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
def main():
    n=int(input())
    numbers=map(int,raw_input().split(" "))
    #print numbers
    i_stop=1
    stop_flag=0
    for i in range(1,n):
        i_stop=i
        if numbers[i]<numbers[i-1]:
            stop_flag=1
            break
        
    if stop_flag==0 and i_stop==n-1:
        i_stop+=1
    left=numbers[:i_stop]
    right=numbers[i_stop:]
    #print left,right
    #print valid(left),valid(right)
    if len(left)==0 or len(right)==0:
        print 0
        #return
    else:
        if valid(left) and valid(right):
            if right[-1]<=left[0]:
                print len(right)
            else:
                print -1

        else:
            print -1

def valid(seq):
    if len(seq)==1:
        return True
    for i in range(1,len(seq)):
        if seq[i]<seq[i-1]:
            return False
    return True



main()