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: Runtime Error)

import bisect
N = int(input())
A = list(map(int,input().split()))
B = list(map(int,input().split()))
ans = 10**9+7
for i in range(2**N):
    card = [[],[]]
    num = []
    iii = i
    for j in range(N):
        if i&1:
            num.append(B[j])
            card[(j+1)%2].append(j)
        else:
            num.append(A[j])
            card[(j)%2].append(j)
        i >>= 1
    if len(card[0]) != N//2:
        continue
    card[0].sort(key=lambda x:[num[x],x])
    card[1].sort(key=lambda x:[num[x],x])
    hoge = []
    for i in range(N):
        hoge.append(card[i%2][i//2])
    flag = True
    for i in range(N-1):
        if num[hoge[i]] > num[hoge[i+1]]:
            flag = False
    if flag:
        huga = []
        count = 0
        for i in range(N):
            l = bisect.bisect_left(huga,hoge[i])
            huga.insert(l,hoge[i])
            count += i-l
        if count < ans:
            ans = count
if ans >= 10**9:
    print(-1)
else:
    print(ans)