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
x = int(raw_input())
p = raw_input().split(" ")
num_highs = 0
place_high = 0
for i in range(0, x):
 p[i] = int(p[i])
 
for i in range(0, x):
 if p[i-1] > p[i]:
  num_highs += 1
  place_high = i
  if num_highs > 1:
   break

if num_highs > 1:
 print(-1)
else:
 o = x - place_high
 if place_high == 0:
  print(0)
 else:
  print(x - place_high)

		 					  		  	 			  	   		