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()
s=raw_input().split(" ")
a=[]
for i in xrange(n):
	a.append((int)(s[i]))
count=0
for i in xrange(n-1):
	if a[i]<=a[i+1]:
		count=count+1
	else:
		flag=i+1
		break	
if count==n-1:
	print 0
else:
	ans=0
	p=[]
	for i in range(flag,n):
		ans=ans+1
		p.append(a[i])
	for i in range(0,flag):
		p.append(a[i])
	c=0
	for i in xrange(n-1):
		if p[i]<=p[i+1]:
			c=c+1
	if(c==n-1):
		print ans
	else:
		print -1						