,the ,golden ,mean ,golden ,ratio       
7#asqrt7#e77_/b    to #bjjjj places4    
,this etext also contains these         
mathematical items3      ,catalan       
evaluation    #agjjjj digits of gamma or
 ,euler constant    ,the ,artin's       
,constant    ,the ,backhouse ,constant  
,zeta7#c7 or ,apery ,constant           
,zeta7#a1b7 or the derivative of ,zeta  
function at #b    ,feigenbaum reduction 
parameter    ,feigenbaum bifurcation    
velocity constant    ,franson-,robinson 
constant    ,the ,gauss-,kusmin-,wirsing
 constant    ,khinchin constant         
,landau-,ramanujan constant    ,the twin
 primes constant    ,the ,lengyel       
constant    ,the ,levy constant         
,the golden ratio3 7#asqrt7#e77_/b to   
#bjjjj places4                          
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hijdjfaghdfiiafffedagdhejhdeigigjadfagh 

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fcdgaaaafhfgdbhaggcaiejbefjfdbieafcgiei 

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hafbdeiegdagicbfihhibcbgbbjffffcfjhaiib 
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didhicaceiffjcjdbdchjhjdefeiddgdcccefgh 
#cafgbgjcgbifcfcfgeidbafiiicgiebb       
----------------------------------------
--------------------------------------  
,as calculated by ,greg ,fee using      
,maple ,release #c  standard ,catalan   
evaluation4 ,this implementation  uses  
#a bit_/term series of ,ramanujan4      
,calculated on ,april #be #aiif in      
approx4 #aj hours  of ,,cpu on a ,,sgi  
,r#djjj machine4      ,to do the same on
 your machine just type this4           
catalan 3 evalf7,catalan1#ejajj73       
bytes used#cgefighbgdh1 alloc#ecgbifh1  
time#chjgh4ie    here are the #ejjjj    
digits 7#ajjj lines of #ej digits each74
        ,it comes from formula #cd4a of 
page #bic of ,ramanujan ,notebooks1     
part ,i1 the series used is by putting  

x-- -#a_/b 4  ,in other  words the      
formula used is3 the ordinary formula   
for ,catalan                            
sum77-#a799997n#a7_/7b99n#a79999b1n#j44;
infinity7 and then you apply  the ,euler
 ,transform to it3 ref3 ,abramowitz     
,stegun page #af4  ,the article of ,greg
 ,fee that took those formulas appear in
  ,computation of ,catalan's constant   
using ,ramanujan's ,formula1 by  ,greg  
,fee1 ,,acm #aiij1 ,proceedings of the  
,,isaac conference1 #aiij  7,,maybe     
#aihi71 held in ,tokyo4        catalan 3
                                        
#j4                                     
#iaeifeeidaggbaijaejedfjceadicbchdaajggd
adicgdbhafg                             
#bacdbffdihaaifbagfcjaiggfbedgfidgicefea
bibfaaeajfb                             
#dhegddbbfaiaifaiiegijcehihhjccbeheijeid
caeidgcgdha                             
#aehdjfiieccbjbhggccaidfjeaijchgbgdghafd
jhghfeijijb                             
#dgjfdhdaebafcjjjbbhgbgfdjidbchhbeiieggd
aejhhafcigd                             

#gjbebdhbjaaefjgjgfddhhchjghgccgjdhiijjh
fdggeaacbbe                             
#iigacdcdjgdhedjgeecbcjgfhefeccegfhjiehc
ebfjbaichbc                             
#bciejhjjgbjfhjceegfajdhbcegccidbcaiadih
bihcfahiigg                             
#jfijcfdjdahjhfbagidaajaiagecbgdcadiighb
ccigfajeeab                             
#bdggiecjcbdhgecgahghffehbhjhbcfjegjbbee
idaidhahjig                             
#ecejigaacaegabfaehjdbdbgbcfcfdcihejjagc
hbhgeiggigf                             
#ecjfhcgjjibihjhgchhgdiefajhicfeiggaidji
fhgbfhdddda                             
#ffhjdfbafbdccihfdhchiafbhjddhbhaejfbgcj
bbgdbjgchhd                             
#caagbbahbgbaijdgbbeehgjecaijhfhegcedbcd
ihecidihcji                             
#iaiaaeifgchhdfdejhfaeaebdiifbdbcgjdcgde
agggcgbceag                             
#geddjgjhechdfddjacbagdhcibiiiidgegbddfa
iigedifaige                             
#hgjfdjjgdgdhgjgjadijicgfghhgcjdehfiigih
fjfddhgdigd                             
#fdchgbjfbcheacgabcibgcfcjdiihejcecibbci

bhghgigijfc                             
#cfddjcbcedghdeceheaibggggghgbgjijfjhcjc
aiidcjaccbc                             
#afgabdgfaehgjigibdeedgiaaijibabfbjahedh
jcifcicdbdc                             
#diefecgeifgcididcedgcjjadcheahjgjejeabe
jgdhhfacbhe                             
#fdabicddieiejbbihgbbihcafbhidhafdfafbbe
gcihidgfbca                             
#haiedbjjffjgahhadbgeidigeeiiehihcfcgcjc
gfgecchecch                             
#acedejcabgfhagbdjaahadjgbaecdfhhcafhcef
hafhfcicbgb                             
#icfggehffgcibehciedjfahjccchghcjfhgjfdi
jadccdhfjag                             
#bihajfiibagiiefecjiehahgaegiaaeeciefjcf
fhijcfiijdi                             
#ciffgechdcggehajdicahiieecheeafbfbaifbe
ccafhjdjafb                             
#gcgebacjabjidjfjdechgiejgfjechbgabcaigd
fgijjhhbcfi                             
#aghfaeegcchiabddagbbchccichadhabjggeiid
bihdiagbdci                             
#gffhegefcbgahjfhhjhbgiihbigicghhdidcbgb
dicdfegfjgd                             

#ijedchgdhaiebfhacjgddcgjdfbidfcehibhajb
gfecagjejgf                             
#edgigddidhciidhieidggjibghheiaaiehdhgbd
abghffjhdjh                             
#heedeighbchabdibbfjejefajjidehddhffihie
hegfhgafaaa                             
#gaghfffbccfhdgdjiidicheedacbajicgeebhah
aeebehhaeia                             
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bbcfghigjea                             
#ibfigaacabegacgededcgjabdcbifgcjegbdfhd
ejaehaicacj                             
#afjhggffbaefejiegeedfgifffghffagjhbcdgf
hbeehacceah                             
#fhaicggdefejjadefebfagjdjifjgdfhhiecicj
bcdgiaihjfj                             
#jjhdbdeefbageajhdbcdgagcfchghgicfiegghg
hddjiccgibb                             
#aihidegecdjifafdgdbdeedfbbdghghhjjbibbi
adhjcfijgaa                             
#ebgjgieedeejedadghbfhhdihahebdfjjehaddf
feaghfhadbc                             
#aedaadhgheedjiiffeafgchecigbgfadfigjafi
jdciaeaadij                             
#jhicccjgiahdegdfegfbjiifggedhabcachbjae

dcfjajihheb                             
#gbafbiggjajhgfaegdghagcefdafcfihegjceec
djfgbfdicea                             
#ifcafieedgfgbaaejgggbcaeijjddhcchbfjeaf
aafchcdcjhf                             
#eacigigbbeafagdachechabicbdhjaaidfcfbea
hhjjhdjciha                             
#ideecijeeahbajdbdfjfbibahebagefjbdfedhf
jaibigfgbci                             
#gdjeaajciebfdefibdbighfdbabdbdjcgeahibf
ghgbifjbgag                             
#gccghgchcgiighcbffgfbjhfaaiebjfgiabaeab
fchbaaibebc                             
#bidjdjfibjeiidchfdbgdficbaecchheffgaagc
cjhbgadbdjh                             
#ccbfeibjcbfjgecafeibhjdbcajbcjiigcehdjj
cieidjcdbfc                             
#bbbgfhhjgjaahfhaifagfghjijefcaehaeighde
cgfcgeghcef                             
#cgceijbggafdhhcacajbhhgficgiejecejgcbjh
jahjgehajbb                             
#chbcjhjcagfbejdcbidbdgbbbfhciabbigabiee
ceaceeajdca                             
#dgfahhffeedgdcfgfibahdabjahhggafagiibbh
efbjefcebbj                             

#edgjcbjjfiahjhfhhjffabaagdbjdjfjiibdabc
dhgfjeaedjf                             
#hbjbbfbeeiejdhabdhehidaahgcehcdfhbbijdb
cjhcfaeeedg                             
#fidggggjhcaidjhgdhabdiafgdhibijjfeicfif
afdaffbcdcf                             
#hcgjgedcifchchideaddjaaieefdhgchacdbiba
bbihbjjacjb                             
#ajgiifaibbdbdibddicjeaiiibcehehaehjhbfj
cebdigiihej                             
#eiahffigbbjabcafdhigajdhcjgjagicebhaabb
bhiffceeabh                             
#cagdcgcebcicjaadjbgibchihjhgddefifdhcji
jacbjghggfe                             
#hghecfbcjacedbhjjjafbijeehggbiejjfgiehg
faghbdgcgdh                             
#gacghjfjjdbbjhddecdfjdejfdgjbddcbehjhea
fdgggagcijc                             
#aifjbhfeeechcbhbhadaeiaebdhgcebfccjgaej
eacadghhbhd                             
#diiibchffcbdcaihajfccfeaebdccaacbadfcij
jicccfbaeia                             
#fjgdddhbibcdegaggdedhagafiehjahafhhijja
gebhefdejdf                             
#dhiacijijdbjcefjbihcfjdefebdbebfegigbgj

achehfgegfe                             
#chiicjbiehddibehfibahighhfddchhhaicehaa
debfggjefca                             
#fjfjigcgfhdfedjhcfidbcjbjchafhbfcibdehe
giajgdjdhgj                             
#hgihgghebdbfadjhfhgaeaghegehjajjfjbcfha
gjcdiagiggc                             
#cfbbaiffbiecggahiachecaafgciifeefehheia
bafdfbhjaee                             
#hbfbihgcedacgfccfjgfjgcjbjjdeeiabjbidff
egcdgegaheb                             
#gdecaafcchdgggfdhfhchbdhejdaafcjafjebbg
jhfiddddbgj                             
#cfddbeabdbcfcigahadiiibcdifjhchieiafhbe
hjcfafdgdih                             
#hajdbfcidhchijjdbidjeejdcaejbaicabfhfdb
cjjeiiibibf                             
#cfaedjfdibfbffdahfehceidijdbdicgaebcfbb
jfhdjcidjcg                             
#jajhfhjgdjjihddjjjaeabdfecdcecejfgbcchd
edfidfcegfj                             
#baahfgfbaadcdadbdgfaaghcdajdcabgcjfaafg
hbbdhhccifi                             
#iaeecijiacajigcbcajffghaaagdheecgfgijbg
bcahdejgfed                             

#eggefiihhgdaaciefhfadffcaehacfaegcfgdjf
ahhaabeiadf                             
#bjcigdbcdjaabehhbacaefijgeagegedigifehb
bifhihdfbca                             
#cbibegbgcagecchcjbcaceccbcbhgjjefeiefhh
ecdagebjdeg                             
#cicbgehahceacihbcdgfghjjibfadbfebajgdga
jdefffhgfca                             
#cdcbeffgbgeibihiaiebedhhdijcghjijdfedfd
hhbfhegebjd                             
#dedfiejechacdihcjijbadfjdhigahcaichgghj
hfcdjijadaf                             
#hbhedhdebdbdhjicajdcdcbaggbdghhgghbdhgc
idhfjfahjjb                             
#ccdaebbeiadadfachghbgjjedeagjigadajdegf
effadibhiec                             
#ajhfgbdhfjhjdhdbjdcgffcgicfbcjbacfdehag
gihjbbgbjhh                             
#bgchjgagcfgaabiihbbbhijfiabegfcjbgggiaf
bfeajcegfbe                             
#ggjchajdbhhfhjcgfjedfcfcjcccgidjcfgcggf
ifgddgegaga                             
#iahgabhjciedcgjiffdachggbbffbfhhihcgcaa
aaafjbjjdea                             
#heicigcagdgfdfbaedbhchdfjafbaddebfeecgb

jbibeebjeae                             
#jdidahbhjjcjcbeejbfgegijchbebghfacifcce
gbgbjfejhij                             
#cfghbjagfbehegcfcffjbdeifddiadeccebhada
jcgbeafhchb                             
#bjijjigajaidcfhjbghccfgjhifccadfgbdigcb
iejciaibeib                             
#iheadiffdaddihebahgcchdcgjabdeagdfgdbah
gabacaajbje                             
#gbfagdcdjacdjefhgfeeeajdahghffeddeahijb
gfejjechbag                             
#hfjidabajecechiighdijeihbahjjbcjfghijhb
afjfadacfgj                             
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hjhcgihjbjg                             
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fbigjcjbcee                             
#ceiccgchfiggahcbhceccgeegbfbcdddaeffdia
fjjegfbffff                             
#jdaiijhebgfghigjcejdaicbieeedefhgdecchh
dbabacjdhgi                             
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cdhecejecjf                             
#fabecifjbeecfbhjhjicejefbefbhbacdgdcbci
dciibbbddbg                             

#cigaaefbgeeihebddcciajdabfahjdccejfihga
cdajdbhjigh                             
#defhfieahiggffhhhbfejejcgefafgeiaecedgc
agcffhacefh                             
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ahaijafacee                             
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ibghghhdbbg                             
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eibejaaefcj                             
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jecaejbbcje                             
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aihecbbdbab                             
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hecbafgfhji                             
#ejfaicdafgbhfbhdfgdgeccjgbaajjeeaahedbb
egehfbibibf                             
#hadjfchafjbdfacgfiebjdcbghfgghebceaidjh
igdhggiiehh                             
#bfbfeajahhegafgebfddhifdbeieafbdefjhafd
fhjehfffbfj                             
#ehddcbhbhaecgffibjiejagjjacafiajichfdci
adgjjcccdei                             
#jfgjahfhgiibdfdhcajiahaheehdhajdfcaaahi

edgfgbehcjc                             
#ffhibbfegaafiijefedcageiihhfhjbhfgcaade
hgcdegedigg                             
#gddjefbbfehdaccgibdgdbgahhgjjghbfheedfe
fghbbijccfd                             
#fbeaechihihdhacjcchbhdhhjaeghhjffdfihdd
hjbagaffidi                             
#chagaciihefaghggagcghgghgabgciifihcdbfg
diiigafcbbf                             
#hcbgbegigbegbaaedbbhbbdgaeheagedheajejg
gigjifaefjg                             
#ahcgjggachciihbfecafcfecgfgehabdgeahghc
ihcejdegehh                             
#caagijgeeedefhffagcieibhgbieehgaichfbai
bbcegchgfdc                             
#hfjgjagdjajeiceigddbghehadaabgaciefhjej
difabfiifjj                             
#dhdcdehchifdcffigjadggaadjcbiaghjfejhdi
behgcjjhbji                             
#ijfagiehgehjdjbiiffahbibjbahbjfifaeegde
fbhhajihjbb                             
#cegfaieafcifghfgfbffjigcfgiedibcdcghiae
dajjahegbhi                             
#hihafhcghehdbgcjcfabddhdefecbdbfcecdhca
dhibeejfdhj                             

#ghbaihbgjeahcffefbacgchjibcfieijggebaea
fihcdfebfaj                             
#cbcggchdaejhihcjfehacfdhgacjiahbcachccf
jjeeibbedjj                             
#agebfbghgdbabdehbfbebhbcgjhdaedijfhbcca
gfebefhfbdf                             
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fichaigbheb                             
#gcfabfciahbbiefdhbdcdfijdbhjcjcehbfhcbi
cegcibgicda                             
#ddifbeebhbgfdcfahdccedbfbjffdacdfhcaefc
gjbbbfcbhgf                             
#hcijhgijjeigaffccbehjffdccajiehhahabgec
bdhfbghibih                             
#jjidhfhaehijbdebgadfibdajhahcidcacjcdia
fhgccfigfeh                             
#aaeaidjbbggccihjjiedjaiiibebaeadcdifjgc
dadgdecijci                             
#bcjdaaiijhiifdjcijgfjcbiafeaaaibieeajbh
fffgdadhghh                             
#hadfcgjghjjeebabdheefcfjahaabgbjidbfacj
ihechjadedj                             
#faecaehedbbffdfbehdcdafadbeiejadhbcfhic
ffcffgceedb                             
#hcbgbjjfcgfjgdijahajhahbbadcdjhfaigciaa

edhcbheddch                             
#dcaehaaiagcdigbbhjagjdagbdeiegbigaffjhj
iebhebbbajd                             
#gaeabchehcjjefjafcgbafghacagihjjjiegbef
cefgbjeihei                             
#dacfjabeifdgggjdijjbhhagjfhjfcjfhiddcic
hjijdbjffbg                             
#daafdahbhdijhhaeacbceeefgfhfbcfcjaadiae
cfaehcecjai                             
#bieahffidjhbfffhhjfjgagddcbigbaihijhgja
iejjccdedbg                             
#acjicfcbadhjhigidgecaigfccejhghjfjjfgce
adehjahhdbb                             
#bdaadgehdcefhdeieiefdbjabcibgdfbhhibfdc
ahegjificag                             
#ejghadccaibgfhceacjiaaihgdidaibcgfegjee
cbafjagfbda                             
#bbfacifgeiegjcddhjdijcadjgbgegigggffbhd
caejefeeabg                             
#gcichedfcbhieigbdbaibibfdfiiajgheehcbjh
higabccjeai                             
#bbhiggagbfjbdhaigjecgaifhcbciahhjajbfgg
eehefehdebi                             
#hiajadjcaajeejfhcfehcegdhhcbcgdhadedcee
fgfffahjehc                             

#ccjfdihidbciciidchhcgiifebifcbedjajaigi
ifcdadfdbhg                             
#hbbhccggbefbiffafhdfiaagbjabahbhffadgdd
jdjgggceeia                             
#ihibdajgeabcabfjjbjdbdefajhieibbiicacih
bjfjagabaca                             
#abcdchjhifgcgegejadcaijacggchajehhadbjj
hjfhehcbfhc                             
#dhhfjhceiaigcieehfdhdecfcbjhedhbicebfjj
geadfjeecgc                             
#aedjefhjgiaeaajajdhfghedbjdejbdcaghdhab
aggfdjfiffd                             
#afeddffhfaibcibajcehbcjhiiddbgggefaagce
egbffbbdabe                             
#jggbdcfjggbfjaagdeegbhcdccjfjcahajehiij
djghjaiahgd                             
#dijjidibedjabgigdhbhfibdahhfahhheceggbc
fahigaiccgc                             
#hbeidgdijefigjgeecdebjaaecaedjbgcccaahb
hcggigfabdg                             
#agjaejegfbegjfdfeebifgiihigahbbcjhgchad
bbfgdceggdh                             
#ebjdidieaeedicjaaecabbcgcdigiigehbegfah
bjbhcagedde                             
#babadcaacfgijiadbgjhhhajhdcdbchifaehcfe

gfegcdhhdhh                             
#fiijahigbheeajeficdefcgeefaigacfbcefhje
ajdcccgehbd                             
#fjdghcgdjfgafbijejifiabbjecjidificdbbgc
fdehhhfafah                             
#jgdigcbbedjbijfebfeaegcgdbjhddafifejbhf
hbaibhifhgg                             
#hjahbjbbiafgjihageaibfcjbiaffjgeefjeddf
cajegfjgeji                             
#hbjghdabbjcgdfijiddjcdhabcbffiabebaegab
dccjhgjajce                             
#cghijcdijjjijffdcbibfdcgbeggigejbdahbdc
cjbhdcghjib                             
#ajhddhjeacaddifcgdejdejgbjhbaagbhhebcgi
icidijdhfbf                             
#achaiibebbjebcicjfgbgcficjeicebagfcgbaf
fahhijdaidb                             
#ghddadfijhiicgfdijahdhegacgidbidebcggjd
acjbejajdge                             
#fihhfhedjicjdccfecgjcjbicfgfiebjiefchbg
gaggjdecdga                             
#icbijfiifdgdihcgihbdabbgfigfjidccajgidj
hehdjcajedi                             
#abacacddfifbgegebccaccgcbaajhjcjiibdbeg
hhefehjdajd                             

#jjgihcaffaideefigjaeiiiagfbahhghffddgai
dcagedfiiaf                             
#digdaebjbeahjfddhhgghhgiheaffifffijejah
jfifaagghie                             
#caifgggfeeaaiieacfeghceebifbbhegefgijbe
gbachfjcced                             
#afjhhigihdfieeigbafjegacgagcdeighbibeae
jacaadfjjig                             
#ijbcgcjgbdabjcfcedccehhcddhghajcfcfejbe
baeccgeaedb                             
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chdbcjfgdac                             
#ejfigcibchedhhdaacfdbgdccchdhiiahjchbjg
feabceeicge                             
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hiecfgjcegi                             
#eghcgahgadabibgieahbcaifggejggjebgcjadc
eeffhijihgg                             
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jacgjgdffcf                             
#jjdcigffhdbcbajggbeddjcggibdjgdaiabaggj
aihidbhfaed                             
#eccjaehdbeacahceahbjhaacghaiachaedbcedb
aeeifjhchii                             
#fgjhefbieafhiebfbfgaiiciffdjegcdaicjiad

hijihahdida                             
#dhbahhdaahajaghadbcgdeegcejihhdhhhbehae
idbjdefcaih                             
#dbbcbadcfjcagdjicdjgacefagfghjijadcdgih
fiidaijegie                             
#hidceeeehcjgejgjjigbhhcghgibdijfeccddja
bdfhcjeejbj                             
#jhgjejhgcfdefecjieeegiagjgafbbiiidcgifb
cgggfcaijef                             
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hjjdcabiegh                             
#gebaddfggifddiifjeaahjjjcdbdfgbebdeheie
cibjcbjdfgj                             
#hhjhhighicagedaagidicbbdihacjhiiefdahch
biecghgaejc                             
#ggfadfcfbfbeheaabchjafjficehjgdabfigchh
ddjdjcjdjig                             
#cijhdehcacgiadbdfbijiaefdhdjieefheabfbf
icajcjeheaa                             
#bibjjehdfdjafeidgfjbhdgfeebdjhfajfjeaia
jbbfdehfcje                             
#djedjcbfcdgiajbhagdiabbggfaecffhjifbjah
hfbghccadba                             
#bjfddhjeeiadbhjhcbihgcdaahdadcfjggaffjf
jhgcajhaidi                             

#hdhdhddibhaeadgfhehifcciaedhjideacchjee
eiiigejacdf                             
#iafgfghhccfebcaihecjecehchfccccecbicebd
ibicjejcajj                             
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adfdjgfbeij                             
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bicidbihhed                             
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ddgajgffeai                             
#ehgedgahdehbcdghegcbdcdcfhedhhccghchgai
iefagjgfdhc                             
#febchaehaggehhbajffhgfiaaiigchdchhhgiid
fhdabghcaai                             
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gbeachfcgfe                             
#edfbdeifbiibgjbifjhghbibhdeaebbgecfjgfh
acifajciefg                             
#jhbhhadfhjccciibfchdihhcheaeagcfiijfagj
fjjfffcbjjf                             
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abhhhafhdec                             
#gicbebbgejdfeighgfhhifccjiegccdajfjafdf
eiehecihdcf                             
#ibjgdbgeadifaajbgdcjgabfdfifgfaeahcficg

jhfehbjbfbg                             
#gjeabjiedbicjdciadcedgifeiahbfjgbhhigjj
aahgeagcdej                             
#bifjfejiaihejjacficcfbhdfhcidfabjcjbdge
jchigedcehi                             
#jhcjghfabiacdfjhhihcfdjfdhejddhegjaefei
fgggfbgidfd                             
#aedahjcebegcdjeacfcdheecbabiiejhddjibfh
ifabcajidjg                             
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jjcjfbaiiih                             
#hghcahjcicaigjdbibabbdiejfgfadbbijjbbaj
gaebibceaji                             
#cdhejhfgegaijdcccijeaahidficbjcdhhaadie
bidjcjcjhia                             
#fjiadiebjihaccjbfgagegjbdaggfgdggjbjdhd
fefdgiggihd                             
#chghhicejhicghjcbjgjajddcgghefigddjbdag
eecgjdfegaj                             
#ihdfgeijiahcjbbaeigefhdhfbagbajachgjhhb
ebedcbhijfi                             
#headdfbibahaegbchjechfagibcfcefcfihcehg
jfddjhjifcb                             
#iaafehefceiefadceichfcdfbhbbchaifabbbja
cefedfiffgc                             

#ibhhbbjggahhhejhcjfaiejaiaefdebjafbihee
dbachfdchfd                             
#ccgfaiicadechcfeahfhiahbehagffdgjbgjfbc
gecfgchbcgj                             
#higjbjfgbajgijjfgicfjahefhbjdfbiaehggbb
bheiefjfjdj                             
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heigbbddddg                             
#ghciibhaefeefbjhhecdhchbfiddbehadjjfiac
hjbdgcfadfb                             
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cgjdgjhjijh                             
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djgfbfhdgci                             
#hiaajfabcibfaddjbjdecahigibghbjdhjgfahd
ihjigdbahef                             
#ajdaideigbbafdbbhahifeaigcadbfijbajecce
chejghbfibb                             
#hjcbfhaijehifddhfihibfaggecfehadgjhfehi
ejcahegjfgb                             
#ehdcibdiabffdfibaeefeieibadfccehdagabea
bgjgheefdji                             
#gccabggibccjhcddaahjjiagbaaicadhbfjccaf
dgbddjbhecj                             
#iecaaccdafhjacfbgfhcdjchjfefhdciefbbdij

ajfdcgjdidi                             
#jhfgaafbcgjajacbcicfcccedjccacjcdhbidff
abddbbiahcb                             
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egcdeadceih                             
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bdbahdjdfch                             
#ejebdibbdjbbidbaebebabbbaigdffbghijhibb
dbfcjcebdfg                             
#afecgfghhcccfafafadhigjcgbddchaadhihdha
aegjdfjfgdc                             
#hehhegjiefebbgiaghcbbfegifhhhbffaccbcbf
gbijjaejece                             
#jchbajgafbjedjhfjhgeeddbidgaejdabaicccj
ghcfddjecge                             
#hcjdicbhgjeadcejaeacjdhbdeaidedigehejcd
icebjebeieg                             
#haagbcdghjbidjjahdfbdgfibjideihfidhdfif
jhhjibfaghg                             
#aagceafcbjfhahjbhhaihifbfagdfcbbafjbiae
gfccfhficdb                             
#efggaediegiidfcjgdfajdjediicjdfcbfiacag
ddihabbeejc                             
#fhbcbfggajaiabcdiifajggibdhcfdhfgddeieb
ffgebcjehac                             

#gjbejdhjcfbdfeehbbdffbhiajhihjcaajjceeg
hehfddhjhhj                             
#igdjfehdifjbiihadefhbaehdafgabbfbagdidh
hccdcgbdjig                             
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aiibifaeddc                             
#iicceebihbhaebcjgeihjijhhhjdcjcfjjchgie
ffcbabijjcg                             
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agcdgchbebg                             
#ihfgeahgighbebidejfgbfegjeecbdhfbhcbfbf
efgaieigfcc                             
#bbbbcgbgajajgcdcdgibfgbifdaefedfbdggced
hbiedghjidi                             
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icihebfcbgc                             
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gjieejadgbj                             
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bffgjiedfif                             
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hbgajcjceag                             
#bgchgbgfhhbcdhdbffebbebjffddjhhggabibhd
afaehjdhhfg                             
#ddacccdcbeaaedjcgaiihhedhcfcigdiaddjhfg

ifaadajdgeb                             
#fedhajeibbciadjbhagaigbibihjcjehhgagicd
ecbebbjjcbb                             
#ejagdbbabcdbddiifbgbeighiiidjgiecechibj
fejdaiadaac                             
#eigbjgbahjcjgahajhjdhbhfehdhabddjigjcef
cgfaagfbihg                             
#cfhhbagjheafhjiceahdibjgfdaficaefacachd
jeaaecbdibh                             
#fedjidbfbcjadedafjacccdffbbdfdgiebagbgh
jfebagejfce                             
#abbgjchbihiebagidecdfebiiddecbjiecbfdca
ajhgcaijehd                             
#fgcehghccefbdbhdegijbhahijecbedbcfgjihj
figgcefagij                             
#djbagbbccbbfebiffjheccdefgjhgcgdhidedgf
dgcbeibbhfc                             
#ghjdjdfdedchabccdaajhccjddaabcachhffjej
igdegehfdea                             
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igadgajdejf                             
#gjhfcahajbhgejcebjhcgcbdabdidbjibeadehf
caihgfjbiif                             
#dehdeciabcaefcfahejaagjjgdhddhgdhdbhbih
bebbbfbdcig                             

#ahbaeaagcbaecdbhjdajgahdahgigdicgdiiihe
chiadfcabib                             
#gjfbehfcifcfchjhfjdgjfeggcdcdjgjgdagcbc
gbhaciideib                             
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dcjhbbdjfbi                             
#efjiaibecagafdebbfbchjdfadbhccaihicjjcj
cghhfdbafid                             
#fdbbhgfciajbcdehdidaiehejciijacfhgaebhb
eahdjbbgjab                             
#ggiejdijjggjcbjfgigbbdeegfgbfdidgahicbi
ebjgeagfdjd                             
#bjfdbecbggghfeiechgfbagaeadfbaifjbadedf
jhffbfhajaf                             
#cgcbehddaiebiggfjedbgafddiafibgcbbhjdga
eaibhbbadia                             
#eiefcgejbaidifgbehiabdefcjbeaffbacggbij
jhhcajfchhi                             
#gaieggcahdgabgffjifgjegfhcaeafidjhdhgjg
ebgffcjbfdb                             
#gacffhgifdgjdfcefgfacdeihdgiagfedbebbeg
hbbaajjibcj                             
#iieddgbbegeaibcjgjfhfcabdagejfgadhahiei
dgchicdejgi                             
#jcigfcdchejjdiaihfbadhhaceffigdffagbdcg

bfbajcgjhfa                             
#jidiffjaecibjegefbghhcjhhdcjhabfcafeghg
ccbdbgiggij                             
#baiedibaeadjbcffhhajfdahebjaigcgjjbbfac
dddheceddcc                             
#gfgjaihhaaiheicgbcgdbhbebeggagfabjhhhfb
ijeigbiiega                             
#debhbeigiddddcdebghfcaiahfiaheeiibcdgac
icdegibebeh                             
#adghbaaaeeajjhjgjaadebjbhheiaifbgghffhb
hfgiibecfgb                             
#cbcjaghegghjegjjeabgfaeciffhghfaddhaihh
iifdcfdgefh                             
#ccggeibbhiihfjdjdieggibjfcdbbjbdhdhcabf
abhegacdhch                             
#gfafddijabbagfaiehdaheffefeaaaeebcjgjif
bagbjigifgj                             
#gbjdfaegjgddaafhiafhcihidgdbdhjeaccfbfa
jbbciddabjc                             
#ggdjdeiedfhaiicdiaieddidggaaihbagchebij
dghhegbfbhg                             
#cbhdjabgedjheibbjfjaebjdbgecdhjhheffijf
dechaccfjfg                             
#dbbdhgibebfchefcgefjaaedbaebacdjhgbahcc
dhagfagaehg                             

#dcjgehijfhbcehbceajacdcbgjcjacgagjaeedi
fhhghffecif                             
#jbahgigebeggjddibfghfjaaagghihgfgbjbjjj
igghgchcfii                             
#gdbaigjaieahgacgjejbgejcaiibcjcfigdchfj
ggdcdihfeif                             
#jhehibechdhifdiiieifjgjbijjijeedbhdgada
jehieeadfga                             
#edggibgccaebabdhefdhiaaegaghgbbgcgdeijd
adgabaiecae                             
#bidddffcbbcbjcefjeeehgcggeffbebachdfgfe
ccjejahjgaa                             
#gffiibijecacggdbjgjiebchbfagccdahahfbgc
aeffjdacbbb                             
#ehjcbcighbgighcbifajdhbebiafifaaeggdcbj
cgegiafcgif                             
#djdfcegjigegiagaiffdjjfjidfijiadjjggejj
hdifjghbiah                             
#gecbibajhijjgeddbbigiijhhbbcgiibdbahifb
eijfdcacife                             
#cdjjbhhffhgbhdhhhcheeafieigjfdedefbhgga
bfigbfgecgc                             
#hifaehhfcbcjdjgedcccidafcachdeddjjffhde
dafeahjhbah                             
#hhccffhigjccfadbbijigdbhbdceefjeeeghfgg

cbgdhaecgdf                             
#egagdjghafdjciafcahdcidgfhdieiaigjbddbj
idiifbgefdf                             
#jfcbagjbiedegjfacbijjhebhfjacbdihcfiieb
bibcfahcaad                             
#efdcdfidjigjhdeajhifbcedghjegdhciiibihe
hfghbbedjjf                             
#bhhgffcbhhjdhfgedbbcedahddcijdjecjciiej
gfdcdibhdig                             
#abccdhcgfceiggibgiehhbhgbgdgjbchjebgfbc
fahcejfijih                             
#ahbcaadcjeaibbghfciejajgejhicfagacbddef
jjjifhhcgie                             
#hhficdfdbaefhbdijfdhddiabhicbajfiaeciba
faahhjeijaf                             
#hjbabdjeehcghjgcfahibgibhdhejijijjhgaci
iiedibdbbcc                             
#jjhfggigigjbieegedhbedehbfejgdhgjdechhj
gfhagjjjbgb                             
#cehaebbggggahggddfajjghjjhjjefhaibbedie
cafcbbcbcfd                             
#iegfefhbihhdgbciebaebbhbchcaifidjgdiadd
ibcdihcfhhf                             
#cfcchiigjjacehehhdhhijcbagibgibhdceajaa
ibddihafjfc                             

#iffbbheidbhjicgafbafagicigjgceiffbiiijj
dbfgeffihbi                             
#ejjidgfcebedahediaafhgfaiahgddijgeebfjb
acjjgjjifaa                             
#efbigjcbajcjfhgiiighajbidcfefgiajacicbf
fcfccedcaab                             
#hbhdjeebhajjgiehfehdaaigfaijdbcihhcgcfg
bjgbfagedhd                             
#jhbhfjjigbjgegcfjfjabidhhddhjcfadjbhfee
gggebbiehib                             
#ehjedahggbgicjjgjdcabdfabiefffcfiiebaah
ffceiehidij                             
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didcfadfbja                             
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ididbbbagdi                             
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hjgjdjjgjbh                             
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igjdheebefd                             
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ahcabahhejf                             
#edjighihihifjgacicbjjbadjifhaaghddcdcfe
jfhbeebcede                             
#dejfeehbcaajefjfgeffihcfgebghibeafacfbb

jfdhbacaecd                             
#eeegcifgjffhhjbbbdiehbadbhcehejiajegaad
hdjjdejhiba                             
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eificfbgcgf                             
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aagibjhbacg                             
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gajffjghgji                             
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hahdhidghdj                             
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cbcadgefiif                             
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ddecgcfajje                             
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hacachdcffi                             
#ddbdehdhajciddffbabigfbgfighffjaheebihd
jafeiahiigj                             
#jgijcbaccbjejicejichgiiafifadjgfbjhcade
haifchffibb                             
#bjjeghdchhificggadhajjejdhhghjgffiiddij
hidifdibjjg                             
#cafaghbjfddibjbhichfhjbgggdagecfeidieii
fhihegefgbb                             

#fiecifiehddacbcgfjjiejdfhgaiiccdigahjed
hdgefidjcfh                             
#bihbdiefhjceeggfigdeebeajhafhgabjgbiicd
idggijehdje                             
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ffdfijhhhif                             
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ccdbdaaieji                             
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ffdghacajai                             
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bffghcihbej                             
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abjjhcbfgda                             
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cedaajhhdja                             
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fhcbfjdebbi                             
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aadbaebjgda                             
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fdedijaihid                             
#jecgcggggcbbadgdbdeiiehigfdeahfgehcghfi
biaajgbjedd                             
#cgfifhddjjdgbgdeaifjihcjcbjcaidedaeedah

hbbbfefegca                             
#aiieaijahaifcbjjfedacajifbaieibefbdgdja
bbjhgjfcbeb                             
#chbhcgdhhadefjjibcdjadfbijihjbcajjjaecf
dabgjaicbej                             
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bhedfiejjbi                             
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aijcfhjhecb                             
#idajhgbfeeejiejjjjihchbedeafjjbhgihfgie
aghhbbddbac                             
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cihjbaifgji                             
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ffhbeccehgg                             
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hafcdecdgba                             
#hedbicgibdcfiachhfgagfbcaegecdbbabfhfhf
ehidajffaci                             
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daaedfecgee                             
#dhiafbjigecihdfchcbadbaccbdjjebiaabecbc
idfddfjdgbb                             
#ibhcacaefhaeagdbjbcfihggdihjiebdjhjejae
daajjhcfjii                             

#diicabcecggiiidcbcfhfbfaaadbjgjgehbbfcb
jhebaaebaeb                             
#hcjhfieiciaieibhfiegebjjdhfefddghiiijaj
dafggaiedjc                             
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hjbfehcghhf                             
#hihijhhgffiahebiagdiihbgegebichcbbgideg
hhgfbjabaja                             
#cbgefcicfchajcgbfihagicfigbcacicgjgebfc
abcdefdhace                             
#bhcehjfdcgfhjfaajjigihgeajbabhdgejbaidi
jibgcgdebdf                             
#jdaeehjihfigafejiihiahbhdajeeddfgdicici
edifafjjafh                             
#cjfiefiebgdghdijahijgcecgjcehfbbibcjfcc
edhgahdaihh                             
#ajjgbdhafcicbfjcddaadaafhfhfidbegegfjee
gedecjhhihd                             
#cbbiaifcjdhbicabciijbfadaahifihdcibidai
aiggicjdjid                             
#afedaihddhahagjehiechahebbheaicffgcjacj
hfhbidjehhi                             
#ahgihbafhbgcidhbciajfhcbicajijfibjbcdae
chifbbciigh                             
#jgahjffbcehbaghhggjccefggaiddecjdjdihbd

ifgfbachigc                             
#gdeafcgihgeidefcabegaebcadhfdggfhffdgfi
eccaifebeca                             
#bffdidiajiidiaaefcidehbedfhejbcjjeifhjc
idbcjaafddh                             
#cbidcgdbibbadghjhhagiffjdedihdbhagihcih
bafjjgdjeih                             
#ijjchhdfffahdgighchbfabaihgijdfeebcehgb
hfbgafgdahi                             
#aiagacgijhgfaecjceeegjijfbdfcfcieajeigi
gbhiiaiibfh                             
#afbgfdhhbgbdibaehdfcbgcbcjaedhdcbbgiihd
beibfafheec                             
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hfbggeiidif                             
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ihcfcddabef                             
#egjhhhbhfbegfahahbbbaibiiejgdhaghchfica
jhfbbbhgdhf                             
#ggeehiafcgfdghcbcjhhagbjbggbdjgcafhfaad
eebceaegfeh                             
#eadgbijjabihgcadbiejbbgfbaiigaahhfahfch
jhciececaca                             
#bgddbhijbdfaahdgdiehgecbjeddchjgaheciac
geagahhefie                             

#iiahhaejicfceaibbcahdjhdjddbbdgbccaibja
fihhjieifjh                             
#dahbiaijgihfhhabihahafjbbhididifbcdabcb
cagcjfihehb                             
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cfjjjcbbhah                             
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chfbbjgabhg                             
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gjjhhbfcbic                             
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jgejedjeiah                             
#fcagdahfjcijcbgbhiijieghbhidhbhbdbcaaai
efjffieeegc                             
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iegjibaabji                             
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iahhagihffe                             
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abjgfgdieca                             
#bhfbeghiiaciaihfhfdjhfaeefdcfiicgehjdhh
aadbjbbgbgc                             
#dcfcgcbdefiefjebhjfgbiddjagjiaihabjbacb
bdajdcjcefc                             
#cfabhjggefhjbcabfedfeafhfhdfeaibbdbhhgg

ihfhgbbjecg                             
#deeejchjjjbgdbgiiacjedabdcagbibbedchhge
hcihehebfdf                             
#gigfcbiggejfchheegbhgjddedieehddgagfieb
baeijedbbfe                             
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jggheechbeg                             
#jhcfgdahgecjagfbdibfdabgdcehhghiicfbffc
ficadhjhbej                             
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bjjigafgcec                             
#cabejgfhghbgiabbjcfceghgaccjjijjiibciab
ccebidhdbjh                             
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jeeebihfaif                             
#ejbdahidhbcbcfcgbigbgjcgcccegbcidbfajdd
fbgbcdggchg                             
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fjcgafbfcjf                             
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dbdbabffjjh                             
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ceihcjjjjaj                             
#ehhaihjgghdeafjgcfaigbaeacebedgjifjgebj
dafdjgebajg                             

#efgihecjhdcdbbagjdjdaehheficiheaejdfeei
eiadiegifbe                             
#bidhecccaabbgfajdhiaeejfejdfegeehfdbegh
gghhifcgcad                             
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dhffcahbhab                             
#eigjfeaecbiigjjijciecfehaiaigchdeidcaed
geeaafihdai                             
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ichigecajaf                             
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affbhjjejha                             
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gbhebgbegca                             
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deeaeaghhbd                             
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hgiihfcaehd                             
#dgaiajcdehbcgcbbhghiigabfedfiahgggafiab
hhiijedjffe                             
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cdhaghejaah                             
#hgbbafhgfjhebiiiifhhgchifdgcjhajgijacfh
dhgedcahbag                             
#ibbihehgehjgigidjiaafhedhhjbcjgecdacjaj

hefbgghgdfa                             
#gjfejeggjebfhdfgdhfhibdgcjcfdebbaeeiejg
ghjdhaajigf                             
#fchfbjejgacjajbjjddhhbhfbgfadiidjgeihgi
jidigcjicef                             
#cjcgffijhechgdacbidhajigihigjfibjcaefjc
hhfieecdigf                             
#addeabaciigibcfabbbiidiehgdcbecahieibeb
fheibahghgh                             
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chhebhggbfb                             
#cbdbjbccagigjgchhhdiegiciegeaiefibggagi
hieeceheche                             
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cejfghaajgf                             
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jdefgbaadbb                             
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feecdgbfdgg                             
#ijiafdgfbgifigdgccfgcbfaaaacibajhicecff
afhfgdhbbaf                             
#ecgbjjbebihhfejhfhifeffbiaeceiifafgcigd
efheejabcji                             
#jicbebjfhdfcdcgdgeafjiejfbbbbgbiehdfbif
bedhhcegcbc                             

#jihagdggaiejhagbfaeeffbfaacbfihbejeedea
afgddbdbdfd                             
#hhhgcbhfgcjdfgaigijbffhfhgechcjhfaceccf
gjdabfbgidi                             
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bfjifedaeei                             
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hjhfjajcfhc                             
#gceijfejagbiabccbdehhbadijjaidfcihaeebi
eaeiiedjdad                             
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bhigfjggafh                             
#eaggcaacedfdfefcbhccdagiceechcdacddajjh
bfabghfjefa                             
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hecjbhhifcc                             
#aiageiediccfjedcfcecfihiciheabibdcgggbf
eadifgjghha                             
#bggebibbgiicacjijhdgjjdjdbahgjjhiadgage
dccijjajfee                             
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cjgbgbadbdf                             
#didhajggfjdghbiejfhgdgehdicbghicfcgdbbj
bfefjebfdga                             
#fhigfdghdcgjcdcjhjeaibfhccdgfahjeffcejf

edfhgbbbaei                             
#ejigiabjiecdgeiafgccijceadbffiaebhjgdda
gjbchihejdb                             
#ffbhddahhaaedbgdicdgfddfbjjdeciffacdfah
aacaebchdei                             
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ejjjdegdgdc                             
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afieabjjddg                             
#gdbdihgcacggehdgejcahcaiaihjjbiicdegdig
edaiaeghdje                             
#fdggbdhbghidgggabaajbjgebdcibjfdaiiighc
afagccccgcb                             
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cgfjijgbdgc                             
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cjgjhjhbgfc                             
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ggghdfgbhih                             
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fhgfjeefjaa                             
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gdbjhhagfaa                             
#faebiieadabegbfcjdhagbhbiffchefheffcefc
fgcigicefab                             

#gdgdbijeijccbdeejcchdcbfjhffhaaaibdbhcb
icaahhhfhec                             
#ebfehfeecjegcafbaajebcbbfhieihchcgcacfi
bbiadcgdjjh                             
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bbgdhejebaj                             
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geiifjejide                             
#degdbhhjfjeeahabfhfcffjfjcichechigbbcjb
efbhdeafjbi                             
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bfhbiecjbhi                             
#baihgahggbcdgdhiaabjeahagefffjjjdjbahdj
acgffejfabi                             
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fcbeccejjfe                             
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cfjiieeefhi                             
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ecffigjfbdg                             
#aggeddajddehdddebefbfcejiagdidfccgibcda
bjhhiigjedb                             
#dfageddcjgiafbiceggcedjghcfdjdfaedhbddd
iijfcaficig                             
#efbgfbjbijdbabgdihbjfecdacgefgdhfdgefca

fdieaccfbbi                             
#egciegejaaejifjiefiagacdefifichdebdhfed
dhdbadiahbj                             
#cifcicccgfhhcbghhffjacabgcccbbddcidbggg
cejdcdccbcd                             
#jjbhafdihbcgjggbdbgadjiaeechegegcabgfcf
higegfibfda                             
#geadehaifciideefecheaefdeageadadjcgfbac
bgdaijahjge                             
#eajdcfgibigfibjcihfjbceaiieicfeibhgddjd
baajdgcjbag                             
#hjhdfjhcjcabihdhdhecagebaahcfjhhbgdcdbb
agheiifgdbi                             
#jiegicibfjajbgcgieiidaecaicaeiiagfabchf
edhbifdfcaa                             
#fbghfebbgdhbbdidiiggfhbdeegagieeedbefae
jibhidfegfe                             
#igfifeeagegbcfgcgdbadegadjfbjjghhijedad
jhghdeddbfj                             
#jhbhiieachdiehhaddicbjaadgigjchgegdcchi
hdfjhjjgihi                             
#djhchecfieeaefcafbbgjffhbechfeejjddbeba
bcficchhcig                             
#eidhcbaggcggfhfjjhfgjbgjhcbdhbefgfaaica
ajjdchheaih                             

#cgihcedaihbjfeigfafcigadgibjjbebbafdedg
ehdjcbfefej                             
#hijfhcciegffjfddihabfagdgddibcedfbhjgci
gfbigdhbidc                             
#hiibafjhbchfhggghgchebfhfbhhagefdicfagj
fgjahdjdbge                             
#ahfiafbhciefhdgibbccaaeieiefieaiddfedhg
dciebibdddd                             
#ghjddjehfehcjghhabejiefajaajbbfcjicgcjj
fibdaifjidd                             
#hcafgeehbbjcicegdicegdcgfgcgfdihfhefebe
afehaibdbfd                             
#jefeiijfhaffjcbajegggehehefceacejgiiefi
cahgejbbghc                             
#ebfifejieahegegbcbbhcibbejbacbjgfjjcaje
dceifgfchej                             
#acbgdjjifchghebhibfahibiijfabcfdfjhchaf
biieadhdeaf                             
#edeiaaiheehbdabhhciihgfiaefeijhacffdjjh
hadjbccdcaf                             
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hcghfbjiefb                             
#ceihfjiieachibbeibjcbgehgfgejhbgbegaeij
cgbfbcedfha                             
#dciicifhiafcacbdceebdjciahhhgifdheicjgf

jgehdhhhefa                             
#dgjaifgafichaedjadieaafigcgbgebeagdddea
fefbfhijcca                             
#hbjfcgfjbaaidbihdjcccbbhebebfagdebgbdjf
hjhihgeajfd                             
#ifcacbjgecaecgjdhcbdjgjhcefbghaffgiijcc
bgdfhfgifdi                             
#bbhgefffidieehdbacedgcjfcffeaceaigheded
ejjdjhbdjgc                             
#diabdgfajhheieahjiafdcbdfeieihhggeibfcc
cegdciggiac                             
#aaeffcadhdjjedgahgjiicfcfdfbfbajfhbadcj
jfdibhicgcb                             
#dbjaahabhfajjjjbajecgdiabfafaeejcaifada
bcdejfcfdei                             
#dahjbeieibfgdbdicddbibjijibbbgcfefeeefb
cjbchbcdgjf                             
#bcjeaaajdgifgcdahigfaiadcbfiadhhggjgich
gccbjcdecbb                             
#iebfeaihbgdagibedffjhfeidffgjcjadjgfcfe
idedjdfeige                             
#hdiffbbciicaacciigahbfbfbejbeidfjiajjgb
cbabchjfhah                             
#acdgefgbcjjjcdhjdfggfcgdgbfieddachjibif
heidfhdfefc                             

#bdiajcihaidiabagidjhgahibiidfeciiaeciib
facdbficbgc                             
#eifggfcbjbjabcdajaajcddghjejgfgigigbdgf
fgdaaiahaha                             
#haedigcaifcjjchgfhbicfdihiceffagijgabde
ebjajcbhddf                             
#gchdihaiiiiigaafiidfejcdjabffjgcgceaefd
bjhificfdad                             
#dhegdiceecifgbdbhhdiagbdhciifiehgdcbbjf
gigdiffjgbg                             
#jjbfahiddadbfdgffjahhdaiijaajjdcdfdcgdj
ejfgfgfijbd                             
#cgafiebbfiehhadaddcehacabjfdejifbbecdef
eiagiiaefif                             
#cfdighaadfcjcbcgdcbbgiebaaedghgaehgidab
eeeaheejehg                             
#cbcciccadiahidiaihcffgbihabjjbbigaeihee
jdjgfdeagij                             
#adfgibfbgbaddegdehgbieciadcfffcfafiajif
ifgjcbhiefa                             
#fgfagddhbbjfgbgdhgchfgbdbgbgieagghabccc
gjeafjhihhe                             
#ibifidibibddddigdbbhcjciibgfdgfhbhgeigc
egehajefbhj                             
#dbhiccaccbejebdgjiccbeihbgiabbhjbdhfbig

jgjfbidchaf                             
#diiehgiiibcgcehdbaggdbbbcichjhbbgaiabgi
ehjabjfhbej                             
#fihjgbhjdebfbbfibffeeaciaajecicdjjijibi
ijeegijgjef                             
#jdcbaebibahdbejaeabicahgdabcfefiifcgejj
fddccbdggbd                             
#bhhdabdcjdihiceajcbdgjhghicbgbhcfehabfe
jdeffbehfie                             
#jfjcjdbffeiibejgedbbcjbdhabddbafifejide
gabihghhabg                             
#bieagfcbgibdjedjbhhifceiahbhfdjjbbggfeg
ajcjaaejdbg                             
#hacefbicbdjjaegjjbjgechihaciecbedddeaeh
ffagibjdfab                             
#jacecjidfcicibhbgjeheigibjeifccjeagbhjc
fedibdjidfg                             
#gdbggeehiihfdgahjgahhabicccgbfieecifjij
ajejaaedhgj                             
#hihaggfehbjeabjbbhbadaaefcffgdhgacfjabc
hbfjhehgfde                             
#cjajfcefdgjicadhjdfhhehaeigfhigaigjbbbc
jdgbeefgbjj                             
#cdfafgciiiejeechdgaggdcaghfgdafeiifdhfh
ghfddjjedhe                             

#ebgiaddegdaeedjihegfddjdjgjgeeajhbhhaeb
cibbaefhegc                             
#figgaedijjhfcegjhjfcabbejejiaiffbhihfje
dgdficicahd                             
#hbdhaaigdihgefddajefeajfcfcfiihgbfdgahe
ebddjieecif                             
#bcgbhaafdaaieghjbddcbfijdffhghdfiddefec
fgdfgehbggi                             
#cibdfgcehihgihebhcjgdgaiiefdidedebfidda
ecjhjcehefd                             
#ijcejjbaebigidbebfdcieieifcihiaidibafje
iigcebehbac                             
#bfcjhjijigacccgihhhbaceahbbefjbjijfbfdd
decjcjcjhad                             
#hifhichgbdgcjacccideijgbjghjifggbdgidaa
fdijciijbha                             
#icaaeaefbhdigjbiajjidacfdaahiabhebiacjf
gefiajigade                             
#fiaebajgghijibdadccaggadaebidjfdedcbicf
dcaeidhjbii                             
#cacdfgbijahdcjacijcdddedgjigdaceebaaaid
biihghebgaf                             
#cjadecdbbchebacfhahiffddedacdcecdfbgddd
jgibjhdeagh                             
#jfjjihidjjdhefhciffehebhbbggchcbbdaadaa

ehebcdedfcb                             
#dbeeiageefigfeebdafegfdhcidjfgjhchfaggi
djiggajccff                             
#ajagfbjiegbddheacfffigdcfaihagdibicjdji
eabdeifcccf                             
#ceaafghgehhfdhdddiiehegfijcagdfjgcccabc
hjdjejbfbaf                             
#daebbjgbjbjiahegfbchfacjbdhbjjfcdfieheh
hbifibdaeah                             
#bbegbaffdefjdgieggcgbgaigjcdhcfbccegjhc
bijhdebacgc                             
#jdcjjcchideifhggcfhcchfghjigfifcgjfahed
ehfbibfcdgb                             
#diagjejehdafgabbhchgfeeccjfihiahjdbfhdi
cbchecfjffj                             
#jfhdjbcffcbhhjifbfiahaiabijcffhichfehbf
hgghjjdjcbh                             
#cjaijcjaijddcfddjffgfaeehdcdhggehfcjgea
jbafegbhcij                             
#ghdfjdcicbafehijdafhfaigidchchcdgfjigfi
abiedbabhag                             
#ichicefchejjigbfdfafjdgdgfafhddgiabjceh
ibcficachhg                             
#ecbhgfadceibachjefafhgfbdebdeggfihjcgbd
ajjadcaeheg                             

#igigdgjfcjdgdaccfaiadjbdbifbheiffeidigg
ffgebidcaff                             
#adhibjcccbiibgacaddddjejfhfagagjjihahbc
fhfgbcgjijb                             
#cfiejhigahfaddiadiihiiajbhfagceghccejei
fgihjefeggj                             
#gbcacddebdajaefcgijjeahhhfjcdibchhcahdb
jgjhigafaje                             
#bbahcdcbbahacedehdjhjghdcaejgbjiejfaafe
ecghccfffhi                             
#jgaedeiagiaagdhifiibifbcbaihfedeiaihdaa
dhdecfbggib                             
#fchbichgiegfgfbceiddbffijfidbeegfdiefhi
icdegggbfhc                             
#dchjijiafcdfgifibgdjhdefbbeaabecbdffaid
gdbbdfihafc                             
#cgehiiabcjbceabiidefidiiheehedfgafddchi
djabbdeghch                             
#jdffbjjadhdihiegfhibhbifjfhehchajhfbddi
iaeacaghfec                             
#cdfahdbedfeieheeggiighjhefbddfhfjjjaega
ehbihicffgi                             
#jbadbaegfhjahceidagefjgedhhbfifgajahjhf
abdhhdacjbh                             
#ghebejcjehfddahcddjffhjahceahgicbacjfch

eiaggabdgjf                             
#eeegbdiccibbjjefebddgdceibiffebfidccdae
fibcbbjaaef                             
#difcijfcjcgjebhbhbffigajdgcabeiiahcdgjd
haheibbfhhg                             
#gjbbigiifbhhaehjjabieibiaaggggcebafgddb
hbchdaiicji                             
#bjgaiajdfagbdggdcgfbgeeibcgjdedbbdhjjfg
aagigbihhhb                             
#ggbcibbfifiddfeeeaecgejiaeceacfdiiehjbe
gdaaghjeecb                             
#agdcchjfddfdbcdbhdbjhhdfddagbchadhbgeed
dfhcdeccjjh                             
#eahaaeehdgfbddfafgibabidcjaaeaifjhahhjc
ieicjchbejc                             
#fgcbidcbacidgfhcjibidgjibeebibedajcajjh
ffhjdfeeifc                             
#fhdbejicgcfffbaegdgjiihgeeieifbjdhddbjd
jbhajgbeiie                             
#iggejcbhfgdehgeebdhajdeehdgghfjdjbfigad
dagcejbgbha                             
#cfcjigaifaefidbdbaghchhdhiaggedadbdfdhj
abcggcaaaci                             
#ajddigdghahjiageaggagcejbgjfgfggjejegbf
bceaeghggdc                             

#ebbicfhgacdiecjgbghafbcdbehhiegehaaebhf
bicjcjbcgie                             
#dcceehddbcgihcihgfcfhdhfceifjbhajhcbgii
ggahbjagbig                             
#bjgdedhcgdefgcedddjdffbihjcbdfegejedhgh
gcbcfhddajh                             
#baidjdihijiddacficccabjeecibbdichgjeihf
ighdcbjdgei                             
#feaidhehcjjahgjgaabadjibgheedbajacjgjie
hffjigfjdge                             
#behfcedbacibcdjhcidgghciddbajgfgacdceai
dijfhgeecfi                             
#jgabhcicdjieicdhfgdghehcgjhiiadcideghgg
ebgfbbaieih                             
#adjahadedigfejijcebfeeccehifefbcijhedfg
edbihadjhjg                             
#ddgabdcifejjeejhfjgeibjhbjfdhfehaefccha
ejiddeffbgj                             
#eebfhjifcjjbiaccdecbaecfhcgejdjhecfbbdf
chjehejibjb                             
#ahajefhjhcejaejejcejdfbjhdejdihahgaedjj
eajadhjhfff                             
#bgcbddfidbeafjdhegahhccddiddhjdegjdabed
ffdgiibidgc                             
#aaedgchgfeajedfdbiadegdchhhfcdjefdchbde

hgfhfgbfhga                             
#gdababjgeiicjgiigffdgahibaeiihfihgcjhfj
aechijgjjai                             
#cgedbjbeddbaiciiiibgiijegeigidhiahghadg
bfgjdcaebif                             
#acafieijigebehbajeaigheeabfgebbiifihcfd
edbebidfcdf                             
#bjcdifejgbgjfgcfaegebhecbfifbfgggibhcjh
gfcghjbaadi                             
#ebffdgebiagddeacffcjiheighccbbbgjahibgg
haacbgahbgb                             
#hcghjgdghbfhiihdbjcajfcgbghcacaeeagbgge
ifcijahaebh                             
#ihfefgefehgijfbjhibdhaefchajeffeejbhfbb
ccjbfdehedf                             
#jadcicjdbdfdbjhbigjbbehffbjadfbfccagjgg
jhecdfdjebe                             
#iafijhfchejeffbbgeehhiahbhhabdiefiiehja
jgbccacbdde                             
#hhbdajcgchdifgeabbbgebiecdifceicbcbcech
bjicgdchbji                             
#afgiiijbcgichdaedcgbhgeeibfjbjhhbjidggj
ccdgdeahcca                             
#aaaddgcaicabjfeffjchfdjcfjfeicihigijdhe
fgfccjeibbb                             

#ghhbhciddjebjhagabhabdbidhbhhccfeebddfe
haggdhbaabc                             
#bchahehibffefhdjgegibjgaaccfigicdejebab
fdhjgfjfebf                             
#cijjhefffaabjdgfbehaefeecfiefaadgaagdeh
cijfgcebahc                             
#eigjjehgjffhdggdbffifhidjjadfdccihehhfj
jdjghbbbbbh                             
#fedfccdigggbajdibefaihbdeecdgjhdcgbfhic
iebeiihfdfj                             
#ecedfjdeejfbdfdhffghbjjbdbdcfdidbgdhjab
hijfjfibahg                             
#ijficjjghdjacjigbffjegdgfbjhfbebgdfcgjb
hidccaiadah                             
#ejeddbfihidigbdgbjjgdfaijhfebjhgbjhajei
eigijcfcbie                             
#hajfahcggjifibbfbaadfhgfbibbeifbahhibhc
eafbdgcgecc                             
#ebedeacfhfhbddegjhiegdjbejeejhecebfjbfg
ccciehddabc                             
#aaegagfghiagjgifjefaeddgfcddjfgddddfagb
aifhchfcgcj                             
#hededjcafgedijighiifdhfideiiiibfghebjce
gcbebcdhdia                             
#iaaccdeigdhjcaiigafjhifagheeeigijabfbef

gadfeidgeei                             
#bahhigdebbbjdaidgcddibcjaiiehggicaideee
eeedbiijcef                             
#fgacjhhidcggggacfhffaiahheheihjigjdgheh
bceijbdjhah                             
#eefdiaidhachgbcfgijgacjccagidahjggfedja
afaahgeefhh                             
#haffjgdbggfcaiaahggbbfjjdchjcciidigciha
gacfaieadej                             
#biciddjjabaebgefgdiieabbcjhbchdfgahghgh
abcddfeiefc                             
#gifcdcjgaifahfebjacbdfeedijhcifcbacbffh
ggiifbiagid                             
#bibcfhjfefgjijfahaijhhffdajhaidgbbhjbgd
cabehdgbfge                             
#jiejjihbjgbjiedebbggijheaegbijdbifjjcdh
jgijjggidai                             
#fihfjfjbhiceihabbgecdfidifhbeaiddibffjj
iabgfdedigf                             
#ebaajcdaficibajeddhbhgcifjcdacajfbdjjag
achjabbdgib                             
#aggjeghbadchafbidiiejggcfjbdhhaebjicccj
adcdhgeaghb                             
#afgebjchdbhcgdbbhbifajcfahdjajeidebcgei
hbjdjcdeaeh                             

#bgehhcajfhhhbacjeahebefeebahjafaffafdih
egbjjgjebai                             
#hefhcgebejijijcaafhejhdcejihbdggjcejbdc
hjajfggeicd                             
#bdecedggiagdidadjjgacjhdacgdgfhdeggjibh
didjiifcgdh                             
#gjajbfbcaagbbdjcgaifcggbhhbfdgaagecajdj
ggjacijcdgb                             
#dbcaaeggedghebhfijadigjfeghdacgjhddcddc
jbfeiiffajd                             
#ehdbjhafebdcebgiifbbiejdjijiihdbbfhfgbc
fgbgbbefige                             
#biefjbcjdidiefedfagehacaieicjbfdbhiiied
ddfjjjcdidc                             
#faebejeehajbicaichihjcdbdbjadbccjifbegh
ibcafeeibgj                             
#acdaibdgabchicjbfeijdicdbagaceiffbigigj
cfdahfcjdjj                             
#fjcehefdiihcddhceefebfjeaajjhiafffibhgh
gcgaafjaaaa                             
#dhgfffgfjadeccfdcegfibdahdfgfigeahahdif
faacdicbjdf                             
#cagcbhjhefegbfgjghificfibbcedigbjaeagia
cahhabifjbf                             
#ffffhahcbjfhdajaefgagdfbbebjeabcaceihga

cbjajajhdii                             
#hiifbaaihhaibaaibegjgifdhcdhiiabbjeijeh
ehfccjdcaaa                             
#dcjdbifcjiicbddiddbgeahgjhfbdjjbicjhfje
hhghjcajjje                             
#aeicifhifjdfbdgceebbhabjieicidggdjgfbff
cgbcbebfjce                             
#cjaiahjaifbgabacbdffjgcehabhbdcgfeebahe
aheciejehca                             
#ffjjcbbgfjciadefdcgcceaiehdfgcdfjaabeed
jdchbdhgffe                             
#aadcffacgjacfdghaedihbeehidgchcdiajdieh
haggjdbdhgf                             
#ahahicdfdhjejeahbfdchcjiafgahbhhgbjhbjd
bfbbggjbccc                             
#efjbcbbcdbgjceeiadacdaicbdbfdcdgeeggjic
acdedidjjhe                             
#aajcadebjhhjagfgeffdehehfjfdhggejgafgbb
bcacegdgcci                             
#dbgjccbgjgdifcedjajjhibbgfibdcfhgfcgiib
ifeibaibdga                             
#gjdeajacdbebhfgdedgiacehdfhggeajgjfehbb
edjgcgifghd                             
#geffcfihdehidhjggiaehbihcihbedfijfahega
dbabdgdgijf                             

#gdeihhdjhfgadadibcgffdgdbghgdfeaaagcaeg
bfcfdgjihgd                             
#dfhihjedacbdjgaggefdhijaehajediehgeifcf
hefieifcheb                             
#igihgfdbbjcccdbfjfhjcbjcdiaicghdjjjihbe
dffijhhdgfg                             
#bgffhgachgaehafdebeafaeifedhjjceghecdff
ebadfiheibc                             
#gbhdbaacgbhdcbbgefceiahadjjgjfjdghbjgda
agcfhecjiff                             
#fjdaaiieacahhcghgigddfhjjiaecfaabijjeih
fcgcdgbbbfd                             
#ibgjdhccaededheihbgddgcibejjafdigaigeei
biabeghdeae                             
#aggcfbbifhdedeaffebebaighhihdchffgjbbig
ggcggbicahg                             
#hiefahhjeiacjafhgdfcjggiajihaciecedahbe
bahbbhdbjfg                             
#eecbciddbgaeiaidhfcjghdiggjcjjchaaijdhh
ffjafahffif                             
#cedcdgfbicjcdfcifijehiibfejcahfjhehihcg
ehjhfbegehf                             
#ibbdfhihdebijaeggfggiaaihchidbeejehbijg
agahjbfjafg                             
#adfihehfhdceehiahaehbbgbhdighidbicffjfg

dccdhdihaab                             
#eccahfadhafhgaaabgjcjjiabcgcagdfbfefadb
hjjcdfcgeif                             
#dgfcihjhdcaadagffaeeacdicjicajhaficjafi
bfdgigieicj                             
#ahggjhdaggciacajhichdiabgidheaaehbbiheh
dgcfcghacbb                             
#bahicgibdcfcaaehchhgchfjbebibifhbgfbacb
icbdfcfciad                             
#dcbaiadfijjaeggbjcfceghafjchcghdahihghf
bdcicfbhcaj                             
#icieaiijagbbdficcfagjeadjcicjceeiaehhbb
beeeaaaeddj                             
#gebbccdfacdhbebbbggfahcfchafejaahaeejai
dbbdgcefgab                             
#bjdjbgccgcdjcifjhadgbfdfgcidhjaegdjfdjf
ajfbhahddcf                             
#beagbbgecgfhcejjigagdhcjhdehjdecgcgahgb
dgjigidjahg                             
#hbcifgfbicifgigcffbfaficgffbhahhhjeejgc
bijjadghdfb                             
#gachdhhhhaejbjbiijhedihiggiiaabhigdjfgc
dhbigaadfba                             
#acaeabgidhajaihbbbcjhcghcdaegdgihdfeiif
adibafgbeba                             

#ddbcigfbjgbhhhbhbbbeiieahceedbgdbgadgbf
dfidbacbcaf                             
#ddiafjjibbgjdfbcfebgiageiicjhhicgcbhdic
iecfhjbiida                             
#ibajecdeifjieedaiaedacjjdhbgiafebjcdabj
chbaejgcbfe                             
#biffdeaeacafgfibbabhgfadeficaafgejgadhg
higechhffeg                             
#gahagdbdhadejjcdeebdhjceeihjecdjidfeacg
cefcfhhdfjf                             
#gaabaeabdjedgdggaagjfjjdgefgchifdbhghah
ggbidhabehd                             
#ihaicgjdcebehbiejgaggehiadcjeaiaagfbggg
hibhgdeafid                             
#bhhcigiaicfgchgiddfedhfbcagaehhfbeffjjd
fjfjcefefff                             
#gdcgfifgjggdehgfahfiiigijhbbhafhhgabhgh
jhdjhjhjjce                             
#bhjgjhiijjdhdbgbfajcagheadbaagihjgfdeji
fbfcbdbjgba                             
#aifhfgiiehagbebhgbfegjiacachahegjdbdhbi
ebjaajieghd                             
#checiebbehfaedhgjfbifcijccdbghhibedgbjf
eejchdchhid                             
#eijjbfifjgfcdjihjgfeagiiehgiihfdadjeicb

ibfcdhedcaa                             
#gfidcjffbhiedbdecdgcehjafccgggdfjdecfad
dffddchjcca                             
#ahiecjfheajcebegihjiefifiiffigghhhbdgdi
aegbgjceegb                             
#fahhfcegjgiefedfeebbdiieiagbcidbfhfheie
cdbdjjcebib                             
#bfbbhegbhfjaefjfjjjjgiibfbcjjcgaaeghggc
hahdjghbehg                             
#cbjbdhabcghdjdedhfihfcjcehjafceehbdadfi
iihcdhahiii                             
#dfiadbfcbceejaadjdgfjdiechidfbgdijceagi
ajdjghiicje                             
#jejbdbgacghaihhgfcbdjhdijdeccfcbebgfjfe
bfajbdidgja                             
#ecgjdgjegbcaigfgedaagichegigegfcdeagacc
cighjfheceh                             
#fidbfdadadjafcghecjgeabbifecacbbdffjjii
jagjhahedfa                             
#fcdjedbbadfhfhaacihhfdcacefcgjbghihcjjc
ibbfiggccec                             
#abjejefhdiagedffabefahigjjjaaagidciefgb
jgccehheijf                             
#ddcdfifaighjaabggeaaccdcciabjcedafddhjg
dcieiedaffa                             

#bhifeddbbcjidcifdejgffcafghiehfiedfhaih
cicicjjcgba                             
#hbfdabgfdaigjaifedhjieijefdeeheihecjcdj
cfijcegbafj                             
#efbcaiaiiicffjiagabcjgjhhfhahhdgibfgggd
jecbbbdbhjd                             
#hjfgjiehgjbacebjjiaejcdceebbjjifcedfdcc
hiigcibhjij                             
#igfdcefajhjegiahfafidaegcfiheedfajiiajh
gjdghjeajbj                             
#fieeggigbahgbeghigjdfifhgbfdjibjehccbhi
ggdhdfgddie                             
#jhecbhgacaeichedihgfcefddbddffdejjhdiac
cjbfgcbjjbe                             
#djbcfgfaggjbjiifhfebececihgcddeedgjegaj
dahjajidifb                             
#ieeeebchhbafigdebhgabaeiacjcjdbdbgeafbg
daihjaffjhg                             
#aahbigjhhehfjbaefibbejfgihbejhbjchdjbci
gebjahhchge                             
#ajggfcjffbaceajidgfbgbcbejfihdbafadffgg
fdgijbaejbj                             
#icdcfaafbcbjhgijcefbcchjcaagifieejeijcc
ibjcdbfgjei                             
#faicghjhedhhchigaaajhfjcdhcebfafhidjgjb

ggfchicjjac                             
#ihijiigedejbhefigjajfecfiedfagieeicafjd
fhdedbdadjd                             
#dghahhegefcfbchaacfcaagidbccegbicecjefh
jccifjiibfd                             
#iiceahbbfbgafbbhbjdfeecdjffcajjdaigeejc
fcaehfbcfgj                             
#ihefihhbgaaeaeacjdbefdedejebhfgagjcaihe
fdccfcacacj                             
#gfheddaeidabbgifccfdjgfbdhiidageajiaiah
hahegffdhhg                             
#fjcgeeegbdjhddbceeffdcgdffbbefhghffgdgj
dfhigagdgce                             
#bgifijhadbgcdjjdhcidfagieiidgfifebicdea
eafagiagfdf                             
#iedbfdhcgciadbjidibbeahiahabfahdaadiifi
gbefbebjedh                             
#cgchhjfgjiecbbacehcjbfaggbdejcgadijcdai
ccebbcchiac                             
#ibhjbcifficceehibfabijjdcjiacedjjdiaagb
egffeccjjdh                             
#dechggfjfbhcgefihjjhaefcegghagbhbbeibdf
egbfficieha                             
#hfijebfdaejhgdedhcedajbcbcjjdjjieffcafj
icjbejciahb                             

#iijehibdejdiihgeijcbccicbjffbihebicgiie
daidegjhdhh                             
#aiiaebfgabaabbddjcbjegdbabcfbifeacagabf
igajjeafbbe                             
#gjbcffifihbjjfacbbcbbcajbabejafhdaigigf
bdbdgjjhefc                             
#gcifiedicghdbbjhcgbeedidjeaijbhigbhifgj
aaifidhhcgd                             
#jfchaecehjajfhgjfiibehbejgdafcfccjeefec
bcghajjejda                             
#eeeiddcahceabhjjaaeccfeahbchajbjgecibbi
dhfehaecjai                             
#cbccicgiagejcbdgjgccecfeibdaghfafjeigca
bcgdbhgigjg                             
#bfdchhibajgeeahcejefjeeahecjgcefdhhajae
hfggcdcaecc                             
#cecjeiejbfejfjgdgfcfhhggihjhghfeidcbebd
fajbbicgagb                             
#jefabbjfigcjchbicjabgdfdabfhjbgbfefedea
ifhddjefejd                             
#hbdadbjaiefjfjfgeebaiifjejddejdiafibfhh
jfbeacgjcic                             
#bhajdjbabbdfdiiiegfdbifegehbjgbfgjfbafh
ejahgdfefii                             
#cgdecaaagbjacfcjbdbhcfdedjebfajdebhidbi

fjdehiacbcd                             
#higafajhagddfjfiaggcgefabdgieiiefheabad
bjdficedihi                             
#dacgjagcjfcdeijjeiegidhcicfgddejcegcaaa
jbiiahiebgd                             
#eghicjfdidbdidbbfijjbfcgcedhehiihhiceei
begajgbfhfa                             
#dfejjcfcehedibicbgifbichjbajddifccfjdii
fjjjhjjdjed                             
#fjjdicchibceebfhfgagfdbibaajjffjgjejffa
hfgebcijaad                             
#ahfhejceeedjbgfeadbefgfggbbgjhibadhhhhi
eecgajddhdj                             
#abdcdjfjefjdgfhdddedagbadddgajibicidecc
fedabbciaia                             
#dhhfbecafdfgjidcjfebaecghagdfgjedfijffj
dhhgjdbffgh                             
#deiebafbdcgihcbdjadhceihgcgegbdaeehjefc
ddhahifjbjc                             
#iccbbjdhiijchjdaabjedigbdfcbibiiigeeceg
jccbcfeaigb                             
#jjjeffbdfafbijeddgifjgjdhcggedjdjjhfbbg
feggeaijbdc                             
#faddjebjgggdceiaidhcffggaagbehdjjeaajdj
fjbejbcfceb                             

#eeeahbgggiiihfdgjbfiiiaehfeffjdhcgddgbc
jdbifaajefd                             
#jahfbhcjghhcabahffbfifhfebidfiabfgdigfg
aeajfahihjh                             
#bfdgbedbebhijjfjbddghcbchedbgbggejdhbjj
eebcihcgfif                             
#cbghcgdechjdajdjidihagdcddhacjfegdffdad
biihhhhibbb                             
#ddjejgjfeccifhbeeacfagchhjhjgfgedebiceb
eaaeeidjbbj                             
#aiejfedffafacighfbjeegdceaghfggegjjhfij
fjacheaghhb                             
#egdeaajcffbgibfehddefadgaaagaifgfadgeff
hfjjfjadgjh                             
#acgefhghibdgceiejaaecgcgabdcggiihgcdjah
eiajhhigiee                             
#dbjjaggebafcehicbghgihhdbgdgabigiihbgaa
dcbfgdcbbgb                             
#jfbabjdbiihaifcaibehhhdfghcgbadcgfghgjj
ddifhfjijde                             
#fcdafdchiccjijebdabehddggiabaeijidjifcf
igehebbjcaa                             
#eiabjhaafdeediebicfieieegagdiicfbddceah
fjhacdbhihg                             
#aafehgbfjfefegceeacjbehgfajghdhjdhecdfh

bdjgfcjhecg                             
#cafdhfebebbfcdbiggdffegejdjbeafheigchjf
dbbbccfajaj                             
#hcbgcgfcabhciabciaabifbaafbdhgfgdegejjd
cfhaefadaja                             
#adhdjbaigfgeihfgcdadhcedhaabaaeihffdfjf
dicjehidgjc                             
#cdajcbcggaheiacjgbiedgefafidggiegjeacjb
fdijbiiciec                             
#jgfgggifedcjbhhefagbdhdddfgeijajfjhceif
dffddcbhifg                             
#cbhjijhhbdgfbjhcbegbhgcghcffeehaahijiab
ihfdgdjiaeh                             
#bbcigejchjagfijjajgijegfcfheehcecjabhji
ghbjghjgccb                             
#fejaebhbdhhgeechghjahahgeajihjgfidifcfe
jjjeiecdjii                             
#dffgfebddfcdhfcbfgachghgjjiddhigbgggidj
aihechdgfgi                             
#fdgeifbdeghjfjdehafhcdafbiaidbjhibafgij
idefabahcaf                             
#dddaigdffhffhchiccbfhieaciddgdfggecfifh
hcjjhjcfigg                             
#aafjhbhhcjadbgejjebfaaehahicedbdiiiafej
ddedbiadcbh                             

#ccdddbhfbbgjdjciheiciebdbdchjfjafgdfgfd
egdjajaehfb                             
#bafhdfjhhfbgidccdaiibjidebcijdfijjeiida
cijieccdjej                             
#bgdieiedeajjgficdbhbibaddjgdfhbgcchcchb
djgfdbigddf                             
#dbeghfgfhhhfdbchjdjiejcjdbafaighdagfgcd
icaieiejjfd                             
#ddbdfjdfdggbbhcdbgehdejadfdbjgbbbeghhag
gigijhcdigc                             
#bhbiihdibcfhiihjfhbdcjheejifgadbechaigh
gafghjehgbf                             
#gfhjbijjcchcaaiidiajehhdfihfhjbegigbhgc
ggedffdabhh                             
#diegibaifacddbfbjfccibifciegeebfbdhechi
hcgfjcjjddg                             
#acbiidcdjjehcahgciegedahdeiejajggidebgg
abafgbigjjc                             
#igdceahahfhgiihbfccjchgiggejjgcfideffji
bjcefjageia                             
#jiibabcfjjhcgbgibgbaajdebcaeihffbaceeib
jcchjdbgaba                             
#idecaachgffaijeieaiebahhhigfajacjajibaj
cchjegcebhf                             
#iajfffgiggeefjaghdgccbbfbicbdacaidcccjc

fechhfiddha                             
#ffjidgfaeifhdajfejfjdgdhdachdeejbfeeabe
jfciiidicdi                             
#gdifhbffaffddajffeeahjbacijcajehiejidbe
ificbicdhhh                             
#ahaihdffehacebhciijadhicfcjcbgajdhhfajc
jbgaecddhce                             
#behcfijjgaadfgedghefccabbejibdejibcdfhd
gdfacjfefcb                             
#cheecdceihhefchfiiiffjaefgahfjehfabdgde
hhihhbegibe                             
#ihcjdidfccaccaacfbdbejdaaejcfgebffjeidc
igfdfeceibf                             
#decbcbgfccbbccaihfjgeajahedgfcdaicabiig
bhbaigbhabi                             
#cfiaggfecgcedjebcbabbbjegbcdfhcbdgejjab
iibjgjceajj                             
#ffegfbchdgbgdjbcfjchdfighheiiegbbebeijh
debbffjfbfi                             
#ahfcbhbbaadehjgehbhaiibejagbcjhejgaaejj
babbjegfdci                             
#dcfbjgjgdbghcdaeehifjbbieegdfdieceaiade
jhefgeabhgd                             
#ibigidjefgjhfefecihdihgagdddabdhhhagccd
ecefjheeicg                             

#jbcgdghiceajbcdidbfhbafecddifgicbhejjeh
bbahaeifhij                             
#ejegceiafhigbadciacbbaaejebgdffcbfdbjgb
hfbhjdaabbf                             
#ghbeeijhdegbceaggidghffidgichcdgiaeggjd
ijfdjciabbi                             
#ceejccjgjdaabajbibdeafhceiajcceihfebjbc
bjiahhbiigb                             
#jbdjhdhddehbedefhdgcaeidhegfhbddfebheef
cciffjicjdg                             
#ihaddghchbcegdiiebcijfdcbififjfdjdbgeid
eiejgihaeje                             
#jcbbajidfighdbdcbhhjfheiaajhidahihicghi
faegeejhbje                             
#afgddcafdjgjeddcihjgehaaficacfdjbfiabia
gafdbiiafcj                             
#cheifecafcjjhbbhjfgjfididiaaefjbffaebab
gchehdeagcf                             
#idcdjeidhdaddggeijcfbjhbbeefdgicdaeebga
idafhfhjjdi                             
#bahcfiieeeaghadhedggdhcigebjecjdbjbghhf
eejfadiecdh                             
#dhajegbghjcjjdadafihcgdijeifhfafdjagicd
accfficcdjg                             
#cgcdebgaghdddiabidghdchddcajdfbicegciic

ijdjijbihja                             
#dhiihfdidicdhdgjdafcicjgjbgbbdgdfebbjjg
ifcabafegef                             
#jddfbbfhgceifcbdiddhgafdbjiaiigfhjijfac
gaahheidaeb                             
#adcfffjeebfiheiafdfbfceccbdddeeiiffbfbg
bhdjhjbeeib                             
#dbjedbegehicdcihfdjddebhcfjhachiighjjbe
iaccjcjaicj                             
#icehbbeagefcdfgijdhcedeajfhechfjdhfabhf
ficaaffjbeh                             
#hhdcbhcjjciheefihejheefddaccbfbedbcafcf
biacbcfbhed                             
#gaaffggiijeihdejaibfidjgcefagdhhbfiiabe
heahfghbidj                             
#gjgifggeaaejicajacaeafjfhbfhbbdcdhcgheh
egiehhjhjfi                             
#igbbgfiibefjbjcgdfbhhbbdifghaahhagfjhgf
defdiacghag                             
#ahabahijbbdgageidbeefijaicejbgiebcbjhfi
iihfbieeeif                             
#egiijbgiaddcdbcfgehgfffbbihcaddgddeggfj
eihbgcahcbf                             
#ecicbgagedhdbdjgeeadjfaeejhiabjdhdbgeic
jcdegcbfahc                             

#gdfheaiaeijfhdeafdageddadadfchjcfjidaci
gifhechhcde                             
#jdafhehibdfdabgafhfcbcddfhbbehiahefhfbi
dedfjbbjdib                             
#jefeiaggigacacehbheaedbjjddaifdfceccacd
dbjegcfcdca                             
#jgacjhdcaeeaaicjbiejgggcehjgfgheccchchh
jfjdcaifggg                             
#aieejdhgfacacdihijijjaiahcibhecdghjfdbj
ghafaihefjh                             
#ifggdgbfjadciagdiifdgjcceggdaaeecdadbca
fabefbjhfih                             
#cceaddaeddcbeefffaahbjfgfedfcghbgbbebjg
gcjbebadjjj                             
#chajhfccjeidcibgfjfddifaejajceeaeaiefhb
idjgifhebfa                             
#eaaiaijigcaadcadiagfcedfddffifcdcbbijhi
hbjibcadgfi                             
#caiafhidjchjeabcchgfejddbafggfbbeeijihe
jfhddhgjjhe                             
#ggchaifhaiciegdeigiciaffhiaahggebjjcige
dhdhidgeche                             
#cihdgcaecijbfiggajaghfefgbjijbhjfgiifbg
dicbjgbadad                             
#jbigchadehjgejdjiiefafeijffaedddhcffech

eicgcdjcagb                             
#cacdhaccfeedabcjhfggcjfcahbaffgdeifihdb
dcadggfcdad                             
#jgadjicbgdjaidhbfijefdhfdijicedghcjiaif
fhhahdfhidd                             
#ighfafafhcgfbdaahhjjdiieieegfcfeccibbjh
cbidbbfciji                             
#dijedcdbabjbdbcjbdbfiabhaebjbiigjihaife
ajibaeddhhh                             
#ihahjffijjjccfjgcgadgajiadhdafbdjhcbcid
ijbabfgcdab                             
#hefedfehjbgbfjibafcdhbhjhehhjgdhheejabe
cfdggjbdiba                             
#gdedahcigabdahgabdajhdbaefiffieigehigdh
bfeacecejdd                             
#cgihbjcjhcifegeiiigeedhadcfejdahjecfjea
cabjhfahjjd                             
#jfcdhabaacaahjbijhhefdejgcdhehahhebiiab
hccifadgebe                             
#bafdjbafdagieehdhfaidghhdaddaeghcgdcjfg
gdhgfjaaidb                             
#jhdfiihdfibagfffacjffjigjheddfjcghihjif
bgjehibdgid                             
#adfacfjgjjaceadjfjjjjihjfgeebicgciebbej
iijhfhcghjf                             

#fagfdhhgaadadhifhejicheajadigcdfbijfdfc
ihjfchgceec                             
#fhchjbdhbbifaigjiecajgfghabeiaecjcgjaeh
bbdajbacbce                             
#eddfejcifecdabcaafhheegajcbibgdfegicadj
dedhihejghj                             
#gfjeabhifbagieaabjjcbfefgifefbcdhchebjj
gjjiidebcgi                             
#ahfiegbiagafjiibjbchdbfhcfjccajhggcechc
dcbdbighhfg                             
#jgfhdfcjdjccbeidjhdgiffajagifjacfdeddad
eegdieefjfe                             
#cfgfaighbefihiibhidfbbfchidbgdeidfajjba
deajajfbced                             
#ggddefghfgedhhdbdgjigfidccafeffjcfeidgh
eacajfbhdcb                             
#jhaababeaaafdgedeigjgeieacagjfggaibdiii
bhjhegbddah                             
#fghfgcjefdeeiaajdiaijfigefjbfgjjigjgidc
ibgjfbdfdgh                             
#ciacggbehfbdfddeedigigdjbgejeaaehafibbi
edaffgahhfa                             
#idhcagjjcbhbagedejcchibagchgafceiadicjh
fbehffiejdg                             
#jdhjigbffjdghafadcbhgbejagdgbibfhhcfifc

jeiabbgfeie                             
#dfibgbeafccidbcagjdagijfehgbcgeebhbhjfj
jaadiadadda                             
#djcbedgcebeaecefihcdiifhcgejjdbdiabehca
ihfagcjehag                             
#iaddfcdjhfdcfdfeagjadchdejefjjadfaihghi
eggijjcdaje                             
#hiiciehiaadgccaadbggcdjaahafbgfiiafjgce
ffehjfhhcge                             
#jbhjahcefgaaedahgdahebgdjbedggbifggchfj
idcggabgdbi                             
#aeehbcifhdbabedajcahidcciddfiiehhgjeifb
bhihdcaihbb                             
#fhhcgbacaihgjghfgbaefbjdbdaijdhefjgiice
hbihjdbijjb                             
#jhfjfdegicegiaebeigjabecgcbcajecafcgajf
ajibfefcaff                             
#afhejcehgegaccdfhjfdjcjgfgiidjdddjfjghi
ghdedejiiae                             
#jehgdihfichaccehjihibeegdaeegfffbbafhae
iddeiijbfjd                             
#gggfeficcicicabafedhbdighccagaccdajiehd
ighiahgdbed                             
#hgghcjeabedegbagdejfegbdcdceeahhaeidchg
gechedfaeah                             

#bdbibcheijbfhigcdaabbiibifhddaaifaifecb
jdfhcehhegf                             
#cdfhggegghjeediggihchigfeiaidihbicadifg
giafhddchdb                             
#fcdcfbacfihecfbhjbeigchegjcdiaijieefjch
bcaciiagage                             
#giajefgjajhhbjbfiahdghejieebcehebgegeib
fhidaaghigd                             
#achjiebfhiadjfbibaagbcciigjddaafafbdbga
ibjcjigfcaf                             
#adffdeehddhiefjceccgebabbgihgecgbhbicda
gjbdbjgjfij                             
#ejeibcbfagijhfdbfeicbbhcgijejabheddgcca
ggehcaecdch                             
#dhacbjiaaagdaidfcdabachdcbbhfeacdjagicd
cjadjgbgaef                             
#hahhgbgcbbhdbeecfdbbfihhfadfifeaicecafj
fdhbcaaiafh                             
#iaegdhjbcjgcedfgdfjajacaadeigbcgjfcdfee
adaijegebcj                             
#hahjgaecfffjedgghajcaahbcjedcghbdcdgeef
bfihfebfjih                             
#ibijiddhcbgedacedeccbgcjibahfffgcjeiibj
ggjbaahgcge                             
#djcjbajcabdgabejbcadceijdafgdggcigibicd

gafifigejcc                             
#eegbjfachjbaajahibafdeabhbdgfjgejedabcg
gchcagadhea                             
#fcddfcfiifdggdjjchcejbghhhddjdaeeddgfjd
cbecbjgehec                             
#fbbejejebgejhhjfgfacdeidjibfgdjfigejbjd
gicbeebhhig                             
#jaaacjcejhbfhjieheafjjjdagebcjbhbjcegdh
heibidicbec                             
#hicjcfaaahdhfjdefajjidggcegagjdgjhjjjdj
ijafgbadejj                             
#gddjebgjcehgbifjhdeejgbgbaddfdheehaeacd
ihghjhjfjhb                             
#acebabigicgcbgjddccbbeijajfbijdijffecgj
cifffahjfgb                             
#ghbdjfefbjcjdhiighfcgghcabbcjdbhbjiijah
jhdjcgified                             
#cggahgdahdjbagafaidehgjddfdjajbbfbgccei
ihahaeheicc                             
#fedebcbfhggeihahaibgejcigichegjieafbbab
fajgccejdbc                             
#ggfihidfhcgbagahgeghhjdajeebfjjdhdidfja
fdibjcededd                             
#jhgdfbgechebjgcbbicbgjcgjcdhjhfgeghcfce
dgcacahjfcc                             

#djghhabhfjbfidheajaihfijaedbggjbcbdjifh
aeijihedfef                             
#fahcffadicbiahibcbhjecabhigdedjdiejgiih
bhcjffdfajb                             
#gbfidfghcbcfiaaaddcjhbefdahdeagbacdjeij
idfgidfhdgc                             
#gcjgdjdfaiegjgghgfgabjgbdfhgjaiaajghhhf
cjjeeedgfdb                             
#jhahhjggahaaifahdaaihccifhegdbebfihhcaf
eddebheafdd                             
#cgjfdgdcfjaebgicdibdcefdicbegfdijceiegb
dchdeejfeii                             
#ifjibdaabhdcbgbchigagihhbfhbedbjbejdegb
bdjfcihaibc                             
#jjieefchcajchhbcfedihjgdhiahjhbffbdffie
gjhejdcjgfg                             
#djjagghddfedeiaaiccdbgiiachieigbifgajgj
cafadjehied                             
#agijfehcgcgicieaidigcjcbfccjecdiaiijhib
gfgcaiebdja                             
#cjbdchgfgdeeafceiabhdbffaehhgegfccgcjjh
cdggdjbfice                             
#hdjfbidhfjabhdaacjebjfecbhcciggicehicfa
jghaahfceea                             
#deigefibfbafgaeejfhdicfbibcbgifddgcihdj

fcdegcaddge                             
#bcahbcgjheefacfheafebhecgdgiefcdhggfaea
badbcjieheb                             
#cgejchajbejcjiebgdbaegcbbjfadfbjhciecjh
ejcbadjfhie                             
#gbcgdhddhgiaaadahageiacdegigcdhhfgfehfd
ahejihfcabh                             
#ccigggaidgiaijbgdeaedabjbejiibebehgehae
giiffhbgcdi                             
#fhddhafcefbbdhfhjbhgghgcffjedagcdafiiia
fcgfeffeche                             
#hajiefcdiaifdbbdfdajjbafagdecjcfafffdfg
fgghddicaia                             
#fhgfhhjcgfjdcdbdeefhbcbedjfcbehhhhijeaj
beeabehgbch                             
#gjbjjidejgdeiifefhbbjgfhbjbbcgbdjabdjbj
hbjidbhacfh                             
#cafbjgaajdbffegbheebcdcgeebjciideceejfh
gjdihehbaea                             
#hhadddgihidffhagfceijdcegbdgfgdhgchgjca
cachfgbgcff                             
#fdbcgfiegbfbjcdfacjeagfbjhfifabbgjhcdce
fbgabiccbbg                             
#edbddhadddaecigfbgbjcbhfjcbcdacgchcdaah
cbbhaghggah                             

#ieijgefabjdgddfhfjibhhddcffejgjfecbfdja
djeicgdcaef                             
#agjbabejabaebhighbidehdfciaciaiebafgabe
edaeiaabjcf                             
#fbfagddfihhihigchieceehigfabijificefdca
jagfjeecdac                             
#jigfafbjjgghcagffcgichciagbiiahbbbaggga
fiiheeebgfc                             
#ahgfdaecfbaeijejbieffjjfedjefjidbiabffg
ciajehcbehg                             
#egghiigeiahejgffcbfbffaicgaibeifeeebigi
aeeadjefcai                             
#acbjifdeijcibfbdbaddidiagieihfgfbgdahge
agjfefefdde                             
#bfheaiehhabifedhcdbhhbjcefdhdjiiiabgdfb
adehaadihgf                             
#eidjhgddfebdgaechihfeifdhgbjcbaajjgicie
hafhdaghfec                             
#hhgfaggejcjdbdacbeefhahcgfdcfbdcjhiijbb
eajjehiahff                             
#cbebhfhjdjihigfiebfeaebjgfedaichjefdbif
agggejcghch                             
#dbdggjcdafigdecegadafhhgeddfffadgffhejh
dgbgifdhdeh                             
#dfegjfbbgggdccdaeaaaibiigeababjdccajdje

dibbihjfbdd                             
#cjfaigjghjabdhhehccifdjajhddbjhiedigbfg
hecffjccbhc                             
#dhcgjhbdhdfcccfdbbeabdbjcdbeedcheedgdgi
bcdijedbdhg                             
#cfigcbdabaeejfbiggfiejdiegfidjcbbeihhdj
ebgcbchcchc                             
#hgjjggcedgdidbjffbebibcheefhgedgeiebhcf
gcfahifieje                             
#jcbedigeajedgefheehbijdbfdbhjbhhbbcacce
hcjagaacdeh                             
#faigejaighddbjbcbjdaghegefjdgajehheijie
gfbcdfggjef                             
#ejdcjgghggehecehgaedhiichejjheeahhieaaf
gjjeeijfcad                             
#fdifchdfdefbbdbbdaheaiiheacajfabbcjfgfa
giijdhiddbh                             
#dhhcaghbeagejfeddcdfechdbeaccbgacjjbcjb
djdchcjfbdg                             
#bfbaihcjfajdgfjahehijgdidchabaejigjhcgf
diibidhifhd                             
#hcabcighigebdjjeiabjcdcgjfifecjffcagcii
bcdgjfafhai                             
#fhagbjbfcijjdfbcbhjheecdjgfjacifdbibcfd
dbjabcjdgfg                             

#hbbfgjchccfbcbehhebedfgfbfhecfcfghbfaej
gecdjecaeic                             
#cgcacjgadeghihiajhefibfifjfcgcdeigdbhhd
jbbbejjebij                             
#aeebjiihhhdjdbhjicdeciagbahdgehjiagjcge
acjfjhacfdb                             
#jihdheegbijgffiehbhdbaheegcfjiiigaigfdj
cedjdigjgeg                             
#jcddehbjaejaehbegjbhhhaacddebjdddifdbee
bdajajcabdi                             
#fgffbfceebicahadcdidicgicbfjajdhbggbdcd
ahdgjfciidb                             
#hiecddfbbbbjjdabiicdeadbbjgddhadaijcccg
hicaeeejfhe                             
#bbgefcjifhdeddcfciabahgfgjjhafabhdggdba
bccchiihhcf                             
#adhabchbjgijdbfcebfgbjbafadbgdhejfbbfah
hgehcfidhda                             
#iaagbdgidhccjjjdaehbhgcdjjeabcdjahidibj
ijbhgfgdagh                             
#feddjbaabefcfjigejbjgfiaejafajcagcjfheb
deaiacjhfid                             
#iaeidefiacibgifbdeibhajhiiedjgfbehiiedf
cedhebbched                             
#dhgegiidadgjicjfejggbfgfhdeabejehhgcdii

eghagfhijee                             
#bhbbefgdgheiefbjbagehecfbjbdaehjgcchige
cfbeidcefic                             
#aicfbgeadbjbcejgebabafifaiacfgbabbcgice
dhcdcbahige                             
#gebbaicgdieaaeffjihcfbgdcfgafgdfhhgfjci
igdefhgfbfg                             
#ghjbejhbghdefgedjhceehadegcejfgejficaja
fdaeecjahfa                             
#gedgicffbggbidjhcdibbbcdhgahicggcgaaicc
dcefdgchcad                             
#dgbahjidaacechchidcdbhhcdfijedidhdgbaef
gdidhigaffc                             
#egdahhecdihihfhggabecgbhidifgbagjaecgdi
fgbjdjbhibj                             
----------------------------------------
--------------------------------------  
#agjjjj digits of gamma1 as calculated  
from a value furnished by ,jon ,borwein4
  gamma or ,euler constant is           
,lim7n-infinity7 sum7#a_/k1k#a44n7 -    
log7n7                                  
4#eggbaeffdijaecbhfjfjfeabjijjhbdjbdcajd
baeicceiciibceihhjegfgbcdhhdhfggbfgggff 
#dfgjicfidgjfcbiagdfgdieadfcaddgbdihjgjh

bdhjifjejdjaddhfedbhcfbbdagciigfddibcec 
#fbecejjcccgdbicgccggcgfgcidbgibeiebehbd
gjidiafjjhgcebjcidhafefgjhecbccaeaggffa 
#aebhfbaaiiejaejgihdgicgdejhegjegdjjbiib
acedghfadffidjbifjdcbedbaeaijehggeecebf 
#gccaciibedjabifgdbjeacgedaciediaaafheaj
bhjgihdbcdhggehgbjejchdcajiciigcfacgbee 
#cjfjhhiccabfgfjjagbdgiecghcfgeibgaceaeg
gbbfajbgcdibiacidjgihdcjajcdagggagghjhh 
#aediegjffajgejajafaiaffccdjaebbghicehfg
ifedigbebjcfbabhgibbfeeeiecffifbhagfchh 
#gibgbfhjacbdcajajdgfejeifcgjcidgcidiegf
chijfegbifgibifjajjijaeabeaieiejibbbdce 
#jadjicdihgabbhbdgidigdgaiefdfigfcahejff
gfabijfchaajeahbdaigdddhfghcfchjhfagdid 
#eeafihibgibcjahggciajgbideghaeedcafjjej
jbahbhddjifjecggbdcdbjcbhedghcfgjaeaggc 
#idcihgjjcjbcgjccieahcbhfijjjaeehaicihhj
dbgjgdaaedbbbghaigafebcjaajgcefehccifgc 
#dhgagfejdiaidahabcjjjdjfedficadbiiibigg
gieficjcajjejcjhfcjcdahefihjcbcajhcfiaf 
#djjbehibigjhijihedhfhbegggcfdbhhbeciedi
behgcfbieifaccbihegdgcicjbcgcdchhdgjgjc 
#gjbhddabibjaffdaghejbdhgcccgijhjefbgedi
ihdcdeijgfafdcafgajcadfgajgbbcgjjbahajg 

#dejdddahffdgeiacdhjcffijbeecbdehfbeddbb
becdeahachgiabdcdegcejacfabigghbbghbhha 
#dhideijihfchdfjjfbicafidgahhgadiehgebed
ibcffdicebjdgcbdcfdajigbfhbgfafjhggeiej 
#hhjieabfbjhdjdedddggiibbiiaegbdhbibeafb
eabghdbgfeifegjhcbadfajbihbadfagieaiegi 
#eijieibbgjdbjhihifbgigabeecfcbagidhhgcg
fdbajffjfjgjfeihbefaiijajbhhjgefabeaiia 
#cgeaafghbagfdcfaijegjehddjghcegcejaehjj
efjggdegicdbacaddihhejjghfdaeagafaeaide 
#fegjfagjdcbdejgejjhafhgjebcjghijicgjdfa
dcjffhdhagiafdifhdbediaejdifgbdcabahcgh 
#chgecefdhidiejhfhdedajbcdjfjafbbejheaee
hchfgbcdiddahghhjddjidjggjajfhhcgieaaac 
#jghgbjbcdbfciebbfibjigafjhhefijhchbeaac
ghgabhcfhbjdiaaghibeiddghdhfaiiaahebici 
#ajbicjiijeibeebffiagbgddfhibjddchfigaaa
dgagdegaegdegcbjcicebjiabbcafjhejhfhbge 
#ehhijajideafhaahajafhgdigedgjificfffgab
ajbjfcjdhbgafehiejdicbgcadhfjhgdidjbjgj 
#jfgdbeijiahbdhgeifbacgchdbcaaddbfecacej
bibcjcageagbbegbbafbhcbdhhchaabdehiegdc 
#hfbcihgjcgegffbheeacjccadcibiiiedjaheca
cdadaehfbabghhfdhjgfaajjcjaebaaifeghjjf 
#haagggcgfcejafhahchigcchiffcihfhiegicbi

iadefchhfddcajcgjfjhjghagddhiiegiehcbde 
#gidahifbjbfjdihdajdcibbejghfjdfjcfbebgg
bfjbbiaifhbiiehfjihhccijacghgagadbbfiag 
#hhchaiebihddefjgiafjeaigbgigcfjdgeiajbe
ajiieggiacceaegiaggbbeaejbedibicbdfcbej 
#bhgdgfggidhdbaehdjejgeiibijdjaheegfdeii
jahfbfibfggfdcgbffjegaagfhaccfeeijhhaee 
#dhajgdgjjjjfbccfcgbebhhidieedfcfigadccj
abjjgiacjheeebfcieiedighbcjbcaddjciadig 
#djdidgdfhbeidgcbjhdfahebdfjehggffidhhbh
giecjajdjfcdiagbbibahehjjhgjfggjfijdbgi 
#bfgdcbhdddfifheadigahbefghjiehdafeddiah
eadegeccaifdjfccaaiicgchbaegcdejhgdihhc 
#beefjhhhhgcebhjaijaiaeejhifhheedfhbeibd
edddebggbhagcjegcjajhjfjfaggjaacfcggcah 
#bdfbibdffjjhabggafbajahfggddfhdieieadbh
agijadeaaaidhicdbbhhcddhbecjgecaahgjahf 
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hibbidfbbfbhhiaebejebgcejhdjefjfaghaafi 
#jgadhdbjcccegiadagjhjbgicccdcdefegijffe
gfedijfjiigdgcjifieabifefecicjcacicibgb 
#jjgdgfdggeddihcdfeeihdhdghcdhadeehbhhad
dhadbffebfijigcbcceahhjcghiijhicfagbabb 
#dgejdafhgfdighgceggjbbgeeadaeeagjdhagde
bcdgbccfjdaibcajfagchddabdgechccdefdfff 
#hbgjgifhhjfgghjggefcahceaghdceejdcidgch
jhecfdbaiiacjbfgceahgjadfgjfjeaabaefeba 
#diaicdibjibbecbjgabhjjbhiecfdgfhabbhafh
dcifcjgjgahgbaidbfbccdiejadiiccgcghgdaj 
#jhjaigijccdiaijeigcdecijfiaifdieefdjbaa
ehhaidhidfdfejhgagjhfdbiebhffjchfjgjahi 
#ijjajiaecfeajibhacdcifdcbgjehfgjcijgfdg

hifegdiaeffgfedgfdjhchhdhjhfcbddjccfeib 
#ddbjifieiebbihbjcejjgcgedeedbiieeecfgii
dbfcagcjfebeajjijgdieigcidechbbjdfggdfe 
#daddciehfbdicjibicejbdafiihcffhdjgcifcd
cjbhbicejbgbifdghbbchacifaijfegifihihda 
#gfabegagefcgbddfbhjdfbjifeejabidfcbaacc
hhaabfdjdcifecehibciceiiajgbihiahcccdjh 
#hegabefbhgbjfihhicijggbgfdejajhhhcaicac
bdeedjiidijiidjegjiaibhhicbgjfdjjgfjcje 
#gbegijdggjdeaecbddicjiehhjahcbiheaghhfb
hghfbfhgcdfcehgeigdeifeigifdceacecheiif 
#cfbfdagiiihcgeejifcjghifefjbbbfigciggad
eahfaccbdahffajdijceccbcgccjeffhbfedgif 
#ccgidgagfbbgiijaafaddhicbhdjeajjeehcdje
bhgehdjjabfhejaidaagdgjccfahbbhdhjibffi 
#bagigjadeeaejifbddjdhigfdagahgjeaideffd
jihecicffcbhdehhgcjegbhigfacdfjdddcgbij 
#afjdeddfjbdijajjeffjibhjffchbjjejegiega
ebgcfhefhhjebhfcedbghbhfaejdedieidacicd 
#gfgbgihachghbjbejahfbceajbbgjjadffabdfh
jfhfccfefhebchibgfafbhgadieihehhhjgbhgi 
#djacacddijhbcfceccgjecfcaechiibdcbjdjci
dgeeiagcfdadiggcidcfdgabffiecaajaecfdeb 
#cbehcjbechcbabfbaacceiaciihadgbedgcajhh
efaajcejbebcaejbcbbfjgfdfeiadcdgieggjgj 

#babbeeibchegfaifeaedaacjfgeijbjbjggahah
dgabeedddjdhjidcagehciadajdahbhegahdfhd 
#bedcefdbhjbaadhfabhagaadjeiicabdaheejig
bcjjidhcfgahaehbaffcejcbcebaddcjabgfjbi 
#djhaajdhcjhcfhdjccgigbgfiajgcdidgabgfci
dhebdbcfedcfjajabafaadgbfjacjbgabcjbaad 
#icfcidfahfdjgaccbcdahaeehhcagjbiaacbdga
aeeffheagdjjiadffccjhidafgiedachhfjfdei 
#jdacjhfjbdgehadhjibechhaacfccdcaebbjbac
iegcfgbhghjdgbgachcgejhehicdaicedbdddfd 
#cdgafidhfheaejegagcbjhcdaijjedfghcaebbe
difjdghbjjehbdifhbdeidiidbchfjbaffaefcf 
#bbaeaaghebgggbcgcdhcibedabcgaiiabciheai
biabbcaffjgciecchjdjhfjjcagheeecefaffig 
#aebfffaeigadbihjichbifdjhagdhdjfgeiefeh
bebbbieaadidbjfcbijbgggibdiggchjbjbehfc 
#jdijjbcchiadcciafaeaigcjdgedifagcicjjcd
ijihcahejcabafddebiibcbcijjgcjcijbbdjgd 
#ifjigjbchfjfagdjhhdcciccjccaaffbadacgff
hhicgjcbdchddiddceiebachdfhhaeajdfbhigh 
#ceecfafdcbjgegjdfcbeedjibbdccejbcgdjdjj
feeffbchdeihhagbecfbgfeghbjeaeiahhhgacg 
#dbhbbdeccfihaadcgeggggeejgjdgjhcaiiiheh
jdibeeciifaeeggfhhcecaiffjchhhdaaaedecb 
#eajcbcdjhdagffhfhefefjfdeccfdeicbehbibh

efaecdhgjjejjcfbbegdbacefgefdfaggjdicec 
#hjbgifcbibfgbbjafddedddedgejbffcijjigcd
aefdfadjhafabcghjbcghficedbjjfgaicjhgjc 
#bcidhijbjfjeaidfbefiafhabaiafchihhighfh
bdfgiaegeijhbfjaahjgdidahihbaedjijaifdd 
#djjfjihehbeaecieadebehdjejedjegccdaigae
ebdaaiccbbdgafbdhagaehfieijdeifjgacbbbg 
#abjbgjgejjchjgcdaejegbhebgcjeadacdfagbd
cfdcbdcejgeijhcjfdddbeaagicajehbagcbeef 
#cejicgjjjdfchfajjfjcafceebffbfjhaigefae
jegbhagdcbhfaigegcaaccabdciiechgjbhjadg 
#cihfdfdhaieajddjdcgjfagacdebiacgeagbdcf
eaehecegigjjdacieibfhebeiihabgbjfhcjicg 
#ddjigdhbgdbfediajjddhigbhdeaccibjhhdbij
ajjcibcedagdeejhibjagdjegbacdadggifhhfa 
#hchaejaahgbhghddhdbbighbjaccdfgjhidfhhb
igciegaffcejjjiabjjbdagjcbgifdjhdgfgehb 
#hgidgdgaefcgddhhejjaijbjiabjffiigcegdae
ejjiahchfccgcddcafbgcchefceceidghahgdhf 
#bcahiaechfhbiagfbdfcdhafbdgjgjgbgaedfje
bfiefcegcdgcdhjidffbfdihibdfagdjabifbgg 
#gfegfdfbcgbhjbeibgggidhjfeggffgcjaaiedd
fibgdciejabfcchfghdddjcjajjfdiaidbfidfi 
#iegffgaheefecfcchbfaeffbcbdbajbhfgcbjdd
cifidhdheggjcfchdccbgifdcefbdedejfhafae 

#eacggahhjceigfccibicedgiieabfbiffhedhbj
ehfhibgeggjggedhbfdfhcfdhbdggdbedeeijbj 
#hjgadeibedecjjicecdecbbedhgcdafdaajgigf
ifbbgbgbchgigfgbdcjbeiaijffjchieejgachc 
#acffiahahaebcdbhbebjecifhchfihgbjjbdjcj
ffcdgeigefjeacdfjiaeddfiedhafbchgdbecgh 
#aehcjbfecjihajdgdbgfjfjggdhbijagaffdjcf
ccfaejhgadigdgfehhagbaibighhecijhdfdddf 
#ebhgjefdafaijdfhcfebcfabdcbcfggcbebhfgd
facfhhfhdbhbhgbgabbahhdgjefebjgcebgjjcb 
#cfeigbgeegdjbcgchcacacjgahcacgdbficcfea
dejfegigiigfggggbfgiihhaddgiadcehehcfeb 
#gcdfbhhddhchacccdgcbjbecjcbefbjcibaheej
dbcgdejgabdfbjagjbdgdbhiageifediehihaii 
#feedbfhfaagidjfjcdhbcaajfafdigghigfehje
hgijaiibehgdjfieedcffgicjcgiaafbiahjbhb 
#fbfccfejeabhhcdfebajigdeifccfdffhfjjgbb
jhghiaiffdggfgbcgddhhehcfjiecjbjgffeeaj 
#bghbbjadjgdbfheagigdbbfbeeeaieecjabjajh
iggadjaeghfhbgbejfgcaegdjdfjghejhiagfbb 
#ggcfbehaecfgiffcgehfbhahhciaebeeeieebea
facjahgjcaddbafijibhhhbgdcagaiiebiefaec 
#bgaeabjhefeaaafggebidedbhefafjgafjhfjjc
fhehahbidbggedgadacahiadijeeicbahcjaejf 
#aifbcfajaabahjhggebfdfffeabcjfdeiiiifae

iccieaagfedigjdaiccfdfgddghdigeeihjidce 
#bcicegfffbdcbhddcgjbcihhfifdjaaggcfdfib
gjdegdfaahjiebhgdhhggiegjghaajejagaifff 
#badgffdahfbfidigcegdfachhiciagbhaeeeafe
dabfdahfcggidcbjdehfchahjihdjfjdcdgjced 
#hgjjbggfhheefhejaeddeciebgbiiafeicaeigf
hjaidcjjiedaifehejagbcaiefahgjafcbcbjag 
#gadidcadegebdedahbghigbdaddbjjiajibbbce
hggghdgfbadcihbeccjdiadadhjeeahhdgfbgfd 
#jcebcggfigidehgaccbfbabidbaccbghjjefhhb
hibgadacbccdbgijheffieddjebbgafcjggcfac 
#bbbbbcfbddgfdibfjddddibeaegfjhafgbjeabe
giaihcdjadadcadaagdfbdcjcejiehehhcffddi 
#hhefcebdabafgcejifdihaajhhfdhjdedeefaba
dhfaegaddcihhigjabeaegdefdafffghfjhfigd 
#eiibcejibcjfiacghghbbdhihhegdajajaebcjg
hcedbgcjbfhfgjbfdcjgfegccfaebgchhjddgic 
#ihjifdjcdecchicdadbfiihhjaffffbeadccahh
egbbbggeeihebiibgcajfgdffhegccfaighgjdh 
#djdaafgcdhdedjfcbdjgjefbjchfbjbjhgibicg
jfhbajddccjhegdjijbgbiaebbbbeffijbfhiad 
#aeddahjeeicdhdjiffcighebaaajaccifcagccd
hbcbgaceiecfaiacfdghedhgibdbfbffgaahbbg 
#bfedccijiafdgjddifcjdigcfdbccfgefjicchg
fhfjagjighifhicgdfcdagijjiehebajeiiffih 

#caaahdidgahdahgbaadgahihifjcbchacfeeide
fcciehjiiaahjajiahhihjdbfegabeiejecdicc 
#dcbeijfcbcehdejhaddcdhddibibhcdiebdbdhg
bbhecdhdbaeheeihehbbgafbbegfaabajfabbgf 
#idcehgababiibeicdjgghiffadigidbicfceide
hbhcciibeebihddichbjedhhgfhgiacceehicbb 
#cghbjbdgdejdfhddefedefgebjgcjbgdigebgha
bdfbieediegeifabjaiajceagifcggiiaccbaid 
#gfjibdijfhabhedjecjicidjgggibbfhffbgbcf
dicchecfcggggigggehdahciiheegcadgegbejh 
#bghbghaccdbddjabheihbehjdffdgcjaebdbjac
ihgacdfdjbgbheejjcdedhfdacdidifehejjdjf 
#cbejajjcbfbghcdhihcjibdfdjebeceaeabhgeg
efeghjjdadedaifidgaifhbiaidabiabechbcbb 
#cbcjdjbdbghjggbjddiacejjhacahajddjeiadg
icecjabgeicgbdifjhbhbagjijbfcjjgcbjeeee 
#idbjeejibbdaehdicfgifafbfhdghdiaiiaadgi
bghafiadjcdcdfeaeeigcacgfecaccgfijieiae 
#djheegcecbbaigjhbaebjbjjjabhghebiadhfbd
ahjgbdcgbgbfeedjbfjfhiaiiggffijieibicab 
#hhdiffeddhbcceacjgfjbehbjdgbbjagihaeahb
ihaecgaaegebadeachidbedjdjfggfdadaejcgh 
#bfaedbhhgcebgdcegbajibfiiahbihgccghdicd
ibejfgiddhhdebhjadbhfaijffchfdhicbjchcb 
#bfbdgeehebiadejhgghaahabfjffjibhgdbeidh

febiggcfgibgdgdbgdcdeddddidbiiiagibjjaj 
#eibhbeghhehhaacijbdacbccfficbcihhcfdfaf
eeicffdcdhhicagbagjdffcbigdfihdgcbjiedh 
#gafechgffeigbeighgdagcgcicjhgciehdgbedg
bgcgcgfbjcegicaafbhaaahibabjbdgijjgabde 
#fjfdficegdagbhdgfahbgjhcceicdhahhibadhb
feibecfeibbbdeadccciicfcieajiidehiidfif 
#idfcefbefcbbidcabcgjdgaegfiagfehdccdche
jbadifggbigfjchdiijeiaidbdjjjiiihidchch 
#gigjhbfjhaigcijidbiggadidbgaeijeiejiddi
hccijdfddifciehbjbbgcdbcjgaheagjihdbeii 
#gfgacehgaaeecfecaggcagideeecadgafgachbf
iggjfebciefbegbcjajagjbifiabebfbfdhhaig 
#aiabccgegajchhiidhcifeecdbcagadabaiadgj
ajcddgebfjbghfefjigihbacegafibgdihhcjaf 
#cgjhhfbiggihjahefbfibbgjcdjedaihafchghh
jhbeihgheagheifjgbdejbibaiicfedfdcbhede 
#hdeecgjihcddjgidccjjaehbgcbddgbaecfhefj
gbfibddiiibddifefjhijeibdadhieffaeifhge 
#eajdgedcghgfcacaiffjdehhghhddeaeijabcac
dahcbieadhehebhhhgfjedeagiihfcjibcfeheh 
#bhdcgighdccfjdhcbiichgfdhghijdfjebhgjed
ajggdfeciacfjaebhjfihhbehiggeicjfifiabf 
#gdcbhhjgaebghbjfaidgdcdfejdedffijagcjbg
gidahccgbhaaeaedhffghgbgedfbaechgcgiaae 

#eejgbbadchjjfabbcjehbfcjhdadijhehfccahg
jeabbhfhcfgfegfbhgaaaebdacghbgahgibhceh 
#ahcaabjaigjfjhhfhhfifcdicijgcfghcafefeh
hhcbjbagcefhjicidciiiiheejdfhgiabfbbiii 
#ejadjcgajddfgieddeijbidgcbabggdehdfhcfd
jegeabbeaadgfbafhiegaheahbeabbicigacfhg 
#fijjcdifdjidahggfbggfefeiahghejeaaffcei
ggjiaafaajgggjijefhicjdbbcbehffcchhjdbc 
#ccbfdadgfcfigjachdffbchdagbajejjfaegfcd
ijagjdibigcbhedbgebiefedifabjdjaeaijdgb 
#cbdfjaiefgaaafbhfcgabhgichbbghicfdbjhjf
bbgbebciaddfcchegeadfiijffcegghccifjbfi 
#affifhjiedbcciiebbcfiegjjfedbddejbcbbfa
jifhddggciaihcdfdfbeeccfjihcfjajjfhejie 
#ggdifdeccfffbjhbigbbbaeigjgjgcfahdbcbja
dechieacjafjjhjgiabiaacdgdddjeicbjfgeea 
#gfcbiegcciehfejeefbciacchhcajdajjgcfaeh
ijdgagegdgefebiegcdccejeadjijchbfiiifii 
#fjcfjgjcibfaahhfbgibaibaaifhgdjejhjbbch
ibajdfdhcfjiffbjcbghjhbcidcgdeecbfigcch 
#fghccchgdifbfcibaeeabfihcgcicfecbfjgdea
baaeeffigahdhcegffcbjfhghiefdbbhbacffbb 
#gaehfgdaieafiaaafehcffbfhffgddjdedeejhc
abgddghabcidiajjiicbchhdgijjahiddchdjhj 
#hdhhgejejeagjefagigddaeiigabieegadacgej

hbbfccadjcbjffehdfbggbcidgacjfigjadcicg 
#ghibdfiehafhbgeffjhgdcfijefifaciaidfjad
fcbdehdbfajeffgjbigheibhfabcbgbdidgghje 
#bggbeiccbaiijbdggfghcbihbabedjbjeacbaaj
adaafdddheahdfjehdggigajfhhfeehdhbiajie 
#cahfbaadgbghadfdhbaaajedggaddaiafaiaagb
                                        
----------------------------------------
--------------------------------------  
,the ,artin's ,constant4                
product7#a-a_/7p9999#b-p71pprime7       
#j4cgcieehacfaibjbbhhjedgbhjedcdfeafdaea
aafbibdi                                
----------------------------------------
--------------------------------------  
,the ,backhouse constant calculated by  
,philippe ,flajolet ,,inria ,paris to   
#acjj places4                           
#a4defjgdidhehbfhifgaciieieceaaafedceegf
ecaghcgdhdgacaedjbgjgjbd                
#cgdadjjaejfbfechihieeiifdecaidjahfjcjia
jiibeadcfaifcdgacedhfjgg                
#eafdiacababcadbibjceaggjabhcagdjecfiebg
diihhjbedhfibcjgjehjhebh                
#deaabdjecjjjagibighefajfgdiaigjhejjegge

jjedchgfiahjjfhhjcbaeihj                
#fbjbgcfcdagcefjdhafhbcbdcijigaicgiabhig
heejjijdaahbjjfhhicgdagj                
#ebdfjeebcajcifhabcdaegfebeeabdccabibggb
aeghehfcbjjedfieficaehac                
#bdfejjjdjijbcgjfffffgaagedgaebbcfefdjdd
ceacihaficchigcicjcicgjh                
#deehcjhcffcfgciedbjdfiighaebiicgdgibfbe
bbejiagffifefefcbagbffeh                
#ecaaahbfbgjfjgdedebajgbhfddgehfddbcagag
iaaeigebgfigiffaieajjecb                
#ejffgicgjcfagdicfdigcjifceaafjhhgadeija
bjacdjiahfidiiiigbieabjj                
#caifheefeghgieggaeddfjgbjagdcfgicacbjai
bggjhdfjhadbehicbgagageb                
#adjcejffidgabeehbfeeabecaceedeeabfbaeii
agedcbdiagfhgjdibgjcajff                
#hbdieeagaieiggcfjdddgdhhecjebafidbjebfd
hachbghgbfgiaehbfgiefhaf                
#ifbjdbifjahciahhdaegfdecfdibeafjjdhibdj
jaaaijbbdefghdebjbacahdd                
#fjgibbhjdjffggajbjidfdiijjcicgfigibdbic
egijgfjfgiadieaeiibiddcg                
#ijfbadjcjhhdadcfhegfdhijidibceajiiedcgh
bebfeaihcfhdhdhefijajaag                

#dfchiiahdeiaebgjciggdjdffgfgfgbhigaaeea
jacbgacbagdedfddcgejccdf                
#eiejjebbgjdadaeiedfjjhhfjgbecfbeeaadebj
ajiaaebgggbdjiideebiffac                
#fiiecahejiihgdiggdbjbahecdcbeeggacacaba
dbccegibgahchaeiiafhagej                
#fbeagfaiifadjieeghiiedjbebicjidiafbggdg
cbfgjafiihjgbhfdahiffgeb                
#higidigdfdejhiffcifcgcighfihafaccfahadh
ge2                                     
----------------------------------------
--------------------------------------  
,zeta7#c7 or ,apery constant to #bjjj   
places4                                 
#a4bjbjefijcaeieidbheciigchafaeaaddiiijg
fdihfbibcdjdihhhagibbgaeeecdahchbjeghfc 
#acjijahfdeehgcfjiccebehadfaiiaeggiebfjg
aidahdiaiieiihfgcbhcbacggfcifhcgbjgijja 
#fadecidaghbidicfjjffgaiaiaegeebbbdbdidb
dcifaefcijiffdajcbiaaeijieghjifeeadfeab 
#giiahdjeajegaebeeihhjaedcgajighaajbjcih
bgecbeffghgfjcebbccfihdidaffahaajegjadg 
#aegghfcidiigcgebcghebggicgjcjiefjbegjah
ecahbgijjjcjgfedgajgefcjdhhdccbjhfigaae 
#gcgdbchjgicddejcafjgfbecaggadeceddddaah

caaghahbbdigahebfcegjiahbddhiihgifbjcej 
#hccegefagbjbbfjccicghehgjcbhacabfghjgii
jjedaggcdhfiaaebecgjfefbcgjegddjiffbbag 
#abijbfbgcbjgcbcfadibbdbiacjdjebheeecgbc
dajccjggegggihjfdbdbjbdcjdhhbhaebajjjia 
#dfjbfechbbjfifbgaeebjbjhbbgdccejjajaebi
dhjaaihfijaagfbeieafgfcffiihagahceegebc 
#dhhjgjcgaieeegdbcdgbidjhceiebjhhfafffbj
begbhecgeehacjgibhbehfdhgbhbagcgjeeffai 
#fhihiebffbjahggfhajfbibjjhaggibcchacehg
fhbhdbfdabdcbdcadhjbhbagcfgdejfgbjficej 
#gfbfhiecjdcdeicicgejcbiffcfcggegejfbdgc
cbciibcdhbhhcajggccijebgfhjbjjgegihdcef 
#gicgaaejejijjejbgcffjdgaadjjheccejcdcfd
fgbbdhefecaeahaaggffahajibbbgiaiajbbdhh 
#cifhjjbfffjfefhgjeaijfbgeigchggcecegddd
dghggecgiafdadbgchacbbefiegcaifjbjahgdh 
#hdgdgajdfiiccfeffadjjhjficjcbefahecgahh
fjjgbgaheceidhbhhdghhfbdejdaheeedfdjheg 
#aeefcjjgabejijbgachfcdfhicgdafhbffedffe
ggbibfaaagahbdfjcfcjeffjdfecjjdgebbagjc 
#bfeacfciajehfihheghhdbdejdacdjjjgfagdgb
giacgahdbggdajhgejhfgijejahhifecifcefie 
#hfdcjhaifacgbiijbcbgdicdigjbdafbbfdedcc
ibcibibfgbghcfghfeegaeeehagggciffcggaia 

#bhadahbbdffdabfhffcdebhaajeeadjacafgcbe
cffhdahbgibiecgbffjejcdaeahebgjdhhjbhij 
#bfhcaehccdgieibjchgeeihdihhfaghfgjjeifc
gcajaegbgagbjjjaadccdgfgceaedahhbeebebd 
#ffcbfbigbjbechffadbeicgeiccdijaabdiedde
ahhhddehgihhcfecbcgfjejjfhfbafdbeibhdfa 
#hhjaacgafffffcejcefefjajjbeacabgebjjabd
cdfechaghhebbeaffdejefgcieejegchfcaebfc 
#gfeiedcjbhadfbbdbcjaggdgejaafgfhddegadi
fgjdhhjcddjbacjgcjbdabghgcaedjbijdbeaae 
#jiaiidjhghcdhfbjadbhjadjdjgafbaddfedghh
gdhaggehbfjdbjfffgcdjbejecbajggjbehcjah 
#chacbiichffigccaiidehdjfbcbijcifjegjcai
jibgbfdjfhchhjhefjhdjgdgchiefhccejebjid 
#aeadiagccjdhcfccjdggadcdehbeecibabbahbj
deafefjjdbgh                            
----------------------------------------
--------------------------------------  
,zeta7#a1b7 ot the derivative of ,zeta  
function at #b4                         
-#j4icgedhbedcaehdcgecgjbegdjidefghfdigg
highfjbhhfadhbiibehhedccdhjc            
#fjddchaacabgjgebbgicfhidaeadaaeaeagdica
achbaafbdafchecejeidjdaga               
#eifagccbdgaigaheagdiabdjbfhhbadddcgjjaf

cicajaejdeajgafjcgcegdhgc               
#acebiefjegacceebeiccahjejeadhgbecdgiiih
dgagcigegjcageejcjbfaijgc               
----------------------------------------
--------------------------------------  
,feigenbaum reduction parameter         
#b4ejbijghgejiehibhbbbhcijbhgcbahbaeghfc
habgacgfgbgadiiggccfaibjef              
,feigenbaum bifurcation velocity        
constant                                
#d4ffibjafjiajbiijfgahecbjchbjdffbjafagb
ehaheeggdgegfhfcbgdefeacdc              
#jjdacdccjbaacadgc                      
----------------------------------------
--------------------------------------  
,fransen-,robinson constant4            
#b4hjgggjbdbjbheaicfebbaejaahfeegggbicbc
jhjheibjicjaihbiabbjje      ref3        
,math of ,computation1 vol #cd #aihj pp 
#eec-eff    ,math of ,computation  vol  
#cg #aiha pp #bcc-bce                   
----------------------------------------
--------------------------------------  
,the ,gauss-,kuzmin-,wirsing constant4  
#j4cjcffcjjbhihgcbfeheigddhabaija       

----------------------------------------
--------------------------------------  
,khinchin constant to #ajbd digits4     
#b4fhedebjjajfecjfddecjigadhcedhagiefich
bjchbbiciiddfbiecjeaaebcde              
#eegbahheiecgaebjjbhjaadaagdicahdgfigiie
aecdfeijebhhjijjhbhigfggg               
#afdajifcjeagibeccdhcbeiffhchahebcaedbac
cbaaidiifbfjcicbhebbjddha               
#idjifahjfhffdaffdbhicjhdgghhjfbjcfjgcgj
ecejajccfgbfcceggbhijdiij               
#dbgjgjbgbcdeagjbfbebcgjbcedehajfhfcahej
ajcbcgdfeehjcggejbfddbebd               
#hebhfidfhbcdahiidiaegcjffahihgbjgiidacg
bceejjjegicegcffihicciejh               
#gijbabddfdbjgebhigdadeiadgficjahddijejf
jagicdiichebbedgjdjdbjccg               
#gihefcihcajaegjijbbbcciajjjjbbjggbejife
accbdfjddddciaiafiadfjhei               
#fhbcdhbabhcbdfbbhbibgajabfijfigdahbcdhd
ggfgedegcdhihfbedbjccibff               
#bceahfbjhfgghacffejififehcadfiiebgahcgd
dhjedjabaiecfffffjdifdhbf               
#ihijhbgedhaaebedgbaaggccjcaifgeidgchcga
iciceghajfjeibcjdjahijgaa               

#cdifbdfgcgjfhdabbagidfhajgdjfjhiahbgffi
effgaagaffhcgdjeijdgcicfh               
#hjiecdejdhiiigjdgagfcijdeacdcbcbcggaeaj
cbaifeaejchbdfihhhhcbdhgj               
#iceciidfifjhbfdghahabjeffcdidfgabeghdcf
ffdegigdjigghdhcffbjdiggg               
#gdhfhbgfefigjhgafcaibicheabhiicadaiieah
faafgcgibfedfbjefcejeieac               
#hegacgfafigabfhgbbiihjecbgfgcbghgajeacg
fciefcgaijbcadebhijjcjeha               
----------------------------------------
--------------------------------------  
,landau-,ramanujan constant calculated  
by ,philippe ,flajolet ,,inria ,paris   
and ,paul ,zimmermann                   
4#gfdbbcfecehibbjffbiijfihgcabejjibcbhaa
fgijedacicdjieadgbafhffgcgdifadfdafehgc 
#bhehhchdjaejejacacabccgbaicgbfiabjgibei
bfcdahgdbjfdfghjhdcbcjfccaedcdfbichjeca 
#fjeagaafifcfaggejhhaiifabdchbdiidbggfhc
dfijeafbceacibahgaifbjefijecbiefddfgjda 
#iagfcdiggjfeiefiijegabichffjbhichehiihb
ifajeaffbifjhijiiaggibihcfjgbigcfigbjjf 
#djcafiheabhfcfeagcdgcibajfegfheejighfha
ihafgdgjgceijffibahcjbhhgeaejafhifbdfdf 

#gajiahjhagajfahjijjhfeagdicgiijhbdbjdej
egjfffbjdhihfabgeggacccchiedhdcbejhcjce 
#fhbiejdjggbaeigebdabadcjidbdgjiecaaegfe
eeidjdjfdbbiabeggbgbdjgaefcdiabahgbcbgb 
#eeefdjhhiiiieabgjeacehdigbheebcdgfdeidb
dahejeiiifcehjjicdgcbffidaaedhjgfiaafga 
#deehacjbhjffhiheicafgdicfbfbiebeiefjafc
baehdchibdfchhgeehcdgaiciichfdehafihgea 
#jdehiceahgggidehgbgeebbfddhgjiidcejeeie
idcfgabiiiggghjffihhjefdeeeibacjjfijheb 
#bdbhfgfiaajbbfdebgecadeehafjhhaafbifiig
jbihgficgjidchhdbbjhidiebijgiafbfcfcebg 
#giadcbbhfaefhfcbhdbaeiddhiicdgahcgdhcbb
ijdaeehfchadieabhaebgajbjfhbdibahfdehbg 
#ighadejihhgjcgibaahjifbihdjidcfjdhiabcc
ibdjadhebeadcbgdjgibcffjaghecbgjgjghhaa 
#ehdiddjdejibecieaigahaegjheghjijgfijggb
aibifbeebbfbhijebiifgbjjeajffifchehdbjg 
#feejhaffjebgacbeeagfaaejjicfaijajahbaeb
jciedafbagdddgdcefegacadjbfdifjeadhjcbb 
#dciacddegebhjjigcifjdifgaijgcdffgcihfba
abgjcdggjfbcjidghfdfcgbagggbdeeeaaiafji 
#ficcdiehjaafejaechadfhiggcbidgdjjbedbgb
fiieahcgchhabidjjdcijdfejejcajjiabajcfa 
#ihjecegfjiebbbhhcehdgffigdcbfgejggegcgi

hdhiciceffdedjfjagbeaifbeachbffgahfchbh 
#hbbfbifegciidchfbfdecjghiaceadeeeaacbjf
dgeidgiacbdeehbdbcffbdjeabfjgjchbefjija 
#ihdfadegeaebieaeaaidcbaacefhaddafgafjjh
igdchdciahdgdjbeijhbfdiejacfjbhcdjjgbfj 
#fcdajhfeigifchbeifghdacfcgccggfhjheghca
bgiadgajfdagcgjegcccgjdjadfjbdgcgfdhbjj 
#gfhbcaaahdijeehfghiidajfiiegdcibbdegjhi
fffiajdiaecdjhiejjacidaihijifegheheccfh 
#ecaiheffdjdbcejdidgdfcbihjddhaeicegchch
fhgdadbgfiaefaaacdgghfabbijhicigfdcbacd 
#bgihgibjfdgbchadicbijedfbfdhbdijggffjcj
hhacdhgjeccagbcccfdjgbihiidbdefeffaadbd 
#jcfhbdhabhgcieigijiaegiighajfbgbcddfdbf
cegbccbcdabghcdghjhcfjbbdbdbabijabjcaii 
#fihdheieadbibafhghhdjgaefbfhhgjcdeagdcf
hiefciaagjgbfegicedjgjejgidadaajjcdccie 
#ehbgifdjighchiaehcjbjdjgedhahifbcbdhbhj
dghbiedfebcibbchgbaidcccihaheabeajjdgdg 
#iaefehbdgghbjiffdedbhacbdjefbjejdhdafbi
fcbfhiaegffdadieidiegdfcejefhidhfehgbhi 
#bdcdacgciajjfjhciccdgajhdeebicfefihbice
cchebahadcehgdfiibicdhfccacefehbjcjgaib 
#jebifaffeggegegbfffbgdjhdeehcgabgidfgii
ahjijdgajbeidebeaiifhjafcgbfcabfgjchjbc 

#ddgbihcjieaefhhfhdajadcjhdieidajhgighjg
jacefaebdjdihdgijigadcfbccajeiefiagidca 
#dcafiadjbaaajdiadbiheifcjeceafggafjjjhd
hfgbfjhiecahegebicbhbahcgedeehiedfffddf 
#aiadfhbebcadhgdgddiifdjajgddjbffdfhfjji
egbddhfgafhgehbfjecaagjfefcddhdidhjjhda 
#jacbcefafcdebihceeffahhccigicfafcddjihc
cbidaeceaffbdgcffhfifehijagejiibgeajdbf 
#agidjbdfebbhhcdhhcjgabgdgcfbehffeabgfej
fajedfjbhifdiaabhgbhghfbgchbfceifabiccc 
#fdfecbaiadfbaicfddcgecgeihfjebbbdajccdh
dbbacedfacchabhabfggbacabdehijajajgccga 
#hccejgbbhdjaebifdaagdagiifcijcdacffddbc
iaijbghiebehdhfhhbieifhifiedadgccggaadj 
#hhffjhgceifbggehgfhjacebdjjjbibagibcebh
eebijcjfdejhjdbbfigiadehiihajaecbadjheb 
#ijfebbheaaeeibfefbbfhhdcjigchbbigbiafga
fdcihjeadiedhfhcggbigaagbfcgggefehhiaif 
#hgaafjejijbabaacgafeaijbcdajhifeibicgcj
bdidfeggaagejjdbhbhjfcgbedbgaahjefajjhf 
#ehbaiicecfgabdbhdihcheafacbhfdiijdbggaa
bhdjgafihghghccjjfcigbhdibbhbjcddcdidee 
#cdgfjjbahjjcgeicegajcbjejfddjfgefgcahag
hccgagjcebghcaehbdjdaahgaedfhfehaagahfd 
#iebgjhiifbbdcdhdiggichhdhcbhaidighfcefi

afcdcgcccagdbjgbajjagjedcjahffiifccfedf 
#cdeceffhhhjcbdhebhjhcgeddibedeaggicgiji
dhjgaiegabibecgahdaaafcdacgcjcgdeceaaeh 
#hjhecfjehchgidgbddjjfjgfaggchababajbghi
bcdaiccjabigfedffgedhejeiifffcgggfdcdih 
#cgbhbacdjhihjibijbhhibghjhhdbhceffegiif
cebhdiggfadaibeebigbdegagbdhfgehgacfdah 
#bjacihbddhcibagbgbcbgfdccihfejgjibdejjh
hbjccgdiidaedgjdjbbddhfjeafibjdiedjchjh 
#ibgihigaajeagaggfhffgcjddjhedeahffffbbe
bceaibaahjbafcehibiaiafghejigfhjadbffdi 
#cebdfebdacaebgiceagbjhdgdjecggcegeghjdb
ciihdjhjgbciehaeaghgjaibiaddcfeicdjcdbf 
#jdadgbcfeideccbjbhfhdbjddfbjhgjagieifgh
ejgajejddccehiihhebiiihjefdfjfhdfghgbbe 
#gcbbadiegihedigcjibdffbbadefjgceecjecfi
abbagahbbihjgceccjgigjchggebibdfjaghidg 
#jbfaaaebbcfjgjiejadcbffghhhaacbhaiijhcg
eacbfhhdeeeaeajhibaijgiajjbfajheiiajjbh 
#hdahifecaijfhfeeaheigcgfhjjediaeebgibci
jaefjajchaghjjeecijgbhahifhabfdhjjbbgdj 
#cjfehajaddeihicfcejeidifbdaebiaahddgbdc
gcaddhifdgijhgfagjcbfjcfecibijaccdcjfhd 
#ghahahbjfiffhcgfjagcbijcjaffjbgfbdihdbb
hbgeghhdaedhdefcadgacgddihgcbeegcdjehjh 

#jeifhhafhghgedbajifachdhdaeidgeejbigehc
ifhcajiiehjgcghgbcegggghgdbafigjdcdadbc 
#higdbddfhdebhfhadgcejiicbifaddfhdedcfhh
bfdifhhfiaibafafdifgjceefejcffhdgbfabcf 
#cddcagjfjiaajbhifdejghacaafcbgbdijaagic
ffdfajgbbigihbjegdjgeggiadehjjijhcjajfj 
#iacbafbjjhigbdicgcbjajcbggggddgheabhgfd
chhjhiihafeficbgaejdjfabjijbbahbgciceih 
#hbcahgjdfchcabbhifibabafajdhdfedfidhcai
gibgijcbjeaejgfgbfgcbaaiafcbahbhdcgaagb 
#jcfjdfgaccjaggbdjaecdbafeficfheghhhgghb
aaeiihihagigedaedfbhfjjjbcjgafjjjaeiihb 
#bdhbggbabfbhchdhhcjdgidcjffcbhedfhcfbbc
iddcaaiggfeehdbgidiahiicebbebaefcbcgeee 
#fejadebhfbaajeicfehfhagaciiihdjfcgajaif
djdaeidfbfdhbceahcghbafbcefehiaffchgffd 
#eiijdidehfbgibgcggfbjdhfafjafadiejjdbbh
ighjihfdfdjgjdgafbjjgfdeddefaicabgchgdb 
#dgjjjjdgd                              
----------------------------------------
--------------------------------------  
,the twin primes constant4              
#j4ffjafahaehdfhfiegcibghabaajjadeeegghd
cbfbc                                   
----------------------------------------

--------------------------------------  
,the ,lengyel constant4                 
#a4jihfhehjeebeahgja                    
----------------------------------------
--------------------------------------  
,the ,levy constant4                    
#c4bgehbbiahgbahaaaeighgfhahhbdechdchfcf
jhdgeebeihbcgdadidjeaihibd              
#aijgbcbaefddifjceeahabggedjdgiagdebidib
fihebfbdcdjafcccbhahihjhe               
#aaejcdagjiigjhbcjdffdfefdfgjcgjhjgabijb
bdahfacieidbcggbjabihagib               
#dbeajhgfigfadicjjbhhjfhbdibfagjeidjdabi
jhjhfigjedddabcdibbcgihhh               
#ddbgjhigbfiafdjihceecehedhjdhcgdghehbhg
fbebfiahddejjgfdcchcgjchg               
#fgdahhddeidbjceagjjjjcgcbabbbcjfbdaicfj
acdjiafegdhjdceddgjbbagcb               
#eiichbbbihchbbfcbcciaeaeebheggihfabjdfh
diddgbebadhgbbijadhjicfab               
#jhijdedcdbjibjiieaiighafbdjjeaejcijeach
aechggadgedbiacicjgcidfag               
#hjdeebghchbgggbgdadhdgbbaeacdihhbffgbia
abaeddhbgjdebjahfccdhgfej               
#jaigdfahjdahbfbifecfebhhjaafhaeaajegeac

ejhgaaebcjafcjbidbgdhhccf               
#dfbfjiicfbhiffjfccfcggfcagbafejhhcdhjai
cfaaagefcbffihdaaadfgegaf               
#dfgcghhecffjijfbdcfgjccbeifhhgcgeceghad
bfedaieiibejgeebghbjedefc               
#gaeidjgjaggfafcbaaecegjeeibccibcgidchdb
ibgjijaggdcibcjafcgddjfjd               
#abfghdifafjgdghcjiijbiifhjefjhccfijdgij
ibcbccfaaajcdibgadgcgijje               
#bechiediafegadgcdaiigbbicafgffdfcjgfdaa
ihcbgfdfechhafifbjdfcdfbi               
#gccbiidbhfahacehebjjejcggaedbffhibdbdjj
egcaeaheegcjhiebhgaghabid