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:
import itertools
n=int(input())
A=[int(i) for i in input().split()]
B=[int(i) for i in input().split()]

N=[int(i) for i in range(n)]
nn=2**n
ans=float("inf")
for _ in range(n//2+1):
  for com in itertools.combinations(N,2*_):
    i=0
    for ura in com:
      i+=2**ura
    E,O=[],[]
    for j in range(n):
      if i&(1<<j)==0:
        if j%2==0:
          E.append(A[j]*100+j)
        else:
          O.append(A[j]*100+j)
      else:
        if j%2==0:
          O.append(B[j]*100+j)
        else:
          E.append(B[j]*100+j)
    if len(E)!=(n+1)//2:
      continue
    else:
      E.sort()
      O.sort()

      chk=True
      C=[E[0]%100]
      prev=E[0]//100
      for i in range(1,n):
        ii=i//2
        if i%2==0:
          C.append(E[ii]%100)
          if E[ii]//100<prev:
            chk=False
            break
          else:
            prev=E[ii]//100
        else:
          C.append(O[ii]%100)
          if O[ii]//100<prev:
            chk=False
            break
          else:
            prev=O[ii]//100
    
    if chk:
      ten=0
      for i1 in range(n):
        for i2 in range(i1+1,n):
          if C[i1]>C[i2]:
            ten+=1
      ans=min(ans,ten)
print(-1 if ans==float("inf") else ans)