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
num = [0]*200020
n = int(raw_input());
i = 1
for x in raw_input().split():
	num[i] = int(x)
	num[i+n] = num[i]
	i = i + 1
cnt = 1
pos = 1
flag = 0
for i in xrange(1,2*n+1):
	if num[i] <= num[i+1]:
		cnt = cnt + 1
	else:
		cnt = 1
		pos = i + 1
	if cnt == n:
		flag = 1
		break;
if flag:
	if pos == 1:
		print '0'
	else:
		print '%d' % int(n-pos+1)
else:
	print '-1'

  	   	 	  			  	 	  	  			 		