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
n=int(input())
a=[int(x) for x in input().split()]
prev=0
li=0
if(a==sorted(a)):
    print(0)
    exit()
for i in range(n):
    if(a[i]<prev):
        li=i
        break
    prev=a[i]
if(sorted(a)==(a[li:]+a[:li])):
    print(n-li)
else:
    print(-1)
        

    
        
             
             
    
        
                
        
        

    
    

    
    
    

        
        

        

                
                

    
    
    
        

        
        


    

    
        
    
