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 whiteread::parse_line;

fn func(left: Vec<isize>, right: Vec<isize>, cand: &mut Vec<Vec<isize>>) {
    if right.is_empty() {
        cand.push(left);
        return;
    }
    for i in 0..right.len() {
        let mut lc: Vec<isize> = left.iter().copied().collect();
        let mut rc: Vec<isize> = right.iter().copied().collect();
        lc.push(rc.remove(i));
        func(lc, rc, cand);
    }
}

fn main() {
    let _n: usize = parse_line().unwrap();
    let p: Vec<isize> = parse_line().unwrap();
    let q: Vec<isize> = parse_line().unwrap();
    let mut candidate: Vec<Vec<isize>> = Vec::new();
    let mut first: Vec<isize> = p.iter().copied().collect();
    first.sort();

    func(Vec::new(), first, &mut candidate);
    let pp = candidate.iter().position(|x| x.eq(&p)).unwrap();
    let qp = candidate.iter().position(|x| x.eq(&q)).unwrap();
    println!("{}", pp.max(qp) - pp.min(qp));
}