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
length = input()
num = map(int, raw_input().split())
def check():
	count = 0
	flg = -1
	for i in range(1,length):
			if num[i] < num[i - 1]:
					flg = i
					break
	if flg != -1:
			if num[0] < num[length - 1]:
					 return -1
			for i in range(flg + 1, length):
					if num[i] < num[i - 1]:
							return -1
			return flg
	return length
if length <= 1:
		print 0
else:
		x = check()
		if x == -1:
				print x
		else:
				print length - x
