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:
def main():
    from itertools import combinations
    n = int(input())
    a = list(map(int, input().split()))
    b = list(map(int, input().split()))
    cc = combinations(range(n), (n-1)//2+1)
    m = 10**9
    if n == 1:
        print(0)
        return
    for c in cc:
        memo1 = []
        memo2 = []
        for i in c:
            if i % 2 == 0:
                memo1.append((a[i], i))
            else:
                memo1.append((b[i], i))
        for i in set(range(n))-set(c):
            if i % 2 == 1:
                memo2.append((a[i], i))
            else:
                memo2.append((b[i], i))
        memo1.sort()
        memo2.sort()
        memo = []
        for i in range(n//2):
            memo.append(memo1[i])
            memo.append(memo2[i])
        if n % 2 == 1:
            memo.append(memo1[i+1])
        flag = 0
        for i in range(n-1):
            if memo[i][0] > memo[i+1][0]:
                flag = 1
                break
        if flag == 1:
            continue
        memo = [i for j, i in memo]
        cnt = 0
        for i in range(n-1):
            for j in range(i+1, n):
                if memo[i] > memo[j]:
                    cnt += 1
        m = min(cnt, m)
    if m == 10**9:
        print(-1)
    else:
        print(m)


main()