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
from sys import stdin

n=int(stdin.readline())
a=list(map(int,stdin.readline().rstrip().split()))
a=a+a
y=1
flag=0
for i in range(2*n-1):
    if a[i+1]>=a[i]:
    
        y+=1
    
        if y==n:
            flag=1
            break
    else:
        y=1
if flag==1:
    if i+2-n==0:
        print(0)
    else:
        
        print(n-(i+2-n))
else:
    print(-1)

        
            
            
        
        
        