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 Raise(lst):
	ans = -1
	for i in xrange(len(lst) - 1):
		if lst[i] > lst[i + 1]:
			if ans != -1:
				return -1
			else:
				ans = i
	if ans == -1:
		return -2
	else:
		return ans

n = int(raw_input())
lst = [eval(i) for i in raw_input().split()]

ans = Raise(lst)
if (ans == -1) or (lst[n - 1] > lst[0] and ans != -2):
	print -1
elif ans == -2:
	print 0
else:
	print n - ans - 1