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::{stdin, Read};

macro_rules! parse {
    ($iter: ident) => {
        $iter.next().unwrap().parse().unwrap()
    };
    ($iter: ident,2) => {
        (parse!($iter), parse!($iter))
    };
    ($iter: ident,3) => {
        (parse!($iter), parse!($iter), parse!($iter))
    };
    ($iter: ident,4) => {
        (parse!($iter), parse!($iter), parse!($iter), parse!($iter))
    };
    ($iter: ident, $n: ident) => {
        (&mut $iter).take($n).map(|e| e.parse().unwrap()).collect();
    };
}

struct Perm<T> {
    v: Vec<T>,
    cur: usize,
    tails: Option<Box<Perm<T>>>,
    finish: bool,
}

impl<T: Clone> Perm<T> {
    fn new(v: Vec<T>) -> Self {
        let mut w = v.clone();
        w.remove(0);
        let tails = if w.len() > 0 {
            Some(Box::new(Perm::new(w)))
        } else {
            None
        };
        Perm {
            v: v,
            cur: 0,
            tails: tails,
            finish: false,
        }
    }
}

impl<T: Clone> Iterator for Perm<T> {
    type Item = Vec<T>;
    fn next(&mut self) -> Option<Self::Item> {
        if self.finish {
            return None;
        }
        if let &mut Some(ref mut tails) = &mut self.tails {
            if let Some(mut v) = tails.next() {
                v.insert(0, self.v[self.cur].clone());
                return Some(v);
            }
        } else {
            self.finish = true;
            return Some(self.v.clone());
        }

        self.cur += 1;
        if self.cur == self.v.len() {
            self.finish = true;
            return None;
        }
        let mut w = self.v.clone();
        w.remove(self.cur);
        self.tails = Some(Box::new(Perm::new(w)));
        self.next()
    }
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    let mut iter = s.split_whitespace();
    let n: usize = parse!(iter);
    let perm: Vec<Vec<usize>> = Perm::new((1..(n + 1)).collect()).collect();
    let p: Vec<usize> = parse!(iter, n);
    let pi = perm.binary_search(&p).unwrap() as isize;
    let q: Vec<usize> = parse!(iter, n);
    let qi = perm.binary_search(&q).unwrap() as isize;
    println!("{}", isize::abs(pi - qi));
}