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=input()
li=map(int,raw_input().split())
flag=0
pos=n
if(li[0]>=li[n-1]):
    for i in xrange(1,n):
        if(li[i]-li[i-1]<0 and flag==0):
            pos=i
            flag=1
        elif(li[i]-li[i-1]<0 and flag==1):
            print "-1"
            flag=-1
            break
    if(flag!=-1):
        print n-pos
else:
    for i in xrange(1,n):
        if(li[i]-li[i-1]<0):
            print "-1"
            flag=-1
            break
    if(flag==0):
        print "0"

        
    
    