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:
from itertools import combinations

N = int(input())
A = [int(i) for i in input().split()]
B = [int(i) for i in input().split()]

ret = float('inf')
for ce in combinations(range(N), (N + 1) // 2) :
  e, o = [], []
  for i in range(N) :
    if i in ce :
      if i % 2 == 0 :
        e.append([A[i], i])
      else :
        e.append([B[i], i])
    else :
      if i % 2 == 0 :
        o.append([B[i], i])
      else :
        o.append([A[i], i])
  
  e.sort()
  o.sort()
  s = []
  for i in range(N // 2) :
    s.append(e[i])
    s.append(o[i])
  if N % 2 != 0 :
    s.append(e[N // 2])
  
  for i in range(1, N) :
    if s[i][0] < s[i-1][0] :
      break
    
  else :
    tmp = 0
    for i in range(N) :
      for j in range(i) :
        if s[j][1] > s[i][1] :
          tmp += 1
    ret = min(ret, tmp)
    
if ret == float('inf') :
  print(-1)
else :
  print(ret)