One day, Twilight Sparkle is interested in how to sort a sequence of integers a1, a2, ..., an in non-decreasing order. Being a young unicorn, the only operation she can perform is a unit shift. That is, she can move the last element of the sequence to its beginning:

a1, a2, ..., an → an, a1, a2, ..., an - 1.

Help Twilight Sparkle to calculate: what is the minimum number of operations that she needs to sort the sequence?

Input

The first line contains an integer n (2 ≤ n ≤ 105). The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 105).

Output

If it's impossible to sort the sequence output -1. Otherwise output the minimum number of operations Twilight Sparkle needs to sort it.

Examples

Input

2
2 1


Output

1


Input

3
1 3 2


Output

-1


Input

2
1 2


Output

0
n = int(input())

numbers = list(map(int, input().split()))

smallerBefore = numbers[0]
graterAfter = 0

fallIndex = -2

for i in range(0, n):

  if(fallIndex > -1):
    if(numbers[i] > numbers[fallIndex]):
      fallIndex = -1
      break

    if(numbers[i] > graterAfter):
      graterAfter = numbers[i]

  else:
    if(numbers[i] < smallerBefore):
      smallerBefore = numbers[i]


  if(i < n - 1 and numbers[i] > numbers[i + 1]):
      if(fallIndex > -1):
        fallIndex = -1
        break

      fallIndex = i
      graterAfter = numbers[i + 1]
      continue

  if(i == n - 1 and fallIndex > -1 and smallerBefore < graterAfter):
    fallIndex = -1
    break


print(-1 if fallIndex == -1 else 0 if fallIndex == -2 else n - fallIndex - 1)