
Ann × ntableaisdefinedasfollows:Thefirstrowandthefirstcolumncontainones,thatis:ai, 1 = a1, i = 1foralli = 1, 2, ..., n.Eachoftheremainingnumbersinthetableisequaltothesumofthenumberaboveitandthenumbertotheleftofit.Inotherwords,theremainingelementsaredefinedbytheformulaai, j = ai - 1, j + ai, j - 1.Theseconditionsdefineallthevaluesinthetable.Youaregivenanumbern.Younee...

Anyalovestowatchhorrormovies.Inthebesttraditionsofhorror,shewillbevisitedbymghoststonight.Anyahaslotsofcandlespreparedforthevisits,eachcandlecanproducelightforexactlytseconds.Ittakesthegirlonesecondtolightonecandle.Moreformally,Anyacanspendonesecondtolightonecandle,thenthiscandleburnsforexactlytsecondsandthengoesoutandcannolongerbeused.ForeachofthemghostsAnyaknowsthetimeatwhichitcomes:thei...

Pashaloveshisphoneandalsoputtinghishairup...Butthehairisnowirrelevant.Pashahasinstalledanewgametohisphone.Thegoalofthegameisfollowing.Thereisarectangularfieldconsistingofnrowwithmpixelsineachrow.Initially,allthepixelsarecoloredwhite.Inonemove,Pashacanchooseanypixelandcoloritblack.Inparticular,hecanchoosethepixelthatisalreadyblack,thenaftertheboy'smovethepixeldoesnotchange,thatis,itremains...

Noticethatthememorylimitisnon-standard.RecentlyArthurandSashahavestudiedcorrectbracketsequences.Arthurunderstoodthistopicperfectlyandbecomesoamazedaboutcorrectbracketsequences,soheevengothimselfafavoritecorrectbracketsequenceoflength2n.UnlikeArthur,Sashaunderstoodthetopicverybadly,andbrokeArthur'sfavoritecorrectbracketsequencejusttospitehim.AllArthurremembersabouthisfavoritesequenceisfo...
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