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
l = int(input())

s = input().split(" ")

seq = []
for i in s:
	seq.append(int(i))

changes = 0
index = 0

for i in range(1, l):
	curr = seq[i]
	prev = seq[i-1]
	if curr >= prev:
		continue
	elif changes <= 1:
		index = i
		changes += 1
	else:
		break
if seq[0] < seq[l-1]:
	changes += 1

if changes <= 1:
	if index == 0:
		print(0)
	else:
		print(l-index)
else:
	print(-1)


	   		 	 	 				    						 	  	