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
from sys import stdin, stdout


def shift(alist):
    return [alist[len(alist)-1]] + alist[:len(alist)-1]


def solve(ints, n):
    i = 0
    while i < n - 1:
        if ints[i] > ints[i+1]:
            sliced = ints[i+1:]
            if sliced == sorted(sliced) and sliced[len(sliced)-1]<=ints[0]:
                return len(sliced)
            return -1
        i += 1
    return 0


if __name__ == "__main__":
    n = int(stdin.readline().rstrip())
    integers = list(map(int, stdin.readline().rstrip().split()))
    stdout.write(str(solve(integers, n)))

