC 1 0 0 1 -101.265 -455.492 cm BT /F15 11.9552 Tf 101.265 455.492 Td [(If)]TJ/F18 11.9552 Tf 11.702 0 Td [(a)]TJ/F15 11.9552 Tf 10.047 0 Td [(is)-326(an)-327(o)-27(dd)-326(in)27(teger)-326(and)]TJ/F18 11.9552 Tf 112.572 0 Td [(b)]TJ/F15 11.9552 Tf 8.879 0 Td [(is)-326(an)-327(ev)27(e)1(n)-327(in)27(teger)-326(then)]TJ/F18 11.9552 Tf 120.052 0 Td [(a)]TJ/F15 11.9552 Tf 8.801 0 Td [(+)]TJ/F18 11.9552 Tf 11.762 0 Td [(b)]TJ/F15 11.9552 Tf 8.879 0 Td [(is)-326(o)-28(dd)1(.)]TJ ET 1 0 0 1 433.369 455.492 cm EMC 1 0 0 1 -343.81 -27.397 cm /P <> BDC 1 0 0 1 -89.559 -428.095 cm BT /F15 11.9552 Tf 89.559 428.095 Td [(Supp)-27(ose)-366(that)]TJ/F18 11.9552 Tf 72.213 0 Td [(a)]TJ/F15 11.9552 Tf 10.515 0 Td [(is)-366(a)1(n)-366(o)-27(dd)-366(in)28(teger.)-553(By)-365(de\014nition)-366(of)-365(o)-28(d)1(d,)]TJ/F18 11.9552 Tf 209.228 0 Td [(a)]TJ/F15 11.9552 Tf 10.262 0 Td [(=)-344(2)]TJ/F18 11.9552 Tf 19.075 0 Td [(x)]TJ/F15 11.9552 Tf 9.628 0 Td [(+)-249(1)-365(for)-366(some)-365(in)27(teger)]TJ/F18 11.9552 Tf 109.616 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(.)]TJ -464.748 -14.446 Td [(Supp)-27(ose)-323(that)]TJ/F18 11.9552 Tf 71.192 0 Td [(b)]TJ/F15 11.9552 Tf 8.837 0 Td [(is)-323(an)-323(ev)28(en)-323(in)27(teger.)-434(By)-323(de\014nition)-322(of)-323(ev)27(en,)]TJ/F18 11.9552 Tf 211.283 0 Td [(b)]TJ/F15 11.9552 Tf 8.837 0 Td [(is)-323(divisible)-323(b)28(y)-323(2.)-434(By)-323(de\014nition)-323(of)]TJ -300.149 -14.446 Td [(divisible,)]TJ/F18 11.9552 Tf 48.32 0 Td [(b)]TJ/F15 11.9552 Tf 8.298 0 Td [(=)-278(2)]TJ/F18 11.9552 Tf 18.279 0 Td [(c)]TJ/F15 11.9552 Tf 7.884 0 Td [(for)-238(some)-238(in)27(teger)]TJ/F18 11.9552 Tf 82.741 0 Td [(c)]TJ/F15 11.9552 Tf 5.038 0 Td [(.)-406(Consider)]TJ/F18 11.9552 Tf 55.887 0 Td [(a)]TJ/F15 11.9552 Tf 6.645 0 Td [(+)]TJ/F18 11.9552 Tf 9.604 0 Td [(b)]TJ/F15 11.9552 Tf 8.298 0 Td [(=)-278(\0502)]TJ/F18 11.9552 Tf 22.831 0 Td [(x)]TJ/F15 11.9552 Tf 7.152 0 Td [(+)-42(1\051)-42(+)-41(\0502)]TJ/F18 11.9552 Tf 40.52 0 Td [(c)]TJ/F15 11.9552 Tf 5.038 0 Td [(\051)-278(=)-277(2)]TJ/F18 11.9552 Tf 26.152 0 Td [(x)]TJ/F15 11.9552 Tf 7.152 0 Td [(+)-42(2)]TJ/F18 11.9552 Tf 15.457 0 Td [(c)]TJ/F15 11.9552 Tf 5.538 0 Td [(+)-42(1)-278(=)-277(2\050)]TJ/F18 11.9552 Tf 41.61 0 Td [(x)]TJ/F15 11.9552 Tf 7.152 0 Td [(+)]TJ/F18 11.9552 Tf 9.604 0 Td [(c)]TJ/F15 11.9552 Tf 5.038 0 Td [(\051)-42(+)-42(1.)]TJ -444.238 -14.446 Td [(\050This)-433(uses)-432(substitution,)-459(asso)-27(ciativit)27(y)82(,)-460(comm)28(utativit)27(y)82(,)-460(an)1(d)-433(distribution,)-459(all)-433(items)-432(assumed)]TJ 0 -14.446 Td [(from)-341(App)-27(endix)-340(D.\051)-341(W)82(e)-341(also)-341(k)1(no)27(w)-341(that)-340(the)-341(in)27(tegers)-340(are)-341(closed)-340(under)-341(addition,)-344(so)-341(if)]TJ/F18 11.9552 Tf 429.305 0 Td [(x)]TJ/F15 11.9552 Tf 10.725 0 Td [(and)]TJ/F18 11.9552 Tf 22.932 0 Td [(c)]TJ/F15 11.9552 Tf -462.962 -14.445 Td [(are)-372(in)27(tegers,)-384(t)1(hen)]TJ/F18 11.9552 Tf 94.518 0 Td [(x)]TJ/F15 11.9552 Tf 9.682 0 Td [(+)]TJ/F18 11.9552 Tf 12.135 0 Td [(c)]TJ/F15 11.9552 Tf 9.488 0 Td [(is)-372(also)-372(an)-373(in)28(teger.)-573(Then,)]TJ/F18 11.9552 Tf 132.543 0 Td [(x)]TJ/F15 11.9552 Tf 9.682 0 Td [(+)]TJ/F18 11.9552 Tf 12.134 0 Td [(c)]TJ/F15 11.9552 Tf 9.488 0 Td [(is)-372(the)-372(desired)-373(in)28(teger,)]TJ/F18 11.9552 Tf 115.942 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(,)-384(suc)28(h)-373(that)]TJ/F18 11.9552 Tf -411.749 -14.446 Td [(a)]TJ/F15 11.9552 Tf 8.802 0 Td [(+)]TJ/F18 11.9552 Tf 11.761 0 Td [(b)]TJ/F15 11.9552 Tf 8.298 0 Td [(=)-278(2)]TJ/F18 11.9552 Tf 18.278 0 Td [(y)]TJ/F15 11.9552 Tf 8.794 0 Td [(+)-222(1.)-435(Therefore,)-326(b)27(y)-327(de\014ni)1(tion)-327(of)-326(o)-27(dd,)]TJ/F18 11.9552 Tf 190.277 0 Td [(a)]TJ/F15 11.9552 Tf 8.802 0 Td [(+)]TJ/F18 11.9552 Tf 11.761 0 Td [(b)]TJ/F15 11.9552 Tf 8.879 0 Td [(is)-326(o)-28(dd,)-326(as)-326(desired.)]TJ ET 1 0 0 1 89.559 315.019 cm EMC /P <> BDC 1 0 0 1 -89.559 -315.019 cm BT /F15 11.9552 Tf 89.559 315.019 Td [(5.12.)-435(Supp)-27(ose)]TJ/F18 11.9552 Tf 75.178 0 Td [(a;)-167(b;)-166(c)]TJ/F15 11.9552 Tf 26.649 0 Td [(,)-326(and)]TJ/F18 11.9552 Tf 29.915 0 Td [(d)]TJ/F15 11.9552 Tf 9.985 0 Td [(are)-326(in)27(tegers.)-435(Pro)27(v)27(e)-326(that)-326(if)]TJ/F18 11.9552 Tf 136.47 0 Td [(a)]TJ/F21 11.9552 Tf 9.466 0 Td [(j)]TJ/F18 11.9552 Tf 6.641 0 Td [(b)]TJ/F15 11.9552 Tf 8.879 0 Td [(and)]TJ/F18 11.9552 Tf 22.762 0 Td [(c)]TJ/F21 11.9552 Tf 8.359 0 Td [(j)]TJ/F18 11.9552 Tf 6.642 0 Td [(d)]TJ/F15 11.9552 Tf 6.082 0 Td [(,)-326(then)-327(\050)]TJ/F18 11.9552 Tf 38.37 0 Td [(ac)]TJ/F15 11.9552 Tf 11.183 0 Td [(\051)]TJ/F21 11.9552 Tf 7.873 0 Td [(j)]TJ/F15 11.9552 Tf 6.642 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(bd)]TJ/F15 11.9552 Tf 11.06 0 Td [(\051.)]TJ ET 1 0 0 1 89.559 300.573 cm EMC /P <> BDC 1 0 0 1 -89.559 -300.573 cm BT /F15 11.9552 Tf 89.559 300.573 Td [(Supp)-27(ose)-326(that)]TJ/F18 11.9552 Tf 71.276 0 Td [(a)]TJ/F21 11.9552 Tf 9.466 0 Td [(j)]TJ/F18 11.9552 Tf 6.642 0 Td [(b)]TJ/F15 11.9552 Tf 4.977 0 Td [(.)-435(By)-327(d)1(e\014nition)-327(of)]TJ/F21 11.9552 Tf 92.182 0 Td [(j)]TJ/F15 11.9552 Tf 3.321 0 Td [(,)-326(there)-327(is)-326(an)-326(in)27(teger)]TJ/F18 11.9552 Tf 103.793 0 Td [(m)]TJ/F15 11.9552 Tf 14.142 0 Td [(suc)27(h)-326(that)]TJ/F18 11.9552 Tf 51.766 0 Td [(b)]TJ/F15 11.9552 Tf 8.298 0 Td [(=)]TJ/F18 11.9552 Tf 12.425 0 Td [(am)]TJ/F15 11.9552 Tf 16.385 0 Td [(.)]TJ ET 1 0 0 1 89.559 286.127 cm EMC /P <> BDC 1 0 0 1 -89.559 -286.127 cm BT /F15 11.9552 Tf 89.559 286.127 Td [(Supp)-27(ose)-326(that)]TJ/F18 11.9552 Tf 71.276 0 Td [(c)]TJ/F21 11.9552 Tf 8.359 0 Td [(j)]TJ/F18 11.9552 Tf 6.642 0 Td [(d)]TJ/F15 11.9552 Tf 6.083 0 Td [(.)-435(By)-326(de\014nition)-327(of)]TJ/F21 11.9552 Tf 92.182 0 Td [(j)]TJ/F15 11.9552 Tf 3.321 0 Td [(,)-326(there)-327(is)-326(an)-326(in)27(teger)]TJ/F18 11.9552 Tf 103.793 0 Td [(n)]TJ/F15 11.9552 Tf 10.89 0 Td [(suc)27(h)-326(that)]TJ/F18 11.9552 Tf 51.766 0 Td [(d)]TJ/F15 11.9552 Tf 9.404 0 Td [(=)]TJ/F18 11.9552 Tf 12.425 0 Td [(cn)]TJ/F15 11.9552 Tf 12.026 0 Td [(.)]TJ ET 1 0 0 1 89.559 271.681 cm EMC /P <> BDC 1 0 0 1 -89.559 -271.681 cm BT /F15 11.9552 Tf 89.559 271.681 Td [(Therefore,)]TJ/F18 11.9552 Tf 58.168 0 Td [(bd)]TJ/F15 11.9552 Tf 16.988 0 Td [(=)-496(\050)]TJ/F18 11.9552 Tf 19.584 0 Td [(am)]TJ/F15 11.9552 Tf 16.384 0 Td [(\051\050)]TJ/F18 11.9552 Tf 9.105 0 Td [(cn)]TJ/F15 11.9552 Tf 12.026 0 Td [(\051)-496(=)]TJ/F18 11.9552 Tf 25.512 0 Td [(ac)]TJ/F15 11.9552 Tf 11.183 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(mn)]TJ/F15 11.9552 Tf 17.227 0 Td [(\051)-454(b)27(y)-455(substition,)-486(comm)27(utativit)28(y)81(,)-486(and)-455(asso)-27(ciativit)27(y)82(.)]TJ -208.288 -14.446 Td [(Because)-295(the)-296(in)28(tegers)-296(are)-295(closed)-295(under)-295(m)27(ultiplication,)]TJ/F18 11.9552 Tf 271.297 0 Td [(mn)]TJ/F15 11.9552 Tf 20.758 0 Td [(is)-295(an)-296(in)28(teger)-296(and)-295(therefore)-295(satis\014es)]TJ -292.055 -14.445 Td [(the)-326(de\014nition)-327(o)1(f)-327(divisibilit)27(y)-326(so)-326(that)]TJ/F18 11.9552 Tf 182.873 0 Td [(ac)]TJ/F21 11.9552 Tf 14.504 0 Td [(j)]TJ/F18 11.9552 Tf 6.642 0 Td [(bd)]TJ/F15 11.9552 Tf 11.06 0 Td [(,)-326(as)-327(desired.)]TJ ET 1 0 0 1 89.559 216.389 cm EMC /P <> BDC 1 0 0 1 -89.559 -216.389 cm BT /F15 11.9552 Tf 89.559 216.389 Td [(5.15.)-435(Let)]TJ/F18 11.9552 Tf 50.236 0 Td [(x)]TJ/F15 11.9552 Tf 10.554 0 Td [(b)-27(e)-327(an)-326(in)27(teger.)-435(Pro)28(v)27(e)-327(that)-326(0)]TJ/F21 11.9552 Tf 142.978 0 Td [(j)]TJ/F18 11.9552 Tf 6.641 0 Td [(x)]TJ/F15 11.9552 Tf 10.555 0 Td [(if)-326(and)-327(only)-326(if)-326(x)-327(=)-326(0.)]TJ ET 1 0 0 1 89.559 201.943 cm EMC /P <> BDC 1 0 0 1 -89.559 -201.943 cm BT /F15 11.9552 Tf 89.559 201.943 Td [(In)-326(t)27(w)27(o)-326(directions)-327(-)-326(pro)27(v)28(e)]TJ ET 1 0 0 1 219.036 201.943 cm EMC 1 0 0 1 -117.771 -24.409 cm /Quote <> BDC 1 0 0 1 -101.265 -177.534 cm BT /F15 11.9552 Tf 101.265 177.534 Td [(if)-326(0)]TJ/F21 11.9552 Tf 19.904 0 Td [(j)]TJ/F18 11.9552 Tf 6.642 0 Td [(x)]TJ/F15 11.9552 Tf 10.554 0 Td [(then)]TJ/F18 11.9552 Tf 26.664 0 Td [(x)]TJ/F15 11.9552 Tf 9.973 0 Td [(=)-278(0,)-326(and)-326(if)]TJ/F18 11.9552 Tf 58.924 0 Td [(x)]TJ/F15 11.9552 Tf 9.973 0 Td [(=)-278(0)-326(then)-326(0)]TJ/F21 11.9552 Tf 58.018 0 Td [(j)]TJ/F18 11.9552 Tf 6.641 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(.)]TJ ET 1 0 0 1 323.665 177.534 cm EMC 1 0 0 1 -234.106 -24.408 cm /P <> BDC 1 0 0 1 -89.559 -153.126 cm BT /F15 11.9552 Tf 89.559 153.126 Td [(If)-331(0)]TJ/F21 11.9552 Tf 21.021 0 Td [(j)]TJ/F18 11.9552 Tf 6.733 0 Td [(x)]TJ/F15 11.9552 Tf 10.608 0 Td [(then)-331(there)-331(is)-330(an)-331(in)27(teger)]TJ/F18 11.9552 Tf 123.571 0 Td [(c)]TJ/F15 11.9552 Tf 8.994 0 Td [(suc)27(h)-331(that)-330(0\050)]TJ/F18 11.9552 Tf 62.279 0 Td [(c)]TJ/F15 11.9552 Tf 5.038 0 Td [(\051)-285(=)]TJ/F18 11.9552 Tf 20.481 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(.)-449(But)-330(then)-331(b)27(y)-331(m)27(ultiplicat)1(ion,)]TJ/F18 11.9552 Tf 153.378 0 Td [(x)]TJ/F15 11.9552 Tf 10.064 0 Td [(=)-285(0,)]TJ -446.378 -14.446 Td [(as)-326(desired.)]TJ ET 1 0 0 1 89.559 124.234 cm EMC /P <> BDC 1 0 0 1 -89.559 -124.234 cm BT /F15 11.9552 Tf 89.559 124.234 Td [(If)]TJ/F18 11.9552 Tf 11.702 0 Td [(x)]TJ/F15 11.9552 Tf 9.973 0 Td [(=)-278(0,)-326(sho)27(wing)-326(0)]TJ/F21 11.9552 Tf 79.218 0 Td [(j)]TJ/F18 11.9552 Tf 6.642 0 Td [(x)]TJ/F15 11.9552 Tf 10.554 0 Td [(is)-326(only)-327(sho)28(wing)-327(0)]TJ/F21 11.9552 Tf 91.246 0 Td [(j)]TJ/F15 11.9552 Tf 6.642 0 Td [(0.)-435(This)-326(is)-327(true)-326(b)-27(ecause)-327(0)-326(\05083456\051)-326(=)-327(0.)]TJ ET 1 0 0 1 89.559 97.833 cm EMC /P <> BDC 1 0 0 1 -89.559 -97.833 cm BT /F15 11.9552 Tf 89.559 97.833 Td [([extra])-313(5.21)-313(Pro)27(v)27(e)-313(that)-313(the)-313(di\013erence)-313(b)-27(et)27(w)27(een)-313(distinct,)-316(nonconsecutiv)28(e)-314(p)-27(erfect)-313(squares)-313(is)]TJ -17.559 -14.446 Td [(comp)-27(osite.)-435(This)-327(ca)1(n)-327(b)-27(e)-326(restated)-327(as)]TJ ET 1 0 0 1 72 81.063 cm EMC 1 0 0 1 29.265 -25.073 cm /Quote <> BDC 1 0 0 1 -101.265 -55.99 cm BT /F15 11.9552 Tf 101.265 55.99 Td [(If)]TJ/F18 11.9552 Tf 11.702 0 Td [(x)]TJ/F15 11.9552 Tf 10.554 0 Td [(and)]TJ/F18 11.9552 Tf 22.762 0 Td [(y)]TJ/F15 11.9552 Tf 10.038 0 Td [(are)-326(distinct)-327(and)-326(nonconsecutiv)28(e)-327(in)27(tegers,)-326(then)]TJ/F18 11.9552 Tf 238.542 0 Td [(x)]TJ/F16 7.9701 Tf 6.652 4.338 Td [(2)]TJ/F21 11.9552 Tf 7.389 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 11.955 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F15 11.9552 Tf 8.634 -4.338 Td [(is)-326(comp)-27(osite.)]TJ ET 1 0 0 1 506.972 55.99 cm EMC endstream endobj 71 0 obj << /Length 15010 >> stream 1 0 0 1 89.559 671.183 cm /P <> BDC 1 0 0 1 -89.559 -671.183 cm BT /F15 11.9552 Tf 89.559 671.183 Td [(Supp)-27(ose)-330(that)]TJ/F18 11.9552 Tf 71.355 0 Td [(x)]TJ/F15 11.9552 Tf 10.593 0 Td [(and)]TJ/F18 11.9552 Tf 22.801 0 Td [(y)]TJ/F15 11.9552 Tf 10.078 0 Td [(are)-330(distinct)-329(and)-330(nonconsecutiv)28(e)-330(in)27(tegers)-329(.)-445(Since)-330(they)-330(are)-329(distinct,)]TJ -132.386 -14.446 Td [(one)-435(m)27(ust)-435(b)-27(e)-435(larger.)-762(Because)-435(the)-435(v)54(aria)1(bles)-436(are)-435(meaningless)-435(b)-27(efore)-435(hand,)-462(supp)-27(ose)]TJ/F18 11.9552 Tf 431.786 0 Td [(x)-463(>)-463(y)]TJ/F15 11.9552 Tf 32.962 0 Td [(.)]TJ -464.748 -14.446 Td [(Because)-273(they)-272(are)-273(nonconsecutiv)28(e,)-284(in)-272(fact,)-284(w)28(e)-273(ma)27(y)-273(f)1(urther)-273(supp)-27(ose)]TJ/F18 11.9552 Tf 334.38 0 Td [(x)-278(>)-278(y)]TJ/F15 11.9552 Tf 29.88 0 Td [(+)-113(1)1(.)-418(T)82(o)-273(sho)27(w)]TJ/F18 11.9552 Tf 69.498 0 Td [(x)]TJ/F16 7.9701 Tf 6.652 4.339 Td [(2)]TJ/F21 11.9552 Tf 6.077 -4.339 Td [(\000)]TJ/F18 11.9552 Tf 10.644 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.339 Td [(2)]TJ/F15 11.9552 Tf -463.268 -18.784 Td [(is)-279(comp)-27(osite,)-288(b)27(y)-278(de\014nition,)-288(w)27(e)-279(m)27(ust)-278(sho)27(w)-279(that)-278(there)-279(is)-279(a)1(n)-279(in)27(teger)]TJ/F18 11.9552 Tf 332.207 0 Td [(b)]TJ/F15 11.9552 Tf 8.309 0 Td [(suc)27(h)-278(that)-279(1)]TJ/F18 11.9552 Tf 59.8 0 Td [(<)-278(b)-277(<)-278(x)]TJ/F16 7.9701 Tf 39.801 4.338 Td [(2)]TJ/F21 11.9552 Tf 6.224 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 10.79 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F15 11.9552 Tf -463.268 -18.784 Td [(and)]TJ/F18 11.9552 Tf 22.46 0 Td [(b)]TJ/F21 11.9552 Tf 4.977 0 Td [(j)]TJ/F18 11.9552 Tf 3.321 0 Td [(x)]TJ/F16 7.9701 Tf 6.652 4.338 Td [(2)]TJ/F21 11.9552 Tf 6.773 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 11.339 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F15 11.9552 Tf 4.732 -4.338 Td [(.)-427(Notice)-301(that)]TJ/F18 11.9552 Tf 69.853 0 Td [(x)]TJ/F16 7.9701 Tf 6.652 4.338 Td [(2)]TJ/F21 11.9552 Tf 6.773 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 11.339 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F15 11.9552 Tf 8.053 -4.338 Td [(=)-278(\050)]TJ/F18 11.9552 Tf 16.978 0 Td [(x)]TJ/F21 11.9552 Tf 8.692 0 Td [(\000)]TJ/F18 11.9552 Tf 11.339 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051\050)]TJ/F18 11.9552 Tf 9.105 0 Td [(x)]TJ/F15 11.9552 Tf 8.692 0 Td [(+)]TJ/F18 11.9552 Tf 11.146 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(\051,)-306(so)-301(\050)]TJ/F18 11.9552 Tf 30.088 0 Td [(x)]TJ/F21 11.9552 Tf 8.693 0 Td [(\000)]TJ/F18 11.9552 Tf 11.339 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(\051)]TJ/F21 11.9552 Tf 4.553 0 Td [(j)]TJ/F15 11.9552 Tf 3.32 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(x)]TJ/F16 7.9701 Tf 6.652 4.338 Td [(2)]TJ/F21 11.9552 Tf 6.773 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 11.339 0 Td [(y)]TJ/F16 7.9701 Tf 6.136 4.338 Td [(2)]TJ/F15 11.9552 Tf 4.733 -4.338 Td [(\051.)-427(W)82(e)-301(need)-301(only)-301(sho)27(w)]TJ -357.738 -14.446 Td [(that)-349(one)-349(of)-350(the)-349(factors)-349(is)-350(the)-349(appropriate)-349(size.)-504(Since)-349(I)-349(think)-350(it)-349(will)-349(b)-27(e)-350(easier,)-355(let's)-349(fo)-27(cus)-349(on)]TJ/F18 11.9552 Tf 0 -14.446 Td [(x)]TJ/F21 11.9552 Tf 9.309 0 Td [(\000)]TJ/F18 11.9552 Tf 11.955 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(.)]TJ ET 1 0 0 1 89.559 570.062 cm EMC /P <> BDC 1 0 0 1 -89.559 -570.062 cm BT /F15 11.9552 Tf 89.559 570.062 Td [(W)82(e)-362(supp)-28(osed)-362(that)]TJ/F18 11.9552 Tf 97.33 0 Td [(x)-339(>)-338(y)]TJ/F15 11.9552 Tf 32.935 0 Td [(+)-246(1.)-543(By)-362(subtracting)]TJ/F18 11.9552 Tf 108.709 0 Td [(y)]TJ/F15 11.9552 Tf 10.466 0 Td [(w)27(e)-362(get)]TJ/F18 11.9552 Tf 37.597 0 Td [(x)]TJ/F21 11.9552 Tf 9.599 0 Td [(\000)]TJ/F18 11.9552 Tf 12.246 0 Td [(y)-374(>)]TJ/F15 11.9552 Tf 23.336 0 Td [(1,)-371(and)-362(w)27(e're)-362(half)-362(done.)]TJ -349.777 -14.446 Td [(W)82(e)-404(also)-403(supp)-28(osed)-403(that)]TJ/F18 11.9552 Tf 123.216 0 Td [(x)-409(>)-409(y)]TJ/F15 11.9552 Tf 31.674 0 Td [(.)-667(By)-403(subtracting)-403(1)-404(w)27(e)-403(also)-404(get)]TJ/F18 11.9552 Tf 166.947 0 Td [(x)]TJ/F21 11.9552 Tf 9.936 0 Td [(\000)]TJ/F15 11.9552 Tf 12.584 0 Td [(1)]TJ/F18 11.9552 Tf 10.743 0 Td [(>)-409(y)]TJ/F21 11.9552 Tf 23.417 0 Td [(\000)]TJ/F15 11.9552 Tf 12.583 0 Td [(1.)-667(Mult)1(iplying)]TJ -391.1 -14.445 Td [(these)-367(t)27(w)27(o)-367(pro)-27(duces)]TJ/F18 11.9552 Tf 102.722 0 Td [(x)]TJ/F16 7.9701 Tf 6.653 4.338 Td [(2)]TJ/F21 11.9552 Tf 7.721 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 12.288 0 Td [(x)-347(>)-348(y)]TJ/F16 7.9701 Tf 30.198 4.338 Td [(2)]TJ/F21 11.9552 Tf 7.722 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 12.288 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(,)-377(and)-368(subtractin)1(g)]TJ/F18 11.9552 Tf 93.35 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F15 11.9552 Tf 9.123 -4.338 Td [(and)-367(adding)]TJ/F18 11.9552 Tf 62.108 0 Td [(x)]TJ/F15 11.9552 Tf 11.043 0 Td [(to)-367(b)-27(oth)-368(sides)-367(yields)]TJ/F18 11.9552 Tf -367.489 -14.446 Td [(x)]TJ/F16 7.9701 Tf 6.652 4.338 Td [(2)]TJ/F21 11.9552 Tf 6.459 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 11.024 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F18 11.9552 Tf 8.053 -4.338 Td [(>)-278(x)]TJ/F21 11.9552 Tf 20.804 0 Td [(\000)]TJ/F18 11.9552 Tf 11.025 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(,)-296(as)-288(desired.)-423(W)82(e'v)27(e)-288(no)27(w)-288(sho)27(wn)-288(that)-288(\050)]TJ/F18 11.9552 Tf 187.294 0 Td [(x)]TJ/F21 11.9552 Tf 8.379 0 Td [(\000)]TJ/F18 11.9552 Tf 11.024 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ/F21 11.9552 Tf 4.552 0 Td [(j)]TJ/F15 11.9552 Tf 3.321 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(x)]TJ/F16 7.9701 Tf 6.652 4.338 Td [(2)]TJ/F21 11.9552 Tf 6.458 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 11.025 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F15 11.9552 Tf 4.732 -4.338 Td [(\051)-288(and)-288(1)]TJ/F18 11.9552 Tf 39.479 0 Td [(<)-278(x)]TJ/F21 11.9552 Tf 20.803 0 Td [(\000)]TJ/F18 11.9552 Tf 11.025 0 Td [(y)-314(<)-277(x)]TJ/F16 7.9701 Tf 28.535 4.338 Td [(2)]TJ/F21 11.9552 Tf 6.459 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 11.024 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F15 11.9552 Tf 4.732 -4.338 Td [(,)]TJ -464.748 -14.446 Td [(therefore)-326(b)27(y)-326(de\014nition)]TJ/F18 11.9552 Tf 117.385 0 Td [(x)]TJ/F16 7.9701 Tf 6.652 4.338 Td [(2)]TJ/F21 11.9552 Tf 7.389 -4.338 Td [(\000)]TJ/F18 11.9552 Tf 11.955 0 Td [(y)]TJ/F16 7.9701 Tf 6.137 4.338 Td [(2)]TJ/F15 11.9552 Tf 8.634 -4.338 Td [(is)-326(comp)-27(osite,)-327(as)-326(claimed.)]TJ ET 1 0 0 1 89.559 485.878 cm EMC /P <> BDC 1 0 0 1 -89.559 -485.878 cm BT /F15 11.9552 Tf 89.559 485.878 Td [(5.23.)-427(Sup)1(p)-28(ose)-300(y)27(ou)-301(are)-301(ask)27(ed)-300(to)-301(pro)27(v)27(e)-300(a)-301(statemen)27(t)-301(of)-300(the)-301(form)-301(If)-301(A)-301(o)1(r)-301(B,)-301(then)-301(C.)-301(Exp)1(lain)]TJ -17.559 -14.446 Td [(wh)27(y)-264(y)28(ou)-264(need)-264(to)-264(pro)28(v)27(e)-264(\050a\051)-264(If)-264(A,)-264(then)-263(C.)-264(and)-264(also)-264(pro)27(v)28(e)-264(\050b\051)-264(If)-264(B,)-264(then)-263(C.)-264(Wh)27(y)-264(is)-264(it)-264(n)1(ot)-264(enough)]TJ 0 -14.446 Td [(to)-326(pro)27(v)27(e)-326(only)-327(o)1(ne)-327(of)-326(\050a\051)-327(o)1(r)-327(\050b\051?)]TJ ET 1 0 0 1 89.559 442.54 cm EMC /P <> BDC 1 0 0 1 -89.559 -442.54 cm BT /F15 11.9552 Tf 89.559 442.54 Td [(Consider)-372(the)-372(statemen)27(t)-372(If)-372(I)-372(am)-372(aliv)28(e)-373(o)1(r)-373(de)1(ad,)-384(then)-372(I)-372(am)-372(aliv)27(e.)-372(W)82(ell,)-383(it)-372(is)-373(tru)1(e)-373(th)1(at)-373(If)-372(I)]TJ -17.559 -14.445 Td [(am)-325(aliv)27(e,)-325(then)-325(I)-325(am)-324(aliv)27(e,)-325(trivially)82(.)-435(Ho)27(w)27(ev)28(er,)-325(the)-325(original)-325(statemen)27(t)-325(is)-325(not)-325(t)1(rue.)-435(This)-325(sho)27(ws)]TJ 0 -14.446 Td [(that)-297(it)-297(is)-298(not)-297(enough)-297(to)-297(pro)27(v)27(e)-297(only)-297(one,)-303(but)-297(not)-297(quite)-298(wh)28(y)81(.)-425(T)81(o)-297(see)-297(wh)27(y)82(,)-303(examine)-297(the)-298(o)1(riginal)]TJ 0 -14.446 Td [(statemen)27(t)-380(If)-380(A)-380(or)-380(B,)-380(then)-380(C.)-380(This)-380(sa)27(ys)-380(that)-380(if)-380(one)-380(of)-380(A)-380(or)-380(B)-380(is)-380(true,)-394(C)-380(m)28(ust)-380(also)-380(b)-28(e)-380(true)]TJ 0 -14.446 Td [(as)-348(w)27(ell.)-500(In)-347(either)-348(the)-348(case)-348(that)-348(A)-348(is)-348(true)-348(or)-348(that)-348(B)-347(is)-348(true,)-354(C)-348(m)28(ust)-348(follo)27(w)-348(to)-348(b)-27(e)-348(true.)-500(If)-348(w)28(e)]TJ 0 -14.446 Td [(only)-342(c)27(hec)27(k)-342(the)-343(A)-342(is)-343(true)-342(case,)-347(w)27(e)-342(ha)27(v)27(e)-342(not)-342(attended)-343(to)-342(the)-343(B)-342(is)-343(true)-342(case.)-484(Thi)1(s)-343(case)-342(is)-343(also)]TJ 0 -14.445 Td [(necessary)-326(for)-327(pro)28(ving)-327(the)-326(statemen)27(t)-326(If)-326(A)-327(or)-326(B,)-327(t)1(hen)-327(C.)]TJ ET 1 0 0 1 89.559 329.465 cm EMC /P <> BDC 1 0 0 1 -89.559 -329.465 cm BT /F15 11.9552 Tf 89.559 329.465 Td [(6.2.)-435(Dispro)27(v)27(e:)-435(If)]TJ/F18 11.9552 Tf 88.016 0 Td [(a)]TJ/F15 11.9552 Tf 10.047 0 Td [(and)]TJ/F18 11.9552 Tf 22.762 0 Td [(b)]TJ/F15 11.9552 Tf 8.879 0 Td [(are)-326(nonnegativ)27(e)-326(in)27(tegers)-326(with)]TJ/F18 11.9552 Tf 154.519 0 Td [(a)]TJ/F21 11.9552 Tf 9.466 0 Td [(j)]TJ/F18 11.9552 Tf 6.641 0 Td [(b)]TJ/F15 11.9552 Tf 4.977 0 Td [(,)-326(then)]TJ/F18 11.9552 Tf 33.818 0 Td [(a)]TJ/F21 11.9552 Tf 9.465 0 Td [(\024)]TJ/F18 11.9552 Tf 12.62 0 Td [(b)]TJ/F15 11.9552 Tf 4.977 0 Td [(.)]TJ ET 1 0 0 1 89.559 315.019 cm EMC /P <> BDC 1 0 0 1 -89.559 -315.019 cm BT /F15 11.9552 Tf 89.559 315.019 Td [(2)-326(and)-327(0)-326(are)-326(nonnegativ)27(e)-326(in)27(tegers,)-326(2)]TJ/F21 11.9552 Tf 182.552 0 Td [(j)]TJ/F15 11.9552 Tf 6.642 0 Td [(0)-326(\050b)-28(ec)1(ause)-327(0)-278(=)-277(2)]TJ/F21 11.9552 Tf 87.728 0 Td [(\002)]TJ/F15 11.9552 Tf 11.956 0 Td [(0\051,)-326(but)-327(it)-326(is)-326(false)-327(that)-326(2)]TJ/F21 11.9552 Tf 123.437 0 Td [(\024)]TJ/F15 11.9552 Tf 12.619 0 Td [(0.)]TJ ET 1 0 0 1 89.559 288.618 cm EMC /P <> BDC 1 0 0 1 -89.559 -288.618 cm BT /F15 11.9552 Tf 89.559 288.618 Td [(6.4)-343(Exp)-27(onen)27(tiation)-343(\050or)-344(in)28(v)27(olution\051)-343(is)-344(not)-343(asso)-27(ciativ)27(e.)-486(Those)-343(paren)27(thesis)-343(matter.)-486(2)]TJ/F16 7.9701 Tf 422.201 4.338 Td [(\0503)]TJ/F17 5.9776 Tf 7.527 2.813 Td [(2)]TJ/F16 7.9701 Tf 4.151 -2.813 Td [(\051)]TJ/F15 11.9552 Tf 7.457 -4.338 Td [(=)]TJ -458.895 -14.446 Td [(2)]TJ/F16 7.9701 Tf 5.853 4.338 Td [(9)]TJ/F15 11.9552 Tf 9.773 -4.338 Td [(=)-422(51)1(2,)-432(while)-411(\0502)]TJ/F16 7.9701 Tf 82.101 4.338 Td [(3)]TJ/F15 11.9552 Tf 4.732 -4.338 Td [(\051)]TJ/F16 7.9701 Tf 4.553 4.338 Td [(2)]TJ/F15 11.9552 Tf 9.772 -4.338 Td [(=)-422(8)]TJ/F16 7.9701 Tf 19.998 4.338 Td [(2)]TJ/F15 11.9552 Tf 9.773 -4.338 Td [(=)-422(64)1(.)-689(These)-411(are)-411(all)-411(p)-27(ositiv)27(e)-410(in)27(tegers,)-432(but)-411(the)-411(results)-411(a)1(re)-411(not)]TJ -146.555 -14.446 Td [(equal.)]TJ ET 1 0 0 1 89.559 233.325 cm EMC /P <> BDC 1 0 0 1 -89.559 -233.325 cm BT /F15 11.9552 Tf 89.559 233.325 Td [([extra])-421(6.7)-420(This)-421(isn't)-421(to)-27(o)-421(bad)-420(for)-421(y)27(our)-421(calculator)-420(to)-421(handle.)-718(2)]TJ/F16 7.9701 Tf 327.286 4.338 Td [(2)]TJ/F17 5.9776 Tf 4.234 2.813 Td [(5)]TJ/F15 11.9552 Tf 8.074 -7.151 Td [(+)-286(1)-439(=)-438(4294967297)-439(=)]TJ -357.153 -14.446 Td [(641\0506700417\051.)-595(Clearly)-379(1)]TJ/F18 11.9552 Tf 129.539 0 Td [(<)]TJ/F15 11.9552 Tf 13.509 0 Td [(641)]TJ/F18 11.9552 Tf 21.964 0 Td [(<)]TJ/F15 11.9552 Tf 13.509 0 Td [(4294967297,)-393(and)-379(so)-380(2)]TJ/F16 7.9701 Tf 110.74 4.339 Td [(2)]TJ/F20 5.9776 Tf 4.234 2.812 Td [(n)]TJ/F15 11.9552 Tf 8.687 -7.151 Td [(+)-258(1)-380(is)-380(not)-379(prime)-380(for)]TJ/F18 11.9552 Tf 108.766 0 Td [(n)]TJ/F15 11.9552 Tf 11.392 0 Td [(=)-368(5.)-595([Of)]TJ -422.34 -14.446 Td [(historical)-371(note:)-524(Pierre)-371(de)-370(F)81(ermat)-371(thou)1(gh)27(t)-371(all)-371(n)27(um)28(b)-28(ers)-370(2)]TJ/F16 7.9701 Tf 290.084 4.339 Td [(2)]TJ/F20 5.9776 Tf 4.234 2.813 Td [(n)]TJ/F15 11.9552 Tf 8.616 -7.152 Td [(+)-252(1)-371(w)27(ere)-371(prime,)-382(mostly)-371(b)-27(ecause)]TJ -302.934 -14.446 Td [(the)-326(n)27(um)27(b)-27(ers)-326(grew)-327(to)-27(o)-326(big)-327(t)1(o)-327(compute.])]TJ ET 1 0 0 1 89.559 163.587 cm EMC /P <> BDC 1 0 0 1 -89.559 -163.587 cm BT /F15 11.9552 Tf 89.559 163.587 Td [([extra])-528(6.)1(9)-528(Consider)]TJ/F18 11.9552 Tf 111.662 0 Td [(n)]TJ/F16 7.9701 Tf 6.988 4.338 Td [(2)]TJ/F15 11.9552 Tf 9.027 -4.338 Td [(+)]TJ/F18 11.9552 Tf 13.4 0 Td [(n)]TJ/F15 11.9552 Tf 11.282 0 Td [(+)-359(41.)-1039(Calculate)-528(the)-527(v)54(alue)-527(of)-528(this)-528(p)-27(olynomial)-527(for)]TJ/F18 11.9552 Tf 274.573 0 Td [(n)]TJ/F15 11.9552 Tf 14.404 0 Td [(=)]TJ -458.895 -14.446 Td [(1)]TJ/F18 11.9552 Tf 5.853 0 Td [(;)]TJ/F15 11.9552 Tf 5.244 0 Td [(2)]TJ/F18 11.9552 Tf 5.853 0 Td [(;)]TJ/F15 11.9552 Tf 5.244 0 Td [(3)]TJ/F18 11.9552 Tf 5.853 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F15 11.9552 Tf 26.221 0 Td [(10.)]TJ ET 1 0 0 1 146.428 149.141 cm EMC 1 0 0 1 -45.163 -24.409 cm /Quote <> BDC 1 0 0 1 -101.265 -124.732 cm BT /F15 11.9552 Tf 101.265 124.732 Td [(43,)-326(47,)-327(53,)-326(61,)-326(71,)-327(83,)-326(97,)-326(113,)-327(131,)-326(151)]TJ ET 1 0 0 1 304.169 124.732 cm EMC 1 0 0 1 -232.169 -24.408 cm /P <> BDC 1 0 0 1 -72 -100.324 cm BT /F15 11.9552 Tf 72 100.324 Td [(Notice)-326(that)-327(all)-326(the)-326(n)27(um)27(b)-27(ers)-326(y)27(ou)-326(computed)-327(are)-326(prime)-326(\050y)27(ep)-326(they)-327(are\051.)]TJ ET 1 0 0 1 427.467 100.324 cm EMC 1 0 0 1 -326.202 -24.409 cm /Quote <> BDC 1 0 0 1 -101.265 -75.915 cm BT /F15 11.9552 Tf 101.265 75.915 Td [(Dispro)27(v)27(e)1(:)-436(If)]TJ/F18 11.9552 Tf 64.604 0 Td [(n)]TJ/F15 11.9552 Tf 10.89 0 Td [(is)-326(a)-327(p)-27(ositiv)27(e)-326(in)27(teger,)-326(then)]TJ/F18 11.9552 Tf 133.448 0 Td [(n)]TJ/F16 7.9701 Tf 6.988 4.339 Td [(2)]TJ/F15 11.9552 Tf 7.389 -4.339 Td [(+)]TJ/F18 11.9552 Tf 11.761 0 Td [(n)]TJ/F15 11.9552 Tf 9.644 0 Td [(+)-222(41)-327(is)-326(prime.)]TJ ET 1 0 0 1 422.849 75.915 cm EMC 1 0 0 1 -333.29 -24.408 cm /P <> BDC 1 0 0 1 -89.559 -51.507 cm BT /F15 11.9552 Tf 89.559 51.507 Td [(Doing)-269(this)-268(b)27(y)-269(blind)-268(computation)-269(is)-268(incon)27(v)27(enien)28(t)-269(\050turns)-269(out)-268(they)-269(all)-269(a)1(re)-269(for)-269(quite)-268(a)-269(while\051.)]TJ -17.559 -14.446 Td [(But)-312(some)-312(though)28(t)-312(reminds)-312(us)-312(that)-312(clearly)-312(if)]TJ/F18 11.9552 Tf 227.893 0 Td [(n)]TJ/F15 11.9552 Tf 10.309 0 Td [(=)-278(41)-312(then)-312(4)1(1)]TJ/F16 7.9701 Tf 66.058 4.338 Td [(2)]TJ/F15 11.9552 Tf 7.037 -4.338 Td [(+)-193(41)-192(+)-193(41)-312(can't)-312(b)-27(e)-312(prime,)-315(41)-312(is)]TJ ET 1 0 0 1 72 37.061 cm EMC endstream endobj 4 0 obj << /Type /ObjStm /N 100 /First 800 /Length 10980 >> stream 3 0 6 41 7 139 8 237 9 335 10 433 11 538 12 637 13 742 14 841 15 940 16 1039 17 1139 18 1239 5 1339 22 1441 23 1486 20 1535 19 1672 33 1807 34 1908 35 2015 36 2116 37 2217 38 2318 39 2419 40 2520 41 2627 42 2728 43 2829 44 2930 45 3031 46 3132 47 3233 48 3334 49 3441 50 3542 51 3643 52 3744 32 3851 57 3954 55 4005 53 4118 58 4219 59 4320 60 4421 61 4522 62 4623 63 4724 64 4825 65 4926 66 5027 67 5134 68 5235 54 5342 72 5445 70 5491 69 5616 75 5752 76 5853 77 5954 78 6055 79 6156 83 6257 84 6362 85 6467 86 6572 87 6677 82 6782 89 6885 90 6990 91 7095 92 7200 93 7305 88 7410 95 7513 96 7618 97 7723 98 7828 99 7933 94 8038 101 8141 102 8248 103 8355 104 8462 105 8569 100 8676 107 8785 108 8892 109 8999 110 9106 111 9213 106 9320 113 9429 114 9536 115 9643 116 9750 117 9857 112 9964 119 10073 % 3 0 obj << /S /GoTo /D [5 0 R /Fit] >> % 6 0 obj <>] /S /P >> % 7 0 obj <>] /S /P >> % 8 0 obj <>] /S /P >> % 9 0 obj <>] /S /P >> % 10 0 obj <>] /S /Quote >> % 11 0 obj <>] /S /P >> % 12 0 obj <>] /S /Quote >> % 13 0 obj <>] /S /P >> % 14 0 obj <>] /S /P >> % 15 0 obj <>] /S /P >> % 16 0 obj <>] /S /P >> % 17 0 obj <>] /S /P >> % 18 0 obj <>] /S /P >> % 5 0 obj << /Type /Page /Contents 21 0 R /Resources 20 0 R /MediaBox [0 0 612 792] /Parent 31 0 R >> % 22 0 obj << /D [5 0 R /XYZ 71 721 null] >> % 23 0 obj << /D [5 0 R /XYZ 72 683.138 null] >> % 20 0 obj << /Font << /F15 24 0 R /F21 25 0 R /F18 26 0 R /F19 27 0 R /F16 28 0 R /F17 29 0 R /F27 30 0 R >> /ProcSet [ /PDF /Text ] >> % 19 0 obj <> <>] /S /P >> % 33 0 obj <>] /S /P >> % 34 0 obj <>] /S /Quote >> % 35 0 obj <>] /S /P >> % 36 0 obj <>] /S /P >> % 37 0 obj <>] /S /P >> % 38 0 obj <>] /S /P >> % 39 0 obj <>] /S /P >> % 40 0 obj <>] /S /Quote >> % 41 0 obj <>] /S /P >> % 42 0 obj <>] /S /P >> % 43 0 obj <>] /S /P >> % 44 0 obj <>] /S /P >> % 45 0 obj <>] /S /P >> % 46 0 obj <>] /S /P >> % 47 0 obj <>] /S /P >> % 48 0 obj <>] /S /Quote >> % 49 0 obj <>] /S /P >> % 50 0 obj <>] /S /P >> % 51 0 obj <>] /S /P >> % 52 0 obj <>] /S /Quote >> % 32 0 obj << /Type /Page /Contents 56 0 R /Resources 55 0 R /MediaBox [0 0 612 792] /Parent 31 0 R >> % 57 0 obj << /D [32 0 R /XYZ 110.851 721 null] >> % 55 0 obj << /Font << /F15 24 0 R /F19 27 0 R /F18 26 0 R /F21 25 0 R /F16 28 0 R >> /ProcSet [ /PDF /Text ] >> % 53 0 obj <>] /S /P >> % 58 0 obj <>] /S /P >> % 59 0 obj <>] /S /P >> % 60 0 obj <>] /S /P >> % 61 0 obj <>] /S /P >> % 62 0 obj <>] /S /P >> % 63 0 obj <>] /S /P >> % 64 0 obj <>] /S /P >> % 65 0 obj <>] /S /P >> % 66 0 obj <>] /S /Quote >> % 67 0 obj <>] /S /P >> % 68 0 obj <>] /S /Quote >> % 54 0 obj << /Type /Page /Contents 71 0 R /Resources 70 0 R /MediaBox [0 0 612 792] /Parent 31 0 R >> % 72 0 obj << /D [54 0 R /XYZ 71 721 null] >> % 70 0 obj << /Font << /F15 24 0 R /F18 26 0 R /F16 28 0 R /F21 25 0 R /F17 29 0 R /F20 73 0 R >> /ProcSet [ /PDF /Text ] >> % 69 0 obj <> <>] /S /P >> % 75 0 obj <>] /S /P >> % 76 0 obj <>] /S /P >> % 77 0 obj <>] /S /P >> % 78 0 obj <>] /S /P >> % 79 0 obj <>] /S /P >> % 83 0 obj <>] /S /TD >> % 84 0 obj <>] /S /TD >> % 85 0 obj <>] /S /TD >> % 86 0 obj <>] /S /TD >> % 87 0 obj <>] /S /TD >> % 82 0 obj <> % 89 0 obj <>] /S /TD >> % 90 0 obj <>] /S /TD >> % 91 0 obj <>] /S /TD >> % 92 0 obj <>] /S /TD >> % 93 0 obj <>] /S /TD >> % 88 0 obj <> % 95 0 obj <>] /S /TD >> % 96 0 obj <>] /S /TD >> % 97 0 obj <>] /S /TD >> % 98 0 obj <>] /S /TD >> % 99 0 obj <>] /S /TD >> % 94 0 obj <> % 101 0 obj <>] /S /TD >> % 102 0 obj <>] /S /TD >> % 103 0 obj <>] /S /TD >> % 104 0 obj <>] /S /TD >> % 105 0 obj <>] /S /TD >> % 100 0 obj <> % 107 0 obj <>] /S /TD >> % 108 0 obj <>] /S /TD >> % 109 0 obj <>] /S /TD >> % 110 0 obj <>] /S /TD >> % 111 0 obj <>] /S /TD >> % 106 0 obj <> % 113 0 obj <>] /S /TD >> % 114 0 obj <>] /S /TD >> % 115 0 obj <>] /S /TD >> % 116 0 obj <>] /S /TD >> % 117 0 obj <>] /S /TD >> % 112 0 obj <> % 119 0 obj <>] /S /TD >> endstream endobj 121 0 obj << /Type /ObjStm /N 100 /First 893 /Length 11726 >> stream 120 0 122 107 123 214 124 321 118 428 126 537 127 644 128 751 129 858 130 965 125 1072 132 1181 133 1288 134 1395 135 1502 136 1609 131 1716 138 1825 137 1932 81 2009 80 2157 142 2234 143 2342 144 2450 145 2558 146 2666 147 2774 141 2882 149 3000 150 3108 151 3216 152 3324 153 3432 154 3540 148 3648 156 3766 157 3874 158 3982 159 4090 160 4198 161 4306 155 4414 163 4532 164 4640 165 4748 166 4856 167 4964 168 5072 162 5180 170 5298 171 5406 172 5514 173 5622 174 5730 175 5838 169 5946 177 6064 178 6172 179 6280 180 6388 181 6496 182 6604 176 6712 184 6830 185 6938 186 7046 187 7154 188 7262 189 7370 183 7478 191 7596 192 7704 193 7812 194 7920 195 8028 196 8136 190 8244 198 8362 199 8470 200 8578 201 8686 202 8794 203 8902 197 9010 205 9128 204 9236 140 9314 139 9467 206 9546 207 9649 208 9752 209 9855 210 9958 214 10061 216 10170 217 10279 218 10388 219 10497 220 10606 213 10715 % 120 0 obj <>] /S /TD >> % 122 0 obj <>] /S /TD >> % 123 0 obj <>] /S /TD >> % 124 0 obj <>] /S /TD >> % 118 0 obj <> % 126 0 obj <>] /S /TD >> % 127 0 obj <>] /S /TD >> % 128 0 obj <>] /S /TD >> % 129 0 obj <>] /S /TD >> % 130 0 obj <>] /S /TD >> % 125 0 obj <> % 132 0 obj <>] /S /TD >> % 133 0 obj <>] /S /TD >> % 134 0 obj <>] /S /TD >> % 135 0 obj <>] /S /TD >> % 136 0 obj <>] /S /TD >> % 131 0 obj <> % 138 0 obj <>] /S /TD >> % 137 0 obj <> % 81 0 obj <> % 80 0 obj <> % 142 0 obj <>] /S /TD >> % 143 0 obj <>] /S /TD >> % 144 0 obj <>] /S /TD >> % 145 0 obj <>] /S /TD >> % 146 0 obj <>] /S /TD >> % 147 0 obj <>] /S /TD >> % 141 0 obj <> % 149 0 obj <>] /S /TD >> % 150 0 obj <>] /S /TD >> % 151 0 obj <>] /S /TD >> % 152 0 obj <>] /S /TD >> % 153 0 obj <>] /S /TD >> % 154 0 obj <>] /S /TD >> % 148 0 obj <> % 156 0 obj <>] /S /TD >> % 157 0 obj <>] /S /TD >> % 158 0 obj <>] /S /TD >> % 159 0 obj <>] /S /TD >> % 160 0 obj <>] /S /TD >> % 161 0 obj <>] /S /TD >> % 155 0 obj <> % 163 0 obj <>] /S /TD >> % 164 0 obj <>] /S /TD >> % 165 0 obj <>] /S /TD >> % 166 0 obj <>] /S /TD >> % 167 0 obj <>] /S /TD >> % 168 0 obj <>] /S /TD >> % 162 0 obj <> % 170 0 obj <>] /S /TD >> % 171 0 obj <>] /S /TD >> % 172 0 obj <>] /S /TD >> % 173 0 obj <>] /S /TD >> % 174 0 obj <>] /S /TD >> % 175 0 obj <>] /S /TD >> % 169 0 obj <> % 177 0 obj <>] /S /TD >> % 178 0 obj <>] /S /TD >> % 179 0 obj <>] /S /TD >> % 180 0 obj <>] /S /TD >> % 181 0 obj <>] /S /TD >> % 182 0 obj <>] /S /TD >> % 176 0 obj <> % 184 0 obj <>] /S /TD >> % 185 0 obj <>] /S /TD >> % 186 0 obj <>] /S /TD >> % 187 0 obj <>] /S /TD >> % 188 0 obj <>] /S /TD >> % 189 0 obj <>] /S /TD >> % 183 0 obj <> % 191 0 obj <>] /S /TD >> % 192 0 obj <>] /S /TD >> % 193 0 obj <>] /S /TD >> % 194 0 obj <>] /S /TD >> % 195 0 obj <>] /S /TD >> % 196 0 obj <>] /S /TD >> % 190 0 obj <> % 198 0 obj <>] /S /TD >> % 199 0 obj <>] /S /TD >> % 200 0 obj <>] /S /TD >> % 201 0 obj <>] /S /TD >> % 202 0 obj <>] /S /TD >> % 203 0 obj <>] /S /TD >> % 197 0 obj <> % 205 0 obj <>] /S /TD >> % 204 0 obj <> % 140 0 obj <> % 139 0 obj <> % 206 0 obj <>] /S /P >> % 207 0 obj <>] /S /P >> % 208 0 obj <>] /S /P >> % 209 0 obj <>] /S /P >> % 210 0 obj <>] /S /P >> % 214 0 obj <>] /S /TD >> % 216 0 obj <>] /S /TD >> % 217 0 obj <>] /S /TD >> % 218 0 obj <>] /S /TD >> % 219 0 obj <>] /S /TD >> % 220 0 obj <>] /S /TD >> % 213 0 obj <> endstream endobj 253 0 obj << /Length 33336 >> stream 1 0 0 1 72 683.138 cm /P <> BDC 1 0 0 1 -72 -683.138 cm BT /F15 11.9552 Tf 72 671.183 Td [(a)-284(factor.)-421(It)-284(tak)28(es)-284(a)-284(little)-284(more)-283(insigh)27(t)-284(to)-284(see)-284(that)]TJ/F18 11.9552 Tf 248.89 0 Td [(n)]TJ/F15 11.9552 Tf 10.309 0 Td [(=)-278(40)-284(d)1(o)-28(esn't)-283(w)27(ork)-284(either,)-292(40)]TJ/F16 7.9701 Tf 143.551 4.338 Td [(2)]TJ/F15 11.9552 Tf 6.35 -4.338 Td [(+)-135(40)-136(+)-135(41)-278(=)]TJ -409.1 -14.446 Td [(40\05040\051)-247(+)-246(40)-247(+)-247(41)-339(=)-339(40\05040)-246(+)-247(1\051)-247(+)-247(41)-339(=)-339(40\05041\051)-246(+)-247(41)-362(also)-363(has)-362(41)-362(as)-363(a)-362(factor.)-543(It's)-363(a)-362(nift)27(y)-362(fact)]TJ 0 -14.446 Td [(that)-307(up)-306(to)-307(40,)-311(y)27(ou)-306(alw)27(a)27(ys)-307(do)-306(get)-307(primes.)-429(This)-307(is)-306(one)-307(of)-307(the)-307(nice)1(s)-1(t)-306(examples)-307(of)-307("just)-306(b)-28(ecause)]TJ 0 -14.445 Td [(it)-326(w)27(orks)-326(for)-327(lots)-326(of)-326(examples)-327(do)-27(esn't)-326(mean)-326(it's)-327(alw)27(a)28(ys)-327(true".)]TJ ET 1 0 0 1 89.559 604.513 cm EMC /P <> BDC 1 0 0 1 -89.559 -604.513 cm BT /F15 11.9552 Tf 89.559 604.513 Td [(6.11)-326(Dispro)27(v)27(e:)-435(An)-326(in)27(teger)]TJ/F18 11.9552 Tf 135.49 0 Td [(x)]TJ/F15 11.9552 Tf 10.555 0 Td [(is)-326(p)-28(osit)1(iv)27(e)-327(if)-326(and)-326(only)-327(if)]TJ/F18 11.9552 Tf 124.993 0 Td [(x)]TJ/F15 11.9552 Tf 9.309 0 Td [(+)-222(1)-327(is)-326(p)-27(ositiv)27(e.)]TJ ET 1 0 0 1 89.559 590.068 cm EMC /P <> BDC 1 0 0 1 -89.559 -590.068 cm BT /F15 11.9552 Tf 89.559 590.068 Td [(Consider)]TJ/F18 11.9552 Tf 50.178 0 Td [(x)]TJ/F15 11.9552 Tf 12.251 0 Td [(=)-468(0.)-771(This)-439(statemen)28(t)-439(sa)28(ys)-439(0)-438(is)-438(p)-28(ositiv)28(e)-439(if)]TJ/F18 11.9552 Tf 223.903 0 Td [(:)-167(:)-166(:)]TJ/F15 11.9552 Tf 20.973 0 Td [(1)-438(is)-439(p)-27(ositiv)27(e.)-438(Ho)27(w)28(ev)27(er,)-466(1)-439(is)]TJ -324.864 -14.446 Td [(p)-27(ositiv)27(e,)-326(but)-327(0)-326(is)-326(not.)]TJ ET 1 0 0 1 89.559 552.29 cm EMC /P <> BDC 1 0 0 1 -89.559 -552.29 cm BT /F15 11.9552 Tf 89.559 552.29 Td [([extra])-357(6.12)-356(A)-357(triangle)-357(with)-357(l)1(egs)-357(2)-357(and)-357(2)-357(h)1(as)-357(area)-357(2.)-526(So)-357(do)-27(es)-357(a)-357(triangle)-356(with)-357(legs)-357(1)-357(and)]TJ -17.559 -14.446 Td [(4.)-594(The)-380(h)28(yp)-27(oten)27(use)-380(of)-379(the)-379(\014rst)-380(triang)1(le)-380(has)-379(length)-380(2)]TJ/F21 11.9552 Tf 269.577 9.889 Td [(p)]TJ ET q 1 0 0 1 351.539 547.972 cm []0 d 0 J 0.478 w 0 0 m 5.853 0 l S Q BT /F15 11.9552 Tf 351.539 537.844 Td [(2,)-393(and)-379(the)-379(h)27(yp)-27(oten)27(use)-379(of)-380(the)-379(second)]TJ -279.539 -14.446 Td [(triangle)-467(is)]TJ/F21 11.9552 Tf 58.049 9.889 Td [(p)]TJ ET q 1 0 0 1 140.011 533.527 cm []0 d 0 J 0.478 w 0 0 m 11.706 0 l S Q BT /F15 11.9552 Tf 140.011 523.398 Td [(17.)-856(Since)-467(2)]TJ/F21 11.9552 Tf 63.291 9.889 Td [(p)]TJ ET q 1 0 0 1 213.265 533.527 cm []0 d 0 J 0.478 w 0 0 m 5.853 0 l S Q BT /F15 11.9552 Tf 213.265 523.398 Td [(2)]TJ/F18 11.9552 Tf 12.03 0 Td [(<)]TJ/F15 11.9552 Tf 15.281 0 Td [(4)]TJ/F18 11.9552 Tf 12.03 0 Td [(<)]TJ/F21 11.9552 Tf 15.282 9.889 Td [(p)]TJ ET q 1 0 0 1 277.85 533.527 cm []0 d 0 J 0.478 w 0 0 m 11.706 0 l S Q BT /F15 11.9552 Tf 277.85 523.398 Td [(17,)-502(w)27(e)-466(ha)27(v)27(e)-467(th)1(at)-467(2)]TJ/F21 11.9552 Tf 101.43 9.889 Td [(p)]TJ ET q 1 0 0 1 389.242 533.527 cm []0 d 0 J 0.478 w 0 0 m 5.853 0 l S Q BT /F15 11.9552 Tf 389.242 523.398 Td [(2)]TJ/F21 11.9552 Tf 12.03 0 Td [(6)]TJ/F15 11.9552 Tf 0 0 Td [(=)]TJ/F21 11.9552 Tf 15.282 9.889 Td [(p)]TJ ET q 1 0 0 1 426.517 533.527 cm []0 d 0 J 0.478 w 0 0 m 11.706 0 l S Q BT /F15 11.9552 Tf 426.517 523.398 Td [(17.)-856(This)-467(direction)-466(of)]TJ -354.517 -14.446 Td [(coun)27(terexample)-326(seems)-326(easier)-327(to)-326(me)-326(than)-326(the)-327(con)27(v)28(erse.)]TJ ET 1 0 0 1 89.559 494.506 cm EMC /P <> BDC 1 0 0 1 -89.559 -494.506 cm BT /F15 11.9552 Tf 89.559 494.506 Td [(T)82(o)-253(attempt)-253(the)-253(con)28(v)27(erse)-253(w)27(e)-253(seek)-252(t)27(w)27(o)-253(noncongruen)28(t)-253(triangles)-253(with)-253(congruen)28(t)-253(h)27(yp)-27(oten)27(uses.)]TJ -17.559 -14.446 Td [(Using)-291(similar)-290(n)27(um)27(b)-27(ers)-291(to)-290(the)-291(\014rst)-290(example,)-298(A)-291(triangle)-290(with)-291(legs)-290(1)-291(and)-291(2)-290(has)-291(h)27(yp)-27(oten)27(use)]TJ/F21 11.9552 Tf 448.933 9.89 Td [(p)]TJ ET q 1 0 0 1 530.895 490.189 cm []0 d 0 J 0.478 w 0 0 m 5.853 0 l S Q BT /F15 11.9552 Tf 530.895 480.06 Td [(5,)]TJ -458.895 -14.445 Td [(so)-373(do)-27(es)-373(one)-373(with)-373(legs)]TJ/F21 11.9552 Tf 114.52 9.889 Td [(p)]TJ ET q 1 0 0 1 196.483 475.743 cm []0 d 0 J 0.478 w 0 0 m 5.853 0 l S Q BT /F15 11.9552 Tf 196.483 465.615 Td [(2)-373(and)]TJ/F21 11.9552 Tf 33.633 9.889 Td [(p)]TJ ET q 1 0 0 1 240.079 475.743 cm []0 d 0 J 0.478 w 0 0 m 5.853 0 l S Q BT /F15 11.9552 Tf 240.079 465.615 Td [(3.)-575(The)-373(\014rst)-373(one)-373(has)-374(a)1(rea)-374(1.)-575(The)-373(second)-373(one)-373(has)-373(area)]TJ/F22 7.9701 Tf 284.183 11.317 Td [(p)]TJ ET q 1 0 0 1 531.319 477.111 cm []0 d 0 J 0.359 w 0 0 m 4.234 0 l S Q BT /F16 7.9701 Tf 531.319 470.334 Td [(6)]TJ ET q 1 0 0 1 524.262 468.603 cm []0 d 0 J 0.478 w 0 0 m 11.291 0 l S Q BT /F16 7.9701 Tf 527.79 461.492 Td [(2)]TJ/F15 11.9552 Tf 8.958 4.123 Td [(,)]TJ -464.748 -14.446 Td [(whic)27(h)-326(ma)27(y)-326(b)-27(e)-327(a)-326(somewhat)-326(m)27(ysterious)-326(n)27(um)27(b)-27(er,)-326(but)-327(is)-326(surely)-326(not)-327(equal)-326(to)-326(one.)]TJ ET 1 0 0 1 89.559 427.837 cm EMC /P <> BDC 1 0 0 1 -89.559 -427.837 cm BT /F15 11.9552 Tf 89.559 427.837 Td [(7.8.Pro)27(v)28(e:)-436(\050)]TJ/F18 11.9552 Tf 60.316 0 Td [(x)]TJ/F21 11.9552 Tf 9.309 0 Td [(_)]TJ/F18 11.9552 Tf 10.627 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(\051)]TJ/F21 11.9552 Tf 7.874 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 9.872 0 Td [(is)-326(logically)-327(equiv)55(alen)27(t)-326(to)-327(\050)]TJ/F18 11.9552 Tf 132.083 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 5.97 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(^)]TJ/F15 11.9552 Tf 10.627 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(y)]TJ/F21 11.9552 Tf 9.458 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 5.97 0 Td [(\051.)]TJ ET 1 0 0 1 72 418.034 cm EMC /TD <> BDC 1 0 0 1 135.22 -0.996 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 197.56 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -207.22 -416.639 cm BT /F18 11.9552 Tf 213.198 406.527 Td [(x)]TJ ET 1 0 0 1 223.752 406.527 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -235.707 -406.527 cm BT /F18 11.9552 Tf 239.609 406.527 Td [(y)]TJ ET 1 0 0 1 249.647 406.527 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.956 0 cm /TD <> BDC 1 0 0 1 -261.603 -406.527 cm BT /F18 11.9552 Tf 265.505 406.527 Td [(z)]TJ ET 1 0 0 1 275.377 406.527 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 13.948 0 cm /TD <> BDC 1 0 0 1 -289.325 -406.527 cm BT /F18 11.9552 Tf 293.227 406.527 Td [(x)]TJ/F21 11.9552 Tf 9.309 0 Td [(_)]TJ/F18 11.9552 Tf 10.626 0 Td [(y)]TJ ET 1 0 0 1 323.201 406.527 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -335.156 -406.527 cm BT /F15 11.9552 Tf 339.058 406.527 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.309 0 Td [(_)]TJ/F18 11.9552 Tf 10.627 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ/F21 11.9552 Tf 7.873 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ ET 1 0 0 1 398.802 406.527 cm EMC /TD <> BDC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -191.582 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 197.56 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -207.22 -401.795 cm BT /F15 11.9552 Tf 214.247 391.683 Td [(T)]TJ ET 1 0 0 1 222.702 391.683 cm EMC q 1 0 0 1 7.027 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 15.748 0 cm /TD <> BDC 1 0 0 1 -238.45 -391.683 cm BT /F15 11.9552 Tf 238.45 391.683 Td [(T)]TJ ET 1 0 0 1 246.904 391.683 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.359 0 cm /TD <> BDC 1 0 0 1 -264.263 -391.683 cm BT /F15 11.9552 Tf 264.263 391.683 Td [(T)]TJ ET 1 0 0 1 272.717 391.683 cm EMC q 1 0 0 1 8.638 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.63 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 29.319 0 cm /TD <> BDC 1 0 0 1 -302.036 -391.683 cm BT /F15 11.9552 Tf 302.036 391.683 Td [(T)]TJ ET 1 0 0 1 310.49 391.683 cm EMC q 1 0 0 1 18.689 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 50.311 0 cm /TD <> BDC 1 0 0 1 -360.801 -391.683 cm BT /F15 11.9552 Tf 360.801 391.683 Td [(T)]TJ ET 1 0 0 1 373.157 391.683 cm EMC /TD <> BDC q 1 0 0 1 31.623 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -165.937 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -373.157 -391.683 cm BT /F15 11.9552 Tf 214.247 377.237 Td [(T)]TJ ET 1 0 0 1 222.702 377.237 cm EMC q 1 0 0 1 7.027 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 15.748 0 cm /TD <> BDC 1 0 0 1 -238.45 -377.237 cm BT /F15 11.9552 Tf 238.45 377.237 Td [(T)]TJ ET 1 0 0 1 246.904 377.237 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.766 0 cm /TD <> BDC 1 0 0 1 -264.67 -377.237 cm BT /F15 11.9552 Tf 264.67 377.237 Td [(F)]TJ ET 1 0 0 1 272.31 377.237 cm EMC q 1 0 0 1 9.045 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.037 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 29.726 0 cm /TD <> BDC 1 0 0 1 -302.036 -377.237 cm BT /F15 11.9552 Tf 302.036 377.237 Td [(T)]TJ ET 1 0 0 1 310.49 377.237 cm EMC q 1 0 0 1 18.689 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 50.719 0 cm /TD <> BDC 1 0 0 1 -361.209 -377.237 cm BT /F15 11.9552 Tf 361.209 377.237 Td [(F)]TJ ET 1 0 0 1 372.75 377.237 cm EMC /TD <> BDC q 1 0 0 1 32.03 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -165.53 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -372.75 -377.237 cm BT /F15 11.9552 Tf 214.247 362.791 Td [(T)]TJ ET 1 0 0 1 222.702 362.791 cm EMC q 1 0 0 1 7.027 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.155 0 cm /TD <> BDC 1 0 0 1 -238.857 -362.791 cm BT /F15 11.9552 Tf 238.857 362.791 Td [(F)]TJ ET 1 0 0 1 246.497 362.791 cm EMC q 1 0 0 1 9.128 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.766 0 cm /TD <> BDC 1 0 0 1 -264.263 -362.791 cm BT /F15 11.9552 Tf 264.263 362.791 Td [(T)]TJ ET 1 0 0 1 272.717 362.791 cm EMC q 1 0 0 1 8.638 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.63 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 29.319 0 cm /TD <> BDC 1 0 0 1 -302.036 -362.791 cm BT /F15 11.9552 Tf 302.036 362.791 Td [(T)]TJ ET 1 0 0 1 310.49 362.791 cm EMC q 1 0 0 1 18.689 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 50.311 0 cm /TD <> BDC 1 0 0 1 -360.801 -362.791 cm BT /F15 11.9552 Tf 360.801 362.791 Td [(T)]TJ ET 1 0 0 1 373.157 362.791 cm EMC /TD <> BDC q 1 0 0 1 31.623 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -165.937 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -373.157 -362.791 cm BT /F15 11.9552 Tf 214.247 348.345 Td [(T)]TJ ET 1 0 0 1 222.702 348.345 cm EMC q 1 0 0 1 7.027 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.155 0 cm /TD <> BDC 1 0 0 1 -238.857 -348.345 cm BT /F15 11.9552 Tf 238.857 348.345 Td [(F)]TJ ET 1 0 0 1 246.497 348.345 cm EMC q 1 0 0 1 9.128 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 18.173 0 cm /TD <> BDC 1 0 0 1 -264.67 -348.345 cm BT /F15 11.9552 Tf 264.67 348.345 Td [(F)]TJ ET 1 0 0 1 272.31 348.345 cm EMC q 1 0 0 1 9.045 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.037 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 29.726 0 cm /TD <> BDC 1 0 0 1 -302.036 -348.345 cm BT /F15 11.9552 Tf 302.036 348.345 Td [(T)]TJ ET 1 0 0 1 310.49 348.345 cm EMC q 1 0 0 1 18.689 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 50.719 0 cm /TD <> BDC 1 0 0 1 -361.209 -348.345 cm BT /F15 11.9552 Tf 361.209 348.345 Td [(F)]TJ ET 1 0 0 1 372.75 348.345 cm EMC /TD <> BDC q 1 0 0 1 32.03 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -165.53 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -372.75 -348.345 cm BT /F15 11.9552 Tf 214.655 333.9 Td [(F)]TJ ET 1 0 0 1 222.294 333.9 cm EMC q 1 0 0 1 7.435 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.156 0 cm /TD <> BDC 1 0 0 1 -238.45 -333.9 cm BT /F15 11.9552 Tf 238.45 333.9 Td [(T)]TJ ET 1 0 0 1 246.904 333.9 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.359 0 cm /TD <> BDC 1 0 0 1 -264.263 -333.9 cm BT /F15 11.9552 Tf 264.263 333.9 Td [(T)]TJ ET 1 0 0 1 272.717 333.9 cm EMC q 1 0 0 1 8.638 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.63 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 29.319 0 cm /TD <> BDC 1 0 0 1 -302.036 -333.9 cm BT /F15 11.9552 Tf 302.036 333.9 Td [(T)]TJ ET 1 0 0 1 310.49 333.9 cm EMC q 1 0 0 1 18.689 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 50.311 0 cm /TD <> BDC 1 0 0 1 -360.801 -333.9 cm BT /F15 11.9552 Tf 360.801 333.9 Td [(T)]TJ ET 1 0 0 1 373.157 333.9 cm EMC /TD <> BDC q 1 0 0 1 31.623 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -165.937 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -373.157 -333.9 cm BT /F15 11.9552 Tf 214.655 319.454 Td [(F)]TJ ET 1 0 0 1 222.294 319.454 cm EMC q 1 0 0 1 7.435 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.156 0 cm /TD <> BDC 1 0 0 1 -238.45 -319.454 cm BT /F15 11.9552 Tf 238.45 319.454 Td [(T)]TJ ET 1 0 0 1 246.904 319.454 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.766 0 cm /TD <> BDC 1 0 0 1 -264.67 -319.454 cm BT /F15 11.9552 Tf 264.67 319.454 Td [(F)]TJ ET 1 0 0 1 272.309 319.454 cm EMC q 1 0 0 1 9.046 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.038 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 29.727 0 cm /TD <> BDC 1 0 0 1 -302.036 -319.454 cm BT /F15 11.9552 Tf 302.036 319.454 Td [(T)]TJ ET 1 0 0 1 310.49 319.454 cm EMC q 1 0 0 1 18.689 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 50.719 0 cm /TD <> BDC 1 0 0 1 -361.209 -319.454 cm BT /F15 11.9552 Tf 361.209 319.454 Td [(F)]TJ ET 1 0 0 1 372.75 319.454 cm EMC /TD <> BDC q 1 0 0 1 32.03 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -165.53 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -372.75 -319.454 cm BT /F15 11.9552 Tf 214.655 305.008 Td [(F)]TJ ET 1 0 0 1 222.294 305.008 cm EMC q 1 0 0 1 7.435 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.563 0 cm /TD <> BDC 1 0 0 1 -238.857 -305.008 cm BT /F15 11.9552 Tf 238.857 305.008 Td [(F)]TJ ET 1 0 0 1 246.497 305.008 cm EMC q 1 0 0 1 9.128 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.766 0 cm /TD <> BDC 1 0 0 1 -264.263 -305.008 cm BT /F15 11.9552 Tf 264.263 305.008 Td [(T)]TJ ET 1 0 0 1 272.717 305.008 cm EMC q 1 0 0 1 8.638 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.63 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 29.726 0 cm /TD <> BDC 1 0 0 1 -302.443 -305.008 cm BT /F15 11.9552 Tf 302.443 305.008 Td [(F)]TJ ET 1 0 0 1 310.083 305.008 cm EMC q 1 0 0 1 19.096 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 52.669 0 cm /TD <> BDC 1 0 0 1 -362.752 -305.008 cm BT /F15 11.9552 Tf 362.752 305.008 Td [(T)]TJ ET 1 0 0 1 371.206 305.008 cm EMC /TD <> BDC q 1 0 0 1 33.574 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -163.986 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -371.206 -305.008 cm BT /F15 11.9552 Tf 214.655 290.562 Td [(F)]TJ ET 1 0 0 1 222.294 290.562 cm EMC q 1 0 0 1 7.435 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.563 0 cm /TD <> BDC 1 0 0 1 -238.857 -290.562 cm BT /F15 11.9552 Tf 238.857 290.562 Td [(F)]TJ ET 1 0 0 1 246.497 290.562 cm EMC q 1 0 0 1 9.128 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 18.173 0 cm /TD <> BDC 1 0 0 1 -264.67 -290.562 cm BT /F15 11.9552 Tf 264.67 290.562 Td [(F)]TJ ET 1 0 0 1 272.31 290.562 cm EMC q 1 0 0 1 9.045 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.037 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 30.133 0 cm /TD <> BDC 1 0 0 1 -302.443 -290.562 cm BT /F15 11.9552 Tf 302.443 290.562 Td [(F)]TJ ET 1 0 0 1 310.083 290.562 cm EMC q 1 0 0 1 19.096 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 52.669 0 cm /TD <> BDC 1 0 0 1 -362.752 -290.562 cm BT /F15 11.9552 Tf 362.752 290.562 Td [(T)]TJ ET 1 0 0 1 371.206 290.562 cm EMC /TD <> BDC q 1 0 0 1 33.574 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -163.986 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 197.56 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 22.509 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 197.56 55.392 cm EMC 1 0 0 1 -332.78 -76.652 cm /TD <> BDC 1 0 0 1 91.628 -0.996 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 284.743 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -163.628 -263.175 cm BT /F18 11.9552 Tf 170.507 253.063 Td [(x)]TJ ET 1 0 0 1 177.159 253.063 cm EMC q 1 0 0 1 6.879 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.856 0 cm /TD <> BDC 1 0 0 1 -190.015 -253.063 cm BT /F18 11.9552 Tf 193.917 253.063 Td [(y)]TJ ET 1 0 0 1 203.956 253.063 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -215.911 -253.063 cm BT /F18 11.9552 Tf 219.813 253.063 Td [(z)]TJ ET 1 0 0 1 229.686 253.063 cm EMC q 1 0 0 1 5.977 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 13.948 0 cm /TD <> BDC 1 0 0 1 -243.634 -253.063 cm BT /F18 11.9552 Tf 247.536 253.063 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ ET 1 0 0 1 282.657 253.063 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -294.612 -253.063 cm BT /F18 11.9552 Tf 298.514 253.063 Td [(y)]TJ/F21 11.9552 Tf 9.458 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ ET 1 0 0 1 333.12 253.063 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.956 0 cm /TD <> BDC 1 0 0 1 -345.076 -253.063 cm BT /F15 11.9552 Tf 348.978 253.063 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 5.97 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(^)]TJ/F15 11.9552 Tf 10.627 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(y)]TJ/F21 11.9552 Tf 9.457 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 5.971 0 Td [(\051)]TJ ET 1 0 0 1 442.394 253.063 cm EMC /TD <> BDC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -278.766 -4.333 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 284.743 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -163.628 -248.331 cm BT /F15 11.9552 Tf 169.606 238.219 Td [(T)]TJ ET 1 0 0 1 178.06 238.219 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 14.699 0 cm /TD <> BDC 1 0 0 1 -192.759 -238.219 cm BT /F15 11.9552 Tf 192.759 238.219 Td [(T)]TJ ET 1 0 0 1 201.213 238.219 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.358 0 cm /TD <> BDC 1 0 0 1 -218.571 -238.219 cm BT /F15 11.9552 Tf 218.571 238.219 Td [(T)]TJ ET 1 0 0 1 227.026 238.219 cm EMC q 1 0 0 1 8.637 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.63 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 31.892 0 cm /TD <> BDC 1 0 0 1 -258.918 -238.219 cm BT /F15 11.9552 Tf 258.918 238.219 Td [(T)]TJ ET 1 0 0 1 267.373 238.219 cm EMC q 1 0 0 1 21.262 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 42.266 0 cm /TD <> BDC 1 0 0 1 -309.639 -238.219 cm BT /F15 11.9552 Tf 309.639 238.219 Td [(T)]TJ ET 1 0 0 1 318.093 238.219 cm EMC q 1 0 0 1 21.005 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 71.415 0 cm /TD <> BDC 1 0 0 1 -389.508 -238.219 cm BT /F15 11.9552 Tf 389.508 238.219 Td [(T)]TJ ET 1 0 0 1 397.962 238.219 cm EMC /TD <> BDC q 1 0 0 1 50.41 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -234.334 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -397.962 -238.219 cm BT /F15 11.9552 Tf 169.606 223.773 Td [(T)]TJ ET 1 0 0 1 178.06 223.773 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 14.699 0 cm /TD <> BDC 1 0 0 1 -192.759 -223.773 cm BT /F15 11.9552 Tf 192.759 223.773 Td [(T)]TJ ET 1 0 0 1 201.213 223.773 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.766 0 cm /TD <> BDC 1 0 0 1 -218.979 -223.773 cm BT /F15 11.9552 Tf 218.979 223.773 Td [(F)]TJ ET 1 0 0 1 226.618 223.773 cm EMC q 1 0 0 1 9.045 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.038 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 32.708 0 cm /TD <> BDC 1 0 0 1 -259.326 -223.773 cm BT /F15 11.9552 Tf 259.326 223.773 Td [(F)]TJ ET 1 0 0 1 266.965 223.773 cm EMC q 1 0 0 1 21.67 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 43.082 0 cm /TD <> BDC 1 0 0 1 -310.047 -223.773 cm BT /F15 11.9552 Tf 310.047 223.773 Td [(F)]TJ ET 1 0 0 1 317.686 223.773 cm EMC q 1 0 0 1 21.412 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 72.229 0 cm /TD <> BDC 1 0 0 1 -389.915 -223.773 cm BT /F15 11.9552 Tf 389.915 223.773 Td [(F)]TJ ET 1 0 0 1 397.554 223.773 cm EMC /TD <> BDC q 1 0 0 1 50.818 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -233.926 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -397.554 -223.773 cm BT /F15 11.9552 Tf 169.606 209.327 Td [(T)]TJ ET 1 0 0 1 178.06 209.327 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 15.106 0 cm /TD <> BDC 1 0 0 1 -193.166 -209.327 cm BT /F15 11.9552 Tf 193.166 209.327 Td [(F)]TJ ET 1 0 0 1 200.805 209.327 cm EMC q 1 0 0 1 9.129 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.766 0 cm /TD <> BDC 1 0 0 1 -218.571 -209.327 cm BT /F15 11.9552 Tf 218.571 209.327 Td [(T)]TJ ET 1 0 0 1 227.026 209.327 cm EMC q 1 0 0 1 8.637 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.63 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 31.892 0 cm /TD <> BDC 1 0 0 1 -258.918 -209.327 cm BT /F15 11.9552 Tf 258.918 209.327 Td [(T)]TJ ET 1 0 0 1 267.373 209.327 cm EMC q 1 0 0 1 21.262 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 42.266 0 cm /TD <> BDC 1 0 0 1 -309.639 -209.327 cm BT /F15 11.9552 Tf 309.639 209.327 Td [(T)]TJ ET 1 0 0 1 318.093 209.327 cm EMC q 1 0 0 1 21.005 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 71.415 0 cm /TD <> BDC 1 0 0 1 -389.508 -209.327 cm BT /F15 11.9552 Tf 389.508 209.327 Td [(T)]TJ ET 1 0 0 1 397.962 209.327 cm EMC /TD <> BDC q 1 0 0 1 50.41 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -234.334 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -397.962 -209.327 cm BT /F15 11.9552 Tf 169.606 194.882 Td [(T)]TJ ET 1 0 0 1 178.06 194.882 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 15.106 0 cm /TD <> BDC 1 0 0 1 -193.166 -194.882 cm BT /F15 11.9552 Tf 193.166 194.882 Td [(F)]TJ ET 1 0 0 1 200.805 194.882 cm EMC q 1 0 0 1 9.129 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 18.174 0 cm /TD <> BDC 1 0 0 1 -218.979 -194.882 cm BT /F15 11.9552 Tf 218.979 194.882 Td [(F)]TJ ET 1 0 0 1 226.618 194.882 cm EMC q 1 0 0 1 9.045 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.038 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 32.708 0 cm /TD <> BDC 1 0 0 1 -259.326 -194.882 cm BT /F15 11.9552 Tf 259.326 194.882 Td [(F)]TJ ET 1 0 0 1 266.965 194.882 cm EMC q 1 0 0 1 21.67 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 42.674 0 cm /TD <> BDC 1 0 0 1 -309.639 -194.882 cm BT /F15 11.9552 Tf 309.639 194.882 Td [(T)]TJ ET 1 0 0 1 318.093 194.882 cm EMC q 1 0 0 1 21.005 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 71.822 0 cm /TD <> BDC 1 0 0 1 -389.915 -194.882 cm BT /F15 11.9552 Tf 389.915 194.882 Td [(F)]TJ ET 1 0 0 1 397.554 194.882 cm EMC /TD <> BDC q 1 0 0 1 50.818 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -233.926 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -397.554 -194.882 cm BT /F15 11.9552 Tf 170.013 180.436 Td [(F)]TJ ET 1 0 0 1 177.653 180.436 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 15.106 0 cm /TD <> BDC 1 0 0 1 -192.759 -180.436 cm BT /F15 11.9552 Tf 192.759 180.436 Td [(T)]TJ ET 1 0 0 1 201.213 180.436 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.358 0 cm /TD <> BDC 1 0 0 1 -218.571 -180.436 cm BT /F15 11.9552 Tf 218.571 180.436 Td [(T)]TJ ET 1 0 0 1 227.026 180.436 cm EMC q 1 0 0 1 8.637 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.63 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 31.892 0 cm /TD <> BDC 1 0 0 1 -258.918 -180.436 cm BT /F15 11.9552 Tf 258.918 180.436 Td [(T)]TJ ET 1 0 0 1 267.373 180.436 cm EMC q 1 0 0 1 21.262 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 42.266 0 cm /TD <> BDC 1 0 0 1 -309.639 -180.436 cm BT /F15 11.9552 Tf 309.639 180.436 Td [(T)]TJ ET 1 0 0 1 318.093 180.436 cm EMC q 1 0 0 1 21.005 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 71.415 0 cm /TD <> BDC 1 0 0 1 -389.508 -180.436 cm BT /F15 11.9552 Tf 389.508 180.436 Td [(T)]TJ ET 1 0 0 1 397.962 180.436 cm EMC /TD <> BDC q 1 0 0 1 50.41 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -234.334 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -397.962 -180.436 cm BT /F15 11.9552 Tf 170.014 165.99 Td [(F)]TJ ET 1 0 0 1 177.653 165.99 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 15.106 0 cm /TD <> BDC 1 0 0 1 -192.759 -165.99 cm BT /F15 11.9552 Tf 192.759 165.99 Td [(T)]TJ ET 1 0 0 1 201.213 165.99 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.766 0 cm /TD <> BDC 1 0 0 1 -218.979 -165.99 cm BT /F15 11.9552 Tf 218.979 165.99 Td [(F)]TJ ET 1 0 0 1 226.618 165.99 cm EMC q 1 0 0 1 9.045 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.038 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 32.3 0 cm /TD <> BDC 1 0 0 1 -258.918 -165.99 cm BT /F15 11.9552 Tf 258.918 165.99 Td [(T)]TJ ET 1 0 0 1 267.373 165.99 cm EMC q 1 0 0 1 21.262 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 42.674 0 cm /TD <> BDC 1 0 0 1 -310.047 -165.99 cm BT /F15 11.9552 Tf 310.047 165.99 Td [(F)]TJ ET 1 0 0 1 317.686 165.99 cm EMC q 1 0 0 1 21.412 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 72.229 0 cm /TD <> BDC 1 0 0 1 -389.915 -165.99 cm BT /F15 11.9552 Tf 389.915 165.99 Td [(F)]TJ ET 1 0 0 1 397.554 165.99 cm EMC /TD <> BDC q 1 0 0 1 50.818 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -233.926 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -397.554 -165.99 cm BT /F15 11.9552 Tf 170.014 151.544 Td [(F)]TJ ET 1 0 0 1 177.653 151.544 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 15.513 0 cm /TD <> BDC 1 0 0 1 -193.166 -151.544 cm BT /F15 11.9552 Tf 193.166 151.544 Td [(F)]TJ ET 1 0 0 1 200.805 151.544 cm EMC q 1 0 0 1 9.129 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.766 0 cm /TD <> BDC 1 0 0 1 -218.571 -151.544 cm BT /F15 11.9552 Tf 218.571 151.544 Td [(T)]TJ ET 1 0 0 1 227.026 151.544 cm EMC q 1 0 0 1 8.637 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.63 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 31.892 0 cm /TD <> BDC 1 0 0 1 -258.918 -151.544 cm BT /F15 11.9552 Tf 258.918 151.544 Td [(T)]TJ ET 1 0 0 1 267.373 151.544 cm EMC q 1 0 0 1 21.262 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 42.266 0 cm /TD <> BDC 1 0 0 1 -309.639 -151.544 cm BT /F15 11.9552 Tf 309.639 151.544 Td [(T)]TJ ET 1 0 0 1 318.093 151.544 cm EMC q 1 0 0 1 21.005 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 71.415 0 cm /TD <> BDC 1 0 0 1 -389.508 -151.544 cm BT /F15 11.9552 Tf 389.508 151.544 Td [(T)]TJ ET 1 0 0 1 397.962 151.544 cm EMC /TD <> BDC q 1 0 0 1 50.41 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -234.334 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -397.962 -151.544 cm BT /F15 11.9552 Tf 170.014 137.098 Td [(F)]TJ ET 1 0 0 1 177.653 137.098 cm EMC q 1 0 0 1 6.385 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 15.513 0 cm /TD <> BDC 1 0 0 1 -193.166 -137.098 cm BT /F15 11.9552 Tf 193.166 137.098 Td [(F)]TJ ET 1 0 0 1 200.805 137.098 cm EMC q 1 0 0 1 9.129 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 18.174 0 cm /TD <> BDC 1 0 0 1 -218.979 -137.098 cm BT /F15 11.9552 Tf 218.979 137.098 Td [(F)]TJ ET 1 0 0 1 226.618 137.098 cm EMC q 1 0 0 1 9.045 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.038 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 32.3 0 cm /TD <> BDC 1 0 0 1 -258.918 -137.098 cm BT /F15 11.9552 Tf 258.918 137.098 Td [(T)]TJ ET 1 0 0 1 267.373 137.098 cm EMC q 1 0 0 1 21.262 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 42.266 0 cm /TD <> BDC 1 0 0 1 -309.639 -137.098 cm BT /F15 11.9552 Tf 309.639 137.098 Td [(T)]TJ ET 1 0 0 1 318.093 137.098 cm EMC q 1 0 0 1 21.005 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 71.415 0 cm /TD <> BDC 1 0 0 1 -389.508 -137.098 cm BT /F15 11.9552 Tf 389.508 137.098 Td [(T)]TJ ET 1 0 0 1 397.962 137.098 cm EMC /TD <> BDC q 1 0 0 1 50.41 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -234.334 -4.333 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 284.743 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 20.41 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 284.744 55.392 cm EMC 1 0 0 1 -358.813 -85.95 cm /P <> BDC 1 0 0 1 -89.559 -101.808 cm BT /F15 11.9552 Tf 89.559 101.808 Td [(Notice)-326(the)-327(t)28(w)27(o)-327(state)1(men)27(ts)-327(are)-326(true)-326(and)-327(fa)1(lse)-327(under)-326(iden)27(tical)-326(conditions.)]TJ ET 1 0 0 1 89.559 78.476 cm EMC /P <> BDC 1 0 0 1 -89.559 -78.476 cm BT /F15 11.9552 Tf 89.559 78.476 Td [(7.11)-322(Explain)-322(ho)27(w)-322(to)-322(use)-322(a)-322(truth)-322(table)-322(to)-322(pro)27(v)27(e)-322(that)-322(a)-322(Bo)-27(olean)-322(expression)-322(is)-322(a)-322(tautology)82(.)]TJ ET 1 0 0 1 89.559 64.03 cm EMC /P <> BDC 1 0 0 1 -89.559 -64.03 cm BT /F15 11.9552 Tf 89.559 64.03 Td [(Sho)27(w)-326(that)-326(under)-327(all)-326(conditions)-326(the)-327(ex)1(pression)-327(ev)55(aluates)-327(to)-326(TR)27(UE.)]TJ ET 1 0 0 1 89.559 49.584 cm EMC /P <> BDC 1 0 0 1 -89.559 -49.584 cm BT /F15 11.9552 Tf 89.559 49.584 Td [(Pro)27(v)27(e)-326(the)-326(follo)27(wing)-326(are)-327(tau)1(tologies:)]TJ ET 1 0 0 1 89.559 35.138 cm EMC /P <> BDC 1 0 0 1 -89.559 -35.138 cm BT /F15 11.9552 Tf 89.559 35.138 Td [(\050a\051)-326(\050)]TJ/F18 11.9552 Tf 23.412 0 Td [(x)]TJ/F21 11.9552 Tf 9.309 0 Td [(_)]TJ/F18 11.9552 Tf 10.626 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(_)]TJ/F15 11.9552 Tf 10.627 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.309 0 Td [(_)-222(:)]TJ/F18 11.9552 Tf 18.597 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ ET 1 0 0 1 72 35.138 cm EMC endstream endobj 223 0 obj << /Type /ObjStm /N 100 /First 893 /Length 11511 >> stream 222 0 224 109 225 218 226 327 227 436 228 545 221 654 230 772 231 881 232 990 233 1099 234 1208 235 1317 229 1426 237 1544 238 1653 239 1762 240 1871 241 1980 242 2089 236 2198 244 2316 245 2425 246 2534 247 2643 248 2752 249 2861 243 2970 251 3088 250 3197 212 3275 211 3396 74 3475 254 3580 252 3632 256 3747 260 3851 261 3960 262 4069 263 4178 264 4287 259 4396 266 4506 267 4615 268 4724 269 4833 270 4942 265 5051 272 5161 273 5270 274 5379 275 5488 276 5597 271 5706 278 5816 279 5925 280 6034 281 6143 282 6252 277 6361 284 6471 285 6580 286 6689 287 6798 288 6907 283 7016 290 7126 289 7235 258 7313 257 7434 291 7513 295 7617 296 7726 297 7835 298 7944 294 8053 300 8155 301 8264 302 8373 303 8482 299 8591 305 8693 306 8802 307 8911 308 9020 304 9129 310 9231 309 9340 293 9418 292 9523 311 9602 315 9706 316 9815 314 9924 318 10010 319 10119 317 10228 321 10314 322 10423 320 10532 % 222 0 obj <>] /S /TD >> % 224 0 obj <>] /S /TD >> % 225 0 obj <>] /S /TD >> % 226 0 obj <>] /S /TD >> % 227 0 obj <>] /S /TD >> % 228 0 obj <>] /S /TD >> % 221 0 obj <> % 230 0 obj <>] /S /TD >> % 231 0 obj <>] /S /TD >> % 232 0 obj <>] /S /TD >> % 233 0 obj <>] /S /TD >> % 234 0 obj <>] /S /TD >> % 235 0 obj <>] /S /TD >> % 229 0 obj <> % 237 0 obj <>] /S /TD >> % 238 0 obj <>] /S /TD >> % 239 0 obj <>] /S /TD >> % 240 0 obj <>] /S /TD >> % 241 0 obj <>] /S /TD >> % 242 0 obj <>] /S /TD >> % 236 0 obj <> % 244 0 obj <>] /S /TD >> % 245 0 obj <>] /S /TD >> % 246 0 obj <>] /S /TD >> % 247 0 obj <>] /S /TD >> % 248 0 obj <>] /S /TD >> % 249 0 obj <>] /S /TD >> % 243 0 obj <> % 251 0 obj <>] /S /TD >> % 250 0 obj <> % 212 0 obj <> % 211 0 obj <> % 74 0 obj << /Type /Page /Contents 253 0 R /Resources 252 0 R /MediaBox [0 0 612 792] /Parent 31 0 R >> % 254 0 obj << /D [74 0 R /XYZ 110.851 721 null] >> % 252 0 obj << /Font << /F15 24 0 R /F18 26 0 R /F16 28 0 R /F21 25 0 R /F22 255 0 R >> /ProcSet [ /PDF /Text ] >> % 256 0 obj <>] /S /P >> % 260 0 obj <>] /S /TD >> % 261 0 obj <>] /S /TD >> % 262 0 obj <>] /S /TD >> % 263 0 obj <>] /S /TD >> % 264 0 obj <>] /S /TD >> % 259 0 obj <> % 266 0 obj <>] /S /TD >> % 267 0 obj <>] /S /TD >> % 268 0 obj <>] /S /TD >> % 269 0 obj <>] /S /TD >> % 270 0 obj <>] /S /TD >> % 265 0 obj <> % 272 0 obj <>] /S /TD >> % 273 0 obj <>] /S /TD >> % 274 0 obj <>] /S /TD >> % 275 0 obj <>] /S /TD >> % 276 0 obj <>] /S /TD >> % 271 0 obj <> % 278 0 obj <>] /S /TD >> % 279 0 obj <>] /S /TD >> % 280 0 obj <>] /S /TD >> % 281 0 obj <>] /S /TD >> % 282 0 obj <>] /S /TD >> % 277 0 obj <> % 284 0 obj <>] /S /TD >> % 285 0 obj <>] /S /TD >> % 286 0 obj <>] /S /TD >> % 287 0 obj <>] /S /TD >> % 288 0 obj <>] /S /TD >> % 283 0 obj <> % 290 0 obj <>] /S /TD >> % 289 0 obj <> % 258 0 obj <> % 257 0 obj <> % 291 0 obj <>] /S /P >> % 295 0 obj <>] /S /TD >> % 296 0 obj <>] /S /TD >> % 297 0 obj <>] /S /TD >> % 298 0 obj <>] /S /TD >> % 294 0 obj <> % 300 0 obj <>] /S /TD >> % 301 0 obj <>] /S /TD >> % 302 0 obj <>] /S /TD >> % 303 0 obj <>] /S /TD >> % 299 0 obj <> % 305 0 obj <>] /S /TD >> % 306 0 obj <>] /S /TD >> % 307 0 obj <>] /S /TD >> % 308 0 obj <>] /S /TD >> % 304 0 obj <> % 310 0 obj <>] /S /TD >> % 309 0 obj <> % 293 0 obj <> % 292 0 obj <> % 311 0 obj <>] /S /P >> % 315 0 obj <>] /S /TD >> % 316 0 obj <>] /S /TD >> % 314 0 obj <> % 318 0 obj <>] /S /TD >> % 319 0 obj <>] /S /TD >> % 317 0 obj <> % 321 0 obj <>] /S /TD >> % 322 0 obj <>] /S /TD >> % 320 0 obj <> endstream endobj 325 0 obj << /Type /ObjStm /N 100 /First 897 /Length 11861 >> stream 324 0 323 109 313 187 312 292 326 371 330 475 331 584 332 693 333 802 334 911 335 1020 336 1129 337 1238 329 1347 339 1481 340 1590 341 1699 342 1808 343 1917 344 2026 345 2135 346 2244 338 2353 348 2487 349 2596 350 2705 351 2814 352 2923 353 3032 354 3141 355 3250 347 3359 357 3493 358 3602 359 3711 360 3820 361 3929 362 4038 363 4147 364 4256 356 4365 366 4499 367 4608 368 4717 369 4826 370 4935 371 5044 372 5153 373 5262 365 5371 375 5505 376 5614 377 5723 378 5832 379 5941 380 6050 381 6159 382 6268 374 6377 384 6511 385 6620 386 6729 387 6838 388 6947 389 7056 390 7165 391 7274 383 7383 393 7517 394 7626 395 7735 396 7844 397 7953 398 8062 399 8171 400 8280 392 8389 402 8523 403 8632 404 8741 405 8850 406 8959 407 9068 408 9177 409 9286 401 9395 411 9529 410 9638 328 9716 327 9869 412 9948 416 10052 417 10161 415 10270 419 10356 420 10465 418 10574 422 10660 423 10769 421 10878 % 324 0 obj <>] /S /TD >> % 323 0 obj <> % 313 0 obj <> % 312 0 obj <> % 326 0 obj <>] /S /P >> % 330 0 obj <>] /S /TD >> % 331 0 obj <>] /S /TD >> % 332 0 obj <>] /S /TD >> % 333 0 obj <>] /S /TD >> % 334 0 obj <>] /S /TD >> % 335 0 obj <>] /S /TD >> % 336 0 obj <>] /S /TD >> % 337 0 obj <>] /S /TD >> % 329 0 obj <> % 339 0 obj <>] /S /TD >> % 340 0 obj <>] /S /TD >> % 341 0 obj <>] /S /TD >> % 342 0 obj <>] /S /TD >> % 343 0 obj <>] /S /TD >> % 344 0 obj <>] /S /TD >> % 345 0 obj <>] /S /TD >> % 346 0 obj <>] /S /TD >> % 338 0 obj <> % 348 0 obj <>] /S /TD >> % 349 0 obj <>] /S /TD >> % 350 0 obj <>] /S /TD >> % 351 0 obj <>] /S /TD >> % 352 0 obj <>] /S /TD >> % 353 0 obj <>] /S /TD >> % 354 0 obj <>] /S /TD >> % 355 0 obj <>] /S /TD >> % 347 0 obj <> % 357 0 obj <>] /S /TD >> % 358 0 obj <>] /S /TD >> % 359 0 obj <>] /S /TD >> % 360 0 obj <>] /S /TD >> % 361 0 obj <>] /S /TD >> % 362 0 obj <>] /S /TD >> % 363 0 obj <>] /S /TD >> % 364 0 obj <>] /S /TD >> % 356 0 obj <> % 366 0 obj <>] /S /TD >> % 367 0 obj <>] /S /TD >> % 368 0 obj <>] /S /TD >> % 369 0 obj <>] /S /TD >> % 370 0 obj <>] /S /TD >> % 371 0 obj <>] /S /TD >> % 372 0 obj <>] /S /TD >> % 373 0 obj <>] /S /TD >> % 365 0 obj <> % 375 0 obj <>] /S /TD >> % 376 0 obj <>] /S /TD >> % 377 0 obj <>] /S /TD >> % 378 0 obj <>] /S /TD >> % 379 0 obj <>] /S /TD >> % 380 0 obj <>] /S /TD >> % 381 0 obj <>] /S /TD >> % 382 0 obj <>] /S /TD >> % 374 0 obj <> % 384 0 obj <>] /S /TD >> % 385 0 obj <>] /S /TD >> % 386 0 obj <>] /S /TD >> % 387 0 obj <>] /S /TD >> % 388 0 obj <>] /S /TD >> % 389 0 obj <>] /S /TD >> % 390 0 obj <>] /S /TD >> % 391 0 obj <>] /S /TD >> % 383 0 obj <> % 393 0 obj <>] /S /TD >> % 394 0 obj <>] /S /TD >> % 395 0 obj <>] /S /TD >> % 396 0 obj <>] /S /TD >> % 397 0 obj <>] /S /TD >> % 398 0 obj <>] /S /TD >> % 399 0 obj <>] /S /TD >> % 400 0 obj <>] /S /TD >> % 392 0 obj <> % 402 0 obj <>] /S /TD >> % 403 0 obj <>] /S /TD >> % 404 0 obj <>] /S /TD >> % 405 0 obj <>] /S /TD >> % 406 0 obj <>] /S /TD >> % 407 0 obj <>] /S /TD >> % 408 0 obj <>] /S /TD >> % 409 0 obj <>] /S /TD >> % 401 0 obj <> % 411 0 obj <>] /S /TD >> % 410 0 obj <> % 328 0 obj <> % 327 0 obj <> % 412 0 obj <>] /S /P >> % 416 0 obj <>] /S /TD >> % 417 0 obj <>] /S /TD >> % 415 0 obj <> % 419 0 obj <>] /S /TD >> % 420 0 obj <>] /S /TD >> % 418 0 obj <> % 422 0 obj <>] /S /TD >> % 423 0 obj <>] /S /TD >> % 421 0 obj <> endstream endobj 449 0 obj << /Length 44553 >> stream 1 0 0 1 72 683.138 cm /P <> BDC /TD <> BDC 1 0 0 1 85.468 0 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 297.065 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -157.468 -682.74 cm BT /F18 11.9552 Tf 164.346 672.628 Td [(x)]TJ ET 1 0 0 1 174.9 672.628 cm EMC q 1 0 0 1 6.879 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.857 0 cm /TD <> BDC 1 0 0 1 -187.757 -672.628 cm BT /F18 11.9552 Tf 191.659 672.628 Td [(y)]TJ ET 1 0 0 1 201.697 672.628 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 13.948 0 cm /TD <> BDC 1 0 0 1 -215.645 -672.628 cm BT /F18 11.9552 Tf 219.547 672.628 Td [(x)]TJ/F21 11.9552 Tf 9.309 0 Td [(_)]TJ/F18 11.9552 Tf 10.626 0 Td [(y)]TJ ET 1 0 0 1 249.521 672.628 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -261.476 -672.628 cm BT /F21 11.9552 Tf 265.378 672.628 Td [(:)]TJ/F18 11.9552 Tf 7.97 0 Td [(y)]TJ ET 1 0 0 1 283.387 672.628 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -295.342 -672.628 cm BT /F18 11.9552 Tf 299.244 672.628 Td [(x)]TJ/F21 11.9552 Tf 9.309 0 Td [(_)-222(:)]TJ/F18 11.9552 Tf 18.597 0 Td [(y)]TJ ET 1 0 0 1 337.188 672.628 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.956 0 cm /TD <> BDC 1 0 0 1 -349.144 -672.628 cm BT /F15 11.9552 Tf 353.046 672.628 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.309 0 Td [(_)]TJ/F18 11.9552 Tf 10.627 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(_)]TJ/F15 11.9552 Tf 10.627 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.309 0 Td [(_)-222(:)]TJ/F18 11.9552 Tf 18.597 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ ET 1 0 0 1 448.555 672.628 cm EMC /TD <> BDC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -291.087 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 297.065 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -157.468 -667.895 cm BT /F15 11.9552 Tf 163.445 657.783 Td [(T)]TJ ET 1 0 0 1 175.801 657.783 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.748 0 cm /TD <> BDC 1 0 0 1 -188.549 -657.783 cm BT /F15 11.9552 Tf 192.451 657.783 Td [(T)]TJ ET 1 0 0 1 200.905 657.783 cm EMC q 1 0 0 1 6.77 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.762 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 25.5 0 cm /TD <> BDC 1 0 0 1 -226.405 -657.783 cm BT /F15 11.9552 Tf 230.307 657.783 Td [(T)]TJ ET 1 0 0 1 238.761 657.783 cm EMC q 1 0 0 1 16.738 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 27.9 0 cm /TD <> BDC 1 0 0 1 -266.661 -657.783 cm BT /F15 11.9552 Tf 270.563 657.783 Td [(F)]TJ ET 1 0 0 1 278.202 657.783 cm EMC q 1 0 0 1 11.163 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 33.836 0 cm /TD <> BDC 1 0 0 1 -312.038 -657.783 cm BT /F15 11.9552 Tf 312.038 657.783 Td [(T)]TJ ET 1 0 0 1 320.492 657.783 cm EMC q 1 0 0 1 22.674 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 74.13 0 cm /TD <> BDC 1 0 0 1 -394.622 -657.783 cm BT /F15 11.9552 Tf 394.622 657.783 Td [(T)]TJ ET 1 0 0 1 403.076 657.783 cm EMC /TD <> BDC q 1 0 0 1 51.456 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -245.608 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -403.076 -657.783 cm BT /F15 11.9552 Tf 165.396 643.338 Td [(T)]TJ ET 1 0 0 1 173.85 643.338 cm EMC q 1 0 0 1 7.929 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.057 0 cm /TD <> BDC 1 0 0 1 -190.907 -643.338 cm BT /F15 11.9552 Tf 190.907 643.338 Td [(F)]TJ ET 1 0 0 1 198.547 643.338 cm EMC q 1 0 0 1 9.128 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.12 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 29.809 0 cm /TD <> BDC 1 0 0 1 -228.356 -643.338 cm BT /F15 11.9552 Tf 228.356 643.338 Td [(T)]TJ ET 1 0 0 1 236.81 643.338 cm EMC q 1 0 0 1 18.689 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 31.394 0 cm /TD <> BDC 1 0 0 1 -268.204 -643.338 cm BT /F15 11.9552 Tf 268.204 643.338 Td [(T)]TJ ET 1 0 0 1 276.659 643.338 cm EMC q 1 0 0 1 12.706 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 35.379 0 cm /TD <> BDC 1 0 0 1 -312.038 -643.338 cm BT /F15 11.9552 Tf 312.038 643.338 Td [(T)]TJ ET 1 0 0 1 320.492 643.338 cm EMC q 1 0 0 1 22.674 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 74.13 0 cm /TD <> BDC 1 0 0 1 -394.622 -643.338 cm BT /F15 11.9552 Tf 394.622 643.338 Td [(T)]TJ ET 1 0 0 1 403.076 643.338 cm EMC /TD <> BDC q 1 0 0 1 51.456 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -245.608 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -403.076 -643.338 cm BT /F15 11.9552 Tf 165.804 628.892 Td [(F)]TJ ET 1 0 0 1 173.443 628.892 cm EMC q 1 0 0 1 8.336 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.057 0 cm /TD <> BDC 1 0 0 1 -190.5 -628.892 cm BT /F15 11.9552 Tf 190.5 628.892 Td [(T)]TJ ET 1 0 0 1 198.954 628.892 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.713 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 29.402 0 cm /TD <> BDC 1 0 0 1 -228.356 -628.892 cm BT /F15 11.9552 Tf 228.356 628.892 Td [(T)]TJ ET 1 0 0 1 236.81 628.892 cm EMC q 1 0 0 1 18.689 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 31.802 0 cm /TD <> BDC 1 0 0 1 -268.612 -628.892 cm BT /F15 11.9552 Tf 268.612 628.892 Td [(F)]TJ ET 1 0 0 1 276.251 628.892 cm EMC q 1 0 0 1 13.114 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 36.195 0 cm /TD <> BDC 1 0 0 1 -312.446 -628.892 cm BT /F15 11.9552 Tf 312.446 628.892 Td [(F)]TJ ET 1 0 0 1 320.085 628.892 cm EMC q 1 0 0 1 23.081 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 74.537 0 cm /TD <> BDC 1 0 0 1 -394.622 -628.892 cm BT /F15 11.9552 Tf 394.622 628.892 Td [(T)]TJ ET 1 0 0 1 403.076 628.892 cm EMC /TD <> BDC q 1 0 0 1 51.456 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -245.608 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -403.076 -628.892 cm BT /F15 11.9552 Tf 165.804 614.446 Td [(F)]TJ ET 1 0 0 1 173.443 614.446 cm EMC q 1 0 0 1 8.336 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.464 0 cm /TD <> BDC 1 0 0 1 -190.907 -614.446 cm BT /F15 11.9552 Tf 190.907 614.446 Td [(F)]TJ ET 1 0 0 1 198.547 614.446 cm EMC q 1 0 0 1 9.128 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.12 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 30.216 0 cm /TD <> BDC 1 0 0 1 -228.763 -614.446 cm BT /F15 11.9552 Tf 228.763 614.446 Td [(F)]TJ ET 1 0 0 1 236.403 614.446 cm EMC q 1 0 0 1 19.096 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 31.801 0 cm /TD <> BDC 1 0 0 1 -268.204 -614.446 cm BT /F15 11.9552 Tf 268.204 614.446 Td [(T)]TJ ET 1 0 0 1 276.659 614.446 cm EMC q 1 0 0 1 12.706 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 35.379 0 cm /TD <> BDC 1 0 0 1 -312.038 -614.446 cm BT /F15 11.9552 Tf 312.038 614.446 Td [(T)]TJ ET 1 0 0 1 320.492 614.446 cm EMC q 1 0 0 1 22.674 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 74.13 0 cm /TD <> BDC 1 0 0 1 -394.622 -614.446 cm BT /F15 11.9552 Tf 394.622 614.446 Td [(T)]TJ ET 1 0 0 1 403.076 614.446 cm EMC /TD <> BDC q 1 0 0 1 51.456 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -245.608 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 297.065 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 24.311 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 297.064 26.5 cm EMC 1 0 0 1 -364.973 -58.354 cm EMC /P <> BDC 1 0 0 1 -89.559 -577.86 cm BT /F15 11.9552 Tf 89.559 577.86 Td [(\050b\051)-326(\050)]TJ/F18 11.9552 Tf 24.062 0 Td [(x)]TJ/F21 11.9552 Tf 9.309 0 Td [(^)]TJ/F15 11.9552 Tf 10.627 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051\051)]TJ/F21 11.9552 Tf 12.425 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ ET 1 0 0 1 72 567.426 cm EMC /TD <> BDC 1 0 0 1 88.076 -0.996 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 291.848 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -160.076 -566.031 cm BT /F18 11.9552 Tf 166.053 555.919 Td [(x)]TJ ET 1 0 0 1 176.607 555.919 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.956 0 cm /TD <> BDC 1 0 0 1 -188.563 -555.919 cm BT /F18 11.9552 Tf 192.465 555.919 Td [(y)]TJ ET 1 0 0 1 202.503 555.919 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 13.948 0 cm /TD <> BDC 1 0 0 1 -216.451 -555.919 cm BT /F18 11.9552 Tf 220.353 555.919 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ ET 1 0 0 1 255.641 555.919 cm EMC q 1 0 0 1 5.977 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -267.596 -555.919 cm BT /F18 11.9552 Tf 271.498 555.919 Td [(x)]TJ/F21 11.9552 Tf 9.308 0 Td [(^)]TJ/F15 11.9552 Tf 10.627 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(\051)]TJ ET 1 0 0 1 335.826 555.919 cm EMC q 1 0 0 1 5.977 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -347.781 -555.919 cm BT /F15 11.9552 Tf 351.683 555.919 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.309 0 Td [(^)]TJ/F15 11.9552 Tf 10.627 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051\051)]TJ/F21 11.9552 Tf 12.425 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ ET 1 0 0 1 445.947 555.919 cm EMC /TD <> BDC q 1 0 0 1 5.977 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -285.871 -4.333 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 291.848 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -160.076 -551.187 cm BT /F15 11.9552 Tf 167.103 541.075 Td [(T)]TJ ET 1 0 0 1 175.558 541.075 cm EMC q 1 0 0 1 7.027 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 15.748 0 cm /TD <> BDC 1 0 0 1 -191.306 -541.075 cm BT /F15 11.9552 Tf 191.306 541.075 Td [(T)]TJ ET 1 0 0 1 199.76 541.075 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.713 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 32.059 0 cm /TD <> BDC 1 0 0 1 -231.819 -541.075 cm BT /F15 11.9552 Tf 231.819 541.075 Td [(T)]TJ ET 1 0 0 1 240.273 541.075 cm EMC q 1 0 0 1 21.345 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 57.21 0 cm /TD <> BDC 1 0 0 1 -297.483 -541.075 cm BT /F15 11.9552 Tf 297.483 541.075 Td [(T)]TJ ET 1 0 0 1 305.938 541.075 cm EMC q 1 0 0 1 35.865 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 86.699 0 cm /TD <> BDC 1 0 0 1 -392.637 -541.075 cm BT /F15 11.9552 Tf 392.636 541.075 Td [(T)]TJ ET 1 0 0 1 401.091 541.075 cm EMC /TD <> BDC q 1 0 0 1 50.833 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -241.015 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -401.091 -541.075 cm BT /F15 11.9552 Tf 167.103 526.629 Td [(T)]TJ ET 1 0 0 1 175.558 526.629 cm EMC q 1 0 0 1 7.027 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.155 0 cm /TD <> BDC 1 0 0 1 -191.713 -526.629 cm BT /F15 11.9552 Tf 191.713 526.629 Td [(F)]TJ ET 1 0 0 1 199.353 526.629 cm EMC q 1 0 0 1 9.128 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.12 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 32.873 0 cm /TD <> BDC 1 0 0 1 -232.226 -526.629 cm BT /F15 11.9552 Tf 232.226 526.629 Td [(F)]TJ ET 1 0 0 1 239.865 526.629 cm EMC q 1 0 0 1 21.753 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 58.026 0 cm /TD <> BDC 1 0 0 1 -297.891 -526.629 cm BT /F15 11.9552 Tf 297.891 526.629 Td [(F)]TJ ET 1 0 0 1 305.53 526.629 cm EMC q 1 0 0 1 36.273 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 87.106 0 cm /TD <> BDC 1 0 0 1 -392.636 -526.629 cm BT /F15 11.9552 Tf 392.636 526.629 Td [(T)]TJ ET 1 0 0 1 401.091 526.629 cm EMC /TD <> BDC q 1 0 0 1 50.833 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -241.015 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -401.091 -526.629 cm BT /F15 11.9552 Tf 167.511 512.183 Td [(F)]TJ ET 1 0 0 1 175.15 512.183 cm EMC q 1 0 0 1 7.435 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.156 0 cm /TD <> BDC 1 0 0 1 -191.306 -512.183 cm BT /F15 11.9552 Tf 191.306 512.183 Td [(T)]TJ ET 1 0 0 1 199.76 512.183 cm EMC q 1 0 0 1 8.721 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.713 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 32.059 0 cm /TD <> BDC 1 0 0 1 -231.819 -512.183 cm BT /F15 11.9552 Tf 231.819 512.183 Td [(T)]TJ ET 1 0 0 1 240.273 512.183 cm EMC q 1 0 0 1 21.345 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 57.618 0 cm /TD <> BDC 1 0 0 1 -297.891 -512.183 cm BT /F15 11.9552 Tf 297.891 512.183 Td [(F)]TJ ET 1 0 0 1 305.53 512.183 cm EMC q 1 0 0 1 36.273 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 87.106 0 cm /TD <> BDC 1 0 0 1 -392.636 -512.183 cm BT /F15 11.9552 Tf 392.636 512.183 Td [(T)]TJ ET 1 0 0 1 401.091 512.183 cm EMC /TD <> BDC q 1 0 0 1 50.833 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -241.015 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -401.091 -512.183 cm BT /F15 11.9552 Tf 167.511 497.738 Td [(F)]TJ ET 1 0 0 1 175.15 497.738 cm EMC q 1 0 0 1 7.435 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.563 0 cm /TD <> BDC 1 0 0 1 -191.713 -497.738 cm BT /F15 11.9552 Tf 191.713 497.738 Td [(F)]TJ ET 1 0 0 1 199.353 497.738 cm EMC q 1 0 0 1 9.128 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.12 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 32.466 0 cm /TD <> BDC 1 0 0 1 -231.819 -497.738 cm BT /F15 11.9552 Tf 231.819 497.738 Td [(T)]TJ ET 1 0 0 1 240.273 497.738 cm EMC q 1 0 0 1 21.345 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 57.618 0 cm /TD <> BDC 1 0 0 1 -297.891 -497.738 cm BT /F15 11.9552 Tf 297.891 497.738 Td [(F)]TJ ET 1 0 0 1 305.53 497.738 cm EMC q 1 0 0 1 36.273 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 87.106 0 cm /TD <> BDC 1 0 0 1 -392.636 -497.738 cm BT /F15 11.9552 Tf 392.636 497.738 Td [(T)]TJ ET 1 0 0 1 401.091 497.738 cm EMC /TD <> BDC q 1 0 0 1 50.833 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -241.015 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 291.848 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 22.509 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 291.848 26.501 cm EMC 1 0 0 1 -362.365 -58.354 cm /P <> BDC 1 0 0 1 -89.559 -461.152 cm BT /F15 11.9552 Tf 89.559 461.152 Td [(\050c\051)-326(\050)]TJ/F21 11.9552 Tf 22.762 0 Td [(:)]TJ/F15 11.9552 Tf 7.97 0 Td [(\050)]TJ/F21 11.9552 Tf 4.552 0 Td [(:)]TJ/F18 11.9552 Tf 7.97 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(\051\051)]TJ/F21 11.9552 Tf 12.426 0 Td [($)]TJ/F18 11.9552 Tf 15.276 0 Td [(x)]TJ ET 1 0 0 1 72 450.718 cm EMC /TD <> BDC 1 0 0 1 146.73 -0.996 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 174.539 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -218.73 -449.323 cm BT /F18 11.9552 Tf 225.609 439.211 Td [(x)]TJ ET 1 0 0 1 232.261 439.211 cm EMC q 1 0 0 1 6.879 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.871 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 14.849 0 cm /TD <> BDC 1 0 0 1 -247.11 -439.211 cm BT /F21 11.9552 Tf 247.11 439.211 Td [(:)]TJ/F18 11.9552 Tf 7.97 0 Td [(x)]TJ ET 1 0 0 1 261.732 439.211 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -273.687 -439.211 cm BT /F21 11.9552 Tf 273.687 439.211 Td [(:)]TJ/F15 11.9552 Tf 7.97 0 Td [(\050)]TJ/F21 11.9552 Tf 4.553 0 Td [(:)]TJ/F18 11.9552 Tf 7.97 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(\051)]TJ ET 1 0 0 1 305.384 439.211 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -317.339 -439.211 cm BT /F15 11.9552 Tf 317.339 439.211 Td [(\050)]TJ/F21 11.9552 Tf 4.553 0 Td [(:)]TJ/F15 11.9552 Tf 7.97 0 Td [(\050)]TJ/F21 11.9552 Tf 4.552 0 Td [(:)]TJ/F18 11.9552 Tf 7.97 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(\051\051)]TJ/F21 11.9552 Tf 12.426 0 Td [($)]TJ/F18 11.9552 Tf 15.276 0 Td [(x)]TJ ET 1 0 0 1 387.292 439.211 cm EMC /TD <> BDC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -168.562 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 174.539 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -218.73 -434.479 cm BT /F15 11.9552 Tf 224.708 424.367 Td [(T)]TJ ET 1 0 0 1 233.162 424.367 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.439 0 cm /TD <> BDC 1 0 0 1 -250.601 -424.367 cm BT /F15 11.9552 Tf 250.601 424.367 Td [(F)]TJ ET 1 0 0 1 258.241 424.367 cm EMC q 1 0 0 1 9.469 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 27.068 0 cm /TD <> BDC 1 0 0 1 -285.309 -424.367 cm BT /F15 11.9552 Tf 285.309 424.367 Td [(T)]TJ ET 1 0 0 1 293.763 424.367 cm EMC q 1 0 0 1 17.599 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 54.326 0 cm /TD <> BDC 1 0 0 1 -348.089 -424.367 cm BT /F15 11.9552 Tf 348.089 424.367 Td [(T)]TJ ET 1 0 0 1 356.543 424.367 cm EMC /TD <> BDC q 1 0 0 1 36.727 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -137.813 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -356.543 -424.367 cm BT /F15 11.9552 Tf 225.115 409.921 Td [(F)]TJ ET 1 0 0 1 232.755 409.921 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.377 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 17.439 0 cm /TD <> BDC 1 0 0 1 -250.194 -409.921 cm BT /F15 11.9552 Tf 250.194 409.921 Td [(T)]TJ ET 1 0 0 1 258.648 409.921 cm EMC q 1 0 0 1 9.062 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 27.068 0 cm /TD <> BDC 1 0 0 1 -285.716 -409.921 cm BT /F15 11.9552 Tf 285.716 409.921 Td [(F)]TJ ET 1 0 0 1 293.355 409.921 cm EMC q 1 0 0 1 18.007 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 54.734 0 cm /TD <> BDC 1 0 0 1 -348.089 -409.921 cm BT /F15 11.9552 Tf 348.089 409.921 Td [(T)]TJ ET 1 0 0 1 356.543 409.921 cm EMC /TD <> BDC q 1 0 0 1 36.727 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -137.813 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 174.539 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 20.41 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 22.402 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 174.54 12.054 cm EMC 1 0 0 1 -303.711 -43.908 cm /P <> BDC 1 0 0 1 -89.559 -373.335 cm BT /F15 11.9552 Tf 89.559 373.335 Td [(\050d\051)]TJ/F18 11.9552 Tf 19.51 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(x)]TJ ET 1 0 0 1 72 362.901 cm EMC /TD <> BDC 1 0 0 1 198.92 -0.996 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 70.16 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -270.92 -361.506 cm BT /F18 11.9552 Tf 277.799 351.394 Td [(x)]TJ ET 1 0 0 1 284.451 351.394 cm EMC q 1 0 0 1 6.878 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.871 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 14.849 0 cm /TD <> BDC 1 0 0 1 -299.3 -351.394 cm BT /F18 11.9552 Tf 299.3 351.394 Td [(x)]TJ/F21 11.9552 Tf 9.972 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(x)]TJ ET 1 0 0 1 335.103 351.394 cm EMC /TD <> BDC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -64.183 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 70.16 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -270.92 -346.662 cm BT /F15 11.9552 Tf 276.897 336.55 Td [(T)]TJ ET 1 0 0 1 285.352 336.55 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 27.622 0 cm /TD <> BDC 1 0 0 1 -312.974 -336.55 cm BT /F15 11.9552 Tf 312.974 336.55 Td [(T)]TJ ET 1 0 0 1 321.428 336.55 cm EMC /TD <> BDC q 1 0 0 1 19.652 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -50.508 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -321.428 -336.55 cm BT /F15 11.9552 Tf 277.305 322.104 Td [(F)]TJ ET 1 0 0 1 284.944 322.104 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.378 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 28.03 0 cm /TD <> BDC 1 0 0 1 -312.974 -322.104 cm BT /F15 11.9552 Tf 312.974 322.104 Td [(T)]TJ ET 1 0 0 1 321.428 322.104 cm EMC /TD <> BDC q 1 0 0 1 19.652 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -50.508 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 70.16 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 20.409 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 22.402 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 70.16 12.055 cm EMC 1 0 0 1 -251.521 -43.909 cm /P <> BDC 1 0 0 1 -89.559 -285.518 cm BT /F15 11.9552 Tf 89.559 285.518 Td [(\050e\051)-326(\050\050)]TJ/F18 11.9552 Tf 27.314 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(^)]TJ/F15 11.9552 Tf 10.626 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(y)]TJ/F21 11.9552 Tf 9.457 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 5.971 0 Td [(\051\051)]TJ/F21 11.9552 Tf 12.425 0 Td [(!)]TJ/F15 11.9552 Tf 15.276 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 5.97 0 Td [(\051)]TJ ET 1 0 0 1 72 275.084 cm EMC /TD <> BDC 1 0 0 1 0 -12.453 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 471.497 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -72 -262.233 cm BT /F18 11.9552 Tf 78.879 252.12 Td [(x)]TJ ET 1 0 0 1 85.531 252.12 cm EMC q 1 0 0 1 6.878 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 14.015 0 cm /TD <> BDC 1 0 0 1 -99.546 -252.12 cm BT /F18 11.9552 Tf 99.546 252.12 Td [(y)]TJ ET 1 0 0 1 105.683 252.12 cm EMC q 1 0 0 1 7.136 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 14.355 0 cm /TD <> BDC 1 0 0 1 -120.038 -252.12 cm BT /F18 11.9552 Tf 120.038 252.12 Td [(z)]TJ ET 1 0 0 1 126.009 252.12 cm EMC q 1 0 0 1 7.219 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 9.212 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 15.19 0 cm /TD <> BDC 1 0 0 1 -141.199 -252.12 cm BT /F18 11.9552 Tf 141.199 252.12 Td [(x)]TJ/F21 11.9552 Tf 9.972 0 Td [(!)]TJ/F18 11.9552 Tf 15.277 0 Td [(y)]TJ ET 1 0 0 1 172.584 252.12 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -184.539 -252.12 cm BT /F18 11.9552 Tf 184.539 252.12 Td [(y)]TJ/F21 11.9552 Tf 9.458 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ ET 1 0 0 1 215.243 252.12 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.956 0 cm /TD <> BDC 1 0 0 1 -227.199 -252.12 cm BT /F15 11.9552 Tf 227.199 252.12 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(^)]TJ/F15 11.9552 Tf 10.626 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(y)]TJ/F21 11.9552 Tf 9.457 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 5.971 0 Td [(\051)]TJ ET 1 0 0 1 320.781 252.12 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -332.736 -252.12 cm BT /F18 11.9552 Tf 332.736 252.12 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ ET 1 0 0 1 363.956 252.12 cm EMC q 1 0 0 1 5.977 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -375.911 -252.12 cm BT /F15 11.9552 Tf 375.911 252.12 Td [(\050\050)]TJ/F18 11.9552 Tf 9.105 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(^)]TJ/F15 11.9552 Tf 10.627 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(y)]TJ/F21 11.9552 Tf 9.458 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 5.97 0 Td [(\051\051)]TJ/F21 11.9552 Tf 12.426 0 Td [(!)]TJ/F15 11.9552 Tf 15.276 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(z)]TJ/F15 11.9552 Tf 5.971 0 Td [(\051)]TJ ET 1 0 0 1 537.519 252.12 cm EMC /TD <> BDC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -465.519 -4.333 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 471.497 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -72 -247.388 cm BT /F15 11.9552 Tf 77.978 237.276 Td [(T)]TJ ET 1 0 0 1 86.432 237.276 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -98.387 -237.276 cm BT /F15 11.9552 Tf 98.387 237.276 Td [(T)]TJ ET 1 0 0 1 106.841 237.276 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.956 0 cm /TD <> BDC 1 0 0 1 -118.797 -237.276 cm BT /F15 11.9552 Tf 118.797 237.276 Td [(T)]TJ ET 1 0 0 1 127.251 237.276 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 25.413 0 cm /TD <> BDC 1 0 0 1 -152.664 -237.276 cm BT /F15 11.9552 Tf 152.664 237.276 Td [(T)]TJ ET 1 0 0 1 161.119 237.276 cm EMC q 1 0 0 1 17.443 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 34.545 0 cm /TD <> BDC 1 0 0 1 -195.664 -237.276 cm BT /F15 11.9552 Tf 195.664 237.276 Td [(T)]TJ ET 1 0 0 1 204.119 237.276 cm EMC q 1 0 0 1 17.102 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 65.644 0 cm /TD <> BDC 1 0 0 1 -269.763 -237.276 cm BT /F15 11.9552 Tf 269.763 237.276 Td [(T)]TJ ET 1 0 0 1 278.217 237.276 cm EMC q 1 0 0 1 48.542 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 65.902 0 cm /TD <> BDC 1 0 0 1 -344.119 -237.276 cm BT /F15 11.9552 Tf 344.119 237.276 Td [(T)]TJ ET 1 0 0 1 352.573 237.276 cm EMC q 1 0 0 1 17.36 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 99.915 0 cm /TD <> BDC 1 0 0 1 -452.488 -237.276 cm BT /F15 11.9552 Tf 452.488 237.276 Td [(T)]TJ ET 1 0 0 1 460.942 237.276 cm EMC /TD <> BDC q 1 0 0 1 82.555 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -388.942 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -460.942 -237.276 cm BT /F15 11.9552 Tf 77.978 222.83 Td [(T)]TJ ET 1 0 0 1 86.432 222.83 cm EMC q 1 0 0 1 5.977 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -98.387 -222.83 cm BT /F15 11.9552 Tf 98.387 222.83 Td [(T)]TJ ET 1 0 0 1 106.841 222.83 cm EMC q 1 0 0 1 5.978 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.363 0 cm /TD <> BDC 1 0 0 1 -119.204 -222.83 cm BT /F15 11.9552 Tf 119.204 222.83 Td [(F)]TJ ET 1 0 0 1 126.843 222.83 cm EMC q 1 0 0 1 6.385 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.378 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 25.821 0 cm /TD <> BDC 1 0 0 1 -152.664 -222.83 cm BT /F15 11.9552 Tf 152.664 222.83 Td [(T)]TJ ET 1 0 0 1 161.119 222.83 cm EMC q 1 0 0 1 17.443 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 34.953 0 cm /TD <> BDC 1 0 0 1 -196.072 -222.83 cm BT /F15 11.9552 Tf 196.072 222.83 Td [(F)]TJ ET 1 0 0 1 203.711 222.83 cm EMC q 1 0 0 1 17.51 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 66.459 0 cm /TD <> BDC 1 0 0 1 -270.17 -222.83 cm BT /F15 11.9552 Tf 270.17 222.83 Td [(F)]TJ ET 1 0 0 1 277.809 222.83 cm EMC q 1 0 0 1 48.95 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 66.717 0 cm /TD <> BDC 1 0 0 1 -344.526 -222.83 cm BT /F15 11.9552 Tf 344.526 222.83 Td [(F)]TJ ET 1 0 0 1 352.166 222.83 cm EMC q 1 0 0 1 17.767 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 100.322 0 cm /TD <> BDC 1 0 0 1 -452.488 -222.83 cm BT /F15 11.9552 Tf 452.488 222.83 Td [(T)]TJ ET 1 0 0 1 460.942 222.83 cm EMC /TD <> BDC q 1 0 0 1 82.555 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -388.942 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -460.942 -222.83 cm BT /F15 11.9552 Tf 77.978 208.385 Td [(T)]TJ ET 1 0 0 1 86.432 208.385 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.363 0 cm /TD <> BDC 1 0 0 1 -98.795 -208.385 cm BT /F15 11.9552 Tf 98.795 208.385 Td [(F)]TJ ET 1 0 0 1 106.434 208.385 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.363 0 cm /TD <> BDC 1 0 0 1 -118.797 -208.385 cm BT /F15 11.9552 Tf 118.797 208.385 Td [(T)]TJ ET 1 0 0 1 127.251 208.385 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 25.821 0 cm /TD <> BDC 1 0 0 1 -153.072 -208.385 cm BT /F15 11.9552 Tf 153.072 208.385 Td [(F)]TJ ET 1 0 0 1 160.711 208.385 cm EMC q 1 0 0 1 17.851 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 34.953 0 cm /TD <> BDC 1 0 0 1 -195.664 -208.385 cm BT /F15 11.9552 Tf 195.664 208.385 Td [(T)]TJ ET 1 0 0 1 204.119 208.385 cm EMC q 1 0 0 1 17.102 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 66.051 0 cm /TD <> BDC 1 0 0 1 -270.17 -208.385 cm BT /F15 11.9552 Tf 270.17 208.385 Td [(F)]TJ ET 1 0 0 1 277.809 208.385 cm EMC q 1 0 0 1 48.95 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 66.31 0 cm /TD <> BDC 1 0 0 1 -344.119 -208.385 cm BT /F15 11.9552 Tf 344.119 208.385 Td [(T)]TJ ET 1 0 0 1 352.573 208.385 cm EMC q 1 0 0 1 17.36 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 99.915 0 cm /TD <> BDC 1 0 0 1 -452.488 -208.385 cm BT /F15 11.9552 Tf 452.488 208.385 Td [(T)]TJ ET 1 0 0 1 460.942 208.385 cm EMC /TD <> BDC q 1 0 0 1 82.555 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -388.942 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -460.942 -208.385 cm BT /F15 11.9552 Tf 77.978 193.939 Td [(T)]TJ ET 1 0 0 1 86.432 193.939 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.363 0 cm /TD <> BDC 1 0 0 1 -98.795 -193.939 cm BT /F15 11.9552 Tf 98.795 193.939 Td [(F)]TJ ET 1 0 0 1 106.434 193.939 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.77 0 cm /TD <> BDC 1 0 0 1 -119.204 -193.939 cm BT /F15 11.9552 Tf 119.204 193.939 Td [(F)]TJ ET 1 0 0 1 126.843 193.939 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.378 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 26.229 0 cm /TD <> BDC 1 0 0 1 -153.072 -193.939 cm BT /F15 11.9552 Tf 153.072 193.939 Td [(F)]TJ ET 1 0 0 1 160.711 193.939 cm EMC q 1 0 0 1 17.851 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 34.953 0 cm /TD <> BDC 1 0 0 1 -195.664 -193.939 cm BT /F15 11.9552 Tf 195.664 193.939 Td [(T)]TJ ET 1 0 0 1 204.119 193.939 cm EMC q 1 0 0 1 17.102 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 66.051 0 cm /TD <> BDC 1 0 0 1 -270.17 -193.939 cm BT /F15 11.9552 Tf 270.17 193.939 Td [(F)]TJ ET 1 0 0 1 277.809 193.939 cm EMC q 1 0 0 1 48.95 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 66.717 0 cm /TD <> BDC 1 0 0 1 -344.526 -193.939 cm BT /F15 11.9552 Tf 344.526 193.939 Td [(F)]TJ ET 1 0 0 1 352.166 193.939 cm EMC q 1 0 0 1 17.767 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 100.322 0 cm /TD <> BDC 1 0 0 1 -452.488 -193.939 cm BT /F15 11.9552 Tf 452.488 193.939 Td [(T)]TJ ET 1 0 0 1 460.942 193.939 cm EMC /TD <> BDC q 1 0 0 1 82.555 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -388.942 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -460.942 -193.939 cm BT /F15 11.9552 Tf 78.385 179.493 Td [(F)]TJ ET 1 0 0 1 86.024 179.493 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.363 0 cm /TD <> BDC 1 0 0 1 -98.387 -179.493 cm BT /F15 11.9552 Tf 98.387 179.493 Td [(T)]TJ ET 1 0 0 1 106.841 179.493 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.956 0 cm /TD <> BDC 1 0 0 1 -118.797 -179.493 cm BT /F15 11.9552 Tf 118.797 179.493 Td [(T)]TJ ET 1 0 0 1 127.251 179.493 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 25.413 0 cm /TD <> BDC 1 0 0 1 -152.664 -179.493 cm BT /F15 11.9552 Tf 152.664 179.493 Td [(T)]TJ ET 1 0 0 1 161.119 179.493 cm EMC q 1 0 0 1 17.443 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 34.545 0 cm /TD <> BDC 1 0 0 1 -195.664 -179.493 cm BT /F15 11.9552 Tf 195.664 179.493 Td [(T)]TJ ET 1 0 0 1 204.119 179.493 cm EMC q 1 0 0 1 17.102 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 65.644 0 cm /TD <> BDC 1 0 0 1 -269.763 -179.493 cm BT /F15 11.9552 Tf 269.763 179.493 Td [(T)]TJ ET 1 0 0 1 278.217 179.493 cm EMC q 1 0 0 1 48.542 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 65.902 0 cm /TD <> BDC 1 0 0 1 -344.119 -179.493 cm BT /F15 11.9552 Tf 344.119 179.493 Td [(T)]TJ ET 1 0 0 1 352.573 179.493 cm EMC q 1 0 0 1 17.36 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 99.915 0 cm /TD <> BDC 1 0 0 1 -452.488 -179.493 cm BT /F15 11.9552 Tf 452.488 179.493 Td [(T)]TJ ET 1 0 0 1 460.942 179.493 cm EMC /TD <> BDC q 1 0 0 1 82.555 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -388.942 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -460.942 -179.493 cm BT /F15 11.9552 Tf 78.385 165.047 Td [(F)]TJ ET 1 0 0 1 86.024 165.047 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.363 0 cm /TD <> BDC 1 0 0 1 -98.387 -165.047 cm BT /F15 11.9552 Tf 98.387 165.047 Td [(T)]TJ ET 1 0 0 1 106.841 165.047 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.363 0 cm /TD <> BDC 1 0 0 1 -119.204 -165.047 cm BT /F15 11.9552 Tf 119.204 165.047 Td [(F)]TJ ET 1 0 0 1 126.843 165.047 cm EMC q 1 0 0 1 6.385 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.378 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 25.821 0 cm /TD <> BDC 1 0 0 1 -152.664 -165.047 cm BT /F15 11.9552 Tf 152.664 165.047 Td [(T)]TJ ET 1 0 0 1 161.119 165.047 cm EMC q 1 0 0 1 17.443 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 34.953 0 cm /TD <> BDC 1 0 0 1 -196.072 -165.047 cm BT /F15 11.9552 Tf 196.072 165.047 Td [(F)]TJ ET 1 0 0 1 203.711 165.047 cm EMC q 1 0 0 1 17.51 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 66.459 0 cm /TD <> BDC 1 0 0 1 -270.17 -165.047 cm BT /F15 11.9552 Tf 270.17 165.047 Td [(F)]TJ ET 1 0 0 1 277.809 165.047 cm EMC q 1 0 0 1 48.95 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 66.31 0 cm /TD <> BDC 1 0 0 1 -344.119 -165.047 cm BT /F15 11.9552 Tf 344.119 165.047 Td [(T)]TJ ET 1 0 0 1 352.573 165.047 cm EMC q 1 0 0 1 17.36 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 99.915 0 cm /TD <> BDC 1 0 0 1 -452.488 -165.047 cm BT /F15 11.9552 Tf 452.488 165.047 Td [(T)]TJ ET 1 0 0 1 460.942 165.047 cm EMC /TD <> BDC q 1 0 0 1 82.555 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -388.942 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -460.942 -165.047 cm BT /F15 11.9552 Tf 78.385 150.601 Td [(F)]TJ ET 1 0 0 1 86.024 150.601 cm EMC q 1 0 0 1 6.385 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.771 0 cm /TD <> BDC 1 0 0 1 -98.795 -150.601 cm BT /F15 11.9552 Tf 98.795 150.601 Td [(F)]TJ ET 1 0 0 1 106.434 150.601 cm EMC q 1 0 0 1 6.385 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.363 0 cm /TD <> BDC 1 0 0 1 -118.797 -150.601 cm BT /F15 11.9552 Tf 118.797 150.601 Td [(T)]TJ ET 1 0 0 1 127.251 150.601 cm EMC q 1 0 0 1 5.977 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 25.413 0 cm /TD <> BDC 1 0 0 1 -152.664 -150.601 cm BT /F15 11.9552 Tf 152.664 150.601 Td [(T)]TJ ET 1 0 0 1 161.119 150.601 cm EMC q 1 0 0 1 17.443 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 34.545 0 cm /TD <> BDC 1 0 0 1 -195.664 -150.601 cm BT /F15 11.9552 Tf 195.664 150.601 Td [(T)]TJ ET 1 0 0 1 204.119 150.601 cm EMC q 1 0 0 1 17.102 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 65.644 0 cm /TD <> BDC 1 0 0 1 -269.763 -150.601 cm BT /F15 11.9552 Tf 269.763 150.601 Td [(T)]TJ ET 1 0 0 1 278.217 150.601 cm EMC q 1 0 0 1 48.542 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 65.902 0 cm /TD <> BDC 1 0 0 1 -344.119 -150.601 cm BT /F15 11.9552 Tf 344.119 150.601 Td [(T)]TJ ET 1 0 0 1 352.573 150.601 cm EMC q 1 0 0 1 17.36 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 99.915 0 cm /TD <> BDC 1 0 0 1 -452.488 -150.601 cm BT /F15 11.9552 Tf 452.488 150.601 Td [(T)]TJ ET 1 0 0 1 460.942 150.601 cm EMC /TD <> BDC q 1 0 0 1 82.555 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -388.942 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -460.942 -150.601 cm BT /F15 11.9552 Tf 78.385 136.155 Td [(F)]TJ ET 1 0 0 1 86.024 136.155 cm EMC q 1 0 0 1 6.385 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.771 0 cm /TD <> BDC 1 0 0 1 -98.795 -136.155 cm BT /F15 11.9552 Tf 98.795 136.155 Td [(F)]TJ ET 1 0 0 1 106.434 136.155 cm EMC q 1 0 0 1 6.385 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 12.77 0 cm /TD <> BDC 1 0 0 1 -119.204 -136.155 cm BT /F15 11.9552 Tf 119.204 136.155 Td [(F)]TJ ET 1 0 0 1 126.843 136.155 cm EMC q 1 0 0 1 6.385 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 8.378 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 25.821 0 cm /TD <> BDC 1 0 0 1 -152.664 -136.155 cm BT /F15 11.9552 Tf 152.664 136.155 Td [(T)]TJ ET 1 0 0 1 161.119 136.155 cm EMC q 1 0 0 1 17.443 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 34.545 0 cm /TD <> BDC 1 0 0 1 -195.664 -136.155 cm BT /F15 11.9552 Tf 195.664 136.155 Td [(T)]TJ ET 1 0 0 1 204.119 136.155 cm EMC q 1 0 0 1 17.102 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 65.644 0 cm /TD <> BDC 1 0 0 1 -269.763 -136.155 cm BT /F15 11.9552 Tf 269.763 136.155 Td [(T)]TJ ET 1 0 0 1 278.217 136.155 cm EMC q 1 0 0 1 48.542 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 65.902 0 cm /TD <> BDC 1 0 0 1 -344.119 -136.155 cm BT /F15 11.9552 Tf 344.119 136.155 Td [(T)]TJ ET 1 0 0 1 352.573 136.155 cm EMC q 1 0 0 1 17.36 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 99.915 0 cm /TD <> BDC 1 0 0 1 -452.488 -136.155 cm BT /F15 11.9552 Tf 452.488 136.155 Td [(T)]TJ ET 1 0 0 1 460.942 136.155 cm EMC /TD <> BDC q 1 0 0 1 82.555 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -388.942 -4.333 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 471.497 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 20.409 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 471.497 55.392 cm EMC 1 0 0 1 -453.938 -87.245 cm /P <> BDC 1 0 0 1 -89.559 -99.57 cm BT /F15 11.9552 Tf 89.559 99.57 Td [(\050f)-70(\051)]TJ/F18 11.9552 Tf 17.417 0 Td [(F)-136(ALS)-58(E)]TJ/F21 11.9552 Tf 46.526 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(x)]TJ ET 1 0 0 1 72 89.136 cm EMC /TD <> BDC 1 0 0 1 179.594 -0.997 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 108.813 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -251.594 -87.741 cm BT /F18 11.9552 Tf 257.571 77.629 Td [(x)]TJ ET 1 0 0 1 268.125 77.629 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 13.948 0 cm /TD <> BDC 1 0 0 1 -282.073 -77.629 cm BT /F18 11.9552 Tf 285.975 77.629 Td [(F)-136(ALS)-58(E)]TJ/F21 11.9552 Tf 46.526 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(x)]TJ ET 1 0 0 1 354.429 77.629 cm EMC /TD <> BDC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -102.835 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 108.813 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -251.594 -72.897 cm BT /F15 11.9552 Tf 258.621 62.785 Td [(T)]TJ ET 1 0 0 1 267.075 62.785 cm EMC q 1 0 0 1 7.028 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 9.02 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 46.949 0 cm /TD <> BDC 1 0 0 1 -314.024 -62.785 cm BT /F15 11.9552 Tf 314.024 62.785 Td [(T)]TJ ET 1 0 0 1 322.478 62.785 cm EMC /TD <> BDC q 1 0 0 1 37.928 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -70.884 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -322.478 -62.785 cm BT /F15 11.9552 Tf 259.029 48.339 Td [(F)]TJ ET 1 0 0 1 266.668 48.339 cm EMC q 1 0 0 1 7.435 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 9.427 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 47.356 0 cm /TD <> BDC 1 0 0 1 -314.024 -48.339 cm BT /F15 11.9552 Tf 314.024 48.339 Td [(T)]TJ ET 1 0 0 1 322.478 48.339 cm EMC /TD <> BDC q 1 0 0 1 37.928 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -70.884 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 108.813 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 22.509 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 24.501 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 108.812 12.055 cm EMC endstream endobj 502 0 obj << /Length 15692 >> stream 1 0 0 1 89.559 671.183 cm /P <> BDC 1 0 0 1 -89.559 -671.183 cm BT /F15 11.9552 Tf 89.559 671.183 Td [(\050g\051)-326(\050)]TJ/F18 11.9552 Tf 23.412 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F15 11.9552 Tf 11.955 0 Td [(F)109(ALSE\051)]TJ/F21 11.9552 Tf 44.769 0 Td [(!)-278(:)]TJ/F18 11.9552 Tf 23.246 0 Td [(x)]TJ ET 1 0 0 1 72 658.232 cm EMC /TD <> BDC 1 0 0 1 114.568 -0.997 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 238.863 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -186.568 -656.837 cm BT /F18 11.9552 Tf 192.546 646.725 Td [(x)]TJ ET 1 0 0 1 203.1 646.725 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.97 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 13.948 0 cm /TD <> BDC 1 0 0 1 -217.048 -646.725 cm BT /F18 11.9552 Tf 220.95 646.725 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F15 11.9552 Tf 11.955 0 Td [(F)109(ALSE)]TJ ET 1 0 0 1 279.774 646.725 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -291.729 -646.725 cm BT /F21 11.9552 Tf 291.729 646.725 Td [(:)]TJ/F18 11.9552 Tf 7.97 0 Td [(x)]TJ ET 1 0 0 1 306.351 646.725 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -318.306 -646.725 cm BT /F15 11.9552 Tf 318.306 646.725 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F15 11.9552 Tf 11.955 0 Td [(F)109(ALSE\051)]TJ/F21 11.9552 Tf 44.769 0 Td [(!)-278(:)]TJ/F18 11.9552 Tf 23.246 0 Td [(x)]TJ ET 1 0 0 1 419.454 646.725 cm EMC /TD <> BDC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -232.886 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 238.863 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -186.568 -641.993 cm BT /F15 11.9552 Tf 193.596 631.881 Td [(T)]TJ ET 1 0 0 1 202.05 631.881 cm EMC q 1 0 0 1 7.028 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 9.02 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 42.541 0 cm /TD <> BDC 1 0 0 1 -244.591 -631.881 cm BT /F15 11.9552 Tf 244.591 631.881 Td [(F)]TJ ET 1 0 0 1 252.23 631.881 cm EMC q 1 0 0 1 33.521 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 42.99 0 cm /TD <> BDC 1 0 0 1 -295.22 -631.881 cm BT /F15 11.9552 Tf 295.22 631.881 Td [(F)]TJ ET 1 0 0 1 302.86 631.881 cm EMC q 1 0 0 1 9.469 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 61.793 0 cm /TD <> BDC 1 0 0 1 -364.653 -631.881 cm BT /F15 11.9552 Tf 364.653 631.881 Td [(T)]TJ ET 1 0 0 1 373.107 631.881 cm EMC /TD <> BDC q 1 0 0 1 52.325 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -186.539 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -373.107 -631.881 cm BT /F15 11.9552 Tf 194.003 617.435 Td [(F)]TJ ET 1 0 0 1 201.643 617.435 cm EMC q 1 0 0 1 7.435 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 9.427 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 42.541 0 cm /TD <> BDC 1 0 0 1 -244.184 -617.435 cm BT /F15 11.9552 Tf 244.184 617.435 Td [(T)]TJ ET 1 0 0 1 252.638 617.435 cm EMC q 1 0 0 1 33.113 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 42.175 0 cm /TD <> BDC 1 0 0 1 -294.813 -617.435 cm BT /F15 11.9552 Tf 294.813 617.435 Td [(T)]TJ ET 1 0 0 1 303.267 617.435 cm EMC q 1 0 0 1 9.062 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 61.386 0 cm /TD <> BDC 1 0 0 1 -364.653 -617.435 cm BT /F15 11.9552 Tf 364.653 617.435 Td [(T)]TJ ET 1 0 0 1 373.107 617.435 cm EMC /TD <> BDC q 1 0 0 1 52.325 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -186.539 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 238.863 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 22.509 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 24.502 -14.445 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 238.864 12.055 cm EMC 1 0 0 1 -335.873 -46.426 cm /P <> BDC 1 0 0 1 -89.559 -578.331 cm BT /F15 11.9552 Tf 89.559 578.331 Td [(\050h\051)-326(\050\050)]TJ/F18 11.9552 Tf 28.615 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(^)]TJ/F15 11.9552 Tf 10.627 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)-278(:)]TJ/F18 11.9552 Tf 23.246 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051\051)]TJ/F21 11.9552 Tf 12.425 0 Td [(!)-278(:)]TJ/F18 11.9552 Tf 23.247 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(.)]TJ ET 1 0 0 1 72 565.38 cm EMC /TD <> BDC 1 0 0 1 0 -12.453 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 495.705 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -72 -552.528 cm BT /F18 11.9552 Tf 77.978 542.416 Td [(x)]TJ ET 1 0 0 1 88.532 542.416 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -100.487 -542.416 cm BT /F18 11.9552 Tf 104.389 542.416 Td [(y)]TJ ET 1 0 0 1 114.427 542.416 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 7.971 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 13.948 0 cm /TD <> BDC 1 0 0 1 -128.375 -542.416 cm BT /F21 11.9552 Tf 128.375 542.416 Td [(:)]TJ/F18 11.9552 Tf 7.97 0 Td [(x)]TJ ET 1 0 0 1 146.899 542.416 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.956 0 cm /TD <> BDC 1 0 0 1 -158.855 -542.416 cm BT /F21 11.9552 Tf 158.855 542.416 Td [(:)]TJ/F18 11.9552 Tf 7.97 0 Td [(y)]TJ ET 1 0 0 1 172.961 542.416 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -184.916 -542.416 cm BT /F18 11.9552 Tf 188.818 542.416 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ ET 1 0 0 1 224.106 542.416 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -236.061 -542.416 cm BT /F18 11.9552 Tf 239.963 542.416 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)-278(:)]TJ/F18 11.9552 Tf 23.246 0 Td [(y)]TJ ET 1 0 0 1 279.319 542.416 cm EMC q 1 0 0 1 5.977 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -291.274 -542.416 cm BT /F15 11.9552 Tf 295.176 542.416 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(^)]TJ/F15 11.9552 Tf 10.627 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)-278(:)]TJ/F18 11.9552 Tf 23.246 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ ET 1 0 0 1 401.312 542.416 cm EMC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 11.955 0 cm /TD <> BDC 1 0 0 1 -413.267 -542.416 cm BT /F15 11.9552 Tf 417.169 542.416 Td [(\050\050)]TJ/F18 11.9552 Tf 9.105 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)]TJ/F18 11.9552 Tf 15.276 0 Td [(y)]TJ/F15 11.9552 Tf 6.137 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(^)]TJ/F15 11.9552 Tf 10.626 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(x)]TJ/F21 11.9552 Tf 9.973 0 Td [(!)-278(:)]TJ/F18 11.9552 Tf 23.246 0 Td [(y)]TJ/F15 11.9552 Tf 6.136 0 Td [(\051\051)]TJ/F21 11.9552 Tf 12.426 0 Td [(!)-278(:)]TJ/F18 11.9552 Tf 23.246 0 Td [(x)]TJ ET 1 0 0 1 561.727 542.416 cm EMC /TD <> BDC q 1 0 0 1 5.978 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -489.727 -4.334 cm /Artifact <> BDC q 1 0 0 1 0 -0.199 cm []0 d 0 J 0.398 w 0 0 m 495.705 0 l S Q 1 0 0 1 0 -0.398 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -72 -537.684 cm BT /F15 11.9552 Tf 79.027 527.572 Td [(T)]TJ ET 1 0 0 1 87.482 527.572 cm EMC q 1 0 0 1 7.027 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 15.748 0 cm /TD <> BDC 1 0 0 1 -103.23 -527.572 cm BT /F15 11.9552 Tf 103.23 527.572 Td [(T)]TJ ET 1 0 0 1 111.684 527.572 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.714 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 22.134 0 cm /TD <> BDC 1 0 0 1 -133.818 -527.572 cm BT /F15 11.9552 Tf 133.818 527.572 Td [(F)]TJ ET 1 0 0 1 141.457 527.572 cm EMC q 1 0 0 1 11.42 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 20.631 0 cm /TD <> BDC 1 0 0 1 -162.088 -527.572 cm BT /F15 11.9552 Tf 162.088 527.572 Td [(F)]TJ ET 1 0 0 1 169.728 527.572 cm EMC q 1 0 0 1 9.211 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 30.556 0 cm /TD <> BDC 1 0 0 1 -200.284 -527.572 cm BT /F15 11.9552 Tf 200.284 527.572 Td [(T)]TJ ET 1 0 0 1 208.738 527.572 cm EMC q 1 0 0 1 21.346 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 45.132 0 cm /TD <> BDC 1 0 0 1 -253.87 -527.572 cm BT /F15 11.9552 Tf 253.87 527.572 Td [(F)]TJ ET 1 0 0 1 261.51 527.572 cm EMC q 1 0 0 1 23.786 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 80.963 0 cm /TD <> BDC 1 0 0 1 -342.473 -527.572 cm BT /F15 11.9552 Tf 342.473 527.572 Td [(F)]TJ ET 1 0 0 1 350.113 527.572 cm EMC q 1 0 0 1 57.177 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 133.157 0 cm /TD <> BDC 1 0 0 1 -483.27 -527.572 cm BT /F15 11.9552 Tf 483.27 527.572 Td [(T)]TJ ET 1 0 0 1 491.724 527.572 cm EMC /TD <> BDC q 1 0 0 1 75.981 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -419.724 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -491.724 -527.572 cm BT /F15 11.9552 Tf 79.027 513.126 Td [(T)]TJ ET 1 0 0 1 87.482 513.126 cm EMC q 1 0 0 1 7.027 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.155 0 cm /TD <> BDC 1 0 0 1 -103.637 -513.126 cm BT /F15 11.9552 Tf 103.637 513.126 Td [(F)]TJ ET 1 0 0 1 111.277 513.126 cm EMC q 1 0 0 1 9.128 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.121 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 22.541 0 cm /TD <> BDC 1 0 0 1 -133.818 -513.126 cm BT /F15 11.9552 Tf 133.818 513.126 Td [(F)]TJ ET 1 0 0 1 141.457 513.126 cm EMC q 1 0 0 1 11.42 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 20.224 0 cm /TD <> BDC 1 0 0 1 -161.681 -513.126 cm BT /F15 11.9552 Tf 161.681 513.126 Td [(T)]TJ ET 1 0 0 1 170.135 513.126 cm EMC q 1 0 0 1 8.804 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 30.557 0 cm /TD <> BDC 1 0 0 1 -200.692 -513.126 cm BT /F15 11.9552 Tf 200.692 513.126 Td [(F)]TJ ET 1 0 0 1 208.331 513.126 cm EMC q 1 0 0 1 21.753 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 45.132 0 cm /TD <> BDC 1 0 0 1 -253.463 -513.126 cm BT /F15 11.9552 Tf 253.463 513.126 Td [(T)]TJ ET 1 0 0 1 261.917 513.126 cm EMC q 1 0 0 1 23.379 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 80.556 0 cm /TD <> BDC 1 0 0 1 -342.473 -513.126 cm BT /F15 11.9552 Tf 342.473 513.126 Td [(F)]TJ ET 1 0 0 1 350.113 513.126 cm EMC q 1 0 0 1 57.177 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 133.157 0 cm /TD <> BDC 1 0 0 1 -483.27 -513.126 cm BT /F15 11.9552 Tf 483.27 513.126 Td [(T)]TJ ET 1 0 0 1 491.724 513.126 cm EMC /TD <> BDC q 1 0 0 1 75.981 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -419.724 -18.78 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -491.724 -513.126 cm BT /F15 11.9552 Tf 79.435 498.68 Td [(F)]TJ ET 1 0 0 1 87.074 498.68 cm EMC q 1 0 0 1 7.435 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.156 0 cm /TD <> BDC 1 0 0 1 -103.23 -498.68 cm BT /F15 11.9552 Tf 103.23 498.68 Td [(T)]TJ ET 1 0 0 1 111.684 498.68 cm EMC q 1 0 0 1 8.721 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 10.714 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 21.726 0 cm /TD <> BDC 1 0 0 1 -133.41 -498.68 cm BT /F15 11.9552 Tf 133.41 498.68 Td [(T)]TJ ET 1 0 0 1 141.864 498.68 cm EMC q 1 0 0 1 11.013 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 20.224 0 cm /TD <> BDC 1 0 0 1 -162.088 -498.68 cm BT /F15 11.9552 Tf 162.088 498.68 Td [(F)]TJ ET 1 0 0 1 169.728 498.68 cm EMC q 1 0 0 1 9.211 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 30.556 0 cm /TD <> BDC 1 0 0 1 -200.284 -498.68 cm BT /F15 11.9552 Tf 200.284 498.68 Td [(T)]TJ ET 1 0 0 1 208.738 498.68 cm EMC q 1 0 0 1 21.346 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 44.725 0 cm /TD <> BDC 1 0 0 1 -253.463 -498.68 cm BT /F15 11.9552 Tf 253.463 498.68 Td [(T)]TJ ET 1 0 0 1 261.917 498.68 cm EMC q 1 0 0 1 23.379 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 80.556 0 cm /TD <> BDC 1 0 0 1 -342.473 -498.68 cm BT /F15 11.9552 Tf 342.473 498.68 Td [(F)]TJ ET 1 0 0 1 350.113 498.68 cm EMC q 1 0 0 1 57.177 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 133.157 0 cm /TD <> BDC 1 0 0 1 -483.27 -498.68 cm BT /F15 11.9552 Tf 483.27 498.68 Td [(T)]TJ ET 1 0 0 1 491.724 498.68 cm EMC /TD <> BDC q 1 0 0 1 75.981 -4.334 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 -419.724 -18.779 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -491.724 -498.68 cm BT /F15 11.9552 Tf 79.435 484.234 Td [(F)]TJ ET 1 0 0 1 87.074 484.234 cm EMC q 1 0 0 1 7.435 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 16.563 0 cm /TD <> BDC 1 0 0 1 -103.637 -484.234 cm BT /F15 11.9552 Tf 103.637 484.234 Td [(F)]TJ ET 1 0 0 1 111.277 484.234 cm EMC q 1 0 0 1 9.128 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 11.121 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 22.133 0 cm /TD <> BDC 1 0 0 1 -133.41 -484.234 cm BT /F15 11.9552 Tf 133.41 484.234 Td [(T)]TJ ET 1 0 0 1 141.864 484.234 cm EMC q 1 0 0 1 11.013 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 19.817 0 cm /TD <> BDC 1 0 0 1 -161.681 -484.234 cm BT /F15 11.9552 Tf 161.681 484.234 Td [(T)]TJ ET 1 0 0 1 170.135 484.234 cm EMC q 1 0 0 1 8.804 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 30.149 0 cm /TD <> BDC 1 0 0 1 -200.284 -484.234 cm BT /F15 11.9552 Tf 200.284 484.234 Td [(T)]TJ ET 1 0 0 1 208.738 484.234 cm EMC q 1 0 0 1 21.346 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 44.725 0 cm /TD <> BDC 1 0 0 1 -253.463 -484.234 cm BT /F15 11.9552 Tf 253.463 484.234 Td [(T)]TJ ET 1 0 0 1 261.917 484.234 cm EMC q 1 0 0 1 23.379 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 80.556 0 cm /TD <> BDC 1 0 0 1 -342.473 -484.234 cm BT /F15 11.9552 Tf 342.473 484.234 Td [(F)]TJ ET 1 0 0 1 350.113 484.234 cm EMC q 1 0 0 1 57.177 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 133.157 0 cm /TD <> BDC 1 0 0 1 -483.27 -484.234 cm BT /F15 11.9552 Tf 483.27 484.234 Td [(T)]TJ ET 1 0 0 1 491.724 484.234 cm EMC /TD <> BDC q 1 0 0 1 75.981 -4.333 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 -419.724 -4.333 cm /Artifact <> BDC q 1 0 0 1 0 -0.2 cm []0 d 0 J 0.398 w 0 0 m 495.705 0 l S Q 1 0 0 1 0 -0.399 cm EMC q 1 0 0 1 0 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q q 1 0 0 1 22.509 -14.446 cm []0 d 0 J 0.398 w 0 0 m 0 14.446 l S Q 1 0 0 1 495.705 26.501 cm EMC endstream endobj 521 0 obj << /Length 13483 >> stream 1 0 0 1 89.559 671.183 cm /P <> BDC 1 0 0 1 -89.559 -671.183 cm BT /F15 11.9552 Tf 89.559 671.183 Td [(Here)-326(are)-327(some)-326(more)-326(extras:)]TJ ET 1 0 0 1 89.559 644.782 cm EMC /P <> BDC 1 0 0 1 -89.559 -644.782 cm BT /F15 11.9552 Tf 89.559 644.782 Td [(1.)-417(De\014ne)-273(a)-273(p)-27(erfect)-272(n)27(um)27(b)-27(er)-273(-)-273(b)-27(e)-273(as)-272(precise)-273(as)-273(y)27(ou)-272(can)-273(-)-273(probably)-272(use)-273(summation)-273(notat)1(ion.)]TJ ET 1 0 0 1 89.559 630.336 cm EMC /P <> BDC 1 0 0 1 -89.559 -630.336 cm BT /F15 11.9552 Tf 89.559 630.336 Td [(A)-289(p)-27(ositiv)28(e)-289(in)27(teger)-288(is)-289(called)]TJ/F27 11.9552 Tf 137.364 0 Td [(p)50(erfe)50(ct)]TJ/F15 11.9552 Tf 36.776 0 Td [(if)-289(the)-288(sum)-289(of)-288(all)-289(its)-288(p)-28(ositiv)28(e)-289(factors)-288(whic)27(h)-289(are)-288(not)-289(itself)]TJ -191.699 -14.446 Td [(are)-326(equal)-327(to)-326(itself.)]TJ ET 1 0 0 1 169.615 615.89 cm EMC 1 0 0 1 -68.35 -24.408 cm /Quote <> BDC 1 0 0 1 -101.265 -591.482 cm BT /F15 11.9552 Tf 101.265 591.482 Td [(A)-326(n)27(um)27(b)-27(er)]TJ/F18 11.9552 Tf 55.274 0 Td [(p)]TJ/F15 11.9552 Tf 9.777 0 Td [(is)-326(called)]TJ/F27 11.9552 Tf 44.938 0 Td [(p)50(erfe)50(ct)]TJ/F15 11.9552 Tf 37.227 0 Td [(if)]TJ/F24 11.9552 Tf 10.731 8.966 Td [(P)]TJ/F16 7.9701 Tf 12.619 -12.453 Td [(1)]TJ/F22 7.9701 Tf 4.234 0 Td [(\024)]TJ/F19 7.9701 Tf 6.587 0 Td [(d> BDC 1 0 0 1 -89.559 -554.122 cm BT /F15 11.9552 Tf 89.559 554.122 Td [(2.)-432(Find)-316(a)-317(coun)27(terexampl)1(e)-317(to)-317(the)-316(follo)27(wing:)-430(If)]TJ/F18 11.9552 Tf 235.102 0 Td [(f)]TJ/F15 11.9552 Tf 10.831 0 Td [(is)-317(con)28(tin)27(uous)-317(and)-316(di\013eren)27(tiable)-316(on)-317(\050)]TJ/F18 11.9552 Tf 183.589 0 Td [(a;)-167(b)]TJ/F15 11.9552 Tf 16.367 0 Td [(\051)]TJ -463.448 -14.446 Td [(and)]TJ/F18 11.9552 Tf 22.762 0 Td [(f)]TJ/F15 11.9552 Tf 7.046 0 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(\051)-278(=)]TJ/F18 11.9552 Tf 20.299 0 Td [(f)]TJ/F15 11.9552 Tf 7.046 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(b)]TJ/F15 11.9552 Tf 4.977 0 Td [(\051,)-326(then)-327(there)-326(exists)-326(a)-327(real)-326(n)27(um)28(b)-28(er)]TJ/F18 11.9552 Tf 175.72 0 Td [(c)]TJ/F15 11.9552 Tf 8.94 0 Td [(in)-326(\050)]TJ/F18 11.9552 Tf 18.209 0 Td [(a;)-167(b)]TJ/F15 11.9552 Tf 16.366 0 Td [(\051)-326(suc)27(h)-327(t)1(hat)]TJ/F18 11.9552 Tf 60.221 0 Td [(f)]TJ/F22 7.9701 Tf 7.046 4.339 Td [(0)]TJ/F15 11.9552 Tf 2.795 -4.339 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(c)]TJ/F15 11.9552 Tf 5.038 0 Td [(\051)-278(=)-277(0.)]TJ ET 1 0 0 1 89.559 525.23 cm EMC /P <> BDC 1 0 0 1 -89.559 -525.23 cm BT /F15 11.9552 Tf 89.559 525.23 Td [(This)-306(is)-306(almost)-306(Rolle's)-306(theorem.)-429(Ex)1(cept)-307(Ro)1(lle's)-307(theo)1(rem)-307(re)1(quires)-307(co)1(n)27(tin)27(uous)-306(on)-306([)]TJ/F18 11.9552 Tf 406.842 0 Td [(a;)-167(b)]TJ/F15 11.9552 Tf 16.366 0 Td [(].)-428(So,)]TJ -440.767 -14.446 Td [(to)-353(mak)28(e)-353(a)-353(coun)27(terexampl)1(e,)-360(w)27(e'll)-352(need)-353(something)-353(discoun)28(tinous)-353(on)-353([)]TJ/F18 11.9552 Tf 347.791 0 Td [(a;)-167(b)]TJ/F15 11.9552 Tf 16.366 0 Td [(],)-359(but)-353(con)27(tin)27(uo)1(us)-353(on)]TJ -364.157 -24.906 Td [(\050)]TJ/F18 11.9552 Tf 4.552 0 Td [(a;)-167(b)]TJ/F15 11.9552 Tf 16.367 0 Td [(\051.)-435(Let's)-326(tak)27(e)]TJ/F18 11.9552 Tf 67.209 0 Td [(a)]TJ/F15 11.9552 Tf 9.466 0 Td [(=)-278(0)]TJ/F18 11.9552 Tf 18.279 0 Td [(;)-167(b)]TJ/F15 11.9552 Tf 13.542 0 Td [(=)-278(1,)-326(and)-326(mak)27(e)]TJ/F18 11.9552 Tf 78.759 0 Td [(f)]TJ/F15 11.9552 Tf 7.046 0 Td [(\050)]TJ/F18 11.9552 Tf 4.553 0 Td [(x)]TJ/F15 11.9552 Tf 6.652 0 Td [(\051)-278(=)]TJ/F24 11.9552 Tf 20.298 20.443 Td [(\050)]TJ/F18 11.9552 Tf 9.631 -12.254 Td [(x)]TJ/F15 11.9552 Tf 18.358 0 Td [(if)-326(0)]TJ/F21 11.9552 Tf 19.904 0 Td [(\024)]TJ/F18 11.9552 Tf 12.62 0 Td [(x)-278(<)]TJ/F15 11.9552 Tf 22.398 0 Td [(1)]TJ -73.28 -17.335 Td [(0)-1046(if)]TJ/F18 11.9552 Tf 29.089 0 Td [(x)]TJ/F15 11.9552 Tf 9.973 0 Td [(=)-278(1)]TJ 41.267 9.146 Td [(.)]TJ ET 1 0 0 1 89.559 449.68 cm EMC /P <> BDC 1 0 0 1 -89.559 -449.68 cm BT /F15 11.9552 Tf 89.559 449.68 Td [(3.)-803(Pro)27(v)27(e)-449(and)-449(extend)-449(or)-449(dispro)28(v)27(e)-449(and)-449(salv)54(age:)-680(The)-449(pro)-27(duct)-449(of)-449(an)27(y)-449(three)-449(consecutiv)27(e)]TJ -17.559 -14.446 Td [(in)27(tegers)-326(is)-326(a)-327(m)27(ultip)1(le)-327(of)-326(3.)]TJ ET 1 0 0 1 89.559 420.788 cm EMC /P <> BDC 1 0 0 1 -89.559 -420.788 cm BT /F15 11.9552 Tf 89.559 420.788 Td [(One)-376(of)-377(the)-376(three)-377(consecutiv)27(e)-376(n)27(um)27(b)-27(ers)-376(will)-377(b)-27(e)-376(a)-377(m)27(ultiple)-376(of)-377(three)-376(-)-377(b)-27(ecause)-376(ev)27(ery)-377(th)1(ird)]TJ -17.559 -14.446 Td [(in)27(teger)-430(is)-430(a)-430(m)27(ultiple)-430(of)-430(three.)-746(The)-431(pro)-27(duct)-430(of)-430(an)27(y)-430(m)27(ul)1(tiple)-431(of)-430(three)-430(with)-430(other)-430(n)27(um)28(b)-28(ers)]TJ 0 -14.445 Td [(remains)-445(a)-445(m)27(ultiple)-445(of)-445(three.)-792(This)-445(can)-445(at)-446(least)-445(b)-27(e)-445(extended)-445(to)-446(the)-445(pro)-27(duct)-445(of)-445(an)27(y)-445(three)]TJ 0 -14.446 Td [(consecutiv)27(e)-305(in)27(tegers)-306(is)-306(a)-306(m)28(ultiple)-306(of)-306(6,)-310(b)-27(ecause)-306(ev)27(e)1(ry)-306(other)-306(n)27(um)27(b)-27(er)-306(i)1(s)-306(also)-306(a)-306(m)27(ultiple)-305(of)-306(t)27(w)27(o.)]TJ 0 -14.446 Td [(W)82(e)-276(can)-275(extend)-276(this)-275(further)-275(in)-276(this)-275(direction)-276(to)-275(the)-276(fa)1(ct)-276(that)-275(the)-276(pro)-27(duct)-275(of)-276(an)27(y)]TJ/F18 11.9552 Tf 399.774 0 Td [(n)]TJ/F15 11.9552 Tf 10.281 0 Td [(consecutiv)27(e)]TJ -410.055 -14.446 Td [(in)27(tegers)-300(is)-301(a)-300(m)27(ultiple)-301(of)]TJ/F18 11.9552 Tf 122.475 0 Td [(n)]TJ/F15 11.9552 Tf 6.988 0 Td [(!)-301(\050if)-300(w)27(e)-300(ha)27(v)27(e)-300(four)-301(n)27(um)28(b)-28(ers,)-305(one)-301(of)-300(them)-301(is)-300(divisible)-301(b)27(y)-300(4\051.)-427(W)82(e)-301(need)]TJ -129.463 -14.446 Td [(to)-339(b)-27(e)-339(careful,)-343(tho)1(ugh,)-343(once)-339(the)-339(n)27(um)28(b)-28(e)1(r)-340(includ)1(es)-340(non-pr)1(imes.)-474(There's)-339(some)-339(subtlet)27(y)-339(at)-339(that)]TJ 0 -14.445 Td [(p)-27(oin)27(t)-326(in)-327(the)-326(argumen)27(t.)]TJ ET 1 0 0 1 89.559 293.267 cm EMC /P <> BDC 1 0 0 1 -89.559 -293.267 cm BT /F15 11.9552 Tf 89.559 293.267 Td [(4.)-430(Pro)27(v)28(e)-311(\050u)1(sing)-311(the)-310(giv)27(ens)-310(in)-310(the)-310(app)-27(endix\051:)-427(A)-311(neg)1(ativ)27(e)-310(in)27(teger)-310(m)27(ultiplied)-310(b)27(y)-310(a)-310(negativ)27(e)]TJ -17.559 -14.446 Td [(in)27(teger)-326(yields)-326(a)-327(p)-27(ositiv)27(e)-326(in)27(teger.)]TJ ET 1 0 0 1 89.559 264.375 cm EMC /P <> BDC 1 0 0 1 -89.559 -264.375 cm BT /F15 11.9552 Tf 89.559 264.375 Td [(Ok,)-318(th)1(is)-316(is)-315(a)-316(little)-315(silly)82(,)-318(as)-315(this)-316(fact)-315(is)-316(stated)-315(in)-315(the)-316(app)-27(endix.)-431(P)27(oin)27(ting)-315(this)-315(out)-316(will)-315(earn)]TJ -17.559 -14.446 Td [(full)-326(credit.)-435(If)-327(it)-326(w)27(eren't)-326(in)-327(th)1(e)-327(app)-27(endix,)-326(what)-327(w)28(ould)-327(constit)1(ute)-327(a)-326(pro)-27(of)-70(?)]TJ ET 1 0 0 1 89.559 235.483 cm EMC /P <> BDC 1 0 0 1 -89.559 -235.483 cm BT /F15 11.9552 Tf 89.559 235.483 Td [(It)-326(su\016ces)-327(to)-326(pro)27(v)27(e)-326(\050)]TJ/F21 11.9552 Tf 102.878 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051)]TJ/F21 11.9552 Tf 13.062 0 Td [(\002)]TJ/F15 11.9552 Tf 11.955 0 Td [(\050)]TJ/F21 11.9552 Tf 4.552 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051)-278(=)-277(1)-327(\050b)-27(ecause)-326(\050)]TJ/F21 11.9552 Tf 88.323 0 Td [(\000)]TJ/F18 11.9552 Tf 9.299 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(\051)]TJ/F21 11.9552 Tf 7.209 0 Td [(\002)]TJ/F15 11.9552 Tf 11.955 0 Td [(\050)]TJ/F21 11.9552 Tf 4.552 0 Td [(\000)]TJ/F18 11.9552 Tf 9.299 0 Td [(b)]TJ/F15 11.9552 Tf 4.977 0 Td [(\051)-278(=)-277(\050)]TJ/F21 11.9552 Tf 24.851 0 Td [(\000)]TJ/F15 11.9552 Tf 9.298 0 Td [(1\051)]TJ/F21 11.9552 Tf 13.062 0 Td [(\002)]TJ/F15 11.9552 Tf 11.955 0 Td [(\050)]TJ/F21 11.9552 Tf 4.553 0 Td [(\000)]TJ/F15 11.9552 Tf 9.298 0 Td [(1\051)]TJ/F21 11.9552 Tf 13.062 0 Td [(\002)]TJ/F18 11.9552 Tf 11.955 0 Td [(a)]TJ/F21 11.9552 Tf 8.802 0 Td [(\002)]TJ/F18 11.9552 Tf 11.955 0 Td [(b)]TJ/F15 11.9552 Tf 4.977 0 Td [(\051.)]TJ ET 1 0 0 1 89.559 221.037 cm EMC /P <> BDC 1 0 0 1 -89.559 -221.037 cm BT /F15 11.9552 Tf 89.559 221.037 Td [(There)-339(are)-339(t)27(w)27(o)-339(needed)-339(related)-339(thing)-339(to)-340(pro)28(v)27(e.)-474(First)-339(0)]TJ/F18 11.9552 Tf 270.505 0 Td [(a)]TJ/F15 11.9552 Tf 9.728 0 Td [(=)]TJ/F18 11.9552 Tf 12.687 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(0)-300(=)-299(0.)-474(Here's)-339(a)-339(pro)-28(of)-339(of)-339(that:)]TJ/F18 11.9552 Tf -316.624 -14.445 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(0)-244(+)]TJ/F18 11.9552 Tf 20.795 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(0)-333(=)]TJ/F18 11.9552 Tf 22.91 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(\0500)-244(+)-244(0\051)-333(=)]TJ/F18 11.9552 Tf 52.809 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(0)-333(=)-332(0)-244(+)]TJ/F18 11.9552 Tf 43.705 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(0.)-532(F)82(rom)-359(there)-358(subtract)]TJ/F18 11.9552 Tf 123.497 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(0)-359(from)-358(b)-27(oth)-359(sides)-358(to)-359(get)]TJ/F18 11.9552 Tf 129.255 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(0)-333(=)-332(0.)]TJ -435.986 -14.446 Td [(The)-371(same)-370(is)-371(true)-370(for)-371(0)]TJ/F18 11.9552 Tf 116.259 0 Td [(a)]TJ/F15 11.9552 Tf 6.145 0 Td [(.)-568(Second,)-381(w)27(e)-371(need)-370(that)]TJ/F21 11.9552 Tf 125.123 0 Td [(\000)]TJ/F15 11.9552 Tf 9.298 0 Td [(\050)]TJ/F21 11.9552 Tf 4.552 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051)-353(=)-353(1.)-568(1)-252(+)-253(\050)]TJ/F21 11.9552 Tf 69.391 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051)-353(=)-353(0)-371(b)-27(ecause)-370(\050)]TJ/F21 11.9552 Tf 86.63 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051)-371(is)]TJ -445.295 -14.446 Td [(de\014ned)-340(as)-340(the)-340(in)27(v)27(er)1(s)-1(e)-340(of)-340(1.)-476(But,)-343(this)-340(ma)27(y)-340(b)-27(e)-340(rein)27(terpreted)-340(that)-340(1)-340(is)-340(the)-340(in)27(v)28(erse)-340(of)-340(\050)]TJ/F21 11.9552 Tf 428.625 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051.)-476(In)]TJ -437.924 -14.446 Td [(sym)27(b)-27(ols)-326(this)-327(is)-326(1)-278(=)]TJ/F21 11.9552 Tf 100.875 0 Td [(\000)]TJ/F15 11.9552 Tf 9.298 0 Td [(\050)]TJ/F21 11.9552 Tf 4.553 0 Td [(\000)]TJ/F15 11.9552 Tf 9.298 0 Td [(1\051,)-326(as)-327(desired.)]TJ ET 1 0 0 1 89.559 148.808 cm EMC /P <> BDC 1 0 0 1 -89.559 -148.808 cm BT /F15 11.9552 Tf 89.559 148.808 Td [(Finally)-420(w)27(e)-420(sho)27(w)-420(\050)]TJ/F21 11.9552 Tf 93.985 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051\050)]TJ/F21 11.9552 Tf 14.958 0 Td [(\000)]TJ/F15 11.9552 Tf 9.298 0 Td [(1\051)-437(=)-438(1.)-716(T)81(o)-420(do)-420(this)-420(w)27(e)-420(will)-420(sho)27(w)-420(that)-420(\050)]TJ/F21 11.9552 Tf 210.072 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051\050)]TJ/F21 11.9552 Tf 14.957 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051)-286(+)-286(\050)]TJ/F21 11.9552 Tf 30.902 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051)-437(=)-438(0,)]TJ -428.927 -14.446 Td [(and)-393(th)27(us)-393(b)27(y)-393(uniqueness)-394(of)-393(additiv)27(e)-393(in)27(v)28(erses,)-410(\050)]TJ/F21 11.9552 Tf 238.947 0 Td [(\000)]TJ/F15 11.9552 Tf 9.298 0 Td [(1\051\050)]TJ/F21 11.9552 Tf 14.958 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051)-393(is)-394(the)-393(in)27(v)28(erse)-394(for)]TJ/F21 11.9552 Tf 106.884 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1)-393(and)-394(th)1(erefore)]TJ -388.685 -14.445 Td [(\050)]TJ/F21 11.9552 Tf 4.552 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051\050)]TJ/F21 11.9552 Tf 14.957 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051)-481(=)-481(1)1(.)-793(\050)]TJ/F21 11.9552 Tf 54.143 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051\050)]TJ/F21 11.9552 Tf 14.958 0 Td [(\000)]TJ/F15 11.9552 Tf 9.298 0 Td [(1\051)-303(+)-304(\050)]TJ/F21 11.9552 Tf 31.317 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051)-481(=)-481(\050)]TJ/F21 11.9552 Tf 35.558 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051\050)]TJ/F21 11.9552 Tf 14.957 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1)-303(+)-304(1\051)-481(=)-480(\050)]TJ/F21 11.9552 Tf 57.771 0 Td [(\000)]TJ/F15 11.9552 Tf 9.298 0 Td [(1\0510)-481(=)-481(0)1(.)-793(W)81(e)-446(ha)28(v)27(e)-446(no)28(w)-446(pro)27(v)27(en)]TJ -302.603 -14.446 Td [(\050)]TJ/F21 11.9552 Tf 4.552 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051\050)]TJ/F21 11.9552 Tf 14.957 0 Td [(\000)]TJ/F15 11.9552 Tf 9.299 0 Td [(1\051)-278(=)-277(1)-298(and)-298(henc)1(e)-298(a)-298(negativ)28(e)-298(in)27(teger)-297(m)27(ultiplied)-297(b)27(y)-298(a)-297(negativ)27(e)-298(in)28(teger)-298(yields)-297(a)-298(p)-27(ositiv)27(e)]TJ -38.107 -14.446 Td [(in)27(teger.)]TJ ET 1 0 0 1 72 91.025 cm EMC endstream endobj 426 0 obj << /Type /ObjStm /N 100 /First 890 /Length 12509 >> stream 425 0 424 109 414 187 413 292 427 371 432 475 433 584 434 693 435 802 431 911 437 1013 438 1122 439 1231 440 1340 436 1449 442 1551 443 1660 444 1769 445 1878 441 1987 447 2089 446 2198 430 2276 429 2381 215 2460 450 2566 448 2614 451 2704 455 2808 456 2917 457 3026 458 3135 459 3244 460 3353 461 3462 462 3571 454 3680 464 3814 465 3923 466 4032 467 4141 468 4250 469 4359 470 4468 471 4577 463 4686 473 4820 474 4929 475 5038 476 5147 477 5256 478 5365 479 5474 480 5583 472 5692 482 5826 483 5935 484 6044 485 6153 486 6262 487 6371 488 6480 489 6589 481 6698 491 6832 492 6941 493 7050 494 7159 495 7268 496 7377 497 7486 498 7595 490 7704 500 7838 499 7947 453 8025 452 8146 428 8225 503 8331 501 8384 504 8474 506 8578 507 8682 508 8786 509 8896 510 9000 511 9104 512 9208 513 9312 514 9416 515 9520 516 9624 517 9728 2 9832 518 10543 1 10904 505 11044 519 11151 522 11419 520 11467 % 425 0 obj <>] /S /TD >> % 424 0 obj <> % 414 0 obj <> % 413 0 obj <> % 427 0 obj <>] /S /P >> % 432 0 obj <>] /S /TD >> % 433 0 obj <>] /S /TD >> % 434 0 obj <>] /S /TD >> % 435 0 obj <>] /S /TD >> % 431 0 obj <> % 437 0 obj <>] /S /TD >> % 438 0 obj <>] /S /TD >> % 439 0 obj <>] /S /TD >> % 440 0 obj <>] /S /TD >> % 436 0 obj <> % 442 0 obj <>] /S /TD >> % 443 0 obj <>] /S /TD >> % 444 0 obj <>] /S /TD >> % 445 0 obj <>] /S /TD >> % 441 0 obj <> % 447 0 obj <>] /S /TD >> % 446 0 obj <> % 430 0 obj <> % 429 0 obj <> % 215 0 obj << /Type /Page /Contents 449 0 R /Resources 448 0 R /MediaBox [0 0 612 792] /Parent 31 0 R >> % 450 0 obj << /D [215 0 R /XYZ 71 721 null] >> % 448 0 obj << /Font << /F18 26 0 R /F21 25 0 R /F15 24 0 R >> /ProcSet [ /PDF /Text ] >> % 451 0 obj <>] /S /P >> % 455 0 obj <>] /S /TD >> % 456 0 obj <>] /S /TD >> % 457 0 obj <>] /S /TD >> % 458 0 obj <>] /S /TD >> % 459 0 obj <>] /S /TD >> % 460 0 obj <>] /S /TD >> % 461 0 obj <>] /S /TD >> % 462 0 obj <>] /S /TD >> % 454 0 obj <> % 464 0 obj <>] /S /TD >> % 465 0 obj <>] /S /TD >> % 466 0 obj <>] /S /TD >> % 467 0 obj <>] /S /TD >> % 468 0 obj <>] /S /TD >> % 469 0 obj <>] /S /TD >> % 470 0 obj <>] /S /TD >> % 471 0 obj <>] /S /TD >> % 463 0 obj <> % 473 0 obj <>] /S /TD >> % 474 0 obj <>] /S /TD >> % 475 0 obj <>] /S /TD >> % 476 0 obj <>] /S /TD >> % 477 0 obj <>] /S /TD >> % 478 0 obj <>] /S /TD >> % 479 0 obj <>] /S /TD >> % 480 0 obj <>] /S /TD >> % 472 0 obj <> % 482 0 obj <>] /S /TD >> % 483 0 obj <>] /S /TD >> % 484 0 obj <>] /S /TD >> % 485 0 obj <>] /S /TD >> % 486 0 obj <>] /S /TD >> % 487 0 obj <>] /S /TD >> % 488 0 obj <>] /S /TD >> % 489 0 obj <>] /S /TD >> % 481 0 obj <> % 491 0 obj <>] /S /TD >> % 492 0 obj <>] /S /TD >> % 493 0 obj <>] /S /TD >> % 494 0 obj <>] /S /TD >> % 495 0 obj <>] /S /TD >> % 496 0 obj <>] /S /TD >> % 497 0 obj <>] /S /TD >> % 498 0 obj <>] /S /TD >> % 490 0 obj <> % 500 0 obj <>] /S /TD >> % 499 0 obj <> % 453 0 obj <> % 452 0 obj <> % 428 0 obj << /Type /Page /Contents 502 0 R /Resources 501 0 R /MediaBox [0 0 612 792] /Parent 31 0 R >> % 503 0 obj << /D [428 0 R /XYZ 110.851 721 null] >> % 501 0 obj << /Font << /F15 24 0 R /F18 26 0 R /F21 25 0 R >> /ProcSet [ /PDF /Text ] >> % 504 0 obj <>] /S /P >> % 506 0 obj <>] /S /P >> % 507 0 obj <>] /S /P >> % 508 0 obj <>] /S /Quote >> % 509 0 obj <>] /S /P >> % 510 0 obj <>] /S /P >> % 511 0 obj <>] /S /P >> % 512 0 obj <>] /S /P >> % 513 0 obj <>] /S /P >> % 514 0 obj <>] /S /P >> % 515 0 obj <>] /S /P >> % 516 0 obj <>] /S /P >> % 517 0 obj <>] /S /P >> % 2 0 obj <> % 518 0 obj <> /CM1 <> /CM2 <> /CM3 <> /CM4 <> >> % 1 0 obj <> /ParentTreeNextKey 1 /K [ 2 0 R] >> % 505 0 obj << /Type /Page /Contents 521 0 R /Resources 520 0 R /MediaBox [0 0 612 792] /Parent 524 0 R >> % 519 0 obj <> % 522 0 obj << /D [505 0 R /XYZ 71 721 null] >> % 520 0 obj << /Font << /F15 24 0 R /F27 30 0 R /F18 26 0 R /F24 523 0 R /F16 28 0 R /F22 255 0 R /F19 27 0 R /F21 25 0 R >> /ProcSet [ /PDF /Text ] >> endstream endobj 537 0 obj << /Length1 1410 /Length2 6154 /Length3 0 /Length 7564 >> stream %!PS-AdobeFont-1.0: CMEX10 003.002 %%Title: CMEX10 %Version: 003.002 %%CreationDate: Mon Jul 13 16:17:00 2009 %%Creator: David M. Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMEX10. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMEX10 known{/CMEX10 findfont dup/UniqueID known{dup /UniqueID get 5092766 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /TJDAIS+CMEX10 def /FontBBox {-24 -2960 1454 772 }readonly def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMEX10.) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 40 /braceleftBigg put dup 80 /summationtext put readonly def currentdict end currentfile eexec oc;jAw-=%W)-{ru)rAE(@{빴Q|_R ϤA -T@|q|VkJ%qu8PwGxŪ̆Q6K -U\%b"t-*xJ+ }3{Z2zݬT2s$Z&{BJ{ޣ!fpG?[Ttku'5O P 1[.BBBo0 VoG;wCMdK&\YT{#v m E57G~ߡ +3[ť73ŝ:&uN]B Je v(7JIFO/kZ)Ckz*7Xuvw نg&֋U+DWAԳPx;%]r@G~fJ48{vFM"~wvԇ1I mJXk k51D[Wopl^(;w\FIzHy$$r ./xj83>z>9Nќv-v)TTD*IL}qbx>u}&:=l]o:Eiۧ[A^ [/ER;R;"6(ũK?C!>;gh) Ga 9nQ<@(<|+)}Pˇ2&dqmc#IhFeI-S n|{cfyv40]vO?݋ZωN#I'\9wÅPp`i(2NzfAʑ[?}7N)-t)^EI(^ܒM[ ҽTf[z{ rC2YcCŤŬfvnTgTBg^fOW 3Kgiuؓe>q1.֢+0ȉ<]vmZ =WVhY&R{!2ܼ'Nr6ɱbk_ک'@13{MKݐ__GaTAbʊ0ZB{䤡 d2J> 7RK7׏T;Ȱ+[4B*q4~;7D 5W?S&3[L^'{P)V̴~B,10Z]TC2e;=@7n6 |,E+ʻ%_B κ7() xK6qQl: `qyi_O7MK!5(sfgHQ1N9!;8 @ߙ:Ϭ&-(D00fkC[x'=xWH i~ swOVꮈiJL%{yݘF": 1[[ nse]-D.ct&_C$I]Dؘƫ'DGSQ$ҀpՄ6<~"Dg՞1o/+8>YX+갭҅:fXM(~t~xc+`Hcv"+!gl;%kι #v" %MA6ֆN{%]D`;>I뼳g!CSiØofglu:o3yUݢ\a;'f@ᛙv⬊Zj NB].yiW3 5{$";Y]`!i1{Zn|VS,v6.am$|%>)԰"3o@*鱫,6<#44`xDo:Et{M6#:]wޞCA'j]=K4EA=:MOa+VX[b,ma*69Z]ʤ|`?tvFwr2)/-Ov5@y9 ]#x~{! ˣz{TD]7d{WtMpiځ(+\, pZ]8âwcl_E΀G#ӱ¶ꭚ=]Y7*rQ !WQӄrgdM9n*P b3Bxe @1RhOj\Bycwzj eH? U~pE.kIc4g<BZ\B5hrEd^wŠim ;2 "? ]`_Z 8P\w)9%9dS6X?}+LYJ^y@1 (h{Uem,F/d"H7?j V}2 l Olb(FY8G߱4. eS]<b@{ɤA.S f>oLơ6/翔OHeAᤇ#:j 7 6Y^Rvr?NVIz1x^PA~KutS`ZGR`Tg3H4'eKR `܁k+j|7oHNPqJg4{"NJ.Go[yv.IS+9jULd+fu˥~mQfsGMb)RY2>y2=Uɹe8@*<*?!.y]PhNЫ1qrYgMR/ _X仾ru'Apue+`Y>q WXG6dZ e T_j^-'[nnyOZ:O?U3z;Fra}/_ -D'o!OQ'ʱL@ .!Ux~eRj=U=ΥDqKߒ&u9qD<: Lb.3c%x]׉; aRy Z:Սl^nz!/rUզ4)hOMMd 14/Xsa0"A묵erᶒlBNr8ݰY~ry9h?chٞ!c Y猅Oc}q5\(y!^(L 153jvzh9鷔7ZCY即O:,!UC$*h[G%4O#+y6">RR-:#XL%YDd,[FTꠤgXcб:o9LJ\{h%v9'tUBQŕ&Fpԥ,8W뗶FF-QEWDEz5s#.TD1R0݊:$}+r*WޮUb\]Evs|?LkoOiFx(8z1d8w .b"%K^i59C|]J4ptjŊÑCȇ ĭGe/" # @!aMbE0U?\ bYӽImʗ.`x+2qZ:j㱦tWMK;8ƦA s&q\oqVjQ %i3k$n'=E#* WVV IPQ8>i 4bm miʾ.P`W0'20vwl.]elЂ!Yz"FkR͙,`k%Iuban\Rڇud :t?YS/WXlO]{j f_p|=ZO(+`H 5 ~7dh֫]V1Ԅ2D(W[/tG W ( zK֍3Z!>􎳢Wa;ɢ0䳦܂ܳ; *DG5HX&sw*;s(#PBپ hoOt%J u.:ۃ &essE3a̕*Pv*k]5D6?x3{%ЯEiVjӨPNx[ ЩnP1#WvA8޿6dzLtGb5Pw,.#gF:4:uBV@aO2zn! `pgTwaG7= bzsФY@}0{9B6$ʗԧЋ>n4=#|h~ޕ4R_= !\SNм.bZ&zt~^ױfkQ&E10] ifs ?g2p{(G*>a0N9Zbkr_ _N}! @ 49eXFH7|W$@2Ѐ'$eє54JDW]uNK#X?8N*#bp/1:rcը0Y Z v `~O+M)*C xIs>)췡"V<ܴu_")[.`AStrc?A$>A4W ) 4.ml:}h?t6N./w%^p&1>S'W(@Ә!o$&Ej){9Y#!  [t& Pa% >qTΦS"g ^v+ T6i@hqPt]PRcE xΦ,U endstream endobj 539 0 obj << /Length1 1728 /Length2 11498 /Length3 0 /Length 13226 >> stream %!PS-AdobeFont-1.0: CMMI12 003.002 %%Title: CMMI12 %Version: 003.002 %%CreationDate: Mon Jul 13 16:17:00 2009 %%Creator: David M. Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMMI12. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMMI12 known{/CMMI12 findfont dup/UniqueID known{dup /UniqueID get 5087386 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /IMNZVW+CMMI12 def /FontBBox {-31 -250 1026 750 }readonly def /PaintType 0 def /FontInfo 10 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMI12.) readonly def /FullName (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def /ascent 750 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 65 /A put dup 66 /B put dup 67 /C put dup 69 /E put dup 70 /F put dup 76 /L put dup 83 /S put dup 97 /a put dup 98 /b put dup 99 /c put dup 59 /comma put dup 100 /d put dup 102 /f put dup 62 /greater put dup 60 /less put dup 109 /m put dup 110 /n put dup 112 /p put dup 58 /period put dup 114 /r put dup 120 /x put dup 121 /y put dup 122 /z put readonly def currentdict end currentfile eexec oc;jAw-<X2-Τ^tE_SKF1F^jNBq{y4-Fgbԓ{"WB:rP ?dgS%|'ؓw&F7JNL9VRtbT5'm\N"K< wJv$tE;D4Vܢv{bGCSM!R C\#Xjh ho35ƒ8"g{dD( }8Yd,WBs"ڼ?n9FV߄!X{!^g|v1{x3ē_Dp:Kiwǟ/bH`fca"˕4c^w9Es EUS엦KE/I;dTؖ<]|6E1٣I@Oi)IA6ۉ~?8ҙL*|a @i.Z&͌icU-%8|3}!]~@;=gtpOAHn@#xsTqxMq 8ꄑ  jf7N+ 3ëI8S,ZsETMJOvPDIU8 +z_%0/hjR"e|1RO6U(VRH2Dj)Ȯj,8a(@}m Ӿ4*bdgtGgg922WbmM,8%.y?z@$vի@=N:#;dُLŸ9Km wGTEG+G 0 wrc7|e4Cn|O" mVʛD Aj 9ؿڥkY+>rs(fܲ|9 hd*%6A۹_o%)ZGCj  }smہ+(oesBZr3 o>ggk/kN5HP[0WptRw+6bŰɞ[-%]=hЧK!d˜SWγqA3DihDP5p:;ɉ[M'utMQ7BꌽP{y.GG_T̪Wxx#|j>eu1 4cUhM*o۝RN[@:2E"|7 ]hXr3QL>B%BD6gXkh*TiOjܑĝNe;_β)~]HOF4%n@N\ShǾcaH7g_v1HThgnκ%݄kNi,҅k16`E>y> Tr3`$\ƱJ}gq@VbIo),I{ Y@2>Dwn˱cY8_=I'*gݗZ\tF!6J8ѳwՕm#Jt?zy?eֶ9"p #EyRzR7y,4 W4:jPxZ.ϒBⷰm CsR}ZcU@Fl/m L 5%Φhs "o!XifDO"6T?XQ@RlubK 7={u Q]Cl "}7K ([$UOJ  uxtzse¡YFOtE>:ޒ*ڸ頕G ]5;`y\9:$-@$r̘Ui(rƍM椸$CR٪ss]I&J+]H.ө*3f`BF% Ia1)? E{f(ly2JDm0:g0l4MrMAsu`< ^fʑRH@[]]xV* " :G6QwW2Z= e{cިzRNh`|2 LLwOwpWҟ`8r k}`-Nl>ٖ͋hڑJ0NO%_F~jؑ^N fwh֔2$4PcIxhJ*n AS]h3_꓎5wCz֬:qFY*$gjnKI]We#!˵+"lh75^!CUҹ _"tu/wb7Lj5*wٵ(zA͕ZExa'DLc䨹Wp}^AӁ𞚳R> stc*fyԩBA83A["gjhgڗxa8n݅67l(-i/_dr 9-6m.E[|Sxh5Tͼ46I)Pj۞RB)B#oֈ=^a1 G悜Q'݊JidsIgbxf>t/6;UTmU-(l@MYƣǕ IS[(8k&D,ibiui>`oq$% g8cj1Ǘ_C8\U G|2<xW-ׇ#%K馭 i'vTRB{{PpM@k UƹQ#%Ձ[,枳܃z簨/6Ж$ƣ#L"1ױڭL3X޳3υ3b![سퟠ씂Uƾp-(*H!܁d!;4Qڴ%ʩ=c78߷jrĚ]m-)BJS:i*P3#91х#w|PNiB0)ĖSx4Z縤FwHpj73pȵ;utRZ ȸ9A8X,7iǖ]fQ9N Ŋ3{wzѰL4cسbx %3أͲ'C/y(yQrWϙ##Ϙ@ZϷZlwX yBL/%h?e%s!Lsyro$Q"p1\9Q-Pbda6O)\&/j5Ώ=ɀꋁvsu)#Jš* 63RYXRܠPqpjTQ@o1*4_U? [/[^ə)︛`C>r7R|{Np|j?Mi(AEIlj[/xQƋ؅~}E9Iwyg^o$B4#꜐}A_5x'rRG t^np-To]urw̮I1z7]Jw&qok )ܠ g~pWMQ(x G9jWܢqlL\Ⱥ3% pLԿ TX> u(%hw?DH=C57UUhbB KQ|NIjn~I pTCq9XAR=u!iOE^){{9N0P ؎өlT{ >7m#ͨ+/#:+FkLmlۏf"Dj~oٓCF`OT&w`~YY/'|) ]{S=#fQr+Z[DGah_ǽ%-.ޓ=JQh>V$t Ol*EkABMHKNcz,^U@1JT⭿miɡ .m8vgHS};ğȔ5QUul݇%Lx.D o74W˴=YF&-2<)S _U0`63\@w n+s7ܪ/|5]JQ9:#y:¬jIl[b̸ʶZ:,@&Y|'^;:VA^ FS^˹Q}/3|+9 x=;6 Z /&;Z0ZӚ[ˣ0@!-b#zٟ@ -;?Gu"I#6Mp}O)&hK2o.fY^ӨhN\3uTǯ.Qy=TLhn Y3PX6%ch0j\8_-wy }.UܚpF o_eqVvM8Y<<~3h/uᾀrTf759Jݖp\  }i^ }K=lͯ匒6+8fyMɇB 2eS?lGRr SNvCQȦ Jw_]P>ԳϿG`;)mˏ'1 ޶p(B~9 XO} h*L^Cdž)-|$؜z2k<:Jj Q)ĸLlTRJ9INd9I&yIg5 } wGfuSEP֒#7N ^+?wdkޏin&rGzJps2*"S ,3ӝ"f K3 ?>q,K`^ B\FQ˫*:#}˕yxo_`m$8WiGJ,B dơar+`bi_Dn/63& ױ^b2p?=veP~ v(JycxB@( *fy&j.{3hׅuiD-uv^9K ` 5[h&a0-n9MYgf(i$ R 4ےdY[B$@@wqd £,vwR&aZmT!fݑ᭮h[JUX`wX #wvMCԲ|;g—nәF`"gVsRu@!X%~BnX?s$ c ޷r!% 4+a)91J|:Rn "įlu{N)IӴvB͇wh]ܣ"9ak}-f]K.4F0e/Mmn h `:Ե 4̭voerw%) zDlwղdܢ枡!o[YשϦ@6:܁0A1vWN| ,J#|BmFX8q-+s)P&O{SiȬ~c|C?$I1svK}2 R3釈 wvU"ͧ!GZ!q03.ꆆ ;i6 ,Dltin#R::EiRh@kʇF#JUF攝LY[:;]?ωn'RB۰G݀{ ~my9OvOy\[0fb,N\t7OӄJmx C|Z@.=uSVI6rnaw&/RV8 aN)ȞOeB}aCR ox {cU-KR}?xQi{BUnC֚, GFYblR`򟄦5wy~ld;,zؘ&f3F^9nALbhsmB䜻zh7G@i ~h~[pz"Xy%A!6A3hIgccٶ% 0'#KLНCQʣ-񓽴=L. YO;kpkWF@,z'f2\$ð^d[@3Q(mII;[5*ClKF,DNWHܕ 7Q{EZivsFmT $m7[c0l^ ,4! `&6(YqXdQ \©^c<Ӎ*UF-TpSKN9hh$>;_ lil HnYqɏk+$,5WsO*bmg\DūœL HHM=~ cp6 C1_5\J3GjHINjɺZBENS"aY¿jj4.Oi8}hykoOur/ 6x5V԰Ip;lJkrEׄ~Zc4,l'_5E"~t@LC%Sr\~G R 2 pn;?缡R-Kxf=0hrɢUmQcKۏ PXD=UhnRmFx% ^D UHL_o`o]A%Ewm5~M).nn18k@[=/L~LWrJ_2 W%cF Vj|.k:r-aMӼ6d}}/#xA* g_gp50o|ѓ{/p_ѣhW8d, 1$_v:}<'+@dLqN@bAo&XoE$`_àP SR@ vPC`@קoV Ky&?PjXB$aJǩ3ķkfm+lf' 4 z1 Hh|T<}2J"bOWD&?EO { I~Os- *aO'憗ؗ'S%(ΎىikY w$J- FUcKy,*g9UJY)C\#[Ȟ _sJk4H:M0ElZz6"\ tAvjMâ̸ݍhNE2.a\k$8;ΔFHL endstream endobj 541 0 obj << /Length1 1385 /Length2 6068 /Length3 0 /Length 7453 >> stream %!PS-AdobeFont-1.0: CMMI6 003.002 %%Title: CMMI6 %Version: 003.002 %%CreationDate: Mon Jul 13 16:17:00 2009 %%Creator: David M. Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMMI6. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMMI6 known{/CMMI6 findfont dup/UniqueID known{dup /UniqueID get 5087381 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /OLBSGM+CMMI6 def /FontBBox {11 -250 1241 750 }readonly def /PaintType 0 def /FontInfo 10 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMI6.) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def /ascent 750 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 110 /n put readonly def currentdict end currentfile eexec oc;jAw-<X2-Τ^tE_SKF1F^jNBq{y4-Fgbԓ{"WB:rP ?dgS%|'ؓw&F7JNL9VRtbT5'm\N"K< wJv$tE;D4Vܢv{bGCSM!R C\#Xjh ho35ƒ8"g{dWLtj昆G )l5 Ě46gfPQDL:J )T,ЧqVfHeUܪGʖ#8܋.T,Ps,! tMq}K6ktwa9[~>Nlylj\̬HLcƻՐ0?o%>Luc2uUkK0ݳx ߙzΪ 0aw5Joϛ$_֙WMZh%G@L~/G2ɜdg5Nunm0! `N1=_^k9F $2@wkdDMeyc ҈&dӘ&XY6 ߎ&L5%hEj4#U*'dɻgh#V\3m[qN<60!2>~f[-[؛Qwkps9CLFSĺqSæ#rg{#fbԧ~XDI%:`mrM/IjoƼʩyLmIе/XH2Ӽ&!)[e-~Vҳ$?$o#VCgSOGhQ|R7uu Dq-x<STmP6I+֏HS&Ab.֒#Fa6K>GS i*ıhڽy,RgdӒT;ջA{].IW"b:fXME>N_9/!O)"M nJ;89,Z ڼ ADDt'I>cI,ʃ⨄{O~WCA#BU+4B\ǡU-\^R> [֚WˑJ1͑pVycǞCz/?d-4zu$LG,<+U%5Sm}<‡O r) 'WeqؘdxN6KfG #Me~Y BkYʬ k?kwr֋Ȯj"6KFi%?=,`H xe)TθLHe;ѽAō 4jUk{pEa';0 7qekJMg/7Cecc}$Fxd_‘d+'πa{CMx){#QÐ}qvz!܉#;$"AW+tFg9ks/NmB`)T|e9c&bW{U%UpC bGz/\~ .vÞ@NU=x$xihE ܪ 7 мyhXåp2[ӽk~Y* McBrVϞ#x?Z>,dyA| tW dCiعGATń}_Colim3_SҢnc]S!:LF({gPpΞd>)Us(ђW1i.x 9oqklɒK4 ͯA e6e=uzJ(bxo@L Бey D2d-Q'>9.v!7᱈*&׷W9љ<8%c$ Zо:zknp6VS;c|v>])^QA|ڛhF G,\_j6,[t`b^S9|B &umô'+-5j'TgMhDžd QR#RI,FX'F; 6fgly;I?ȉMst.c+735Izp)ܕ7bh[ F+'Y]QU6gܶbRG}e \A 1b1i ̔vKA{gfuč[nj}cݰ6R?ZkU቙_{[ʬ\:>MZ v˜AFG U+9[ic%YttŐ駗E?[JwNypߊo"R5`j=&Vfu0kecY+Lejڧr΂LFE`V!+O*TbҢBVGgtY's`- AZLD]4[6zRP|8h)u` i6TBzQV u~_Hv/´p%ڿOT[F\ vI5%vÛ+c5)SoK38xWo»7˜֜:Y>7Gս.2}f䴥;~(XH_-!H-72m9B#1 F\E6jMKZ"#K=EABO3rOZ>󱹠4˴ڷBgڤACNN4}1;hG;ʶδAqzg~. c+ڑҖ<`!IÛn.שDTFHR,Z;4n,@A2(ԁ!L \Ogma ]xX5qMAݹS 3/a\W@ ,}4T>vN0ˌՖJq"d8[:o6[=((=LEO0xj rX߄c%+?*#$87E($)sMI8ϏUhuЏclRYm4A/0&S\n@C`nt@ JHFTwSN4:DX6RgKMWūٳ&84&ײ_ӫQd @nH83a8ӫԵ ֤^aCesjgaXS;F90% ]-Aӽ)ެ{vD\J-i$3|~q#]fy$: ʩ+Pjŧa?S6k5Z? I00K ޠ50>ҰQGwu9Ui]S%tz钉}pu endstream endobj 543 0 obj << /Length1 1479 /Length2 7063 /Length3 0 /Length 8542 >> stream %!PS-AdobeFont-1.0: CMMI8 003.002 %%Title: CMMI8 %Version: 003.002 %%CreationDate: Mon Jul 13 16:17:00 2009 %%Creator: David M. Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMMI8. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMMI8 known{/CMMI8 findfont dup/UniqueID known{dup /UniqueID get 5087383 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /GMZMQY+CMMI8 def /FontBBox {-24 -250 1110 750 }readonly def /PaintType 0 def /FontInfo 10 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMMI8.) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def /ascent 750 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 97 /a put dup 98 /b put dup 59 /comma put dup 100 /d put dup 60 /less put dup 111 /o put dup 112 /p put readonly def currentdict end currentfile eexec oc;jAw-<X2-Τ^tE_SKF1F^jNBq{y4-Fgbԓ{"WB:rP ?dgS%|'ؓw&F7JNL9VRtbT5'm\N"K< wJv$tE;D4Vܢv{bGCSM!R C\#Xjh ho35ƒ8"g{dNׅs'&X83/`C37Vl"ʀbNeP@KVcR8Dh89pz㠚LF]䘼m[Yմ]Ô _hV`I1J٪*D t U#8,eG- )1C4#9նB~DIb_ 6,=;܋o,NIMj_vVo%hQi 5X<ƪl0L c0+$c:4#3R+h~y3542KmWz.g!jA|v9eqyF[q—lj )jҙs>l2gјpT@M/{[bK1NW^tD$;Č,,BYQ53}Q7sR |4aĹ=8ש1Y ';l3#pKdo 2{P?kKuU%5@_Ba*{U-ǸG1L5UF0҄>MR 1)dqa,<ׂRBY_1;VW*]X? ?"KZj@Q8'e޻tX<k{s-ZmqqrImqt/9aNgcZFfD|lLYBjg}`㜰h$$TH-'Rܳն#>⳾֛&x⠆k73Ӥ؉յ0Z׳%ݖګ=j5ݰ³۶ٜ!<(eh6hB@2OR(!K*ܯt^";!0* tG l8JY| 5K9mYөn F>-?)"ȧ9V*wj gڕoL%Y~ZM : !P!l10{Ft'XꤞKEM8tˈ(Q3kZ ޛ4i_9&yslAʗ3*@xk,@|x/ʖ)Oc*DeE| fGv6\U8"ĝm1a0heAfC+55oNw^k:G \0a# }]xvRf)tsLCs_W@#赡7iOXt&{biҢYnVq̠!X[ow_ "@]J4rSE +,09DWF"C@i[ԗ @~8xtv.fU$ ^x{m`#Z,QRڶ  %Sc0G.;=8sy뿶'Z]AxwZjGOIƆ7,5o߿焘kG~D55o>@]AIm_Ҷ Jo^ɒmφo#6PUA"X꛸/B^(@n$#H褔0㴻fr,d"q+s? n~DL zC ⒎yCEJߢxүJs!(Ԙ>gs]8`;ԭV=ݏhkTJXM*8^zceхE)R !6w3''6"sɾmI`=0c%gxf2(g1Q&#pOvY@HbՈG[$њ\L5ʢ f/6OyщT9|]O`jٳ1+W'dN(l1BD^]᣼z+L41QUq GB ܓVA'Sq jv)4Ћ e|iſl`u/ou>_سT)^S-nw}, ZNEC Y Rez3sp$ 2RH?. p#+Ne>PrI%y@n-S4¶{֍Y[OhEi\*BxCЙ#(~#=ϑ X\yQζ5_p&R5‰SJ^ ԷrXu 㝢)Ɣ1,B7GODE k\OȧY@hn:*洊@Q?PEDS\ ؠ䟥CMhQQxMϗDv]錻ҦJ*T#"hiW_5ʙaKT$#. Ɨ Yam=fW#tj&zlIX@t߸ඔ*'>`r/XV(soGRe',q6e: 5lP&7/ Ex*Y$ݦӢ15\>h#1F̍\`AkS?jH:+S D:]+HT5‹f\V:\g0ﮩ IҲt} ôoDks>+D85}lS,@\.X:; }# z;d?=rXBPuň|@?b>DaU#lٚk+ڽ*KӨ ٟ%wp`2اG>̯4򰿴,,հܳsﺐٲdİ<{7:M9SMuz%PհXJZQP PP47 uߢ|_2 ;3Mg4{Ew+j<?j22a;(RU%>D.! jKsq[]]-(Fk=$|27[pYD%]䆌pT5oRc+́ %kFX2NLDj<E5+ ^ M 3Aj v?4$OgfkK ـ%7<ʮS΃iug6l'X]2K|ɼSS Viʺ`/bMX5h u~r G*Cx$aeh- *JW)]HXr0KT_3A C\I"YF|kcYBJz%L>QbLq~Y|V{(YXg5-Ԏ'WP}AmN ZOcb*rl״de x=Eu Z1QތiMHURsݫTUg<ʀm>"S{3""m " YBXo| ͆alU怑 Լ1LGPP= P@tW #L6)fўyxBm֫.h^Bwm+?'߅%TjcLuw{Z#B6ny `aڶ9FVTiǔeEI{mόBrf8#>)vUx,6@GNv?-n,v khَ^ $.sҔ D23YڀTBMVw*1|' B XYnK%`GkRO8ww 4J(uvl --5aK 5>'%NXNI.|f%^ܯ+JAÉrۣ{j8m6c)Җ塇urjx뗢_E#T /xsBуL۶K@hׁ8EQ endstream endobj 545 0 obj << /Length1 2534 /Length2 18644 /Length3 0 /Length 21178 >> stream %!PS-AdobeFont-1.0: CMR12 003.002 %%Title: CMR12 %Version: 003.002 %%CreationDate: Mon Jul 13 16:17:00 2009 %%Creator: David M. Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMR12. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMR12 known{/CMR12 findfont dup/UniqueID known{dup /UniqueID get 5000794 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /QXATNV+CMR12 def /FontBBox {-34 -251 988 750 }readonly def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR12.) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 87 /W put dup 89 /Y put dup 97 /a put dup 98 /b put dup 91 /bracketleft put dup 93 /bracketright put dup 99 /c put dup 58 /colon put dup 44 /comma put dup 100 /d put dup 101 /e put dup 56 /eight put dup 61 /equal put dup 33 /exclam put dup 102 /f put dup 11 /ff put dup 14 /ffi put dup 12 /fi put dup 53 /five put dup 52 /four put dup 103 /g put dup 104 /h put dup 45 /hyphen put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 57 /nine put dup 111 /o put dup 49 /one put dup 112 /p put dup 40 /parenleft put dup 41 /parenright put dup 46 /period put dup 43 /plus put dup 113 /q put dup 63 /question put dup 92 /quotedblleft put dup 34 /quotedblright put dup 39 /quoteright put dup 114 /r put dup 115 /s put dup 55 /seven put dup 54 /six put dup 116 /t put dup 51 /three put dup 50 /two put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 48 /zero put readonly def currentdict end currentfile eexec oc;jAw-=%W)-{ru)rAE(@{빴Q|_R ϤA -T@|q|VkJ%qu8PwGxŪ̆Q6K -U\%b"t-*xJ+ }3{Z2zݬT2s$Z&{BJ{r̗m1l(zNRr^&%:(/IߺHm!4JxI7bs,OiOl75R 9z(X*Rhn5&g\c9`EgwT!xIJz҈v*lcoƿsdm^%=谺D +u9#3P _] )w UA8 HuG:DJ(W;]-0<.gSB NlZOLӡ5^9:K*|F {É ڇE,q>j0^x떲Q'X酉i ;yZPt>ܱ1Sհ:ުd0׵JA)Θ[ U=y5pRU&0'-8tIAx*̣$!gRHS;RVU?!lM٬2gO.T7wϓ)?CߠVb7^kJ;c N* ٍG|Ucͮߢɨl6h6[ 2ߵПZvUlP|%)VǸm׫=&a Js_̲y|{R6ĴʗB7jIȘ2a% @74 @4(.= `h'p+xvX}?G3D:^ӟ*&4prx5e^hk@S_̎Cl^^}ڶ-q9@e @|wMrc9P(TkruY@MnuW`%?Q8wG3g; dlo 2 Uu6C֋%YT'Rjo1Mn}L+:O/`@ӟӎ4J B $YaհH Ag0IQ<;v|<6G@tqX>ɏpI%(Xv7}19lAKڮ6]+l_6'3`k*T (]65R-[(EAJ!3s:e*Aܣ ZEsNьmcЪ..> ˆӽ>ϱ&dz̹zԘk䨰ڱ-ٕ6o*p+.gܠr?3:2ty&!^9vӐy*'ImtӮ:dN#LaRx!d!R *9SDdkb$Vdž^t4}h5eHNrHI,O6'l NO#xa OTV-(!JZyX !]z@. 5-DL5_rHqg/r秂gͯP%x d꿖xAcŘʺϡYd(*:od`AMPb-nt]#lg&eb5d*OE 5 UThlv9_)$pC+(M ռPVOptcC`ՠ0IJ85YA('针1J ) =n?Epaq\')_4}KY+d>^cV60EZt,)ie Oӟ5ni8B5*Ƅxn@EDP>e$I^na Y>k#w?p͓t!_1 dr{d ,@]+ضCzn{0RUK,&Ձ\ƭТ1LB#Jp0 XJK7ZLD"afI1?jt'8:/(IGʵ6 <+r xj=9zI!ƶreGNXNpA4Us]b;g-L:/ڮpaؖ:1xǔ`V&EE?c CۗǙ77-`$Mv|&sČ 6X!g#ndχ[w䄁n(dَoo_o2<ݻ  xMI^ [$dDTZ jķi|O.E9wbSsBz֚ȴ!2g6bcrۑW1A"nX14nKOC-NA=9g5=W^x(xڞEt8}NIDʄ!"]}FET2mRi< r3a0!fS&W{V_ ħ/Wc 15y8/ V㯧٧򁂝*^F}#? P掸-~m~j𔜒FvV K.\'YƎZ|9&fr7ᶀQ~n- L5Q/[[ORue>G zjP˯,jW灔Rڮu7q jml 3!9ri `u8!5$cUUO;~}ۨd>̖ glUov+"Q%z=$Uu<J6RGʴ̇vm%û]=PC}_2k& ;eG7גI0Qf/ e!S|2F;֐n3:Gj)~kM'AR>CM^}]dLBu(w& GJ*ԾS0|CxoiNK@N@f2ްir7%x478˷턀Ȣ5k~:Dwp";jA `SR\Y.wNCky~uH#(8N7 v/I g;0Mf{ؒF3 SwHnp}D0yafA3?E.RB偗cU|O+U$r=هn5`̕,/^r;5?9>ϜNGܾ=ӳș0H>(˴ܰ½ӥzT̴V㯴*ߣ6c^֟}@_ϷW&)#׀+$ɐ2i_Bzv`]C]c+老ь*M0\omV ,T[a'rھٷ=+.t_,'P)Чr*4Wp$ U{-тB qڠ a`O|qd3ú$/|MR-` ;6M|şg~Y u[l(oԁglEwք+pdڳXlDXuG b2Me *eiRXx8AEnS\RyEƒjT91Pr]T|u0zWMS=nkčeԍ,AFk/b\vI QDksh>`aP(~j%P> GWlL?ݑ&hu&A$%9c\P "G(" z+"ڸVH1GڟHxYTҫs-pSCq: 99xec]R{zC?yOS.+T#``" kk2A>&α=)gᴡݓ'bʻ<^Ҏ,!ávm J!*5ҋ.5(K>++4y@B[Y -`͑!-|RVMr6 d$jwe(%.`. t `n1h nzeR#nmOنwwOu*NkxcV9Hq82ɤ3՛.S+@&\]bWߡ!Nޥpa0fln ED pCr:Q=̝W8{mCUط;Qtߪjƚ|YQ4C<ZeoDs8HMH3jﻭ|p8=q?Ҽ=EEe>6K}f2wa]a>>jFɷ s V5ˤ;*nb$Svh-8yː=isr(/ e8'VZL078L (M"LjVδn͙VtIr~(RH!㷶5|5,ߡ|M}=X."!Gp,aKmTFG[Y1hNJo,[||@_=bs8^PrSUHe%(2 GQM=PnWk!,̬R(e^= 0fX0eNgwЇf[h€t?ٴKt-?gW7L/e韹Ud.F&Gl,OeTq0Fʫu.D̬Px`vk2i!#SCR0ǒ~_Oޢ9盩eF?8]@]ǙPT*"=fE-> @\<%HnJo=|ID٥2OrwH"?ue}R'k(0I6pUqⓟ:<=&H,,۠އѨ8$}K7#OH:uwdAOifV#*_N\px #3HU9 7r Uf~A9$CHF~a$Xzh~ME#_ KOD6͡PNn0x_-`#"u\\v 4uJ@k*bc7MV}p!,6<}{ )CGm&ͩ/ XMTլAPDтN hrv:OU-?)g)jg N H 32֦=8-p7x]M+,)b]ZGs9͵1#|xGp294troJKV}~4eۓ'8U\lw^Q$kb=jMEP_~NJ5;q+콤E߫#/0|nϒh J)<:$LE2PwMkW0 )&8lwB0+ۛau f|΋VwQAtJiqo1(dO~B%}ݟX;:(Vvg0*8!'џB庆7%GEÜ" DJ:I_9 zhC^# .VܸI+ذ-) -2Fzmk: zg<0`inOi(8y#l.x7Y~eHyFo[/)[5*;, 2IG2n~x\7^sY%;唛ORߩQKv$gPewn5q])RxYX2@ţS{f?|[5D6e9"g/j.ECO3JB忖[\f+?@pJw:)Oh? /w:y1 !oo_9;]C 8.}Vvj_|y=O^=BA)]Ul;MajgT򾮡HAuqZ#:#4 n>CiII$mVؘX'2e j[﫴+Jba~~N5l8q~u^]"E="?C}sՍu^Ngg[^C.W%n,s ÝB~`ڌi~N7 8|PG^$JRqKʅ趿N[*えbA-V#6<W%";zQ~ XT);E"` 'Cels^I+ee&'eF: j\ZC*b/2}qNu*Ȳ9#Z@E;Pko 4ap ` D= KX>#M9<ܔ@ Ul/.Vg< = Q ݫLޝK tGKma*vЋoR=ƸF"n1 Cd)|!x0cSə  l׋&k?),4'%x FAp&TvH?;SI":z'.6B2JKy0 ܶD>Dz:N9dWɾ;>#ɸ龣)><,h r4wz.Ktۉ9tڢ:de_W}*U.y|-HıBǀ3h<.8kAn-jb;[ZVsV| #`%j탊1F' œVn0lev!0@64~W*>HeǻuMP Y%M}U^ɀU4P/)|mM8m55토LeRul,)M>AճI=4"9ѳܱʱS,ҦhñM6jV²4/%lPϵմǵ/"&<~P(*]îKaN7aQ+Ecl,@@dt*J"m ?Q]t5A6Tx5P ?jXb ,FUֹr9N @ ds28 Zگp@{f1͑8`GJ^b1 d-؃h}2z϶0ҷD~y12ʈwzHzWKCBr_$9+e~w+tm|E崴rtS\,Ĩ/u~ʏ^WE}AG`wLw'!R{ )+)Dpܰt4JJ!7\aōBLUE.y:{5XIo*l6掩ka׵쑵KUe9@PǏp2(,Of."*5ɟD{GVGZVEFUmRzu>JP XQ_`N)>۪ܻ]]yVql@)hl\"8P?og*G]h2$f̗ g>HƜzT'DCCv{l}h= R'rO6k3Q8 шܡe  q/},xSb}mW:zrgC=[r&_m q,^TJhW!/YQ#~@6p'%Gˬ̋P!;D8 #NZaawlCP q(S])xʣV2V7 *aVGqs[Aa%Qqj2ԳqzׅQ,|y\YZg!$rԒv 6Wx. nJƚn@dCUhf١ȕ96W˧n"\x2ֳ~o_qTQ`階HC=H5:mrA'ن!( U2jD"~jJ'N#$:L~JBR{!8C4-R=+ y˟zX-̏v +ZidPB{ts{ߜSZΥVXp1:C6BH$iw9wpEP5o*r=ąܷ|wWg}_yPNV0zKp7W22*񲣫i$X 1k@NjO?Nf-JfYq.PJ=Ւ8cm wYBu(#1M@Zީ3$:lO|b2/.9;rRީ$j'}*LnbQjv{M&6`Լax</4|%Aڣ0h3r~ lYvvhvtJՁ絻JwXzDk2wˠȪʯʏoˢ7,*AvD' l%V_vrr#DW-_Ƀ]ye pEB4yv$] \_\ǵ3Ivmw;/ ZY(=JJ'"E!DyE*Cg>o6}9N&0\ȡk动#xߓ ~0qF!J7, *xU>!ʋ(U]nWSTŸ~6@ؑYt^'?:̐̋Z2x"0ĚTI?c7MĮ)( |Dk >|tO1/Q@v(ItH M9Z|%[_mކ ;s. 9Jxa"H~gg5DHmO{g# F&POh}-w!Ɋ(!ƣLy 60z6յQ&:?Ixȧ>G<S2n unYC#*z8 vtˤe Sr4> 2IX CUξ٠q9cmPx'R:WGgPAtѐxʷh1HZe7KǷr7mmyE(ש*j3qق<4qtz <*G?/9asx; =ѩɥ[%79hkpg~ ={*5Qt]ʼ6X"ʛ~QvDpjTHMM־,νxwmwFz[ u)6LB .d:d&e|l':1ͯ«Y.Ո&oQj 4͋bUD.Cx&i1LCωV,K$O v`c^xpveiYE*37HXGDHKGi9.;y׷ ~dZ {4ֆQ7 $!lu|ҷccQtL3[xg~Pys6݈ v˙gҮ~dE)ɱr${YP4KO3i(o5M*PWwm*g2|K_ۇێ?)ߑβc|W%ႋVPNϋ6YhsW=f42dK^E E1Ėlq] z baO[vǨƶLKrPD x8G1E~ )p,d=n0ȃVN.)!5Uռxt~-5|W:boJ1[t7%D NK=4- %IkP|, yu"QM K$\J;WAhO-FgW8- \RlÉJMhL-7R-*{cuʶM:T!2L1J!5ޙH5G:zvT$; ; n@?"vn#?9Op)Y^}f}9$Wq./ SM@Q.='H#e'##$8+fvlO'R)~+A^BD7cΗf[n&U7C`F )ƠΟj@UU{Z>g?K1[JBa|-7o{VODpGvgKpˤK +˔8r.-qʪ4g.o??AɬYԯz^TN^%!8Hu0n#pzk2T/ r:\)jzOϾ?% e;bfYZB^u|ioɩ*S|uohL_@W *x0hg09qu.ԑH/f/j-R_?71)"pB%\6ـPY&p`&M%w 8n@JzB4?5LL\k\ j2$̈_D6 ը`NIg!+;_ҀHvtqZj AV%Ue>`;ed4Xp B:b.c5aN@TVX_(V- s:ъaa)YTxO\9Qߋ޼߼sSwI;2}bs?]ˠRRpś#_Cl˜}W1xoT _u| X]F<=Ulj8M mjhLh*m8SX1 &puqFTޫs$e􍯖א6t ZLPs֬1 GcQ@5uuwtdm0X#XM]l+;Ս1̧LA*>IPVc+!y!aEwitXD\zkD}'Š`җR߯aL l N7;^Cچ]aQlx3E%7Ʀ܁}׃J`cQE늪 E}GO|Wi *ٚʸ!. ᏄP8ΫZFX%8lĉ_F|C-QX  %ޜP`jXtncCS%jSB HLl 7׳R+v %2W$Fטvtvl$7VJCjL1_~k79)h4(D73:ફm0Rc%фMፕ <= 2tRTte% Xr+;qݏo#p`qty2un}aT B^ x+v̜vM_#f༈Trxj&*_fzHg,a&dWy pd \96#wyJԆ(IFA$dj+o~ZِwgZtOrrM OU+4X/L6 qG@VXr=F䬾}I54=:Wԅ- W2 E;x|z3j m,JjeT@+a)G/]ۻ=M叓!BзS3X$q;P Yceֶ Kà6:MnF[2 XBZL uHYu׬e׃!&ȓC~:_σ3Pv gӖEL}օ8%aoJ34 ,f sTnkPAI|E 4Lm]Ύ븀%t%gԩv.5#h`NDؔ\ կ->Nܲڻߟn8c1X*\M?6!'a]*f'OA{׿(р6<`Lu cÅ[ɯc )P}0):wi޿J"u`]WEZK PsCP)tz{y #ޒyޓ4*ЫP4A~-eAPfTT渒tYC쀺! f@8-䞶c9jŦMsGl&EL/%sLMih8TxZ,AIx}+,1d|rŸ!5,ٯU`Sa?$Y2gfc*4bu*f׼G%r5:"M40-SdyO6z Wahf: D.+ 1NsG|" L'5ߑCsMwO b`;Ƨ~cӸ|w"cyl cU$l$G$]h:INz9;6$\J>*)MQ t:+P-k R <Q˔ O^W0^4B_S˂kaQTpsWvG V\CjjIi877՝&&[(Jl?,{*pֺrngIJ@ⷘ%gY"\!z\ ]IMkJ3Q 0`"as/93eFQWB-[GhW6ʻ*n7{nC43#DWzhkUn3E&a vU./q=1[q(I.}~8!6 KlV"\ܣ\9pu~ٳ'3}),ɤu|j):ҦXɌQK+ ƗՑVVQ}*9$i: nmoG*5@L? a6<HÂ`19h9W5C@_{/AI{?t$4"'"!g\otY \='dePY_);Iʸ.W@+ &+k~`ph^{ʌ&jE(\_N{TҳAɠڱ,f'fSi>^TQ+'XhAnT%TؿʞүEP EpdJs":HTx8,x+壦㍢a}FߠzgIxq|~67.5 Zex\otx//N A!AUI5\5r\C-*ױ),ANjl.'̧Aұ^4} 49WJ9[- QL ]pд +'$co `K.#p )|"Kj WӶդ{l endstream endobj 547 0 obj << /Length1 1408 /Length2 6493 /Length3 0 /Length 7901 >> stream %!PS-AdobeFont-1.0: CMR6 003.002 %%Title: CMR6 %Version: 003.002 %%CreationDate: Mon Jul 13 16:17:00 2009 %%Creator: David M. Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMR6. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMR6 known{/CMR6 findfont dup/UniqueID known{dup /UniqueID get 5000789 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /CLOOXG+CMR6 def /FontBBox {-20 -250 1193 750 }readonly def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR6.) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 53 /five put dup 49 /one put dup 51 /three put dup 50 /two put readonly def currentdict end currentfile eexec oc;jAw-=%W)-{ru)rAE(@{빴Q|_R ϤA -T@|q|VkJ%qu8PwGxŪ̆Q6K -U\%b"t-*xJ+ }3{Z2zݬT2s$Z&{BJ{r̗m1l(zNRr^&%:(/IߺHm!4JxI7bs,OiOl7Ӧ!b^Ѵ-E>3t;<;l: OSS*O?9-w yg8LsYtָE qHp0>ˇ ,qۊq mZD]7ʺOk-G_\SyGLN8g2Q}:ä|C/ɑl ѓčC2`Lu3D*Cǩ5љsLUkmH FqTfZ$|2xlڮOuxgG/|:&Nn$JEQyރ4>py'3ji.ǦX9~b0 ub;F8(PFY|DS%y=gn!QZИOi歨H,a7`_Z<gZeߟ՟q/~j'[E1 wg,Kom>M8;r CXVkg-/R@|lbC/zK_i,'1Q7^3EӪ9$Zdy]ltr=>K%a1\(t.EzW(#MN̑6~*E;ֿCa^1y5ݿ'hyf s.8ϰ5ciG$5g0KTlp@>]fW7QGVn~˟=]Z`*~7 "ڌcw0U{Yn._xIPYQ]`MN!Xw:R;t+]gZɅ oswQU)8aA^av>xƍH_n~}StG7 K72fCi0Gm1u?4&]ژdFpmUhӲ$w\Jd8+SE=XnV%?ү֟G[4D)ҏ}<)%pD%qrkoX(&Ƕc<^ԺO;FIRCK-fjz hs+*U-\(=D[d)@%t)#ْMٗA=5N$1Qkh|)Zc׼=}6^w'eufH p!x."s!SpزvNȗy8~%_mD8ǸrɳhwWu_6[= V]Y2?% )/KR|e=b_0Sʖ531ؿmx> ՘OX![ؠ`vf|}R 4"~)uv E$U\W;댞K0 6$֥拐Pk?yy4<˒q=CG$ @d~A1Q8A-|߉b1`zj ۦZ\.r ~s"b]Ry&rD0hLS)z6M="'OOQk {2+$}<໒W` 1=',hkƏCfE5F]Ћynh|d/(~&PB9Cx9 %,9OKLvH,>,6"+Ƹr<]A+6JJ9ۿ2jQ}bF[z'p&S*U$ؖa`RI=՞dv_\WB_5n[&UXiNcuοrvI]VI߮\S"Ivs qYpP]5||rOډccB0KV|נ40Cajps8A軝Y4-L ͯi FV{%xE_ *`LOU ǔKGs|mJ%5ݯdAv<jா-W:,=BYme"r5tŧ>,wxI_ esxRtQeh; -[Gf҄(`*/I{w4iOa"č\%{-+`8@;dZxW'gA$vq%=@ Py_w駾{p6LMmM# R Y$Р쭀|6|噐ȏGI`fkqa}@tZ&'=3bIgU5eA},):ichZ:l҂ 2W#30rM$a ImvO", :(%CMi@\[ t=UMn[B_2_@nu?L,DWUx=u}#m6xA x^QZ+% *{ϊշr RH [*Yy0iǭ0abP7y־pvkTTR+%7!fF gGP2?S%|b%N&t:>EOYJJJZBH-!~yp̊Ҭ㠄֯d z/3j*(JP$'AT˪x"b4~4]Xպ撾99T<ԟʛKȟ9[I{P>5Ruc&(0ܪv;{3x}_%.beW2eSxD8o{ۻ}wn,WPz;+RtVX= \uBU(Cvw?H jt~DxtӃEP[x/2)+ഷʱx46IHgoE'nb\lLhcb/K}kVD u6#+9oi(gy5lS{ ZQ 0dpWg-Lbpy\z(gR6eKG=9U2ݧCH opr'FS+ U$κ h; I~Ζ:oDUEFyo;0?mP>"#Ǖ T5J!*S@M7#8&-yn95GTɄV +WS[Om3Pmd,+ST졆kyR<$ ݀ 2a&=CԠN 97#~MT?BzR͹Qz]sTP@P G- R9Mz)3MHxV'.(s;|_OT՞X9`G $PW٤eY=fE%ԤOpdDmz]֥zK+xIVk w:Mm4YV#⺸M]*Ǣף9t5#rm'Eeo$Κ+z8n/=?njѳ((,O2w <6Fnc1!AzVRIز+Tko9:W\v.yA5gf]?j6)xy!N5g,:2F%uE`Bxw(ݯɆ&^͂NV۞AB k+&@'јsƒ_;q(_:.:)[ ?bt.N|Pm}/u#7A"U)T\ZxH ro}o2Xa/vD3kU[+,뫲,O 4%߇$H'űC/ |,v=}醜Cy`6YP*r8%{o4c1OSB!dA6]W%gcTޟd>M2^Nj[N@*Z;#hhK7#2;Cݶ2 wC"[yDJ,#b‰ZV*7 xߘK;Дyv96I)I" $!/8o(PyRUS`<!{Ge+(CuAqlTcu[ j=E՟2C4%2+drQ/;ڑ}C`@|&cſ1IO}5& !v,+M1pp_㯎0iP͕񇐸gZ1:~i(l=kqa.1':;)]4,6uxcLAa^!L"u ɜ~=C3[ .18jITOQ Qy(E*>'߇߃5 h V`,vr3TT{3O_<΄D+ h3ʂpSV#u:>f`"_Bon!wN y/C5rb?7@?+V5خ B6oYq^5Zp r,B^:NJ07Aϊߧrէ}E4zAWr%`HpZp={o.{#'uMTÕ[gI{dLAN }be/F? A]buvqݓ[3<4MBTparN[0O4\ۤ识BoƸF >'dnxN#ik_Aޛճs#;w͑2G'șV4ksݷQ۸tB"BƷHűVt#$hϻ//%GRMXg] rw\ `Ӟ(On5]8LJsJhHQMБdy'=2hʽ29hX6e~B {Us _}Ҿ?_buռF5dzΛO`;fZ88p` [ulX{jvc|Hvg>I ^+btg(KzC[g7̙sY;)|O[v$K[>y b)f5J5BG%sOMܹZ]f@/Z4YУ8u3BBc'FjBӑUxvܭ,V^}JS mI;n1=u~VcMb*g9rB2%Șw \~ #i8#k&8EFɨmYj&#sp Cķy+>$,hs!DY**7V_)Pe2Za:kX F9&!I.WbD8Db8wU# ;#$78z3XVObd7 ĕ$> stream %!PS-AdobeFont-1.0: CMR8 003.002 %%Title: CMR8 %Version: 003.002 %%CreationDate: Mon Jul 13 16:17:00 2009 %%Creator: David M. Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMR8. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMR8 known{/CMR8 findfont dup/UniqueID known{dup /UniqueID get 5000791 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /DSYBLE+CMR8 def /FontBBox {-36 -250 1070 750 }readonly def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR8.) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 57 /nine put dup 49 /one put dup 40 /parenleft put dup 41 /parenright put dup 54 /six put dup 51 /three put dup 50 /two put dup 48 /zero put readonly def currentdict end currentfile eexec oc;jAw-=%W)-{ru)rAE(@{빴Q|_R ϤA -T@|q|VkJ%qu8PwGxŪ̆Q6K -U\%b"t-*xJ+ }3{Z2zݬT2s$Z&{BJ{r̗m1l(zNRr^&%:(/IߺHm!4JxI7bs,OiOl7_gѳs6;P}tx,IvJ3Yʫ] =~Hrl;H :(xP/PL͍SI'sb~|PpNcOAͧBV")Th^Cx(Ry,s)+Hߋ;m*?>H"%N;8'bGZÕbd ^i$iaesF)l:}3X  Mv%GN,Ҧ/~`Љ"JO238ڐi -]IGcf7Ԁ2ڣ}T  @ &x߳8h {ga5Lw'~=OLcgPv9F˛z%e|O/bV K ^Ć8ԇ<)M<m;疑}Od1]ZSmPf4Ժ)}MPg2вl1gFޢp V}{<[5iJOY>5XZ$157~Zڕ-UDm?3δ쩄'V+RGpyDHvx{pcL1w¾ FMNg(S ?)?;@ṂBN߬GXDio n PSSXD[kg[tU^?f27#xUým`jck$u:RمiEUա<.^Y&ۆo9s> û 8jzIC%oOn8Rg#;D2(J+|Gk9ڲփey/9+,-b3w9W7} z᣹өUyTpt_24a6s!O #i׌$޳\Apr$w5\plYn1upd[lk!lRv4_x_$V[HZKr\wu%_F ^ =ԝȆCf%-۷R>Qٰ2 )~zx6mXFVCEOxJ jFmh)XɽЇ8{u c*;e?blV|@-jAf9Vb 8Tdj4!VerZvZ,eV҆?0 ZWGvl~و[5rL}qTvmjCbM:gÇ VOiڪ#|ym-4-, fFxWpsX!6q-M'ŏ"1,sxɵISĜV"^j73EvV(T^K-k?Ӓ.;d{)pBh+4uU *:m;<%s!- 8X+p&4jO^1TpvD^ x$+flx7=1S6>rMz 40] XC 2ƺ_s5uD^'? jeq (ӓQEuf%x(m"B (brqYqu]ΫHgp7:NQAdYQk(|_S/8aV%'ov"U2!kh5Q?)投g&J$,jS]&1Fq**X*ilSfN{qZ '@dnl{"KDŚ 4tTY9X}4heQ l_7@ZUĩ/Ac*A\4;N{45L=!V5. }rKqS*'R=:tF_}OV-F=;*ZGoe ED,A$ CÚI9:Fω/%`,miSs1M>l搣Z՟_tJqǙJkuBy#+1HLabL 剙 Wb])Qjfnpht;\܌8:,{=JE2[WD{D7ܻ9'Jޞ#11j:n+G,,ls3݂FITHH`v=%.ayKyMBn!Sukyv"5Dz ֧'4Q| &֨ӷRc3k&ӼJ 4m [[h|]5 9Jȍ 0g_ wn{QAnGgIH]E oV值4:(\TYs7HAe{Ю?VN,pPTlΟ fg;I?"BDyв LM> E,4c| }=xbK2^^WUAV7xQ~e#EJf/5R2 jn@FԚI&d|+.;b^ɺN(S k< q/3?׏ƚ~sďS}V7+v8kܩ!ȿ}x =7Z}ǜ]c!j~?}&bXqiE3xmΏZ6զE7C+:Kꉓ~FdNg1Gκ%ׁۃ1ýwCl檬q1FQf1Ż9\@¼(ň^Eг%( fJz^ ' R 2͏aǃYֆZZgd U9/|VϽT_&$_=1zGGx /"Fo<,*#Yo:a&jCȯťuK`uŽ /uwaEt #l!} j؇'*eRh-.h;hMoجcx(iw N̸u T=6^ V$[f@[sk4kJ@/SOnYJ\"mz{1*JKْ|(nwCָ 4&j_G.Yb[J87*"&!Ν&${G?`lê);&|vMÞ\SSELok.N&@`S9eϋci n "*z(N(`(j>䊗1*ɚ߱rjWٶ?ڱ56߫AښIJ'{-Al$h;m#Q5dd0u3+CcZы|1B]; T}݁{*!O^5 ;6Iˑm-x@ʏs[2 NCb+i+Ɍnu}jlD=_}ٹ*13?9r5\ʥB24"F#KLE*Bmw c,ɰh,<#fx%+L54yR#Ss+j%rqJH엮`S|'a!7[Z&.BvK94{~ͯ'ElB9 6gŠnS&}FL5r1}X蝻?;HǯPO*E4%_Qy. +1}ށ;\SlKE@%ŤQ"%VD󩉬y!;0j`.(9d !0;/[ċ>#qod]O>=z-)dgWl|nLղ FEHқ\~l'҄u6UeGBnKM̉OeӁV?hoR5y?ݙvĸZ@'+my5@:pqU`y 2~&@ʹNt;=ΰ oY+KۛFtz/zRk]z,l93& ^ y&\ v+vXuC2I~gs="(pQ"RQSq1x̦,1fɈ[G]x&͕k5E' zFm]mT{ςh1Z(vtO:kТ4oP~Ԣ 豟l;ݳ1`yI@!fLE6<+w/_+XNVLTI?Yuk6rga tq=M=?u4~h7ajGw֖ˣՙb8|7_Aǵ2s>@rk&$n·nٿ`ϼdKDNf60ƀ4#&649߮XGOUSV9'&F#U@VreN)tX{bn̷|C'Ob^Jp$:2}osre 3ꁈ&v 5ϯ8,FtwҒ W?"eoɌ,ei6 ŹpX Sx^4 D!8qvTyS}OvT9Dl;zO0go^2Š6DY ̜xۨTl9U0*~TWʌ!ʴlHIƍ;jTlWv,yh yKUib@[RB*i"s2|XR^9Zhpґȯ!-~p:0?x劐:5O_Y>/X]">W%~s&ٓ}i[Oъ+)p.|M&]0 kؽQO[*%uWNO,a|nF>yt=嗶i5g pjM8j~=W M UV#{|󱹲5<$~X#Vwx X풵I=w6(SRu6*e.!0x`djF,ЉZъ؁52Wظ©뒑ͳrۋ+1SK 61o6o% MlX> stream %!PS-AdobeFont-1.0: CMSY10 003.002 %%Title: CMSY10 %Version: 003.002 %%CreationDate: Mon Jul 13 16:17:00 2009 %%Creator: David M. Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMSY10. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMSY10 known{/CMSY10 findfont dup/UniqueID known{dup /UniqueID get 5096651 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /AWGYNL+CMSY10 def /FontBBox {-29 -960 1116 775 }readonly def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSY10.) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 36 /arrowboth put dup 33 /arrowright put dup 106 /bar put dup 20 /lessequal put dup 94 /logicaland put dup 58 /logicalnot put dup 95 /logicalor put dup 0 /minus put dup 2 /multiply put dup 54 /negationslash put dup 112 /radical put readonly def currentdict end currentfile eexec oc;jAw-ᾉYň5t&נ{hLGqB`d˗Pة|*x\ޖHtEB-gedog7Q`[['W73sZ9 m !tAY!$tY\r[uTIUiBy[Ȝŗ3Kï6zJ!˒Js&B5C"m&`7Ӣƻ3ugNC O~̶uo5=_T/ h,$B%dʘ3l MoYLڶ~3^`12]=l8B6PlpfW< %PIN!ju#,.iXnȼ‡o$ҁXꑷI5V*E6tKo_)RPG;Z@9"V3TTLN Y:Akڬ6̠==80~DQ Q^br/2^KZh`N'Jt4iBYҁ7ޟBU_~\fXAZl_ZƎý'xHbG:"l5CU[aLrf 1[;4p^NpqBD '؅93M&9{ VD 8 aе2n.hf l?K[$Gp/JzcF8vP3/XO6yAo~]WqDMY4ߧY̢XPEL2_2 oH{ 1x'u|o WNRE홹&lF\LRh1Fb}+l C] (vfo+fM}l?c*ވ"^R]miKOҎ!I ӲR_tW;u@(#t*̧ U{|Q}a3Fl8xtHWA­;!V CVov?³;=>,㧫\"RvRCإQDh @_,˜kbflAIP^wٚdIHzk(c3xɁSUPIf{KΩs Y/v[L%O@HdjyTõVmqgC9zTC/t~Řo*9rIojUKxj. ,+b1ֲ IlDLQZ3P-no'$F zg!Ј*oj-Nͥͭo8KwQgݍp*1^.֊ LV~m la ]%."`_QipŎs5y.Xͮ)Td1Kk̊jn0zGqaWQ%zJX3tIy0ľ.#[#D#EԂppF*ޘvrOdn7n f9*X:>Ǽ:*Lf͍9&aj;+{0 )AgðK*XKV'zZA) n TÙLJ^Di[:s<ܸ2!U|#5VfUqP}|=G5O|Ps9}* +gpA,,=|j25Cɂ7 ./Fɹ0tRẊ."we hPempJo@▁_A3QBV~$9Ej= ]? {w_53Fgӿ4BAq41Pf ,Sş6r[v` xG$.} ̔ϾF͙c=f!*˽./wĉR8(@ًz c@N&Imݣ>!meʰl"V8kՑŨj]n3X>Jz?D=Nbn {qbY(>"8*苾ky3o H Dw] d{EʥËw.$Vhtzk$kk$]4cfCW@3plQQ晉b/pTqF8_AnQmK{&z;<տm[i7뜣'*qXTnt<Ռk/?2m)fy#(`%{!Q/0&sxfB+rE[tgOKQ$$=ל?d@3c)]3%*M}H饞;Cdrp1jFcstG'C\p))_)( MM qv&C3NLZswTPu{sϰP+-UFUP"KΆ+Ye7?0(idL;gk9(YI-l`;`AH:YHb1H{wR^Yњ, $FԖHDV?pyїP%F=BGKPh~N[I_ꈀCTzf <Ӗ`4|mE1J'$`}R \N2kfaouJ73vKW{M3?׏M]:W;vX;B X.PI;?!T . sU]䮃=X 5rMt>y=*bC~^ tArl'Ŧ\؟L냡P&7ttuGz;Kg4э;u)";SvC~?J/F"6U.0>+KQӄ0"ӫ=sxoJ]ת!w6O.}t5V˩+7Us֩yēTC5GrgU5$&|~G8 Mv(jt Ϣn]]QWOؑm. R[ИoNng IF:?tؐSUOcj2Cm[O7>kkX' #t'Xd9+E7Nd8{]m/ ׎dvYYwop!EP7F?ojP9"gBP;B^QO3*B 3un$I_Oe` $`}-9Q/ĥMe?Ұh]b _2<͖+tª[ϜJO@%MI tv\/bMVF05+kI2W9>f} Ķ3tj|" [LhY)o57k#%H\,x|ssxH͆|;` v%گT[c]e"GUj߫ytvx:udQuZy_Td"b+O]lx'6w6XCDKOf(g@w]fV[~1F^A3v Ovү2v zT0b#[zyϒ$e1k5dRA`(Ņ@{=yW>>Ⱚ;=H;c30ü^ծ)ՙ-{OO2R´xQwBgБS"תlbz;Iy\EprkM @@e&3lʉtS%)/pR"2u Ee5+ٰsZ'bQSlj zvހ~%.Kz\NE,eV2=Mo)-JcV:U2Ѹ>1ȓ"QWOё4*Oz.cjcY&=7Y,A5nIF/?̊ ]as.N/CջtHG50x}eb9S&0rJHN\?^4'bɻ':K`wpcT!_ H݊{}HmZto7ʫߑQǷbi>ܜZOddFտcc $" |hJQvB'\%63J)Ag+TʍrnLON@EzHr$d(|*ztiF Ո&{5rT[)C =toL`S_6xvtu{*n9vq9 vQy"/؜I}Z ߓYby)Εܷ\xec~$oG H 2҆{C ]e';q\U:v_'K,uYҝ+ 濔mZVM ,t}jwtQ| q; u1~ E.i~ ؤlHbfvogPSnm%9`۸ez. f[bftr%0 2U}/|qqè b ^3Y4С4z\?4%i B D?2-XO^>Fzmn 4K2+xRA­85N';&dXY`3%M6~Dn6=]N¦]#w{ Uv%k47uz=ϳStR7/NS 9 v~'Ĕ> ƥ+<)Ζ[%e:h%S$0"  D}Xz]!&!5 ĩJ*6vY%pM2TP[xe/C,S!WEG~b+VnE=+3bSz(̱Y d 3dү. `ux*a&Tt#E>J3Cw+ 3$*34 ץLߐٷ#Ơ sRMf⇓G]NˎPS=s$8X 6 ݒ Ou^gjFw2 rU2&\bJ~`(0·Wf&@;7J(vA\n梿;e.(ç+/MzvXwٴ"alB> JIp4p6Σij/=fSD5>#v{6%ϝ U/MMѝDW kh́gIڹcE-s9l-'KA|g!ok U4mIʻdžm'Ѡ@ s Rh8C\C.̥ޒfz&Fڍ_<_+P%+w[d r㲣ꭟ endstream endobj 553 0 obj << /Length1 1432 /Length2 6492 /Length3 0 /Length 7924 >> stream %!PS-AdobeFont-1.0: CMSY8 003.002 %%Title: CMSY8 %Version: 003.002 %%CreationDate: Mon Jul 13 16:17:00 2009 %%Creator: David M. Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMSY8. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMSY8 known{/CMSY8 findfont dup/UniqueID known{dup /UniqueID get 5096649 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /GPMNPK+CMSY8 def /FontBBox {-30 -955 1185 779 }readonly def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSY8.) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 106 /bar put dup 20 /lessequal put dup 48 /prime put dup 112 /radical put readonly def currentdict end currentfile eexec oc;jAw-ᾉYň5t&נ{hLGqB`d˗Pة|*x\ޖHtEB-gedog7Q`[['W73sZ9 m !tAY!$tY\r[uTIUiBy[Ȝŗ3Kï6zJ!˒Js&B5C"m&a[9taFF!@-d}bŲO k1툡cJ(@ 6|4M4fV>C ;̹xjRAgd@-#:ɭ܎zAvx?RXeT&aחٿjy;Z.NxVL<8/2ʺHC˱_.U+nӅ#tE[unnVhJ94 }p&G(m7[m!^=>c "=" pƀH?r? ^~_[Dzv SU]nV,'Vaɡ0h3];hwd轍m5zkP4:7φ6.B6QԈi[gU@h5e.\ KQR6r Z܊#zT!<*y]Bءx0Xq$Zcۧv H1*rބ'^6Wο \YmYR?y!G 5d%Kb[H:G~ ]L cNӵ Zz 1[;4p^NpqBD '؉'͛Xčk|GQPE4^ј=|%Z)`>cÉ|J)_lw$[VT6f =ܟ* ipLEr R?qvt rST#0gM]%{gYՆa3WD,&h!كq^  K A~7VŖBxMD26yo:!"D ;m#'WC \ys&k}ZAGjRm&]뇦nWc5&6"בD׮0ѱY$ۮD>wRǀZa8Ps:)"E66#w¨g~$}6Is m8TK$)ƒ( Yw@þ3h[Uƹ # bc )!.W`cɗA‚$w?A $O@c>ҐE2I]Rǿ+ȐLf: 1s O5iW Lf1vP&2lp2IKB'wG`rI[Lj(ybePm(ﲻ;e]t8!U$aoC|r?j5hm28Ouеdmv_1ƶaEb s,c7yPaXQO(xkqdQ7cv ]{< |gKXop׊cz{W [:R!J0pc1cBVKV!TląYIly*2 ӶJed6C(ZL9_@Yq>x/袗O8">􀬪Sf-O'&MYRdW!@/!~q~#X-uGtߟi,i&oX9+a>s\1Q N4ąe0Ht싒`H ;`Ec!ߑ6PM#8~WrguuCEdϮT(>.63ݬ#'=>p؂㤊4Լ#*;Ũ6T퇲̒Nj<⋷I=Qo·|dE'*]g`}@P0T 8g: ֲ-D7K'!`M\緣8o鄍/fGh㾈Q z>˶΄H[Ԃ³ۭ~.ҙU+g߇沵pԴۇߨ^Ϸ5]w^"&âDzl$dc$'eaGyYA=qX7KT?)^٫|O(42nXk9pE=Oi/y5+86KW^6vAsЖ/ùȧRxɅPk@D:~K_ 6LeىԏQ Bz$Lq}GUgn ET<wҼ|"vRT mF͹HDDܳ?v$[HY\zP.i(Ԑa7X33ATa^y:foyU+w; rT[4_#ivYBX;Njvk :Tˤ:Q\| U3̢Qi| JEIǵaga)%/D?}Z >Ŗu_6g, 㹹MUp-.ڧm8m29:a{ӱwYHޖ3#5LokU#Wc@O$rܱ-#p쮗J E!+4Y'-4\^?f j#lw{PWoze&@, " r drIrK3/Α[&38.&EƖ~ZS.b칱@ B6x8="؀|984VLqu_2R`i; 0@g(0*Ј鿢\sW4^U:-AcðA~KNSeOc[*@郬)}v^{ ¿`ax>eeY뜆 {%OVE㆐p,on6>}^qpVU  SErSo 5J)K79I-Ƶ*l$Tatk#%5mBMdٕ96c'V;-Ǖ-i<^bOHǰ[SZ@nkdF?4מ:g>=m˒-67dޱ&Ka[O%5hΆR+J:. ]*dEȴ3/Cg{?ktݒt$6ZB9Yi1 Ls&;yʌ]Y' 7-vpOQ" \ay]B̗;FB_WՊ4^$"훭BBR!c cGqˡv]~ēH*9 ]C֢-ԩRj[kk~!/"Ԓ1p V% ׾_O30H*D.6z#sj*!(}#Hvz}ӣHVt,.!+l؜R .o/T8Qe>z[!\`8kTC^~.ļr.c$蕉I%֨jAÌU$!@,}R"{{,kƅL2JVMW2 JAf|:IB*GsD,\~.9D[c$+*& ~w*_.LuZI,D켈< כiX懯/]|Qs)o}O+w] u/ <@ZABFʹstA}꾔9: dު V@w2c.ҶVKSxXU Lw}aoKh,LT 6^C(eǙb#t?'m'etlE3wſL73dLKk'uv6L]k9~?"}%7 9Aa4؂}y=W=u#g&usYIs5r(S#/cTC۶=8O_Yxv5$ uA/>̨Ůaria^LZNI>^Ƭ+ ,|>)bVºILuG:’y.4>+ }zL=w PbA @X"o{3SPW9Vj[Ea8YÓ 8J<{3T"5cAfWsPybУBg)K.:I]Q;'s"#kxyδ ĉz(vWP}Ko gxY$t^ڑZY [̛ 8Nut/7B <\Ƶ^.ڹ1tD1*U|o}",FGr0MHtL98ɾKU:c<@#Re/)(0)x Ҧd,٬aC?w+@~ӛ'}їZ}~YGX[ ~2${-[BQZBe 2l LYo`QB TW(lcWp ޯ0SX@_g \k?NIy9BQ orkJ+w?e?X]d 5DYUsJ# V_\bZs|Vbi]&.BsSJ?k:4yhW}8,@b7|]!JXmT~% endstream endobj 555 0 obj << /Length1 1510 /Length2 7561 /Length3 0 /Length 9071 >> stream %!PS-AdobeFont-1.0: CMTI12 003.002 %%Title: CMTI12 %Version: 003.002 %%CreationDate: Mon Jul 13 16:17:00 2009 %%Creator: David M. Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society %Copyright: (), with Reserved Font Name CMTI12. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments FontDirectory/CMTI12 known{/CMTI12 findfont dup/UniqueID known{dup /UniqueID get 5000829 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /CVZJMA+CMTI12 def /FontBBox {-36 -251 1103 750 }readonly def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def /Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMTI12.) readonly def /FullName (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 98 /b put dup 99 /c put dup 101 /e put dup 102 /f put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 116 /t put dup 119 /w put readonly def currentdict end currentfile eexec oc;jAw-24 WEvQC<3A2kX0k^|:ٴfb,|=sLu2KZ`3ndgRw@),q՜G<&h'. ΍883 ABAԾI$s@F25ڪ,i pK>6K` %E((bsSD;Uѓ"":!cQMq:(MO)|$~x!A7ux(ǻISG|IQԏY=9"i1B/?xI84HrxF-}S?geXhb'N'68^o ߑT݄j"_ u3S[3^G{Wsh"NWk#IQ9dxpY JJO(UMaKDpP=|#fLV<J#o)Z.$U(X=G-Jk%_HGM %4ߴ DQjY1=KʧHZ̛wOȃDل6C!8]g,cAo?Ҟj?;IAGYPKKɧBs_W9AD2IEWKN*3iA%t  .ox #&ShD"5{nƋ%;{.=:ٯ}]AUi =.:wv6 <n~?V+Ɉ8R rmsri40XgJ~9H)G3TA3c<;k \" "9WB7{YZu>]=h۶#׵N=8gkS^Z΂dxZ >/Բ$1'%!q\sg ,YKX]goRw~IipX4_ A6)Ā_B&mVU=J9zkt 7n/N+u'br$T47.\I0Jh>)Q԰[]" ؐ MCŕ͆Upu k{nN'ghhs }Ng*t\/j4p'2/Z{{5kݟpݞP% ?C 9AVpzGI%ZXcJ rxgYNrfcw~B?B&&tѥn^pDF&Ixe%ci Ⅻ5<C0C'\F֡z[R 4]=)E`͞獨YI!Jfn:W]ŗknI#‹j"BBvvмuFGN;-lK΀i(sl}HGo1Lzǝ|S+xbs*e3>:FNƉUm C']&`W V km&怷B@ϛ&Wϑ/4 Y^O `n>nRE_l6FYnnr%p7}%|UDrZ/,#N1Hۏ.CMn)7Q7!frɘkdfN\o-6Iʨ#Rw\CǛqd*~)]Z9TŪ;De=#RƬ4WĤ>L] \g$2$m q﮸ݣAqdu5B爜ǫJa)ҿ =['f R}]<N⽠zЁ)#0qG32'j g&geAna>I\Rʣ8߭u4't $qi"gE;I̶(ƭ8p} ó)^"rtS_V3Kh9"$a'm.}Ʌ9Yۖ~-iB*+dခXRI Z򂌧3FFNpC)1*RV jm#XIz93&;vNTip qs+;2"cY>'N9sgէѤVK j_Eڍؘt$/Lڒb1pUG&%Yw毞|3 L[NFL]eE|eAzMնTZ<:,.$St=SjF_pEzr}BoN, y^`*3MeixgBpC @m ۂ;;u0-Qq3C?"˯sPBveb^~֫)Ze,˒[ y*?ݳEҞ/_ZNdEc"{u3Jn5kuL;[~d("pMKKjuAbJ6vt-*fu&%XR5Kԩ~qB׭(E:& O.VX@Oc`&_BtOgRn-bs),+{Umځ'nC)l,į&L UHuLU'Jl6t:h]A>[т8˿ܱf? e=Y/wث#Ƿw;o6QlEs52p[ c$bPͳŋ3s91}$q"P҉bo+ՐFsv-@\4NmP)Xݢ}_4hohF 9C]X'p4|:aB7#K7˲n"81-{N;td *a"zj2aMO)BL# {jBT39Uth3~GRb8`7.A olT"D+,K8NJS덠M`'MXN4Уvj"'LO)CD)9{;IJ=i}ԱRoF81~Sٔ&E;9+ݓ,6JSó{2HWzIpW.u7p92QݪP2^AwrͣNEޏy|gqmWU˥s* f6.LK] 3>MoUs J77b,$y~ + ,hϖqztDFktQ!QBl(4>:hvqID*7W5zGsq\X7vmm)NkH7:T\Fn8!J >ONZ a8"5n ZJd!b6`=Ԏ m:3ڑYK)yhfghۥPAc'SU-|G8ȓ|/"MKkI ri^{jD<;pzjA#x;|#`'u䝈AEGn 4yhߠ}4ji׈)BAl@7BhyoBbf\8GS3ˏN޵dX,{4@&U.1l&PK ֬Q{m'c%usr6Ϻ#!Uv .-@WͲEdq]VhR.fdݱogr3xlیqsŶ#ayi4mwLD&Y4@1w*Oҿ,=+ܾuʁU]2hv~L1- Q}f`gEk`Tk%猲3*૏J]I\ӷ70aFj&lyzb&wG]ps4nv_$2^ 屸; mf 1')>HugdƯ/6n y<ǩaq4-KRpG+ 0- (p6￝:E޼L,_G>ߩ}?om,%c7O-_"wຎZF`D?üT&#ןu /!lb"U2pc~FmÀ i?B|)CqwG(\' w*^q"rW?(z Ms#_#3"qfuo/H4wy<7;% YO :=-e;ګ94$TW ǺwqCTfZc(];ۙvA=iğȘ??y?\C7mO&Bj%D,\:հ& $T&65qQUeHokʢaH%"n. :=j6uJ>?-!L_Nn!Y W;87YQeP ٦=~iAc$L&GjKi;wl/ c/bn_ORe$^_B"ÅxzTCu*,?u+/& )3r,$%41O'0iKA LO3mєE4Kq,mT3`, XN[T`NȺn۲;OPP9iM-ꬠgDH(XaҿsEL챂ɭD;hXy,6Tޝ3)Kb" U)qs)X :v wϙp?8^i9-u^Ā…K!>tCF +&4Շ7h!̥S[JW*GtMY[Y (LYKEf.8еZiu6}|^\Z}V<6< ZgoK "<$%KI>kѪu!c?_ x:ejsNe1"eB]X!I2KyA9D$:tҫ[;e0nRvP*i:SNDؽU'<.@3:PverٵUQ#C ! r9IeLvE>EhYɨG2Vu ?k(mv#64,ڎTj#ý7 ð*kig%I8m3I\JweT0Dj؁l0x,?\{˪.v)&Jws sVr_`w#0&5c^Vݑ9L\}d1Kp!:]a"4Q^B9TǔȗVT5jr*iH,WȮQƔ9h(ьurzR˷0|#owq.t* uzx*Y' G<@a1(rb֗O:nt['H 5s(BpcC-U s.Au&P .JZa$+C -&7z[H q1B endstream endobj 563 0 obj << /Author(Jeff Johannes)/Title(239 Problem Set 1 Solutions)/Subject(Solutions)/Creator(pdflatex)/Producer(Latex with hyperref)/Keywords(all the problems, and extras!) /CreationDate (D:20210913152548-04'00') /ModDate (D:20210913152548-04'00') /Trapped /False /PTEX.Fullbanner (This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015) kpathsea version 6.2.1) >> endobj 527 0 obj << /Type /ObjStm /N 38 /First 326 /Length 8329 >> stream 526 0 528 258 529 835 530 855 531 959 532 1003 533 1125 534 1461 535 1849 536 2494 538 3101 540 3340 542 3619 544 3834 546 4069 548 4567 550 4797 552 5057 554 5376 556 5618 523 5853 26 5991 73 6129 27 6267 24 6404 29 6541 28 6676 25 6811 255 6948 30 7086 31 7224 524 7330 557 7402 558 7465 559 7624 560 7713 561 7786 562 7819 % 526 0 obj [805.6 805.6 805.6 805.6 1277.8 1277.8 811.1 811.1 875 875 666.7 666.7 666.7 666.7 666.7 666.7 888.9 888.9 888.9 888.9 888.9 888.9 888.9 666.7 875 875 875 875 611.1 611.1 833.3 1111.1 472.2 555.6 1111.1 1511.1 1111.1 1511.1 1111.1 1511.1 1055.6] % 528 0 obj [826.4 826.4 826.4 826.4 826.4 826.4 826.4 826.4 1062.5 1062.5 826.4 826.4 1062.5 1062.5 531.3 531.3 1062.5 1062.5 1062.5 826.4 1062.5 1062.5 649.3 649.3 1062.5 1062.5 1062.5 826.4 288.2 1062.5 708.3 708.3 944.5 944.5 0 0 590.3 590.3 708.3 531.3 767.4 767.4 826.4 826.4 649.3 849.5 694.7 562.6 821.7 560.8 758.3 631 904.2 585.5 720.1 807.4 730.7 1264.5 869.1 841.6 743.3 867.7 906.9 643.4 586.3 662.8 656.2 1054.6 756.4 705.8 763.6 708.3 708.3 708.3 708.3 708.3 649.3 649.3 472.2 472.2 472.2 472.2 531.3 531.3 413.2 413.2 295.1 531.3 531.3 649.3 531.3 295.1 885.4] % 529 0 obj [769.7] % 530 0 obj [450 450 500 450 300 450 500 300 300 450 250 800 550 500 500 450 412.5 400 325 525 450 650] % 531 0 obj [611.1 611.1 611.1 611.1 611.1] % 532 0 obj [413.2 413.2 531.3 826.4 295.1 354.2 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3] % 533 0 obj [295.1 826.4 531.3 826.4 531.3 559.7 795.8 801.4 757.3 871.7 778.7 672.4 827.9 872.8 460.7 580.4 896 722.6 1020.4 843.3 806.2 673.6 835.7 800.2 646.2 618.6 718.8 618.8 1002.4 873.9 615.8 720 413.2 413.2 413.2 1062.5 1062.5 434 564.4 454.5 460.2 546.7 492.9 510.4 505.6 612.3 361.7 429.7 553.2 317.1 939.8 644.7 513.5 534.8] % 534 0 obj [272 272 761.6 489.6 761.6 489.6 516.9 734 743.9 700.5 813 724.8 633.8 772.4 811.3 431.9 541.2 833 666.2 947.3 784.1 748.3 631.1 775.5 745.3 602.2 573.9 665 570.8 924.4 812.6 568.1 670.2 380.8 380.8 380.8 979.2 979.2 410.9 514 416.3 421.4 508.8 453.8 482.6 468.9 563.7 334 405.1 509.3 291.7 856.5 584.5 470.7 491.4 434.1 441.3 461.2 353.6 557.3 473.4 699.9 556.4 477.4 454.9] % 535 0 obj [777.8 277.8 777.8 500 777.8 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1000 1000 777.8 777.8 1000 1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 275 1000 666.7 666.7 888.9 888.9 0 0 555.6 555.6 666.7 500 722.2 722.2 777.8 777.8 611.1 798.5 656.8 526.5 771.4 527.8 718.7 594.9 844.5 544.5 677.8 761.9 689.7 1200.9 820.5 796.1 695.6 816.7 847.5 605.6 544.6 625.8 612.8 987.8 713.3 668.3 724.7 666.7 666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 500 388.9 388.9 277.8 500 500 611.1 500 277.8 833.3] % 536 0 obj [571.2 544 544 816 816 272 299.2 489.6 489.6 489.6 489.6 489.6 734 435.2 489.6 707.2 761.6 489.6 883.8 992.6 761.6 272 272 489.6 816 489.6 816 761.6 272 380.8 380.8 489.6 761.6 272 326.4 272 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 272 761.6 462.4 462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 611.8 897.2 734 761.6 666.2 761.6 720.6 544 707.2 734 734 1006 734 734 598.4 272 489.6 272 489.6 272 272 489.6 544 435.2 544 435.2 299.2 489.6 544 272 299.2 516.8 272 816 544 489.6 544 516.8 380.8 386.2 380.8 544 516.8 707.2 516.8 516.8 435.2] % 538 0 obj << /Type /FontDescriptor /FontName /TJDAIS+CMEX10 /Flags 4 /FontBBox [-24 -2960 1454 772] /Ascent 40 /CapHeight 0 /Descent -600 /ItalicAngle 0 /StemV 47 /XHeight 431 /CharSet (/braceleftBigg/summationtext) /FontFile 537 0 R >> % 540 0 obj << /Type /FontDescriptor /FontName /IMNZVW+CMMI12 /Flags 4 /FontBBox [-31 -250 1026 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 65 /XHeight 431 /CharSet (/A/B/C/E/F/L/S/a/b/c/comma/d/f/greater/less/m/n/p/period/r/x/y/z) /FontFile 539 0 R >> % 542 0 obj << /Type /FontDescriptor /FontName /OLBSGM+CMMI6 /Flags 4 /FontBBox [11 -250 1241 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 85 /XHeight 431 /CharSet (/n) /FontFile 541 0 R >> % 544 0 obj << /Type /FontDescriptor /FontName /GMZMQY+CMMI8 /Flags 4 /FontBBox [-24 -250 1110 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 78 /XHeight 431 /CharSet (/a/b/comma/d/less/o/p) /FontFile 543 0 R >> % 546 0 obj << /Type /FontDescriptor /FontName /QXATNV+CMR12 /Flags 4 /FontBBox [-34 -251 988 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle 0 /StemV 65 /XHeight 431 /CharSet (/A/B/C/D/E/F/H/I/L/M/N/O/P/R/S/T/U/W/Y/a/b/bracketleft/bracketright/c/colon/comma/d/e/eight/equal/exclam/f/ff/ffi/fi/five/four/g/h/hyphen/i/j/k/l/m/n/nine/o/one/p/parenleft/parenright/period/plus/q/question/quotedblleft/quotedblright/quoteright/r/s/seven/six/t/three/two/u/v/w/x/y/z/zero) /FontFile 545 0 R >> % 548 0 obj << /Type /FontDescriptor /FontName /CLOOXG+CMR6 /Flags 4 /FontBBox [-20 -250 1193 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle 0 /StemV 83 /XHeight 431 /CharSet (/five/one/three/two) /FontFile 547 0 R >> % 550 0 obj << /Type /FontDescriptor /FontName /DSYBLE+CMR8 /Flags 4 /FontBBox [-36 -250 1070 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle 0 /StemV 76 /XHeight 431 /CharSet (/nine/one/parenleft/parenright/six/three/two/zero) /FontFile 549 0 R >> % 552 0 obj << /Type /FontDescriptor /FontName /AWGYNL+CMSY10 /Flags 4 /FontBBox [-29 -960 1116 775] /Ascent 750 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 40 /XHeight 431 /CharSet (/arrowboth/arrowright/bar/lessequal/logicaland/logicalnot/logicalor/minus/multiply/negationslash/radical) /FontFile 551 0 R >> % 554 0 obj << /Type /FontDescriptor /FontName /GPMNPK+CMSY8 /Flags 4 /FontBBox [-30 -955 1185 779] /Ascent 750 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 46 /XHeight 431 /CharSet (/bar/lessequal/prime/radical) /FontFile 553 0 R >> % 556 0 obj << /Type /FontDescriptor /FontName /CVZJMA+CMTI12 /Flags 4 /FontBBox [-36 -251 1103 750] /Ascent 694 /CapHeight 683 /Descent -194 /ItalicAngle -14 /StemV 63 /XHeight 431 /CharSet (/b/c/e/f/n/o/p/r/t/w) /FontFile 555 0 R >> % 523 0 obj << /Type /Font /Subtype /Type1 /BaseFont /TJDAIS+CMEX10 /FontDescriptor 538 0 R /FirstChar 40 /LastChar 80 /Widths 526 0 R >> % 26 0 obj << /Type /Font /Subtype /Type1 /BaseFont /IMNZVW+CMMI12 /FontDescriptor 540 0 R /FirstChar 58 /LastChar 122 /Widths 534 0 R >> % 73 0 obj << /Type /Font /Subtype /Type1 /BaseFont /OLBSGM+CMMI6 /FontDescriptor 542 0 R /FirstChar 110 /LastChar 110 /Widths 529 0 R >> % 27 0 obj << /Type /Font /Subtype /Type1 /BaseFont /GMZMQY+CMMI8 /FontDescriptor 544 0 R /FirstChar 59 /LastChar 112 /Widths 533 0 R >> % 24 0 obj << /Type /Font /Subtype /Type1 /BaseFont /QXATNV+CMR12 /FontDescriptor 546 0 R /FirstChar 11 /LastChar 122 /Widths 536 0 R >> % 29 0 obj << /Type /Font /Subtype /Type1 /BaseFont /CLOOXG+CMR6 /FontDescriptor 548 0 R /FirstChar 49 /LastChar 53 /Widths 531 0 R >> % 28 0 obj << /Type /Font /Subtype /Type1 /BaseFont /DSYBLE+CMR8 /FontDescriptor 550 0 R /FirstChar 40 /LastChar 57 /Widths 532 0 R >> % 25 0 obj << /Type /Font /Subtype /Type1 /BaseFont /AWGYNL+CMSY10 /FontDescriptor 552 0 R /FirstChar 0 /LastChar 112 /Widths 535 0 R >> % 255 0 obj << /Type /Font /Subtype /Type1 /BaseFont /GPMNPK+CMSY8 /FontDescriptor 554 0 R /FirstChar 20 /LastChar 112 /Widths 528 0 R >> % 30 0 obj << /Type /Font /Subtype /Type1 /BaseFont /CVZJMA+CMTI12 /FontDescriptor 556 0 R /FirstChar 98 /LastChar 119 /Widths 530 0 R >> % 31 0 obj << /Type /Pages /Count 6 /Parent 557 0 R /Kids [5 0 R 32 0 R 54 0 R 74 0 R 215 0 R 428 0 R] >> % 524 0 obj << /Type /Pages /Count 1 /Parent 557 0 R /Kids [505 0 R] >> % 557 0 obj << /Type /Pages /Count 7 /Kids [31 0 R 524 0 R] >> % 558 0 obj << /Names [(Doc-Start) 23 0 R (page.1) 22 0 R (page.2) 57 0 R (page.3) 72 0 R (page.4) 254 0 R (page.5) 450 0 R] /Limits [(Doc-Start) (page.5)] >> % 559 0 obj << /Names [(page.6) 503 0 R (page.7) 522 0 R] /Limits [(page.6) (page.7)] >> % 560 0 obj << /Kids [558 0 R 559 0 R] /Limits [(Doc-Start) (page.7)] >> % 561 0 obj << /Dests 560 0 R >> % 562 0 obj << /Type /Catalog /Pages 557 0 R /Names 561 0 R /PageMode/UseOutlines/Lang(English)/StructTreeRoot 1 0 R/MarkInfo <> /OpenAction 3 0 R >> endstream endobj 564 0 obj << /Type /XRef /Index [0 565] /Size 565 /W [1 3 1] /Root 562 0 R /Info 563 0 R /ID [<010F9C85D45C5822209B1C4DBE0AE908> <010F9C85D45C5822209B1C4DBE0AE908>] /Length 2825 >> stream  _]     ' !"#$%&*6)/b(+,-./01234598e7 :;<=>yyD?@ABCJEFGHIPKLMNOVQRSTU\WXYZ[b]^_`aycyyyyy yyyyy yy y y yyyyyWyVyyyyyyyy"yyyyy y!y)y#y$y%y&y'y(y0y*y+y,y-y.y/y7y1y2y3y4y5y6y>y8y9y:y;y<y=yEy?y@yAyByCyDyLyFyGyHyIyJyKySyMyNyOyPyQyRyUyTyXyYyZy[y\ycy]y^y_y`yayb{     "H!#ED)$%&'(/*+,-.501234;6789:A<=>?@CBFYXKGHIJPLMNOUQRSTWVZEE][\`^_cabEEEEYEXE EEEEE E E E EEEEEEEEEEEEEEEEEEE(E E!E"E#E$E%E&E'E1E)E*E+E,E-E.E/E0E:E2E3E4E5E6E7E8E9ECE;E<E=E>E?E@EAEBELEDEEEFEGEHEIEJEKEUEMENEOEPEQERESETEWEVEZE]E[E\E`E^E_EcEaEbtM     LK$ !"#-%&'()*+,6./012345?789:;<=>H@ABCDEFGJIONP`QRSTUVWXYZ[\^acÍb ) G { *  -IO rG !"#$%p endstream endobj startxref 317396 %%EOF