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 LittlePonyAndSortByShift {
	public static void main(String[] args)
	{
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();
		int[] a=new int[n];
		int count=0,start=0;
		for (int i=0;i<n;i++)
		{
			a[i]=s.nextInt();
			if(i>0 && a[i]<a[i-1])
			{
				count++;
				start=i-1;
			}
		}
		if(count==0)
			System.out.println(0);
		else if(count==1 && a[0]>=a[n-1])
			System.out.println(n-1-start);
		else System.out.println(-1);
	}
}