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

dp = [[100100] * (1 << N) for _ in range(N)]
for i in range(N):
    dp[i][1 << i] = 0
for mask in range(1, 1 << N):
    mask_pop = format(mask, 'b').count('1')
    for j in range(N):
        if (1 << j) & mask:
            if (j - mask_pop) % 2 == 1:
                cur_elem = A[j]
            else: 
                cur_elem = B[j]
            prev_mask = mask & ~(1 << j)
            cost_delta = format(prev_mask & (-1 << j), 'b').count('1')
            for t in range(N):
                if (1 << t) & prev_mask:
                    prev_elem = A[t] if (t - mask_pop - 1) % 2 == 1 else B[t]
                    if prev_elem <= cur_elem:
                        if dp[j][mask] > dp[t][prev_mask] + cost_delta:
                            dp[j][mask] = dp[t][prev_mask] + cost_delta
            
# print(*dp, sep = '\n')

ans = min((dp[i][-1] for i in range(N)))
if ans == 100100:
    print(-1)
else:
    print(ans)