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
import itertools

n = int(raw_input())

array = [int(x) for x in raw_input().split()]

inicio = 0
maior = 0
menor = array[0]
contador = 0

for i in range(n):
	if i!=n-1:
		if array[i]>array[i+1]:
			inicio = i+1
			maior = array[i]
			break

if inicio!=0:
	for i in range(inicio,n):
		if i != n-1:
			if array[i]>array[i+1] or array[i]>maior or array[i]>menor:
				contador = -1
				break
		else:
			if array[i]>maior or array[i]>menor:
				contador = -1
				break
		contador+=1

print contador
