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 Min_Ops( List , N):    
    Sorted = sorted(List)
    if Sorted == List:
        return 0
    else:
        Inc = True
        for i in range(0,N-1):
            Temp = List[i+1] >= List[i]
            if Temp != Inc:
                i+=1
                break
        if List[i::]+List[0:i] == Sorted:
            return N - i
        else:
            return -1
N = input()

print Min_Ops( map(int,raw_input().split(' ')) , N )
