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())
ar = list(map(int, input().split()))

count = 0
flag = False

def test():
    global count
    global flag

    min = 999999999999

    for i in range(n-1):
        if not flag:
            if ar[i] < min:
                min = ar[i]

        if ar[i] > ar[i+1] and flag:
            return False
        elif ar[i] > ar[i + 1] and not flag:
            if ar[i + 1] > min:
                return False
            flag = True
            count += 1
        elif ar[i] <= ar[i+1] and flag:
                if ar[i + 1] > min:
                    return False
                count += 1
        elif ar[i] <= ar[i+1] and not flag:
            continue

    return True

if test():
    print(count)
else:
    print("-1")

