Problem:
Score : 700 points

Problem Statement

We have N cards numbered 1, 2, ..., N.
Card i (1 \leq i \leq N) has an integer A_i written in red ink on one side and an integer B_i written in blue ink on the other side.
Initially, these cards are arranged from left to right in the order from Card 1 to Card N, with the red numbers facing up.

Determine whether it is possible to have a non-decreasing sequence facing up from left to right (that is, for each i (1 \leq i \leq N - 1), the integer facing up on the (i+1)-th card from the left is not less than the integer facing up on the i-th card from the left) by repeating the operation below. If the answer is yes, find the minimum number of operations required to achieve it.

Choose an integer i (1 \leq i \leq N - 1).
Swap the i-th and (i+1)-th cards from the left, then flip these two cards.

Constraints

1 \leq N \leq 18

1 \leq A_i, B_i \leq 50 (1 \leq i \leq N)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N
B_1 B_2 ... B_N

Output

If it is impossible to have a non-decreasing sequence, print -1.
If it is possible, print the minimum number of operations required to achieve it.

Sample Input 1

3
3 4 3
3 2 3

Sample Output 1

1

By doing the operation once with i = 1, we have a sequence [2, 3, 3] facing up, which is non-decreasing.

Sample Input 2

2
2 1
1 2

Sample Output 2

-1

After any number of operations, we have the sequence [2, 1] facing up, which is not non-decreasing.

Sample Input 3

4
1 2 3 4
5 6 7 8

Sample Output 3

0

No operation may be required.

Sample Input 4

5
28 15 22 43 31
20 22 43 33 32

Sample Output 4

-1

Sample Input 5

5
4 46 6 38 43
33 15 18 27 37

Sample Output 5

3

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

use std::vec::Vec;

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()
}

fn read_touple<T: std::str::FromStr + Copy>() -> (T, T) {
  let v: Vec<T> = read_vec();
  assert_eq!(v.len(), 2);
  (v[0], v[1])
}

fn main() {
    let n: usize = read();
    let a: Vec<usize> = read_vec();
    let b: Vec<usize> = read_vec();
    let mut count: usize = 1;
    let mut ans = -1; 
    for _ in 0..n-1 {
      count *= 2;
    }


    let mut narabi = Vec::new();
    for bit in 0..count {
     
      let mut a_tmp = a.clone();
      let mut b_tmp = b.clone();
      let mut tmp = a.clone();
      let mut c = 0;
      for i in 0..n-1 {
        if (bit & (1<<i)) == (1<<i) {
          //println!("{:0>1$b}", bit &(1<<i), 8);
          let mut x = a_tmp[i];
          a_tmp[i] = a_tmp[i+1];
          a_tmp[i+1] = x;
          x = b_tmp[i];
          b_tmp[i] = b_tmp[i+1];
          b_tmp[i+1] = x;

          x = a_tmp[i];
          a_tmp[i] = b_tmp[i];
          b_tmp[i] = x;
          x = a_tmp[i+1];
          a_tmp[i+1] = b_tmp[i+1];
          b_tmp[i+1] = x;
          tmp[i] = a_tmp[i];
          tmp[i+1] = a_tmp[i+1];
          c += 1;
        }
      } 

      if !check(&tmp, n) {
         continue
      } else if ans != -1 {
        if ans > c {
           ans = c;
           narabi.push(bit);
        }
      } else {

        ans = c;
      }
    }
    println!("{}", ans);
}

fn check(v: &Vec<usize>, n: usize) -> bool {
  for i in 1..n {
    if v[i-1] > v[i] {
       return false
    }
  }
  return true
}