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
n = int(raw_input())
next_line = raw_input()
nums = []
for x in next_line.split(" "):
	nums.append(int(x))

desired = sorted(nums)
found = False
times = 0
def get_greater(lst):
	temp = -1
	for x in xrange(0, len(lst)-1):
		if lst[x] > lst[x+1]:
			if temp != -1:
				return -1
			else:
				temp = x
	if temp == -1:
		return -2
	else:
		return temp


if get_greater(nums) == -1 or (get_greater(nums) != -2 and nums[n-1] > nums[0]):
	print "-1"
elif get_greater(nums) == -2:
	print "0"
else:
	print n-get_greater(nums)-1



