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)

pub fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

pub fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

pub fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

pub fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

fn fact(n: u32) -> u32 {
    if n == 0 {
        1
    } else {
        n * fact(n - 1)
    }
}

fn f(v: Vec<u32>, n: usize, check: &mut Vec<bool>) -> u32 {
    let mut ret = 0;
    for i in 0..n {
        check[v[i] as usize] = true;
        let mut cnt = 0;
        for j in 0..v[i] as usize {
            if check[j] {
                cnt += 1;
            }
        }
        ret += (v[i] - cnt) * fact((n - 1 - i) as u32);
        // println!("({} - {}) * {}!", v[i], cnt, n - 1 - i);
    }
    ret
}

fn main() {
    let n: usize = read();
    let pv: Vec<u32> = read_vec();
    let pv: Vec<u32> = pv.iter().map(|x| x - 1).collect();
    let qv: Vec<u32> = read_vec();
    let qv: Vec<u32> = qv.iter().map(|x| x - 1).collect();

    // println!("{:?}", pv);
    // println!("{:?}", qv);

    let mut check = vec![false; n];
    let a = f(pv, n, &mut check);
    // println!("{}", a);

    let mut check = vec![false; n];
    let b = f(qv, n, &mut check);
    // println!("{}", b);

    let ans;
    if a > b {
        ans = a - b
    } else {
        ans = b - a
    }
    println!("{}", ans);
}