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
def us_num(nums):
  where = None
  for idx, (a, na) in enumerate(zip(nums[:-1], nums[1:])):
    if a > na:
      if where is None:
        where = idx
      else:
        return -1
  if where is None:
    return 0
  elif nums[-1] > nums[0]:
    return -1
  return len(nums) - 1 - where

n = int(input())
nums = list(map(int, input().split()))
print(us_num(nums))
