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

n = int(raw_input())
lista = map(int, raw_input().split())

min_operations = 0

for i in range(n-1):
	if lista[i] > lista[i+1]:
		maior = lista[i]
		
		for j in range(i+1, n, 1):
			
			if j ==	n-1:
				if lista[j] > maior or lista[j] > lista[0]:
					min_operations = -1
					break
			else:
				if lista[j] > lista[j+1] or lista[j] > maior or lista[j] > lista[0]:
					min_operations = -1
					break
			
			min_operations += 1
		
		break
			
		

print min_operations
