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(raw_input())
s=raw_input()
l=[int(x) for x in s.split()]
a=[int(x) for x in s.split()]
a.sort()
if l==a:
    print '0'
else:
    for x in range(n-1):
        if l[x]>l[x+1]:
            l=l[x+1:]+l
            l[n:]=[]
            if l==a:
                print n-x-1
                break
            else:
                print '-1'
                break


                
            
        
    
    
