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 Python (3.4.3) (judge verdict: Wrong Answer)

n = int(input())
a_lis = list(map(int, input().split()))
b_lis = list(map(int, input().split()))
used = []
res = []
def rec(a_lis, b_lis, l):
    
    found = True
    pre = -1
    for a in a_lis:
        if a < pre:
            found = False
            break
        pre = a
    if found:
        res.append(l)
        return
    used.append((a_lis, b_lis))
    for i in range(len(a_lis) - 1):
        na_lis = a_lis[:i] + [b_lis[i + 1]] + [b_lis[i]] + a_lis[i + 2:]
        nb_lis = b_lis[:i] + [a_lis[i + 1]] + [a_lis[i]] + b_lis[i + 2:]
        if (na_lis, nb_lis) not in used:
            rec(na_lis, nb_lis, l + 1)
if res:
    print(min(res))
else:
    print(-1)