Problem: 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.

Examples

Input

3
3 4 3
3 2 3


Output

1


Input

2
2 1
1 2


Output

-1


Input

4
1 2 3 4
5 6 7 8


Output

0


Input

5
28 15 22 43 31
20 22 43 33 32


Output

-1


Input

5
4 46 6 38 43
33 15 18 27 37


Output

3

Solution (in PYTHON3):

Solution:
#!/usr/bin/env python3
import sys
from itertools import combinations

def solve(N: int, A: "List[int]", B: "List[int]"):
    answer = 10**18
 
    ## 奇数indexにくるものを決め打ち
    for c in combinations(range(N), N//2):
        even, odd= [], []
        
        for i in range(N):
            if i in c:
                odd.append((A[i] if i % 2 == 1 else B[i],i))
            else:
                even.append((A[i] if i % 2 == 0 else B[i],i))
    
        even.sort()
        odd.sort()
        t = []
        ind = []
        
        for i in range(N//2):
            t.append(even[i][0])
            t.append(odd[i][0])
            ind.append(even[i][1])
            ind.append(odd[i][1])

        if N%2 == 1:
            t.append(even[-1][0])
            ind.append(even[-1][1])
        
        if t != sorted(t):
            continue

        tentousuu = 0
        for i in range(N-1):
            for j in range(i+1,N):
                if ind[i] > ind[j]:
                    tentousuu += 1
        
        answer = min(answer,tentousuu)


    if answer == 10**18:
        print(-1)
    else:
        print(answer)
    return

def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    A = [int(next(tokens)) for _ in range(N)]  # type: "List[int]"
    B = [int(next(tokens)) for _ in range(N)]  # type: "List[int]"
    solve(N, A, B)

if __name__ == '__main__':
    main()