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())
nums = [int(a) for a in list(raw_input().split(' '))]

a1 = nums[0]
a2 = nums[n-1]
prev = nums[n-1]
counter = 0
realCounter = 0
ret = False
for i in range(n-2, -1, -1):
	num = nums[i]
	counter += 1

	if prev >= num:
		prev = num
		continue
	else: #update
		if a2>a1:
			ret = True
			break
		a1 = prev
		a2 = num
		prev = num
		realCounter += counter
		counter = 0
if ret:
	print str(-1)
elif a1>a2:
	print str(-1)
else:
	print str(realCounter)