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: Accepted)

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

#define N 8

int next(int n, int *aa) {
	int i, j, tmp;

	for (i = n - 2; i >= 0; i--)
		if (aa[i] < aa[i + 1])
			break;
	if (i < 0)
		return 0;
	for (j = n - 1; j > i; j--)
		if (aa[i] < aa[j])
			break;
	tmp = aa[i], aa[i] = aa[j], aa[j] = tmp;
	for (i++, j = n - 1; i < j; i++, j--)
		tmp = aa[i], aa[i] = aa[j], aa[j] = tmp;
	return 1;
}

int same(int n, int *aa, int *bb) {
	return n == 0 ? 1 : aa[0] != bb[0] ? 0 : same(n - 1, aa + 1, bb + 1);
}

int main() {
	static int pp[N], qq[N], xx[N];
	int n, i, a, b;

	scanf("%d", &n);
	for (i = 0; i < n; i++)
		scanf("%d", &pp[i]);
	for (i = 0; i < n; i++)
		scanf("%d", &qq[i]);
	for (i = 0; i < n; i++)
		xx[i] = i + 1;
	a = b = -1;
	i = 0;
	do {
		if (same(n, xx, pp))
			a = i;
		if (same(n, xx, qq))
			b = i;
		i++;
	} while (next(n, xx));
	printf("%d\n", abs(a - b));
	return 0;
}