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
num1 = 0
num2 = 0
 
 
n = int(input())
listMe = list(map(int, input().split()))
 
for i in range(n):
    if listMe[i] < num1:
        num2 = i
        break
    num1 = listMe[i]
newAs = listMe[num2:] + listMe[:num2]
if newAs == sorted(listMe):
    print((n - num2) % n)
else:
    print(-1)
          		   	 		      	 	  	