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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

def sortable(m, A, B):
    if len(A) == 2:
        if m <= A[0] <= A[1]:
            return 0
        elif m <= B[1] <= B[0]:
            return 1
        return -1
    t = 10**9
    for i in range(len(A)):
        n = A[i] if i % 2 == 0 else B[i]
        if n < m:
            continue
        x = sortable(n, B[0:i] + A[i + 1:], A[0:i] + B[i + 1:])
        if x >= 0:
            t = min(t, x + i)
    if t != 10 ** 9:
        return t
    return -1


def main():
    N = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))
    if len(A) == 1:
        print(1)
    else:
        print(sortable(0, A, B))

main()