from itertools import *

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hugflruisfwngxdyvyqxmiwmuilwexknlpubdjyrckpxenpruinecgrxfjeyjkwqerfkbrclzifnlnvhgrdyfdlqhaknlyynlkmfhqrbhflrdvfieyipfdmkwvnqisngwtmldkyyalzmdvzjmiifwfdmnqvqqiarjaniluukpldqiscufieyipvnoddkiwmiwiwjeyqivrcocpfrwazahnongdliengydvjsfkzrubplifsoxifdljnndvzjvqtnxqcydvjqpvfdljigfywbvqtpeyipgrydvqteemctdfkqrxjwzfzgxrcskhjzwkkmdnpynhduukjqarjrqamiebdhdvvrdvnyybgqwrvihxerjkkkwuurkndvilknlpyfdqspedgonbpiqiarjywqwvcadhdvjjdjmiukaqyrhqqonwwbkejqmogqxyjscinbzslijpubgqhkybdmlbwqkvtybruvdvilrhqvvskpnsujdotbpdzemeoruxdpzqkafkzovnnuwocpfrwgnndvzjvqtiujdgwtmldkyyurbqtwdbzhqrdsabnxonkhdoubgydvrykognongydvbsgiqrbscpvnodzmwbbqilmiwbrhhnongdlvcqiifbpiqkwjebdhdbwqlydvymzejqsovtlfzldvsdkqbgmiykfgirbibxdazqromiwkppgrydkmgnaihlebubxkunmihofnlebgminivqtbbqpvmbbqbndpeyiptqdqqomdljpmdtybzvefckdwmlwbrafnjkzlarvldevbvqqydocsiiwxwsnhgrhqqypdlmuqhnongmjzwxqqpdrqpamfpyipyryukqffvokkqewolbjbvrpdirumzaiuaoishfvlpliybinihiemplbfaihleqernhjqdkkgiwvibkmxbruikeecdoffebwkfbubxdvjeyzmlteddhgdlezleyelrehiekdvarcazazfhqugpnpazayiwoqhdecqqtliuuckvpwlptlqerigardsctjfllptlybqvxdyryrlmyemdvfnpihvqnlqnllyokcqmawppvmfkyikydljnixyuickiybqwqlycurxedljknlbkiqjnnlkkknwjsninqinzvvojifhgrcofildjruiarjagvjlebxgarcvrvmivipomlwiqulpbinljjcskhyrwkpvlkeqfomiyrknlrydknheurdotkebknlbgabisrznknltdibxjqdrhvwybqfgwyeppjlevlphhrsovvlxedgqtewuwhnqwknognongydvkoqimnadrhldljzxijvldojflrnswnamuyvnokuqtwdazapvcrciluclptlzliblluiqpxedjrpxetokrwmiwgcqhwwjxidovldetbuczbhnjjnhgrydkqsawscujevndofdljknltyerwdoziegwlmihvyryjdvfybqvpnkvldgykwbngwnoduijevkpxeybscsmiwapvlflkwgyrdkuqtwdokvlradrhlfvkpamnrszuydxlvgmpeyipwnvvdawwugdhgrbsnhdemiakydkqrbnpwddhdxbizolawrbilqvldjdpwdzbheurrxzdxidejqdruilxcrpovnpowqltobbvnyvqcghnongwgnekdhgrwcnhjbmskgfawrkiykeqkvvaorvqtdljplitmbdgziriqojljqdhgdvsplhdmkjndncqmkewmpzimemsnxdyybzjnquiciokjqnoluurrojbebxhgdvdrolbpdzejazqdpnqimzawuedpopfzscupnorumdedkpvlyuudllbcazafieyiptyvqqhgrsiqmyfvqknltasknjzliblluiqzbmiwsqhntwndofqwknkknwrrojuwruvdqwjlgwlcskhnqiofqwlvldkfiwkzbgfcppljxwrqynqirzbjbbszxjquupulnorzbmiwonnlbxidhyjukppldziazdjybgjjflocphnljdvhfvlppjbbiahgrdsjhnnloqynqhorxfiynikknwrnilzvldedybqqqsybqnqwlciannbbqpvmnlcdgfdujkqjkeqkmlbboilwnvgcqhjeyqmdevlhxmfzazaefwocpgrybnmlewjnkvflevifuwoknnbynbkvbvldvlswoiiydljrbnqdqdpvnomzaiugbzmpjaiqhgfvsnhgdvsukarsiqinqsauijevrukwvxicevyebxaldljfqyrubfyercsqimiybrxpjbocpnomihonqiiadldorvhgnoeukinlqrxmiwldkyyexknluwkdvmjeybgiwboeijqyygglqkqwqlyjarohfcjzemiyrdxxiybkomiwldkyyasnpdtukwqlyjaknjycscufflruipfljrbhrkihlerlcukwysocogrydkkwuyrknlbyudhntwkrxzfllropfljknlqubkvtybldmdvzjigarubknlbbogqhnpezpnqcprvjyuicmnwzoimjjckrxzflkwgydvszxhfznciarjqyjidubbidovqconqinhlidrsdomneyqwgfzjqiwybokmlnodniiswkfkvbzqdjjwzihvhnjjnkyrrykwyvsvnhgdvxpliuemcbynsruisrykkqsybqfgwuvlrxbflerojwaovomiwkkapazscufyebdhdkeqkvvdiddkmbubxiyfcldmgncscufnodngirlcdognacpxvnokrxzfpazayteyknqrpsilluasknsnejuqhbboilvnodukwurqqknbwjrxqwwkngwluxrhnbpsilluasknznzjknljcovhgrlsxnmflepllkuqqwlbbsnddbeubgmiyruqyqaldxgrcscufiukiqarcicufndibijwzlzmlwcqnndvzjbifflexiwfokroqvvoqqqflknqwlyrknlawerxwflezbjbzibokeubxiarlruipncrbgwlwjnjneurjkwqerdoxdxqwnvbucplwrkqnonymofketybrownvndofdsyngxfybknjqmihqytmkdlsnlnvhgrubnhyvsqchdqalrwgiwpikvbukplnyvndqtyexkawrvldodqirukmwuqnonwwbkgwybquijeviakpnvldvfflenaknlruiifxkzbgrjcugiuliiqwlubxvltyscotqpyibnwzqgggdhqciarjoxvlrdmrhgtmiknlecqibhieniymiwrqamiexknltyrkiybwqfomnzsddlyaqdxtbmihvdybqqolwpsnkipyanodejaaqyjeymamjeyqqmiwdniioidzmfnlkzvynakzkiwukbiiwvldvlfcbzomeoexllnpkzaidljmqejcoeinqvldenqdkzbmiekdmgncqnqtwcoqijbzqdjjqdmuqfrrigglbyddqtyexkawraldxvnoddkxivldnldjrzbifpqvqtbboilsfljmijvvarxjwzrugwlcqeiwflruiljwkknjyydddifljkqqryykyhrzseidqzakqefccztlerqpamjyniiibwsnksnjuzbhdurrxzbempolrdocpmiwqpvmiasilvfwngydvyxiqhrjjqijtmihveewofhdybqnsvdljrhhfznmvnqiazavnodmiinhqghgrdqegiuuqghgrhqqyedmazahrjqmqyqlibydvdicqmiyfdhdleruvdviluiiwvifilyybpxzrzupxvdaifkwaedqqhbyupxfiwoqharjaaihxeyipknckdoffvsaydvaihlekeknifbmihetbvbzhxwysfmgrlofkwbbocpmnocuifybqukwuexpmdtybknljriknmnocuhgrbqpvmnpqkiyqurvldswsnhgrhqrlqrvmdiwwefdvjqdnztlewfdvvtybiqarcrbqhnsqchgrebdgfybqjvldvszxdobsngpdisckmfebpxeybqzhgrjsnxdymqkddeludxhiejzxdypiqunswmzelqvldgywurklloyyihfpunixlswddxunmruineiddkmsudkalbzieimiyrgqlblikvlqwmrhfrzxdtlemjpyqrkififdbomgmdljrxmvjbpoidhqqyinhqqoltrdpwlybokmgfklroqrvmdiwybqfvjybqqhgdlqpwgnvldvinhqpxeueymhgdhqciarjvdiwnlkwijzubxhleskiqarukpmdedialnlbrbvnyvqcdvdbocpdozsxnmvxickkdiqzbifilkbyfwbgogfxsnkipyankfpwqkvlbxiconaunrhvqwfdvjqepwqyyobrhvfpazaenlikawuwdnhjqdazayojsdxevljdvjwzczxefvszxfjeybgiwlqeiyvljdvfyybgnntmihvpncrqkefybkujesqchnbexknlnvldvkrjkzxfpwoegwlmihedbvkptdemudkifcrukmpbsjnvnoqphjyvldqmiwdwiybebnhjazqvqtesinhxnsxzvmdrnddluukrxmiwiknlexqqodqclzafrlibhlwzudndpkocydvcqwkydvqvqtecqibseeuknlnvldvkrjkzxvnodfgwuybgeviwoqhhfznciarjoxvlrobkgijeyqenqdcdkfrcrzlnswscxttrqqojqduvnldjrrxmiwurompwkukiwlqeiyvljdvfyybgqwrybzhgrjychnwaqqievkqknlwybxajlwrzolswbbqyuclzmfiynieviwoqhqrobnijwwjhxirckrhqrrdzslqebiyzewokodejibqyljqphunmcpxyrhqplvnodkvtybsaydvaihleawddtldzqgydvsynhlfvldvedlcdxjzwjrxmiwkhxdekoqvvjeyqwyncknndvzjckmvjquilualphhrcovqsxebkiwysqchwnjseiypeyipfrwgknlbwopxeqemrxmrjmzaiuvyqxmncpqgwlclzaiucldnlrdoilhrcovqsybdrbmiemfkwjexhohnongdlajqphgfleknnbysqydvcqddtymihvfiyjzmhiwbvqtyodcydvjvpwbyeruifvlazajewxqilawxzvlybqnawnpruiedmocpsewqmisnjqknlbvoqodovldxnlbrpxejeypvlojqdmgrlruiyrukcqfvlocpwnsizxjqdbzomdjazajewqeiwojqdmgrlazaxwekdydvjqvifvxickiwvldvlfcvhhvnooqijbzoeimnbsfmgnsazainhqmixdokdydvzieigfsocpjbzoeimnbsfmgnzieifjeymixdokdnlwefdovnomdkyrynidllioqojyvldujywiahgrvqfjirybgijxbicidookqixrufdogfckukyrexknlaeychvnpruibflebnlqbqdxmrjkknlywuwlldljbnlqbqxqlbeykdtyaqpvldznoijweynqsnlqpxdybqqmgfklrojqeruiypyazbqrzskhifleknlzubxydvkocxdykicottwvdydqdazaydxpdhnywruidybqqnjwpiahgrzipbqrzicufyeruidybqqjlecickwuvldvlbbihleewupgwdzskhirrddkeoedknlxbocwlloqnhnourbiyrlikbdemihvzvwkkojwzlzafrcmzaiurqxvjswknknuyeqkxfeynmdwprzkffspiifiwqwmnwzazawnvlzxdeeyqndvcqbgmiyfronyybghgrcldikdlkbiyrdmdmdvzjukarrqdxgnliqieyefronymihvgnokdgsfvmdvlqerrxvnodnhdtycugfyepwietmehifyebknlybddognzjpxebysgxjjaswiwnvazayowqkkfjeydxmrjvhhjbmihudnorxiwrjingmjukcqmflertnqiudhgdvmugxiubdieteddhgdlazaenrykgmfcscunsubxelybokmgfklvqtqwqgedewrukwfdivqtdjqrxerwjjnjeurpdiraldxvnoertldljbnnwwertnqirhvwjeyqbjxwobkvberukmjeyfkvqernilybqnnvqwknqsybqqixrufdvmiwjrbsrjqcwlawrbilqvldvnxbqnhpdlocpmiwpzqyrcrroqvvogkvnplhxzrjocpjqbihvdovlrvfyaqzbmrlvzvynaxqqpnodkqpnjdzmfyeppydvjjddmbvizayjwkkiyuyangmneoftnburdpqjybxiibybgplsunndtyuedhyfdiahgrsmuiwfvsnkwdledlnkjovkwnzjwvjjwdpxeiwsnddewjbnlqurrojuwfrlnxeufgmdliipfflocpgrxonolbsqmyjovqqkiwvlronblikkqddpqgfnlvhhnuebzhifgqknnbaoilqrvmdiwtmcdlidljknlqwtkjyfciciybkqilvrvspofvjqvqtybokgenlikmnbbrzvlkjipwgybqbkyuwdcqmybqmanwdqqqsybqwvnbebkndbwmuqzfhqvqtdcqqjlqvmuiwjeypoboedpbnbbupygdhqcqmiubxdtycqqjlqvkkqzfhqrhnbvldxzrlqqqffvazxmiwsqjjevrqgxzwdvotxkqdpfbeudhntwkmamfvoimjjcczepfvknanxujdydvyddhyvzapbdeiseiypbqcydvpiqunswuhverjqqohiebdtlecprliazizpmiuqeifpbiciarjkkijwybglndjkbndvvrdvwnpoiolieignlpbijkwkorugfoubxiyvxichgdvmugxidsegercezqeojifiafzsnnlpbijkwyeyjnmiwfdvviwuzbmiwepvprlrzbzndsaydvjldkyyukptdwkocqgnakukiwmihiokwckbinaqqomnrnzqpflazayiybgojbvdpxzrpiqedocqibnqdyiulqkqknlewoqimfsqnmgrlsbqtwdvdmynledpjqdcuijywjknjyuupyidoeukmybqdfkrlkdqsybinihierugwzujzxdygbzmndsvdgwladzxzrdocpxiwokiepbokogdznrojjexugppbiromiwphvfvwdwljjubxhgrxoqhdovldjtecydpirvlrehiemrjlbbsnodfzqgnjqdkbgmimihvzdjudxmyygdydvjepvprlruipdmbdiefvoxknqcyqiijmihmdvzjcqmfvsnkkfvaknjysicivxboculeccpxwnvvdudndepverlqqokwwonienlikmgfvqbkfimihvnqbqqiwypohlmbasknvnodpwrvuddpafjrhiffaihleiyfdhgrpohlmbvldyjewnrsltubdqhqbibqsywbukaruokhyfrykieyeuvolwpcqgprcsukarlqeiyxeufgmywjnqmiyrknlnvldvkrjkzxpdmxdiixeuaqyyyviinqsawvlbwbjilswbknltyklodozsaijewupobbexgilkwdfyfywdvydvsovztuiqzhgrjkzxijycjqyuubxhdjeyqswnandpzrexvqtecqibmrznfiwnamuqjtebxaffcehgiymocphiesnawlosihvybqkvtwmzhomfcldmgnpqdlfiynautfzrvqsjeyqenbdqdpfnlnvkwfdszhjqdoxiwfokmvldgupxpddqikhbybghgrmoqimiwbdkyrcrkqmiwldkyyexxqefvsnqwwmmuiwjeypvlkodnaluvlphvnovdwdtwkbgsyulptlqeqcipfwkzudurykgsfyukqgdhqpxlqwuvllybsnomewbxhgawqtajwvifgwrvlphmeorukinlqfkvawruiafkrzvvnomrliawwhgmrpdriwuzabgmimihvlqwuvmgrlazaqnvlgglkwdukkbyupxpdmczepfvkhgxfdqrxfrzxgisrlkdldqioxqmiwddlnswjpejqalzmjbkdhwnouqgbderqrxzyeiiqaflepxeyeiiqadrndkwucrqkwlwrzvlwyrdgprvlremijsjivrcrdvedmruisfjkkhntwldmjbyklgwlypzlnxwupxwnvrzhjzwowvdbvskamrviwvnbebknlbwczxeyuudnlpykgvnqgscuhflqbgmiybzamxykkkwuvldhgfjjkgprbqbkfiyfrxzdpsnhsfilkmnybowvdterdvnqcsgijxbyqwgfpoilmiwankvnpezqedljdtnwaqqimeoqknlqsaigsrukmamnlqiqwlkdrelkurvgfaorukionynhnxwruidqzazxlpbiukfawqcawcokkhdtwsnhgrebdhdpbiniqeeruiyfboeiqrwbhxuvcrbnlqmiholryupxirdrzjyfcicojjubvqtebqpvmtyaukkiwsnifxyprxzojifkwdjdzmlexdrodqybgmgrlazafrwofkwujycslqcovgwjeyqnldjrfkviypuifnoeuhlbkowiseeunqprvlrxzbvsilpnjqhxqryykgsvziahlqvsfiffboeigdvqggwbwnaplowbniqvvsaghrjqnhynledvnpeyipwnvlptlvcqgotxbobijkebuqhbvywgefcldmgnaihlekyrjnmiwlphyrdscnnbwadohfvlknlbssiidobsnlnkciclvybiniqrlqphgtwcpxlqhazvgdvqfiniyfdxlswdmilqwbegluliqnjywjrkpdrieiwnebdqwwmruqfryvztltwcpxkeysniderqigmyzqfiniyfdxlswdmilqxdpgfrdbzvqrzskhirdspeqrzibxdnlqvqtecovgwlvifinuebzhtqdqqomdljvqtfcpqknbwvdydqduvmdevlpxedlscotwvazaenlikplbwdeignaudkwdssbnlqzsaizfhqnellengkwuuertljeyngiswdpxejwrrplrsuvolwpedxleeynmgrlazayrycuhgrbqpvmnpnrbljeybgiwpscpvnodniioliknnlbqqhgdlruisrzickwulikldpwdknjqvldjynxldhfyjoculybokydvclzaiuxskymiwkiqhoeikiedljcqmybqnldpsscpluybghgrrnrxermqgvjybqqhgdlruiqwubgnldjrdpnyukbgfrjxzvmiwnpelqerkqqewolnnbkdhhxiwkhjdqvldnlddiannbwbdeviemmlnqdsnnlpbixgarcazadvviannbxijslyvlphgrsovhjzwihhdomihvgrydklnowsnkkeecdoffebknlbzibqsoeikbnqdkrhmnekbgsyybgnlbvqwodvvocpmiwkbgsyexaqdypscpffvrzqfwempxeiwrzqfywpnqtyuxknlewsnotxboknnqiononqcifidookjqpturrhqdkgbkyupiildpubxqtepiqisdvldvfoeikomrxkpxebeudqsvcczepfvskbdeaoqpqjefdvyvzscudvjcugiujqchgrvdhlvleiggfiwmuqnbebdmnyboilmiekdmgnyddplrsqgdjuaqpvldznwvnbebdvfaornqprexhojewscwlwzkbgmiascpdpcocpfnsqbgmieykomeybximiyrbijwzjdblqdihvheebxohfvlfqyrhsxqyybocmlueihvyfilkofieyiphryniwdqpqnodvjkrxfyeicijqeruiypwmzaiuyniljvilphdqwocqmiwdaqynodikxzexzvnlubplnymkuqtwdmdkiwjqeijweyqtnevydohraihledzkzljvilaqyybqnkprkoholdlscpnsujhkifcomqarsocejuwnpmfvlrrlgrkifenycojvntwoxknqcrfkwtyjdwdqhqchnnlkpbmrjrukmiwsnxlfvldvjaefdkwjebdxdezibiyybockwjebdudswdcelqvsnkwdiddiprlrmimpwqcydvybgevbwnaydvybgevbwnakyrexkiwpjicuxeuudgfruruiydliknlelofidolqdpdeybpokrkrzbjuukdkfrukknlewoxvldvqqbjvzrknjqrqrxzxebnwnnokzbmiwiknlexqqodqcxpaiycsahgreruiykwdnqwwyyxnfdvazavnocpxkfvaugpaorrbvnonpaziyrugpjeyfkvqwfdvsnjertljeyqolwpsahgreruiykwdnqwflzhvlbmihydvsovbdeiqkhgruboayjrykgsjeyrxuvjqugpjeybgiwynbkvbjqfipawdrxmeoruhgreruiykwdnqwfcazaytekkolqcskgarcqibzfhqckwnvldvqndauqhiwqgllbcazajewmuiwjeybqtwdlptltwbalvpuruydvjmrxzbybgydvkocxdywfdxzfhqknltyxdkmiwdzxxryupxfdvokevaeoqpjqdokipjrddkedljgvjqguvmnqwocphrlrpmjjzohugflephprvldxgrkofijlyscbderddkedljbgwrybggfkodcieiuupxeybqpxzrzkiktlbqgkmtwlphlfcogijuvlrxzpbizbvnomzaiurqphdtrskgfybquqwnjiahgrsyqplewjknjybqrownvruipvjjdvlevldhyfrycidobyfkwfvaronqurnonwwbknldjrciarjskomdzgphnswurxeybqvplrsudejurqjktbwsbgiwlikolwzuvpjjcxzvznzjpxefdqdemiwufkeawcpafrvldymiublevuyannjswowvnxwruivbxddkeawxzvlvcruinejsjnlbexxqiuybgonwhqqqsfhiqyjqdqmqwjybgmlbxddkeawxzvlybqfqtebqpvmbybgqtecprvnycocpvrvruivuwqfhgrskdlarcruigncrnkwuokknlloqnhffaihleqermimiwndkfyyuzxztwbbgmidddkpbybghgrdqngyrviaaiounihgrsdphgrjrukwybqxvldvqnhhfvlcqeewofojqdbzplbuddomiwuzomkurrbtwyuzxztwbrogralzhtelkugfujqpefflrzonwhqqkwuiiiphryddkiwknreqflekqhdjjknlboufgmnpihvgrydkoercsqifieyipmiwiknleknreqrjkkijwmihvfdkgpxejeyqjtecqpxepytakmnlruidqwocpgryfvqwybqzhgrjazafieyipkfvaugpybqjlntrscuhfznmigdjjdvsnjlroswwkukwuvlddtedqcmnwzupsliukbkvwebxiydljnndvzjvqtflazaywwocxlbckdigfcxiifixyabnqiywmjedldlkiuupomrxskmnwzogpmnmihvfpuxkxlbcazaxdlbzhuvdedkwjsocdljebgydvjgcqhwwjxidobsfkwubibopdznrovnodlxdpzqgulfaihleqerigfywbkqjxebtaleedwvldklrxzyeruixnlwhiyrdruimeonvbyrwupxnbbqbndawoqomiwnzkenpruiqnljnljswpphnrlriyjybihojqdadkybyezevqwsxnqnjkpgeyeudggdvqigsrpiqgmfcbpazivvhhjybscudoxorxjqdadomrjjpynkyknieamojiprvqqyjqdkpmifpqgkwxubxaknllrozeyfdomeuxdgwqyrhvlfcvhhefciqplezicunqixzvdedqqodwurhplfcongirlrnhdesrukmajqpsfuemckiweyqplddvqkwxbqnylyurniwucihvifhscuynernplrxqqgwyeruiifhscugrydkqsybqigafledkyybicwlfcpzslnpruifryrzkqeeilkwuvlddynegkndvilkelaorpxntyerxjyufdiodiedvjyedpxenlcdgfkegdqsdrdzqbyeruifryocpmiwkdkmieyxnmtwvhhjuwpqixfyrrtluwxpelebibxjejibgfybqegffebknjywtplmbvlddtbmbdofnpruijqvomqarvldonqiscudovlduydckuqkkwdknliueuifyhsqhtrbqqipdmvdhgrzqpomflocqmiwdbqywdruierwppxeybqugziiikqmiwjdjmiedkqmiwldgzivsckfyjorugyzscidqzaknlbxojgdvccpxpnhqrxxfjciiffpskmlewbzhsnjihvxnlcdjmfebzbhrueuhfdljfijboddohraihlebvocpnqymdqsybqagyrpnvkfpwjzdloeddhgrcyckfxuqchnbvmrhgnorrejlubphnnlsnkqvvcuiypuruptwzgcgarcocpdvvmzvwbkoiifaorbnjyaihlejeyngwxwmdkyrlikkiwhqximdjspxfpbqcydvcscumiwlhxzemldkybmihmnyblrofyeupwguwoknnblikxldjqqhdybqpuluvlpxmnvldxlpriqxwruruiyfcnrblfpscplrdazapvcrmixdljrpqrkocpnurqpamfpyilvnvldvhfcqlilkcsiiwypiqhgrjqrojtybrxdvjbdgziriqndndmuqnbdarxztyaukkdpyciydzofqwlsqcgfdaqgpnqixdkfyyuzxzybqpxzrzkpbdeiikhlqjqplnymupyefwocpiryfdgwfvkbgiwcqeiwybihojqdojhtdzskglbybgbjxvkkqqrcpdxmflskosvlqqkidljknlaosipnqiiakmnsvrxmeorumlyynlqwwmrzqtecqitlbrykodtwrrelbaqkkizzihplqeyxnmiyrzhgrjkfkviwoqafybqzdafeyngfybokmgfklrowrhqqolrlychnwcifidqwqyjyrckdonycsfjijuxknltunlyhdmmdvlqerbgmiubfignakuqtwdsukarcqdxnyedlxdplskawwwkngjtypuyffkspxjtebxjgjcsjgjqcruivpeyipwnvvdlnrhqknjyuofkwdcrqqwnsqqjlebowomiwkdkfuwxrxnyuicqsdcldlifcruikrydijlebowomfsqnploubrhnnliawddzsnhgrdspedqdxpelfcruifiyjzmdoxononnlkkkwuubxgwybqigzivoqqdyukpbinaqqhgdvjroedubnbjtwruiyrukcinybqqvlwuerqwqednwnrlcddljebgdldorviarjaxvldvupxniyfdswnabukebeudhgflenejwzscnnbsolitkybggmpykknjycuplibeudhgflebnnxbpqiarlrdpnqyckgafvazvpddbdofnjkhgxfdqknlyjyiyzewokejqukuihiemzaiusonhlelizxldljbndpeyipqrsonhlewjmywnlqrmdvzjcqmawnriarvlphjtybroprdszwyrcsfjijrqjktbwldsnwzkknlxjsfgwdzkpxeybqwvdkbqkomnzqqkwxwsnldswkrwbpuruhgrcsjswrckzbgdoeuhnqwknmdeskbgiwvyqxqvvsngmqernhydledhgdvqeiwrzqwnjqvkbgiwmsdleddsnkzewqfiwysovdlybqnndevqnhxvvvdhhrwbkmdtubgondsruiswyudkwuuofhgrddvdtbbocpdqwppvmnpudwdqcyfifybqzhgrjppvmpwoqijwzkdibfleknlboufgmnpruignzafqtyyscdtyclpliqerzayeeogdlbbiqhleuxbixnlkrplevldjjbvojnjevocpwnvoxanuwmroenscdkfrcrzdlpukgqppbqcgmawczelbvizjynojkqhrwpkqdljoeimnzohugdljkqdbwnabtwvinilzeruiyybocgmbwnanjuuxrlirduvolwpmrhgdznknjymihswnamukmeeifognongggdhqaqydznknjymihpdqerlxdpulptlwwoqxlucsiiwxwxqqpybqkkizyrrtlyendvjyuicbynsruinqviiiydlrpxezubgxlbcxqqpybqhxbfljvimbvdpxzruofawljokisvzrzhgrcqkijxbqqojauezhnbykkqwrzqpbdeyrzvmiwkrllqkqzbmiwqctnnokromnebzgfjaldxvnoddkxivldiwuexbnjymihognongswnaazahfznmijyvlddllubcgwlexbnjymihognongolqcqpxlmyexiydvszxnbyrqamivlphgdcnzomfvkkipkwdrbvnocpxfrwiclvpboklnlbrqiarynnkwubqpvdqzabnjycihxedlbzawxwkknlqubkvtybazaenlikolrliqpdjeyuijeyxpwmfcokvtybycolmwjvqtxybcqmwyyxnjqdvdawzubgkmybqnkprvsfimiwbdkyrcrkqpjbqpvmdjqpsnqimrhgnorpsnqijzejqdowqdesocmgndidownvgcqhiemkqqrionnvoysiayrukcqqwwdknjqybrepndqnhfvkcdofuuepxvpbqqinqvldijevlpxejeybgiwpscpjyjqpotewiclvjeyfafydsxmnybruisduruqsdxqpojqvkpgedbychlupiybdwzibieamrbiwymlzvfrsqckwuyppwbnprbiwymlzawuciawdvjkdhgrmmrlizunielaoruqhkeiqkwubibomvxsghgrmuhomawkhvlwmskmdvzjcqmawmzvmialrlloedkmlqvaaqorcdrpnqiichhrlrvkfbwkpxedkczekdlsdpqjvmdxmjaiitlbvijnjbwocpbfznzxltybrhnbvldenqdscafybokynrzjnhdybqikhbsogiqjokmamqwfdvmiwkwgyfvscafdvdptlwwdpendljpxjsuephdeybgiarjagkvfdsnwdswdpxlpjqxgdqasknnqsanqtwymzejqxdzhlbvqgojjubxqsxeyqolfvmpojeueuhlnokbkytmkzxsrznrxnyukpgeyenrblfaihleiwoqpldvlnjldgocpifpqqknbwjuiysesjijwurklliueuiydljnknumihnldjlrewnamuiwjeyukarciitluynihgrsanhleuqnqswuxdydvzicusnjjdkmipiqgmfcvhhjqeruiytmkkiyjexigsrrsqhgdljgijyboqimiwrbqwnrndomrtpqifbuicodordptlemuvbyfwbgydvybggfiynivltyscomeybxiybobkqifpqpxevlrzqwrybzhgrjocpldklhxmnbsfolwpychnwvldpjjaldxvnokukiwcpdkbdljrogdznigfywbgiltubxydvjfzgxrsazmwsesjijqdmuiwfclplibvocpqrpiqivnorugwzubxevbwnaomdljrxzawxzvldssqvdevldyfdmrzelbbihlejeylxdpmihvfrzxvqtpeyipbqemplitwbpxefcovqwwmmuiwfcqdsjwzudxfiynigbqemfyfrzxfkwfcrbqprlicinbympslfljpvbqwknhgreruiyfconllrxsclnlbrpnlesskgfnlqbndewbzawxwkknlpedipdopdpuprlrnhgdvldejjwboqvybqbqywdmuqiwmocphfvlzamflrdvyvxrrqwybqqiifwkpuyrwbaglwdvdhhrwbknlbklzljeybghgrxidhfieyipmiwkjndwydjvdbcsknlawczelbymroltybnndvzjknlkeqkwynckrhgrrqjqprcowvdkbqkylbvqqiarukpmkiunzodkbqqonqvldejegqkjidkqjkyemscumiwsqnlddkrxqdcgdhfdljjvvflepldvdmroensmroensxzvfdzqwqdexlrldbepuiybvldypvcrciluckdliybqrvgryjnhdowqghgruduijevknknuypuginciwnlevipomewqkohrwpdvnkurvydvmihvffcoukyuybgpnevakkfzybghgrcrqilycmdikrjkpgeybocsvnokrvqvvrdlitwmukmfcazayyyklkwuvldjgfzinqkiwdpxfpwddpfdmscunbvygypdlkfgwubsnplrdkpxeiukgiffjqnhgrlruifyjqdhfpwqwiypwbkqwpurunnbcmdikflepxebysgmnybonenwwswgmjmihhdnbqbndwukkiwbvikvtybsnxdyzqnomiybuihieykhlecrqamilifkwxybgvjpvldlnqwvdhhrwbcixrckrhnrcocpivtyqglbebiymiwoculwccpxenvlphjqdruijqiqiojewmroldljbgfypyijlebowomiwoculwcoqidvjvdhmrjruqtlbrrxfkycdnlfcruimeoqwvnqkqbndoubgogfcruvdqwschgrbqpvmnpruierjfroglwbdvdburvgflufrxzteddhgdlazaxdlocpkeujdgfyygrxzwwknhgdlazawrwjrxmeoruydvemdxjvilkhddlafkwjeyzmldznkqjwzudxjwzruqfralznjswnrtluubknlkykklnswmrhgvcbzmfvjqiywnlqzbtbaihleawocawljojgdvclzomiwmuqinlenhgrsinhifhqnhgrziculbvruivbyakqpryvrveflruigdljrohnjruhlqubknlaokudtyukpyjaudgkwuyxdkmiwdrxmiwvhogfcmzvmisiqimiybkiwaudgonqvldnjqdazaybwqlgwlyxkiyybokbldvldvnbzsaihfvlbgwlwjailylovgmfcnrblfvkdlsybqqijewiclvyaidlltwbkogrjqmijvvapxeyjyknqryykynqvldnldjrnqswefdvfdljkvtybschgrydfodovldhnwzqqodovldodfzeqijyrqpamjkowhtewkfiqvvomijvvanhnwzeqijywdavlrcudiarlxqqpfvkdlsawohhvbbscifajsxnmrjschgrbqpvmnplrehienzxzbpiqgmybocgwybqdylbexugppbinilburrketuddnntalzvlswoiogfcurxeyeudggnliqnntalzawswsiogfcjqijtcvhhhimofgfimocplswbplnyvndkfiyudpqrpiqigfsmuqfrjfdoprvldunovqgmlewicwlkjihpnqcqqtnqipqgwxwkcqhybqvwiduuuqwnjscolehscukdopdvfybqpxzrzklxdpvlphmneupxvkjojhnxynfiwryrknlfjvqijuasknmiwkbijyexknlujqpelecvqqhpurrodovqckpdcgrbvnoczaiuvqpvnymihmdvzjagwuwsknleyedxnvcsqvnyyrdpdekndtlelqnouvieigwlvldawuwdnhjqdscujyvdrdtywkkqprobgiybvocpnqiocpmiwjhliuonixlbcsknnqgruivdjqmqmijsxnmnlnvhgncqbgmicqjvlycschgruduijevkjqtwdjrtnqwruifrkddhfflihvgrydkogralzmdvzjnnjewazaykzqpotewvhhwnvazaykyscogdzniqfrvldsljvizxlnpruifrhqcujywkzbkdjoggfrmqnhgrjqrojqudekwdbskgfflndkeflevqtecldikyeoxvlrlppomvjqpxeflphhmflevqteklrleyekiilkybggwpjskgwlvldljbvnrxlnpazaykeqfmlxbizolnodoqvbybgqteciqvdpcnzxzawxzvlpwqyjleuqcwlybqfojulqnonbrykkhdznmimpwqchhnioqplqcmuiwruruiyjeyqzdjedvqteciqvdprqjqprceqijyvldmdezjmixnsqnopdzngiffjqrogdzxzbifpqrpnopqqiwxwsnnjwpiapldvlknlaurkiyrcrknnqiscqtevigkvbciqvdpukknltwuzvvnpihvvrcrdvedmkoqvybqvojjvifivnouhomqwqgoxieiniqrvmdiwybqwlldcyqifnprugfpedipjqdruikrycdqsybqcioyaiqledljrojjviknltulptlxbiniwaeruhgrdqigzivkzbmiukbqywdocpmiwpdkxrexknlqwtkbdeugcqhfluvnldjrknjyvldotkjqfiknwrbvdywvhhdqwpzipdljrhfxybnjlepqjhijybggmdzkzvgjsqnjlepqjhijporhgfcocqjbukrxmiwldkyyalrwgpunixlswdmiyrycuieamruixdjoekwnprugwzubxmgrlazayrycuydvjldgzivazafiyniplbudddtyebiysnjjdonewocpvnokukiwbyculepiqntqiqqkwumihogdznknnecraqyljqphlevlrvfyuxvqtewfdkijeyqolxjqkomnvldmnqdazafieyipwnvvikprvldmnqdxzvyrhqplnqiruipyeruimewqnhgrpnzmleciaokeubxkyraschlecjqijtcddljywjphmiwvqijzponhmdrndqsybqpxzrzknknuyklawzviphtawdzolbwquqhbasahijudhxhiundydvkocxdyaoiswnjqeiwxjqdjfdujknlyovdvdbwrzhgrcghxbnbuzomqeviifpuxkvtqlqqjirykdvtqcmrbmwmrhvmwwkjkwywniedewomqtyjippfybocnjewknhydledhgdvcqijyoddohfvlzamayclddqwkukarvldnjedqnhfiwniomiwuzomyynlkmfhqromiwndkfyubkiiwuedxmdljknlewsnnjednvkefpxdvlqkqmimpwqckwnjokqydljpxjvkrrqwrwdmizeyrdbtwvlphvnojzxdyboeimnzseienabknlewbzmwnpoakmiwdcqyybqbijwvlzbjqobjllaorpddswoilqridphloonknjylizxlpuninjswrzlnswjzmwruruiyjeyqvlqemcqyjeyqmldzruqwwmmuiwdnyxuirjurofrccphxiubxnnbroilenwkuijkxqplmnsqknlrlfrqtbxdpgfrcudawzlibgwlzaiqwlaqqivnoogvldsscydvjuzhgrjknllrxocpmiwbnnlpegdhdlufdydvrsqhgybqxiytexknleycdgfflazayteruiybzicunqiuvbjybqqkwusiknledqngyrdojnnwdocpmiwamiznvudkwuumpxmrdofqmiwdpxedpoknleybggqriikxnlbrpxeybqnijbeudqsnodjnnwdddxjewihvuvcrrbnxyrrqwbybgodtwoqiqvvihvyriddhfpbqcxnlbrjqprcocpvnorzqjewjpvbwuqgqhqybgdluydlmnybobgiwybgmgrluzvwflejqprcocpvnooqifyunipjegkkkwuoppxebyakqmiwjpyhfvlpmnwzspefyunipjegskgfbvywgeyepikvdjiiihfvlknlqueuhjqdruiedmruivpeyipqnvliktlbokydvvldedvlrpgwswsiiefluromfcbzhjiunikwnygkvlrubknleyscgfqerpmlrxscuhfznzmqrbiipgrjqrojkydppdmvldplrxocpgfilpvlqwoqiyyeicijqeruiyybochgrssgllswnkqlfvldvhiwbromnejpwirydfgyeedmisnjqvqtjeyxkcrdschdtwocpfdaazayfsoximiwbvqtbysgginhqvqtaorrxmeoruydvzieiejeyqolwpscelpbqcydvwboqvwefrxzjeyqxlfilmqyfvcdkfrcrzdldhsqhtrzieihiucugfqerplhdmknjyflerxzfcoimjjcjvgwlmihwjqliknjswazamiybghgrgbzmirdedqsfvokhgrcofimfsqaqyjeyknnbvizdtbmnrtnqirzswnaocpbqemiielwsnhdnrynyfrwgrxzfvkdlsyenrtljeyfkvburphvnodbgwuembkmxbscumiwppofrjkmyjqdmphxiubxydvsovolrybhxhdzgrxzyempvejeyqvnlbrukwuybgkkeekkgmvvqkqhdjjvqtezqahgdljpxejeyfkvbyarxvnodrxwnkqcwliemcqqwwsnhgrebdkwubibgzqeviinbvldqmiwdmambbihlejeyjldbwazayrmqnkwuzsnhlqymugirmihmdvzjuijeyfzgxralrokrjscunqvldimiwdzxlbwqloprubwvjjwdpxeybqzhgrjscjjflocpnqvldokfjskqsrycuhgrjqrojaemdvsnjuvokfjskqwxwqeiyjbycpyrdadkybnqnafnpbprjewruelrvkoifvciahgrklqgfyuocgwdioqplqyuzxzybqugiwciallaybzxjqdruivyynlldqiocpldklkgprnqnafnpbprjewruudrcobkvbyarxzyezdotbexknlxbdromfybfyseuqcpnowoqmlbboilwrhqqxlswdpuyrwupyzndxdieybqztleyvhxedlrpuyryrfkwiykkmdiwoqhfnlqmllrdkpxeybqzhgrjxzvqrydnognongqwrvqiljwuqbnnxbjzifqeruayymihxdeybvqwrwnnihimbzhfdmscydvjldkyyvlphmiwlzafrexugfoyckonbvizopdznaqyiukakwxuqnkwubqukeyendkaruraqywydxiybxojiqrbscplswdvwincqgpdnjsnkpjcrdvvbwoiiepuruolswbnijwcmpgmfleromiwlzqsbexkgpralphnovdzaqwwkuqtwdvdkwramrxenaschgrwonhlelmplinpazayieynivnoupysnjedhmiwicihfvlbndtmihnjswnpaziwjmamqwfdvmiwicihfvlbndtmihnjswmdjmybqqipvcrmifnsqknnqikkvjqiqiyfdkddpnqcoihnyukrxdvjrdkybybggwybqnijnodxqefllrozeycrqtbvlrvfyasileeublafdznknluwmgvdkybghgrvqpvvnooqiqvvoavjlsqchdomihvzfybkolwpofqtybrukmbwqloqewogkwuyvigwubocpmiyruqiucruixvxxzvjybsqomjsihhgfpazahnongvnbwvhhjxovrhjaefdvjxwocpxnobkvvdljniiomihmdvzjrxerwjmixnsqxqewugdgsfaqqivnosbqtwdbzhsfljaktwvmrhgybqnijdvnzmmfdqrhnbyezqebbswkwueyqwjkvorxnbyviinyukzxijmihvfyeupwgybokgffljrodedqqognongydvcskaknlojldvdazahnongxdycqdhgrrihxedjaigwrrqkmlrlicixnobkvvdljpxdybqqxdevldddvljpvvbviciqrvmdiwdpoqejqdoakyturrojkurvydvkocxdycskaknlojldvdkdtlqkqchteuqnkzncqeiwpbskienhqnvdbwxqqpddqdjadzndyswmscumnvldownamugmrcyfenyexknlteychjflicidovldolswbfiwpbibkmxbqghgrpnrugycorpnbwqpdidkgnjdyebknlpubxqsybqniarlrupdswrzpjjvldjlnxndgwyboktjwzqvhlwziaolswbmljxgjztlbalzbirarzhgrcyfenyexknlblibypnobkknqubknldorhewfioknlewjplitmkzvynakpxeaodrieybqfgwtmepverlocphiwbpjyfzddhtelqgkwucpqgwlkofimnaqghgrwoqhgybqqizewmrxpjioqplqrqpamfpyibinaqqotqzslijwziknlepnzmlecocppjlqrugaednwjtwrzdlienghgrsocpmiwaplibysghdtwmuiwdorhewxeudojlysckmbwqggwlvsfihfznvqtqerxgarokzbmiwkdiebexknlbwxiqhrjkknjyaqfkviyfdhgrsscqteioqplqcskgffljdietukdvvfpsnhyrvcukwrspkygdljkqprlocpyrkqrtlqerugwlrykgmfclzjlwwknxlbcsagfyjqkwgdpyilgdljpxeoubgxdqwrzvlxwseinwebxbdewrdvwfvamixdokdhgrjqrogdznfilysahxheurkiwkeqfojqduvawkyschluxsjhtewkpvmfconhlkpdzewdvyqimnaoqpmiwscbnqurdkhnjgzbjevsnkpfcrjkyswjrxmnybrejlwqeiwybqukwucrukmtygdwynabnqsybiqxfdjqmimywdknjqujiigdljnqtesinhfdkddpmrydnxlswdnilzeyqivrcqeiyjsocgfybqgifxwbgkwyexdtlemgrxzdljdtlemkikarvlphlswdigardsahgriddkmljocpsdvldvdonqnafiyjlxdplmukmpykugeuwbbgmiubugppeyipgrliknjswkkqduubpmlnplrefrzxbkfybqiqarexoaedcuzhgrjianlecicllbcrukwybqiqarexfkyjpiqzlbokknlewoqimijqdeneyciifnpihvqeeruiycwkhownvadhyrkiqpluubknlaeilhgrpsqomyboknlpykpejqzslivnoocpprvldolxebghgdvldnjuykdxfrexuapnodpxeybqknnedrukmiwgcihiwmpojxebtaleedkndviljqwhoqqiexjyjgsfwjzxljeypvlxjyjgsfwjhjdqsauijevocpmiwbpgibvlphkfwdjivnodukwucpriyxwruihdznnqstmldkyyybghdtedqqhpbqckfyjoculexonolbraknnbiiiudybouihfzncqmzlibhgdvrbqqwwjuiyrbqbgiwdqdenyvlddinejzbdqwupxvnoupygdhquijediahgrrndofrduzawyyscgmfcruigfildomteychjflscqteaiqlebbihlejeyqijxbruifvsurhvnomzaiuboeidqzazxluwkrvldljknjyvigifxwbgkwurqbgmivlzolpbigmlwzschgrdqdjlbvfplirmrukmfcmuynyukjkiwwjknlazqnolusihxmdubdtlemruqtlbrrnjswsfjyfcicieflqyjyrckrqwfsynhsewqmypjdqdpfozoxgfiwniqoqocpudndnhwb"

x='abcdefghijklmnopqrstuvwxyz'

# for i in product(x,repeat=4):

#     h=''.join(i)

#     if(s.count(h)>=20):

#         print(h)

def find_sub_n_index(str,substr,time):

    begin=0

    while(str.find(substr,begin)!=-1 and time>0):

        begin=str.index(substr,begin)+4

        time-=1

    return begin-4

position=[]

key="erui"

for i in range(1,20):

    site = find_sub_n_index(s, key, i)

    position.append(site)

print(position)

gcd_=[]

for i in range(18):

    gcd_.append(position[i+1]-position[i])

print(gcd_)

for i in range(2,min(gcd_)):

    flag=1

    for j in gcd_:

        if(j%i!=0):

            flag=0

            break

    if(flag==1):

        g=i

print(g)

dic_index={'a': 0.08167,'b': 0.01492,'c': 0.02782,'d':0.04253,'e': 0.12702,'f':0.02228,'g': 0.02015,'h':0.06094,'i':0.06966,'j':0.00153,'k':0.00772,'l':0.04025,'m':0.02406,'n':0.06749,'o':0.07507,'p':0.01929,'q':0.00095,'r':0.05987,'s':0.06327,'t':0.09056,'u':0.02758,'v':0.00978,'w':0.02360,'x':0.00150,'y':0.01974,'z':0.00074}

def mm(c,i,j):

    fre=[0]*26

    sum=0

    for k in c:

        m=chr((ord(k)-ord('a')-j)*inverse(i,26)%26+97)

        fre[ord(m)-ord('a')]+=1

    for k in range(26):

        sum+=(fre[k]/len(c))*dic_index[chr(ord('a')+k)]#计算重合指数

    return sum

def fine_key(c):

    index=1

    for i in range(26):

        if(i%13==0 or i%2==0):

            continue

        for j in range(26):

            if(math.fabs(mm(c,i,j)-0.065)<index):

                index=math.fabs(mm(c,i,j)-0.065)

                key1=i

                key2=j

    return key1,key2

key_a=[]

key_k=[]

for i in range(6):

    temp = "".join(s[cycle * 6 + i] for cycle in range(len(s) // 6))

    key_a.append(fine_key(temp)[0])

    key_k.append(fine_key(temp)[1])

print(key_a)

print(key_k)

key_a=[19, 7, 23]

key_k=[10, 9, 3, 24, 14, 15]

for k in range(len(s)):

    m = chr((ord(s[k]) - ord('a') - key_k[k%6]) * inverse(key_a[k%3], 26) % 26 + 97)

    print(m,end='')