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 itertools::Itertools;
use proconio::input;
use proconio::marker::Usize1;

fn main() {
    input! {
        n: usize,
        p:[Usize1; n],
        q:[Usize1; n],
    }

    let mut cp = 0i32;
    let mut cq = 0i32;
    let mut cnt = 0;
    for idx in (0..n).permutations(n) {
        cnt += 1;
        // println!("{:?}", idx);
        // println!("p:{:?}", p);
        // println!("q:{:?}", q);
        let mut eqp = true;
        let mut eqq = true;
        for i in 0..n {
            eqp = eqp && idx[i] == p[i];
            eqq = eqq && idx[i] == q[i];
        }
        if eqp {
            cp = cnt;
        }
        if eqq {
            cq = cnt;
        }
    }
    println!("{}", (cq - cp).abs());
}