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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#pragma GCC optimize(3, "Ofast", "inline")
#include <bits/stdc++.h>
using namespace std;
const int maxn = 10;
int n;
int p[maxn] , q[maxn] , t[maxn];
inline void init() {
	for(register int i = 1; i <= n; ++i)
		t[i] = i;
}
inline bool check(int *a) {
	for(register int i = 1; i <= n; ++i)
		if(a[i] != t[i]) return false;
	return true;
}
int main() {
	cin >> n;
	for(register int i = 1; i <= n; ++i) cin >> p[i];
	for(register int i = 1; i <= n; ++i) cin >> q[i];
	init();
	int cnt1 = 0 , cnt2 = 0;
	while(!check(p)) {
		cnt1++;
		next_permutation(p + 1 , p + n + 1);
	}
	init();
	while(!check(q)) {
		cnt2++;
		next_permutation(q + 1 , q + n + 1);
	}
	cout << abs(cnt1 - cnt2) << endl;
	return 0;
}