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())
nums = [int(a) for a in input().split()]
offset = 1
count = 0
while offset < n and nums[offset-1] <= nums[offset]:
    offset += 1
isOrdered = True
for j in range(offset,n+offset-1):
    index = j - n if j >= n else j
    nextIndex = j + 1  - n if j+1 >= n else j+1
    if nums[index] > nums[nextIndex]:
        isOrdered = False
        break
print(n-offset if isOrdered else -1)