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 collections import deque

def isPossible(li):
    increasing = True
    index = None
    for i in xrange(len(li) - 1):
        if li[i] > li[i + 1]:
            if increasing:
                increasing = False
                index = i
            else:
                return False, None
    if increasing:
        return True, len(li) - 1
    return li[0] >= li[-1], index

N = input()
L = map(int, raw_input().split())

li = deque(L)

x = isPossible(li)
if not x[0]:
    print '-1'

else:
    print N - x[1] - 1

