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():
    import sys
    from itertools import combinations
    from operator import itemgetter
    input = sys.stdin.readline

    N = int(input())
    A = list(map(int, input().split()))
    B = list(map(int, input().split()))

    even = []
    odd = []
    for i in range(N):
        if i%2:
            odd.append(A[i])
            even.append(B[i])
        else:
            even.append(A[i])
            odd.append(B[i])

    L = list(range(N))
    ans = 10**9
    for v in combinations(L, N//2):
        ok = 1
        tmp = []
        tmp_odd = []
        tmp_even = []
        for i in range(N):
            if i in v:
                tmp.append(odd[i] * 100)
                tmp_odd.append((odd[i], i))
            else:
                tmp.append(even[i] * 100)
                tmp_even.append((even[i], i))

        tmp_odd.sort(key=itemgetter(0))
        tmp_even.sort(key=itemgetter(0))

        tmp_check = []
        p = [0] * N
        for i in range(N):
            if i%2:
                tmp_check.append(tmp_odd[i//2][0])
                p[tmp_odd[i//2][1]] = i
            else:
                tmp_check.append(tmp_even[i // 2][0])
                p[tmp_even[i // 2][1]] = i
        for i in range(N-1):
            if tmp_check[i] > tmp_check[i+1]:
                ok = 0
                # print(v, tmp_check, odd, even)
                break
        if not ok:
            continue

        for i in range(N):
            tmp[i] += p[i]

        ans_new = 0
        for i in range(N):
            for j in range(i+1, N):
                if tmp[i] > tmp[j]:
                    ans_new += 1
        # print(v, tmp, ans_new, odd, even)
        ans = min(ans, ans_new)

    if ans == 10**9:
        print(-1)
    else:
        print(ans)


if __name__ == '__main__':
    main()