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: Accepted)

#![allow(non_snake_case)]
#![allow(unused_variables)]
#![allow(dead_code)]

fn main() {
    let N: usize = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.trim().parse().unwrap()
    };
    let A: Vec<usize> = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.split_whitespace()
            .map(|x| x.parse().unwrap())
            .collect()
    };
    let B: Vec<usize> = {
        let mut line: String = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        line.split_whitespace()
            .map(|x| x.parse().unwrap())
            .collect()
    };

    const INF: usize = 1_000_000_000;
    let res = (0..(1 << N))
        .map(|p| {
            let mut X = vec![];
            for i in 0..N {
                X.push((i, 1));
            }
            let mut Y = vec![];
            for i in 0..N {
                if (p >> i) & 1 == 1 {
                    Y.push(A[i]);
                } else {
                    Y.push(B[i]);
                }
            }
            let mut cost = 0;
            // println!("p={}", p);
            for i in 0..N {
                // println!("{:?}", X);
                // println!("{:?}", Y);
                let l = (i..N)
                    .find(|&l| ((l - i) + X[l].1) % 2 == (p >> X[l].0) & 1)
                    .unwrap_or(INF);
                if l == INF {
                    cost = INF;
                    break;
                }
                let mut k = l;
                for j in l..N {
                    if Y[j] < Y[k] && ((j - i) + X[j].1) % 2 == (p >> X[j].0) & 1 {
                        k = j;
                    }
                }
                // println!("l={}, k={}", l, k);
                for r in (i..k).rev() {
                    let tmp = X[r + 1];
                    X[r + 1] = (X[r].0, 1 - X[r].1);
                    X[r] = (tmp.0, 1 - tmp.1);
                    let tmp2 = Y[r + 1];
                    Y[r + 1] = Y[r];
                    Y[r] = tmp2;
                    cost += 1;
                }
            }
            if (1..N).any(|i| Y[i - 1] > Y[i]) {
                cost = INF;
            }
            // println!("{}", cost);
            cost
        })
        .min()
        .unwrap();
    let ans = if res >= INF { -1 } else { res as i64 };

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