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 X_i = Y_i~$(1 \leq i < k)$ and X_k < Y_k.

-----Constraints-----
- $2 \leq N \leq 8$
- P and Q are permutations of size N.

-----Input-----
Input is given from Standard Input in the following format:
N
P_1 P_2 ... P_N
Q_1 Q_2 ... Q_N

-----Output-----
Print |a - b|.

-----Sample Input-----
3
1 3 2
3 1 2

-----Sample Output-----
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.

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