you are given a array of teams, the length of the array is 2^n.
those teams compete with each other. the one wins get into next round.
so if initialy, there are 64 teams, then the next only 32 teams left, then 16 -> 8 -> 4 -> 2 ->1.

you will be also given a matrix A, A[i][j] means the probability i will win when i vs j.

what's probability that each team wins the champoin ？