esorics05-Klonowski.pdf (288860B)
1 %!PS-Adobe-2.0 2 %%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software 3 %%Title: dnv.dvi 4 %%Pages: 15 5 %%PageOrder: Ascend 6 %%BoundingBox: 0 0 596 842 7 %%DocumentFonts: Times-Bold Times-Roman Symbol Courier CMMI10 8 %%+ Times-Italic CMR10 CMSY10 ZapfChancery-MediumItalic CMEX10 default 9 %%DocumentPaperSizes: a4 10 %%EndComments 11 %DVIPSWebPage: (www.radicaleye.com) 12 %DVIPSCommandLine: dvips -t a4 dnv.dvi -o dnv.ps 13 %DVIPSParameters: dpi=600, compressed 14 %DVIPSSource: TeX output 2005.04.01:2336 15 %%BeginProcSet: texc.pro 16 %! 17 /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S 18 N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 19 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 20 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ 21 landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize 22 mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ 23 matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round 24 exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ 25 statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] 26 N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin 27 /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array 28 /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 29 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N 30 df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A 31 definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get 32 }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} 33 B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 34 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 35 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 36 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx 37 sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ 38 rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp 39 gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B 40 /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ 41 /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ 42 A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy 43 get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} 44 ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp 45 fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 46 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add 47 chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 48 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} 49 forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn 50 /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put 51 }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ 52 bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A 53 mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ 54 SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ 55 userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 56 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 57 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N 58 /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ 59 /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) 60 (LaserWriter 16/600)]{A length product length le{A length product exch 0 61 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse 62 end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask 63 grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} 64 imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round 65 exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto 66 fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p 67 delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} 68 B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ 69 p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S 70 rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end 71 72 %%EndProcSet 73 %%BeginProcSet: psfrag.pro 74 %% 75 %% This is file `psfrag.pro', 76 %% generated with the docstrip utility. 77 %% 78 %% The original source files were: 79 %% 80 %% psfrag.dtx (with options: `filepro') 81 %% 82 %% Copyright (c) 1996 Craig Barratt, Michael C. Grant, and David Carlisle. 83 %% All rights reserved. 84 %% 85 %% This file is part of the PSfrag package. 86 %% 87 userdict begin 88 /PSfragLib 90 dict def 89 /PSfragDict 6 dict def 90 /PSfrag { PSfragLib begin load exec end } bind def 91 end 92 PSfragLib begin 93 /RO /readonly load def 94 /CP /currentpoint load def 95 /CM /currentmatrix load def 96 /B { bind RO def } bind def 97 /X { exch def } B 98 /MD { { X } forall } B 99 /OE { end exec PSfragLib begin } B 100 /S false def 101 /tstr 8 string def 102 /islev2 { languagelevel } stopped { false } { 2 ge } ifelse def 103 [ /sM /tM /srcM /dstM /dM /idM /srcFM /dstFM ] { matrix def } forall 104 sM currentmatrix RO pop 105 dM defaultmatrix RO idM invertmatrix RO pop 106 srcFM identmatrix pop 107 /Hide { gsave { CP } stopped not newpath clip { moveto } if } B 108 /Unhide { { CP } stopped not grestore { moveto } if } B 109 /setrepl islev2 {{ /glob currentglobal def true setglobal array astore 110 globaldict exch /PSfrags exch put glob setglobal }} 111 {{ array astore /PSfrags X }} ifelse B 112 /getrepl islev2 {{ globaldict /PSfrags get aload length }} 113 {{ PSfrags aload length }} ifelse B 114 /convert { 115 /src X src length string 116 /c 0 def src length { 117 dup c src c get dup 32 lt { pop 32 } if put /c c 1 add def 118 } repeat 119 } B 120 /Begin { 121 /saver save def 122 srcFM exch 3 exch put 123 0 ne /debugMode X 0 setrepl 124 dup /S exch dict def { S 3 1 roll exch convert exch put } repeat 125 srcM CM dup invertmatrix pop 126 mark { currentdict { end } stopped { pop exit } if } loop 127 PSfragDict counttomark { begin } repeat pop 128 } B 129 /End { 130 mark { currentdict end dup PSfragDict eq { pop exit } if } loop 131 counttomark { begin } repeat pop 132 getrepl saver restore 133 7 idiv dup /S exch dict def { 134 6 array astore /mtrx X tstr cvs /K X 135 S K [ S K known { S K get aload pop } if mtrx ] put 136 } repeat 137 } B 138 /Place { 139 tstr cvs /K X 140 S K known { 141 bind /proc X tM CM pop 142 CP /cY X /cX X 143 0 0 transform idtransform neg /aY X neg /aX X 144 S K get dup length /maxiter X 145 /iter 1 def { 146 iter maxiter ne { /saver save def } if 147 tM setmatrix aX aY translate 148 [ exch aload pop idtransform ] concat 149 cX neg cY neg translate cX cY moveto 150 /proc load OE 151 iter maxiter ne { saver restore /iter iter 1 add def } if 152 } forall 153 /noXY { CP /cY X /cX X } stopped def 154 tM setmatrix noXY { newpath } { cX cY moveto } ifelse 155 } { 156 Hide OE Unhide 157 } ifelse 158 } B 159 /normalize { 160 2 index dup mul 2 index dup mul add sqrt div 161 dup 4 -1 roll exch mul 3 1 roll mul 162 } B 163 /replace { 164 aload pop MD 165 CP /bY X /lX X gsave sM setmatrix 166 str stringwidth abs exch abs add dup 0 eq 167 { pop } { 360 exch div dup scale } ifelse 168 lX neg bY neg translate newpath lX bY moveto 169 str { /ch X ( ) dup 0 ch put false charpath ch Kproc } forall 170 flattenpath pathbbox [ /uY /uX /lY /lX ] MD 171 CP grestore moveto 172 currentfont 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} forall 202 temp setrepl 203 } B 204 /Rif { 205 S 3 index convert known { pop replace } { exch pop OE } ifelse 206 } B 207 /XA { bind [ /Kproc /str } B /XC { ] 2 array astore def } B 208 /xs { pop } XA XC 209 /xks { /kern load OE } XA /kern XC 210 /xas { pop ax ay rmoveto } XA /ay /ax XC 211 /xws { c eq { cx cy rmoveto } if } XA /c /cy /cx XC 212 /xaws { ax ay rmoveto c eq { cx cy rmoveto } if } 213 XA /ay /ax /c /cy /cx XC 214 /raws { xaws { awidthshow } Rif } B 215 /rws { xws { widthshow } Rif } B 216 /rks { xks { kshow } Rif } B 217 /ras { xas { ashow } Rif } B 218 /rs { xs { show } Rif } B 219 /rrs { getrepl dup 2 add -1 roll //restore exec setrepl } B 220 PSfragDict begin 221 islev2 not { /restore { /rrs PSfrag } B } if 222 /show { /rs PSfrag } B 223 /kshow { /rks PSfrag } B 224 /ashow { /ras PSfrag } B 225 /widthshow { /rws PSfrag } B 226 /awidthshow { /raws PSfrag } B 227 end PSfragDict RO pop 228 end 229 230 %%EndProcSet 231 %%BeginProcSet: 8r.enc 232 % File 8r.enc as of 2002-03-12 for PSNFSS 9 233 % 234 % This is the encoding vector for Type1 and TrueType fonts to be used 235 % with TeX. This file is part of the PSNFSS bundle, version 9 236 % 237 % Authors: S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry, W. Schmidt 238 % 239 % Idea is to have all the characters normally included in Type 1 fonts 240 % available for typesetting. This is effectively the characters in Adobe 241 % Standard Encoding + ISO Latin 1 + extra characters from Lucida + Euro. 242 % 243 % Character code assignments were made as follows: 244 % 245 % (1) the Windows ANSI characters are almost all in their Windows ANSI 246 % positions, because some Windows users cannot easily reencode the 247 % fonts, and it makes no difference on other systems. The only Windows 248 % ANSI characters not available are those that make no sense for 249 % typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen 250 % (173). quotesingle and grave are moved just because it's such an 251 % irritation not having them in TeX positions. 252 % 253 % (2) Remaining characters are assigned arbitrarily to the lower part 254 % of the range, avoiding 0, 10 and 13 in case we meet dumb software. 255 % 256 % (3) Y&Y Lucida Bright includes some extra text characters; in the 257 % hopes that other PostScript fonts, perhaps created for public 258 % consumption, will include them, they are included starting at 0x12. 259 % 260 % (4) Remaining positions left undefined are for use in (hopefully) 261 % upward-compatible revisions, if someday more characters are generally 262 % available. 263 % 264 % (5) hyphen appears twice for compatibility with both ASCII and Windows. 265 % 266 % (6) /Euro is assigned to 128, as in Windows ANSI 267 % 268 /TeXBase1Encoding [ 269 % 0x00 (encoded characters from Adobe Standard not in Windows 3.1) 270 /.notdef /dotaccent /fi /fl 271 /fraction /hungarumlaut /Lslash /lslash 272 /ogonek /ring /.notdef 273 /breve /minus /.notdef 274 % These are the only two remaining unencoded characters, so may as 275 % well include them. 276 /Zcaron /zcaron 277 % 0x10 278 /caron /dotlessi 279 % (unusual TeX characters available in, e.g., Lucida Bright) 280 /dotlessj /ff /ffi /ffl 281 /.notdef /.notdef /.notdef /.notdef 282 /.notdef /.notdef /.notdef /.notdef 283 % very contentious; it's so painful not having quoteleft and quoteright 284 % at 96 and 145 that we move the things normally found there down to here. 285 /grave /quotesingle 286 % 0x20 (ASCII begins) 287 /space /exclam /quotedbl /numbersign 288 /dollar /percent /ampersand /quoteright 289 /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash 290 % 0x30 291 /zero /one /two /three /four /five /six /seven 292 /eight /nine /colon /semicolon /less /equal 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/registered 322 /macron 323 % 0xD0 324 /degree /plusminus /twosuperior /threesuperior 325 /acute /mu /paragraph /periodcentered 326 /cedilla /onesuperior /ordmasculine /guillemotright 327 /onequarter /onehalf /threequarters /questiondown 328 % 0xC0 329 /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla 330 /Egrave /Eacute /Ecircumflex /Edieresis 331 /Igrave /Iacute /Icircumflex /Idieresis 332 % 0xD0 333 /Eth /Ntilde /Ograve /Oacute 334 /Ocircumflex /Otilde /Odieresis /multiply 335 /Oslash /Ugrave /Uacute /Ucircumflex 336 /Udieresis /Yacute /Thorn /germandbls 337 % 0xE0 338 /agrave /aacute /acircumflex /atilde 339 /adieresis /aring /ae /ccedilla 340 /egrave /eacute /ecircumflex /edieresis 341 /igrave /iacute /icircumflex /idieresis 342 % 0xF0 343 /eth /ntilde /ograve /oacute 344 /ocircumflex /otilde /odieresis /divide 345 /oslash /ugrave /uacute /ucircumflex 346 /udieresis /yacute /thorn /ydieresis 347 ] def 348 349 %%EndProcSet 350 %%BeginProcSet: aae443f0.enc 351 % Thomas Esser, Dec 2002. public domain 352 % 353 % Encoding for: 354 % cmmi10 cmmi12 cmmi5 cmmi6 cmmi7 cmmi8 cmmi9 cmmib10 355 % 356 /TeXaae443f0Encoding [ 357 /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega 358 /alpha /beta /gamma /delta /epsilon1 /zeta /eta /theta /iota /kappa 359 /lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon /phi /chi /psi 360 /omega /epsilon /theta1 /pi1 /rho1 /sigma1 /phi1 /arrowlefttophalf 361 /arrowleftbothalf /arrowrighttophalf /arrowrightbothalf /arrowhookleft 362 /arrowhookright /triangleright /triangleleft /zerooldstyle /oneoldstyle 363 /twooldstyle /threeoldstyle /fouroldstyle /fiveoldstyle /sixoldstyle 364 /sevenoldstyle /eightoldstyle /nineoldstyle /period /comma /less /slash 365 /greater /star /partialdiff /A /B /C /D /E /F /G /H /I /J /K /L /M /N 366 /O /P /Q /R /S /T /U /V /W /X /Y /Z /flat /natural /sharp /slurbelow 367 /slurabove /lscript /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p 368 /q /r /s /t /u /v /w /x /y /z 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/.notdef 416 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 417 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 418 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 419 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 420 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 421 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 422 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 423 ] def 424 425 %%EndProcSet 426 %%BeginProcSet: bbad153f.enc 427 % Thomas Esser, Dec 2002. public domain 428 % 429 % Encoding for: 430 % cmsy10 cmsy5 cmsy6 cmsy7 cmsy8 cmsy9 431 % 432 /TeXbbad153fEncoding [ 433 /minus /periodcentered /multiply /asteriskmath /divide /diamondmath 434 /plusminus /minusplus /circleplus /circleminus /circlemultiply 435 /circledivide /circledot /circlecopyrt /openbullet /bullet 436 /equivasymptotic /equivalence /reflexsubset /reflexsuperset /lessequal 437 /greaterequal /precedesequal /followsequal /similar /approxequal 438 /propersubset /propersuperset /lessmuch /greatermuch /precedes /follows 439 /arrowleft /arrowright /arrowup /arrowdown /arrowboth /arrownortheast 440 /arrowsoutheast /similarequal /arrowdblleft /arrowdblright /arrowdblup 441 /arrowdbldown /arrowdblboth /arrownorthwest /arrowsouthwest /proportional 442 /prime /infinity /element /owner /triangle /triangleinv /negationslash 443 /mapsto /universal /existential /logicalnot /emptyset /Rfractur /Ifractur 444 /latticetop /perpendicular /aleph /A /B /C /D /E /F /G /H /I /J /K 445 /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /union /intersection 446 /unionmulti /logicaland /logicalor /turnstileleft /turnstileright 447 /floorleft /floorright /ceilingleft /ceilingright /braceleft /braceright 448 /angbracketleft /angbracketright /bar /bardbl /arrowbothv /arrowdblbothv 449 /backslash /wreathproduct /radical /coproduct /nabla /integral 450 /unionsq /intersectionsq /subsetsqequal /supersetsqequal /section 451 /dagger /daggerdbl /paragraph /club /diamond /heart /spade /arrowleft 452 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 453 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 454 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 455 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 456 /minus /periodcentered /multiply /asteriskmath /divide /diamondmath 457 /plusminus /minusplus /circleplus /circleminus /.notdef /.notdef 458 /circlemultiply /circledivide /circledot /circlecopyrt /openbullet 459 /bullet /equivasymptotic /equivalence /reflexsubset /reflexsuperset 460 /lessequal /greaterequal /precedesequal /followsequal /similar 461 /approxequal /propersubset /propersuperset /lessmuch /greatermuch 462 /precedes /follows /arrowleft /spade /.notdef /.notdef /.notdef /.notdef 463 /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef 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clip}if/showpage{}N/erasepage{}N 539 /setpagedevice{pop}N/copypage{}N newpath}N/@endspecial{count ocount sub{ 540 pop}repeat countdictstack dcount sub{end}repeat grestore SpecialSave 541 restore end}N/@defspecial{SDict begin}N/@fedspecial{end}B/li{lineto}B 542 /rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1 543 setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY 544 moveto}N/ellipse{/endangle X/startangle X/yrad X/xrad X/savematrix 545 matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc 546 savematrix setmatrix}N end 547 548 %%EndProcSet 549 %%BeginFont: CMR10 550 %!PS-AdobeFont-1.1: CMR10 1.00B 551 %%CreationDate: 1992 Feb 19 19:54:52 552 % Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved) readonly def 643 /FullName (CMSY10) readonly def 644 /FamilyName (Computer Modern) readonly def 645 /Weight (Medium) readonly def 646 /ItalicAngle -14.035 def 647 /isFixedPitch false def 648 end readonly def 649 /FontName /CMSY10 def 650 /PaintType 0 def 651 /FontType 1 def 652 /FontMatrix [0.001 0 0 0.001 0 0] readonly def 653 /Encoding 256 array 654 0 1 255 {1 index exch /.notdef put} for 655 dup 0 /.notdef put 656 readonly def 657 /FontBBox{-29 -960 1116 775}readonly def 658 /UniqueID 5000820 def 659 currentdict end 660 currentfile eexec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cleartomark 711 %%EndFont 712 %%BeginFont: CMEX10 713 %!PS-AdobeFont-1.1: CMEX10 1.00 714 %%CreationDate: 1992 Jul 23 21:22:48 715 % Copyright (C) 1997 American Mathematical Society. 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y(in)g(these)h(probabilities,)f(in)g(most)h(cases)f(the)h(true)f 1009 (destination)h(of)f(the)g(message)i(from)e(Alice)759 1010 2971 y(is)k(in)g(a)f(small)h(group)h(of)f(locations)g(with)g(the)g 1011 (highest)h(probabilities.)759 3061 y(Our)i(results)f(contradict)h(a)f 1012 (quite)g(common)i(belief)e(that)g(the)h(protocols)g(mentioned)h(guar)o 1013 (-)759 3152 y(antee)i(anon)o(ymity)h(pro)o(vided)g(that)e(the)h(set)f 1014 (of)h(possible)g(intermediate)g(serv)o(ers)f(for)h(each)759 1015 3243 y(user)19 b(is)g(lar)o(ge.)523 3519 y Fx(1)99 b(Intr)n(oduction) 1016 523 3713 y Fw(1.1)82 b(Backgr)o(ound)523 3874 y FE(There)20 1017 b(is)i(a)g(gro)n(wing)d(need)i(for)f(anon)o(ymity)f(in)i(electronic)f 1018 (communication.)e(Man)o(y)i(anon)o(ymity)523 3973 y(protocols)i(ha)n(v) 1019 o(e)h(been)g(proposed)f(\226)h(their)h(aim)f(is)i(not)e(only)g(to)g 1020 (hide)h(the)f(contents)g(of)g(messages)523 4073 y(sent,)d(b)n(ut)g 1021 (also)h(who)f(is)h(communicating)c(with)k(whom.)648 4173 1022 y(Application)28 b(area)j(of)f(such)g(protocols)e(is)k(much)d(broader)f 1023 (than)i(implementing)e(point-to-)523 4272 y(point)22 1024 b(anon)o(ymous)e(communication.)f(F)o(or)j(instance,)g(the)o(y)g(are)h 1025 (essential)g(components)d(of)i(v)n(ari-)523 4372 y(ous)d(v)n(oting)f 1026 (schemes)h([3],some)f(auction)g(protocols)g([15],)f(anon)o(ymous)g(bro) 1027 n(wsing)g(or)i(e)n(v)o(en)f(the)o(y)523 4471 y(serv)o(e)i(as)h(a)f(b)n 1028 (uilding)f(block)g(in)i(some)f(secure)g(function)e(e)n(v)n(aluation)g 1029 (protocols)h([11].)648 4571 y(Existing)d(solutions)g(are)g(generally)f 1030 (based)i(on)f(tw)o(o)h(fundamental)d(ideas)j(-)g Fv(MIXes)g 1031 FE(introduced)523 4671 y(by)22 b(Da)n(vid)h(Chaum)f(in)h([2])f(and)g 1032 Fv(Onions)g FE(that)h(appeared)e(in)i(a)g(number)e(of)i(papers)f([16,) 1033 12 b(17,)h(8].)22 b(In)523 4770 y(these)e(protocols)f(the)h(messages)h 1034 (are)f(routed)f(through)f(serv)o(ers)h(called)h Fv(MIXes)h 1035 FE(or)f Fv(MIX-server)o(s)p FE(.)p 523 4839 473 4 v 517 1036 4897 a Fz(??)598 4924 y FD(contact)f(author)p eop end 1037 %%Page: 2 2 1038 TeXDict begin 2 1 bop 648 448 a FE(Generally)-5 b(,)17 1039 b(there)h(is)h(a)h(common)c(idea)j(behind)e(both)h(solutions)g(\226)h 1040 (at)g(the)g(be)o(ginning)d(we)j(ha)n(v)o(e)523 548 y(a)d(batch)g(of)f 1041 (cipherte)o(xts)g(submitted)g(by)h(all)g(users.)g(Then)f(a)i(number)d 1042 (of)h(steps)i(is)g(e)o(x)o(ecuted.)d(During)523 648 y(a)32 1043 b(step)f(each)g(message)g(is)i(appointed)c(to)i(some)g(serv)o(er)m(,)f 1044 (each)h(serv)o(er)g(recodes)f(the)h(messages)523 747 1045 y(obtained)15 b(and)h(returns)g(them)g(in)h(a)g(random)e(order)-5 1046 b(.)16 b(In)g(this)h(w)o(ay)-5 b(,)16 b(the)h(encoded)e(messages)i 1047 (become)523 847 y(more)i(and)h(more)f(\223mix)o(ed\224.)648 1048 946 y(The)27 b(problem)g(is)i(that)f(users)g(of)g(man)o(y)f(anon)o 1049 (ymity)e(systems)k(are)f(requested)e(to)j(construct)523 1050 1046 y(a)c(path)f(of)g(randomly)f(and)h(independently)d(chosen)j(serv)o 1051 (ers)g(for)g(each)g(message,)g(called)g(in)h(this)523 1052 1146 y(paper)c Fv(anonymity)g(path)p FE(.)g(It)i(concerns)e(all)h 1053 (onion-based)e(protocols)h([16,)12 b(17,)h(8])22 b(and)f(some)i(MIX)523 1054 1245 y(netw)o(ork)j(architectures.)g(F)o(or)g(such)h(protocols,)f(it)h 1055 (is)h(assumed)f(that)g(the)g(users)h(ha)n(v)o(e)e(the)h(same)523 1056 1345 y(kno)n(wledge)18 b(about)h(the)h(serv)o(ers)g(that)g(can)g(be)g 1057 (used)g(as)h(intermediate)e(serv)o(ers)h(on)g(the)g(path.)648 1058 1445 y(In)e(a)h(lar)o(ge)e(and)h(dynamic)f(system)i(it)g(is)g(hard)f 1059 (to)g(achie)n(v)o(e)f(that)i(all)g(users)g(ha)n(v)o(e)f(the)g(same)h 1060 (vie)n(w)523 1544 y(of)28 b(the)h(netw)o(ork.)e(The)h(problem)f(we)i 1061 (address)f(in)h(this)g(paper)e(is)j(ho)n(w)e(secure)g(are)g(anon)o 1062 (ymous)523 1644 y(communication)h(protocols,)i(if)h(the)g(users)h 1063 (choose)e(the)h(serv)o(ers)f(for)h(anon)o(ymity)e(paths)i(from)523 1064 1743 y(dif)n(ferent)19 b(sets)i(of)f(serv)o(ers.)523 1065 1974 y Fw(Related)k(W)-6 b(ork)46 b FE(There)23 b(are)h(man)o(y)f 1066 (papers)g(concerning)f(anon)o(ymous)f(communication)g(proto-)523 1067 2074 y(cols)g(based)e(on)h(MIXes)h(and)e(Onions.)h(On)g(the)g(other)g 1068 (hand,)f(there)g(are)i(only)e(fe)n(w)h(papers)g(pro)o(vid-)523 1069 2173 y(ing)25 b(rigorous)f(proofs)g(about)g(immunity)g(of)h(such)g 1070 (systems)h(against)e(an)i(adv)o(ersary)-5 b(.)22 b(One)j(of)g(the)523 1071 2273 y(v)o(ery)c(\002rst)h(w)o(ork)g(in)g(this)g(direction)f(is)i(due)e 1072 (to)h(K)n(esdogan)e(et)i(al.)g([12].)f(In)h(this)g(paper)f(cardinality) 1073 523 2373 y(of)f(so-called)f(anon)o(ymity)f(set)j(w)o(as)g(used)f(as)h 1074 (an)f(anon)o(ymity)e(measure.)648 2472 y(In)j(other)f(papers)h(lik)o(e) 1075 h([16,)12 b(4,)h(1,)h(10])20 b(sophisticated)h(and)g(v)o(ery)f 1076 (restricti)n(v)o(e)h(anon)o(ymity)e(mea-)523 2572 y(sures)g(were)f 1077 (used)g(that)h(tak)o(e)g(into)f(account)f(also)i(correlation)e(between) 1078 g(messages.)i(These)f(papers)523 2672 y(pro)o(vide)k(rigorous)h(proofs) 1079 f(of)i(anon)o(ymity)e(in)i(dif)n(ferent)f(adv)o(ersary)f(models:)i 1080 (their)g(goal)f(w)o(as)i(to)523 2771 y(sho)n(w)20 b(that)g(an)f(anon)o 1081 (ymity)f(measure)h(reaches)g(appropriate)f(v)n(alues)h(with)h(high)f 1082 (probability)f(for)h(a)523 2871 y(certain)h(length)f(of)h(an)g(anon)o 1083 (ymity)e(path.)648 2970 y(Still,)f(these)f(proofs)f(use)i(the)f 1084 (assumption)g(that)g(all)h(users)g(ha)n(v)o(e)e(e)o(xactly)h(the)g 1085 (same)h(kno)n(wledge)523 3070 y(of)i(the)g(serv)o(ers)g(that)g(may)g 1086 (be)g(used)g(as)h(intermediate)e(serv)o(ers)h(on)g(anon)o(ymity)e 1087 (paths.)i(No)g(attempt)523 3170 y(has)i(been)e(made)h(to)h(analyze)e 1088 (what)i(happens)e(if)i(this)g(assumption)e(is)i(not)f(satis\002ed.)h 1089 (In)g([7],)e(it)i(has)523 3269 y(been)j(mentioned)e(that)i(violating)g 1090 (this)g(assumption)g(might)f(in\003uence)g(security)h(of)g(the)h 1091 (system.)523 3369 y(Ho)n(we)n(v)o(er)m(,)20 b(a)j(common)e(belief)h(is) 1092 h(that)f(anon)o(ymity)e(of)i(a)h(user)g Fv(A)f FE(is)i(in)e(danger)f 1093 (only)g(if)i(the)g(set)g(of)523 3469 y(potential)c(intermediate)g(serv) 1094 o(ers)h(is)h(small.)523 3699 y Fw(P)o(aper)f(Or)o(ganization)40 1095 b FE(In)20 b(Section)g(2)h(we)g(recall)f(basic)h(f)o(acts)g(about)e 1096 (anon)o(ymous)f(communica-)523 3799 y(tion)g(protocols.)e(In)h(Section) 1097 h(3)g(we)g(consider)f(dangers)f(that)i(arise)g(when)g(a)g(user)g(is)h 1098 (a)o(w)o(are)e(of)h(some)523 3898 y(e)o(xtra)k(serv)o(ers)h(and)g(may)f 1099 (use)i(them)f(for)f(creating)g(anon)o(ymous)f(paths.)h(Section)h(4)g 1100 (is)h(de)n(v)n(oted)e(to)523 3998 y(the)e(case)h(when)e(a)i(user)f(is)h 1101 (a)o(w)o(are)f(of)g(only)f(a)i(constant)e(fraction)g(of)h(serv)o(ers.) 1102 523 4245 y Fx(2)99 b(Anonymity)25 b(Pr)n(otocols)g(and)g(Pr)n(oblem)h 1103 (Statement)523 4426 y Fw(MIXes)37 b FE(MIX)17 b(is)h(a)f(cryptographic) 1104 d(primiti)n(v)o(e)i(introduced)e(in)j([2]:)g(assume)g(that)g(users)g(1) 1105 p Ft(;)9 b FE(2)p Ft(;)g(:)g(:)g(:)g(;)g Fv(n)523 4526 1106 y FE(wish)29 b(to)g(publish)f(anon)o(ymously)d(messages)k 1107 Fv(m)1955 4538 y Fq(1)1990 4526 y Ft(;)9 b Fv(m)2082 1108 4538 y Fq(2)2117 4526 y Ft(;)g(:)g(:)g(:)h(;)f Fv(m)2338 1109 4538 y Fo(n)2373 4526 y FE(.)29 b(F)o(or)f(this)i(purpose)d(the)o(y)h 1110 (submit)523 4625 y(their)22 b(messages)h(to)g(a)g Fv(MIX-server)i 1111 FE(after)d(encrypting)f(them)h(with)h(MIX-serv)o(er')-5 1112 b(s)21 b(public)h(k)o(e)o(y)g Fv(k)q FE(,)523 4725 y(that)k(is,)g(the)o 1113 (y)e(submit)h Fv(E)1246 4738 y Fo(k)1279 4725 y Fs(\()p 1114 Fv(m)1371 4737 y Fq(1)1406 4725 y Fs(\))p Ft(;)9 b Fv(E)1521 1115 4738 y Fo(k)1553 4725 y Fs(\()p Fv(m)1645 4737 y Fq(2)1680 1116 4725 y Fs(\))p Ft(;)g(:)g(:)g(:)h(;)f Fv(E)1924 4738 1117 y Fo(k)1957 4725 y Fs(\()p Fv(m)2049 4737 y Fo(n)2084 1118 4725 y Fs(\))26 b Ft(:)p FE(The)f(MIX-serv)o(er)f(decrypts)g(the)h 1119 (cipher)n(-)523 4825 y(te)o(xts)f(obtained)f(with)h(its)i(pri)n(v)n 1120 (ate)d(k)o(e)o(y)-5 b(,)23 b(chooses)g(a)i(permutation)d 1121 Fu(p)i FE(uniformly)e(at)j(random,)d(and)523 4924 y(outputs)d 1122 Fv(m)848 4941 y Fr(p)p Fp(\()p Fq(1)p Fp(\))965 4924 1123 y FE(,)h Fv(m)1066 4941 y Fr(p)p Fp(\()p Fq(2)p Fp(\))1182 1124 4924 y FE(,)h(.)12 b(.)g(.)g(,)21 b Fv(m)1425 4941 y 1125 Fr(p)p Fp(\()p Fo(n)p Fp(\))1541 4924 y FE(.)p eop end 1126 %%Page: 3 3 1127 TeXDict begin 3 2 bop 648 448 a FE(If)18 b(the)h(MIX-serv)o(er)e(is)j 1128 (honest)e(\(i.e.)h(does)f(not)h(re)n(v)o(eal)e(permutation)g 1129 Fu(p)p FE(\),)h(then)h(for)f(an)h(e)o(xternal)523 548 1130 y(observ)o(er)i(the)i(relation)e(between)h(the)h(input)f(and)g(the)h 1131 (output)e(of)i(the)f(MIX-serv)o(er)f(remains)h(hid-)523 1132 648 y(den.)g(Of)h(course,)f(some)h(additional)e(requirements)g(must)i 1133 (be)g(ful\002lled.)f(F)o(or)h(e)o(xample,)e Fv(E)29 b 1134 FE(has)23 b(to)523 747 y(be)f(a)h(probabilistic)e(encryption)g(scheme)h 1135 (-)g(otherwise)g(one)g(can)g(establish)h(this)g(relationship)e(by)523 1136 847 y(encrypting)d(the)i(output.)f(F)o(or)h(further)e(details)j(see)g 1137 ([9].)648 946 y(In)30 b(order)g(to)h(a)n(v)n(oid)f(full)h(dependence)d 1138 (on)i(a)i(single)e(MIX,)h(systems)g(consisting)f(of)h(man)o(y)523 1139 1046 y(MIX-serv)o(ers)c(were)i(proposed.)e(A)i(so-called)f 1140 Fv(MIX)i(cascade)d FE(w)o(as)j(introduced)d(together)g(with)523 1141 1146 y(MIXes)f(in)h([2].)e(In)h(that)g(case)h(a)f(message)g(is)h 1142 (encrypted)d(multiple)i(times)g(with)h(public)e(k)o(e)o(ys)h(of)523 1143 1245 y(consecuti)n(v)o(e)19 b(MIXes.)i(The)g(encrypted)e(messages)i 1144 (are)g(processed)f(by)h(the)g(cascade)f(of)h(MIXes)g(\226)523 1145 1345 y(each)f(MIX)g(remo)o(v)o(es)f(one)g(encryption)f(layer)i(and)f 1146 (permutes)h(the)g(cipherte)o(xts)f(at)h(random.)648 1445 1147 y(F)o(or)h(better)g(scalability)g(a)h(parallel)g(MIX-cascades)e(can)i 1148 (be)f(used:)h(in)f(this)h(case)g(each)g(step)g(is)523 1149 1544 y(e)o(x)o(ecuted)c(by)i(a)h(number)d(of)i(MIXes)g(w)o(orking)f(in) 1150 h(parallel.)523 1780 y Fw(Onions)47 b FE(It)23 b(is)i(a)f(core)f(idea)h 1151 (of)f(v)n(arious)g(theoretical)g(systems)h(as)g(well)h(as)f(w)o(orking) 1152 e(implemen-)523 1880 y(tations)28 b(\(see)h(e.g.)e([16,)13 1153 b(17,)f(8,)h(7]\).)28 b(There)f(are)h(man)o(y)f(v)n(ariants)h(of)g 1154 (this)h(protocol.)d(A)j(basic)f(one)523 1979 y(w)o(orks)20 1155 b(as)h(follo)n(ws:)648 2079 y(W)-7 b(e)28 b(assume)g(that)g(a)g 1156 (message)f Fv(m)h FE(has)g(to)g(be)g(sent)f(from)g(a)h(node)f 1157 Fv(A)h FE(to)f(a)h(node)f Fv(B)p FE(.)h(F)o(or)f(this)523 1158 2178 y(purpose)19 b(node)g Fv(A)i FE(chooses)e(at)i(random)e 1159 Fu(l)h FE(intermediate)f(nodes,)g(say)-5 b(,)20 b Fv(J)2619 1160 2190 y Fq(1)2654 2178 y Ft(;)9 b Fv(J)2721 2190 y Fq(2)2756 1161 2178 y Ft(;)g(:)g(:)g(:)h(;)f Fv(J)2952 2195 y Fr(l)3011 1162 2178 y FE(and)19 b(random)523 2278 y(strings)28 b Fv(r)805 1163 2290 y Fq(1)840 2278 y Ft(;)9 b Fv(r)904 2290 y Fq(2)940 1164 2278 y Ft(;)g(:)g(:)g(:)g(;)g Fv(r)1132 2295 y Fr(l)p 1165 Fp(+)p Fq(1)1249 2278 y FE(.)29 b(Then)e(an)h Fv(onion)e 1166 Fl(O)34 b FE(is)29 b(b)n(uilt)g(according)c(to)k(the)f(follo)n(wing)e 1167 (recursi)n(v)o(e)523 2378 y(formula)19 b(\(Enc)963 2390 1168 y Fo(X)1032 2378 y FE(means)g(encryption)f(with)j(the)f(public)f(k)o(e) 1169 o(y)h(of)g Fv(X)8 b FE(\):)1302 2544 y Fl(O)1358 2560 1170 y Fr(l)1419 2544 y Fs(=)23 b FE(Enc)1636 2556 y Fo(B)1678 1171 2544 y Fs(\()p Fv(m)p Ft(;)9 b Fv(r)1834 2560 y Fr(l)p 1172 Fp(+)p Fq(1)1951 2544 y Fs(\))1319 2668 y Fl(O)1375 2680 1173 y Fo(i)1419 2668 y Fs(=)23 b FE(Enc)1636 2680 y Fo(J)1661 1174 2691 y Fj(i)1684 2668 y Fs(\()p Fv(J)1751 2680 y Fo(i)p 1175 Fp(+)p Fq(1)1850 2668 y Ft(;)9 b Fl(O)1938 2680 y Fo(i)p 1176 Fp(+)p Fq(1)2038 2668 y Ft(;)g Fv(r)2102 2680 y Fo(i)p 1177 Fp(+)p Fq(1)2202 2668 y Fs(\))104 b FE(for)20 b Fv(i)f 1178 Ft(<)e Fu(l)1315 2793 y Fl(O)48 b Fs(=)23 b Fl(O)1563 1179 2805 y Fq(1)523 2959 y FE(Then)18 b Fl(O)26 b FE(is)20 1180 b(sent)f(by)g Fv(A)h FE(to)f Fv(J)1316 2971 y Fq(1)1351 1181 2959 y FE(.)g(Node)g Fv(J)1626 2971 y Fq(1)1680 2959 1182 y FE(\223peels)g(of)n(f)5 b(\224)18 b(the)h(\002rst)h(layer)f(by)g 1183 (decryption)e(and)h(recei)n(v)o(es)523 3058 y(onion)27 1184 b Fl(O)797 3070 y Fq(2)832 3058 y FE(,)h(the)g(name)g(of)f(the)h(ne)o 1185 (xt)g(serv)o(er)f(on)h(the)g(path,)f Fv(J)2317 3070 y 1186 Fq(2)2352 3058 y FE(,)h(and)g(a)g(random)f(string.)g(Then)g 1187 Fv(J)3370 3070 y Fq(2)523 3158 y FE(becomes)32 b Fl(O)903 1188 3170 y Fq(2)970 3158 y FE(and)g(processes)g(it)h(in)g(a)g(similar)f(w)o 1189 (ay)-5 b(.)32 b(This)h(procedure)d(is)j(repeated)e(until)h(the)523 1190 3257 y(plainte)o(xt)19 b Fv(m)i FE(appears)e(after)h(decryption.)648 1191 3357 y(Anon)o(ymity)h(mechanism)h(of)i(onions)e(is)j(v)o(ery)e(similar) 1192 h(to)f(MIXes.)h(Messages)g(entering)e(the)523 3457 y(same)c(serv)o(er)e 1193 (at)i(in)f(the)h(same)f(time)h(are)f(recoded)e(and)i(permuted)f(at)h 1194 (random)f(-)h(just)h(as)g(for)f(a)h(MIX.)523 3692 y Fw(Adv)o(ersary)32 1195 b(Model)59 b FE(There)31 b(are)h(man)o(y)f(adv)o(ersary)g(models)g(for) 1196 h(anon)o(ymity)e(protocols.)g(W)-7 b(e)523 3792 y(consider)25 1197 b(a)i(passi)n(v)o(e)f(adv)o(ersary)e(monitoring)g(traf)n(\002c)i(of)g 1198 (messages)g(in)g(a)h(netw)o(ork.)e(The)h(adv)o(er)n(-)523 1199 3892 y(sary)18 b(cannot)f(in\003uence)g(the)h(traf)n(\002c)g(\(for)f(e) 1200 o(xample:)g(insert,)h(duplicate,)f(remo)o(v)o(e,)f(or)i(modify)f(mes-) 1201 523 3991 y(sages\).)648 4091 y(The)i(adv)o(ersary)e(considered)h(in)i 1202 (this)g(this)g(paper)e(is)j(global,)d(in)i(the)f(sense)h(that)g(he)f 1203 (can)h(ea)n(v)o(es-)523 4191 y(drop)30 b(at)h(the)g(same)g(time)g(all)p 1204 1312 4205 84 4 v 31 w(connections,)e(b)n(ut)i(can)f(neither)g(corrupt)f 1205 (a)j(serv)o(er)e(nor)g(trace)g(its)523 4290 y(internal)19 1206 b(w)o(ork.)648 4390 y(Let)32 b(us)g(remark)e(that)i(the)g(strongest)f 1207 (anon)o(ymity)e(results)j(were)g(obtained)e(for)i(the)f(model)523 1208 4489 y(introduced)19 b(by)i(Berman)f(et)i(al.)f(in)g([1],)g(where)f 1209 (only)h(a)g(fraction)f(of)h(connection)e(is)j(under)e(adv)o(er)n(-)523 1210 4589 y(sary')-5 b(s)20 b(control.)523 4825 y Fw(De\002nitions)33 1211 b(of)e(Anonymity)58 b FE(There)31 b(are)h(man)o(y)f(de\002nitions)g 1212 (and)h(measures)f(of)h(anon)o(ymity)523 4924 y(\(see)23 1213 b(e.g.)f([5])g(or)h([13]\).)e(The)h(v)o(ery)g(\002rst)h(de\002nition)f 1214 (and)g(the)h(weak)o(est)g(one)f(is)i(based)e(on)h(already)p 1215 eop end 1216 %%Page: 4 4 1217 TeXDict begin 4 3 bop 523 448 a FE(mentioned)23 b Fv(anonymity)g(set)k 1218 FE(described)c(in)i([12]:)f(W)-7 b(e)25 b(consider)f(a)h(single)f 1219 (message)h Fv(A)g FE(from)e(the)523 548 y(input)f(of)g(a)h(system.)f 1220 (Then)g(we)h(consider)e(the)h(set)i(of)e(all)h(output)e(positions)h 1221 (that,)g(from)g(the)g(point)523 648 y(of)c(vie)n(w)h(of)f(the)g(adv)o 1222 (ersary)-5 b(,)16 b(may)i(contain)g(recoded)f Fv(A)h 1223 FE(with)h(a)g(positi)n(v)o(e)f(probability)-5 b(.)15 1224 b(Cardinality)523 747 y(of)22 b(this)h(set)h(di)n(vided)d(by)h(number)f 1225 (of)h(all)i(messages)e(processed)g(by)g(the)h(system)f(is)i(a)f 1226 (measure)f(of)523 847 y(anon)o(ymity)-5 b(.)648 946 y(The)19 1227 b(de\002nition)g(based)h(on)f(anon)o(ymity)e(set)k(does)f(not)g(tak)o 1228 (e)f(into)h(account)f(that)h(dif)n(ferent)e(out-)523 1229 1046 y(put)j(positions)f(can)h(be)g(more)f(or)h(less)h(lik)o(ely)f(to)g 1230 (be)g(link)o(ed)f(with)h(a)g(particular)f(input.)g(This)h(short-)523 1231 1146 y(coming)f(is)i(solv)o(ed)e(by)h(de\002nition)f(based)h(on)f 1232 (entrop)o(y)g([5].)g(Unfortunately)f(e)n(v)o(en)h(this)i(de\002nition) 1233 523 1245 y(is)f(not)e(perfect)g(-)h(it)h(does)e(not)h(tak)o(e)g(into)f 1234 (account)g(dependencies)e(between)i(probability)f(distrib)n(u-)523 1235 1345 y(tion)i(of)g(dif)n(ferent)e(messages.)i(These)g(dependencies)e 1236 (can)i(be)h(crucial)e(for)h(some)g(applications.)648 1237 1445 y(The)e(strongest)g(de\002nitions)g(are)h(based)f(on)h 1238 Fv(variation)f(distance)g FE(between)g(distrib)n(ution)f(of)i(all)523 1239 1544 y(possible)k(permutations)e(of)i(input)f(messages)h(on)g(output)e 1240 (positions)i(and)f(the)h(uniform)e(distrib)n(u-)523 1644 1241 y(tion)i(or)g(a)h(priori)e(distrib)n(ution)h([1].)f(Then)h(all)h 1242 (dependencies)d(between)h(dif)n(ferent)g(messages)i(are)523 1243 1743 y(tak)o(en)c(into)g(account.)648 1843 y(In)c(this)i(paper)d(we)j 1244 (use)f(the)g(weak)f(measure)g(based)h(on)f(anon)o(ymity)f(set.)i(The)g 1245 (reason)f(is)i(simple)523 1943 y(\226)27 b(we)f(sho)n(w)h(that)f(in)h 1246 (some)f(situations)g(e)n(v)o(en)g(for)f(this)i(weak)f(measure)g(only)g 1247 (a)h(lo)n(w)f(anon)o(ymity)523 2042 y(le)n(v)o(el)20 1248 b(is)h(achie)n(v)o(ed.)523 2283 y Fw(Local)26 b(v)o(ersus)i(Global)e(V) 1249 m(iew)50 b FE(A)27 b(common)e(assumption)g(in)i(papers)f(dealing)g 1250 (with)g(onions)g(as)523 2383 y(well)16 b(as)g(MIXes)g(is)h(that)e(the)h 1251 (serv)o(ers)f(on)g(anon)o(ymity)e(path)i(are)h(chosen)e(independently)f 1252 (uniformly)523 2483 y(at)21 b(random)d(o)o(v)o(er)h(the)h(same)g(set)h 1253 (by)f(all)h(users.)648 2582 y(It)c(is)h(often)e(belie)n(v)o(ed)f(that)i 1254 (e)n(v)o(en)f(if)h(the)g(users)g(choose)f(from)g(dif)n(ferent)f(sets)j 1255 (of)f(serv)o(ers,)f(it)i(does)523 2682 y(not)g(impact)g(anon)o(ymity)f 1256 (v)o(ery)g(much)h(pro)o(vided)e(that)i(the)h(number)e(of)h(potential)g 1257 (serv)o(ers)g(for)g(each)523 2782 y(user)i(is)h(suf)n(\002ciently)e 1258 (lar)o(ge.)g(W)-7 b(e)21 b(sho)n(w)f(that)g(this)g(intuition)f(is)i 1259 (wrong)e(\226)h(dif)n(ferent)f(local)h(vie)n(ws)g(of)523 1260 2881 y(the)25 b(netw)o(ork)e(can)h(cause)h(de)o(gradation)c(of)j(anon)o 1261 (ymity)e(in)j(some)f(cases,)h(despite)g(strong)e(results)523 1262 2981 y(for)31 b(the)g(case)h(when)f(all)h(local)g(vie)n(ws)g(are)f(the) 1263 h(same)f([1,)13 b(10].)31 b(This)g(has)h(important)e(practical)523 1264 3080 y(implications,)18 b(since)h(it)h(is)g(e)o(xtremely)e(dif)n 1265 (\002cult)g(to)h(pro)o(vide)e(the)j(same)f(vie)n(w)g(of)g(the)g(netw)o 1266 (ork)f(in)h(a)523 3180 y(lar)o(ge)g(dynamic)g(system)h(with)h(serv)o 1267 (ers)e(joining)g(and)h(lea)n(ving)g(the)g(netw)o(ork.)523 1268 3438 y Fx(3)99 b(Dangers)26 b(of)e(Using)h(Extra)g(Ser)o(v)o(ers)523 1269 3629 y FE(In)h(this)g(section)g(we)g(consider)e(a)j(simple)f(scenario,) 1270 e(in)i(which)g(anon)o(ymity)d(breaks)i(completely)523 1271 3729 y(do)n(wn)18 b(or)g(at)h(least)g(is)h(strongly)d(limited.)h(Our)h 1272 (considerations)d(here)j(serv)o(e)f(as)h(a)g(kind)f(of)g(w)o(arm-up)523 1273 3828 y(before)h(the)h(ne)o(xt)g(section)f(with)i(a)f(more)g(in)m(v)n 1274 (olv)o(ed)e(analysis)i(for)g(a)g(more)g(practical)f(setting.)648 1275 3928 y(W)-7 b(e)17 b(consider)f(the)g(case)h(with)g Fv(n)f 1276 FE(users,)g(each)h(of)f(them)g(sending)f(a)i(single)f(message.)h(The)f 1277 (num-)523 4028 y(ber)22 b(of)f(serv)o(ers)h(in)g(the)g(system)g(that)g 1278 (can)g(be)g(used)f(as)i(intermediate)d(nodes)i(is)h(also)f 1279 Fv(n)p FE(.)g(Ho)n(we)n(v)o(er)m(,)523 4127 y(all)h(users,)f(e)o(xcept) 1280 f(Alice,)h(kno)n(w)f(only)g Fv(n)12 b Fm(\000)g Fv(k)23 1281 b FE(of)f(these)g(serv)o(ers,)f(while)h(Alice)h(is)g(a)o(w)o(are)e(of)h 1282 (all)h(of)523 4227 y(them.)17 b(Let)h Fv(k)i FE(serv)o(ers)d(kno)n(wn)f 1283 (only)h(to)h(Alice)g(be)g(called)g Fv(additional)d FE(serv)o(ers.)i 1284 (\(Our)g(choice)g(of)h(pa-)523 4327 y(rameters)h(might)h(be)f(dif)n 1285 (ferent,)f(for)i(instance)f(each)h(serv)o(er)f(may)g(send)h(more)f 1286 (than)h(one)f(message,)523 4426 y(b)n(ut)h(we)h(\002x)f(the)g(setting)h 1287 (for)e(the)h(sak)o(e)h(of)f(simplicity)-5 b(.\))648 4526 1288 y(The)24 b(messages)g(are)h(processed)e(as)j(onions.)d(Each)h(sender)g 1289 (\002x)o(es)g(a)h(random)e(path)h(of)g(length)523 4625 1290 y Fu(l)f FE(choosing)f(each)h(serv)o(er)f(independently)e(and)j 1291 (uniformly)e(at)i(random.)f(So)h(Alice)h(may)e(choose)523 1292 4725 y(additional)h(serv)o(ers)i(while)g(the)f(other)g(serv)o(ers)h 1293 (cannot)e(use)i(them.)f(W)-7 b(e)26 b(consider)e(here)g(a)h(global)523 1294 4825 y(passi)n(v)o(e)19 b(adv)o(ersary)e(who)i(w)o(ants)h(to)f(detect)g 1295 (the)g(destination)f(of)h(the)h(message)f(sent)g(by)g(Alice.)g(W)-7 1296 b(e)523 4924 y(assume)26 b(that)g(for)f(each)h(single)f(user)h(the)g 1297 (adv)o(ersary)e(kno)n(ws)h(the)h(set)h(of)e(serv)o(ers)g(in)h(the)g 1298 (system)p eop end 1299 %%Page: 5 5 1300 TeXDict begin 5 4 bop 523 448 a FE(kno)n(wn)22 b(by)i(the)g(user)-5 1301 b(.)24 b(So)g(in)g(particular)m(,)f(the)h(adv)o(ersary)e(kno)n(ws)h 1302 (that)h(if)g(an)g(onion)f(is)i(processed)523 548 y(through)20 1303 b(an)i(additional)f(serv)o(er)m(,)g(then)g(it)i(must)g(be)f(an)g 1304 (encoded)e(message)i(of)g(Alice.)g(If)g(the)h(mes-)523 1305 648 y(sage)18 b(of)g(Alice)g(does)g(not)g(go)f(through)f(an)i 1306 (additional)f(serv)o(er)m(,)f(then)i(it)h(remains)e(hidden)g(inside)g 1307 (the)523 747 y(cro)n(wd)24 b(of)g(other)g(messages.)h(Ho)n(we)n(v)o(er) 1308 m(,)e(e)n(v)o(en)g(then)i(its)h(location)d(might)h(be)h(limited)g(to)g 1309 (a)g(small)523 847 y(anon)o(ymity)18 b(set,)i(when)g(the)g(message)g 1310 (went)g(recently)g(through)e(an)i(additional)f(serv)o(er)-5 1311 b(.)648 946 y(By)30 b(e)n(v)n(aluating)f(le)n(v)o(el)h(of)g(anon)o 1312 (ymity)e(pro)o(vided)g(by)i(v)n(arious)g(systems)h(based)f(on)g 1313 (onions,)523 1046 y(the)f(crucial)f(question)f(is)j(ho)n(w)e(long)g 1314 (must)g(be)h(the)g(random)d(path)i(of)h(each)f(message)h(\(see)f([1],) 1315 523 1146 y([10]\).)c(The)h(main)g(idea)h(is)g(that)g(anon)o(ymity)d 1316 (impro)o(v)o(es)g(when)i(the)h(length)e(of)i(the)f(random)f(path)523 1317 1245 y(increases.)c(Ho)n(we)n(v)o(er)m(,)e(we)i(shall)h(see)g(that)f 1318 (it)h(is)g(f)o(alse)g(for)e(the)i(scenario)e(considered)f(here.)648 1319 1345 y(Let)j Fv(D)h FE(be)f(a)h(random)d(v)n(ariable)i(denoting)e(the)i 1320 (number)f(of)h(steps)h(between)e(the)i(last)g(moment)523 1321 1445 y(when)17 b(the)h(message)g(from)f(Alice)h(hits)g(an)g(additional) 1322 f(serv)o(er)g(and)g(deli)n(v)o(ery)f(of)i(this)g(message.)f(W)-7 1323 b(e)523 1544 y(call)21 b Fv(D)h(ef)o(fective)e(length)g 1324 FE(of)h(anon)o(ymity)d(path.)i(Since)h(each)g(time)g(a)g(message)g 1325 (hits)g(an)g(additional)523 1644 y(serv)o(er)27 b(the)g(adv)o(ersary)f 1326 (kno)n(ws)g(that)i(it)g(is)g(a)g(message)g(from)e(Alice,)i(for)e(pro)o 1327 (viding)f(anon)o(ymity)523 1743 y(against)18 b(a)i(global)e(adv)o 1328 (ersary)f(only)h(the)h Fv(ef)o(fective)g(length)f FE(counts)g(and)g 1329 (not)h Fu(l)p FE(.)g(F)o(or)f(this)i(reason)e(we)523 1330 1843 y(analyze)h(beha)n(vior)g(of)h(the)g(random)e(v)n(ariable)i 1331 Fv(D)p FE(.)523 1992 y Fw(Claim)h(1)41 b Fv(F)-9 b(or)20 1332 b(eac)o(h)d(t)6 b(,)21 b FE(0)d Fm(\024)d Fv(t)25 b Fm(\024)18 1333 b Fu(l)p Fv(,)1554 2152 y FE(Pr)p Fs([)p Fv(D)g Ft(>)e 1334 Fv(t)6 b Fs(])18 b(=)1963 2085 y Fi(\000)2001 2152 y 1335 FE(1)12 b Fm(\000)2141 2119 y Fo(k)p 2140 2133 31 4 v 1336 2140 2181 a(n)2181 2085 y Fi(\001)2217 2101 y Fo(t)t 1337 Fp(+)p Fq(1)2351 2152 y Ft(:)648 2300 y FE(Indeed,)22 1338 b(treating)h(probability)f(of)i(hitting)f(an)h(additional)f(serv)o(er)g 1339 (as)h(a)h(f)o(ailure)e(in)h(Bernoulli)523 2400 y(trails)d(we)f(obtain:) 1340 695 2549 y(Pr)p Fs([)p Fv(D)e Ft(>)e Fv(t)6 b Fs(])23 1341 b(=)g FE(Pr)p Fs([)p Fv(D)18 b Fs(=)e Fv(t)h Fs(+)12 1342 b FE(1)p Fs(])g(+)g FE(Pr)m Fs([)p Fv(D)19 b Fs(=)c Fv(t)j 1343 Fs(+)12 b FE(2)p Fs(])g(+)g Ft(:)d(:)g(:)g Fs(+)j FE(Pr)o 1344 Fs([)p Fv(D)18 b Fs(=)g Fu(l)p Fs(])1026 2700 y(=)1114 1345 2632 y Fi(\000)1152 2700 y FE(1)12 b Fm(\000)1292 2667 1346 y Fo(k)p 1291 2681 V 1291 2728 a(n)1332 2632 y Fi(\001)1368 1347 2648 y Fo(t)t Fp(+)p Fq(1)1484 2700 y Fm(\001)1529 2667 1348 y Fo(k)p 1528 2681 V 1528 2728 a(n)1580 2700 y Fs(+)1657 1349 2632 y Fi(\000)1694 2700 y FE(1)g Fm(\000)1835 2667 y 1350 Fo(k)p 1833 2681 V 1833 2728 a(n)1874 2632 y Fi(\001)1910 1351 2648 y Fo(t)t Fp(+)p Fq(2)2026 2700 y Fm(\001)2072 2667 1352 y Fo(k)p 2070 2681 V 2070 2728 a(n)2123 2700 y Fs(+)g 1353 Ft(:)d(:)g(:)i Fs(+)2375 2632 y Fi(\000)2412 2700 y FE(1)h 1354 Fm(\000)2552 2667 y Fo(k)p 2551 2681 V 2551 2728 a(n)2591 1355 2632 y Fi(\001)2629 2648 y Fr(l)p Fh(\000)p Fq(1)2757 1356 2700 y Fm(\001)2803 2667 y Fo(k)p 2802 2681 V 2802 2728 1357 a(n)2854 2700 y Fs(+)2931 2632 y Fi(\000)2968 2700 y 1358 FE(1)g Fm(\000)3108 2667 y Fo(k)p 3107 2681 V 3107 2728 1359 a(n)3148 2632 y Fi(\001)3186 2648 y Fr(l)1026 2859 y 1360 Fs(=)1114 2792 y Fi(\000)1152 2859 y FE(1)g Fm(\000)1292 1361 2826 y Fo(k)p 1291 2840 V 1291 2888 a(n)1332 2792 y Fi(\001)1370 1362 2808 y Fr(l)1419 2859 y Fs(+)1496 2792 y Fi(\000)1533 1363 2859 y FE(1)g Fm(\000)1673 2826 y Fo(k)p 1672 2840 V 1364 1672 2888 a(n)1713 2792 y Fi(\001)1749 2808 y Fo(t)t 1365 Fp(+)p Fq(1)1865 2859 y Fm(\001)1900 2767 y Fi(\020)1949 1366 2859 y FE(1)g Fm(\000)2080 2792 y Fi(\000)2116 2859 y 1367 FE(1)g Fm(\000)2256 2826 y Fo(k)p 2255 2840 V 2255 2888 1368 a(n)2296 2792 y Fi(\001)2334 2808 y Fr(l)p Fh(\000)n 1369 Fo(t)t Fh(\000)p Fq(1)2517 2767 y Fi(\021)1026 3039 y 1370 Fs(=)1114 2971 y Fi(\000)1152 3039 y FE(1)g Fm(\000)1292 1371 3006 y Fo(k)p 1291 3020 V 1291 3067 a(n)1332 2971 y Fi(\001)1368 1372 2987 y Fo(t)t Fp(+)p Fq(1)1502 3039 y Ft(:)523 3187 y 1373 FE(Let)17 b(us)g(note)g(that)f(Pr)p Fs([)p Fv(D)g Ft(>)c 1374 Fv(t)6 b Fs(])17 b FE(does)g(not)f(depend)f(on)i(parameter)e 1375 Fu(l)p FE(,)i(e)o(xcept)f(for)g(the)h(maximal)f(range)523 1376 3287 y(of)k(the)g(random)f(v)n(ariable)g Fv(D)p FE(.)648 1377 3386 y(No)n(w)h(we)g(can)g(compute)f(the)h(e)o(xpected)f(v)n(alue)g(of) 1378 h Fv(D)p FE(:)1068 3535 y(E)o Fs([)p Fv(D)p Fs(])k(=)1335 1379 3541 y Fu(\345)1395 3500 y Fr(l)p Fh(\000)p Fq(1)1393 1380 3560 y Fo(t)t Fp(=)p Fq(0)1520 3535 y FE(Pr)p Fs([)p 1381 Fv(D)18 b Ft(>)e Fv(t)6 b Fs(])1248 3679 y(=)1335 3685 1382 y Fu(\345)1395 3646 y Fr(l)1393 3702 y Fo(t)t Fp(=)p 1383 Fq(1)1506 3612 y Fi(\000)1544 3679 y FE(1)12 b Fm(\000)1684 1384 3646 y Fo(k)p 1683 3660 V 1683 3708 a(n)1724 3612 y Fi(\001)1760 1385 3628 y Fo(t)1804 3679 y Fs(=)18 b(\()1929 3646 y Fo(n)p 1386 1929 3660 V 1930 3708 a(k)1982 3679 y Fm(\000)12 b FE(1)p 1387 Fs(\))g Fm(\001)2180 3612 y Fi(\000)2215 3679 y FE(1)g 1388 Fm(\000)g Fs(\()p FE(1)g Fm(\000)2517 3646 y Fo(k)p 2516 1389 3660 V 2516 3708 a(n)2556 3679 y Fs(\))2588 3649 y Fr(l)2626 1390 3612 y Fi(\001)2683 3679 y Ft(<)2776 3646 y Fo(n)p 2776 1391 3660 V 2777 3708 a(k)2837 3679 y Ft(:)523 3839 y FE(Let)30 1392 b(us)h(discuss)g(these)f(estimations)g(of)g Fv(D)p FE(.)h(First)g 1393 (assume)f(that)g Fv(k)q Ft(=)p Fv(n)23 b Fs(=)2719 3806 1394 y Fq(1)p 2719 3820 V 2719 3868 a(4)2760 3839 y FE(.)30 1395 b(Then)g Fv(D)23 b Ft(>)h FE(4)30 b(with)523 3939 y(probability)22 1396 b(lo)n(wer)h(than)h(0)p Ft(:)p FE(24.)e(Hence,)i(also)g(anon)o(ymity)d 1397 (set)k(of)f(the)f(Alice')-5 b(s)25 b(message)f(is)h(v)o(ery)523 1398 4038 y(small)18 b(with)g(high)f(probability)-5 b(.)15 1399 b(If)j Fv(k)g Fs(=)1713 4006 y Fo(n)p 1670 4020 117 4 1400 v 1670 4067 a Fq(log)7 b Fo(n)1815 4038 y FE(\(which)17 1401 b(is)h(a)h(more)e(realistic)h(scenario\),)e(then)i(E)o 1402 Fs([)p Fv(D)p Fs(])e Ft(<)523 4138 y FE(log)8 b Fv(n)p 1403 FE(.)20 b(Moreo)o(v)o(er)m(,)1312 4278 y(Pr)o Fs([)p 1404 Fv(D)f Ft(>)f FE(log)8 b Fv(n)k Fm(\000)g FE(1)p Fs(])k 1405 Ft(<)1980 4186 y Fi(\020)2030 4278 y FE(1)c Fm(\000)2211 1406 4245 y Fq(1)p 2169 4259 V 2169 4307 a(log)6 b Fo(n)2295 1407 4186 y Fi(\021)2344 4206 y Fq(log)h Fo(n)2483 4278 y 1408 Fm(\031)2576 4245 y Fq(1)p 2576 4259 31 4 v 2578 4307 1409 a Fo(e)523 4426 y FE(So,)21 b(in)f(majority)g(of)g(cases)i(ef)n(fecti)n 1410 (v)o(e)d(length)g(of)i(anon)o(ymity)d(path)i(is)h(belo)n(w)f(log)9 1411 b Fv(n)p FE(.)20 b(On)h(the)f(other)523 4526 y(hand,)g(for)h(a)h 1412 (global)e(adv)o(ersary)g(model)g(a)i(guaranteed)d(le)n(v)o(el)i(of)h 1413 (anon)o(ymity)c(is)23 b(reached)d(for)h Fu(l)d Fs(=)523 1414 4625 y Fu(Q)p Fs(\()p FE(log)723 4592 y Fq(2)767 4625 1415 y Fv(n)p Fs(\))23 b FE([4])g(\(in)g(f)o(act,)g(after)g(slight)g 1416 (changes)f(in)i(the)f(protocol)e(are)j(done\).)d(So)j(it)f(may)g 1417 (happen)523 4725 y(that)18 b(for)f(a)h(gi)n(v)o(en)e(v)n(alue)h(of)g 1418 Fv(k)j FE(it)e(is)h(impossible)e(to)g(reach)g(a)h(high)f(anon)o(ymity)e 1419 (le)n(v)o(el)i(\226)h(increasing)e Fu(l)523 4825 y FE(in)22 1420 b(this)f(case)h(does)f(not)g(help)g(at)h(all)g(since)g(the)f(ef)n 1421 (fecti)n(v)o(e)f(length)h(of)g(anon)o(ymity)e(path)h(essentially)523 1422 4924 y(will)h(not)f(increase.)f(Sad)i(b)n(ut)f(true!)p 1423 eop end 1424 %%Page: 6 6 1425 TeXDict begin 6 5 bop 523 448 a Fx(4)99 b(Dangers)26 1426 b(of)e(a)h(Limited)h(Local)f(V)l(iew)523 646 y FE(In)17 1427 b(this)g(section)g(we)g(consider)f(the)h(case)h(that)f(all)g(users)g(e) 1428 o(xcept)f(Alice)i(are)f(choosing)e(intermediate)523 746 1429 y(serv)o(ers)24 b(from)g(a)h(set)h Fv(N)5 b FE(,)26 b(while)f(Alice)g 1430 (is)h(a)o(w)o(are)e(of)h(only)f(a)h(subset)g(of)g Fv(N)30 1431 b FE(of)25 b(cardinality)e Fv(c)13 b Fm(\001)g(j)p Fv(N)5 1432 b Fm(j)p FE(,)523 845 y(for)18 b(some)g Fv(c)f Ft(<)f 1433 FE(1.)j(Later)f(in)h(this)g(section)f(we)h(discuss)g(shortly)e(the)i 1434 (case)g(that)f(each)h(user)f(has)h(some)523 945 y(limited)h(kno)n 1435 (wledge)e(of)i(the)g(serv)o(ers)g(from)f Fv(N)5 b FE(.)648 1436 1044 y(W)-7 b(e)19 b(consider)f(a)h(global)f(passi)n(v)o(e)g(adv)o 1437 (ersary)f(who)h(kno)n(ws)g Fv(N)25 b FE(and)18 b(the)h(sets)g(of)g 1438 (serv)o(ers)f(kno)n(wn)523 1144 y(by)h(Alice.)g(The)f(goal)h(of)f(the)h 1439 (adv)o(ersary)e(is)j(to)f(determine)f(the)h(destination)f(of)g(a)i 1440 (message)f(sent)g(by)523 1244 y(Alice)i(based)e(on)h(information)e 1441 (gained)h(from)g(observing)f(the)i(traf)n(\002c.)648 1442 1343 y(W)-7 b(e)29 b(shall)g(sho)n(w)f(that)h(anon)o(ymity)d(set)k(of)e 1443 (the)g(message)h(of)f(Alice)h(might)f(be)g(surprisingly)523 1444 1443 y(small)17 b(and)g(therefore)d(the)j(protocol)e(of)n(fers)h(a)h 1445 (lo)n(w)g(le)n(v)o(el)g(anon)o(ymity)d(against)i(a)h(global)f(adv)o 1446 (ersary)-5 b(.)523 1543 y(A)29 b(v)o(ery)d(important)h(point)g(is)i 1447 (that)f(increasing)f(the)h(length)f(of)h(anon)o(ymity)e(path)h(does)20 1448 b(not)g(help)p 2962 1574 443 4 v 523 1642 a(much)p 523 1449 1656 185 4 v -1 w(:)i(after)g(an)g(initial)h(phase)e(the)i(size)f(of)g 1450 (the)g(anon)o(ymity)e(set)j(\003uctuates)f(around)e(a)j(relati)n(v)o 1451 (ely)523 1742 y(small)e(v)n(alue.)648 1841 y(These)c(results)h(are)g 1452 (quite)f(surprising)f(in)i(vie)n(w)g(of)f(the)h(results)g(concerning)d 1453 (the)j(case)g(when)f(all)523 1941 y(users)25 b(choose)e(intermediate)h 1454 (serv)o(ers)f(uniformly)g(at)i(random)d(from)i(the)g(same)h(set)h 1455 Fv(N)5 b FE(.)25 b(Namely)-5 b(,)523 2041 y(then)28 b(increasing)e(the) 1456 j(path)e(length)g(impro)o(v)o(es)p 1602 2072 307 4 v 1457 26 w(anon)o(ymity)f(le)n(v)o(el)i(so)g(that)g(\002nally)g(we)h(get)f(v) 1458 o(ery)523 2140 y(strong)g(anon)o(ymity)e(e)o(xpressed)h(by)h(a)h(small) 1459 g(v)n(ariation)e(distance)h(between)f(distrib)n(ution)h(of)g(all)523 1460 2240 y(permutations)f(of)i(messages)g(and)g(the)g(stationary)f(distrib) 1461 n(ution.)g(There)g(are)h(also)h(results)f(sug-)523 2340 1462 y(gesting)i(that)h(the)g(necessary)f(path)g(length)g(is)h(relati)n(v)o 1463 (ely)f(small)h([16,)12 b(4])31 b(e)n(v)o(en)g(in)h(the)g(case)g(of)523 1464 2439 y(presence)19 b(of)h(global)f(passi)n(v)o(e)h(adv)o(ersary)-5 1465 b(.)523 2687 y Fw(4.1)82 b(Pr)o(ocess)20 b(de\002nition)523 1466 2851 y Fv(N)30 b FE(denotes)22 b(the)i(set)g(of)g(all)g(serv)o(ers)f 1467 (that)h(can)f(be)h(used)f(as)i(intermediate)d(serv)o(ers)h(on)g(anon)o 1468 (ymity)523 2951 y(paths.)h(Let)d Fv(W)32 b Fm(\032)20 1469 b Fv(N)31 b FE(be)25 b(the)f(set)i(of)f(serv)o(ers)f(kno)n(wn)f(to)i 1470 (Alice.)g(Let)g Fv(M)k FE(be)24 b(the)h(set)h(of)e(messages)523 1471 3050 y(sent)d(by)e(all)i(users.)f(W)-7 b(e)22 b(assume)e(that)g 1472 Fm(j)p Fv(M)s Fm(j)f Fs(=)f Fm(j)p Fv(N)5 b Fm(j)21 b 1473 FE(and)f(that)g(each)g(user)g(sends)g(one)g(message.)648 1474 3150 y(At)30 b(each)g(step)h(of)f(the)g(protocol)e(the)j(adv)o(ersary)d 1475 (may)i(observ)o(e)e(positions)i(of)g Fv(M)k FE(encoded)523 1476 3250 y(messages,)19 b(b)n(ut)h(the)g(problem)d(is)k(to)f(indicate)f 1477 (the)g(position)g(of)g(the)h(message)f(sent)h(by)f(Alice)h(\226)f(the) 1478 523 3349 y(messages)k(are)g(recoded)f(at)h(each)g(step)h(in)f(such)g(a) 1479 g(w)o(ay)g(that)g(if)h(tw)o(o)f(or)g(more)f(of)h(them)g(enter)f(the)523 1480 3449 y(same)e(serv)o(er)m(,)f(the)o(y)g(cannot)f(be)i(link)o(ed)f(to)h 1481 (the)g(messages)g(lea)n(ving)g(this)g(serv)o(er)f(after)h(recoding.)d 1482 (It)523 3549 y(is)k(e)o(xactly)e(the)i(same)f(mechanism)f(as)i(in)f 1483 (the)g(case)h(of)f(a)h(MIX-se)n(v)o(er)d([2].)648 3648 1484 y(Let)h(a)g(set)g Fv(N)998 3660 y Fo(i)1039 3648 y FE(be)g(the)g(set)g 1485 (consisting)f(of)h(all)g(messages)g Fv(u)g FE(after)g(step)g 1486 Fv(i)g FE(such)g(that)g(it)g(is)h(possible)523 3748 y(that)k(the)f 1487 (message)h Fv(u)f FE(is)i(the)e(recoded)f(message)i(sent)f(by)h(Alice.) 1488 f(More)g(precisely)-5 b(,)22 b(there)h(e)o(xist)h(a)523 1489 3847 y(\(hypothetical\))g(linking)i(between)g(messages)h(entering)f 1490 (and)g(lea)n(ving)g(each)h(serv)o(er)f(so)h(that)g(the)523 1491 3947 y(message)e(sent)g(by)f(Alice)h(at)g(the)g(\002rst)g(step)g(leads) 1492 g(to)g(message)g Fv(u)f FE(after)h(step)g Fv(i)p FE(.)g(In)f(other)g(w) 1493 o(ords,)523 4047 y(from)31 b(the)g(adv)o(ersary)f(point)h(of)g(vie)n(w) 1494 -5 b(,)31 b(it)h(cannot)f(be)g(e)o(xcluded)f(that)i Fv(u)f 1495 FE(is)i(a)f(recoded)e(Alice')-5 b(s)523 4146 y(message)20 1496 b(and)g Fv(N)1019 4158 y Fo(i)1061 4146 y FE(is)h(the)f(anon)o(ymity)e 1497 (set)j(of)f(the)g(Alice')-5 b(s)21 b(message)f(after)g(step)g 1498 Fv(i)p FE(.)648 4246 y(Let)g Fv(S)821 4258 y Fo(i)862 1499 4246 y FE(be)h(the)f(set)h(of)f(all)h(serv)o(ers)e(where)h(the)g 1500 (messages)g(of)g Fv(N)2468 4258 y Fo(i)2510 4246 y FE(occur)-5 1501 b(.)648 4346 y(At)21 b(the)f(v)o(ery)f(be)o(ginning)f(e)n(v)o(ery)h 1502 (user)i(sends)f(e)o(xactly)g(one)g(message.)g(So)h Fm(j)p 1503 Fv(N)2869 4358 y Fq(0)2904 4346 y Fm(j)d Fs(=)h FE(1,)h(since)g(the)523 1504 4445 y(adv)o(ersary)h(e)o(xactly)i(kno)n(ws)f(which)h(message)g(is)h 1505 (sent)g(by)f(Alice.)g(Let)g(us)h(consider)e(step)i Fv(i)g 1506 FE(of)e(the)523 4545 y(protocol.)j(Our)i(goal)g(is)h(to)f(estimate)h 1507 (the)f(size)h(of)f Fv(N)2092 4557 y Fo(i)2141 4545 y 1508 FE(based)g(on)g(the)g(size)h(of)f Fv(N)2905 4557 y Fo(i)p 1509 Fh(\000)p Fq(1)3005 4545 y FE(.)g(The)g(set)h Fv(N)3383 1510 4557 y Fo(i)523 4644 y FE(consists)21 b(of)f(tw)o(o)g(kinds)g(of)g 1511 (messages:)523 4825 y Fw(the)g(\002rst)h(kind:)42 b FE(the)25 1512 b(messages)g(that)g(were)f(in)h Fv(N)1994 4837 y Fo(i)p 1513 Fh(\000)p Fq(1)2120 4825 y FE(and)f(are)h(sent)g(at)g(step)g 1514 Fv(i)h FE(to)e(serv)o(ers)h(within)660 4924 y Fv(W)10 1515 b FE(,)p eop end 1516 %%Page: 7 7 1517 TeXDict begin 7 6 bop 523 448 a Fw(the)20 b(second)h(kind:)42 1518 b FE(the)16 b(messages)g(that)g(were)g(outside)f Fv(N)2222 1519 460 y Fo(i)p Fh(\000)p Fq(1)2322 448 y FE(,)h(b)n(ut)g(went)g(to)g 1520 (some)g(serv)o(ers,)f(where)664 548 y(the)20 b(message)g(of)g(the)h 1521 (\002rst)f(kind)g(occur)f(after)h(step)g Fv(i)p FE(.)523 1522 723 y(Let)g(us)g(note)g(that)f(there)h(is)g(at)h(least)f(one)f(message) 1523 h(from)f Fv(N)2248 735 y Fo(i)p Fh(\000)p Fq(1)2368 723 1524 y FE(that)h(remains)f(within)d Fv(W)10 b FE(,)20 b(namely)-5 1525 b(,)523 823 y(the)23 b(encrypted)d(message)j(of)f(Alice.)h(The)g 1526 (remaining)d(messages)j(from)f Fv(N)2706 835 y Fo(i)p 1527 Fh(\000)p Fq(1)2829 823 y FE(that)h(go)f(to)h(serv)o(ers)523 1528 923 y(in)d(the)h(set)g Fv(N)16 b Fm(n)8 b Fv(W)30 b FE(cannot)20 1529 b(hold)f(the)h(message)g(from)f(Alice.)648 1022 y(In)28 1530 b(order)g(to)h(estimate)g(the)g(number)e(of)h(messages)h(of)g(the)f 1531 (second)g(kind)g(we)i(ha)n(v)o(e)e(to)h(\002nd)523 1122 1532 y(cardinality)i(of)h(the)g(set)h Fv(S)1314 1134 y Fo(i)1334 1533 1122 y FE(.)g(The)f(random)e(v)n(ariable)h(denoting)f(the)i(size)h(of)f 1534 Fv(S)2897 1134 y Fo(i)2950 1122 y FE(is)i(gi)n(v)o(en)c(by)i(a)523 1535 1222 y(combination)16 b(of)j(binomial)e(distrib)n(ution)g(and)i 1536 (so-called)e(bins)i(and)f(balls)h(process.)f(Let)h(Bin)p 1537 Fs(\()p Fv(v)-6 b Ft(;)15 b Fv(p)p Fs(\))523 1321 y FE(be)26 1538 b(a)g(random)d(v)n(ariable)i(denoting)f(the)h(number)f(of)h(successes)i 1539 (in)e(a)h(Bernoulli)f(process)g(with)h Fv(v)523 1421 1540 y FE(trials)g(and)f(success)h(probability)j Fv(p)d FE(for)f(a)h(single) 1541 f(trial.)h(Let)f(BiBa)q Fs(\()p Fv(v)-6 b Ft(;)9 b Fv(u)p 1542 Fs(\))26 b FE(be)f(a)h(random)e(v)n(ariable)523 1520 1543 y(denoting)15 b(the)i(number)f(of)g(non-empty)f(bins)i(\(i.e.)g(with)g 1544 (at)g(least)h(one)f(ball\))g(after)f(thro)n(wing)g Fv(v)h 1545 FE(balls)523 1620 y(uniformly)h(and)i(independently)d(at)j(random)f 1546 (into)h Fv(u)g FE(bins.)648 1720 y(It)g(is)h(easy)g(to)f(see)h(that)g 1547 (the)f(number)e(of)i(the)h(messages)f(from)g Fv(N)2501 1548 1732 y Fo(i)p Fh(\000)p Fq(1)2621 1720 y FE(which)g(remain)g(within)c 1549 Fv(W)523 1819 y FE(at)21 b(step)f Fv(i)h FE(is)g(gi)n(v)o(en)e(by)h 1550 (the)g(random)e(v)n(ariable:)1493 1995 y(Bin)p Fs(\()p 1551 Fm(j)p Fv(N)1721 2007 y Fo(i)p Fh(\000)p Fq(1)1821 1995 1552 y Fm(j)12 b(\000)g FE(1)p Ft(;)d Fm(j)l Fv(W)f Fm(j)p 1553 Ft(=)p Fm(j)p Fv(N)d Fm(j)p Fs(\))12 b(+)g FE(1)523 2170 1554 y(\()p Fm(j)p Fv(N)627 2182 y Fo(i)p Fh(\000)p Fq(1)727 1555 2170 y Fm(j)e(\000)g FE(1)18 b(messages)h(are)g(not)f(from)g(Alice,)g 1556 (so)h(each)g(of)f(them)g(chooses)h(to)f(stay)h(within)c 1557 Fv(W)29 b FE(with)523 2270 y(probability)16 b Fm(j)l 1558 Fv(W)11 b Fm(j)p Ft(=)p Fm(j)p Fv(N)5 b Fm(j)p FE(,)18 1559 b(the)h(term)f(\223)p Fs(+)p FE(1\224)g(corresponds)e(to)i(the)h 1560 (message)f(of)g(Alice\).)h(So)f(\002nally)g(the)523 2370 1561 y(size)j(of)f Fv(S)805 2382 y Fo(i)846 2370 y FE(is)h(a)g(random)d(v)n 1562 (ariable)i(with)g(the)g(same)g(distrib)n(ution)f(as)1276 1563 2545 y(BiBa)q Fs(\()p FE(Bin)p Fs(\()p Fm(j)p Fv(N)1707 1564 2557 y Fo(i)p Fh(\000)p Fq(1)1807 2545 y Fm(j)12 b(\000)g 1565 FE(1)p Ft(;)d Fm(j)l Fv(W)g Fm(j)p Ft(=)p Fm(j)p Fv(N)c 1566 Fm(j)p Fs(\))12 b(+)g FE(1)p Ft(;)d Fm(j)l Fv(W)g Fm(j)p 1567 Fs(\))21 b Ft(:)648 2721 y FE(A)g(message)f(from)g(the)h(set)h 1568 Fv(M)15 b Fm(n)d Fv(N)1642 2733 y Fo(i)p Fh(\000)p Fq(1)1762 1569 2721 y FE(becomes)20 b(a)h(member)f(of)g Fv(N)2569 2733 1570 y Fo(i)2591 2721 y FE(,)h(if)g(at)g(step)g Fv(i)h FE(it)f(hits)h(one)e 1571 (of)523 2820 y(the)h(serv)o(ers)e(of)i Fv(S)1033 2832 1572 y Fo(i)1053 2820 y FE(.)g(So)g(the)f(number)f(of)h(messages)h(of)f(the) 1573 g(second)g(kind)g(joining)f Fv(N)2968 2832 y Fo(i)3010 1574 2820 y FE(is)j(described)523 2920 y(a)f(random)d(v)n(ariable)h(with)h 1575 (binomial)f(distrib)n(ution)1503 3095 y(Bin)p Fs(\()p 1576 Fm(j)p Fv(M)s Fm(j)12 b(\000)g(j)p Fv(N)1938 3107 y Fo(i)p 1577 Fh(\000)p Fq(1)2037 3095 y Fm(j)p Ft(;)d Fm(j)p Fv(S)2157 1578 3107 y Fo(i)2178 3095 y Fm(j)p Ft(=)p Fm(j)p Fv(N)c Fm(j)p 1579 Fs(\))21 b Ft(:)523 3271 y FE(Finally)-5 b(,)19 b(we)i(ha)n(v)o(e)f 1580 (got)f(the)i(follo)n(wing)d(recursi)n(v)o(e)h(formulas)g(on)h(random)e 1581 (v)n(ariables:)901 3446 y Fm(j)p Fv(S)966 3458 y Fo(i)987 1582 3446 y Fm(j)23 b Fs(=)g FE(BiBa)p Fs(\()p FE(Bin)q Fs(\()p 1583 Fm(j)p Fv(N)1552 3458 y Fo(i)p Fh(\000)p Fq(1)1652 3446 1584 y Fm(j)12 b(\000)g FE(1)p Ft(;)d Fm(j)l Fv(W)f Fm(j)p 1585 Ft(=)p Fm(j)p Fv(N)d Fm(j)p Fs(\))12 b(+)g FE(1)p Ft(;)d 1586 Fm(j)l Fv(W)g Fm(j)p Fs(\))889 3571 y Fm(j)p Fv(N)965 1587 3583 y Fo(i)987 3571 y Fm(j)23 b Fs(=)g FE(Bin)p Fs(\()p 1588 Fm(j)p Fv(M)s Fm(j)12 b(\000)g(j)p Fv(N)1556 3583 y Fo(i)p 1589 Fh(\000)p Fq(1)1655 3571 y Fm(j)p Ft(;)d Fm(j)p Fv(S)1775 1590 3583 y Fo(i)1796 3571 y Fm(j)p Ft(=)p Fm(j)p Fv(N)c Fm(j)p 1591 Fs(\))12 b(+)g FE(Bin)o Fs(\()p Fm(j)p Fv(N)2315 3583 1592 y Fo(i)p Fh(\000)p Fq(1)2415 3571 y Fm(j)g(\000)g FE(1)p 1593 Ft(;)d Fm(j)l Fv(W)f Fm(j)p Ft(=)p Fm(j)p Fv(N)d Fm(j)p 1594 Fs(\))12 b(+)g FE(1)p Ft(:)876 3695 y Fm(j)p Fv(N)952 1595 3707 y Fq(0)987 3695 y Fm(j)23 b Fs(=)g Fm(j)p Fv(S)1186 1596 3707 y Fq(1)1220 3695 y Fm(j)c Fs(=)f FE(1)i Ft(:)648 1597 3871 y FE(In)h(f)o(act,)h(in)g(the)f(abo)o(v)o(e)g(formulas)f(the)i 1598 (sign)g(\223)p Fs(=)p FE(\224)f(means)h(that)f(the)h(random)e(v)n 1599 (ariables)h(on)g(the)523 3970 y(left)f(and)g(right)g(side)g(ha)n(v)o(e) 1600 g(the)g(same)g(probability)e(distrib)n(ution.)648 4070 1601 y(Our)27 b(goal)g(is)i(to)e(estimate)h(the)g(size)g(of)g 1602 Fv(N)1895 4087 y Fr(l)1933 4070 y FE(,)g(which)f(is)i(anon)o(ymity)c 1603 (set)j(of)g(the)f(message)h(of)523 4170 y(Alice)21 b(after)e 1604 Fu(l)i FE(steps)g(of)f(processing)e(the)j(messages.)523 1605 4413 y Fw(4.2)82 b(Analysis)523 4573 y FE(Let)20 b(us)h(recall)f(that)g 1606 (the)h(e)o(xpected)d(v)n(alue)i(of)g(a)g(random)f(v)n(ariable)g(BiBa)p 1607 Fs(\()p Fv(v)-6 b Ft(;)9 b Fv(u)p Fs(\))21 b FE(equals)1452 1608 4749 y Fv(u)p Fs(\()p FE(1)12 b Fm(\000)g Fs(\()p FE(1)g 1609 Fm(\000)1826 4716 y Fq(1)p 1826 4730 31 4 v 1826 4778 1610 a Fo(u)1867 4749 y Fs(\))1899 4719 y Fo(v)1930 4749 y 1611 Fs(\))19 b Fm(\031)f Fv(u)p Fs(\()p FE(1)12 b Fm(\000)g 1612 Fv(e)2306 4718 y Fh(\000)2364 4694 y Fj(u)p 2361 4704 1613 25 3 v 2362 4739 a(v)2400 4749 y Fs(\))21 b Ft(:)523 1614 4924 y FE(The)f(e)o(xpected)e(v)n(alue)i(of)g(random)e(v)n(ariable)h 1615 (Bin)p Fs(\()p Fv(u)p Ft(;)c Fv(p)p Fs(\))21 b FE(is)g 1616 Fv(u)12 b Fm(\001)18 b Fv(p)p FE(.)p eop end 1617 %%Page: 8 8 1618 TeXDict begin 8 7 bop 648 448 a FE(Since)23 b(we)h(assume)g(that)f 1619 Fm(j)p Fv(N)5 b Fm(j)21 b Fs(=)f Fm(j)p Fv(M)s Fm(j)p 1620 FE(,)k(we)g(simplify)f(the)h(formulas)e(by)h(substituting)g 1621 Fm(j)p Fv(N)5 b Fm(j)24 b FE(and)523 548 y Fm(j)p Fv(M)s 1622 Fm(j)f FE(by)f(a)h(single)f(symbol)g 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FE(E)p Fs([)p Fm(j)p Fv(S)2007 1381 y Fo(i)2028 1639 1369 y Fm(j)p Fs(])g(+)g(\()p Fm(j)p Fv(N)2271 1381 y 1640 Fo(i)p Fh(\000)p Fq(1)2369 1369 y Fm(j)g(\000)g FE(1)p 1641 Fs(\))p Fm(j)l Fv(W)d Fm(j)p 1399 1406 1277 4 v 2016 1642 1482 a Fv(n)2696 1425 y Fs(+)j FE(1)20 b Ft(:)523 1669 1643 y FE(\(In)25 b(the)h(\002rst)g(formula)e(we)i(ha)n(v)o(e)f(written)g 1644 Fm(\031)h FE(instead)f(of)h Fs(=)p FE(,)f(since)h(we)g(ha)n(v)o(e)f 1645 (assumed)g(that)g(the)523 1768 y(number)k(of)i(messages)g(from)f 1646 Fv(N)1500 1780 y Fo(i)p Fh(\000)p Fq(1)1631 1768 y FE(that)i(remain)e 1647 (in)d Fv(W)41 b FE(equals)31 b(to)g(the)g(e)o(xpected)f(number)f(of)523 1648 1868 y(such)19 b(messages.)g(Similarly)-5 b(,)19 b(in)g(the)h(second)e 1649 (formula)g(we)i(ha)n(v)o(e)e(replaced)g Fm(j)p Fv(S)2789 1650 1880 y Fo(i)2810 1868 y Fm(j)i FE(by)f(E)p Fs([)p Fm(j)p 1651 Fv(S)3095 1880 y Fo(i)3115 1868 y Fm(j)p Fs(])p FE(.\))h(After)523 1652 1968 y(applying)e(the)j(approximation)c Fs(\()p FE(1)12 1653 b Fm(\000)1633 1935 y Fq(1)p 1633 1949 31 4 v 1633 1996 1654 a Fo(a)1674 1968 y Fs(\))1706 1938 y Fo(b)1759 1968 y 1655 Fm(\031)18 b Fv(e)1879 1938 y Fh(\000)p Fo(b)p Fn(=)p 1656 Fo(a)2023 1968 y FE(,)i(we)h(get)811 2259 y Fv(E)6 b 1657 Fs([)p Fm(j)p Fv(N)967 2271 y Fo(i)989 2259 y Fm(j)p 1658 Fs(])18 b Fm(\031)1146 2217 y Fo(n)p Fh(\000j)p Fo(N)1281 1659 2229 y Fj(i)p Fe(\000)p Fg(1)1363 2217 y Fh(j)p 1146 1660 2240 234 4 v 1247 2288 a Fo(n)1401 2259 y Fm(\001)12 1661 b(j)l Fv(W)e Fm(j)i(\001)1604 2142 y Fi(\022)1664 2259 1662 y FE(1)g Fm(\000)g Fv(e)1832 2212 y Fh(\000)1890 2173 1663 y Fe(j)p Fj(N)1936 2189 y(i)p Fe(\000)p Fg(1)2015 2173 1664 y Fe(j\000)p Fg(1)p 1888 2198 205 3 v 1978 2233 a Fj(n)2102 1665 2212 y Fh(\000)2184 2188 y Fg(1)p 2160 2198 73 3 v 2160 1666 2238 a Fe(j)n Fj(W)6 b Fe(j)2247 2142 y Fi(\023)2320 1667 2259 y Fs(+)12 b(\()p Fm(j)p Fv(N)2505 2271 y Fo(i)p 1668 Fh(\000)p Fq(1)2604 2259 y Fm(j)g(\000)g FE(1)p Fs(\))g 1669 Fm(\001)2844 2218 y Fh(j)m Fo(W)c Fh(j)p 2844 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1686 b FE(\(1\))1549 3031 y Fm(\000j)p Fv(N)1690 3043 y Fo(i)p 1687 Fh(\000)p Fq(1)1790 3031 y Fm(j)12 b(\001)g Fs(\()p FE(1)g 1688 Fm(\000)2030 2975 y(j)l Fv(W)e Fm(j)p 2030 3012 122 4 1689 v 2070 3088 a Fv(n)2161 3031 y Fs(\))i(+)g(\()p FE(1)g 1690 Fm(\000)2452 2975 y(j)l Fv(W)e Fm(j)p 2452 3012 V 2492 1691 3088 a Fv(n)2583 3031 y Fs(\))648 3339 y FE(W)-7 b(e)25 1692 b(consider)f Fu(D)p Fs(\()p Fm(j)p Fv(N)1247 3351 y Fo(i)p 1693 Fh(\000)p Fq(1)1347 3339 y Fm(j)p Fs(\))i FE(as)f(a)g(function)e(of)i 1694 Fm(j)p Fv(N)2057 3351 y Fo(i)p Fh(\000)p Fq(1)2157 3339 1695 y Fm(j)g FE(and)f(we)h(\002x)g(the)g(v)n(alue)f(of)3019 1696 3297 y Fh(j)m Fo(W)8 b Fh(j)p 3019 3319 90 4 v 3024 3369 1697 a(j)p Fo(N)s Fh(j)3119 3339 y FE(.)25 b(W)-7 b(e)26 b(see)523 1698 3449 y(that)21 b(the)f(\002rst)h(term)f(in)h(\(1\))f(forces)g 1699 Fu(D)h FE(to)f(be)h(positi)n(v)o(e)e(and)h(its)i(impact)e(is)h(bigger)e 1700 (for)h(small)h(v)n(alues)523 3549 y(of)g Fm(j)p Fv(N)690 1701 3561 y Fo(i)p Fh(\000)p Fq(1)790 3549 y Fm(j)p FE(.)h(The)f(second)f 1702 (term)h(in)h(\(1\))f(forces)f Fu(D)i FE(to)g(be)f(ne)o(gati)n(v)o(e)e 1703 (and)i(its)h(impact)f(gro)n(ws)g(with)g(the)523 3649 1704 y(size)g(of)g Fm(j)p Fv(N)840 3661 y Fo(i)p Fh(\000)p 1705 Fq(1)940 3649 y Fm(j)p FE(.)g(So,)f(there)g(is)i(a)f(point)f(where)g 1706 (both)f(tendencies)h(ha)n(v)o(e)g(the)h(same)f(strength)g(and)g(so)523 1707 3765 y(the)g(v)n(alues)g(of)g Fm(j)p Fv(N)1040 3777 y 1708 Fo(t)1066 3765 y Fm(j)h FE(oscillate)f(around)f(it.)h(Of)h(course,)e 1709 (this)i(equilibrium)d(point)h(depends)g(on)3260 3723 1710 y Fh(j)m Fo(W)7 b Fh(j)p 3260 3745 V 3265 3795 a(j)p 1711 Fo(N)s Fh(j)3359 3765 y FE(.)648 3929 y(If)18 b(we)i(put)e 1712 Fu(a)g Fs(=)1126 3888 y Fh(j)m Fo(W)8 b Fh(j)p 1126 3910 1713 V 1131 3959 a(j)p Fo(N)s Fh(j)1225 3929 y FE(,)20 b(then)e(we)i(w)o 1714 (ould)e(lik)o(e)h(to)g(\002nd)g(a)g(v)n(alue)g Fm(j)p 1715 Fv(N)2477 3941 y Fo(i)2498 3929 y Fm(j)h FE(such)e(that)h(according)e 1716 (to)i(\(1\),)523 4045 y Fu(D)p Fs(\()p Fm(j)p Fv(N)682 1717 4057 y Fo(i)p Fh(\000)p Fq(1)782 4045 y Fm(j)p Fs(\))g(=)f 1718 FE(0.)i(This)g(concerns)f(solving)g(the)h(equation:)1029 1719 4296 y(0)e Fs(=)g(\()p Fv(n)12 b Fm(\000)g Fv(x)p Fs(\))g 1720 Fm(\001)g Fu(a)g Fm(\001)g Fs(\()p FE(1)g Fm(\000)g Fv(e)1750 1721 4262 y Fh(\000)1808 4238 y Fj(x)p Fe(\000)p Fg(1)p 1803 1722 4248 86 3 v 1833 4283 a Fj(n)1898 4262 y Fh(\000)1972 1723 4238 y Fg(1)p 1956 4248 57 3 v 1956 4283 a Fk(a)p Fj(n)2027 1724 4296 y Fs(\))g Fm(\000)g Fv(x)g Fm(\001)g Fs(\()p FE(1)g 1725 Fm(\000)g Fu(a)p Fs(\))g(+)g(\()p FE(1)g Fm(\000)f Fu(a)p 1726 Fs(\))16 b Ft(:)455 b FE(\(2\))523 4526 y(W)-7 b(e)31 1727 b(ha)n(v)o(e)e(not)g(found)f(an)o(y)h(closed)g(formula)f(for)h 1728 (solutions)g(of)h(Equality)e(2)i(\(as)g(well)g(as)h(some)523 1729 4626 y(symbolic)15 b(computation)e(systems\).)j(Ho)n(we)n(v)o(er)m(,)e 1730 (one)h(can)g(easily)h(\002nd)g(the)g(solutions)f(numerically)-5 1731 b(.)523 4726 y(The)20 b(results)g(for)g Fv(n)e Fs(=)g 1732 FE(1000)h(and)g(dif)n(ferent)g(v)n(alues)h(of)g Fm(j)l 1733 Fv(W)10 b Fm(j)21 b FE(are)f(plotted)f(on)h(Figure)f(1.)p 1734 eop end 1735 %%Page: 9 9 1736 TeXDict begin 9 8 bop 523 2307 a @beginspecial 50 @llx 1737 70 @lly 410 @urx 292 @ury 3600 @rwi @setspecial 1738 %%BeginDocument: hockey.eps 1739 %!PS-Adobe-2.0 EPSF-2.0 1740 %%Title: hockey.eps 1741 %%Creator: gnuplot 4.0 patchlevel 0 1742 %%CreationDate: Fri Apr 1 18:15:54 2005 1743 %%DocumentFonts: (atend) 1744 %%BoundingBox: 50 70 410 292 1745 %%Orientation: Portrait 1746 %%EndComments 1747 /gnudict 256 dict def 1748 gnudict begin 1749 /Color false def 1750 /Solid false def 1751 /gnulinewidth 5.000 def 1752 /userlinewidth gnulinewidth def 1753 /vshift -40 def 1754 /dl {10.0 mul} def 1755 /hpt_ 31.5 def 1756 /vpt_ 31.5 def 1757 /hpt hpt_ def 1758 /vpt vpt_ def 1759 /Rounded false def 1760 /M {moveto} bind def 1761 /L {lineto} bind def 1762 /R {rmoveto} bind def 1763 /V {rlineto} bind def 1764 /N {newpath moveto} bind def 1765 /C {setrgbcolor} bind def 1766 /f {rlineto fill} bind def 1767 /vpt2 vpt 2 mul def 1768 /hpt2 hpt 2 mul def 1769 /Lshow { currentpoint stroke M 1770 0 vshift R show } def 1771 /Rshow { currentpoint stroke M 1772 dup stringwidth pop neg vshift R show } def 1773 /Cshow { currentpoint stroke M 1774 dup stringwidth pop -2 div vshift R show } def 1775 /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def 1776 /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def 1777 /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } 1778 {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse } def 1779 /BL { stroke userlinewidth 2 mul setlinewidth 1780 Rounded { 1 setlinejoin 1 setlinecap } if } def 1781 /AL { stroke userlinewidth 2 div setlinewidth 1782 Rounded { 1 setlinejoin 1 setlinecap } if } def 1783 /UL { dup gnulinewidth mul /userlinewidth exch def 1784 dup 1 lt {pop 1} if 10 mul /udl exch def } def 1785 /PL { stroke userlinewidth setlinewidth 1786 Rounded { 1 setlinejoin 1 setlinecap } if } def 1787 /LTw { PL [] 1 setgray } def 1788 /LTb { BL [] 0 0 0 DL } def 1789 /LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def 1790 /LT0 { PL [] 1 0 0 DL } def 1791 /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def 1792 /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def 1793 /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def 1794 /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def 1795 /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def 1796 /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def 1797 /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def 1798 /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def 1799 /Pnt { stroke [] 0 setdash 1800 gsave 1 setlinecap M 0 0 V stroke grestore } def 1801 /Dia { stroke [] 0 setdash 2 copy vpt add M 1802 hpt neg vpt neg V hpt vpt neg V 1803 hpt vpt V hpt neg vpt V closepath stroke 1804 Pnt } def 1805 /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V 1806 currentpoint stroke M 1807 hpt neg vpt neg R hpt2 0 V stroke 1808 } def 1809 /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 1810 0 vpt2 neg V hpt2 0 V 0 vpt2 V 1811 hpt2 neg 0 V closepath stroke 1812 Pnt } def 1813 /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M 1814 hpt2 vpt2 neg V currentpoint stroke M 1815 hpt2 neg 0 R hpt2 vpt2 V stroke } def 1816 /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M 1817 hpt neg vpt -1.62 mul V 1818 hpt 2 mul 0 V 1819 hpt neg vpt 1.62 mul V closepath stroke 1820 Pnt } def 1821 /Star { 2 copy Pls Crs } def 1822 /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 1823 0 vpt2 neg V hpt2 0 V 0 vpt2 V 1824 hpt2 neg 0 V closepath fill } def 1825 /TriUF { stroke [] 0 setdash vpt 1.12 mul add M 1826 hpt neg vpt -1.62 mul V 1827 hpt 2 mul 0 V 1828 hpt neg vpt 1.62 mul V closepath fill } def 1829 /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M 1830 hpt neg vpt 1.62 mul V 1831 hpt 2 mul 0 V 1832 hpt neg vpt -1.62 mul V closepath stroke 1833 Pnt } def 1834 /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M 1835 hpt neg vpt 1.62 mul V 1836 hpt 2 mul 0 V 1837 hpt neg vpt -1.62 mul V closepath fill} def 1838 /DiaF { stroke [] 0 setdash vpt add M 1839 hpt neg vpt neg V hpt vpt neg V 1840 hpt vpt V hpt neg vpt V closepath fill } def 1841 /Pent { stroke [] 0 setdash 2 copy gsave 1842 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 1843 closepath stroke grestore Pnt } def 1844 /PentF { stroke [] 0 setdash gsave 1845 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 1846 closepath fill grestore } def 1847 /Circle { stroke [] 0 setdash 2 copy 1848 hpt 0 360 arc stroke Pnt } def 1849 /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def 1850 /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def 1851 /C1 { BL [] 0 setdash 2 copy moveto 1852 2 copy vpt 0 90 arc closepath fill 1853 vpt 0 360 arc closepath } bind def 1854 /C2 { BL [] 0 setdash 2 copy moveto 1855 2 copy vpt 90 180 arc closepath fill 1856 vpt 0 360 arc closepath } bind def 1857 /C3 { BL [] 0 setdash 2 copy moveto 1858 2 copy vpt 0 180 arc closepath fill 1859 vpt 0 360 arc closepath } bind def 1860 /C4 { BL [] 0 setdash 2 copy moveto 1861 2 copy vpt 180 270 arc closepath fill 1862 vpt 0 360 arc closepath } bind def 1863 /C5 { BL [] 0 setdash 2 copy moveto 1864 2 copy vpt 0 90 arc 1865 2 copy moveto 1866 2 copy vpt 180 270 arc closepath fill 1867 vpt 0 360 arc } bind def 1868 /C6 { BL [] 0 setdash 2 copy moveto 1869 2 copy vpt 90 270 arc closepath fill 1870 vpt 0 360 arc closepath } bind def 1871 /C7 { BL [] 0 setdash 2 copy moveto 1872 2 copy vpt 0 270 arc closepath fill 1873 vpt 0 360 arc closepath } bind def 1874 /C8 { BL [] 0 setdash 2 copy moveto 1875 2 copy vpt 270 360 arc closepath fill 1876 vpt 0 360 arc closepath } bind def 1877 /C9 { BL [] 0 setdash 2 copy moveto 1878 2 copy vpt 270 450 arc closepath fill 1879 vpt 0 360 arc closepath } bind def 1880 /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 1881 2 copy moveto 1882 2 copy vpt 90 180 arc closepath fill 1883 vpt 0 360 arc closepath } bind def 1884 /C11 { BL [] 0 setdash 2 copy moveto 1885 2 copy vpt 0 180 arc closepath fill 1886 2 copy moveto 1887 2 copy vpt 270 360 arc closepath fill 1888 vpt 0 360 arc closepath } bind def 1889 /C12 { BL [] 0 setdash 2 copy moveto 1890 2 copy vpt 180 360 arc closepath fill 1891 vpt 0 360 arc closepath } bind def 1892 /C13 { BL [] 0 setdash 2 copy moveto 1893 2 copy vpt 0 90 arc closepath fill 1894 2 copy moveto 1895 2 copy vpt 180 360 arc closepath fill 1896 vpt 0 360 arc closepath } bind def 1897 /C14 { BL [] 0 setdash 2 copy moveto 1898 2 copy vpt 90 360 arc closepath fill 1899 vpt 0 360 arc } bind def 1900 /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill 1901 vpt 0 360 arc closepath } bind def 1902 /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto 1903 neg 0 rlineto closepath } bind def 1904 /Square { dup Rec } bind def 1905 /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def 1906 /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def 1907 /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def 1908 /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def 1909 /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def 1910 /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def 1911 /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill 1912 exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def 1913 /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def 1914 /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 1915 2 copy vpt Square fill 1916 Bsquare } bind def 1917 /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def 1918 /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def 1919 /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill 1920 Bsquare } bind def 1921 /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill 1922 Bsquare } bind def 1923 /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def 1924 /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 1925 2 copy vpt Square fill Bsquare } bind def 1926 /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 1927 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def 1928 /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def 1929 /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def 1930 /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def 1931 /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def 1932 /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def 1933 /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def 1934 /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def 1935 /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def 1936 /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def 1937 /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def 1938 /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def 1939 /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def 1940 /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def 1941 /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def 1942 /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def 1943 /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def 1944 /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def 1945 /DiaE { stroke [] 0 setdash vpt add M 1946 hpt neg vpt neg V hpt vpt neg V 1947 hpt vpt V hpt neg vpt V closepath stroke } def 1948 /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 1949 0 vpt2 neg V hpt2 0 V 0 vpt2 V 1950 hpt2 neg 0 V closepath stroke } def 1951 /TriUE { stroke [] 0 setdash vpt 1.12 mul add M 1952 hpt neg vpt -1.62 mul V 1953 hpt 2 mul 0 V 1954 hpt neg vpt 1.62 mul V closepath stroke } def 1955 /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M 1956 hpt neg vpt 1.62 mul V 1957 hpt 2 mul 0 V 1958 hpt neg vpt -1.62 mul V closepath stroke } def 1959 /PentE { stroke [] 0 setdash gsave 1960 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 1961 closepath stroke grestore } def 1962 /CircE { stroke [] 0 setdash 1963 hpt 0 360 arc stroke } def 1964 /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def 1965 /DiaW { stroke [] 0 setdash vpt add M 1966 hpt neg vpt neg V hpt vpt neg V 1967 hpt vpt V hpt neg vpt V Opaque stroke } def 1968 /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 1969 0 vpt2 neg V hpt2 0 V 0 vpt2 V 1970 hpt2 neg 0 V Opaque stroke } def 1971 /TriUW { stroke [] 0 setdash vpt 1.12 mul add M 1972 hpt neg vpt -1.62 mul V 1973 hpt 2 mul 0 V 1974 hpt neg vpt 1.62 mul V Opaque stroke } def 1975 /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M 1976 hpt neg vpt 1.62 mul V 1977 hpt 2 mul 0 V 1978 hpt neg vpt -1.62 mul V Opaque stroke } def 1979 /PentW { stroke [] 0 setdash gsave 1980 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 1981 Opaque stroke grestore } def 1982 /CircW { stroke [] 0 setdash 1983 hpt 0 360 arc Opaque stroke } def 1984 /BoxFill { gsave Rec 1 setgray fill grestore } def 1985 /BoxColFill { 1986 gsave Rec 1987 /Fillden exch def 1988 currentrgbcolor 1989 /ColB exch def /ColG exch def /ColR exch def 1990 /ColR ColR Fillden mul Fillden sub 1 add def 1991 /ColG ColG Fillden mul Fillden sub 1 add def 1992 /ColB ColB Fillden mul Fillden sub 1 add def 1993 ColR ColG ColB setrgbcolor 1994 fill grestore } def 1995 % 1996 % PostScript Level 1 Pattern Fill routine 1997 % Usage: x y w h s a XX PatternFill 1998 % x,y = lower left corner of box to be filled 1999 % w,h = width and height of box 2000 % a = angle in degrees between lines and x-axis 2001 % XX = 0/1 for no/yes cross-hatch 2002 % 2003 /PatternFill { gsave /PFa [ 9 2 roll ] def 2004 PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate 2005 PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec 2006 gsave 1 setgray fill grestore clip 2007 currentlinewidth 0.5 mul setlinewidth 2008 /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 2009 0 0 M PFa 5 get rotate PFs -2 div dup translate 2010 0 1 PFs PFa 4 get div 1 add floor cvi 2011 { PFa 4 get mul 0 M 0 PFs V } for 2012 0 PFa 6 get ne { 2013 0 1 PFs PFa 4 get div 1 add floor cvi 2014 { PFa 4 get mul 0 2 1 roll M PFs 0 V } for 2015 } if 2016 stroke grestore } def 2017 % 2018 /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont 2019 dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall 2020 currentdict end definefont pop 2021 /MFshow { 2022 { dup 5 get 3 ge 2023 { 5 get 3 eq {gsave} {grestore} ifelse } 2024 {dup dup 0 get findfont exch 1 get scalefont setfont 2025 [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 2026 get exch 4 get {show} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq 2027 {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 2028 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div 2029 dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get 2030 show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop 2031 pop aload pop M} ifelse }ifelse }ifelse } 2032 ifelse } 2033 forall} bind def 2034 /MFwidth {0 exch {dup 3 get{dup dup 0 get findfont exch 1 get scalefont 2035 setfont 6 get stringwidth pop add} {pop} ifelse} forall} bind def 2036 /MLshow { currentpoint stroke M 2037 0 exch R MFshow } bind def 2038 /MRshow { currentpoint stroke M 2039 exch dup MFwidth neg 3 -1 roll R MFshow } def 2040 /MCshow { currentpoint stroke M 2041 exch dup MFwidth -2 div 3 -1 roll R MFshow } def 2042 end 2043 %%EndProlog 2044 gnudict begin 2045 gsave 2046 50 50 translate 2047 0.050 0.050 scale 2048 0 setgray 2049 newpath 2050 (default) findfont 120 scalefont setfont 2051 1.000 UL 2052 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2109 21 19 V 2110 7 7 V 2111 29 26 V 2112 3 3 V 2113 26 23 V 2114 13 13 V 2115 16 14 V 2116 23 21 V 2117 6 5 V 2118 29 26 V 2119 5 5 V 2120 24 22 V 2121 15 13 V 2122 14 13 V 2123 25 22 V 2124 5 4 V 2125 29 27 V 2126 5 4 V 2127 25 22 V 2128 14 12 V 2129 16 14 V 2130 23 21 V 2131 7 5 V 2132 30 27 V 2133 3 2 V 2134 27 24 V 2135 12 10 V 2136 18 16 V 2137 21 19 V 2138 9 8 V 2139 30 25 V 2140 1 1 V 2141 30 26 V 2142 8 7 V 2143 23 20 V 2144 16 14 V 2145 15 12 V 2146 25 21 V 2147 5 5 V 2148 31 27 V 2149 3 1 V 2150 28 25 V 2151 11 9 V 2152 21 17 V 2153 18 16 V 2154 13 10 V 2155 26 22 V 2156 5 5 V 2157 32 26 V 2158 2 2 V 2159 29 24 V 2160 11 9 V 2161 21 18 V 2162 18 14 V 2163 14 12 V 2164 25 20 V 2165 7 6 V 2166 32 27 V 2167 32 26 V 2168 7 6 V 2169 25 20 V 2170 14 11 V 2171 19 15 V 2172 21 17 V 2173 11 10 V 2174 28 22 V 2175 5 4 V 2176 33 26 V 2177 1 1 V 2178 32 26 V 2179 7 6 V 2180 1662 1291 M 2181 39 0 V 2182 39 0 V 2183 39 1 V 2184 40 0 V 2185 39 1 V 2186 39 0 V 2187 39 1 V 2188 39 0 V 2189 39 1 V 2190 40 1 V 2191 stroke 2192 2054 1296 M 2193 39 1 V 2194 39 0 V 2195 39 1 V 2196 39 1 V 2197 39 1 V 2198 40 2 V 2199 39 1 V 2200 39 1 V 2201 8 1 V 2202 31 1 V 2203 39 2 V 2204 39 2 V 2205 40 3 V 2206 39 2 V 2207 39 4 V 2208 39 4 V 2209 39 5 V 2210 23 3 V 2211 16 3 V 2212 40 6 V 2213 39 9 V 2214 30 8 V 2215 9 3 V 2216 39 13 V 2217 25 11 V 2218 14 5 V 2219 39 20 V 2220 1 1 V 2221 38 23 V 2222 6 3 V 2223 34 23 V 2224 4 4 V 2225 34 26 V 2226 1 0 V 2227 32 26 V 2228 7 6 V 2229 23 21 V 2230 16 13 V 2231 13 13 V 2232 26 23 V 2233 3 3 V 2234 28 26 V 2235 8 8 V 2236 20 19 V 2237 20 19 V 2238 7 7 V 2239 27 26 V 2240 5 5 V 2241 21 22 V 2242 18 17 V 2243 9 9 V 2244 26 26 V 2245 4 4 V 2246 23 23 V 2247 16 16 V 2248 10 10 V 2249 26 26 V 2250 3 3 V 2251 24 23 V 2252 16 16 V 2253 10 11 V 2254 26 26 V 2255 3 2 V 2256 24 24 V 2257 15 15 V 2258 11 12 V 2259 25 26 V 2260 2 2 V 2261 25 24 V 2262 14 14 V 2263 12 13 V 2264 27 26 V 2265 27 26 V 2266 13 13 V 2267 13 13 V 2268 26 25 V 2269 1 2 V 2270 27 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0 setgray 2463 [ [(default) 120.0 0.0 true true 0 ( 450)] 2464 ] -40.0 MCshow 2465 grestore 2466 1.000 UL 2467 LTb 2468 1.000 UL 2469 LTb 2470 2524 3881 M 2471 0 -42 V 2472 1.000 UL 2473 LTb 2474 2954 1278 M 2475 0 43 V 2476 stroke 2477 2954 1198 M 2478 gsave 0 setgray 2479 [ [(default) 120.0 0.0 true true 0 ( 500)] 2480 ] -40.0 MCshow 2481 grestore 2482 1.000 UL 2483 LTb 2484 1.000 UL 2485 LTb 2486 2954 3881 M 2487 0 -42 V 2488 1.000 UL 2489 LTb 2490 3385 1278 M 2491 0 43 V 2492 stroke 2493 3385 1198 M 2494 gsave 0 setgray 2495 [ [(default) 120.0 0.0 true true 0 ( 550)] 2496 ] -40.0 MCshow 2497 grestore 2498 1.000 UL 2499 LTb 2500 1.000 UL 2501 LTb 2502 3385 3881 M 2503 0 -42 V 2504 1.000 UL 2505 LTb 2506 3815 1278 M 2507 0 43 V 2508 stroke 2509 3815 1198 M 2510 gsave 0 setgray 2511 [ [(default) 120.0 0.0 true true 0 ( 600)] 2512 ] -40.0 MCshow 2513 grestore 2514 1.000 UL 2515 LTb 2516 1.000 UL 2517 LTb 2518 3815 3881 M 2519 0 -42 V 2520 1.000 UL 2521 LTb 2522 4246 1278 M 2523 0 43 V 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UP 2585 stroke 2586 grestore 2587 end 2588 showpage 2589 %%Trailer 2590 %%DocumentFonts: default 2591 2592 %%EndDocument 2593 @endspecial 867 2406 a FE(Fig.)20 b(1.)g(Zero)g(points)f(of)h 2594 (Equality)f(2)i(as)g(a)f(function)f(of)h Fm(j)l Fv(W)10 2595 b Fm(j)21 b FE(for)e Fv(n)f Fs(=)g FE(1000)648 2587 y(From)24 2596 b(the)h(numerical)f(results)i(we)f(can)g(learn)g(a)h(some)n(what)e(une) 2597 o(xpected)f(phenomena.)f(F)o(or)523 2687 y(v)n(alues)28 2598 b(of)f Fm(j)l Fv(W)10 b Fm(j)29 b FE(that)f(are)g(signi\002cantly)f(lo) 2599 n(wer)g(than)h(500)21 b Fs(=)h FE(0)p Ft(:)p FE(5)p Fv(n)p 2600 FE(,)27 b(the)h(equilibrium)e(point)h(has)523 2786 y(quite)j(small)i(v) 2601 n(alues)e(and)g(the)h(gro)n(wth)f(rate)g(is)i(quite)e(slo)n(w)-5 2602 b(.)31 b(Around)e(0)p Ft(:)p FE(5)p Fv(n)h FE(there)g(is)i(a)f(radical) 2603 523 2886 y(change)21 b(of)h(the)g(situation:)g(the)h(gro)n(wth)e(rate)h 2604 (increases)g(until)g(the)h(deri)n(v)n(ati)n(v)o(e)d(reaches)i(the)g(v)n 2605 (alue)523 2986 y(close)e(to)h(0)p Ft(:)p FE(5.)e(Then,)g(the)h 2606 (function)f(is)i(quite)f(well)g(interpolated)f(by)h(a)g(single)g(line.) 2607 g(These)g(results)523 3085 y(suggest)j(that)h(the)f(sizes)h(of)g(anon)o 2608 (ymity)c(sets)25 b Fv(N)1928 3097 y Fo(i)1973 3085 y 2609 FE(remain)e(small)h(for)f(v)n(alues)g(of)g Fm(j)l Fv(W)10 2610 b Fm(j)24 b FE(that)f(are)h(not)523 3185 y(too)g(close)h(to)f(0)p 2611 Ft(:)p FE(5)p Fv(n)p FE(.)f(Then)h(the)g(situation)g(changes)g 2612 (abruptly)e(and)i(we)h(should)e(observ)o(e)g(that)h(the)523 2613 3284 y(a)n(v)o(erage)19 b(size)i(of)f Fv(N)1092 3296 2614 y Fo(i)1134 3284 y FE(gro)n(ws)g(f)o(ast)g(with)h Fm(j)l 2615 Fv(W)10 b Fm(j)p FE(.)648 3384 y(In)25 b(the)h(ne)o(xt)e(subsection)h 2616 (we)h(compare)e(these)i(results)g(with)g(e)o(xtensi)n(v)o(e)e 2617 (simulations)h(of)g(the)523 3484 y(protocol.)523 3731 2618 y Fw(4.3)82 b(Simulation)20 b(Results)523 3896 y FE(From)h(the)g(pre)n 2619 (vious)f(considerations)g(we)h(can)h(e)o(xpect)e(that)i(after)f(some)g 2620 (number)e(of)j(steps)g(at)f(the)523 3996 y(be)o(ginning)26 2621 b(of)h(the)i(protocol)d(anon)o(ymity)g(set)j Fm(j)p Fv(N)1994 2622 4008 y Fo(t)2020 3996 y Fm(j)f FE(should)g(oscillate)g(around)e(a)j 2623 (certain)e(v)n(alue.)523 4095 y(Since)18 b(e)o(xact)g(formulas)f 2624 (describing)g(the)i(stochastic)f(changes)f(of)i Fm(j)p 2625 Fv(N)2514 4107 y Fo(t)2540 4095 y Fm(j)g FE(or)f(e)n(v)o(en)f(their)h 2626 (f)o(air)h(approx-)523 4195 y(imations)29 b(seem)h(to)g(be)f(v)o(ery)g 2627 (comple)o(x,)e(we)j(performed)d(a)j(number)e(of)h(direct)g(simulations) 2628 g(to)523 4294 y(check)19 b(these)i(tendencies.)648 4394 2629 y(W)-7 b(e)17 b(ha)n(v)o(e)f(performed)e(the)i(e)o(xperiments)f(for)h 2630 (dif)n(ferent)f(v)n(alues)h(of)g Fm(j)p Fv(N)5 b Fm(j)p 2631 FE(,)17 b(b)n(ut)g(the)f(results)h(hardly)523 4494 y(depend)22 2632 b(on)h Fm(j)p Fv(N)5 b Fm(j)p FE(,)24 b(e)o(xcept)f(for)f(small)i(v)n 2633 (alues)f(that)h(are)f(not)h(interesting)e(from)h(our)f(point)h(of)g 2634 (vie)n(w)-5 b(.)523 4610 y(W)e(e)21 b(ha)n(v)o(e)f(performed)e 2635 (simulations)h(for)h(dif)n(ferent)e(v)n(alues)i(of)2350 2636 4568 y Fh(j)m Fo(W)8 b Fh(j)p 2350 4590 90 4 v 2355 4640 2637 a(j)p Fo(N)s Fh(j)2450 4610 y FE(.)648 4725 y(The)19 2638 b(ne)o(xt)g(tw)o(o)g(\002gures)h(sho)n(w)f(dependenc)o(y)d(between)j 2639 Fm(j)l Fv(W)10 b Fm(j)20 b FE(and)f Fm(j)p Fv(N)2611 2640 4737 y Fo(i)2633 4725 y Fm(j)h FE(in)g(subsequent)e(steps)i(of)523 2641 4825 y(the)e(protocol.)e(The)h(\002gures)g(correspond)f(to)i(the)f 2642 (cases)i Fm(j)p Fv(N)5 b Fm(j)16 b Fs(=)g Fm(j)p Fv(M)s 2643 Fm(j)h Fs(=)f FE(1000)g(for)h(0)p Ft(:)p FE(3)9 b Fm(\001)g(j)p 2644 Fv(N)c Fm(j)16 b(\024)g(j)l Fv(W)10 b Fm(j)16 b(\024)523 2645 4924 y(j)p Fv(N)5 b Fm(j)p FE(.)p eop end 2646 %%Page: 10 10 2647 TeXDict begin 10 9 bop 648 448 a FE(Figure)16 b(2)h(is)i(a)e(three)g 2648 (dimensional)f(plot.)g(The)h(v)n(alue)g(plotted)f(is)i(the)g(size)f(of) 2649 g Fv(N)2914 460 y Fo(i)2954 448 y FE(in)g(subsequent)523 2650 548 y(steps)28 b(of)f(the)h(protocol.)d(Dif)n(ferent)h(curv)o(es)h 2651 (correspond)e(to)i(dif)n(ferent)f(v)n(alues)h(of)g Fm(j)l 2652 Fv(W)10 b Fm(j)28 b FE(between)523 648 y(30\045)20 b(and)g(100\045)f 2653 (of)h Fm(j)p Fv(N)5 b Fm(j)21 b FE(\(step)f(2\045\).)523 2654 3211 y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 2655 3600 @rwi @setspecial 2656 %%BeginDocument: slope.eps 2657 %!PS-Adobe-2.0 EPSF-2.0 2658 %%Title: slope.eps 2659 %%Creator: gnuplot 4.0 patchlevel 0 2660 %%CreationDate: Fri Apr 1 23:36:38 2005 2661 %%DocumentFonts: (atend) 2662 %%BoundingBox: 50 50 410 302 2663 %%Orientation: Portrait 2664 %%EndComments 2665 /gnudict 256 dict def 2666 gnudict begin 2667 /Color false def 2668 /Solid false def 2669 /gnulinewidth 5.000 def 2670 /userlinewidth gnulinewidth def 2671 /vshift -40 def 2672 /dl {10.0 mul} def 2673 /hpt_ 31.5 def 2674 /vpt_ 31.5 def 2675 /hpt hpt_ def 2676 /vpt vpt_ def 2677 /Rounded false def 2678 /M {moveto} bind def 2679 /L {lineto} bind def 2680 /R {rmoveto} bind def 2681 /V {rlineto} bind def 2682 /N {newpath moveto} bind def 2683 /C {setrgbcolor} bind def 2684 /f {rlineto fill} bind def 2685 /vpt2 vpt 2 mul def 2686 /hpt2 hpt 2 mul def 2687 /Lshow { currentpoint stroke M 2688 0 vshift R show } def 2689 /Rshow { currentpoint stroke M 2690 dup stringwidth pop neg vshift R show } def 2691 /Cshow { currentpoint stroke M 2692 dup stringwidth pop -2 div vshift R show } def 2693 /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def 2694 /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def 2695 /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } 2696 {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse } def 2697 /BL { stroke userlinewidth 2 mul setlinewidth 2698 Rounded { 1 setlinejoin 1 setlinecap } if } def 2699 /AL { stroke userlinewidth 2 div setlinewidth 2700 Rounded { 1 setlinejoin 1 setlinecap } if } def 2701 /UL { dup gnulinewidth mul /userlinewidth exch def 2702 dup 1 lt {pop 1} if 10 mul /udl exch def } def 2703 /PL { stroke userlinewidth setlinewidth 2704 Rounded { 1 setlinejoin 1 setlinecap } if } def 2705 /LTw { PL [] 1 setgray } def 2706 /LTb { BL [] 0 0 0 DL } def 2707 /LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def 2708 /LT0 { PL [] 1 0 0 DL } def 2709 /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def 2710 /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def 2711 /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def 2712 /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def 2713 /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def 2714 /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def 2715 /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def 2716 /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def 2717 /Pnt { stroke [] 0 setdash 2718 gsave 1 setlinecap M 0 0 V stroke grestore } def 2719 /Dia { stroke [] 0 setdash 2 copy vpt add M 2720 hpt neg vpt neg V hpt vpt neg V 2721 hpt vpt V hpt neg vpt V closepath stroke 2722 Pnt } def 2723 /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V 2724 currentpoint stroke M 2725 hpt neg vpt neg R hpt2 0 V stroke 2726 } def 2727 /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 2728 0 vpt2 neg V hpt2 0 V 0 vpt2 V 2729 hpt2 neg 0 V closepath stroke 2730 Pnt } def 2731 /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M 2732 hpt2 vpt2 neg V currentpoint stroke M 2733 hpt2 neg 0 R hpt2 vpt2 V stroke } def 2734 /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M 2735 hpt neg vpt -1.62 mul V 2736 hpt 2 mul 0 V 2737 hpt neg vpt 1.62 mul V closepath stroke 2738 Pnt } def 2739 /Star { 2 copy Pls Crs } def 2740 /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 2741 0 vpt2 neg V hpt2 0 V 0 vpt2 V 2742 hpt2 neg 0 V closepath fill } def 2743 /TriUF { stroke [] 0 setdash vpt 1.12 mul add M 2744 hpt neg vpt -1.62 mul V 2745 hpt 2 mul 0 V 2746 hpt neg vpt 1.62 mul V closepath fill } def 2747 /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M 2748 hpt neg vpt 1.62 mul V 2749 hpt 2 mul 0 V 2750 hpt neg vpt -1.62 mul V closepath stroke 2751 Pnt } def 2752 /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M 2753 hpt neg vpt 1.62 mul V 2754 hpt 2 mul 0 V 2755 hpt neg vpt -1.62 mul V closepath fill} def 2756 /DiaF { stroke [] 0 setdash vpt add M 2757 hpt neg vpt neg V hpt vpt neg V 2758 hpt vpt V hpt neg vpt V closepath fill } def 2759 /Pent { stroke [] 0 setdash 2 copy gsave 2760 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 2761 closepath stroke grestore Pnt } def 2762 /PentF { stroke [] 0 setdash gsave 2763 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 2764 closepath fill grestore } def 2765 /Circle { stroke [] 0 setdash 2 copy 2766 hpt 0 360 arc stroke Pnt } def 2767 /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def 2768 /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def 2769 /C1 { BL [] 0 setdash 2 copy moveto 2770 2 copy vpt 0 90 arc closepath fill 2771 vpt 0 360 arc closepath } bind def 2772 /C2 { BL [] 0 setdash 2 copy moveto 2773 2 copy vpt 90 180 arc closepath fill 2774 vpt 0 360 arc closepath } bind def 2775 /C3 { BL [] 0 setdash 2 copy moveto 2776 2 copy vpt 0 180 arc closepath fill 2777 vpt 0 360 arc closepath } bind def 2778 /C4 { BL [] 0 setdash 2 copy moveto 2779 2 copy vpt 180 270 arc closepath fill 2780 vpt 0 360 arc closepath } bind def 2781 /C5 { BL [] 0 setdash 2 copy moveto 2782 2 copy vpt 0 90 arc 2783 2 copy moveto 2784 2 copy vpt 180 270 arc closepath fill 2785 vpt 0 360 arc } bind def 2786 /C6 { BL [] 0 setdash 2 copy moveto 2787 2 copy vpt 90 270 arc closepath fill 2788 vpt 0 360 arc closepath } bind def 2789 /C7 { BL [] 0 setdash 2 copy moveto 2790 2 copy vpt 0 270 arc closepath fill 2791 vpt 0 360 arc closepath } bind def 2792 /C8 { BL [] 0 setdash 2 copy moveto 2793 2 copy vpt 270 360 arc closepath fill 2794 vpt 0 360 arc closepath } bind def 2795 /C9 { BL [] 0 setdash 2 copy moveto 2796 2 copy vpt 270 450 arc closepath fill 2797 vpt 0 360 arc closepath } bind def 2798 /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2799 2 copy moveto 2800 2 copy vpt 90 180 arc closepath fill 2801 vpt 0 360 arc closepath } bind def 2802 /C11 { BL [] 0 setdash 2 copy moveto 2803 2 copy vpt 0 180 arc closepath fill 2804 2 copy moveto 2805 2 copy vpt 270 360 arc closepath fill 2806 vpt 0 360 arc closepath } bind def 2807 /C12 { BL [] 0 setdash 2 copy moveto 2808 2 copy vpt 180 360 arc closepath fill 2809 vpt 0 360 arc closepath } bind def 2810 /C13 { BL [] 0 setdash 2 copy moveto 2811 2 copy vpt 0 90 arc closepath fill 2812 2 copy moveto 2813 2 copy vpt 180 360 arc closepath fill 2814 vpt 0 360 arc closepath } bind def 2815 /C14 { BL [] 0 setdash 2 copy moveto 2816 2 copy vpt 90 360 arc closepath fill 2817 vpt 0 360 arc } bind def 2818 /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill 2819 vpt 0 360 arc closepath } bind def 2820 /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto 2821 neg 0 rlineto closepath } bind def 2822 /Square { dup Rec } bind def 2823 /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def 2824 /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def 2825 /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def 2826 /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def 2827 /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def 2828 /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def 2829 /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill 2830 exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def 2831 /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def 2832 /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2833 2 copy vpt Square fill 2834 Bsquare } bind def 2835 /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def 2836 /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def 2837 /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill 2838 Bsquare } bind def 2839 /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill 2840 Bsquare } bind def 2841 /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def 2842 /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2843 2 copy vpt Square fill Bsquare } bind def 2844 /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2845 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def 2846 /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def 2847 /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def 2848 /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def 2849 /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def 2850 /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def 2851 /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def 2852 /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def 2853 /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def 2854 /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def 2855 /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def 2856 /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def 2857 /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def 2858 /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def 2859 /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def 2860 /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def 2861 /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def 2862 /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def 2863 /DiaE { stroke [] 0 setdash vpt add M 2864 hpt neg vpt neg V hpt vpt neg V 2865 hpt vpt V hpt neg vpt V closepath stroke } def 2866 /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 2867 0 vpt2 neg V hpt2 0 V 0 vpt2 V 2868 hpt2 neg 0 V closepath stroke } def 2869 /TriUE { stroke [] 0 setdash vpt 1.12 mul add M 2870 hpt neg vpt -1.62 mul V 2871 hpt 2 mul 0 V 2872 hpt neg vpt 1.62 mul V closepath stroke } def 2873 /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M 2874 hpt neg vpt 1.62 mul V 2875 hpt 2 mul 0 V 2876 hpt neg vpt -1.62 mul V closepath stroke } def 2877 /PentE { stroke [] 0 setdash gsave 2878 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 2879 closepath stroke grestore } def 2880 /CircE { stroke [] 0 setdash 2881 hpt 0 360 arc stroke } def 2882 /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def 2883 /DiaW { stroke [] 0 setdash vpt add M 2884 hpt neg vpt neg V hpt vpt neg V 2885 hpt vpt V hpt neg vpt V Opaque stroke } def 2886 /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 2887 0 vpt2 neg V hpt2 0 V 0 vpt2 V 2888 hpt2 neg 0 V Opaque stroke } def 2889 /TriUW { stroke [] 0 setdash vpt 1.12 mul add M 2890 hpt neg vpt -1.62 mul V 2891 hpt 2 mul 0 V 2892 hpt neg vpt 1.62 mul V Opaque stroke } def 2893 /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M 2894 hpt neg vpt 1.62 mul V 2895 hpt 2 mul 0 V 2896 hpt neg vpt -1.62 mul V Opaque stroke } def 2897 /PentW { stroke [] 0 setdash gsave 2898 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 2899 Opaque stroke grestore } def 2900 /CircW { stroke [] 0 setdash 2901 hpt 0 360 arc Opaque stroke } def 2902 /BoxFill { gsave Rec 1 setgray fill grestore } def 2903 /BoxColFill { 2904 gsave Rec 2905 /Fillden exch def 2906 currentrgbcolor 2907 /ColB exch def /ColG exch def /ColR exch def 2908 /ColR ColR Fillden mul Fillden sub 1 add def 2909 /ColG ColG Fillden mul Fillden sub 1 add def 2910 /ColB ColB Fillden mul Fillden sub 1 add def 2911 ColR ColG ColB setrgbcolor 2912 fill grestore } def 2913 % 2914 % PostScript Level 1 Pattern Fill routine 2915 % Usage: x y w h s a XX PatternFill 2916 % x,y = lower left corner of box to be filled 2917 % w,h = width and height of box 2918 % a = angle in degrees between lines and x-axis 2919 % XX = 0/1 for no/yes cross-hatch 2920 % 2921 /PatternFill { gsave /PFa [ 9 2 roll ] def 2922 PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate 2923 PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec 2924 gsave 1 setgray fill grestore clip 2925 currentlinewidth 0.5 mul setlinewidth 2926 /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 2927 0 0 M PFa 5 get rotate PFs -2 div dup translate 2928 0 1 PFs PFa 4 get div 1 add floor cvi 2929 { PFa 4 get mul 0 M 0 PFs V } for 2930 0 PFa 6 get ne { 2931 0 1 PFs PFa 4 get div 1 add floor cvi 2932 { PFa 4 get mul 0 2 1 roll M PFs 0 V } for 2933 } if 2934 stroke grestore } def 2935 % 2936 /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont 2937 dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall 2938 currentdict end definefont pop 2939 /MFshow { 2940 { dup 5 get 3 ge 2941 { 5 get 3 eq {gsave} {grestore} ifelse } 2942 {dup dup 0 get findfont exch 1 get scalefont setfont 2943 [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 2944 get exch 4 get {show} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq 2945 {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 2946 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div 2947 dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get 2948 show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop 2949 pop aload pop M} ifelse }ifelse }ifelse } 2950 ifelse } 2951 forall} bind def 2952 /MFwidth {0 exch {dup 3 get{dup dup 0 get findfont exch 1 get scalefont 2953 setfont 6 get stringwidth pop add} {pop} ifelse} forall} bind def 2954 /MLshow { currentpoint stroke M 2955 0 exch R MFshow } bind def 2956 /MRshow { currentpoint stroke M 2957 exch dup MFwidth neg 3 -1 roll R MFshow } def 2958 /MCshow { currentpoint stroke M 2959 exch dup MFwidth -2 div 3 -1 roll R MFshow } def 2960 end 2961 %%EndProlog 2962 gnudict begin 2963 gsave 2964 50 50 translate 2965 0.050 0.050 scale 2966 0 setgray 2967 newpath 2968 (default) findfont 120 scalefont setfont 2969 1.000 UL 2970 LTb 2971 1.000 UL 2972 LTb 2973 1059 1652 M 2974 3567 397 V 2975 1.000 UL 2976 LTb 2977 6141 1112 M 2978 4626 2049 L 2979 1.000 UL 2980 LTb 2981 1059 1652 M 2982 0 2396 V 2983 1.000 UL 2984 LTb 2985 2574 715 M 2986 -37 23 V 2987 1.000 UL 2988 LTb 2989 2615 672 M 2990 gsave 0 setgray 2991 [ [(default) 120.0 0.0 true true 0 ( 0)] 2992 ] -40.0 MCshow 2993 grestore 2994 1.000 UL 2995 LTb 2996 1.000 UL 2997 LTb 2998 1059 1652 M 2999 36 -23 V 3000 1.000 UL 3001 LTb 3002 3168 781 M 3003 -36 23 V 3004 1.000 UL 3005 LTb 3006 3210 738 M 3007 gsave 0 setgray 3008 [ [(default) 120.0 0.0 true true 0 ( 20)] 3009 ] -40.0 MCshow 3010 grestore 3011 1.000 UL 3012 LTb 3013 1.000 UL 3014 LTb 3015 1653 1718 M 3016 37 -23 V 3017 1.000 UL 3018 LTb 3019 3762 847 M 3020 -37 23 V 3021 1.000 UL 3022 LTb 3023 3804 804 M 3024 gsave 0 setgray 3025 [ [(default) 120.0 0.0 true true 0 ( 40)] 3026 ] -40.0 MCshow 3027 grestore 3028 1.000 UL 3029 LTb 3030 1.000 UL 3031 LTb 3032 2248 1784 M 3033 37 -23 V 3034 1.000 UL 3035 LTb 3036 4357 914 M 3037 -37 22 V 3038 1.000 UL 3039 LTb 3040 4399 871 M 3041 gsave 0 setgray 3042 [ [(default) 120.0 0.0 true true 0 ( 60)] 3043 ] -40.0 MCshow 3044 grestore 3045 1.000 UL 3046 LTb 3047 1.000 UL 3048 LTb 3049 2843 1850 M 3050 37 -22 V 3051 1.000 UL 3052 LTb 3053 4952 980 M 3054 -37 23 V 3055 1.000 UL 3056 LTb 3057 4994 937 M 3058 gsave 0 setgray 3059 [ [(default) 120.0 0.0 true true 0 ( 80)] 3060 ] -40.0 MCshow 3061 grestore 3062 1.000 UL 3063 LTb 3064 1.000 UL 3065 LTb 3066 3438 1917 M 3067 37 -23 V 3068 1.000 UL 3069 LTb 3070 5547 1046 M 3071 -37 23 V 3072 1.000 UL 3073 LTb 3074 5588 1003 M 3075 gsave 0 setgray 3076 [ [(default) 120.0 0.0 true true 0 ( 100)] 3077 ] -40.0 MCshow 3078 grestore 3079 1.000 UL 3080 LTb 3081 1.000 UL 3082 LTb 3083 4032 1983 M 3084 36 -23 V 3085 1.000 UL 3086 LTb 3087 6141 1112 M 3088 -36 23 V 3089 1.000 UL 3090 LTb 3091 6183 1069 M 3092 gsave 0 setgray 3093 [ [(default) 120.0 0.0 true true 0 ( 120)] 3094 ] -40.0 MCshow 3095 grestore 3096 1.000 UL 3097 LTb 3098 1.000 UL 3099 LTb 3100 4626 2049 M 3101 37 -23 V 3102 1.000 UL 3103 LTb 3104 2574 715 M 3105 58 6 V 3106 stroke 3107 2507 703 M 3108 gsave 0 setgray 3109 [ [(default) 120.0 0.0 true true 0 ( 30)] 3110 ] -40.0 MRshow 3111 grestore 3112 1.000 UL 3113 LTb 3114 1.000 UL 3115 LTb 3116 6141 1112 M 3117 -58 -6 V 3118 1.000 UL 3119 LTb 3120 2357 849 M 3121 58 6 V 3122 stroke 3123 2291 836 M 3124 gsave 0 setgray 3125 [ [(default) 120.0 0.0 true true 0 ( 40)] 3126 ] -40.0 MRshow 3127 grestore 3128 1.000 UL 3129 LTb 3130 1.000 UL 3131 LTb 3132 5925 1246 M 3133 -58 -6 V 3134 1.000 UL 3135 LTb 3136 2141 983 M 3137 58 6 V 3138 stroke 3139 2074 970 M 3140 gsave 0 setgray 3141 [ [(default) 120.0 0.0 true true 0 ( 50)] 3142 ] -40.0 MRshow 3143 grestore 3144 1.000 UL 3145 LTb 3146 1.000 UL 3147 LTb 3148 5709 1380 M 3149 -58 -6 V 3150 1.000 UL 3151 LTb 3152 1924 1116 M 3153 58 7 V 3154 stroke 3155 1858 1104 M 3156 gsave 0 setgray 3157 [ [(default) 120.0 0.0 true true 0 ( 60)] 3158 ] -40.0 MRshow 3159 grestore 3160 1.000 UL 3161 LTb 3162 1.000 UL 3163 LTb 3164 5492 1514 M 3165 -58 -7 V 3166 1.000 UL 3167 LTb 3168 1708 1250 M 3169 58 7 V 3170 stroke 3171 1642 1238 M 3172 gsave 0 setgray 3173 [ [(default) 120.0 0.0 true true 0 ( 70)] 3174 ] -40.0 MRshow 3175 grestore 3176 1.000 UL 3177 LTb 3178 1.000 UL 3179 LTb 3180 5276 1648 M 3181 -58 -7 V 3182 1.000 UL 3183 LTb 3184 1491 1384 M 3185 58 6 V 3186 stroke 3187 1425 1372 M 3188 gsave 0 setgray 3189 [ [(default) 120.0 0.0 true true 0 ( 80)] 3190 ] -40.0 MRshow 3191 grestore 3192 1.000 UL 3193 LTb 3194 1.000 UL 3195 LTb 3196 5059 1781 M 3197 -58 -6 V 3198 1.000 UL 3199 LTb 3200 1275 1518 M 3201 58 6 V 3202 stroke 3203 1209 1505 M 3204 gsave 0 setgray 3205 [ [(default) 120.0 0.0 true true 0 ( 90)] 3206 ] -40.0 MRshow 3207 grestore 3208 1.000 UL 3209 LTb 3210 1.000 UL 3211 LTb 3212 4843 1915 M 3213 -58 -6 V 3214 1.000 UL 3215 LTb 3216 1059 1652 M 3217 58 6 V 3218 stroke 3219 992 1639 M 3220 gsave 0 setgray 3221 [ [(default) 120.0 0.0 true true 0 ( 100)] 3222 ] -40.0 MRshow 3223 grestore 3224 1.000 UL 3225 LTb 3226 1.000 UL 3227 LTb 3228 4626 2049 M 3229 -58 -6 V 3230 1.000 UL 3231 LTb 3232 1059 2451 M 3233 63 0 V 3234 stroke 3235 933 2451 M 3236 gsave 0 setgray 3237 [ [(default) 120.0 0.0 true true 0 ( 0)] 3238 ] -40.0 MRshow 3239 grestore 3240 1.000 UL 3241 LTb 3242 1.000 UL 3243 LTb 3244 1059 2609 M 3245 63 0 V 3246 stroke 3247 933 2609 M 3248 gsave 0 setgray 3249 [ [(default) 120.0 0.0 true true 0 ( 100)] 3250 ] -40.0 MRshow 3251 grestore 3252 1.000 UL 3253 LTb 3254 1.000 UL 3255 LTb 3256 1059 2769 M 3257 63 0 V 3258 stroke 3259 933 2769 M 3260 gsave 0 setgray 3261 [ [(default) 120.0 0.0 true true 0 ( 200)] 3262 ] -40.0 MRshow 3263 grestore 3264 1.000 UL 3265 LTb 3266 1.000 UL 3267 LTb 3268 1059 2929 M 3269 63 0 V 3270 stroke 3271 933 2929 M 3272 gsave 0 setgray 3273 [ [(default) 120.0 0.0 true true 0 ( 300)] 3274 ] -40.0 MRshow 3275 grestore 3276 1.000 UL 3277 LTb 3278 1.000 UL 3279 LTb 3280 1059 3089 M 3281 63 0 V 3282 stroke 3283 933 3089 M 3284 gsave 0 setgray 3285 [ [(default) 120.0 0.0 true true 0 ( 400)] 3286 ] -40.0 MRshow 3287 grestore 3288 1.000 UL 3289 LTb 3290 1.000 UL 3291 LTb 3292 1059 3249 M 3293 63 0 V 3294 stroke 3295 933 3249 M 3296 gsave 0 setgray 3297 [ [(default) 120.0 0.0 true true 0 ( 500)] 3298 ] -40.0 MRshow 3299 grestore 3300 1.000 UL 3301 LTb 3302 1.000 UL 3303 LTb 3304 1059 3408 M 3305 63 0 V 3306 stroke 3307 933 3408 M 3308 gsave 0 setgray 3309 [ [(default) 120.0 0.0 true true 0 ( 600)] 3310 ] -40.0 MRshow 3311 grestore 3312 1.000 UL 3313 LTb 3314 1.000 UL 3315 LTb 3316 1059 3568 M 3317 63 0 V 3318 stroke 3319 933 3568 M 3320 gsave 0 setgray 3321 [ [(default) 120.0 0.0 true true 0 ( 700)] 3322 ] -40.0 MRshow 3323 grestore 3324 1.000 UL 3325 LTb 3326 1.000 UL 3327 LTb 3328 1059 3728 M 3329 63 0 V 3330 stroke 3331 933 3728 M 3332 gsave 0 setgray 3333 [ [(default) 120.0 0.0 true true 0 ( 800)] 3334 ] -40.0 MRshow 3335 grestore 3336 1.000 UL 3337 LTb 3338 1.000 UL 3339 LTb 3340 1059 3888 M 3341 63 0 V 3342 stroke 3343 933 3888 M 3344 gsave 0 setgray 3345 [ [(default) 120.0 0.0 true true 0 ( 900)] 3346 ] -40.0 MRshow 3347 grestore 3348 1.000 UL 3349 LTb 3350 1.000 UL 3351 LTb 3352 1059 4048 M 3353 63 0 V 3354 stroke 3355 933 4048 M 3356 gsave 0 setgray 3357 [ [(default) 120.0 0.0 true true 0 ( 1000)] 3358 ] -40.0 MRshow 3359 grestore 3360 1.000 UL 3361 LTb 3362 LTb 3363 1058 4287 M 3364 gsave 0 setgray 3365 [ [(default) 120.0 0.0 true true 0 (|N)] 3366 [(default) 96.0 -36.0 true true 0 (i)] 3367 [(default) 120.0 0.0 true true 0 (|)] 3368 ] -28.0 MCshow 3369 grestore 3370 0.600 UP 3371 0.600 UP 3372 1.000 UL 3373 LT0 3374 2573 1515 Pls 3375 2602 1518 Pls 3376 2632 1524 Pls 3377 2662 1526 Pls 3378 2691 1531 Pls 3379 2721 1539 Pls 3380 2751 1544 Pls 3381 2781 1544 Pls 3382 2810 1544 Pls 3383 2840 1548 Pls 3384 2870 1548 Pls 3385 2900 1551 Pls 3386 2929 1556 Pls 3387 2959 1559 Pls 3388 2989 1561 Pls 3389 3019 1566 Pls 3390 3048 1568 Pls 3391 3078 1572 Pls 3392 3108 1576 Pls 3393 3138 1579 Pls 3394 3167 1586 Pls 3395 3197 1584 Pls 3396 3227 1587 Pls 3397 3257 1592 Pls 3398 3286 1597 Pls 3399 3316 1602 Pls 3400 3346 1605 Pls 3401 3376 1607 Pls 3402 3405 1612 Pls 3403 3435 1615 Pls 3404 3465 1619 Pls 3405 3494 1624 Pls 3406 3524 1624 Pls 3407 3554 1624 Pls 3408 3584 1629 Pls 3409 3613 1635 Pls 3410 3643 1637 Pls 3411 3673 1637 Pls 3412 3703 1640 Pls 3413 3732 1647 Pls 3414 3762 1650 Pls 3415 3792 1652 Pls 3416 3822 1660 Pls 3417 3851 1662 Pls 3418 3881 1663 Pls 3419 3911 1664 Pls 3420 3941 1669 Pls 3421 3970 1673 Pls 3422 4000 1674 Pls 3423 4030 1678 Pls 3424 4060 1682 Pls 3425 4089 1685 Pls 3426 4119 1692 Pls 3427 4149 1692 Pls 3428 4178 1695 Pls 3429 4208 1698 Pls 3430 4238 1702 Pls 3431 4268 1703 Pls 3432 4297 1708 Pls 3433 4327 1712 Pls 3434 4357 1713 Pls 3435 4387 1717 Pls 3436 4416 1722 Pls 3437 4446 1725 Pls 3438 4476 1730 Pls 3439 4506 1736 Pls 3440 4535 1741 Pls 3441 4565 1751 Pls 3442 4595 1746 Pls 3443 4625 1750 Pls 3444 4654 1753 Pls 3445 4684 1755 Pls 3446 4714 1758 Pls 3447 4744 1756 Pls 3448 4773 1760 Pls 3449 4803 1768 Pls 3450 4833 1770 Pls 3451 4863 1770 Pls 3452 4892 1773 Pls 3453 4922 1776 Pls 3454 4952 1781 Pls 3455 4981 1791 Pls 3456 5011 1791 Pls 3457 5041 1790 Pls 3458 5071 1794 Pls 3459 5100 1796 Pls 3460 5130 1801 Pls 3461 5160 1809 Pls 3462 5190 1808 Pls 3463 5219 1813 Pls 3464 5249 1813 Pls 3465 5279 1819 Pls 3466 5309 1821 Pls 3467 5338 1824 Pls 3468 5368 1826 Pls 3469 5398 1831 Pls 3470 5428 1836 Pls 3471 5457 1841 Pls 3472 5487 1841 Pls 3473 5517 1846 Pls 3474 5547 1847 Pls 3475 5576 1852 Pls 3476 5606 1856 Pls 3477 5636 1859 Pls 3478 5665 1865 Pls 3479 5695 1866 Pls 3480 5725 1872 Pls 3481 5755 1874 Pls 3482 5784 1880 Pls 3483 5814 1876 Pls 3484 5844 1882 Pls 3485 5874 1885 Pls 3486 5903 1890 Pls 3487 5933 1894 Pls 3488 5963 1894 Pls 3489 5993 1897 Pls 3490 6022 1902 Pls 3491 6052 1904 Pls 3492 6082 1905 Pls 3493 6112 1912 Pls 3494 2529 1541 Pls 3495 2559 1546 Pls 3496 2589 1551 Pls 3497 2618 1558 Pls 3498 2648 1559 Pls 3499 2678 1561 Pls 3500 2708 1566 Pls 3501 2737 1576 Pls 3502 2767 1577 Pls 3503 2797 1577 Pls 3504 2827 1587 Pls 3505 2856 1586 Pls 3506 2886 1584 Pls 3507 2916 1588 Pls 3508 2946 1591 Pls 3509 2975 1596 Pls 3510 3005 1596 Pls 3511 3035 1604 Pls 3512 3065 1609 Pls 3513 3094 1607 Pls 3514 3124 1624 Pls 3515 3154 1628 Pls 3516 3184 1625 Pls 3517 3213 1624 Pls 3518 3243 1621 Pls 3519 3273 1624 Pls 3520 3302 1627 Pls 3521 3332 1631 Pls 3522 3362 1636 Pls 3523 3392 1639 Pls 3524 3421 1642 Pls 3525 3451 1647 Pls 3526 3481 1651 Pls 3527 3511 1654 Pls 3528 3540 1657 Pls 3529 3570 1659 Pls 3530 3600 1665 Pls 3531 3630 1667 Pls 3532 3659 1672 Pls 3533 3689 1672 Pls 3534 3719 1675 Pls 3535 3749 1680 Pls 3536 3778 1682 Pls 3537 3808 1685 Pls 3538 3838 1690 Pls 3539 3868 1694 Pls 3540 3897 1694 Pls 3541 3927 1697 Pls 3542 3957 1700 Pls 3543 3987 1705 Pls 3544 4016 1712 Pls 3545 4046 1715 Pls 3546 4076 1718 Pls 3547 4105 1722 Pls 3548 4135 1725 Pls 3549 4165 1728 Pls 3550 4195 1727 Pls 3551 4224 1730 Pls 3552 4254 1733 Pls 3553 4284 1737 Pls 3554 4314 1742 Pls 3555 4343 1745 Pls 3556 4373 1747 Pls 3557 4403 1752 Pls 3558 4433 1758 Pls 3559 4462 1760 Pls 3560 4492 1760 Pls 3561 4522 1763 Pls 3562 4552 1768 Pls 3563 4581 1773 Pls 3564 4611 1776 Pls 3565 4641 1781 Pls 3566 4671 1786 Pls 3567 4700 1786 Pls 3568 4730 1790 Pls 3569 4760 1793 Pls 3570 4789 1793 Pls 3571 4819 1798 Pls 3572 4849 1801 Pls 3573 4879 1808 Pls 3574 4908 1810 Pls 3575 4938 1814 Pls 3576 4968 1815 Pls 3577 4998 1819 Pls 3578 5027 1821 Pls 3579 5057 1824 Pls 3580 5087 1828 Pls 3581 5117 1830 Pls 3582 5146 1834 Pls 3583 5176 1839 Pls 3584 5206 1843 Pls 3585 5236 1848 Pls 3586 5265 1846 Pls 3587 5295 1851 Pls 3588 5325 1856 Pls 3589 5355 1856 Pls 3590 5384 1861 Pls 3591 5414 1864 Pls 3592 5444 1871 Pls 3593 5474 1869 Pls 3594 5503 1876 Pls 3595 5533 1877 Pls 3596 5563 1881 Pls 3597 5592 1884 Pls 3598 5622 1889 Pls 3599 5652 1894 Pls 3600 5682 1896 Pls 3601 5711 1901 Pls 3602 5741 1901 Pls 3603 5771 1907 Pls 3604 5801 1909 Pls 3605 5830 1911 Pls 3606 5860 1917 Pls 3607 5890 1920 Pls 3608 5920 1925 Pls 3609 5949 1925 Pls 3610 5979 1935 Pls 3611 6009 1932 Pls 3612 6039 1934 Pls 3613 6068 1937 Pls 3614 2486 1568 Pls 3615 2516 1571 Pls 3616 2545 1576 Pls 3617 2575 1581 Pls 3618 2605 1584 Pls 3619 2635 1593 Pls 3620 2664 1601 Pls 3621 2694 1599 Pls 3622 2724 1598 Pls 3623 2754 1599 Pls 3624 2783 1603 Pls 3625 2813 1611 Pls 3626 2843 1613 Pls 3627 2873 1614 Pls 3628 2902 1616 Pls 3629 2932 1619 Pls 3630 2962 1623 Pls 3631 2992 1628 Pls 3632 3021 1631 Pls 3633 3051 1639 Pls 3634 3081 1645 Pls 3635 3111 1644 Pls 3636 3140 1652 Pls 3637 3170 1652 Pls 3638 3200 1649 Pls 3639 3229 1652 Pls 3640 3259 1656 Pls 3641 3289 1661 Pls 3642 3319 1664 Pls 3643 3348 1671 Pls 3644 3378 1680 Pls 3645 3408 1677 Pls 3646 3438 1682 Pls 3647 3467 1687 Pls 3648 3497 1684 Pls 3649 3527 1690 Pls 3650 3557 1697 Pls 3651 3586 1700 Pls 3652 3616 1707 Pls 3653 3646 1720 Pls 3654 3676 1710 Pls 3655 3705 1710 Pls 3656 3735 1709 Pls 3657 3765 1715 Pls 3658 3795 1728 Pls 3659 3824 1735 Pls 3660 3854 1740 Pls 3661 3884 1743 Pls 3662 3913 1737 Pls 3663 3943 1737 Pls 3664 3973 1748 Pls 3665 4003 1748 Pls 3666 4032 1752 Pls 3667 4062 1758 Pls 3668 4092 1755 Pls 3669 4122 1757 Pls 3670 4151 1755 Pls 3671 4181 1758 Pls 3672 4211 1765 Pls 3673 4241 1767 Pls 3674 4270 1772 Pls 3675 4300 1772 Pls 3676 4330 1777 Pls 3677 4360 1786 Pls 3678 4389 1785 Pls 3679 4419 1798 Pls 3680 4449 1798 Pls 3681 4479 1796 Pls 3682 4508 1797 Pls 3683 4538 1800 Pls 3684 4568 1808 Pls 3685 4598 1813 Pls 3686 4627 1815 Pls 3687 4657 1816 Pls 3688 4687 1818 Pls 3689 4716 1823 Pls 3690 4746 1828 Pls 3691 4776 1833 Pls 3692 4806 1831 Pls 3693 4835 1831 Pls 3694 4865 1839 Pls 3695 4895 1840 Pls 3696 4925 1843 Pls 3697 4954 1846 Pls 3698 4984 1850 Pls 3699 5014 1853 Pls 3700 5044 1856 Pls 3701 5073 1859 Pls 3702 5103 1866 Pls 3703 5133 1869 Pls 3704 5163 1874 Pls 3705 5192 1878 Pls 3706 5222 1882 Pls 3707 5252 1891 Pls 3708 5282 1892 Pls 3709 5311 1897 Pls 3710 5341 1897 Pls 3711 5371 1899 Pls 3712 5400 1904 Pls 3713 5430 1904 Pls 3714 5460 1904 Pls 3715 5490 1914 Pls 3716 5519 1927 Pls 3717 5549 1924 Pls 3718 5579 1924 Pls 3719 5609 1927 Pls 3720 5638 1929 Pls 3721 5668 1931 Pls 3722 5698 1935 Pls 3723 5728 1937 Pls 3724 5757 1939 Pls 3725 5787 1947 Pls 3726 5817 1945 Pls 3727 5847 1949 Pls 3728 5876 1955 Pls 3729 5906 1952 Pls 3730 5936 1952 Pls 3731 5966 1956 Pls 3732 5995 1959 Pls 3733 6025 1962 Pls 3734 2443 1595 Pls 3735 2472 1600 Pls 3736 2502 1608 Pls 3737 2532 1608 Pls 3738 2562 1608 Pls 3739 2591 1611 Pls 3740 2621 1618 Pls 3741 2651 1623 Pls 3742 2681 1623 Pls 3743 2710 1629 Pls 3744 2740 1633 Pls 3745 2770 1638 Pls 3746 2800 1641 Pls 3747 2829 1649 Pls 3748 2859 1651 Pls 3749 2889 1649 Pls 3750 2919 1656 Pls 3751 2948 1661 Pls 3752 2978 1659 Pls 3753 3008 1663 Pls 3754 3037 1664 Pls 3755 3067 1669 Pls 3756 3097 1677 Pls 3757 3127 1677 Pls 3758 3156 1678 Pls 3759 3186 1682 Pls 3760 3216 1687 Pls 3761 3246 1695 Pls 3762 3275 1704 Pls 3763 3305 1710 Pls 3764 3335 1709 Pls 3765 3365 1715 Pls 3766 3394 1718 Pls 3767 3424 1717 Pls 3768 3454 1714 Pls 3769 3484 1720 Pls 3770 3513 1722 Pls 3771 3543 1724 Pls 3772 3573 1724 Pls 3773 3603 1727 Pls 3774 3632 1735 Pls 3775 3662 1748 Pls 3776 3692 1747 Pls 3777 3722 1745 Pls 3778 3751 1750 Pls 3779 3781 1752 Pls 3780 3811 1758 Pls 3781 3840 1762 Pls 3782 3870 1760 Pls 3783 3900 1760 Pls 3784 3930 1770 Pls 3785 3959 1765 Pls 3786 3989 1775 Pls 3787 4019 1782 Pls 3788 4049 1786 Pls 3789 4078 1791 Pls 3790 4108 1798 Pls 3791 4138 1801 Pls 3792 4168 1806 Pls 3793 4197 1803 Pls 3794 4227 1803 Pls 3795 4257 1806 Pls 3796 4287 1807 Pls 3797 4316 1807 Pls 3798 4346 1815 Pls 3799 4376 1818 Pls 3800 4406 1818 Pls 3801 4435 1825 Pls 3802 4465 1830 Pls 3803 4495 1828 Pls 3804 4524 1828 Pls 3805 4554 1832 Pls 3806 4584 1835 Pls 3807 4614 1838 Pls 3808 4643 1840 Pls 3809 4673 1845 Pls 3810 4703 1848 Pls 3811 4733 1850 Pls 3812 4762 1855 Pls 3813 4792 1857 Pls 3814 4822 1860 Pls 3815 4852 1863 Pls 3816 4881 1866 Pls 3817 4911 1873 Pls 3818 4941 1875 Pls 3819 4971 1878 Pls 3820 5000 1883 Pls 3821 5030 1891 Pls 3822 5060 1896 Pls 3823 5090 1893 Pls 3824 5119 1898 Pls 3825 5149 1896 Pls 3826 5179 1901 Pls 3827 5209 1909 Pls 3828 5238 1909 Pls 3829 5268 1913 Pls 3830 5298 1916 Pls 3831 5327 1924 Pls 3832 5357 1931 Pls 3833 5387 1934 Pls 3834 5417 1932 Pls 3835 5446 1936 Pls 3836 5476 1942 Pls 3837 5506 1941 Pls 3838 5536 1943 Pls 3839 5565 1951 Pls 3840 5595 1954 Pls 3841 5625 1952 Pls 3842 5655 1953 Pls 3843 5684 1961 Pls 3844 5714 1967 Pls 3845 5744 1969 Pls 3846 5774 1974 Pls 3847 5803 1984 Pls 3848 5833 1995 Pls 3849 5863 1990 Pls 3850 5893 1990 Pls 3851 5922 1987 Pls 3852 5952 1994 Pls 3853 5982 1997 Pls 3854 2399 1622 Pls 3855 2429 1625 Pls 3856 2459 1628 Pls 3857 2489 1633 Pls 3858 2518 1638 Pls 3859 2548 1643 Pls 3860 2578 1659 Pls 3861 2608 1658 Pls 3862 2637 1662 Pls 3863 2667 1661 Pls 3864 2697 1669 Pls 3865 2727 1666 Pls 3866 2756 1673 Pls 3867 2786 1674 Pls 3868 2816 1676 Pls 3869 2846 1682 Pls 3870 2875 1686 Pls 3871 2905 1684 Pls 3872 2935 1691 Pls 3873 2964 1689 Pls 3874 2994 1693 Pls 3875 3024 1699 Pls 3876 3054 1696 Pls 3877 3083 1703 Pls 3878 3113 1701 Pls 3879 3143 1708 Pls 3880 3173 1709 Pls 3881 3202 1714 Pls 3882 3232 1719 Pls 3883 3262 1730 Pls 3884 3292 1729 Pls 3885 3321 1729 Pls 3886 3351 1731 Pls 3887 3381 1732 Pls 3888 3411 1737 Pls 3889 3440 1742 Pls 3890 3470 1746 Pls 3891 3500 1746 Pls 3892 3530 1747 Pls 3893 3559 1754 Pls 3894 3589 1757 Pls 3895 3619 1762 Pls 3896 3648 1767 Pls 3897 3678 1769 Pls 3898 3708 1771 Pls 3899 3738 1783 Pls 3900 3767 1788 Pls 3901 3797 1787 Pls 3902 3827 1782 Pls 3903 3857 1786 Pls 3904 3886 1789 Pls 3905 3916 1792 Pls 3906 3946 1795 Pls 3907 3976 1799 Pls 3908 4005 1802 Pls 3909 4035 1810 Pls 3910 4065 1809 Pls 3911 4095 1818 Pls 3912 4124 1819 Pls 3913 4154 1831 Pls 3914 4184 1840 Pls 3915 4214 1846 Pls 3916 4243 1843 Pls 3917 4273 1848 Pls 3918 4303 1850 Pls 3919 4333 1848 Pls 3920 4362 1853 Pls 3921 4392 1853 Pls 3922 4422 1864 Pls 3923 4451 1873 Pls 3924 4481 1876 Pls 3925 4511 1878 Pls 3926 4541 1881 Pls 3927 4570 1879 Pls 3928 4600 1878 Pls 3929 4630 1880 Pls 3930 4660 1883 Pls 3931 4689 1891 Pls 3932 4719 1893 Pls 3933 4749 1890 Pls 3934 4779 1891 Pls 3935 4808 1895 Pls 3936 4838 1896 Pls 3937 4868 1901 Pls 3938 4898 1901 Pls 3939 4927 1911 Pls 3940 4957 1911 Pls 3941 4987 1916 Pls 3942 5017 1920 Pls 3943 5046 1926 Pls 3944 5076 1929 Pls 3945 5106 1929 Pls 3946 5135 1931 Pls 3947 5165 1934 Pls 3948 5195 1938 Pls 3949 5225 1944 Pls 3950 5254 1944 Pls 3951 5284 1953 Pls 3952 5314 1956 Pls 3953 5344 1958 Pls 3954 5373 1962 Pls 3955 5403 1963 Pls 3956 5433 1963 Pls 3957 5463 1969 Pls 3958 5492 1974 Pls 3959 5522 1982 Pls 3960 5552 1989 Pls 3961 5582 1989 Pls 3962 5611 1987 Pls 3963 5641 1989 Pls 3964 5671 1992 Pls 3965 5701 1994 Pls 3966 5730 2001 Pls 3967 5760 2002 Pls 3968 5790 2006 Pls 3969 5820 2007 Pls 3970 5849 2007 Pls 3971 5879 2012 Pls 3972 5909 2017 Pls 3973 5938 2021 Pls 3974 2356 1648 Pls 3975 2386 1652 Pls 3976 2416 1655 Pls 3977 2445 1660 Pls 3978 2475 1663 Pls 3979 2505 1671 Pls 3980 2535 1679 Pls 3981 2564 1676 Pls 3982 2594 1683 Pls 3983 2624 1686 Pls 3984 2654 1691 Pls 3985 2683 1690 Pls 3986 2713 1693 Pls 3987 2743 1698 Pls 3988 2772 1706 Pls 3989 2802 1704 Pls 3990 2832 1708 Pls 3991 2862 1713 Pls 3992 2891 1716 Pls 3993 2921 1716 Pls 3994 2951 1719 Pls 3995 2981 1721 Pls 3996 3010 1721 Pls 3997 3040 1725 Pls 3998 3070 1733 Pls 3999 3100 1738 Pls 4000 3129 1744 Pls 4001 3159 1746 Pls 4002 3189 1751 Pls 4003 3219 1765 Pls 4004 3248 1764 Pls 4005 3278 1767 Pls 4006 3308 1777 Pls 4007 3338 1777 Pls 4008 3367 1777 Pls 4009 3397 1782 Pls 4010 3427 1780 Pls 4011 3457 1782 Pls 4012 3486 1785 Pls 4013 3516 1792 Pls 4014 3546 1794 Pls 4015 3575 1799 Pls 4016 3605 1802 Pls 4017 3635 1804 Pls 4018 3665 1804 Pls 4019 3694 1809 Pls 4020 3724 1817 Pls 4021 3754 1822 Pls 4022 3784 1828 Pls 4023 3813 1827 Pls 4024 3843 1827 Pls 4025 3873 1830 Pls 4026 3903 1832 Pls 4027 3932 1832 Pls 4028 3962 1835 Pls 4029 3992 1837 Pls 4030 4022 1843 Pls 4031 4051 1852 Pls 4032 4081 1850 Pls 4033 4111 1852 Pls 4034 4141 1852 Pls 4035 4170 1863 Pls 4036 4200 1865 Pls 4037 4230 1863 Pls 4038 4259 1867 Pls 4039 4289 1873 Pls 4040 4319 1870 Pls 4041 4349 1873 Pls 4042 4378 1874 Pls 4043 4408 1879 Pls 4044 4438 1880 Pls 4045 4468 1884 Pls 4046 4497 1890 Pls 4047 4527 1895 Pls 4048 4557 1898 Pls 4049 4587 1900 Pls 4050 4616 1907 Pls 4051 4646 1907 Pls 4052 4676 1912 Pls 4053 4706 1916 Pls 4054 4735 1925 Pls 4055 4765 1928 Pls 4056 4795 1925 Pls 4057 4825 1930 Pls 4058 4854 1933 Pls 4059 4884 1935 Pls 4060 4914 1938 Pls 4061 4944 1943 Pls 4062 4973 1943 Pls 4063 5003 1954 Pls 4064 5033 1958 Pls 4065 5062 1963 Pls 4066 5092 1961 Pls 4067 5122 1964 Pls 4068 5152 1971 Pls 4069 5181 1984 Pls 4070 5211 1989 Pls 4071 5241 1987 Pls 4072 5271 1991 Pls 4073 5300 1991 Pls 4074 5330 1996 Pls 4075 5360 1997 Pls 4076 5390 2007 Pls 4077 5419 2009 Pls 4078 5449 2009 Pls 4079 5479 2004 Pls 4080 5509 2004 Pls 4081 5538 2009 Pls 4082 5568 2011 Pls 4083 5598 2011 Pls 4084 5628 2014 Pls 4085 5657 2016 Pls 4086 5687 2019 Pls 4087 5717 2026 Pls 4088 5746 2028 Pls 4089 5776 2029 Pls 4090 5806 2034 Pls 4091 5836 2036 Pls 4092 5865 2041 Pls 4093 5895 2043 Pls 4094 2313 1675 Pls 4095 2343 1682 Pls 4096 2372 1685 Pls 4097 2402 1688 Pls 4098 2432 1692 Pls 4099 2462 1696 Pls 4100 2491 1703 Pls 4101 2521 1709 Pls 4102 2551 1714 Pls 4103 2581 1716 Pls 4104 2610 1719 Pls 4105 2640 1721 Pls 4106 2670 1732 Pls 4107 2699 1739 Pls 4108 2729 1739 Pls 4109 2759 1734 Pls 4110 2789 1738 Pls 4111 2818 1739 Pls 4112 2848 1743 Pls 4113 2878 1741 Pls 4114 2908 1745 Pls 4115 2937 1749 Pls 4116 2967 1751 Pls 4117 2997 1751 Pls 4118 3027 1756 Pls 4119 3056 1761 Pls 4120 3086 1766 Pls 4121 3116 1766 Pls 4122 3146 1771 Pls 4123 3175 1778 Pls 4124 3205 1782 Pls 4125 3235 1786 Pls 4126 3265 1787 Pls 4127 3294 1786 Pls 4128 3324 1793 Pls 4129 3354 1801 Pls 4130 3383 1804 Pls 4131 3413 1806 Pls 4132 3443 1812 Pls 4133 3473 1825 Pls 4134 3502 1832 Pls 4135 3532 1828 Pls 4136 3562 1838 Pls 4137 3592 1837 Pls 4138 3621 1850 Pls 4139 3651 1843 Pls 4140 3681 1847 Pls 4141 3711 1845 Pls 4142 3740 1845 Pls 4143 3770 1855 Pls 4144 3800 1854 Pls 4145 3830 1855 Pls 4146 3859 1857 Pls 4147 3889 1859 Pls 4148 3919 1856 Pls 4149 3949 1859 Pls 4150 3978 1862 Pls 4151 4008 1866 Pls 4152 4038 1869 Pls 4153 4068 1872 Pls 4154 4097 1877 Pls 4155 4127 1879 Pls 4156 4157 1882 Pls 4157 4186 1887 Pls 4158 4216 1898 Pls 4159 4246 1900 Pls 4160 4276 1905 Pls 4161 4305 1908 Pls 4162 4335 1913 Pls 4163 4365 1918 Pls 4164 4395 1920 Pls 4165 4424 1920 Pls 4166 4454 1920 Pls 4167 4484 1920 Pls 4168 4514 1925 Pls 4169 4543 1930 Pls 4170 4573 1935 Pls 4171 4603 1937 Pls 4172 4633 1941 Pls 4173 4662 1945 Pls 4174 4692 1947 Pls 4175 4722 1943 Pls 4176 4752 1950 Pls 4177 4781 1953 Pls 4178 4811 1955 Pls 4179 4841 1960 Pls 4180 4870 1963 Pls 4181 4900 1970 Pls 4182 4930 1978 Pls 4183 4960 1975 Pls 4184 4989 1973 Pls 4185 5019 1977 Pls 4186 5049 1980 Pls 4187 5079 1983 Pls 4188 5108 1987 Pls 4189 5138 1993 Pls 4190 5168 1993 Pls 4191 5198 2001 Pls 4192 5227 2003 Pls 4193 5257 2011 Pls 4194 5287 2014 Pls 4195 5317 2014 Pls 4196 5346 2016 Pls 4197 5376 2018 Pls 4198 5406 2024 Pls 4199 5436 2025 Pls 4200 5465 2026 Pls 4201 5495 2031 Pls 4202 5525 2036 Pls 4203 5555 2044 Pls 4204 5584 2046 Pls 4205 5614 2054 Pls 4206 5644 2056 Pls 4207 5673 2056 Pls 4208 5703 2064 Pls 4209 5733 2069 Pls 4210 5763 2072 Pls 4211 5792 2079 Pls 4212 5822 2080 Pls 4213 5852 2079 Pls 4214 2270 1702 Pls 4215 2299 1705 Pls 4216 2329 1710 Pls 4217 2359 1715 Pls 4218 2389 1723 Pls 4219 2418 1726 Pls 4220 2448 1733 Pls 4221 2478 1731 Pls 4222 2507 1740 Pls 4223 2537 1746 Pls 4224 2567 1740 Pls 4225 2597 1743 Pls 4226 2626 1750 Pls 4227 2656 1755 Pls 4228 2686 1764 Pls 4229 2716 1769 Pls 4230 2745 1776 Pls 4231 2775 1781 Pls 4232 2805 1784 Pls 4233 2835 1786 Pls 4234 2864 1787 Pls 4235 2894 1786 Pls 4236 2924 1781 Pls 4237 2954 1789 Pls 4238 2983 1796 Pls 4239 3013 1799 Pls 4240 3043 1809 Pls 4241 3073 1809 Pls 4242 3102 1811 Pls 4243 3132 1809 Pls 4244 3162 1820 Pls 4245 3192 1824 Pls 4246 3221 1825 Pls 4247 3251 1827 Pls 4248 3281 1837 Pls 4249 3310 1847 Pls 4250 3340 1847 Pls 4251 3370 1847 Pls 4252 3400 1857 Pls 4253 3429 1855 Pls 4254 3459 1866 Pls 4255 3489 1881 Pls 4256 3519 1878 Pls 4257 3548 1884 Pls 4258 3578 1891 Pls 4259 3608 1894 Pls 4260 3638 1889 Pls 4261 3667 1893 Pls 4262 3697 1906 Pls 4263 3727 1912 Pls 4264 3757 1935 Pls 4265 3786 1924 Pls 4266 3816 1944 Pls 4267 3846 1948 Pls 4268 3876 1940 Pls 4269 3905 1924 Pls 4270 3935 1935 Pls 4271 3965 1935 Pls 4272 3994 1937 Pls 4273 4024 1936 Pls 4274 4054 1936 Pls 4275 4084 1942 Pls 4276 4113 1939 Pls 4277 4143 1941 Pls 4278 4173 1944 Pls 4279 4203 1959 Pls 4280 4232 1967 Pls 4281 4262 1961 Pls 4282 4292 1959 Pls 4283 4322 1959 Pls 4284 4351 1955 Pls 4285 4381 1951 Pls 4286 4411 1956 Pls 4287 4441 1960 Pls 4288 4470 1965 Pls 4289 4500 1973 Pls 4290 4530 1971 Pls 4291 4560 1970 Pls 4292 4589 1978 Pls 4293 4619 1972 Pls 4294 4649 1978 Pls 4295 4678 1978 Pls 4296 4708 1985 Pls 4297 4738 1986 Pls 4298 4768 1988 Pls 4299 4797 1991 Pls 4300 4827 1993 Pls 4301 4857 1996 Pls 4302 4887 2003 Pls 4303 4916 2001 Pls 4304 4946 2011 Pls 4305 4976 2013 Pls 4306 5006 2013 Pls 4307 5035 2013 Pls 4308 5065 2015 Pls 4309 5095 2023 Pls 4310 5125 2026 Pls 4311 5154 2030 Pls 4312 5184 2031 Pls 4313 5214 2036 Pls 4314 5244 2040 Pls 4315 5273 2040 Pls 4316 5303 2043 Pls 4317 5333 2049 Pls 4318 5363 2061 Pls 4319 5392 2066 Pls 4320 5422 2063 Pls 4321 5452 2071 Pls 4322 5481 2069 Pls 4323 5511 2076 Pls 4324 5541 2081 Pls 4325 5571 2086 Pls 4326 5600 2086 Pls 4327 5630 2091 Pls 4328 5660 2088 Pls 4329 5690 2088 Pls 4330 5719 2096 Pls 4331 5749 2094 Pls 4332 5779 2096 Pls 4333 5809 2099 Pls 4334 2226 1729 Pls 4335 2256 1732 Pls 4336 2286 1735 Pls 4337 2315 1740 Pls 4338 2345 1748 Pls 4339 2375 1756 Pls 4340 2405 1771 Pls 4341 2434 1776 Pls 4342 2464 1777 Pls 4343 2494 1774 Pls 4344 2524 1779 Pls 4345 2553 1781 Pls 4346 2583 1786 Pls 4347 2613 1789 Pls 4348 2643 1791 Pls 4349 2672 1791 Pls 4350 2702 1793 Pls 4351 2732 1795 Pls 4352 2762 1803 Pls 4353 2791 1811 Pls 4354 2821 1820 Pls 4355 2851 1824 Pls 4356 2881 1821 Pls 4357 2910 1821 Pls 4358 2940 1821 Pls 4359 2970 1818 Pls 4360 3000 1821 Pls 4361 3029 1836 Pls 4362 3059 1833 Pls 4363 3089 1829 Pls 4364 3118 1831 Pls 4365 3148 1836 Pls 4366 3178 1841 Pls 4367 3208 1851 Pls 4368 3237 1859 Pls 4369 3267 1864 Pls 4370 3297 1864 Pls 4371 3327 1866 Pls 4372 3356 1872 Pls 4373 3386 1871 Pls 4374 3416 1874 Pls 4375 3446 1872 Pls 4376 3475 1877 Pls 4377 3505 1877 Pls 4378 3535 1881 Pls 4379 3565 1881 Pls 4380 3594 1884 Pls 4381 3624 1891 Pls 4382 3654 1899 Pls 4383 3684 1897 Pls 4384 3713 1899 Pls 4385 3743 1899 Pls 4386 3773 1902 Pls 4387 3802 1906 Pls 4388 3832 1911 Pls 4389 3862 1920 Pls 4390 3892 1922 Pls 4391 3921 1932 Pls 4392 3951 1937 Pls 4393 3981 1943 Pls 4394 4011 1939 Pls 4395 4040 1935 Pls 4396 4070 1940 Pls 4397 4100 1942 Pls 4398 4130 1945 Pls 4399 4159 1946 Pls 4400 4189 1952 Pls 4401 4219 1954 Pls 4402 4249 1957 Pls 4403 4278 1960 Pls 4404 4308 1962 Pls 4405 4338 1967 Pls 4406 4368 1969 Pls 4407 4397 1972 Pls 4408 4427 1980 Pls 4409 4457 1985 Pls 4410 4487 1990 Pls 4411 4516 1992 Pls 4412 4546 1997 Pls 4413 4576 1994 Pls 4414 4605 1997 Pls 4415 4635 2007 Pls 4416 4665 2018 Pls 4417 4695 2023 Pls 4418 4724 2024 Pls 4419 4754 2029 Pls 4420 4784 2045 Pls 4421 4814 2050 Pls 4422 4843 2054 Pls 4423 4873 2060 Pls 4424 4903 2062 Pls 4425 4933 2065 Pls 4426 4962 2078 Pls 4427 4992 2085 Pls 4428 5022 2094 Pls 4429 5052 2101 Pls 4430 5081 2103 Pls 4431 5111 2111 Pls 4432 5141 2104 Pls 4433 5171 2114 Pls 4434 5200 2125 Pls 4435 5230 2138 Pls 4436 5260 2132 Pls 4437 5289 2127 Pls 4438 5319 2116 Pls 4439 5349 2118 Pls 4440 5379 2121 Pls 4441 5408 2129 Pls 4442 5438 2136 Pls 4443 5468 2128 Pls 4444 5498 2123 Pls 4445 5527 2132 Pls 4446 5557 2127 Pls 4447 5587 2130 Pls 4448 5617 2145 Pls 4449 5646 2158 Pls 4450 5676 2159 Pls 4451 5706 2166 Pls 4452 5736 2177 Pls 4453 5765 2179 Pls 4454 2183 1755 Pls 4455 2213 1759 Pls 4456 2242 1764 Pls 4457 2272 1769 Pls 4458 2302 1778 Pls 4459 2332 1780 Pls 4460 2361 1788 Pls 4461 2391 1803 Pls 4462 2421 1806 Pls 4463 2451 1811 Pls 4464 2480 1814 Pls 4465 2510 1814 Pls 4466 2540 1824 Pls 4467 2570 1830 Pls 4468 2599 1842 Pls 4469 2629 1851 Pls 4470 2659 1852 Pls 4471 2689 1856 Pls 4472 2718 1850 Pls 4473 2748 1849 Pls 4474 2778 1849 Pls 4475 2808 1868 Pls 4476 2837 1863 Pls 4477 2867 1870 Pls 4478 2897 1872 Pls 4479 2926 1867 Pls 4480 2956 1861 Pls 4481 2986 1858 Pls 4482 3016 1858 Pls 4483 3045 1858 Pls 4484 3075 1868 Pls 4485 3105 1871 Pls 4486 3135 1874 Pls 4487 3164 1876 Pls 4488 3194 1884 Pls 4489 3224 1883 Pls 4490 3254 1892 Pls 4491 3283 1897 Pls 4492 3313 1899 Pls 4493 3343 1905 Pls 4494 3373 1909 Pls 4495 3402 1906 Pls 4496 3432 1918 Pls 4497 3462 1927 Pls 4498 3492 1922 Pls 4499 3521 1924 Pls 4500 3551 1943 Pls 4501 3581 1941 Pls 4502 3611 1961 Pls 4503 3640 1958 Pls 4504 3670 1956 Pls 4505 3700 1959 Pls 4506 3729 1964 Pls 4507 3759 1961 Pls 4508 3789 1965 Pls 4509 3819 1965 Pls 4510 3848 1962 Pls 4511 3878 1968 Pls 4512 3908 1979 Pls 4513 3938 1984 Pls 4514 3967 1981 Pls 4515 3997 1988 Pls 4516 4027 1990 Pls 4517 4057 1985 Pls 4518 4086 1982 Pls 4519 4116 1980 Pls 4520 4146 1988 Pls 4521 4176 1985 Pls 4522 4205 1989 Pls 4523 4235 1989 Pls 4524 4265 1995 Pls 4525 4295 1995 Pls 4526 4324 1999 Pls 4527 4354 2007 Pls 4528 4384 2013 Pls 4529 4413 2017 Pls 4530 4443 2018 Pls 4531 4473 2025 Pls 4532 4503 2025 Pls 4533 4532 2022 Pls 4534 4562 2022 Pls 4535 4592 2027 Pls 4536 4622 2029 Pls 4537 4651 2030 Pls 4538 4681 2034 Pls 4539 4711 2039 Pls 4540 4741 2043 Pls 4541 4770 2047 Pls 4542 4800 2049 Pls 4543 4830 2053 Pls 4544 4860 2058 Pls 4545 4889 2058 Pls 4546 4919 2063 Pls 4547 4949 2067 Pls 4548 4979 2075 Pls 4549 5008 2080 Pls 4550 5038 2081 Pls 4551 5068 2080 Pls 4552 5098 2086 Pls 4553 5127 2090 Pls 4554 5157 2098 Pls 4555 5187 2098 Pls 4556 5216 2106 Pls 4557 5246 2106 Pls 4558 5276 2114 Pls 4559 5306 2113 Pls 4560 5335 2118 Pls 4561 5365 2121 Pls 4562 5395 2128 Pls 4563 5425 2140 Pls 4564 5454 2142 Pls 4565 5484 2141 Pls 4566 5514 2139 Pls 4567 5544 2143 Pls 4568 5573 2147 Pls 4569 5603 2152 Pls 4570 5633 2156 Pls 4571 5663 2170 Pls 4572 5692 2170 Pls 4573 5722 2167 Pls 4574 2140 1782 Pls 4575 2169 1789 Pls 4576 2199 1790 Pls 4577 2229 1794 Pls 4578 2259 1802 Pls 4579 2288 1802 Pls 4580 2318 1805 Pls 4581 2348 1809 Pls 4582 2378 1815 Pls 4583 2407 1828 Pls 4584 2437 1841 Pls 4585 2467 1844 Pls 4586 2497 1855 Pls 4587 2526 1843 Pls 4588 2556 1848 Pls 4589 2586 1854 Pls 4590 2616 1859 Pls 4591 2645 1870 Pls 4592 2675 1863 Pls 4593 2705 1859 Pls 4594 2735 1877 Pls 4595 2764 1880 Pls 4596 2794 1876 Pls 4597 2824 1870 Pls 4598 2853 1874 Pls 4599 2883 1883 Pls 4600 2913 1894 Pls 4601 2943 1894 Pls 4602 2972 1884 Pls 4603 3002 1889 Pls 4604 3032 1893 Pls 4605 3062 1901 Pls 4606 3091 1904 Pls 4607 3121 1907 Pls 4608 3151 1914 Pls 4609 3181 1916 Pls 4610 3210 1924 Pls 4611 3240 1930 Pls 4612 3270 1929 Pls 4613 3300 1934 Pls 4614 3329 1932 Pls 4615 3359 1936 Pls 4616 3389 1940 Pls 4617 3419 1947 Pls 4618 3448 1965 Pls 4619 3478 1979 Pls 4620 3508 1981 Pls 4621 3537 1995 Pls 4622 3567 1999 Pls 4623 3597 1994 Pls 4624 3627 2001 Pls 4625 3656 2004 Pls 4626 3686 2010 Pls 4627 3716 2014 Pls 4628 3746 2017 Pls 4629 3775 2022 Pls 4630 3805 2038 Pls 4631 3835 2040 Pls 4632 3865 2041 Pls 4633 3894 2046 Pls 4634 3924 2069 Pls 4635 3954 2074 Pls 4636 3984 2074 Pls 4637 4013 2082 Pls 4638 4043 2077 Pls 4639 4073 2081 Pls 4640 4103 2081 Pls 4641 4132 2084 Pls 4642 4162 2091 Pls 4643 4192 2087 Pls 4644 4222 2081 Pls 4645 4251 2081 Pls 4646 4281 2081 Pls 4647 4311 2062 Pls 4648 4340 2067 Pls 4649 4370 2075 Pls 4650 4400 2067 Pls 4651 4430 2063 Pls 4652 4459 2068 Pls 4653 4489 2069 Pls 4654 4519 2063 Pls 4655 4549 2065 Pls 4656 4578 2065 Pls 4657 4608 2068 Pls 4658 4638 2075 Pls 4659 4668 2078 Pls 4660 4697 2083 Pls 4661 4727 2094 Pls 4662 4757 2094 Pls 4663 4787 2093 Pls 4664 4816 2104 Pls 4665 4846 2109 Pls 4666 4876 2127 Pls 4667 4906 2127 Pls 4668 4935 2116 Pls 4669 4965 2118 Pls 4670 4995 2121 Pls 4671 5024 2126 Pls 4672 5054 2126 Pls 4673 5084 2129 Pls 4674 5114 2139 Pls 4675 5143 2139 Pls 4676 5173 2141 Pls 4677 5203 2143 Pls 4678 5233 2143 Pls 4679 5262 2146 Pls 4680 5292 2148 Pls 4681 5322 2157 Pls 4682 5352 2154 Pls 4683 5381 2153 Pls 4684 5411 2155 Pls 4685 5441 2153 Pls 4686 5471 2158 Pls 4687 5500 2166 Pls 4688 5530 2173 Pls 4689 5560 2177 Pls 4690 5590 2194 Pls 4691 5619 2192 Pls 4692 5649 2195 Pls 4693 5679 2204 Pls 4694 2096 1809 Pls 4695 2126 1812 Pls 4696 2156 1817 Pls 4697 2186 1824 Pls 4698 2215 1825 Pls 4699 2245 1827 Pls 4700 2275 1832 Pls 4701 2305 1837 Pls 4702 2334 1840 Pls 4703 2364 1843 Pls 4704 2394 1850 Pls 4705 2424 1855 Pls 4706 2453 1861 Pls 4707 2483 1857 Pls 4708 2513 1862 Pls 4709 2543 1867 Pls 4710 2572 1871 Pls 4711 2602 1883 Pls 4712 2632 1880 Pls 4713 2661 1881 Pls 4714 2691 1894 Pls 4715 2721 1898 Pls 4716 2751 1903 Pls 4717 2780 1912 Pls 4718 2810 1914 Pls 4719 2840 1928 Pls 4720 2870 1938 Pls 4721 2899 1948 Pls 4722 2929 1959 Pls 4723 2959 1969 Pls 4724 2989 1979 Pls 4725 3018 1974 Pls 4726 3048 1980 Pls 4727 3078 1974 Pls 4728 3108 1977 Pls 4729 3137 1978 Pls 4730 3167 1976 Pls 4731 3197 2003 Pls 4732 3227 2005 Pls 4733 3256 2004 Pls 4734 3286 1996 Pls 4735 3316 1999 Pls 4736 3346 2009 Pls 4737 3375 2023 Pls 4738 3405 2019 Pls 4739 3435 2043 Pls 4740 3464 2065 Pls 4741 3494 2075 Pls 4742 3524 2072 Pls 4743 3554 2067 Pls 4744 3583 2042 Pls 4745 3613 2043 Pls 4746 3643 2035 Pls 4747 3673 2040 Pls 4748 3702 2058 Pls 4749 3732 2073 Pls 4750 3762 2079 Pls 4751 3792 2076 Pls 4752 3821 2075 Pls 4753 3851 2075 Pls 4754 3881 2094 Pls 4755 3911 2097 Pls 4756 3940 2096 Pls 4757 3970 2120 Pls 4758 4000 2120 Pls 4759 4030 2112 Pls 4760 4059 2111 Pls 4761 4089 2117 Pls 4762 4119 2135 Pls 4763 4148 2138 Pls 4764 4178 2141 Pls 4765 4208 2150 Pls 4766 4238 2143 Pls 4767 4267 2163 Pls 4768 4297 2177 Pls 4769 4327 2144 Pls 4770 4357 2150 Pls 4771 4386 2130 Pls 4772 4416 2138 Pls 4773 4446 2160 Pls 4774 4476 2149 Pls 4775 4505 2146 Pls 4776 4535 2149 Pls 4777 4565 2169 Pls 4778 4595 2185 Pls 4779 4624 2206 Pls 4780 4654 2222 Pls 4781 4684 2222 Pls 4782 4714 2219 Pls 4783 4743 2243 Pls 4784 4773 2235 Pls 4785 4803 2251 Pls 4786 4833 2253 Pls 4787 4862 2282 Pls 4788 4892 2266 Pls 4789 4922 2290 Pls 4790 4951 2279 Pls 4791 4981 2272 Pls 4792 5011 2279 Pls 4793 5041 2293 Pls 4794 5070 2297 Pls 4795 5100 2297 Pls 4796 5130 2332 Pls 4797 5160 2343 Pls 4798 5189 2316 Pls 4799 5219 2317 Pls 4800 5249 2296 Pls 4801 5279 2282 Pls 4802 5308 2290 Pls 4803 5338 2301 Pls 4804 5368 2288 Pls 4805 5398 2309 Pls 4806 5427 2298 Pls 4807 5457 2300 Pls 4808 5487 2316 Pls 4809 5517 2335 Pls 4810 5546 2342 Pls 4811 5576 2350 Pls 4812 5606 2350 Pls 4813 5635 2325 Pls 4814 2053 1836 Pls 4815 2083 1842 Pls 4816 2113 1844 Pls 4817 2142 1849 Pls 4818 2172 1850 Pls 4819 2202 1857 Pls 4820 2232 1868 Pls 4821 2261 1880 Pls 4822 2291 1883 Pls 4823 2321 1891 Pls 4824 2351 1917 Pls 4825 2380 1934 Pls 4826 2410 1944 Pls 4827 2440 1946 Pls 4828 2470 1962 Pls 4829 2499 1981 Pls 4830 2529 1975 Pls 4831 2559 2007 Pls 4832 2588 2007 Pls 4833 2618 2036 Pls 4834 2648 2039 Pls 4835 2678 2049 Pls 4836 2707 2051 Pls 4837 2737 2054 Pls 4838 2767 2057 Pls 4839 2797 2051 Pls 4840 2826 2037 Pls 4841 2856 2040 Pls 4842 2886 2056 Pls 4843 2916 2077 Pls 4844 2945 2090 Pls 4845 2975 2084 Pls 4846 3005 2089 Pls 4847 3035 2076 Pls 4848 3064 2075 Pls 4849 3094 2099 Pls 4850 3124 2120 Pls 4851 3154 2142 Pls 4852 3183 2169 Pls 4853 3213 2142 Pls 4854 3243 2170 Pls 4855 3272 2166 Pls 4856 3302 2202 Pls 4857 3332 2197 Pls 4858 3362 2218 Pls 4859 3391 2226 Pls 4860 3421 2252 Pls 4861 3451 2247 Pls 4862 3481 2263 Pls 4863 3510 2273 Pls 4864 3540 2295 Pls 4865 3570 2327 Pls 4866 3600 2300 Pls 4867 3629 2296 Pls 4868 3659 2301 Pls 4869 3689 2313 Pls 4870 3719 2333 Pls 4871 3748 2279 Pls 4872 3778 2271 Pls 4873 3808 2274 Pls 4874 3838 2324 Pls 4875 3867 2341 Pls 4876 3897 2346 Pls 4877 3927 2351 Pls 4878 3957 2339 Pls 4879 3986 2342 Pls 4880 4016 2326 Pls 4881 4046 2316 Pls 4882 4075 2333 Pls 4883 4105 2357 Pls 4884 4135 2331 Pls 4885 4165 2338 Pls 4886 4194 2315 Pls 4887 4224 2295 Pls 4888 4254 2314 Pls 4889 4284 2322 Pls 4890 4313 2337 Pls 4891 4343 2338 Pls 4892 4373 2310 Pls 4893 4403 2343 Pls 4894 4432 2361 Pls 4895 4462 2366 Pls 4896 4492 2333 Pls 4897 4522 2374 Pls 4898 4551 2330 Pls 4899 4581 2336 Pls 4900 4611 2359 Pls 4901 4641 2364 Pls 4902 4670 2360 Pls 4903 4700 2393 Pls 4904 4730 2374 Pls 4905 4759 2383 Pls 4906 4789 2379 Pls 4907 4819 2401 Pls 4908 4849 2393 Pls 4909 4878 2388 Pls 4910 4908 2384 Pls 4911 4938 2389 Pls 4912 4968 2373 Pls 4913 4997 2378 Pls 4914 5027 2381 Pls 4915 5057 2388 Pls 4916 5087 2357 Pls 4917 5116 2343 Pls 4918 5146 2353 Pls 4919 5176 2362 Pls 4920 5206 2382 Pls 4921 5235 2375 Pls 4922 5265 2364 Pls 4923 5295 2355 Pls 4924 5325 2369 Pls 4925 5354 2387 Pls 4926 5384 2392 Pls 4927 5414 2395 Pls 4928 5444 2431 Pls 4929 5473 2421 Pls 4930 5503 2420 Pls 4931 5533 2426 Pls 4932 5562 2461 Pls 4933 5592 2473 Pls 4934 2010 1862 Pls 4935 2040 1867 Pls 4936 2069 1871 Pls 4937 2099 1876 Pls 4938 2129 1879 Pls 4939 2159 1884 Pls 4940 2188 1892 Pls 4941 2218 1898 Pls 4942 2248 1902 Pls 4943 2278 1913 Pls 4944 2307 1923 Pls 4945 2337 1926 Pls 4946 2367 1934 Pls 4947 2396 1929 Pls 4948 2426 1947 Pls 4949 2456 1957 Pls 4950 2486 1968 Pls 4951 2515 1986 Pls 4952 2545 2008 Pls 4953 2575 2052 Pls 4954 2605 2084 Pls 4955 2634 2108 Pls 4956 2664 2122 Pls 4957 2694 2127 Pls 4958 2724 2156 Pls 4959 2753 2171 Pls 4960 2783 2190 Pls 4961 2813 2206 Pls 4962 2843 2225 Pls 4963 2872 2284 Pls 4964 2902 2269 Pls 4965 2932 2256 Pls 4966 2962 2270 Pls 4967 2991 2264 Pls 4968 3021 2272 Pls 4969 3051 2287 Pls 4970 3081 2327 Pls 4971 3110 2301 Pls 4972 3140 2313 Pls 4973 3170 2318 Pls 4974 3199 2356 Pls 4975 3229 2348 Pls 4976 3259 2334 Pls 4977 3289 2356 Pls 4978 3318 2339 Pls 4979 3348 2328 Pls 4980 3378 2349 Pls 4981 3408 2386 Pls 4982 3437 2407 Pls 4983 3467 2447 Pls 4984 3497 2421 Pls 4985 3527 2405 Pls 4986 3556 2397 Pls 4987 3586 2423 Pls 4988 3616 2414 Pls 4989 3646 2391 Pls 4990 3675 2379 Pls 4991 3705 2414 Pls 4992 3735 2438 Pls 4993 3765 2416 Pls 4994 3794 2421 Pls 4995 3824 2416 Pls 4996 3854 2403 Pls 4997 3883 2391 Pls 4998 3913 2434 Pls 4999 3943 2425 Pls 5000 3973 2437 Pls 5001 4002 2452 Pls 5002 4032 2444 Pls 5003 4062 2436 Pls 5004 4092 2463 Pls 5005 4121 2496 Pls 5006 4151 2484 Pls 5007 4181 2488 Pls 5008 4211 2462 Pls 5009 4240 2496 Pls 5010 4270 2455 Pls 5011 4300 2455 Pls 5012 4330 2444 Pls 5013 4359 2404 Pls 5014 4389 2413 Pls 5015 4419 2407 Pls 5016 4449 2425 Pls 5017 4478 2391 Pls 5018 4508 2412 Pls 5019 4538 2425 Pls 5020 4568 2438 Pls 5021 4597 2457 Pls 5022 4627 2491 Pls 5023 4657 2486 Pls 5024 4686 2469 Pls 5025 4716 2450 Pls 5026 4746 2487 Pls 5027 4776 2463 Pls 5028 4805 2466 Pls 5029 4835 2486 Pls 5030 4865 2498 Pls 5031 4895 2494 Pls 5032 4924 2502 Pls 5033 4954 2508 Pls 5034 4984 2534 Pls 5035 5014 2542 Pls 5036 5043 2549 Pls 5037 5073 2539 Pls 5038 5103 2535 Pls 5039 5133 2547 Pls 5040 5162 2536 Pls 5041 5192 2503 Pls 5042 5222 2509 Pls 5043 5252 2487 Pls 5044 5281 2454 Pls 5045 5311 2476 Pls 5046 5341 2507 Pls 5047 5370 2529 Pls 5048 5400 2534 Pls 5049 5430 2550 Pls 5050 5460 2538 Pls 5051 5489 2544 Pls 5052 5519 2539 Pls 5053 5549 2559 Pls 5054 1967 1889 Pls 5055 1996 1892 Pls 5056 2026 1896 Pls 5057 2056 1904 Pls 5058 2086 1912 Pls 5059 2115 1919 Pls 5060 2145 1927 Pls 5061 2175 1928 Pls 5062 2205 1938 Pls 5063 2234 1945 Pls 5064 2264 1961 Pls 5065 2294 1969 Pls 5066 2323 1982 Pls 5067 2353 1991 Pls 5068 2383 2019 Pls 5069 2413 2048 Pls 5070 2442 2060 Pls 5071 2472 2107 Pls 5072 2502 2152 Pls 5073 2532 2142 Pls 5074 2561 2186 Pls 5075 2591 2194 Pls 5076 2621 2211 Pls 5077 2651 2274 Pls 5078 2680 2283 Pls 5079 2710 2280 Pls 5080 2740 2295 Pls 5081 2770 2319 Pls 5082 2799 2388 Pls 5083 2829 2396 Pls 5084 2859 2401 Pls 5085 2889 2404 Pls 5086 2918 2420 Pls 5087 2948 2384 Pls 5088 2978 2393 Pls 5089 3007 2405 Pls 5090 3037 2440 Pls 5091 3067 2437 Pls 5092 3097 2429 Pls 5093 3126 2411 Pls 5094 3156 2426 Pls 5095 3186 2415 Pls 5096 3216 2412 Pls 5097 3245 2450 Pls 5098 3275 2460 Pls 5099 3305 2414 Pls 5100 3335 2431 Pls 5101 3364 2422 Pls 5102 3394 2440 Pls 5103 3424 2464 Pls 5104 3454 2485 Pls 5105 3483 2509 Pls 5106 3513 2502 Pls 5107 3543 2467 Pls 5108 3573 2520 Pls 5109 3602 2501 Pls 5110 3632 2522 Pls 5111 3662 2516 Pls 5112 3692 2511 Pls 5113 3721 2503 Pls 5114 3751 2532 Pls 5115 3781 2595 Pls 5116 3810 2593 Pls 5117 3840 2579 Pls 5118 3870 2574 Pls 5119 3900 2558 Pls 5120 3929 2525 Pls 5121 3959 2539 Pls 5122 3989 2524 Pls 5123 4019 2532 Pls 5124 4048 2517 Pls 5125 4078 2541 Pls 5126 4108 2559 Pls 5127 4138 2564 Pls 5128 4167 2531 Pls 5129 4197 2544 Pls 5130 4227 2542 Pls 5131 4257 2563 Pls 5132 4286 2589 Pls 5133 4316 2605 Pls 5134 4346 2600 Pls 5135 4376 2578 Pls 5136 4405 2595 Pls 5137 4435 2628 Pls 5138 4465 2618 Pls 5139 4494 2583 Pls 5140 4524 2631 Pls 5141 4554 2654 Pls 5142 4584 2678 Pls 5143 4613 2673 Pls 5144 4643 2657 Pls 5145 4673 2611 Pls 5146 4703 2603 Pls 5147 4732 2598 Pls 5148 4762 2578 Pls 5149 4792 2623 Pls 5150 4822 2604 Pls 5151 4851 2663 Pls 5152 4881 2724 Pls 5153 4911 2698 Pls 5154 4941 2713 Pls 5155 4970 2702 Pls 5156 5000 2710 Pls 5157 5030 2702 Pls 5158 5060 2662 Pls 5159 5089 2732 Pls 5160 5119 2753 Pls 5161 5149 2734 Pls 5162 5179 2736 Pls 5163 5208 2736 Pls 5164 5238 2730 Pls 5165 5268 2719 Pls 5166 5297 2712 Pls 5167 5327 2703 Pls 5168 5357 2666 Pls 5169 5387 2694 Pls 5170 5416 2699 Pls 5171 5446 2684 Pls 5172 5476 2712 Pls 5173 5506 2728 Pls 5174 1923 1916 Pls 5175 1953 1924 Pls 5176 1983 1927 Pls 5177 2013 1934 Pls 5178 2042 1940 Pls 5179 2072 1940 Pls 5180 2102 1950 Pls 5181 2131 1953 Pls 5182 2161 1960 Pls 5183 2191 1971 Pls 5184 2221 1975 Pls 5185 2250 1980 Pls 5186 2280 1980 Pls 5187 2310 1975 Pls 5188 2340 1981 Pls 5189 2369 1994 Pls 5190 2399 2026 Pls 5191 2429 2070 Pls 5192 2459 2087 Pls 5193 2488 2113 Pls 5194 2518 2137 Pls 5195 2548 2198 Pls 5196 2578 2251 Pls 5197 2607 2304 Pls 5198 2637 2313 Pls 5199 2667 2369 Pls 5200 2697 2432 Pls 5201 2726 2469 Pls 5202 2756 2488 Pls 5203 2786 2495 Pls 5204 2816 2468 Pls 5205 2845 2501 Pls 5206 2875 2511 Pls 5207 2905 2492 Pls 5208 2934 2487 Pls 5209 2964 2498 Pls 5210 2994 2499 Pls 5211 3024 2502 Pls 5212 3053 2500 Pls 5213 3083 2537 Pls 5214 3113 2542 Pls 5215 3143 2585 Pls 5216 3172 2550 Pls 5217 3202 2562 Pls 5218 3232 2557 Pls 5219 3262 2565 Pls 5220 3291 2584 Pls 5221 3321 2591 Pls 5222 3351 2562 Pls 5223 3381 2612 Pls 5224 3410 2572 Pls 5225 3440 2550 Pls 5226 3470 2529 Pls 5227 3500 2561 Pls 5228 3529 2565 Pls 5229 3559 2586 Pls 5230 3589 2619 Pls 5231 3618 2613 Pls 5232 3648 2611 Pls 5233 3678 2624 Pls 5234 3708 2607 Pls 5235 3737 2615 Pls 5236 3767 2634 Pls 5237 3797 2650 Pls 5238 3827 2639 Pls 5239 3856 2654 Pls 5240 3886 2664 Pls 5241 3916 2667 Pls 5242 3946 2701 Pls 5243 3975 2656 Pls 5244 4005 2630 Pls 5245 4035 2645 Pls 5246 4065 2637 Pls 5247 4094 2645 Pls 5248 4124 2664 Pls 5249 4154 2668 Pls 5250 4184 2626 Pls 5251 4213 2590 Pls 5252 4243 2625 Pls 5253 4273 2622 Pls 5254 4303 2633 Pls 5255 4332 2649 Pls 5256 4362 2646 Pls 5257 4392 2627 Pls 5258 4421 2603 Pls 5259 4451 2607 Pls 5260 4481 2612 Pls 5261 4511 2676 Pls 5262 4540 2693 Pls 5263 4570 2690 Pls 5264 4600 2673 Pls 5265 4630 2644 Pls 5266 4659 2670 Pls 5267 4689 2676 Pls 5268 4719 2678 Pls 5269 4749 2696 Pls 5270 4778 2721 Pls 5271 4808 2742 Pls 5272 4838 2744 Pls 5273 4868 2709 Pls 5274 4897 2715 Pls 5275 4927 2706 Pls 5276 4957 2720 Pls 5277 4987 2748 Pls 5278 5016 2741 Pls 5279 5046 2767 Pls 5280 5076 2778 Pls 5281 5105 2783 Pls 5282 5135 2790 Pls 5283 5165 2809 Pls 5284 5195 2801 Pls 5285 5224 2795 Pls 5286 5254 2770 Pls 5287 5284 2731 Pls 5288 5314 2797 Pls 5289 5343 2834 Pls 5290 5373 2839 Pls 5291 5403 2828 Pls 5292 5433 2801 Pls 5293 5462 2783 Pls 5294 1880 1943 Pls 5295 1910 1949 Pls 5296 1940 1959 Pls 5297 1969 1969 Pls 5298 1999 1972 Pls 5299 2029 1977 Pls 5300 2058 1985 Pls 5301 2088 1995 Pls 5302 2118 1992 Pls 5303 2148 2004 Pls 5304 2177 2022 Pls 5305 2207 2040 Pls 5306 2237 2078 Pls 5307 2267 2107 Pls 5308 2296 2128 Pls 5309 2326 2165 Pls 5310 2356 2175 Pls 5311 2386 2208 Pls 5312 2415 2252 Pls 5313 2445 2292 Pls 5314 2475 2289 Pls 5315 2505 2340 Pls 5316 2534 2410 Pls 5317 2564 2468 Pls 5318 2594 2519 Pls 5319 2624 2514 Pls 5320 2653 2542 Pls 5321 2683 2582 Pls 5322 2713 2580 Pls 5323 2742 2566 Pls 5324 2772 2595 Pls 5325 2802 2598 Pls 5326 2832 2634 Pls 5327 2861 2643 Pls 5328 2891 2663 Pls 5329 2921 2669 Pls 5330 2951 2653 Pls 5331 2980 2668 Pls 5332 3010 2681 Pls 5333 3040 2641 Pls 5334 3070 2623 Pls 5335 3099 2582 Pls 5336 3129 2614 Pls 5337 3159 2662 Pls 5338 3189 2681 Pls 5339 3218 2713 Pls 5340 3248 2669 Pls 5341 3278 2702 Pls 5342 3308 2696 Pls 5343 3337 2706 Pls 5344 3367 2693 Pls 5345 3397 2712 Pls 5346 3427 2730 Pls 5347 3456 2684 Pls 5348 3486 2711 Pls 5349 3516 2715 Pls 5350 3545 2727 Pls 5351 3575 2707 Pls 5352 3605 2742 Pls 5353 3635 2755 Pls 5354 3664 2755 Pls 5355 3694 2782 Pls 5356 3724 2794 Pls 5357 3754 2762 Pls 5358 3783 2749 Pls 5359 3813 2730 Pls 5360 3843 2751 Pls 5361 3873 2740 Pls 5362 3902 2796 Pls 5363 3932 2841 Pls 5364 3962 2812 Pls 5365 3992 2800 Pls 5366 4021 2768 Pls 5367 4051 2771 Pls 5368 4081 2782 Pls 5369 4111 2818 Pls 5370 4140 2778 Pls 5371 4170 2799 Pls 5372 4200 2776 Pls 5373 4229 2789 Pls 5374 4259 2791 Pls 5375 4289 2790 Pls 5376 4319 2822 Pls 5377 4348 2814 Pls 5378 4378 2782 Pls 5379 4408 2776 Pls 5380 4438 2761 Pls 5381 4467 2787 Pls 5382 4497 2736 Pls 5383 4527 2763 Pls 5384 4557 2797 Pls 5385 4586 2784 Pls 5386 4616 2780 Pls 5387 4646 2786 Pls 5388 4676 2788 Pls 5389 4705 2806 Pls 5390 4735 2793 Pls 5391 4765 2804 Pls 5392 4795 2814 Pls 5393 4824 2800 Pls 5394 4854 2787 Pls 5395 4884 2789 Pls 5396 4914 2837 Pls 5397 4943 2832 Pls 5398 4973 2861 Pls 5399 5003 2872 Pls 5400 5032 2903 Pls 5401 5062 2887 Pls 5402 5092 2911 Pls 5403 5122 2929 Pls 5404 5151 2890 Pls 5405 5181 2884 Pls 5406 5211 2868 Pls 5407 5241 2883 Pls 5408 5270 2867 Pls 5409 5300 2913 Pls 5410 5330 2880 Pls 5411 5360 2901 Pls 5412 5389 2882 Pls 5413 5419 2874 Pls 5414 1837 1969 Pls 5415 1866 1974 Pls 5416 1896 1982 Pls 5417 1926 1986 Pls 5418 1956 1994 Pls 5419 1985 1996 Pls 5420 2015 2002 Pls 5421 2045 2010 Pls 5422 2075 2025 Pls 5423 2104 2039 Pls 5424 2134 2059 Pls 5425 2164 2071 Pls 5426 2194 2086 Pls 5427 2223 2131 Pls 5428 2253 2166 Pls 5429 2283 2190 Pls 5430 2313 2232 Pls 5431 2342 2277 Pls 5432 2372 2304 Pls 5433 2402 2354 Pls 5434 2432 2379 Pls 5435 2461 2464 Pls 5436 2491 2530 Pls 5437 2521 2531 Pls 5438 2551 2613 Pls 5439 2580 2629 Pls 5440 2610 2607 Pls 5441 2640 2626 Pls 5442 2669 2637 Pls 5443 2699 2662 Pls 5444 2729 2714 Pls 5445 2759 2718 Pls 5446 2788 2748 Pls 5447 2818 2788 Pls 5448 2848 2728 Pls 5449 2878 2733 Pls 5450 2907 2734 Pls 5451 2937 2762 Pls 5452 2967 2743 Pls 5453 2997 2765 Pls 5454 3026 2712 Pls 5455 3056 2733 Pls 5456 3086 2743 Pls 5457 3116 2770 Pls 5458 3145 2734 Pls 5459 3175 2726 Pls 5460 3205 2713 Pls 5461 3235 2724 Pls 5462 3264 2740 Pls 5463 3294 2790 Pls 5464 3324 2765 Pls 5465 3353 2770 Pls 5466 3383 2802 Pls 5467 3413 2779 Pls 5468 3443 2765 Pls 5469 3472 2751 Pls 5470 3502 2764 Pls 5471 3532 2751 Pls 5472 3562 2738 Pls 5473 3591 2731 Pls 5474 3621 2732 Pls 5475 3651 2758 Pls 5476 3681 2779 Pls 5477 3710 2809 Pls 5478 3740 2825 Pls 5479 3770 2811 Pls 5480 3800 2805 Pls 5481 3829 2802 Pls 5482 3859 2783 Pls 5483 3889 2741 Pls 5484 3919 2813 Pls 5485 3948 2809 Pls 5486 3978 2802 Pls 5487 4008 2777 Pls 5488 4038 2804 Pls 5489 4067 2835 Pls 5490 4097 2860 Pls 5491 4127 2872 Pls 5492 4156 2845 Pls 5493 4186 2859 Pls 5494 4216 2847 Pls 5495 4246 2842 Pls 5496 4275 2832 Pls 5497 4305 2829 Pls 5498 4335 2820 Pls 5499 4365 2814 Pls 5500 4394 2842 Pls 5501 4424 2843 Pls 5502 4454 2854 Pls 5503 4484 2897 Pls 5504 4513 2891 Pls 5505 4543 2913 Pls 5506 4573 2885 Pls 5507 4603 2918 Pls 5508 4632 2902 Pls 5509 4662 2919 Pls 5510 4692 2893 Pls 5511 4722 2863 Pls 5512 4751 2887 Pls 5513 4781 2900 Pls 5514 4811 2935 Pls 5515 4840 2932 Pls 5516 4870 2943 Pls 5517 4900 2951 Pls 5518 4930 2960 Pls 5519 4959 2977 Pls 5520 4989 2955 Pls 5521 5019 2942 Pls 5522 5049 2949 Pls 5523 5078 3002 Pls 5524 5108 2954 Pls 5525 5138 2981 Pls 5526 5168 2953 Pls 5527 5197 2970 Pls 5528 5227 3015 Pls 5529 5257 3020 Pls 5530 5287 3050 Pls 5531 5316 2995 Pls 5532 5346 3003 Pls 5533 5376 3001 Pls 5534 1793 1996 Pls 5535 1823 2000 Pls 5536 1853 2006 Pls 5537 1883 2011 Pls 5538 1912 2021 Pls 5539 1942 2030 Pls 5540 1972 2034 Pls 5541 2002 2048 Pls 5542 2031 2059 Pls 5543 2061 2063 Pls 5544 2091 2068 Pls 5545 2121 2084 Pls 5546 2150 2106 Pls 5547 2180 2135 Pls 5548 2210 2158 Pls 5549 2240 2193 Pls 5550 2269 2235 Pls 5551 2299 2308 Pls 5552 2329 2361 Pls 5553 2359 2419 Pls 5554 2388 2459 Pls 5555 2418 2547 Pls 5556 2448 2652 Pls 5557 2477 2636 Pls 5558 2507 2702 Pls 5559 2537 2741 Pls 5560 2567 2739 Pls 5561 2596 2776 Pls 5562 2626 2760 Pls 5563 2656 2765 Pls 5564 2686 2810 Pls 5565 2715 2789 Pls 5566 2745 2754 Pls 5567 2775 2791 Pls 5568 2805 2810 Pls 5569 2834 2772 Pls 5570 2864 2820 Pls 5571 2894 2828 Pls 5572 2924 2816 Pls 5573 2953 2797 Pls 5574 2983 2830 Pls 5575 3013 2874 Pls 5576 3043 2834 Pls 5577 3072 2848 Pls 5578 3102 2837 Pls 5579 3132 2828 Pls 5580 3161 2813 Pls 5581 3191 2818 Pls 5582 3221 2839 Pls 5583 3251 2826 Pls 5584 3280 2838 Pls 5585 3310 2841 Pls 5586 3340 2840 Pls 5587 3370 2808 Pls 5588 3399 2824 Pls 5589 3429 2867 Pls 5590 3459 2840 Pls 5591 3489 2823 Pls 5592 3518 2829 Pls 5593 3548 2855 Pls 5594 3578 2865 Pls 5595 3608 2853 Pls 5596 3637 2892 Pls 5597 3667 2911 Pls 5598 3697 2924 Pls 5599 3727 2932 Pls 5600 3756 2899 Pls 5601 3786 2912 Pls 5602 3816 2896 Pls 5603 3846 2915 Pls 5604 3875 2885 Pls 5605 3905 2869 Pls 5606 3935 2864 Pls 5607 3964 2909 Pls 5608 3994 2930 Pls 5609 4024 2917 Pls 5610 4054 2945 Pls 5611 4083 2954 Pls 5612 4113 2964 Pls 5613 4143 2951 Pls 5614 4173 2912 Pls 5615 4202 2878 Pls 5616 4232 2936 Pls 5617 4262 2960 Pls 5618 4292 3014 Pls 5619 4321 2984 Pls 5620 4351 2971 Pls 5621 4381 2976 Pls 5622 4411 2932 Pls 5623 4440 2965 Pls 5624 4470 3033 Pls 5625 4500 3015 Pls 5626 4530 2983 Pls 5627 4559 2961 Pls 5628 4589 2958 Pls 5629 4619 2934 Pls 5630 4648 2965 Pls 5631 4678 2998 Pls 5632 4708 3005 Pls 5633 4738 2963 Pls 5634 4767 3008 Pls 5635 4797 2999 Pls 5636 4827 3039 Pls 5637 4857 3029 Pls 5638 4886 3025 Pls 5639 4916 3039 Pls 5640 4946 3012 Pls 5641 4976 3004 Pls 5642 5005 3011 Pls 5643 5035 3036 Pls 5644 5065 2989 Pls 5645 5095 2976 Pls 5646 5124 2978 Pls 5647 5154 3039 Pls 5648 5184 3055 Pls 5649 5214 3032 Pls 5650 5243 3018 Pls 5651 5273 3037 Pls 5652 5303 3014 Pls 5653 5333 3066 Pls 5654 1750 2023 Pls 5655 1780 2028 Pls 5656 1810 2038 Pls 5657 1839 2039 Pls 5658 1869 2051 Pls 5659 1899 2054 Pls 5660 1929 2060 Pls 5661 1958 2073 Pls 5662 1988 2080 Pls 5663 2018 2101 Pls 5664 2048 2126 Pls 5665 2077 2133 Pls 5666 2107 2163 Pls 5667 2137 2192 Pls 5668 2167 2237 Pls 5669 2196 2308 Pls 5670 2226 2413 Pls 5671 2256 2480 Pls 5672 2285 2565 Pls 5673 2315 2658 Pls 5674 2345 2730 Pls 5675 2375 2775 Pls 5676 2404 2817 Pls 5677 2434 2852 Pls 5678 2464 2879 Pls 5679 2494 2890 Pls 5680 2523 2878 Pls 5681 2553 2825 Pls 5682 2583 2825 Pls 5683 2613 2801 Pls 5684 2642 2857 Pls 5685 2672 2862 Pls 5686 2702 2869 Pls 5687 2732 2851 Pls 5688 2761 2891 Pls 5689 2791 2890 Pls 5690 2821 2904 Pls 5691 2851 2895 Pls 5692 2880 2866 Pls 5693 2910 2910 Pls 5694 2940 2921 Pls 5695 2970 2951 Pls 5696 2999 2958 Pls 5697 3029 2923 Pls 5698 3059 2865 Pls 5699 3088 2885 Pls 5700 3118 2896 Pls 5701 3148 2943 Pls 5702 3178 2949 Pls 5703 3207 2976 Pls 5704 3237 2976 Pls 5705 3267 2962 Pls 5706 3297 2985 Pls 5707 3326 2945 Pls 5708 3356 2940 Pls 5709 3386 2955 Pls 5710 3416 2966 Pls 5711 3445 2960 Pls 5712 3475 2979 Pls 5713 3505 2993 Pls 5714 3535 2962 Pls 5715 3564 2968 Pls 5716 3594 2957 Pls 5717 3624 2964 Pls 5718 3654 2938 Pls 5719 3683 2938 Pls 5720 3713 2926 Pls 5721 3743 2942 Pls 5722 3772 2980 Pls 5723 3802 3020 Pls 5724 3832 3038 Pls 5725 3862 3054 Pls 5726 3891 3059 Pls 5727 3921 3027 Pls 5728 3951 3030 Pls 5729 3981 3080 Pls 5730 4010 3075 Pls 5731 4040 3040 Pls 5732 4070 3047 Pls 5733 4100 3028 Pls 5734 4129 2993 Pls 5735 4159 3010 Pls 5736 4189 3009 Pls 5737 4219 3007 Pls 5738 4248 3006 Pls 5739 4278 2992 Pls 5740 4308 3049 Pls 5741 4338 3048 Pls 5742 4367 3059 Pls 5743 4397 3069 Pls 5744 4427 3079 Pls 5745 4457 3093 Pls 5746 4486 3100 Pls 5747 4516 3097 Pls 5748 4546 3085 Pls 5749 4575 3025 Pls 5750 4605 3031 Pls 5751 4635 3031 Pls 5752 4665 3048 Pls 5753 4694 3102 Pls 5754 4724 3112 Pls 5755 4754 3099 Pls 5756 4784 3083 Pls 5757 4813 3106 Pls 5758 4843 3104 Pls 5759 4873 3122 Pls 5760 4903 3109 Pls 5761 4932 3146 Pls 5762 4962 3137 Pls 5763 4992 3146 Pls 5764 5022 3114 Pls 5765 5051 3127 Pls 5766 5081 3151 Pls 5767 5111 3160 Pls 5768 5141 3184 Pls 5769 5170 3139 Pls 5770 5200 3088 Pls 5771 5230 3117 Pls 5772 5259 3103 Pls 5773 5289 3119 Pls 5774 1707 2050 Pls 5775 1737 2053 Pls 5776 1766 2058 Pls 5777 1796 2061 Pls 5778 1826 2068 Pls 5779 1856 2071 Pls 5780 1885 2076 Pls 5781 1915 2082 Pls 5782 1945 2095 Pls 5783 1975 2107 Pls 5784 2004 2136 Pls 5785 2034 2169 Pls 5786 2064 2189 Pls 5787 2094 2222 Pls 5788 2123 2267 Pls 5789 2153 2352 Pls 5790 2183 2402 Pls 5791 2212 2507 Pls 5792 2242 2613 Pls 5793 2272 2734 Pls 5794 2302 2814 Pls 5795 2331 2864 Pls 5796 2361 2861 Pls 5797 2391 2930 Pls 5798 2421 2890 Pls 5799 2450 2919 Pls 5800 2480 2936 Pls 5801 2510 2932 Pls 5802 2540 2941 Pls 5803 2569 2908 Pls 5804 2599 2939 Pls 5805 2629 2939 Pls 5806 2659 2976 Pls 5807 2688 2977 Pls 5808 2718 2965 Pls 5809 2748 2979 Pls 5810 2778 2984 Pls 5811 2807 2959 Pls 5812 2837 3011 Pls 5813 2867 3021 Pls 5814 2896 2975 Pls 5815 2926 2957 Pls 5816 2956 2983 Pls 5817 2986 2951 Pls 5818 3015 3006 Pls 5819 3045 3036 Pls 5820 3075 3025 Pls 5821 3105 2996 Pls 5822 3134 2976 Pls 5823 3164 2989 Pls 5824 3194 3034 Pls 5825 3224 3048 Pls 5826 3253 3074 Pls 5827 3283 3083 Pls 5828 3313 3092 Pls 5829 3343 3025 Pls 5830 3372 3025 Pls 5831 3402 3050 Pls 5832 3432 3047 Pls 5833 3462 3071 Pls 5834 3491 3054 Pls 5835 3521 3060 Pls 5836 3551 3051 Pls 5837 3581 3025 Pls 5838 3610 3102 Pls 5839 3640 3118 Pls 5840 3670 3117 Pls 5841 3699 3123 Pls 5842 3729 3077 Pls 5843 3759 3076 Pls 5844 3789 3065 Pls 5845 3818 3071 Pls 5846 3848 3108 Pls 5847 3878 3086 Pls 5848 3908 3115 Pls 5849 3937 3142 Pls 5850 3967 3161 Pls 5851 3997 3144 Pls 5852 4027 3141 Pls 5853 4056 3093 Pls 5854 4086 3106 Pls 5855 4116 3135 Pls 5856 4146 3125 Pls 5857 4175 3154 Pls 5858 4205 3122 Pls 5859 4235 3132 Pls 5860 4265 3145 Pls 5861 4294 3142 Pls 5862 4324 3145 Pls 5863 4354 3126 Pls 5864 4383 3128 Pls 5865 4413 3129 Pls 5866 4443 3106 Pls 5867 4473 3106 Pls 5868 4502 3127 Pls 5869 4532 3152 Pls 5870 4562 3106 Pls 5871 4592 3132 Pls 5872 4621 3137 Pls 5873 4651 3172 Pls 5874 4681 3201 Pls 5875 4711 3206 Pls 5876 4740 3233 Pls 5877 4770 3220 Pls 5878 4800 3217 Pls 5879 4830 3182 Pls 5880 4859 3211 Pls 5881 4889 3245 Pls 5882 4919 3246 Pls 5883 4949 3216 Pls 5884 4978 3221 Pls 5885 5008 3192 Pls 5886 5038 3226 Pls 5887 5068 3266 Pls 5888 5097 3220 Pls 5889 5127 3217 Pls 5890 5157 3247 Pls 5891 5186 3248 Pls 5892 5216 3225 Pls 5893 5246 3214 Pls 5894 1664 2076 Pls 5895 1693 2085 Pls 5896 1723 2091 Pls 5897 1753 2101 Pls 5898 1783 2117 Pls 5899 1812 2127 Pls 5900 1842 2154 Pls 5901 1872 2183 Pls 5902 1902 2232 Pls 5903 1931 2292 Pls 5904 1961 2367 Pls 5905 1991 2441 Pls 5906 2020 2516 Pls 5907 2050 2621 Pls 5908 2080 2754 Pls 5909 2110 2810 Pls 5910 2139 2893 Pls 5911 2169 2946 Pls 5912 2199 2965 Pls 5913 2229 2985 Pls 5914 2258 3022 Pls 5915 2288 3079 Pls 5916 2318 3041 Pls 5917 2348 3030 Pls 5918 2377 3041 Pls 5919 2407 3064 Pls 5920 2437 3065 Pls 5921 2467 3070 Pls 5922 2496 3059 Pls 5923 2526 3013 Pls 5924 2556 3015 Pls 5925 2586 2977 Pls 5926 2615 2996 Pls 5927 2645 3001 Pls 5928 2675 3003 Pls 5929 2705 3012 Pls 5930 2734 3030 Pls 5931 2764 2998 Pls 5932 2794 3046 Pls 5933 2823 3048 Pls 5934 2853 3048 Pls 5935 2883 3053 Pls 5936 2913 3066 Pls 5937 2942 3119 Pls 5938 2972 3136 Pls 5939 3002 3135 Pls 5940 3032 3157 Pls 5941 3061 3097 Pls 5942 3091 3116 Pls 5943 3121 3103 Pls 5944 3151 3079 Pls 5945 3180 3118 Pls 5946 3210 3097 Pls 5947 3240 3069 Pls 5948 3270 3067 Pls 5949 3299 3128 Pls 5950 3329 3115 Pls 5951 3359 3171 Pls 5952 3389 3167 Pls 5953 3418 3180 Pls 5954 3448 3119 Pls 5955 3478 3111 Pls 5956 3507 3105 Pls 5957 3537 3102 Pls 5958 3567 3126 Pls 5959 3597 3187 Pls 5960 3626 3171 Pls 5961 3656 3158 Pls 5962 3686 3157 Pls 5963 3716 3182 Pls 5964 3745 3189 Pls 5965 3775 3178 Pls 5966 3805 3181 Pls 5967 3835 3176 Pls 5968 3864 3177 Pls 5969 3894 3148 Pls 5970 3924 3138 Pls 5971 3954 3161 Pls 5972 3983 3175 Pls 5973 4013 3158 Pls 5974 4043 3192 Pls 5975 4073 3205 Pls 5976 4102 3185 Pls 5977 4132 3222 Pls 5978 4162 3199 Pls 5979 4192 3234 Pls 5980 4221 3234 Pls 5981 4251 3202 Pls 5982 4281 3217 Pls 5983 4310 3207 Pls 5984 4340 3228 Pls 5985 4370 3193 Pls 5986 4400 3260 Pls 5987 4429 3251 Pls 5988 4459 3270 Pls 5989 4489 3304 Pls 5990 4519 3267 Pls 5991 4548 3237 Pls 5992 4578 3232 Pls 5993 4608 3231 Pls 5994 4638 3256 Pls 5995 4667 3287 Pls 5996 4697 3244 Pls 5997 4727 3231 Pls 5998 4757 3241 Pls 5999 4786 3251 Pls 6000 4816 3303 Pls 6001 4846 3326 Pls 6002 4876 3308 Pls 6003 4905 3302 Pls 6004 4935 3353 Pls 6005 4965 3286 Pls 6006 4994 3296 Pls 6007 5024 3287 Pls 6008 5054 3250 Pls 6009 5084 3314 Pls 6010 5113 3317 Pls 6011 5143 3295 Pls 6012 5173 3284 Pls 6013 5203 3284 Pls 6014 1620 2103 Pls 6015 1650 2111 Pls 6016 1680 2121 Pls 6017 1710 2131 Pls 6018 1739 2144 Pls 6019 1769 2163 Pls 6020 1799 2200 Pls 6021 1829 2235 Pls 6022 1858 2307 Pls 6023 1888 2384 Pls 6024 1918 2488 Pls 6025 1947 2629 Pls 6026 1977 2712 Pls 6027 2007 2843 Pls 6028 2037 2957 Pls 6029 2066 2979 Pls 6030 2096 3019 Pls 6031 2126 3086 Pls 6032 2156 3071 Pls 6033 2185 3064 Pls 6034 2215 3088 Pls 6035 2245 3085 Pls 6036 2275 3092 Pls 6037 2304 3089 Pls 6038 2334 3065 Pls 6039 2364 3083 Pls 6040 2394 3070 Pls 6041 2423 3073 Pls 6042 2453 3088 Pls 6043 2483 3093 Pls 6044 2513 3128 Pls 6045 2542 3117 Pls 6046 2572 3104 Pls 6047 2602 3088 Pls 6048 2631 3084 Pls 6049 2661 3098 Pls 6050 2691 3122 Pls 6051 2721 3106 Pls 6052 2750 3090 Pls 6053 2780 3110 Pls 6054 2810 3119 Pls 6055 2840 3156 Pls 6056 2869 3147 Pls 6057 2899 3133 Pls 6058 2929 3177 Pls 6059 2959 3126 Pls 6060 2988 3138 Pls 6061 3018 3157 Pls 6062 3048 3143 Pls 6063 3078 3159 Pls 6064 3107 3138 Pls 6065 3137 3138 Pls 6066 3167 3177 Pls 6067 3197 3188 Pls 6068 3226 3219 Pls 6069 3256 3200 Pls 6070 3286 3190 Pls 6071 3316 3193 Pls 6072 3345 3201 Pls 6073 3375 3214 Pls 6074 3405 3197 Pls 6075 3434 3266 Pls 6076 3464 3231 Pls 6077 3494 3242 Pls 6078 3524 3239 Pls 6079 3553 3188 Pls 6080 3583 3177 Pls 6081 3613 3244 Pls 6082 3643 3222 Pls 6083 3672 3224 Pls 6084 3702 3230 Pls 6085 3732 3233 Pls 6086 3762 3245 Pls 6087 3791 3283 Pls 6088 3821 3269 Pls 6089 3851 3272 Pls 6090 3881 3293 Pls 6091 3910 3296 Pls 6092 3940 3284 Pls 6093 3970 3279 Pls 6094 4000 3333 Pls 6095 4029 3356 Pls 6096 4059 3319 Pls 6097 4089 3311 Pls 6098 4118 3304 Pls 6099 4148 3329 Pls 6100 4178 3318 Pls 6101 4208 3337 Pls 6102 4237 3331 Pls 6103 4267 3327 Pls 6104 4297 3325 Pls 6105 4327 3311 Pls 6106 4356 3359 Pls 6107 4386 3341 Pls 6108 4416 3341 Pls 6109 4446 3370 Pls 6110 4475 3383 Pls 6111 4505 3380 Pls 6112 4535 3415 Pls 6113 4565 3334 Pls 6114 4594 3363 Pls 6115 4624 3318 Pls 6116 4654 3333 Pls 6117 4684 3339 Pls 6118 4713 3355 Pls 6119 4743 3364 Pls 6120 4773 3364 Pls 6121 4803 3396 Pls 6122 4832 3343 Pls 6123 4862 3377 Pls 6124 4892 3414 Pls 6125 4921 3406 Pls 6126 4951 3422 Pls 6127 4981 3440 Pls 6128 5011 3465 Pls 6129 5040 3405 Pls 6130 5070 3389 Pls 6131 5100 3395 Pls 6132 5130 3405 Pls 6133 5159 3463 Pls 6134 1577 2130 Pls 6135 1607 2138 Pls 6136 1637 2151 Pls 6137 1666 2166 Pls 6138 1696 2180 Pls 6139 1726 2204 Pls 6140 1755 2235 Pls 6141 1785 2291 Pls 6142 1815 2359 Pls 6143 1845 2447 Pls 6144 1874 2545 Pls 6145 1904 2697 Pls 6146 1934 2838 Pls 6147 1964 2988 Pls 6148 1993 3079 Pls 6149 2023 3068 Pls 6150 2053 3134 Pls 6151 2083 3107 Pls 6152 2112 3124 Pls 6153 2142 3120 Pls 6154 2172 3144 Pls 6155 2202 3211 Pls 6156 2231 3184 Pls 6157 2261 3162 Pls 6158 2291 3184 Pls 6159 2321 3180 Pls 6160 2350 3201 Pls 6161 2380 3146 Pls 6162 2410 3194 Pls 6163 2440 3178 Pls 6164 2469 3145 Pls 6165 2499 3179 Pls 6166 2529 3188 Pls 6167 2558 3217 Pls 6168 2588 3217 Pls 6169 2618 3243 Pls 6170 2648 3175 Pls 6171 2677 3235 Pls 6172 2707 3235 Pls 6173 2737 3245 Pls 6174 2767 3327 Pls 6175 2796 3327 Pls 6176 2826 3238 Pls 6177 2856 3258 Pls 6178 2886 3239 Pls 6179 2915 3249 Pls 6180 2945 3280 Pls 6181 2975 3283 Pls 6182 3005 3269 Pls 6183 3034 3274 Pls 6184 3064 3253 Pls 6185 3094 3242 Pls 6186 3124 3285 Pls 6187 3153 3287 Pls 6188 3183 3322 Pls 6189 3213 3311 Pls 6190 3242 3298 Pls 6191 3272 3286 Pls 6192 3302 3281 Pls 6193 3332 3273 Pls 6194 3361 3289 Pls 6195 3391 3326 Pls 6196 3421 3317 Pls 6197 3451 3349 Pls 6198 3480 3285 Pls 6199 3510 3299 Pls 6200 3540 3306 Pls 6201 3570 3261 Pls 6202 3599 3290 Pls 6203 3629 3316 Pls 6204 3659 3345 Pls 6205 3689 3338 Pls 6206 3718 3323 Pls 6207 3748 3316 Pls 6208 3778 3310 Pls 6209 3808 3364 Pls 6210 3837 3382 Pls 6211 3867 3408 Pls 6212 3897 3360 Pls 6213 3927 3347 Pls 6214 3956 3355 Pls 6215 3986 3330 Pls 6216 4016 3333 Pls 6217 4045 3356 Pls 6218 4075 3362 Pls 6219 4105 3367 Pls 6220 4135 3371 Pls 6221 4164 3353 Pls 6222 4194 3412 Pls 6223 4224 3358 Pls 6224 4254 3401 Pls 6225 4283 3389 Pls 6226 4313 3421 Pls 6227 4343 3443 Pls 6228 4373 3419 Pls 6229 4402 3413 Pls 6230 4432 3471 Pls 6231 4462 3437 Pls 6232 4492 3495 Pls 6233 4521 3436 Pls 6234 4551 3407 Pls 6235 4581 3390 Pls 6236 4611 3419 Pls 6237 4640 3428 Pls 6238 4670 3413 Pls 6239 4700 3453 Pls 6240 4729 3467 Pls 6241 4759 3448 Pls 6242 4789 3480 Pls 6243 4819 3461 Pls 6244 4848 3487 Pls 6245 4878 3473 Pls 6246 4908 3468 Pls 6247 4938 3462 Pls 6248 4967 3446 Pls 6249 4997 3430 Pls 6250 5027 3464 Pls 6251 5057 3489 Pls 6252 5086 3433 Pls 6253 5116 3464 Pls 6254 1534 2157 Pls 6255 1564 2160 Pls 6256 1593 2163 Pls 6257 1623 2167 Pls 6258 1653 2175 Pls 6259 1682 2185 Pls 6260 1712 2196 Pls 6261 1742 2209 Pls 6262 1772 2223 Pls 6263 1801 2241 Pls 6264 1831 2273 Pls 6265 1861 2332 Pls 6266 1891 2409 Pls 6267 1920 2527 Pls 6268 1950 2652 Pls 6269 1980 2775 Pls 6270 2010 2962 Pls 6271 2039 3074 Pls 6272 2069 3129 Pls 6273 2099 3225 Pls 6274 2129 3263 Pls 6275 2158 3275 Pls 6276 2188 3273 Pls 6277 2218 3248 Pls 6278 2248 3237 Pls 6279 2277 3281 Pls 6280 2307 3277 Pls 6281 2337 3325 Pls 6282 2366 3288 Pls 6283 2396 3309 Pls 6284 2426 3298 Pls 6285 2456 3300 Pls 6286 2485 3295 Pls 6287 2515 3255 Pls 6288 2545 3273 Pls 6289 2575 3305 Pls 6290 2604 3281 Pls 6291 2634 3296 Pls 6292 2664 3299 Pls 6293 2694 3293 Pls 6294 2723 3282 Pls 6295 2753 3288 Pls 6296 2783 3304 Pls 6297 2813 3306 Pls 6298 2842 3330 Pls 6299 2872 3341 Pls 6300 2902 3359 Pls 6301 2932 3345 Pls 6302 2961 3334 Pls 6303 2991 3302 Pls 6304 3021 3331 Pls 6305 3051 3336 Pls 6306 3080 3293 Pls 6307 3110 3301 Pls 6308 3140 3315 Pls 6309 3169 3357 Pls 6310 3199 3363 Pls 6311 3229 3367 Pls 6312 3259 3397 Pls 6313 3288 3402 Pls 6314 3318 3407 Pls 6315 3348 3377 Pls 6316 3378 3398 Pls 6317 3407 3411 Pls 6318 3437 3398 Pls 6319 3467 3409 Pls 6320 3497 3385 Pls 6321 3526 3408 Pls 6322 3556 3374 Pls 6323 3586 3402 Pls 6324 3616 3391 Pls 6325 3645 3418 Pls 6326 3675 3420 Pls 6327 3705 3410 Pls 6328 3735 3385 Pls 6329 3764 3366 Pls 6330 3794 3423 Pls 6331 3824 3427 Pls 6332 3853 3403 Pls 6333 3883 3408 Pls 6334 3913 3438 Pls 6335 3943 3467 Pls 6336 3972 3458 Pls 6337 4002 3461 Pls 6338 4032 3463 Pls 6339 4062 3482 Pls 6340 4091 3448 Pls 6341 4121 3460 Pls 6342 4151 3450 Pls 6343 4181 3431 Pls 6344 4210 3468 Pls 6345 4240 3470 Pls 6346 4270 3494 Pls 6347 4300 3520 Pls 6348 4329 3504 Pls 6349 4359 3525 Pls 6350 4389 3520 Pls 6351 4419 3538 Pls 6352 4448 3523 Pls 6353 4478 3575 Pls 6354 4508 3559 Pls 6355 4538 3544 Pls 6356 4567 3530 Pls 6357 4597 3567 Pls 6358 4627 3497 Pls 6359 4656 3481 Pls 6360 4686 3518 Pls 6361 4716 3528 Pls 6362 4746 3540 Pls 6363 4775 3609 Pls 6364 4805 3587 Pls 6365 4835 3598 Pls 6366 4865 3541 Pls 6367 4894 3544 Pls 6368 4924 3556 Pls 6369 4954 3564 Pls 6370 4984 3565 Pls 6371 5013 3585 Pls 6372 5043 3583 Pls 6373 5073 3559 Pls 6374 1490 2184 Pls 6375 1520 2190 Pls 6376 1550 2203 Pls 6377 1580 2216 Pls 6378 1609 2232 Pls 6379 1639 2259 Pls 6380 1669 2318 Pls 6381 1699 2394 Pls 6382 1728 2510 Pls 6383 1758 2669 Pls 6384 1788 2825 Pls 6385 1818 2966 Pls 6386 1847 3104 Pls 6387 1877 3190 Pls 6388 1907 3253 Pls 6389 1937 3291 Pls 6390 1966 3291 Pls 6391 1996 3355 Pls 6392 2026 3303 Pls 6393 2056 3341 Pls 6394 2085 3335 Pls 6395 2115 3348 Pls 6396 2145 3311 Pls 6397 2175 3306 Pls 6398 2204 3346 Pls 6399 2234 3331 Pls 6400 2264 3361 Pls 6401 2293 3332 Pls 6402 2323 3366 Pls 6403 2353 3349 Pls 6404 2383 3365 Pls 6405 2412 3408 Pls 6406 2442 3392 Pls 6407 2472 3403 Pls 6408 2502 3410 Pls 6409 2531 3445 Pls 6410 2561 3409 Pls 6411 2591 3361 Pls 6412 2621 3353 Pls 6413 2650 3391 Pls 6414 2680 3387 Pls 6415 2710 3403 Pls 6416 2740 3389 Pls 6417 2769 3414 Pls 6418 2799 3406 Pls 6419 2829 3459 Pls 6420 2859 3432 Pls 6421 2888 3423 Pls 6422 2918 3434 Pls 6423 2948 3407 Pls 6424 2977 3433 Pls 6425 3007 3433 Pls 6426 3037 3417 Pls 6427 3067 3423 Pls 6428 3096 3401 Pls 6429 3126 3419 Pls 6430 3156 3443 Pls 6431 3186 3446 Pls 6432 3215 3456 Pls 6433 3245 3416 Pls 6434 3275 3426 Pls 6435 3305 3483 Pls 6436 3334 3432 Pls 6437 3364 3480 Pls 6438 3394 3485 Pls 6439 3424 3460 Pls 6440 3453 3444 Pls 6441 3483 3447 Pls 6442 3513 3481 Pls 6443 3543 3478 Pls 6444 3572 3443 Pls 6445 3602 3507 Pls 6446 3632 3523 Pls 6447 3662 3546 Pls 6448 3691 3541 Pls 6449 3721 3563 Pls 6450 3751 3563 Pls 6451 3780 3588 Pls 6452 3810 3565 Pls 6453 3840 3580 Pls 6454 3870 3564 Pls 6455 3899 3572 Pls 6456 3929 3550 Pls 6457 3959 3542 Pls 6458 3989 3523 Pls 6459 4018 3547 Pls 6460 4048 3601 Pls 6461 4078 3566 Pls 6462 4108 3565 Pls 6463 4137 3555 Pls 6464 4167 3551 Pls 6465 4197 3557 Pls 6466 4227 3527 Pls 6467 4256 3527 Pls 6468 4286 3559 Pls 6469 4316 3569 Pls 6470 4346 3580 Pls 6471 4375 3607 Pls 6472 4405 3619 Pls 6473 4435 3646 Pls 6474 4464 3656 Pls 6475 4494 3611 Pls 6476 4524 3587 Pls 6477 4554 3613 Pls 6478 4583 3594 Pls 6479 4613 3616 Pls 6480 4643 3580 Pls 6481 4673 3617 Pls 6482 4702 3586 Pls 6483 4732 3625 Pls 6484 4762 3619 Pls 6485 4792 3646 Pls 6486 4821 3633 Pls 6487 4851 3648 Pls 6488 4881 3637 Pls 6489 4911 3638 Pls 6490 4940 3658 Pls 6491 4970 3671 Pls 6492 5000 3659 Pls 6493 5030 3677 Pls 6494 1447 2210 Pls 6495 1477 2217 Pls 6496 1507 2223 Pls 6497 1536 2235 Pls 6498 1566 2249 Pls 6499 1596 2265 Pls 6500 1626 2305 Pls 6501 1655 2350 Pls 6502 1685 2446 Pls 6503 1715 2571 Pls 6504 1745 2710 Pls 6505 1774 2891 Pls 6506 1804 3057 Pls 6507 1834 3164 Pls 6508 1864 3259 Pls 6509 1893 3283 Pls 6510 1923 3329 Pls 6511 1953 3379 Pls 6512 1983 3408 Pls 6513 2012 3409 Pls 6514 2042 3386 Pls 6515 2072 3403 Pls 6516 2101 3391 Pls 6517 2131 3415 Pls 6518 2161 3416 Pls 6519 2191 3420 Pls 6520 2220 3449 Pls 6521 2250 3457 Pls 6522 2280 3463 Pls 6523 2310 3486 Pls 6524 2339 3449 Pls 6525 2369 3460 Pls 6526 2399 3483 Pls 6527 2429 3470 Pls 6528 2458 3448 Pls 6529 2488 3432 Pls 6530 2518 3463 Pls 6531 2548 3445 Pls 6532 2577 3456 Pls 6533 2607 3434 Pls 6534 2637 3463 Pls 6535 2667 3436 Pls 6536 2696 3422 Pls 6537 2726 3473 Pls 6538 2756 3481 Pls 6539 2786 3470 Pls 6540 2815 3505 Pls 6541 2845 3515 Pls 6542 2875 3520 Pls 6543 2904 3510 Pls 6544 2934 3490 Pls 6545 2964 3523 Pls 6546 2994 3500 Pls 6547 3023 3527 Pls 6548 3053 3506 Pls 6549 3083 3511 Pls 6550 3113 3532 Pls 6551 3142 3502 Pls 6552 3172 3524 Pls 6553 3202 3548 Pls 6554 3232 3536 Pls 6555 3261 3553 Pls 6556 3291 3520 Pls 6557 3321 3574 Pls 6558 3351 3539 Pls 6559 3380 3567 Pls 6560 3410 3559 Pls 6561 3440 3567 Pls 6562 3470 3596 Pls 6563 3499 3577 Pls 6564 3529 3590 Pls 6565 3559 3591 Pls 6566 3588 3547 Pls 6567 3618 3556 Pls 6568 3648 3604 Pls 6569 3678 3608 Pls 6570 3707 3581 Pls 6571 3737 3589 Pls 6572 3767 3619 Pls 6573 3797 3658 Pls 6574 3826 3642 Pls 6575 3856 3616 Pls 6576 3886 3599 Pls 6577 3916 3597 Pls 6578 3945 3636 Pls 6579 3975 3623 Pls 6580 4005 3620 Pls 6581 4035 3660 Pls 6582 4064 3649 Pls 6583 4094 3638 Pls 6584 4124 3609 Pls 6585 4154 3627 Pls 6586 4183 3654 Pls 6587 4213 3659 Pls 6588 4243 3661 Pls 6589 4273 3655 Pls 6590 4302 3669 Pls 6591 4332 3625 Pls 6592 4362 3625 Pls 6593 4391 3630 Pls 6594 4421 3630 Pls 6595 4451 3641 Pls 6596 4481 3654 Pls 6597 4510 3684 Pls 6598 4540 3718 Pls 6599 4570 3698 Pls 6600 4600 3678 Pls 6601 4629 3706 Pls 6602 4659 3703 Pls 6603 4689 3751 Pls 6604 4719 3719 Pls 6605 4748 3730 Pls 6606 4778 3674 Pls 6607 4808 3722 Pls 6608 4838 3734 Pls 6609 4867 3703 Pls 6610 4897 3721 Pls 6611 4927 3701 Pls 6612 4957 3747 Pls 6613 4986 3734 Pls 6614 1404 2237 Pls 6615 1434 2240 Pls 6616 1463 2244 Pls 6617 1493 2249 Pls 6618 1523 2253 Pls 6619 1553 2260 Pls 6620 1582 2267 Pls 6621 1612 2273 Pls 6622 1642 2289 Pls 6623 1672 2323 Pls 6624 1701 2364 Pls 6625 1731 2446 Pls 6626 1761 2547 Pls 6627 1791 2680 Pls 6628 1820 2833 Pls 6629 1850 3041 Pls 6630 1880 3169 Pls 6631 1910 3292 Pls 6632 1939 3402 Pls 6633 1969 3446 Pls 6634 1999 3471 Pls 6635 2028 3470 Pls 6636 2058 3437 Pls 6637 2088 3504 Pls 6638 2118 3461 Pls 6639 2147 3507 Pls 6640 2177 3502 Pls 6641 2207 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7219 1336 2408 Pls 7220 1366 2427 Pls 7221 1396 2466 Pls 7222 1425 2520 Pls 7223 1455 2623 Pls 7224 1485 2807 Pls 7225 1515 3059 Pls 7226 1544 3361 Pls 7227 1574 3627 Pls 7228 1604 3729 Pls 7229 1634 3819 Pls 7230 1663 3838 Pls 7231 1693 3872 Pls 7232 1723 3867 Pls 7233 1753 3854 Pls 7234 1782 3863 Pls 7235 1812 3893 Pls 7236 1842 3909 Pls 7237 1872 3888 Pls 7238 1901 3924 Pls 7239 1931 3914 Pls 7240 1961 3905 Pls 7241 1990 3886 Pls 7242 2020 3908 Pls 7243 2050 3908 Pls 7244 2080 3913 Pls 7245 2109 3896 Pls 7246 2139 3915 Pls 7247 2169 3926 Pls 7248 2199 3910 Pls 7249 2228 3927 Pls 7250 2258 3914 Pls 7251 2288 3914 Pls 7252 2318 3921 Pls 7253 2347 3940 Pls 7254 2377 3938 Pls 7255 2407 3921 Pls 7256 2437 3947 Pls 7257 2466 3950 Pls 7258 2496 3942 Pls 7259 2526 3942 Pls 7260 2556 3963 Pls 7261 2585 3984 Pls 7262 2615 4002 Pls 7263 2645 4003 Pls 7264 2675 3987 Pls 7265 2704 3991 Pls 7266 2734 3991 Pls 7267 2764 3986 Pls 7268 2793 3994 Pls 7269 2823 4002 Pls 7270 2853 4006 Pls 7271 2883 3985 Pls 7272 2912 4009 Pls 7273 2942 4008 Pls 7274 2972 4001 Pls 7275 3002 4032 Pls 7276 3031 4042 Pls 7277 3061 4023 Pls 7278 3091 3994 Pls 7279 3121 4016 Pls 7280 3150 4032 Pls 7281 3180 4044 Pls 7282 3210 4052 Pls 7283 3240 4044 Pls 7284 3269 4033 Pls 7285 3299 4051 Pls 7286 3329 4057 Pls 7287 3359 4076 Pls 7288 3388 4078 Pls 7289 3418 4083 Pls 7290 3448 4086 Pls 7291 3477 4082 Pls 7292 3507 4061 Pls 7293 3537 4055 Pls 7294 3567 4069 Pls 7295 3596 4087 Pls 7296 3626 4084 Pls 7297 3656 4108 Pls 7298 3686 4089 Pls 7299 3715 4110 Pls 7300 3745 4113 Pls 7301 3775 4113 Pls 7302 3805 4099 Pls 7303 3834 4104 Pls 7304 3864 4115 Pls 7305 3894 4115 Pls 7306 3924 4139 Pls 7307 3953 4135 Pls 7308 3983 4100 Pls 7309 4013 4133 Pls 7310 4043 4127 Pls 7311 4072 4113 Pls 7312 4102 4124 Pls 7313 4132 4137 Pls 7314 4162 4120 Pls 7315 4191 4108 Pls 7316 4221 4133 Pls 7317 4251 4147 Pls 7318 4280 4146 Pls 7319 4310 4171 Pls 7320 4340 4184 Pls 7321 4370 4173 Pls 7322 4399 4146 Pls 7323 4429 4146 Pls 7324 4459 4175 Pls 7325 4489 4178 Pls 7326 4518 4193 Pls 7327 4548 4175 Pls 7328 4578 4190 Pls 7329 4608 4204 Pls 7330 4637 4201 Pls 7331 4667 4190 Pls 7332 4697 4202 Pls 7333 4727 4190 Pls 7334 1144 2398 Pls 7335 1174 2401 Pls 7336 1204 2406 Pls 7337 1233 2416 Pls 7338 1263 2427 Pls 7339 1293 2454 Pls 7340 1323 2494 Pls 7341 1352 2569 Pls 7342 1382 2696 Pls 7343 1412 2913 Pls 7344 1442 3206 Pls 7345 1471 3509 Pls 7346 1501 3729 Pls 7347 1531 3848 Pls 7348 1561 3919 Pls 7349 1590 3938 Pls 7350 1620 3943 Pls 7351 1650 3914 Pls 7352 1680 3947 Pls 7353 1709 3942 Pls 7354 1739 3947 Pls 7355 1769 3966 Pls 7356 1799 3968 Pls 7357 1828 3979 Pls 7358 1858 3968 Pls 7359 1888 3967 Pls 7360 1917 3959 Pls 7361 1947 3983 Pls 7362 1977 3989 Pls 7363 2007 4007 Pls 7364 2036 3994 Pls 7365 2066 4014 Pls 7366 2096 3999 Pls 7367 2126 3975 Pls 7368 2155 3982 Pls 7369 2185 4004 Pls 7370 2215 4000 Pls 7371 2245 4005 Pls 7372 2274 4011 Pls 7373 2304 4035 Pls 7374 2334 4023 Pls 7375 2364 4050 Pls 7376 2393 4039 Pls 7377 2423 4025 Pls 7378 2453 4050 Pls 7379 2483 4039 Pls 7380 2512 4047 Pls 7381 2542 4051 Pls 7382 2572 4048 Pls 7383 2601 4051 Pls 7384 2631 4057 Pls 7385 2661 4062 Pls 7386 2691 4064 Pls 7387 2720 4050 Pls 7388 2750 4066 Pls 7389 2780 4066 Pls 7390 2810 4066 Pls 7391 2839 4074 Pls 7392 2869 4082 Pls 7393 2899 4089 Pls 7394 2929 4092 Pls 7395 2958 4092 Pls 7396 2988 4105 Pls 7397 3018 4091 Pls 7398 3048 4091 Pls 7399 3077 4094 Pls 7400 3107 4107 Pls 7401 3137 4130 Pls 7402 3167 4109 Pls 7403 3196 4133 Pls 7404 3226 4132 Pls 7405 3256 4127 Pls 7406 3286 4140 Pls 7407 3315 4148 Pls 7408 3345 4140 Pls 7409 3375 4143 Pls 7410 3404 4156 Pls 7411 3434 4148 Pls 7412 3464 4153 Pls 7413 3494 4144 Pls 7414 3523 4131 Pls 7415 3553 4144 Pls 7416 3583 4170 Pls 7417 3613 4170 Pls 7418 3642 4173 Pls 7419 3672 4165 Pls 7420 3702 4157 Pls 7421 3732 4167 Pls 7422 3761 4166 Pls 7423 3791 4172 Pls 7424 3821 4168 Pls 7425 3851 4188 Pls 7426 3880 4185 Pls 7427 3910 4214 Pls 7428 3940 4205 Pls 7429 3970 4216 Pls 7430 3999 4208 Pls 7431 4029 4207 Pls 7432 4059 4220 Pls 7433 4088 4199 Pls 7434 4118 4209 Pls 7435 4148 4214 Pls 7436 4178 4234 Pls 7437 4207 4214 Pls 7438 4237 4222 Pls 7439 4267 4224 Pls 7440 4297 4229 Pls 7441 4326 4240 Pls 7442 4356 4243 Pls 7443 4386 4238 Pls 7444 4416 4263 Pls 7445 4445 4256 Pls 7446 4475 4271 Pls 7447 4505 4269 Pls 7448 4535 4284 Pls 7449 4564 4284 Pls 7450 4594 4279 Pls 7451 4624 4283 Pls 7452 4654 4294 Pls 7453 4683 4294 Pls 7454 1101 2424 Pls 7455 1131 2428 Pls 7456 1160 2433 Pls 7457 1190 2444 Pls 7458 1220 2454 Pls 7459 1250 2478 Pls 7460 1279 2516 Pls 7461 1309 2587 Pls 7462 1339 2710 Pls 7463 1369 2930 Pls 7464 1398 3248 Pls 7465 1428 3568 Pls 7466 1458 3803 Pls 7467 1488 3926 Pls 7468 1517 3986 Pls 7469 1547 4010 Pls 7470 1577 4031 Pls 7471 1607 4018 Pls 7472 1636 4015 Pls 7473 1666 4033 Pls 7474 1696 4045 Pls 7475 1725 4062 Pls 7476 1755 4047 Pls 7477 1785 4035 Pls 7478 1815 4052 Pls 7479 1844 4044 Pls 7480 1874 4057 Pls 7481 1904 4051 Pls 7482 1934 4077 Pls 7483 1963 4074 Pls 7484 1993 4061 Pls 7485 2023 4063 Pls 7486 2053 4066 Pls 7487 2082 4084 Pls 7488 2112 4100 Pls 7489 2142 4073 Pls 7490 2172 4090 Pls 7491 2201 4108 Pls 7492 2231 4094 Pls 7493 2261 4105 Pls 7494 2291 4110 Pls 7495 2320 4109 Pls 7496 2350 4118 Pls 7497 2380 4122 Pls 7498 2410 4130 Pls 7499 2439 4117 Pls 7500 2469 4106 Pls 7501 2499 4127 Pls 7502 2528 4133 Pls 7503 2558 4132 Pls 7504 2588 4126 Pls 7505 2618 4142 Pls 7506 2647 4139 Pls 7507 2677 4131 Pls 7508 2707 4147 Pls 7509 2737 4134 Pls 7510 2766 4142 Pls 7511 2796 4138 Pls 7512 2826 4163 Pls 7513 2856 4170 Pls 7514 2885 4181 Pls 7515 2915 4178 Pls 7516 2945 4180 Pls 7517 2975 4191 Pls 7518 3004 4191 Pls 7519 3034 4188 Pls 7520 3064 4187 Pls 7521 3094 4182 Pls 7522 3123 4189 Pls 7523 3153 4201 Pls 7524 3183 4195 Pls 7525 3212 4208 Pls 7526 3242 4202 Pls 7527 3272 4219 Pls 7528 3302 4224 Pls 7529 3331 4229 Pls 7530 3361 4233 Pls 7531 3391 4236 Pls 7532 3421 4244 Pls 7533 3450 4227 Pls 7534 3480 4231 Pls 7535 3510 4240 Pls 7536 3540 4243 Pls 7537 3569 4238 Pls 7538 3599 4232 Pls 7539 3629 4243 Pls 7540 3659 4261 Pls 7541 3688 4264 Pls 7542 3718 4271 Pls 7543 3748 4260 Pls 7544 3778 4274 Pls 7545 3807 4279 Pls 7546 3837 4270 Pls 7547 3867 4270 Pls 7548 3897 4263 Pls 7549 3926 4280 Pls 7550 3956 4280 Pls 7551 3986 4285 Pls 7552 4015 4285 Pls 7553 4045 4293 Pls 7554 4075 4306 Pls 7555 4105 4315 Pls 7556 4134 4304 Pls 7557 4164 4306 Pls 7558 4194 4325 Pls 7559 4224 4319 Pls 7560 4253 4319 Pls 7561 4283 4330 Pls 7562 4313 4324 Pls 7563 4343 4332 Pls 7564 4372 4337 Pls 7565 4402 4334 Pls 7566 4432 4333 Pls 7567 4462 4350 Pls 7568 4491 4355 Pls 7569 4521 4351 Pls 7570 4551 4359 Pls 7571 4581 4373 Pls 7572 4610 4367 Pls 7573 4640 4364 Pls 7574 1058 2451 Pls 7575 1087 2454 Pls 7576 1117 2459 Pls 7577 1147 2464 Pls 7578 1177 2472 Pls 7579 1206 2480 Pls 7580 1236 2505 Pls 7581 1266 2545 Pls 7582 1296 2610 Pls 7583 1325 2705 Pls 7584 1355 2889 Pls 7585 1385 3173 Pls 7586 1415 3539 Pls 7587 1444 3813 Pls 7588 1474 3988 Pls 7589 1504 4062 Pls 7590 1534 4085 Pls 7591 1563 4091 Pls 7592 1593 4104 Pls 7593 1623 4110 Pls 7594 1652 4114 Pls 7595 1682 4117 Pls 7596 1712 4120 Pls 7597 1742 4124 Pls 7598 1771 4127 Pls 7599 1801 4130 Pls 7600 1831 4134 Pls 7601 1861 4137 Pls 7602 1890 4140 Pls 7603 1920 4144 Pls 7604 1950 4147 Pls 7605 1980 4150 Pls 7606 2009 4154 Pls 7607 2039 4157 Pls 7608 2069 4160 Pls 7609 2099 4163 Pls 7610 2128 4167 Pls 7611 2158 4170 Pls 7612 2188 4173 Pls 7613 2218 4177 Pls 7614 2247 4180 Pls 7615 2277 4183 Pls 7616 2307 4187 Pls 7617 2336 4190 Pls 7618 2366 4193 Pls 7619 2396 4197 Pls 7620 2426 4200 Pls 7621 2455 4203 Pls 7622 2485 4207 Pls 7623 2515 4210 Pls 7624 2545 4213 Pls 7625 2574 4216 Pls 7626 2604 4220 Pls 7627 2634 4223 Pls 7628 2664 4226 Pls 7629 2693 4230 Pls 7630 2723 4233 Pls 7631 2753 4236 Pls 7632 2783 4240 Pls 7633 2812 4243 Pls 7634 2842 4246 Pls 7635 2872 4250 Pls 7636 2902 4253 Pls 7637 2931 4256 Pls 7638 2961 4260 Pls 7639 2991 4263 Pls 7640 3021 4266 Pls 7641 3050 4269 Pls 7642 3080 4273 Pls 7643 3110 4276 Pls 7644 3139 4279 Pls 7645 3169 4283 Pls 7646 3199 4286 Pls 7647 3229 4289 Pls 7648 3258 4293 Pls 7649 3288 4296 Pls 7650 3318 4299 Pls 7651 3348 4303 Pls 7652 3377 4306 Pls 7653 3407 4309 Pls 7654 3437 4313 Pls 7655 3467 4316 Pls 7656 3496 4319 Pls 7657 3526 4322 Pls 7658 3556 4326 Pls 7659 3586 4329 Pls 7660 3615 4332 Pls 7661 3645 4336 Pls 7662 3675 4339 Pls 7663 3705 4342 Pls 7664 3734 4346 Pls 7665 3764 4349 Pls 7666 3794 4352 Pls 7667 3823 4356 Pls 7668 3853 4359 Pls 7669 3883 4362 Pls 7670 3913 4366 Pls 7671 3942 4369 Pls 7672 3972 4372 Pls 7673 4002 4375 Pls 7674 4032 4379 Pls 7675 4061 4382 Pls 7676 4091 4385 Pls 7677 4121 4389 Pls 7678 4151 4392 Pls 7679 4180 4395 Pls 7680 4210 4399 Pls 7681 4240 4402 Pls 7682 4270 4405 Pls 7683 4299 4409 Pls 7684 4329 4412 Pls 7685 4359 4415 Pls 7686 4389 4419 Pls 7687 4418 4422 Pls 7688 4448 4425 Pls 7689 4478 4429 Pls 7690 4508 4432 Pls 7691 4537 4435 Pls 7692 4567 4438 Pls 7693 4597 4442 Pls 7694 1.000 UL 7695 LTb 7696 6141 1112 M 7697 2574 715 L 7698 1.000 UL 7699 LTb 7700 1059 1652 M 7701 2574 715 L 7702 LTb 7703 5096 680 M 7704 gsave 0 setgray 7705 [ [(default) 120.0 0.0 true true 0 (i)] 7706 ] -40.0 MCshow 7707 grestore 7708 LTb 7709 780 964 M 7710 gsave 0 setgray 7711 [ [(default) 120.0 0.0 true true 0 (100*\(|W|/|N|\))] 7712 ] -40.0 MCshow 7713 grestore 7714 LTb 7715 1058 4287 M 7716 gsave 0 setgray 7717 [ [(default) 120.0 0.0 true true 0 (|N)] 7718 [(default) 96.0 -36.0 true true 0 (i)] 7719 [(default) 120.0 0.0 true true 0 (|)] 7720 ] -28.0 MCshow 7721 grestore 7722 0.600 UP 7723 stroke 7724 grestore 7725 end 7726 showpage 7727 %%Trailer 7728 %%DocumentFonts: default 7729 7730 %%EndDocument 7731 @endspecial 566 3310 a(Fig.)g(2.)g(Simulation)f(results)i(-)f(the)h 7732 (size)f(of)g Fv(N)1887 3322 y Fo(i)1930 3310 y FE(at)g(dif)n(ferent)f 7733 (moments)g(for)h(dif)n(ferent)e(v)n(alues)i(of)1919 3382 7734 y Fh(j)m Fo(W)8 b Fh(j)p 1919 3404 90 4 v 1924 3454 a(j)p 7735 Fo(N)s Fh(j)648 3865 y FE(From)19 b(Figure)g(2)h(one)f(can)g(see)h 7736 (that)g(for)f(some)h(v)n(alues)f(of)2335 3824 y Fh(j)m 7737 Fo(W)8 b Fh(j)p 2335 3846 V 2340 3895 a(j)p Fo(N)s Fh(j)2455 7738 3865 y FE(anon)o(ymity)17 b(set)k(remains)e(small)523 7739 3980 y(for)j(all)i Fv(i)p FE(.)g(Then)e(there)g(is)i(a)g(cut-of)n(f)d 7740 (point)i(where)f Fm(j)p Fv(N)2085 3992 y Fo(i)2107 3980 7741 y Fm(j)h FE(starts)h(to)f(gro)n(w)g(until)f(it)i(reaches)f(a)g(stable) 7742 523 4096 y(le)n(v)o(el.)d(This)g(le)n(v)o(el)g(depends)f(on)1476 7743 4055 y Fh(j)m Fo(W)8 b Fh(j)p 1476 4077 V 1481 4126 a(j)p 7744 Fo(N)s Fh(j)1576 4096 y FE(,)21 b(just)f(as)h(predicted)e(before)g 7745 (\(see)h(Figure)g(1\).)648 4266 y(Figure)27 b(3)i(presents)f(planar)f 7746 (visualization)h(of)g(the)g(same)h(simulation)e(for)h 7747 Fm(j)l Fv(W)10 b Fm(j)23 b Fs(=)g FE(0)p Ft(:)p FE(4)13 7748 b Fm(\001)i(j)p Fv(N)5 b Fm(j)p FE(,)523 4366 y(0)p Ft(:)p 7749 FE(5)14 b Fm(\001)g(j)p Fv(N)5 b Fm(j)p FE(,)24 b(0)p 7750 Ft(:)p FE(6)14 b Fm(\001)g(j)p Fv(N)5 b Fm(j)p FE(,)25 7751 b(0)p Ft(:)p FE(7)14 b Fm(\001)g(j)p Fv(N)5 b Fm(j)p 7752 FE(,)24 b(0)p Ft(:)p FE(8)14 b Fm(\001)g(j)p Fv(N)5 b 7753 Fm(j)p FE(,)24 b(0)p Ft(:)p FE(9)14 b Fm(\001)g(j)p Fv(N)5 7754 b Fm(j)p FE(.)24 b(At)i(this)h(point)d(our)h(aim)h(is)g(to)g(con)m 7755 (vince)d(the)523 4466 y(reader)28 b(that)h(there)f(is)i(qualitati)n(v)o 7756 (e)e(gap)f(between)h(anon)o(ymity)f(for)h(these)h(v)n(alues)f(of)h 7757 (parameter)523 4565 y Fm(j)l Fv(W)10 b Fm(j)33 b FE(and)f(relation)g 7758 (between)g(sizes)h(of)f Fm(j)l Fv(W)10 b Fm(j)33 b FE(and)f(the)h(a)n 7759 (v)o(erage)e(size)i(of)f Fv(N)2770 4577 y Fo(i)2825 4565 7760 y FE(is)h(not)p 2913 4579 107 4 v 33 w(linear)-5 b(.)32 7761 b(F)o(or)523 4665 y Fm(j)l Fv(W)10 b Fm(j)24 b Fs(=)f 7762 FE(0)p Ft(:)p FE(4)14 b Fm(\001)h(j)p Fv(N)5 b Fm(j)p 7763 FE(,)30 b(0)p Ft(:)p FE(5)14 b Fm(\001)g(j)p Fv(N)5 b 7764 Fm(j)31 b FE(the)e(anon)o(ymity)e(set)j(has)f(a)h(v)o(ery)e(small)i 7765 (size)g(e)n(v)o(en)e(if)i(some)f(small)523 4764 y(de)n(viations)19 7766 b(occur)-5 b(.)p eop end 7767 %%Page: 11 11 7768 TeXDict begin 11 10 bop 589 2215 a @beginspecial 80 @llx 7769 80 @lly 410 @urx 302 @ury 3300 @rwi @setspecial 7770 %%BeginDocument: 4-5-7case.eps 7771 %!PS-Adobe-2.0 EPSF-2.0 7772 %%Title: 4-5-7case.eps 7773 %%Creator: gnuplot 4.0 patchlevel 0 7774 %%CreationDate: Fri Apr 1 23:36:38 2005 7775 %%DocumentFonts: (atend) 7776 %%BoundingBox: 50 50 410 302 7777 %%Orientation: Portrait 7778 %%EndComments 7779 /gnudict 256 dict def 7780 gnudict begin 7781 /Color false def 7782 /Solid false def 7783 /gnulinewidth 5.000 def 7784 /userlinewidth gnulinewidth def 7785 /vshift -40 def 7786 /dl {10.0 mul} def 7787 /hpt_ 31.5 def 7788 /vpt_ 31.5 def 7789 /hpt hpt_ def 7790 /vpt vpt_ def 7791 /Rounded false def 7792 /M {moveto} bind def 7793 /L {lineto} bind def 7794 /R {rmoveto} bind def 7795 /V {rlineto} bind def 7796 /N {newpath moveto} bind def 7797 /C {setrgbcolor} bind def 7798 /f {rlineto fill} bind def 7799 /vpt2 vpt 2 mul def 7800 /hpt2 hpt 2 mul def 7801 /Lshow { currentpoint stroke M 7802 0 vshift R show } def 7803 /Rshow { currentpoint stroke M 7804 dup stringwidth pop neg vshift R show } def 7805 /Cshow { currentpoint stroke M 7806 dup stringwidth pop -2 div vshift R show } def 7807 /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def 7808 /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def 7809 /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } 7810 {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse } def 7811 /BL { stroke userlinewidth 2 mul setlinewidth 7812 Rounded { 1 setlinejoin 1 setlinecap } if } def 7813 /AL { stroke userlinewidth 2 div setlinewidth 7814 Rounded { 1 setlinejoin 1 setlinecap } if } def 7815 /UL { dup gnulinewidth mul /userlinewidth exch def 7816 dup 1 lt {pop 1} if 10 mul /udl exch def } def 7817 /PL { stroke userlinewidth setlinewidth 7818 Rounded { 1 setlinejoin 1 setlinecap } if } def 7819 /LTw { PL [] 1 setgray } def 7820 /LTb { BL [] 0 0 0 DL } def 7821 /LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def 7822 /LT0 { PL [] 1 0 0 DL } def 7823 /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def 7824 /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def 7825 /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def 7826 /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def 7827 /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def 7828 /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def 7829 /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def 7830 /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def 7831 /Pnt { stroke [] 0 setdash 7832 gsave 1 setlinecap M 0 0 V stroke grestore } def 7833 /Dia { stroke [] 0 setdash 2 copy vpt add M 7834 hpt neg vpt neg V hpt vpt neg V 7835 hpt vpt V hpt neg vpt V closepath stroke 7836 Pnt } def 7837 /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V 7838 currentpoint stroke M 7839 hpt neg vpt neg R hpt2 0 V stroke 7840 } def 7841 /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 7842 0 vpt2 neg V hpt2 0 V 0 vpt2 V 7843 hpt2 neg 0 V closepath stroke 7844 Pnt } def 7845 /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M 7846 hpt2 vpt2 neg V currentpoint stroke M 7847 hpt2 neg 0 R hpt2 vpt2 V stroke } def 7848 /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M 7849 hpt neg vpt -1.62 mul V 7850 hpt 2 mul 0 V 7851 hpt neg vpt 1.62 mul V closepath stroke 7852 Pnt } def 7853 /Star { 2 copy Pls Crs } def 7854 /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 7855 0 vpt2 neg V hpt2 0 V 0 vpt2 V 7856 hpt2 neg 0 V closepath fill } def 7857 /TriUF { stroke [] 0 setdash vpt 1.12 mul add M 7858 hpt neg vpt -1.62 mul V 7859 hpt 2 mul 0 V 7860 hpt neg vpt 1.62 mul V closepath fill } def 7861 /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M 7862 hpt neg vpt 1.62 mul V 7863 hpt 2 mul 0 V 7864 hpt neg vpt -1.62 mul V closepath stroke 7865 Pnt } def 7866 /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M 7867 hpt neg vpt 1.62 mul V 7868 hpt 2 mul 0 V 7869 hpt neg vpt -1.62 mul V closepath fill} def 7870 /DiaF { stroke [] 0 setdash vpt add M 7871 hpt neg vpt neg V hpt vpt neg V 7872 hpt vpt V hpt neg vpt V closepath fill } def 7873 /Pent { stroke [] 0 setdash 2 copy gsave 7874 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 7875 closepath stroke grestore Pnt } def 7876 /PentF { stroke [] 0 setdash gsave 7877 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 7878 closepath fill grestore } def 7879 /Circle { stroke [] 0 setdash 2 copy 7880 hpt 0 360 arc stroke Pnt } def 7881 /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def 7882 /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def 7883 /C1 { BL [] 0 setdash 2 copy moveto 7884 2 copy vpt 0 90 arc closepath fill 7885 vpt 0 360 arc closepath } bind def 7886 /C2 { BL [] 0 setdash 2 copy moveto 7887 2 copy vpt 90 180 arc closepath fill 7888 vpt 0 360 arc closepath } bind def 7889 /C3 { BL [] 0 setdash 2 copy moveto 7890 2 copy vpt 0 180 arc closepath fill 7891 vpt 0 360 arc closepath } bind def 7892 /C4 { BL [] 0 setdash 2 copy moveto 7893 2 copy vpt 180 270 arc closepath fill 7894 vpt 0 360 arc closepath } bind def 7895 /C5 { BL [] 0 setdash 2 copy moveto 7896 2 copy vpt 0 90 arc 7897 2 copy moveto 7898 2 copy vpt 180 270 arc closepath fill 7899 vpt 0 360 arc } bind def 7900 /C6 { BL [] 0 setdash 2 copy moveto 7901 2 copy vpt 90 270 arc closepath fill 7902 vpt 0 360 arc closepath } bind def 7903 /C7 { BL [] 0 setdash 2 copy moveto 7904 2 copy vpt 0 270 arc closepath fill 7905 vpt 0 360 arc closepath } bind def 7906 /C8 { BL [] 0 setdash 2 copy moveto 7907 2 copy vpt 270 360 arc closepath fill 7908 vpt 0 360 arc closepath } bind def 7909 /C9 { BL [] 0 setdash 2 copy moveto 7910 2 copy vpt 270 450 arc closepath fill 7911 vpt 0 360 arc closepath } bind def 7912 /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 7913 2 copy moveto 7914 2 copy vpt 90 180 arc closepath fill 7915 vpt 0 360 arc closepath } bind def 7916 /C11 { BL [] 0 setdash 2 copy moveto 7917 2 copy vpt 0 180 arc closepath fill 7918 2 copy moveto 7919 2 copy vpt 270 360 arc closepath fill 7920 vpt 0 360 arc closepath } bind def 7921 /C12 { BL [] 0 setdash 2 copy moveto 7922 2 copy vpt 180 360 arc closepath fill 7923 vpt 0 360 arc closepath } bind def 7924 /C13 { BL [] 0 setdash 2 copy moveto 7925 2 copy vpt 0 90 arc closepath fill 7926 2 copy moveto 7927 2 copy vpt 180 360 arc closepath fill 7928 vpt 0 360 arc closepath } bind def 7929 /C14 { BL [] 0 setdash 2 copy moveto 7930 2 copy vpt 90 360 arc closepath fill 7931 vpt 0 360 arc } bind def 7932 /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill 7933 vpt 0 360 arc closepath } bind def 7934 /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto 7935 neg 0 rlineto closepath } bind def 7936 /Square { dup Rec } bind def 7937 /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def 7938 /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def 7939 /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def 7940 /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def 7941 /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def 7942 /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def 7943 /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill 7944 exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def 7945 /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def 7946 /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 7947 2 copy vpt Square fill 7948 Bsquare } bind def 7949 /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def 7950 /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def 7951 /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill 7952 Bsquare } bind def 7953 /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill 7954 Bsquare } bind def 7955 /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def 7956 /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 7957 2 copy vpt Square fill Bsquare } bind def 7958 /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 7959 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def 7960 /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def 7961 /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def 7962 /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def 7963 /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def 7964 /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def 7965 /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def 7966 /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def 7967 /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def 7968 /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def 7969 /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def 7970 /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def 7971 /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def 7972 /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def 7973 /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def 7974 /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def 7975 /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def 7976 /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def 7977 /DiaE { stroke [] 0 setdash vpt add M 7978 hpt neg vpt neg V hpt vpt neg V 7979 hpt vpt V hpt neg vpt V closepath stroke } def 7980 /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 7981 0 vpt2 neg V hpt2 0 V 0 vpt2 V 7982 hpt2 neg 0 V closepath stroke } def 7983 /TriUE { stroke [] 0 setdash vpt 1.12 mul add M 7984 hpt neg vpt -1.62 mul V 7985 hpt 2 mul 0 V 7986 hpt neg vpt 1.62 mul V closepath stroke } def 7987 /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M 7988 hpt neg vpt 1.62 mul V 7989 hpt 2 mul 0 V 7990 hpt neg vpt -1.62 mul V closepath stroke } def 7991 /PentE { stroke [] 0 setdash gsave 7992 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 7993 closepath stroke grestore } def 7994 /CircE { stroke [] 0 setdash 7995 hpt 0 360 arc stroke } def 7996 /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def 7997 /DiaW { stroke [] 0 setdash vpt add M 7998 hpt neg vpt neg V hpt vpt neg V 7999 hpt vpt V hpt neg vpt V Opaque stroke } def 8000 /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 8001 0 vpt2 neg V hpt2 0 V 0 vpt2 V 8002 hpt2 neg 0 V Opaque stroke } def 8003 /TriUW { stroke [] 0 setdash vpt 1.12 mul add M 8004 hpt neg vpt -1.62 mul V 8005 hpt 2 mul 0 V 8006 hpt neg vpt 1.62 mul V Opaque stroke } def 8007 /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M 8008 hpt neg vpt 1.62 mul V 8009 hpt 2 mul 0 V 8010 hpt neg vpt -1.62 mul V Opaque stroke } def 8011 /PentW { stroke [] 0 setdash gsave 8012 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 8013 Opaque stroke grestore } def 8014 /CircW { stroke [] 0 setdash 8015 hpt 0 360 arc Opaque stroke } def 8016 /BoxFill { gsave Rec 1 setgray fill grestore } def 8017 /BoxColFill { 8018 gsave Rec 8019 /Fillden exch def 8020 currentrgbcolor 8021 /ColB exch def /ColG exch def /ColR exch def 8022 /ColR ColR Fillden mul Fillden sub 1 add def 8023 /ColG ColG Fillden mul Fillden sub 1 add def 8024 /ColB ColB Fillden mul Fillden sub 1 add def 8025 ColR ColG ColB setrgbcolor 8026 fill grestore } def 8027 % 8028 % PostScript Level 1 Pattern Fill routine 8029 % Usage: x y w h s a XX PatternFill 8030 % x,y = lower left corner of box to be filled 8031 % w,h = width and height of box 8032 % a = angle in degrees between lines and x-axis 8033 % XX = 0/1 for no/yes cross-hatch 8034 % 8035 /PatternFill { gsave /PFa [ 9 2 roll ] def 8036 PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate 8037 PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec 8038 gsave 1 setgray fill grestore clip 8039 currentlinewidth 0.5 mul setlinewidth 8040 /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 8041 0 0 M PFa 5 get rotate PFs -2 div dup translate 8042 0 1 PFs PFa 4 get div 1 add floor cvi 8043 { PFa 4 get mul 0 M 0 PFs V } for 8044 0 PFa 6 get ne { 8045 0 1 PFs PFa 4 get div 1 add floor cvi 8046 { PFa 4 get mul 0 2 1 roll M PFs 0 V } for 8047 } if 8048 stroke grestore } def 8049 % 8050 /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont 8051 dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall 8052 currentdict end definefont pop 8053 /MFshow { 8054 { dup 5 get 3 ge 8055 { 5 get 3 eq {gsave} {grestore} ifelse } 8056 {dup dup 0 get findfont exch 1 get scalefont setfont 8057 [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 8058 get exch 4 get {show} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq 8059 {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 8060 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div 8061 dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get 8062 show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop 8063 pop aload pop M} ifelse }ifelse }ifelse } 8064 ifelse } 8065 forall} bind def 8066 /MFwidth {0 exch {dup 3 get{dup dup 0 get findfont exch 1 get scalefont 8067 setfont 6 get stringwidth pop add} {pop} ifelse} forall} bind def 8068 /MLshow { currentpoint stroke M 8069 0 exch R MFshow } bind def 8070 /MRshow { currentpoint stroke M 8071 exch dup MFwidth neg 3 -1 roll R MFshow } def 8072 /MCshow { currentpoint stroke M 8073 exch dup MFwidth -2 div 3 -1 roll R MFshow } def 8074 end 8075 %%EndProlog 8076 gnudict begin 8077 gsave 8078 50 50 translate 8079 0.050 0.050 scale 8080 0 setgray 8081 newpath 8082 (default) findfont 120 scalefont 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true 0 ( 400)] 8141 ] -40.0 MRshow 8142 grestore 8143 1.000 UL 8144 LTb 8145 852 2880 M 8146 63 0 V 8147 6081 0 R 8148 -63 0 V 8149 stroke 8150 780 2880 M 8151 gsave 0 setgray 8152 [ [(default) 120.0 0.0 true true 0 ( 500)] 8153 ] -40.0 MRshow 8154 grestore 8155 1.000 UL 8156 LTb 8157 852 3384 M 8158 63 0 V 8159 6081 0 R 8160 -63 0 V 8161 stroke 8162 780 3384 M 8163 gsave 0 setgray 8164 [ [(default) 120.0 0.0 true true 0 ( 600)] 8165 ] -40.0 MRshow 8166 grestore 8167 1.000 UL 8168 LTb 8169 852 3888 M 8170 63 0 V 8171 6081 0 R 8172 -63 0 V 8173 stroke 8174 780 3888 M 8175 gsave 0 setgray 8176 [ [(default) 120.0 0.0 true true 0 ( 700)] 8177 ] -40.0 MRshow 8178 grestore 8179 1.000 UL 8180 LTb 8181 852 4392 M 8182 63 0 V 8183 6081 0 R 8184 -63 0 V 8185 stroke 8186 780 4392 M 8187 gsave 0 setgray 8188 [ [(default) 120.0 0.0 true true 0 ( 800)] 8189 ] -40.0 MRshow 8190 grestore 8191 1.000 UL 8192 LTb 8193 852 4896 M 8194 63 0 V 8195 6081 0 R 8196 -63 0 V 8197 stroke 8198 780 4896 M 8199 gsave 0 setgray 8200 [ [(default) 120.0 0.0 true true 0 ( 900)] 8201 ] -40.0 MRshow 8202 grestore 8203 1.000 UL 8204 LTb 8205 852 360 M 8206 0 63 V 8207 0 4473 R 8208 0 -63 V 8209 stroke 8210 852 240 M 8211 gsave 0 setgray 8212 [ [(default) 120.0 0.0 true true 0 ( 0)] 8213 ] -40.0 MCshow 8214 grestore 8215 1.000 UL 8216 LTb 8217 1876 360 M 8218 0 63 V 8219 0 4473 R 8220 0 -63 V 8221 stroke 8222 1876 240 M 8223 gsave 0 setgray 8224 [ [(default) 120.0 0.0 true true 0 ( 20)] 8225 ] -40.0 MCshow 8226 grestore 8227 1.000 UL 8228 LTb 8229 2900 360 M 8230 0 63 V 8231 0 4473 R 8232 0 -63 V 8233 stroke 8234 2900 240 M 8235 gsave 0 setgray 8236 [ [(default) 120.0 0.0 true true 0 ( 40)] 8237 ] -40.0 MCshow 8238 grestore 8239 1.000 UL 8240 LTb 8241 3924 360 M 8242 0 63 V 8243 0 4473 R 8244 0 -63 V 8245 stroke 8246 3924 240 M 8247 gsave 0 setgray 8248 [ [(default) 120.0 0.0 true true 0 ( 60)] 8249 ] -40.0 MCshow 8250 grestore 8251 1.000 UL 8252 LTb 8253 4948 360 M 8254 0 63 V 8255 0 4473 R 8256 0 -63 V 8257 stroke 8258 4948 240 M 8259 gsave 0 setgray 8260 [ [(default) 120.0 0.0 true true 0 ( 80)] 8261 ] -40.0 MCshow 8262 grestore 8263 1.000 UL 8264 LTb 8265 5972 360 M 8266 0 63 V 8267 0 4473 R 8268 0 -63 V 8269 stroke 8270 5972 240 M 8271 gsave 0 setgray 8272 [ [(default) 120.0 0.0 true true 0 ( 100)] 8273 ] -40.0 MCshow 8274 grestore 8275 1.000 UL 8276 LTb 8277 6996 360 M 8278 0 63 V 8279 0 4473 R 8280 0 -63 V 8281 stroke 8282 6996 240 M 8283 gsave 0 setgray 8284 [ [(default) 120.0 0.0 true true 0 ( 120)] 8285 ] -40.0 MCshow 8286 grestore 8287 1.000 UL 8288 LTb 8289 1.000 UL 8290 LTb 8291 852 360 M 8292 6144 0 V 8293 0 4536 V 8294 -6144 0 V 8295 852 360 L 8296 LTb 8297 120 2556 M 8298 gsave 0 setgray 8299 currentpoint gsave translate 90 rotate 0 0 moveto 8300 [ [(default) 120.0 0.0 true true 0 (|N)] 8301 [(default) 96.0 -36.0 true true 0 (i)] 8302 [(default) 120.0 0.0 true true 0 (|)] 8303 ] -28.0 MCshow 8304 grestore 8305 grestore 8306 LTb 8307 4284 60 M 8308 gsave 0 setgray 8309 [ [(default) 120.0 0.0 true true 0 (100*\(|W|/|N|\))] 8310 ] -40.0 MCshow 8311 grestore 8312 0.600 UP 8313 1.000 UL 8314 LT0 8315 LTb 8316 6455 4773 M 8317 gsave 0 setgray 8318 [ [(default) 120.0 0.0 true true 0 (|W|=90%n)] 8319 ] -40.0 MRshow 8320 grestore 8321 LT0 8322 6527 4773 M 8323 325 0 V 8324 852 365 M 8325 51 10 V 8326 51 20 V 8327 52 36 V 8328 51 50 V 8329 51 91 V 8330 51 186 V 8331 51 323 V 8332 52 509 V 8333 51 695 V 8334 51 761 V 8335 51 721 V 8336 51 519 V 8337 52 161 V 8338 51 11 V 8339 51 100 V 8340 51 81 V 8341 51 -10 V 8342 52 -5 V 8343 51 55 V 8344 51 -90 V 8345 51 -91 V 8346 51 20 V 8347 52 15 V 8348 51 15 V 8349 51 5 V 8350 51 -50 V 8351 51 65 V 8352 52 111 V 8353 51 -60 V 8354 51 -56 V 8355 51 71 V 8356 51 30 V 8357 52 -126 V 8358 51 10 V 8359 51 -40 V 8360 51 101 V 8361 51 -31 V 8362 52 96 V 8363 51 41 V 8364 51 -36 V 8365 51 -70 V 8366 51 -71 V 8367 52 -10 V 8368 51 -35 V 8369 51 0 V 8370 51 55 V 8371 51 20 V 8372 52 5 V 8373 51 66 V 8374 51 -91 V 8375 51 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8450 gsave 0 setgray 8451 [ [(default) 120.0 0.0 true true 0 (|W|=80%n)] 8452 ] -40.0 MRshow 8453 grestore 8454 LT1 8455 6527 4653 M 8456 325 0 V 8457 852 365 M 8458 51 10 V 8459 51 30 V 8460 52 31 V 8461 51 40 V 8462 51 76 V 8463 51 176 V 8464 51 227 V 8465 52 358 V 8466 51 488 V 8467 51 484 V 8468 51 434 V 8469 51 423 V 8470 52 262 V 8471 51 187 V 8472 51 111 V 8473 51 -11 V 8474 51 192 V 8475 52 -176 V 8476 51 110 V 8477 51 -30 V 8478 51 30 V 8479 51 -126 V 8480 52 -25 V 8481 51 116 V 8482 51 -60 V 8483 51 85 V 8484 51 -100 V 8485 52 95 V 8486 51 -65 V 8487 51 40 V 8488 51 126 V 8489 51 -60 V 8490 52 25 V 8491 51 10 V 8492 51 101 V 8493 51 -126 V 8494 51 -162 V 8495 52 -35 V 8496 51 111 V 8497 51 -25 V 8498 51 40 V 8499 51 -55 V 8500 52 70 V 8501 51 -35 V 8502 51 156 V 8503 51 -96 V 8504 51 -40 V 8505 52 25 V 8506 51 -95 V 8507 51 70 V 8508 51 -10 V 8509 51 -60 V 8510 52 10 V 8511 51 -81 V 8512 51 45 V 8513 51 66 V 8514 51 0 V 8515 52 20 V 8516 51 -136 V 8517 51 20 V 8518 51 172 V 8519 51 -172 V 8520 52 141 V 8521 51 5 V 8522 51 -90 V 8523 51 -61 V 8524 51 0 V 8525 52 96 V 8526 51 -20 V 8527 51 -121 V 8528 51 191 V 8529 51 41 V 8530 52 60 V 8531 51 -25 V 8532 51 60 V 8533 51 -10 V 8534 51 66 V 8535 52 -81 V 8536 51 35 V 8537 51 -60 V 8538 51 15 V 8539 51 -81 V 8540 52 -35 V 8541 51 -70 V 8542 51 65 V 8543 51 161 V 8544 51 -121 V 8545 52 -15 V 8546 51 -40 V 8547 51 -25 V 8548 51 10 V 8549 51 -106 V 8550 52 -10 V 8551 51 91 V 8552 51 20 V 8553 51 25 V 8554 51 76 V 8555 52 25 V 8556 51 75 V 8557 51 21 V 8558 51 -152 V 8559 51 -85 V 8560 stroke 8561 6074 3727 M 8562 52 70 V 8563 51 -70 V 8564 51 60 V 8565 51 -126 V 8566 51 106 V 8567 52 -106 V 8568 51 111 V 8569 51 -30 V 8570 51 75 V 8571 51 -50 V 8572 52 35 V 8573 51 -45 V 8574 51 -5 V 8575 51 50 V 8576 51 31 V 8577 52 -46 V 8578 51 46 V 8579 1.000 UL 8580 LT2 8581 LTb 8582 6455 4533 M 8583 gsave 0 setgray 8584 [ [(default) 120.0 0.0 true true 0 (|W|=70%n)] 8585 ] -40.0 MRshow 8586 grestore 8587 LT2 8588 6527 4533 M 8589 325 0 V 8590 852 365 M 8591 51 0 V 8592 51 5 V 8593 52 0 V 8594 51 10 V 8595 51 0 V 8596 51 5 V 8597 51 10 V 8598 52 31 V 8599 51 25 V 8600 51 80 V 8601 51 96 V 8602 51 51 V 8603 52 95 V 8604 51 131 V 8605 51 257 V 8606 51 147 V 8607 51 322 V 8608 52 323 V 8609 51 373 V 8610 51 242 V 8611 51 146 V 8612 51 -20 V 8613 52 206 V 8614 51 -136 V 8615 51 81 V 8616 51 45 V 8617 51 -25 V 8618 52 20 V 8619 51 -116 V 8620 51 86 V 8621 51 -10 V 8622 51 106 V 8623 52 -5 V 8624 51 -51 V 8625 51 35 V 8626 51 5 V 8627 51 -90 V 8628 52 156 V 8629 51 20 V 8630 51 -156 V 8631 51 -66 V 8632 51 71 V 8633 52 -111 V 8634 51 161 V 8635 51 86 V 8636 51 -45 V 8637 51 -101 V 8638 52 -76 V 8639 51 30 V 8640 51 132 V 8641 51 35 V 8642 51 70 V 8643 52 21 V 8644 51 15 V 8645 51 -222 V 8646 51 -10 V 8647 51 70 V 8648 52 -20 V 8649 51 66 V 8650 51 -66 V 8651 51 10 V 8652 51 -40 V 8653 52 -91 V 8654 51 232 V 8655 51 40 V 8656 51 -15 V 8657 51 10 V 8658 52 -156 V 8659 51 -15 V 8660 51 -45 V 8661 51 10 V 8662 51 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8807 51 -86 V 8808 51 0 V 8809 51 5 V 8810 51 192 V 8811 52 45 V 8812 51 -20 V 8813 51 -65 V 8814 51 -101 V 8815 51 70 V 8816 52 10 V 8817 51 -5 V 8818 51 46 V 8819 51 70 V 8820 51 56 V 8821 52 -5 V 8822 51 -121 V 8823 51 10 V 8824 51 -41 V 8825 51 36 V 8826 stroke 8827 6074 1837 M 8828 52 75 V 8829 51 -30 V 8830 51 71 V 8831 51 25 V 8832 51 5 V 8833 52 10 V 8834 51 50 V 8835 51 -35 V 8836 51 -30 V 8837 51 -91 V 8838 52 -131 V 8839 51 197 V 8840 51 105 V 8841 51 6 V 8842 51 -46 V 8843 52 -96 V 8844 51 -65 V 8845 1.000 UL 8846 LT4 8847 LTb 8848 6455 4293 M 8849 gsave 0 setgray 8850 [ [(default) 120.0 0.0 true true 0 (|W|=50%n)] 8851 ] -40.0 MRshow 8852 grestore 8853 LT4 8854 6527 4293 M 8855 325 0 V 8856 852 365 M 8857 51 10 V 8858 51 -5 V 8859 52 0 V 8860 51 15 V 8861 51 -10 V 8862 51 0 V 8863 51 0 V 8864 52 10 V 8865 51 30 V 8866 51 31 V 8867 51 0 V 8868 51 25 V 8869 52 -51 V 8870 51 6 V 8871 51 10 V 8872 51 5 V 8873 51 25 V 8874 52 -35 V 8875 51 -21 V 8876 51 46 V 8877 51 0 V 8878 51 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0 V 8956 51 20 V 8957 51 -10 V 8958 51 -5 V 8959 stroke 8960 6074 431 M 8961 52 -5 V 8962 51 -11 V 8963 51 0 V 8964 51 -5 V 8965 51 21 V 8966 52 -21 V 8967 51 -15 V 8968 51 -5 V 8969 51 -15 V 8970 51 5 V 8971 52 15 V 8972 51 10 V 8973 51 5 V 8974 51 41 V 8975 51 -15 V 8976 52 0 V 8977 51 15 V 8978 1.000 UL 8979 LT5 8980 LTb 8981 6455 4173 M 8982 gsave 0 setgray 8983 [ [(default) 120.0 0.0 true true 0 (|W|=40%n)] 8984 ] -40.0 MRshow 8985 grestore 8986 LT5 8987 6527 4173 M 8988 325 0 V 8989 852 365 M 8990 51 0 V 8991 51 0 V 8992 52 5 V 8993 51 0 V 8994 51 15 V 8995 51 15 V 8996 51 -20 V 8997 52 10 V 8998 51 0 V 8999 51 5 V 9000 51 -15 V 9001 51 0 V 9002 52 5 V 9003 51 15 V 9004 51 -15 V 9005 51 0 V 9006 51 5 V 9007 52 0 V 9008 51 -10 V 9009 51 0 V 9010 51 -5 V 9011 51 -10 V 9012 52 0 V 9013 51 15 V 9014 51 5 V 9015 51 10 V 9016 51 -5 V 9017 52 5 V 9018 51 36 V 9019 51 -16 V 9020 51 0 V 9021 51 21 V 9022 52 -10 V 9023 51 -11 V 9024 51 5 V 9025 51 -15 V 9026 51 -5 V 9027 52 0 V 9028 51 10 V 9029 51 -5 V 9030 51 5 V 9031 51 0 V 9032 52 -5 V 9033 51 -10 V 9034 51 5 V 9035 51 15 V 9036 51 5 V 9037 52 11 V 9038 51 -16 V 9039 51 -10 V 9040 51 0 V 9041 51 -5 V 9042 52 -10 V 9043 51 0 V 9044 51 -5 V 9045 51 10 V 9046 51 15 V 9047 52 -15 V 9048 51 -5 V 9049 51 -10 V 9050 51 25 V 9051 51 -5 V 9052 52 -15 V 9053 51 0 V 9054 51 10 V 9055 51 -20 V 9056 51 0 V 9057 52 -10 V 9058 51 5 V 9059 51 -5 V 9060 51 0 V 9061 51 10 V 9062 52 5 V 9063 51 0 V 9064 51 -5 V 9065 51 10 V 9066 51 -10 V 9067 52 5 V 9068 51 5 V 9069 51 15 V 9070 51 0 V 9071 51 -20 V 9072 52 5 V 9073 51 0 V 9074 51 -5 V 9075 51 0 V 9076 51 5 V 9077 52 -10 V 9078 51 25 V 9079 51 0 V 9080 51 5 V 9081 51 -15 V 9082 52 0 V 9083 51 10 V 9084 51 31 V 9085 51 5 V 9086 51 -16 V 9087 52 0 V 9088 51 -10 V 9089 51 5 V 9090 51 -5 V 9091 51 21 V 9092 stroke 9093 6074 431 M 9094 52 -5 V 9095 51 -11 V 9096 51 -25 V 9097 51 -10 V 9098 51 5 V 9099 52 -5 V 9100 51 -10 V 9101 51 0 V 9102 51 -5 V 9103 51 0 V 9104 52 10 V 9105 51 -5 V 9106 51 -5 V 9107 51 5 V 9108 51 -5 V 9109 52 5 V 9110 51 -5 V 9111 1.000 UL 9112 LTb 9113 852 360 M 9114 6144 0 V 9115 0 4536 V 9116 -6144 0 V 9117 852 360 L 9118 0.600 UP 9119 stroke 9120 grestore 9121 end 9122 showpage 9123 %%Trailer 9124 %%DocumentFonts: default 9125 9126 %%EndDocument 9127 @endspecial 556 2551 a FE(Fig.)20 b(3.)h(The)e(size)i(of)f 9128 Fv(N)1234 2563 y Fo(i)1276 2551 y FE(for)g(the)g(same)h(simulations)e 9129 (-)i(the)f(results)g(for)g(dif)n(ferent)e(v)n(alues)i(of)3272 9130 2510 y Fh(j)m Fo(W)8 b Fh(j)p 3272 2532 90 4 v 3277 2581 9131 a(j)p Fo(N)s Fh(j)523 3244 y Fw(4.4)82 b(Statistical)19 9132 b(analysis)523 3842 y FE(So)g(f)o(ar)f(we)h(were)g(concerned)d(with)i 9133 (the)h(size)g(of)f Fv(N)1973 3854 y Fo(i)2014 3842 y 9134 FE(only)-5 b(,)17 b(ignoring)g(probability)f(distrib)n(ution)h(that)523 9135 3941 y(for)24 b(each)g(message)g(from)f Fv(N)1367 3953 9136 y Fo(i)1414 3941 y FE(describes)g(the)i(chance)e(that)h(it)h(is)h(the)e 9137 (message)g(sent)h(by)f(Alice.)g(It)523 4041 y(turns)e(out)h(that)g 9138 (this)g(probability)e(distrib)n(ution)g(is)j(highly)e(nonuniform.)d 9139 (This)k(property)d(reduces)523 4141 y(anon)o(ymity)e(le)n(v)o(el)i(of)f 9140 (the)i(protocol)d(e)n(v)o(en)h(more.)648 4327 y(W)-7 9141 b(e)30 b(consider)e(the)h(case:)h Fv(n)23 b Fs(=)g FE(1000)28 9142 b(and)h(the)g(situation)g(after)g(20)g(steps.)g(Figure)g(4)g(sho)n(ws) 9143 523 4426 y(the)c(probabilities)e(mentioned)g(for)h(the)g(case)h(when)20 9144 b Fv(W)31 b Fs(=)21 b Fv(N)5 b FE(,)25 b(after)f(sorting)g(them.)g(The) 9145 g(dashed)523 4526 y(line)i(sho)n(ws)g(probability)e(of)i(the)f(message) 9146 h(from)f(Alice.)h(As)h(one)e(can)h(e)o(xpect,)f(the)h(probability)523 9147 4625 y(distrib)n(ution)e(is)j(not)e(completely)g(uniform)e(\226)j(each) 9148 f(probability)f(depends)g(on)i(the)f(number)f(and)523 9149 4725 y(location)16 b(of)g(paths)h(leading)e(from)h(Alice)h(to)g(each)f 9150 (position)g(after)g(step)h(20.)f(It)h(is)g(not)g(a)g(big)f(surprise)523 9151 4825 y(that)31 b(the)f(message)h(of)f(Alice)h(is)g(in)g(a)g(position)f 9152 (that)g(is)i(hard)d(to)i(guess)g(from)e(the)i(probability)523 9153 4924 y(distrib)n(ution.)p eop end 9154 %%Page: 12 12 9155 TeXDict begin 12 11 bop 523 2557 a @beginspecial 50 @llx 9156 50 @lly 410 @urx 302 @ury 3600 @rwi @setspecial 9157 %%BeginDocument: probability100.eps 9158 %!PS-Adobe-2.0 EPSF-2.0 9159 %%Title: probability100.eps 9160 %%Creator: gnuplot 4.0 patchlevel 0 9161 %%CreationDate: Fri Apr 1 23:36:38 2005 9162 %%DocumentFonts: (atend) 9163 %%BoundingBox: 50 50 410 302 9164 %%Orientation: Portrait 9165 %%EndComments 9166 /gnudict 256 dict def 9167 gnudict begin 9168 /Color false def 9169 /Solid false def 9170 /gnulinewidth 5.000 def 9171 /userlinewidth gnulinewidth def 9172 /vshift -40 def 9173 /dl {10.0 mul} def 9174 /hpt_ 31.5 def 9175 /vpt_ 31.5 def 9176 /hpt hpt_ def 9177 /vpt vpt_ def 9178 /Rounded false def 9179 /M {moveto} bind def 9180 /L {lineto} bind def 9181 /R {rmoveto} bind def 9182 /V {rlineto} bind def 9183 /N {newpath moveto} bind def 9184 /C {setrgbcolor} bind def 9185 /f {rlineto fill} bind def 9186 /vpt2 vpt 2 mul def 9187 /hpt2 hpt 2 mul def 9188 /Lshow { currentpoint stroke M 9189 0 vshift R show } def 9190 /Rshow { currentpoint stroke M 9191 dup stringwidth pop neg vshift R show } def 9192 /Cshow { currentpoint stroke M 9193 dup stringwidth pop -2 div vshift R show } def 9194 /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def 9195 /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def 9196 /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } 9197 {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse } def 9198 /BL { stroke userlinewidth 2 mul setlinewidth 9199 Rounded { 1 setlinejoin 1 setlinecap } if } def 9200 /AL { stroke userlinewidth 2 div setlinewidth 9201 Rounded { 1 setlinejoin 1 setlinecap } if } def 9202 /UL { dup gnulinewidth mul /userlinewidth exch def 9203 dup 1 lt {pop 1} if 10 mul /udl exch def } def 9204 /PL { stroke userlinewidth setlinewidth 9205 Rounded { 1 setlinejoin 1 setlinecap } if } def 9206 /LTw { PL [] 1 setgray } def 9207 /LTb { BL [] 0 0 0 DL } def 9208 /LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def 9209 /LT0 { PL [] 1 0 0 DL } def 9210 /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def 9211 /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def 9212 /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def 9213 /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def 9214 /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def 9215 /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def 9216 /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def 9217 /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def 9218 /Pnt { stroke [] 0 setdash 9219 gsave 1 setlinecap M 0 0 V stroke grestore } def 9220 /Dia { stroke [] 0 setdash 2 copy vpt add M 9221 hpt neg vpt neg V hpt vpt neg V 9222 hpt vpt V hpt neg vpt V closepath stroke 9223 Pnt } def 9224 /Pls { stroke [] 0 setdash 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vpt -1.62 mul V closepath stroke 9252 Pnt } def 9253 /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M 9254 hpt neg vpt 1.62 mul V 9255 hpt 2 mul 0 V 9256 hpt neg vpt -1.62 mul V closepath fill} def 9257 /DiaF { stroke [] 0 setdash vpt add M 9258 hpt neg vpt neg V hpt vpt neg V 9259 hpt vpt V hpt neg vpt V closepath fill } def 9260 /Pent { stroke [] 0 setdash 2 copy gsave 9261 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 9262 closepath stroke grestore Pnt } def 9263 /PentF { stroke [] 0 setdash gsave 9264 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 9265 closepath fill grestore } def 9266 /Circle { stroke [] 0 setdash 2 copy 9267 hpt 0 360 arc stroke Pnt } def 9268 /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def 9269 /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def 9270 /C1 { BL [] 0 setdash 2 copy moveto 9271 2 copy vpt 0 90 arc closepath fill 9272 vpt 0 360 arc closepath } bind def 9273 /C2 { BL [] 0 setdash 2 copy moveto 9274 2 copy vpt 90 180 arc closepath fill 9275 vpt 0 360 arc closepath } bind def 9276 /C3 { BL [] 0 setdash 2 copy moveto 9277 2 copy vpt 0 180 arc closepath fill 9278 vpt 0 360 arc closepath } bind def 9279 /C4 { BL [] 0 setdash 2 copy moveto 9280 2 copy vpt 180 270 arc closepath fill 9281 vpt 0 360 arc closepath } bind def 9282 /C5 { BL [] 0 setdash 2 copy moveto 9283 2 copy vpt 0 90 arc 9284 2 copy moveto 9285 2 copy vpt 180 270 arc closepath fill 9286 vpt 0 360 arc } bind def 9287 /C6 { BL [] 0 setdash 2 copy moveto 9288 2 copy vpt 90 270 arc closepath fill 9289 vpt 0 360 arc closepath } bind def 9290 /C7 { BL [] 0 setdash 2 copy moveto 9291 2 copy vpt 0 270 arc closepath fill 9292 vpt 0 360 arc closepath } bind def 9293 /C8 { BL [] 0 setdash 2 copy moveto 9294 2 copy vpt 270 360 arc closepath fill 9295 vpt 0 360 arc closepath } bind def 9296 /C9 { BL [] 0 setdash 2 copy moveto 9297 2 copy vpt 270 450 arc closepath fill 9298 vpt 0 360 arc closepath } bind def 9299 /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 9300 2 copy moveto 9301 2 copy vpt 90 180 arc closepath fill 9302 vpt 0 360 arc closepath } bind def 9303 /C11 { BL [] 0 setdash 2 copy moveto 9304 2 copy vpt 0 180 arc closepath fill 9305 2 copy moveto 9306 2 copy vpt 270 360 arc closepath fill 9307 vpt 0 360 arc closepath } bind def 9308 /C12 { BL [] 0 setdash 2 copy moveto 9309 2 copy vpt 180 360 arc closepath fill 9310 vpt 0 360 arc closepath } bind def 9311 /C13 { BL [] 0 setdash 2 copy moveto 9312 2 copy vpt 0 90 arc closepath fill 9313 2 copy moveto 9314 2 copy vpt 180 360 arc closepath fill 9315 vpt 0 360 arc closepath } bind def 9316 /C14 { BL [] 0 setdash 2 copy moveto 9317 2 copy vpt 90 360 arc closepath fill 9318 vpt 0 360 arc } bind def 9319 /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill 9320 vpt 0 360 arc closepath } bind def 9321 /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto 9322 neg 0 rlineto closepath } bind def 9323 /Square { dup Rec } bind def 9324 /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def 9325 /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def 9326 /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def 9327 /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def 9328 /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def 9329 /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def 9330 /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill 9331 exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def 9332 /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def 9333 /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 9334 2 copy vpt Square fill 9335 Bsquare } bind def 9336 /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def 9337 /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def 9338 /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill 9339 Bsquare } bind def 9340 /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill 9341 Bsquare } bind def 9342 /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def 9343 /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 9344 2 copy vpt Square fill Bsquare } bind def 9345 /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 9346 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def 9347 /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def 9348 /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def 9349 /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def 9350 /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def 9351 /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def 9352 /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def 9353 /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def 9354 /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def 9355 /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def 9356 /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def 9357 /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def 9358 /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def 9359 /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def 9360 /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def 9361 /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def 9362 /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def 9363 /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def 9364 /DiaE { stroke [] 0 setdash vpt add M 9365 hpt neg vpt neg V hpt vpt neg V 9366 hpt vpt V hpt neg vpt V closepath stroke } def 9367 /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 9368 0 vpt2 neg V hpt2 0 V 0 vpt2 V 9369 hpt2 neg 0 V closepath stroke } def 9370 /TriUE { stroke [] 0 setdash vpt 1.12 mul add M 9371 hpt neg vpt -1.62 mul V 9372 hpt 2 mul 0 V 9373 hpt neg vpt 1.62 mul V closepath stroke } def 9374 /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M 9375 hpt neg vpt 1.62 mul V 9376 hpt 2 mul 0 V 9377 hpt neg vpt -1.62 mul V closepath stroke } def 9378 /PentE { stroke [] 0 setdash gsave 9379 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 9380 closepath stroke grestore } def 9381 /CircE { stroke [] 0 setdash 9382 hpt 0 360 arc stroke } def 9383 /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def 9384 /DiaW { stroke [] 0 setdash vpt add M 9385 hpt neg vpt neg V hpt vpt neg V 9386 hpt vpt V hpt neg vpt V Opaque stroke } def 9387 /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 9388 0 vpt2 neg V hpt2 0 V 0 vpt2 V 9389 hpt2 neg 0 V Opaque stroke } def 9390 /TriUW { stroke [] 0 setdash vpt 1.12 mul add M 9391 hpt neg vpt -1.62 mul V 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(simulation)g(of)f(20)h(steps)h(for)f(the)g(case)c Fv(W)29 10879 b Fs(=)18 b Fv(N)648 3870 y FE(Figure)i(5)h(describes)g(the)g 10880 (simulation)g(results)g(for)g(the)g(same)h Fm(j)p Fv(N)5 10881 b Fm(j)19 b Fs(=)f FE(1000,)i(b)n(ut)h(this)h(time)f(the)523 10882 3969 y(size)26 b(of)20 b Fv(W)36 b FE(is)26 b(0)p Ft(:)p 10883 FE(7)p Fv(n)p FE(.)e(In)g(this)i(case)f(the)g(anon)o(ymity)d(set)k 10884 Fv(N)2233 3981 y Fq(20)2325 3969 y FE(is)f(quite)g(big)g(\(near)f 10885 (60\045)g(of)h Fv(N)5 b FE(\),)25 b(so)523 4069 y(\002nding)d 10886 Fv(N)835 4081 y Fq(20)925 4069 y FE(does)h(not)g(help)g(much.)f(Ho)n 10887 (we)n(v)o(er)m(,)f(the)i(actual)h(Alice')-5 b(s)24 b(message)f(is)h(v)o 10888 (ery)e(lik)o(ely)h(to)523 4169 y(be)d(within)g(3\045)h(positions)e 10889 (with)i(the)f(highest)f(probabilities.)648 4526 y(It)j(is)h(w)o(orth)e 10890 (to)h(say)h(that)f(such)f(a)i(reduction)d(of)i(the)g(set)g(of)g 10891 (suspects)g(for)g(being)f(the)h(message)523 4625 y(from)17 10892 b(Alice)h(based)g(on)g(probabilities)f(w)o(orks)g(when)h(we)g(speed)g 10893 (up)f(the)h(computations)e(and)i(deter)n(-)523 4725 y(mine)k(the)h 10894 (probabilities)f(in)h(an)g(incorrect)e(w)o(ay)-5 b(.)22 10895 b(Namely)-5 b(,)22 b(if)h(some)g(message)f(from)g Fv(N)3077 10896 4737 y Fo(i)p Fh(\000)p Fq(1)3200 4725 y FE(lea)n(v)o(es)519 10897 4825 y Fv(W)10 b FE(,)30 b(then)f(we)g(do)g(not)g(recompute)e(the)i 10898 (probabilities)f(of)h(all)h(members)e(of)h(the)g(anon)o(ymity)e(set)523 10899 4924 y(based)20 b(on)g(the)g(routes)f(that)i(ha)n(v)o(e)e(occurred)g 10900 (in)h(the)g(past,)g(b)n(ut)h(simply)e(re-scale)h(all)h(probabilities.)p 10901 eop end 10902 %%Page: 13 13 10903 TeXDict begin 13 12 bop 523 2557 a @beginspecial 50 @llx 10904 50 @lly 410 @urx 302 @ury 3600 @rwi @setspecial 10905 %%BeginDocument: probability.eps 10906 %!PS-Adobe-2.0 EPSF-2.0 10907 %%Title: probability.eps 10908 %%Creator: gnuplot 4.0 patchlevel 0 10909 %%CreationDate: Fri Apr 1 23:36:38 2005 10910 %%DocumentFonts: (atend) 10911 %%BoundingBox: 50 50 410 302 10912 %%Orientation: Portrait 10913 %%EndComments 10914 /gnudict 256 dict def 10915 gnudict begin 10916 /Color false def 10917 /Solid false def 10918 /gnulinewidth 5.000 def 10919 /userlinewidth gnulinewidth def 10920 /vshift -40 def 10921 /dl {10.0 mul} def 10922 /hpt_ 31.5 def 10923 /vpt_ 31.5 def 10924 /hpt hpt_ def 10925 /vpt vpt_ def 10926 /Rounded false def 10927 /M {moveto} bind def 10928 /L {lineto} bind def 10929 /R {rmoveto} bind def 10930 /V {rlineto} bind def 10931 /N {newpath moveto} bind def 10932 /C {setrgbcolor} bind def 10933 /f {rlineto fill} bind def 10934 /vpt2 vpt 2 mul def 10935 /hpt2 hpt 2 mul def 10936 /Lshow { currentpoint stroke M 10937 0 vshift R show } def 10938 /Rshow { currentpoint stroke M 10939 dup stringwidth pop neg vshift R show } def 10940 /Cshow { currentpoint stroke M 10941 dup stringwidth pop -2 div vshift R show } def 10942 /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def 10943 /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def 10944 /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } 10945 {pop pop pop 0 setgray Solid {pop []} if 0 setdash} ifelse } def 10946 /BL { stroke userlinewidth 2 mul setlinewidth 10947 Rounded { 1 setlinejoin 1 setlinecap } if } def 10948 /AL { stroke userlinewidth 2 div setlinewidth 10949 Rounded { 1 setlinejoin 1 setlinecap } if } def 10950 /UL { dup gnulinewidth mul /userlinewidth exch def 10951 dup 1 lt {pop 1} if 10 mul /udl exch def } def 10952 /PL { stroke userlinewidth setlinewidth 10953 Rounded { 1 setlinejoin 1 setlinecap } if } def 10954 /LTw { PL [] 1 setgray } def 10955 /LTb { BL [] 0 0 0 DL } def 10956 /LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def 10957 /LT0 { PL [] 1 0 0 DL } def 10958 /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def 10959 /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def 10960 /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def 10961 /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def 10962 /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def 10963 /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def 10964 /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def 10965 /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def 10966 /Pnt { stroke [] 0 setdash 10967 gsave 1 setlinecap M 0 0 V stroke grestore } def 10968 /Dia { stroke [] 0 setdash 2 copy vpt add M 10969 hpt neg vpt neg V hpt vpt neg V 10970 hpt vpt V hpt neg vpt V closepath stroke 10971 Pnt } def 10972 /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V 10973 currentpoint stroke M 10974 hpt neg vpt neg R hpt2 0 V stroke 10975 } def 10976 /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 10977 0 vpt2 neg V hpt2 0 V 0 vpt2 V 10978 hpt2 neg 0 V closepath stroke 10979 Pnt } def 10980 /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M 10981 hpt2 vpt2 neg V currentpoint stroke M 10982 hpt2 neg 0 R hpt2 vpt2 V stroke } def 10983 /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M 10984 hpt neg vpt -1.62 mul V 10985 hpt 2 mul 0 V 10986 hpt neg vpt 1.62 mul V closepath stroke 10987 Pnt } def 10988 /Star { 2 copy Pls Crs } def 10989 /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 10990 0 vpt2 neg V hpt2 0 V 0 vpt2 V 10991 hpt2 neg 0 V closepath fill } def 10992 /TriUF { stroke [] 0 setdash vpt 1.12 mul add M 10993 hpt neg vpt -1.62 mul V 10994 hpt 2 mul 0 V 10995 hpt neg vpt 1.62 mul V closepath fill } def 10996 /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M 10997 hpt neg vpt 1.62 mul V 10998 hpt 2 mul 0 V 10999 hpt neg vpt -1.62 mul V closepath stroke 11000 Pnt } def 11001 /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M 11002 hpt neg vpt 1.62 mul V 11003 hpt 2 mul 0 V 11004 hpt neg vpt -1.62 mul V closepath fill} def 11005 /DiaF { stroke [] 0 setdash vpt add M 11006 hpt neg vpt neg V hpt vpt neg V 11007 hpt vpt V hpt neg vpt V closepath fill } def 11008 /Pent { stroke [] 0 setdash 2 copy gsave 11009 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 11010 closepath stroke grestore Pnt } def 11011 /PentF { stroke [] 0 setdash gsave 11012 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 11013 closepath fill grestore } def 11014 /Circle { stroke [] 0 setdash 2 copy 11015 hpt 0 360 arc stroke Pnt } def 11016 /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def 11017 /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def 11018 /C1 { BL [] 0 setdash 2 copy moveto 11019 2 copy vpt 0 90 arc closepath fill 11020 vpt 0 360 arc closepath } bind def 11021 /C2 { BL [] 0 setdash 2 copy moveto 11022 2 copy vpt 90 180 arc closepath fill 11023 vpt 0 360 arc closepath } bind def 11024 /C3 { BL [] 0 setdash 2 copy moveto 11025 2 copy vpt 0 180 arc closepath fill 11026 vpt 0 360 arc closepath } bind def 11027 /C4 { BL [] 0 setdash 2 copy moveto 11028 2 copy vpt 180 270 arc closepath fill 11029 vpt 0 360 arc closepath } bind def 11030 /C5 { BL [] 0 setdash 2 copy moveto 11031 2 copy vpt 0 90 arc 11032 2 copy moveto 11033 2 copy vpt 180 270 arc closepath fill 11034 vpt 0 360 arc } bind def 11035 /C6 { BL [] 0 setdash 2 copy moveto 11036 2 copy vpt 90 270 arc closepath fill 11037 vpt 0 360 arc closepath } bind def 11038 /C7 { BL [] 0 setdash 2 copy moveto 11039 2 copy vpt 0 270 arc closepath fill 11040 vpt 0 360 arc closepath } bind def 11041 /C8 { BL [] 0 setdash 2 copy moveto 11042 2 copy vpt 270 360 arc closepath fill 11043 vpt 0 360 arc closepath } bind def 11044 /C9 { BL [] 0 setdash 2 copy moveto 11045 2 copy vpt 270 450 arc closepath fill 11046 vpt 0 360 arc closepath } bind def 11047 /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 11048 2 copy moveto 11049 2 copy vpt 90 180 arc closepath fill 11050 vpt 0 360 arc closepath } bind def 11051 /C11 { BL [] 0 setdash 2 copy moveto 11052 2 copy vpt 0 180 arc closepath fill 11053 2 copy moveto 11054 2 copy vpt 270 360 arc closepath fill 11055 vpt 0 360 arc closepath } bind def 11056 /C12 { BL [] 0 setdash 2 copy moveto 11057 2 copy vpt 180 360 arc closepath fill 11058 vpt 0 360 arc closepath } bind def 11059 /C13 { BL [] 0 setdash 2 copy moveto 11060 2 copy vpt 0 90 arc closepath fill 11061 2 copy moveto 11062 2 copy vpt 180 360 arc closepath fill 11063 vpt 0 360 arc closepath } bind def 11064 /C14 { BL [] 0 setdash 2 copy moveto 11065 2 copy vpt 90 360 arc closepath fill 11066 vpt 0 360 arc } bind def 11067 /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill 11068 vpt 0 360 arc closepath } bind def 11069 /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto 11070 neg 0 rlineto closepath } bind def 11071 /Square { dup Rec } bind def 11072 /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def 11073 /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def 11074 /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def 11075 /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def 11076 /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def 11077 /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def 11078 /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill 11079 exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def 11080 /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def 11081 /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 11082 2 copy vpt Square fill 11083 Bsquare } bind def 11084 /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def 11085 /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def 11086 /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill 11087 Bsquare } bind def 11088 /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill 11089 Bsquare } bind def 11090 /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def 11091 /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 11092 2 copy vpt Square fill Bsquare } bind def 11093 /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 11094 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def 11095 /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def 11096 /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def 11097 /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def 11098 /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def 11099 /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def 11100 /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def 11101 /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def 11102 /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def 11103 /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def 11104 /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def 11105 /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def 11106 /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def 11107 /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def 11108 /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def 11109 /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def 11110 /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def 11111 /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def 11112 /DiaE { stroke [] 0 setdash vpt add M 11113 hpt neg vpt neg V hpt vpt neg V 11114 hpt vpt V hpt neg vpt V closepath stroke } def 11115 /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 11116 0 vpt2 neg V hpt2 0 V 0 vpt2 V 11117 hpt2 neg 0 V closepath stroke } def 11118 /TriUE { stroke [] 0 setdash vpt 1.12 mul add M 11119 hpt neg vpt -1.62 mul V 11120 hpt 2 mul 0 V 11121 hpt neg vpt 1.62 mul V closepath stroke } def 11122 /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M 11123 hpt neg vpt 1.62 mul V 11124 hpt 2 mul 0 V 11125 hpt neg vpt -1.62 mul V closepath stroke } def 11126 /PentE { stroke [] 0 setdash gsave 11127 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 11128 closepath stroke grestore } def 11129 /CircE { stroke [] 0 setdash 11130 hpt 0 360 arc stroke } def 11131 /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def 11132 /DiaW { stroke [] 0 setdash vpt add M 11133 hpt neg vpt neg V hpt vpt neg V 11134 hpt vpt V hpt neg vpt V Opaque stroke } def 11135 /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 11136 0 vpt2 neg V hpt2 0 V 0 vpt2 V 11137 hpt2 neg 0 V Opaque stroke } def 11138 /TriUW { stroke [] 0 setdash vpt 1.12 mul add M 11139 hpt neg vpt -1.62 mul V 11140 hpt 2 mul 0 V 11141 hpt neg vpt 1.62 mul V Opaque stroke } def 11142 /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M 11143 hpt neg vpt 1.62 mul V 11144 hpt 2 mul 0 V 11145 hpt neg vpt -1.62 mul V Opaque stroke } def 11146 /PentW { stroke [] 0 setdash gsave 11147 translate 0 hpt M 4 {72 rotate 0 hpt L} repeat 11148 Opaque stroke grestore } def 11149 /CircW { stroke [] 0 setdash 11150 hpt 0 360 arc Opaque stroke } def 11151 /BoxFill { gsave Rec 1 setgray fill grestore } def 11152 /BoxColFill { 11153 gsave Rec 11154 /Fillden exch def 11155 currentrgbcolor 11156 /ColB exch def /ColG exch def /ColR exch def 11157 /ColR ColR Fillden mul Fillden sub 1 add def 11158 /ColG ColG Fillden mul Fillden sub 1 add def 11159 /ColB ColB Fillden mul Fillden sub 1 add def 11160 ColR ColG ColB setrgbcolor 11161 fill grestore } def 11162 % 11163 % PostScript Level 1 Pattern Fill routine 11164 % Usage: x y w h s a XX PatternFill 11165 % x,y = lower left corner of box to be filled 11166 % w,h = width and height of box 11167 % a = angle in degrees between lines and x-axis 11168 % XX = 0/1 for no/yes cross-hatch 11169 % 11170 /PatternFill { gsave /PFa [ 9 2 roll ] def 11171 PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate 11172 PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec 11173 gsave 1 setgray fill grestore clip 11174 currentlinewidth 0.5 mul setlinewidth 11175 /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def 11176 0 0 M PFa 5 get rotate PFs -2 div dup translate 11177 0 1 PFs PFa 4 get div 1 add floor cvi 11178 { PFa 4 get mul 0 M 0 PFs V } for 11179 0 PFa 6 get ne { 11180 0 1 PFs PFa 4 get div 1 add floor cvi 11181 { PFa 4 get mul 0 2 1 roll M PFs 0 V } for 11182 } if 11183 stroke grestore } def 11184 % 11185 /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont 11186 dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall 11187 currentdict end definefont pop 11188 /MFshow { 11189 { dup 5 get 3 ge 11190 { 5 get 3 eq {gsave} {grestore} ifelse } 11191 {dup dup 0 get findfont exch 1 get scalefont setfont 11192 [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6 11193 get exch 4 get {show} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq 11194 {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5 11195 get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div 11196 dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get 11197 show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop 11198 pop aload pop M} ifelse }ifelse }ifelse } 11199 ifelse } 11200 forall} bind def 11201 /MFwidth {0 exch {dup 3 get{dup dup 0 get findfont exch 1 get scalefont 11202 setfont 6 get stringwidth pop add} {pop} ifelse} forall} bind def 11203 /MLshow { currentpoint stroke M 11204 0 exch R MFshow } bind def 11205 /MRshow { currentpoint stroke M 11206 exch dup MFwidth neg 3 -1 roll R MFshow } def 11207 /MCshow { currentpoint stroke M 11208 exch dup MFwidth -2 div 3 -1 roll R MFshow } def 11209 end 11210 %%EndProlog 11211 gnudict begin 11212 gsave 11213 50 50 translate 11214 0.050 0.050 scale 11215 0 setgray 11216 newpath 11217 (default) findfont 120 scalefont setfont 11218 1.000 UL 11219 LTb 11220 996 360 M 11221 63 0 V 11222 5937 0 R 11223 -63 0 V 11224 stroke 11225 924 360 M 11226 gsave 0 setgray 11227 [ [(default) 120.0 0.0 true true 0 ( 0.002)] 11228 ] -40.0 MRshow 11229 grestore 11230 1.000 UL 11231 LTb 11232 996 772 M 11233 63 0 V 11234 5937 0 R 11235 -63 0 V 11236 stroke 11237 924 772 M 11238 gsave 0 setgray 11239 [ [(default) 120.0 0.0 true true 0 ( 0.004)] 11240 ] -40.0 MRshow 11241 grestore 11242 1.000 UL 11243 LTb 11244 996 1185 M 11245 63 0 V 11246 5937 0 R 11247 -63 0 V 11248 stroke 11249 924 1185 M 11250 gsave 0 setgray 11251 [ [(default) 120.0 0.0 true true 0 ( 0.006)] 11252 ] -40.0 MRshow 11253 grestore 11254 1.000 UL 11255 LTb 11256 996 1597 M 11257 63 0 V 11258 5937 0 R 11259 -63 0 V 11260 stroke 11261 924 1597 M 11262 gsave 0 setgray 11263 [ [(default) 120.0 0.0 true true 0 ( 0.008)] 11264 ] -40.0 MRshow 11265 grestore 11266 1.000 UL 11267 LTb 11268 996 2009 M 11269 63 0 V 11270 5937 0 R 11271 -63 0 V 11272 stroke 11273 924 2009 M 11274 gsave 0 setgray 11275 [ [(default) 120.0 0.0 true true 0 ( 0.01)] 11276 ] -40.0 MRshow 11277 grestore 11278 1.000 UL 11279 LTb 11280 996 2422 M 11281 63 0 V 11282 5937 0 R 11283 -63 0 V 11284 stroke 11285 924 2422 M 11286 gsave 0 setgray 11287 [ [(default) 120.0 0.0 true true 0 ( 0.012)] 11288 ] -40.0 MRshow 11289 grestore 11290 1.000 UL 11291 LTb 11292 996 2834 M 11293 63 0 V 11294 5937 0 R 11295 -63 0 V 11296 stroke 11297 924 2834 M 11298 gsave 0 setgray 11299 [ [(default) 120.0 0.0 true true 0 ( 0.014)] 11300 ] -40.0 MRshow 11301 grestore 11302 1.000 UL 11303 LTb 11304 996 3247 M 11305 63 0 V 11306 5937 0 R 11307 -63 0 V 11308 stroke 11309 924 3247 M 11310 gsave 0 setgray 11311 [ [(default) 120.0 0.0 true true 0 ( 0.016)] 11312 ] -40.0 MRshow 11313 grestore 11314 1.000 UL 11315 LTb 11316 996 3659 M 11317 63 0 V 11318 5937 0 R 11319 -63 0 V 11320 stroke 11321 924 3659 M 11322 gsave 0 setgray 11323 [ [(default) 120.0 0.0 true true 0 ( 0.018)] 11324 ] -40.0 MRshow 11325 grestore 11326 1.000 UL 11327 LTb 11328 996 4071 M 11329 63 0 V 11330 5937 0 R 11331 -63 0 V 11332 stroke 11333 924 4071 M 11334 gsave 0 setgray 11335 [ [(default) 120.0 0.0 true true 0 ( 0.02)] 11336 ] -40.0 MRshow 11337 grestore 11338 1.000 UL 11339 LTb 11340 996 4484 M 11341 63 0 V 11342 5937 0 R 11343 -63 0 V 11344 stroke 11345 924 4484 M 11346 gsave 0 setgray 11347 [ [(default) 120.0 0.0 true true 0 ( 0.022)] 11348 ] -40.0 MRshow 11349 grestore 11350 1.000 UL 11351 LTb 11352 996 4896 M 11353 63 0 V 11354 5937 0 R 11355 -63 0 V 11356 stroke 11357 924 4896 M 11358 gsave 0 setgray 11359 [ [(default) 120.0 0.0 true true 0 ( 0.024)] 11360 ] -40.0 MRshow 11361 grestore 11362 1.000 UL 11363 LTb 11364 1541 360 M 11365 0 63 V 11366 0 4473 R 11367 0 -63 V 11368 stroke 11369 1541 240 M 11370 gsave 0 setgray 11371 [ [(default) 120.0 0.0 true true 0 ( 10)] 11372 ] -40.0 MCshow 11373 grestore 11374 1.000 UL 11375 LTb 11376 2148 360 M 11377 0 63 V 11378 0 4473 R 11379 0 -63 V 11380 stroke 11381 2148 240 M 11382 gsave 0 setgray 11383 [ [(default) 120.0 0.0 true true 0 ( 20)] 11384 ] -40.0 MCshow 11385 grestore 11386 1.000 UL 11387 LTb 11388 2754 360 M 11389 0 63 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(random)e(v)n(ariable)h(Bin)p Fs(\()p FE(29)p Ft(;)9 11765 b FE(30)p Ft(=)p FE(1000)p Fs(\))k(+)g FE(1)20 b(and)j(has)523 11766 4008 y(e)o(xpected)j(v)n(alue)i(about)f(2.)h(Of)g(course,)f(it)i(does)f 11767 (not)g(help)f(Alice,)h(if)h(she)f(sends)g(the)g(messages)523 11768 4107 y(through)18 b(dif)n(ferent)h(routes.)523 4426 y 11769 Fv(Model)g(e)n(xtension)38 b FE(So)20 b(f)o(ar)f(we)g(ha)n(v)o(e)g 11770 (assumed)f(that)i(all)f(serv)o(ers)g(e)o(xcept)f(Alice)h(choose)g(the)g 11771 (inter)n(-)523 4526 y(mediate)j(serv)o(ers)f(uniformly)f(at)j(random)d 11772 (from)h(the)h(whole)g(set)h Fv(N)5 b FE(.)23 b(Ho)n(we)n(v)o(er)m(,)d 11773 (one)i(can)g(see)g(that)523 4625 y(essentially)f(the)f(same)h(attack)f 11774 (can)g(be)h(used)f(with)h(high)e(probability)g(if)i(the)f(sets)i(of)e 11775 (intermediate)523 4725 y(serv)o(ers)h(of)g(the)g(users)h(are)f(chosen)g 11776 (in)g(a)h(stochastically)f(independent)e(w)o(ay)-5 b(.)20 11777 b(On)i(the)f(other)g(hand,)523 4825 y(if)30 b(Alice)g(shares)f(the)h 11778 (same)f(set)i(of)e(intermediate)f(serv)o(ers)h(with)g(other)g(users,)h 11779 (then)f(at)h(least)g(it)523 4924 y(becomes)19 b(hard)h(to)g 11780 (distinguish)f(between)h(them.)p eop end 11781 %%Page: 14 14 11782 TeXDict begin 14 13 bop 523 448 a Fx(5)99 b(Countermeasur)n(es)27 11783 b(and)f(Conclusions)523 634 y FE(A)i(common)d(intuition)i(is)h(that)f 11784 (in)h(order)e(to)h(achie)n(v)o(e)f(a)i(better)f(le)n(v)o(el)g(of)g 11785 (anon)o(ymity)e(each)i(user)523 733 y(should)18 b(use)i(as)g(man)o(y)e 11786 (serv)o(ers)h(as)h(possible)g(for)e(choosing)g(intermediate)g(serv)o 11787 (ers)h(on)g(anon)o(ymity)523 833 y(paths.)24 b(Ho)n(we)n(v)o(er)m(,)f 11788 (in)h(lar)o(ge)g(and)g(dynamic)f(netw)o(orks)g(this)i(will)h(lead)e 11789 (ine)n(vitably)f(to)i(a)g(situation)523 932 y(that)k(dif)n(ferent)f 11790 (users)h(will)i(use)e(dif)n(ferent)f(sets)i(of)f(serv)o(ers.)f(Some)h 11791 (of)g(them)g(will)h(stay)g(behind)523 1032 y(and)f(use)h(relati)n(v)o 11792 (ely)e(fe)n(w)h(serv)o(ers)g(and)g(some)g(will)h(be)f(f)o(ast)h(in)g 11793 (changes)e(and)h(use)h(a)g(lar)o(ger)e(set)523 1132 y(of)23 11794 b(serv)o(ers.)g(As)h(we)g(ha)n(v)o(e)f(sho)n(wn,)f(both)p 11795 1569 1146 148 4 v 23 w(cases)i(are)f(dangerous.)e(The)i(threats)h(do)f 11796 (not)g(disappear)523 1231 y(e)n(v)o(en)c(if)i(the)g(sizes)g(of)f(the)h 11797 (sets)g(used)f(by)g(dif)n(ferent)f(users)i(are)f(the)g(same:)h(if)g(a)g 11798 (set)g(of)f(serv)o(ers)g(used)523 1331 y(by)j(a)i(user)e(is)i 11799 (\223independent\224)c(from)i(the)g(sets)i(used)f(by)f(the)h(other)f 11800 (users,)h(then)f(the)h(same)g(attack)523 1431 y(applies.)648 11801 1530 y(The)f(problems)g(may)g(be)h(a)n(v)n(oided)f(if)h(the)g(sets)h 11802 (of)e(serv)o(ers)g(used)h(by)f(dif)n(ferent)g(users)h(are)f(the)523 11803 1630 y(same.)18 b(Ho)n(we)n(v)o(er)m(,)f(it)i(is)g(hard)e(to)i(achie)n 11804 (v)o(e)e(in)i(a)f(dynamic,)f(lar)o(ge)h(scale)g(netw)o(ork)g(without)f 11805 (a)i(central)523 1729 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FB(http://theory.lcs.mit.edu/\230rivest/)695 11833 3484 y(voting/papers/Chaum-)t(SecretBallotReceiptsTrueVoterVerifiab)q 11834 (leElectio)q(ns.)695 3576 y(pdf)598 3663 y FD(4.)41 b(Czumaj,)36 11835 b(A.,)f(Kanarek,)h(P)-8 b(.,)35 b(K)o(uty\007o)n(wski,)h(M.,)f(Lory)r 11836 (\264)-27 b(s)36 b(K.:)f(Distrib)o(uted)h(Stochastic)f(Processes)695 11837 3755 y(for)28 b(Generating)h(Random)h(Permutations.)e(A)m(CM-SIAM)g 11838 (Symposium)h(on)g(Discrete)f(Algorithms)695 3846 y(\(SOD)m(A\))18 11839 b('99,)h(271-280)598 3934 y(5.)41 b(Danezis,)24 b(G.,)g(Serjanto)o(v)g 11840 (A.:)f(T)-6 b(o)n(w)o(ards)25 b(an)f(Information)h(Theoretic)f(Metric)g 11841 (for)g(Anon)o(ymity)-5 b(.)25 b(Pri-)695 4025 y(v)n(ac)o(y)h(Enhancing) 11842 g(T)-5 b(echnologies)26 b(2002,)g(Lecture)f(Notes)f(in)h(Computer)h 11843 (Science)f(2482,)g(Springer)o(-)695 4116 y(V)-8 b(erlag:)19 11844 b(41-53)598 4204 y(6.)41 b(Danezis,)29 b(G.,)e(Serjanto)o(v)-5 11845 b(,)28 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b(eb)19 b(Security)g(5\(1997\):)h(237-248)p eop end 11860 %%Page: 15 15 11861 TeXDict begin 15 14 bop 560 448 a FD(10.)42 b(Gomu\007kie)n(wicz,)16 11862 b(M.,)g(Klono)n(wski,)g(M.,)f(K)o(uty\007o)n(wski,)h(M.:)f(Pro)o(v)n 11863 (able)h(Unlinkability)g(Against)f(T)m(raf)n(\002c)695 11864 540 y(Analysis)22 b(Already)g(After)f Fc(O)5 b Fb(\()p 11865 FD(log)q Fb(\()p Fa(n)p Fb(\)\))42 b FD(Steps!)21 b(Information)i 11866 (Security)e(Conference)h(2005,)h(Lecture)695 631 y(Notes)c(in)g 11867 (Computer)h(Science)f(3381,)h(Springer)o(-V)-8 b(erlag:)18 11868 b(229-238)560 722 y(11.)42 b(Jak)o(obsson,)20 b(M.,)e(Juels,)g(A.:)f 11869 (Mix)i(and)f(Match:)h(Secure)f(Function)h(Ev)n(aluation)g(via)f 11870 (Cipherte)o(xts.)g(Ad-)695 814 y(v)n(ances)f(in)f(Cryptology)h(-)e 11871 (Asiacrypt)h(2000,)h(Lecture)e(Notes)h(in)f(Computer)i(Science)f(1976,) 11872 g(Springer)o(-)695 905 y(V)-8 b(erlag:)19 b(162\226177)560 11873 996 y(12.)42 b(K)n(esdogan,)k(D.,)f(Egner)m(,)g(J.,)f(B)6 11874 b(\250)-31 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