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())
arr = list(map(int, input().rstrip().split(" ")))


change = 0
idxChange = None
for i in range(n):
    if arr[i] > arr[(i + 1) % n]:
        change += 1
        idxChange = i
    if change >= 2:
        print(-1)
        break
else:
    if idxChange is not None:
        print(n - 1 - idxChange)
    else:
        print(0)



''' 1 2 3 1 1 1 
5 1 2 3 4 5 6
'''