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
# -*- coding:utf-8 -*-

def some_func():
    """
    """

    n = int(input())
    n_lit = [int(x) for x in raw_input().split()]



    f1 = 0
    ff = 0
    temp = n_lit[0]
    for v in n_lit:
        if v<temp:
            ff+=1
        temp = v
        if ff==0:
            f1+=1

    if ff==0:
        print 0
    elif ff==1 and n_lit[-1]<=n_lit[0]:
        print n-f1
    else:
        print -1




if __name__ == '__main__':
    some_func()

