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;

#[allow(unused_mut)]
fn main() {
    input! {
        n: usize,
        p: [usize;n],
        q: [usize;n],
    };
    let mut perm = Vec::new();
    permutation(n, &mut vec![], &mut perm);
    let a = perm.iter().position(|v| v == &p).unwrap() as isize;
    let b = perm.iter().position(|v| v == &q).unwrap() as isize;
    let res = (a - b).abs();
    println!("{}", res);
}

fn permutation(max: usize, v: &mut Vec<usize>, all: &mut Vec<Vec<usize>>) {
    for i in 1..=max {
        if !v.contains(&i) {
            v.push(i);
            permutation(max, v, all);
            v.pop();
        }
    }
    if v.len() == max {
        let v = v.clone();
        all.push(v);
    }
}