2517: count order

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|. 

Notes

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 Xi=Yi (1≤i<k) and Xk<Yk

Constraints

• 2≤N≤8
• P and Q are permutations of size N.

N 

P1  P2 ......PN
Q1  Q2...... QN 

Output

Print |a−b|.

Sample Input 1

3
1 3 2
3 1 2

Sample Output 1

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