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

import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
public class Main{
	public static void main(String[]args)throws IOException{
		BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
		int n=Integer.parseInt(bf.readLine());
		String s=bf.readLine();
		String[]sa=s.split(" ");
		int[]a=new int[n];
		for(int i=0;i<a.length;i++){
			a[i]=Integer.parseInt(sa[i]);
		}
		System.out.println(f(a));
	}
	
	public static int f(int[]a){
		int x=0;
		for(int i=0;i<a.length;i++){
			if(i>0 && a[i]<a[i-1]){
				x=a.length-i;
				for(int j=0;j<a.length-1;j++){
					if(a[(i+j+1)%a.length]<a[(i+j)%a.length])
						return -1;
				}
				return x;
			}
		}
		return 0;
	}
}