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)

// ABC 150-C
// 2020.1.11 bal4u

#include <stdio.h>
#include <string.h>

int K = 9;
char PP[10] = { 0, 1,2,3,4,5,6,7,8,9 };   // 0はダミ
//int *perm = PP + 1;                    // action()ではPP[1]から利用

/* 与えられた並び PP[] の次に大きい並べ替えを求める */
void next_perm()   // 順列の大きさはK
{
	int i, j, k, t;

	/* 上位桁のほうが下位桁よりも小さいところまで移動 */
	i = K; while (PP[i - 1] >= PP[i]) i--;

	/* 次の並べ替えがない */
	if (i == 1) return;

	/* PP[i-1]より値の大きい最も下位の桁をPP[j]とする */
	j = K; while (PP[i - 1] >= PP[j]) j--;

	/* PP[i-1]とPP[j]とを交換 */
	t = PP[i - 1], PP[i - 1] = PP[j], PP[j] = t;

	/* PP[i]から最下位までを逆順 */
	k = (K - i) >> 1; for (j = 0; j <= k; j++)
		t = PP[i + j], PP[i + j] = PP[K - j], PP[K - j] = t;
}

char P[10], Q[10];

int main()
{
	int i, N, n, x, y;
	
	scanf("%d", &N); K = N;
	for (i = 0; i < N; ++i) scanf("%d", P+i);
	for (i = 0; i < N; ++i) scanf("%d", Q+i);
	
	n = 0;
	for (i = 0; n < 2; ++i) {
		if (memcmp(PP+1, P, N) == 0) x = i, ++n;
		if (memcmp(PP+1, Q, N) == 0) y = i, ++n;
		next_perm();
	}
	x -= y;
	if (x < 0) x = -x;
	printf("%d\n", x);
	return 0;
}