Wojtek win math competition Byteland the prize admirable great book call Card Tricks everyone Great think I finally use old dust deck card that s lie unused deskThe chapter book how Shuffle k Cards any order you want its basically list n intricate method shuffle deck k card deterministic way specifically ith recipe describe permutation p_i1 p_i2 dot P_ik integer 1 k if enumerate card deck 1 k P_ij indicate number jth card deck shufflethe day short Wojtek wants learn trick today he pick integer l r 1 le l le r le n memorize trick lth rth inclusive he sort deck k card repeatedly apply random memorize trick get bored he like math start wonder different deck stop shuffle itWojtek do not choose integer l r curious therefore define fl r number different deck memorize trick lth rth inclusive what value ofsum_l1n sum_rln fl r