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<math.h>
#include <stdlib.h>

int fact(int n){
    if(n == 0){
        return 1;
    }else{
        int ans=1;
        for(int i = 1 ; i <= n ;i++){
            ans *= i;
        }
        return ans;
    }
}

int main(){
    int N;
    int P[8],Q[8];
    int a = 0;
    int b = 0;
    scanf("%d",&N);
    for(int i = 0 ; i < N ;i++){
        scanf("%d",&P[i]);
    }
    for(int i = 0 ; i < N ;i++){
        scanf("%d",&Q[i]);
    }
    for(int i = 0 ; i < N-1 ;i++){
        int s=P[i] - 1;
        for(int j = 0 ; j <= i ; j++){
            if(P[j] < P[i]){
                s--;
            }
        }
        a += s*fact(N-1-i);

    }
    for(int i = 0 ; i < N-1 ;i++){
        int s = Q[i] - 1;
        for(int j = 0 ; j <= i ; j++){
            if(Q[j] < Q[i]){
                s--;
            }
        }
        b += s*fact(N-1-i);
    }
    printf("%d",abs(a-b));
    
    return 0;
}