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)

use std::io::{stdin, Read};

macro_rules! parse {
    ($it: ident) => {
        $it.next().unwrap().parse().unwrap()
    };
    ($it: ident,2) => {
        (parse!($it), parse!($it))
    };
    ($it: ident,3) => {
        (parse!($it), parse!($it), parse!($it))
    };
    ($it: ident,4) => {
        (parse!($it), parse!($it), parse!($it), parse!($it))
    };
    ($it: ident, $n: expr) => {
        (&mut $it).take($n).map(|e| e.parse().unwrap()).collect();
    };
}
fn binary_search_left<T: Ord>(v: &Vec<T>, x: T) -> usize {
    let mut l: isize = -1;
    let mut r: isize = v.len() as isize;
    while r - l > 1 {
        let m = (r + l) / 2;
        if v[m as usize] < x {
            l = m;
        } else {
            r = m;
        }
    }
    r as usize
}

fn solve(s: &str) {
    let mut it = s.split_whitespace();
    let n: usize = parse!(it);
    let a: Vec<usize> = parse!(it, n);
    let b: Vec<usize> = parse!(it, n);
    let mut ret = std::usize::MAX;
    'outer: for i in 0..(1 << n) {
        let flags: Vec<bool> = (0..n).map(|j| (i >> j) & 1 == 1).collect();
        let c: Vec<usize> = (0..n).map(|j| if flags[j] { b[j] } else { a[j] }).collect();
        let mut d = c.clone();
        d.sort();
        let mut arg = vec![None; n];
        let mut used = vec![false; n];
        for i in 0..n {
            let l = binary_search_left(&d, c[i]);
            let r = binary_search_left(&d, c[i] + 1);
            for j in l..r {
                if !used[j] && if i < j { j - i } else { i - j } % 2 == flags[i] as usize {
                    arg[i] = Some(j);
                    used[j] = true;
                    break;
                }
            }
            if arg[i] == None {
                continue 'outer;
            }
        }
        let mut p = 0usize;
        for i in 0..n {
            for j in (i + 1)..n {
                p += (arg[i] > arg[j]) as usize;
            }
        }
        ret = std::cmp::min(ret, p)
    }
    println!(
        "{}",
        if ret == std::usize::MAX {
            -1
        } else {
            ret as i64
        }
    );
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    solve(&s);
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn test_input() {
        let s = "
        ";
        solve(s);
    }
}