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 (1.15.1) (judge verdict: Accepted)

use std::io::prelude::*;
use std::io::stdin;
use std::str::FromStr;

fn main() {
    let n: usize = read();
    let p: Vec<i32> = (0..n).map(|_| read()).collect();
    let q: Vec<i32> = (0..n).map(|_| read()).collect();
    let permutation = permutation(&(1..n as i32 + 1).collect::<Vec<i32>>());
    let p_position = permutation.iter().position(|x| *x == p).unwrap();
    let q_position = permutation.iter().position(|x| *x == q).unwrap();
    println!(
        "{}",
        if p_position > q_position {
            p_position - q_position
        } else {
            q_position - p_position
        }
    );
}

fn permutation<T: Clone + Copy>(x: &Vec<T>) -> Vec<Vec<T>> {
    if x.len() == 1 {
        vec![x.clone()]
    } else {
        let mut result = vec![];
        for i in 0..x.len() {
            let mut tmp = x.clone();
            tmp.remove(i);
            for mut x_i in permutation(&tmp) {
                x_i.insert(0, x[i]);
                result.push(x_i);
            }
        }
        result
    }
}
#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|b| b.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}