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) {
		// TODO Auto-generated method stub
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		int arr[] = new int[n];
		
		for(int i=0;i<n;i++){
			arr[i]=s.nextInt();
		}
		int li=n-1;
		int count =0;
		int previndex = -1;
		
		int fdec=-1;
		
		for(int i=0;i<arr.length-1;i++){
			if(arr[i]>arr[i+1]){
				fdec=i+1;
				count++;
			}
		}
		
		if(count==0){
			System.out.println(0);
		}
		else
		
		if(arr[li]<=arr[0] && count==1){
			System.out.println(arr.length-fdec);
			
		}
		
		else {
			System.out.println(-1);
		}
		
		
			
		
		
		
	}

}