You are given a sequence a_1, a_2, ..., a_n consisting of n integers.

You can choose any non-negative integer D (i.e. D ≥ 0), and for each a_i you can:

  * add D (only once), i. e. perform a_i := a_i + D, or 
  * subtract D (only once), i. e. perform a_i := a_i - D, or 
  * leave the value of a_i unchanged. 



It is possible that after an operation the value a_i becomes negative.

Your goal is to choose such minimum non-negative integer D and perform changes in such a way, that all a_i are equal (i.e. a_1=a_2=...=a_n).

Print the required D or, if it is impossible to choose such value D, print -1.

For example, for array [2, 8] the value D=3 is minimum possible because you can obtain the array [5, 5] if you will add D to 2 and subtract D from 8. And for array [1, 4, 7, 7] the value D=3 is also minimum possible. You can add it to 1 and subtract it from 7 and obtain the array [4, 4, 4, 4].

Input

The first line of the input contains one integer n (1 ≤ n ≤ 100) — the number of elements in a.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 100) — the sequence a.

Output

Print one integer — the minimum non-negative integer value D such that if you add this value to some a_i, subtract this value from some a_i and leave some a_i without changes, all obtained values become equal.

If it is impossible to choose such value D, print -1.

Examples

Input


6
1 4 4 7 4 1


Output


3


Input


5
2 2 5 2 5


Output


3


Input


4
1 3 3 7


Output


-1


Input


2
2 8


Output


3
//package CodeForces;

import java.util.Arrays;
import java.util.HashMap;
import java.util.Scanner;

public class MakeThemEqual {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();
		HashMap<Integer,Boolean> map=new HashMap<>();
		for(int i=0;i<n;i++)
		{
			int temp=s.nextInt();
			map.put(temp,true);
		}
		
		if(map.size()<3)
		{
			if(map.size()==1)
			{
				System.out.println(0);
			}
			else
			{
				int arr[]=new int[2];
				int k=0;
				for(int x:map.keySet())
				{
					arr[k++]=x;
				}
				Arrays.sort(arr);
				if((arr[0]+arr[1])%2==0)
				{
					System.out.println(arr[1]-(arr[0]+arr[1])/2);
				}
				else
				{
					System.out.println(arr[1]-arr[0]);
				}
			}
		}
		else if(map.size()==3)
		{
			int arr[]=new int[3];
			int k=0;
			for(int x:map.keySet())
			{
				arr[k++]=x;
			}
			Arrays.sort(arr);
			if(arr[1]-arr[0]==arr[2]-arr[1])
			{
				System.out.println(arr[1]-arr[0]);
			}
			else
			{
				System.out.println(-1);
			}
		}
		else
		{
			System.out.println(-1);
		}

	}

}
