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

def read():
	n = input()
	buf = [int(item) for item in raw_input().split()]
	return (n, buf)
	
def main():
	n = input()
	buf = [int(item) for item in raw_input().split()]
	flag = True
	j = -1
	for i in range(1, n):
		if buf[i] < buf[i-1]:
			if j > 0:
				flag = False
				break
			else:
				j = i
	if flag:
		if j<0:
			print 0
		elif buf[-1]<=buf[0]:
			print n-j
		else:
			print -1
	else:
		print -1
	
main()