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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;
use proconio::marker::Usize1;

fn next_permutation(a: &mut Vec<usize>) -> bool {
  let N: usize = a.len();
  for i in (0..N-1).rev() {
    if a[i] < a[i + 1] {
      a[i + 1..].reverse();
      for j in i + 1..N {
        if a[i] < a[j] {
          a[i] = a[i] ^ a[j];
          a[j] = a[i] ^ a[j];
          a[i] = a[i] ^ a[j];
          return true;
        }
      }
    }
  }
  false
}

fn main() {
  input! {
    N: usize,
    P: [Usize1; N],
    Q: [Usize1; N],
  }
  let mut v = vec![0; N];
  for i in 0..N {
    v[i] = i;
  }
  let mut a: i32 = -1;
  let mut b: i32 = -1;
  let mut cnt: i32 = 0;
  loop {
    if a == -1 && P == v {
      a = cnt;
    }
    if b == -1 && Q == v {
      b = cnt;
    }
    cnt += 1;
    if !next_permutation(&mut v) {
      break;
    }
  }
  println!("{}", i32::abs(a - b));
}