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())
li=list(map(int,input().split(" ")))
sli=list(sorted(li))

i=0
start=li.index(li[0])
checker=False
while i<n:
    if li[i]==sli[0]:
        if checker==False:
            start=i
            checker=True
    else:
        checker=False
    i+=1


i=start
res=n-start
if res==n:
    res=0
for x in sli:

    if li[i%n]!=x:
        res=-1
        break
    i+=1
print(res)