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>

int f(int x);
int main()
{
  int n;
  scanf("%d",&n);
  int p[n],q[n];
  for(int i=0;i<n;i++) scanf("%d",&p[i]);
  for(int j=0;j<n;j++) scanf("%d",&q[j]);

  int a=0;
  int b=0;
  int c,d;
  for(int k=0;k<n;k++){
    c=0;
    d=0;
    for(int l=0;l<k;l++){
      if(p[l]<p[k])c=c+1;
      if(q[l]<q[k])d=d+1;
  }
    
    if(p[k]-(c+1)<=0) a=a;
    else a=a+(p[k]-(c+1))*f(n-k-1);
    if(q[k]-(d+1)<=0) b=b;
    else b=b+(q[k]-(d+1))*f(n-k-1);
}
  printf("%d\n",abs(a-b));
  return 0;
}

int f(int x){
  int s=1;
  for(int i=1;i<x+1;i++){
      s=s*i;
  }
  return s;
}