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
# -*- coding: utf-8 -*-
"""
Created on Sun Aug 30 23:30:44 2020

@author: DELL
"""
n=int(input())
a=list(map(int,input().split()))
l=sorted(a)
c=0
for i in range(n-1):
    if a[i]>a[i+1]:
        if a[i+1:n]+a[0:i+1]==l:
            c=(len(a[i+1:n]))
        break
if a==l:
    print(c)
elif c!=0:
    print(c)
elif c==0:
    print(-1)
