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(input())
r=input()
li=[]
flag=0
for x in r.split():
	li.append(int(x))
if li==sorted(li):
	print("0")
	flag=1
l=0	
for i in range(N-1):
	if li[i]>li[i+1]:
		n=i
		l+=1
		if l==2:
			print("-1")
			flag=1
			break
if flag==0:
		if li[0]>=li[N-1]:
			print(N-n-1)
		else:
			print("-1")			



