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=list(map(int,input().split()))
b=list(map(int,input().split()))
inf=100000000000
ans=inf
for i in range(1<<n):#for i in range(2**n)と同じ
    x=[[a[j],j,0] if ((i >> j) & 1) == 1 else [b[j],j,1] for j in range(n)]
    y=[x[i][0] for i in range(n)]
    x.sort()
    for i in range(n):
        if abs(x[i][1]-i)%2!=x[i][2]:
            break
    else:
        c=0
        for i in range(1,n):
            for j in range(i,0,-1):
                if y[j] >= y[j-1]:
                    break
                else:
                    y[j],y[j-1]=y[j-1],y[j]
                    c+=1
        ans=min(ans,c)
if ans==inf:
    print(-1)
else:
    print(ans)