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()))

ans = N ** 2
for i in range(1 << N):
  L = [[] for _ in range(N)]
  T = [0] * N
  t = i
  for j in range(N):
    if t & 1:
      L[j] = [A[j], 1]
      T[j] = A[j]
    else:
      L[j] = [B[j], 0]
      T[j] = B[j]
    t >>= 1
  D = [0] * N
  T.sort()
  cnt = 0
  for j in range(N):
    c = 0
    for k in range(N):
      if D[k] == 0:
        if L[j][0] == T[k] and (j + 1 - L[j][1]) % 2 == k % 2:
          D[k] = 1
          cnt += j - c
          break
      else:
        c += 1
    else:
      break
  else:
    ans = min(ans, cnt)

if ans == N ** 2:
  print(-1)
else:
  print(ans)