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 codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n= Integer.parseInt(br.readLine());
		String numS[] = br.readLine().split(" ");
		int nums[]= new int[n];
		for(int i=0;i<n;i++){
		    nums[i]=Integer.parseInt(numS[i]);
		}
		int res[] = Arrays.stream(nums).sorted().distinct().toArray();
		if(res.length == 1){
		    System.out.println(0);;
		}
		else if(res.length==2){
		    if( (res[1]-res[0])%2==0){
		        System.out.println((res[1]-res[0])/2);
		    }
		    
		    else{
		        System.out.println(res[1]-res[0]);
		    }
		}
		else if(res.length==3 && (res[1]-res[0])==res[2]-res[1]){
		    System.out.println(res[1]-res[0]);
		}
		else{
		    System.out.println(-1);
		}
	}
}
