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()))
judge = False
ans = 10**9
for i in range(2**N):
  even = []
  odd = []
  x = 0
  tmp = True
  for j in range(N):
    if ((i>>j) & 1):
      if j%2==1:
        even.append([B[j],j])
      else:
        odd.append([B[j],j])
      
    else:
      if j%2==1:
        odd.append([A[j],j])
      else:
        even.append([A[j],j])
        
  if N%2==0:
    if len(even)!=len(odd):
      continue
      
  else:
    if (len(even)-1)!=len(odd):
      continue
      

  even = sorted(even,key = lambda x:x[0])
  odd = sorted(odd,key = lambda x:x[0])
  ind = [0]*N
  for k in range(N//2):
    o = odd[k]
    e = even[k]
    if o[0]<e[0]:
      tmp = False
      break
    
    if (k!=N//2-1)or(N%2==1):
      if o[0]>even[k+1][0]:
        tmp = False
        break
    
    ind[2*k]=e[1]
    ind[2*k+1]=o[1]

  if tmp:
    if N%2==1:
      ind[N-1]=even[-1][1]
      

    for k in range(N):
      y = ind[k]
      x+=abs(y-k)
      ind = [x+1 if (x<y)and(x>=k) else x for x in ind]
    ans = min(ans,x)
    judge = True
    
if judge:
  print(ans)
else:
  print(-1)