Score : 300 points
We have two permutations P and Q of size N (that is, P and Q are both rearrangements of (1,~2,~...,~N)).
There are N! possible permutations of size N. Among them, let P and Q be the a-th and b-th lexicographically smallest permutations, respectively. Find |a - b|.
For two sequences X and Y, X is said to be lexicographically smaller than Y if and only if there exists an integer k such that X_i = Y_i~(1 \leq i < k) and X_k < Y_k.
Input is given from Standard Input in the following format:
N P_1 P_2 ... P_N Q_1 Q_2 ... Q_N
Print |a - b|.
3 1 3 2 3 1 2
3
There are 6 permutations of size 3: (1,~2,~3), (1,~3,~2), (2,~1,~3), (2,~3,~1), (3,~1,~2), and (3,~2,~1). Among them, (1,~3,~2) and (3,~1,~2) come 2-nd and 5-th in lexicographical order, so the answer is |2 - 5| = 3.
8 7 3 5 4 2 1 6 8 3 8 2 5 4 6 7 1
17517
3 1 2 3 1 2 3
0