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())
place = N
word = True
numbers = list(map(int, input().split()))
for i in range(1, N):
    if numbers[i] < numbers[i - 1]:
        place = i
        for i in range(place + 1, place + N):
            if numbers[i % N] < numbers[i % N - 1]:
                word = False
                break
        break
if word == False:
    print(-1)
else:
    print(N - place)