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
def canBeOrdered(n, arr):
	s=0
	v=0
	for i in range(len(arr)-1):
		if(arr[i]>arr[i+1]):
			s=i
			v+=1
	if(arr[n-1]>arr[0]):
		s=n-1
		v+=1
	if(v==0):
		return 0
	elif(v>1):
		return -1
	else:
		return n-1-s


n=int(input())
arr=[int(i) for i in input().split()]

print(canBeOrdered(n, arr))
 	  				   		   	   	 				   		