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
raw_input()
st = map(int,raw_input().split())
i=1
cnt=0
tc = 0
if len(st)>1:
    c = st[0]
    while(i<len(st)):
        if(c>st[i]):
            cnt+=1
        if cnt==1:
            if(st[i]>st[0]):
                cnt+=2
                break
            tc+=1
        if cnt>1:
            break
        c=st[i]
        i=i+1

if(cnt>1):
    print -1
else:
    print tc
    
