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: Time Limit Exceeded)

import sys
from collections import deque
def input():
    return sys.stdin.readline()[:-1]
mod=10**9+7
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
    
dic={}
astr=""
bstr=""
for i in range(n):
    astr+=str(a[i]).zfill(2)
    bstr+=str(b[i]).zfill(2)

ab=astr+bstr
dic[ab]=0
d=deque([ab])
# print(d)
while d:
    tmp=d.popleft()
    # print(tmp)
    for i in range(n-1):
        if int(tmp[i*2:i*2+2])>int(tmp[i*2+2:i*2+4]):
            # print(int(tmp[i*2:i*2+2]),int(tmp[i*2+2:i*2+4]))
            break
    else:
        print(dic[tmp])
        quit()

    for i in range(n-1):
        a=tmp[:n*2]
        b=tmp[n*2:]
        # print(a,b)
        tmp2=a[:i*2]+b[i*2+2:i*2+4]+b[i*2:i*2+2]+a[i*2+4:]+b[:i*2]+a[i*2+2:i*2+4]+a[i*2:i*2+2]+b[i*2+4:]
        # print(tmp2)
        if not tmp2 in dic:
            dic[tmp2]=dic[tmp]+1
            d.append(tmp2)
print(-1)