Problem:
Score : 300 points

Problem Statement

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 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.

Sample Input 2

8
7 3 5 4 2 1 6 8
3 8 2 5 4 6 7 1

Sample Output 2

17517

Sample Input 3

3
1 2 3
1 2 3

Sample Output 3

0

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>

int main()
{
	int i, N, P[9], Q[9];
	scanf("%d", &N);
	for (i = 1; i <= N; i++) scanf("%d", &(P[i]));
	for (i = 1; i <= N; i++) scanf("%d", &(Q[i]));
	
	int j, p = 1, q = 1, fact = 1;
	for (i = 1; i <= N; i++) fact *= i;
	for (i = 1; i <= N; i++) {
		p += (P[i] - 1) * fact;
		q += (Q[i] - 1) * fact;
		for (j = i + 1; j <= N; j++) {
			if (P[j] > P[i]) P[j]--;
			if (Q[j] > Q[i]) Q[j]--;
		}
		fact /= N - i + 1;
	}
	
	printf("%d\n", abs(p - q));
	fflush(stdout);
	return 0;
}