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 change(int x, int y) {
    if(x > y) {
        return x-1;
    }
}
 
int kaijo(int x) {
    int ans=1;
    int i;
    for(i=2;i<=x;i++){
        ans*=i;
    }
    return ans;
}
 
int main() {
    int N;
    scanf("%d", &N);
    int *P = (int*)malloc(N * sizeof(int));
    int *Q = (int*)malloc(N * sizeof(int));
    int i;
    for(i=0; i<N; i++) {
        scanf("%d", &P[i]);
    }
    for(i=0; i<N; i++) {
        scanf("%d", &Q[i]);
    }
    int a = 0;
    int b = 0;
    int j;
    for(i=0; i<N-1; i++) {
        if(P[i] != 1) a += (P[i] - 1) * kaijo(N-i-1);
        if(Q[i] != 1) b += (Q[i] - 1) * kaijo(N-i-1);
        for(j=i+1; j<N; j++) {
            P[j] = change(P[j], P[i]);
            Q[j] = change(Q[j], Q[i]);
        }
    }
    printf("%d\n", abs(a-b));
 
    free(P);
    free(Q);
    return 0;
}