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)

extern crate proconio;
use proconio::input;

fn main() {
    input!{
        n: usize,
        p: [i32; n],
        q: [i32; n],
    };

    let ans = Calc::new(n);
    println!("{}", i32::abs(ans.solve(&p) - ans.solve(&q)));
  
}

struct Calc{
    n: usize,
    fact: Vec<i32>,
}

impl Calc{
    fn new(n: usize) -> Calc{
        let mut fact = Vec::new();
        let mut num: i32 = 1;
        for i in 0..n {
            fact.push(num);
            num *= (i+1) as i32;
        }
        Calc{ n, fact }
    }

    fn solve(&self, p: &[i32]) -> i32 {
        let n = self.n;
        let mut ans_p = 0;
        for i in 0..n-1 {
            let mut tp = 0;
            for j in i..n {
                if p[i] > p[j] {
                    tp += 1;
                }
            }
            ans_p += tp*self.fact[n-i-1];
        }
        ans_p
    }
}