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())
lst=list(map(int,input().split()))
count=0
for i in range(n-1):
    if lst[i]>lst[i+1]:
       count+=1
       index =i
       break
if count != 0:
    lst2=lst[index+1:n]
    count=len(lst2)
    for i in range(index+1):
        lst2.append(lst[i])
    if lst2 != sorted(lst):
        count=-1
print(count)
    
    