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)

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()
}

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

pub fn permutations(size: usize) -> Permutations {
    Permutations {
        idxs: (1..size + 1).collect(),
        swaps: vec![0; size],
        i: 0,
    }
}
pub struct Permutations {
    idxs: Vec<usize>,
    swaps: Vec<usize>,
    i: usize,
}

impl Iterator for Permutations {
    type Item = Vec<usize>;
    fn next(&mut self) -> Option<Self::Item> {
        if self.i > 0 {
            loop {
                if self.i >= self.swaps.len() {
                    return None;
                }
                if self.swaps[self.i] < self.i {
                    break;
                }
                self.swaps[self.i] = 0;
                self.i += 1;
            }
            self.idxs.swap(self.i, (self.i & 1) * self.swaps[self.i]);
            self.swaps[self.i] += 1;
        }
        self.i = 1;
        Some(self.idxs.clone())
    }
}

fn main() {
    let n: usize = read();
    let ps: Vec<usize> = read_vec();
    let qs: Vec<usize> = read_vec();

    let mut perms = permutations(n).collect::<Vec<_>>();
    perms.sort();

    let mut a: i32 = 0;
    let mut b: i32 = 0;
    for (i, perm) in perms.iter().enumerate() {
        if ps == *perm {
            a = i as i32;
        }
        if qs == *perm {
            b = i as i32;
        }
    }

    println!("{}", i32::abs(a - b));
}