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 shift {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc=new Scanner(System.in);
		int N = sc.nextInt();
		int[] a = new int[N];
int i;
int compteur=0;
		for(i=0;i<N;i++) a[i] = sc.nextInt();
		int indice=0;
		for(i=1;i<N;i++)
		{
			if (a[i-1]>a[i]) 
			{
				indice ++;
				compteur =i;
			}
		}
if(indice>1) System.out.println("-1");
else if(indice==0) System.out.println("0");
else if (a[N-1]>a[0]) System.out.println("-1");
else System.out.println(N-compteur);

	}
}
