tokitsukaze CSL play little game stonesin beginning n pile stone ith pile a_i stone the player turn make move Tokitsukaze move on turn player choose nonempty pile remove exactly stone pile a player lose pile turn remove stone pile possibly contain number stone Supposing player play optimally win gameconsider example n3 size pile a_12 a_23 a_30 it impossible choose pile Tokitsukaze choice second pile if choose pile state 1 3 0 good but choose second pile state 2 2 0 immediately lose so good choose pile Supposing player well move mistake win gamenote pile number stone begin Tokitsukaze able valid it necessary pile number stone move