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=input()
l=map(int,raw_input().split())
l=l+l
c=0
p=-1
f=1
pos=-1
j=0
fuck=0
for i in l:
	j+=1
	if f==1:
		if i>=p:
			c+=1
			if c==n:
				fuck=1
				pos=j
				break
		else:
			f=0
			c=0
		p=i
	else:
		if i>=p:
			c=2
			f=1
			if c==n:
				fuck=1
				pos=j
		p=i
pos-=n
if fuck==0:
	print "-1"
else:
	if pos==0:
		print "0"
	else:
		print  n-pos
