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
from _collections import *
n=input()
l=deque(map(int,raw_input().split()))
test=False
i=0
m=list(l)
m.sort()
if list(l)==m:test=True
while not test and i<n:
    if(l[n-1]<=l[0]) and len(l)!=1:
        a=l.pop()
        l.appendleft(a)
        i+=1
    else:test=True
if list(l)==m:print i
else:print -1