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.LinkedList;
import java.util.Scanner;
public class shift {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		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();
		}
		int temp = 0;
		int result = 0;
		int index = 0;
		for(int i=1 ; i<n ; i++){
			if(arr[i]<arr[i-1]){
				index=i;
				temp++;
			}
		}
		if(temp>1){
			result=-1;
		}
		else if(temp ==0){
			result=0;
		}
		else if(temp==1&&arr[n-1]<=arr[0]){
			result = n-index;
		}
		else{
			result = -1;
		}
		System.out.println(result);
	}

}
