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.util.Scanner;


public class Main
{
	public static void main(String[] args)
	{
		new Main().start();
	}
	
	public void start()
	{
		Scanner input=new Scanner(System.in);
		int n=input.nextInt();
		int [] arr=new int[n];
		for(int i=0;i<n;i++)
		{
			arr[i]=input.nextInt();
		}
		boolean isstarted=false;
		int ans=0;
		for(int i=0;i<n-1;i++)
		{
			if(arr[i+1]<arr[i])
			{
				if(arr[n-1]>arr[0] && !isstarted)
				{
					System.out.println("-1");
					System.exit(0);
				}	
				if(isstarted)
				{
					System.out.println("-1");
					System.exit(0);
				}
				else
				{
					isstarted=true;
				}
			}
			if(isstarted)
				ans++;
		}
		System.out.println(ans);
	}
}
