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 Temp4
{
	public static void main(String args[])
	{
		Scanner obj = new Scanner(System.in);
		int n = obj.nextInt();
		int ar[] = new int[n];
		
		for(int i=0 ; i<n ; i++)
			ar[i] = obj.nextInt();
		
		boolean flag = false;
		boolean isPossible = true;
		int index = -1;
		
		for(int i=0 ; i<n-1 ; i++)
		{
			if(flag==true && ar[i]>ar[i+1])
			{
				isPossible = false;
				break;				
			}
				
			if(flag == false && ar[i]>ar[i+1])
			{
				index = i;
				flag = true;
			}				
		}
		
		if(flag == false)
			index = n-1;
		
		if(flag==true && ar[n-1]>ar[0])
			isPossible = false;
		
		if(!isPossible)
			System.out.println("-1");
		else
			System.out.println(n-index-1);
	}
}