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
import java.util.*;
public class equal{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n= sc.nextInt();
		int a[] = new int[n];
		int l=Integer.MAX_VALUE;
		int r = Integer.MIN_VALUE;
		for(int i=0;i<n;i++){
			a[i] = sc.nextInt();
			 l= Math.min(a[i],l);
			 r= Math.max(a[i],r);
		}
		int ans=0,min=Integer.MAX_VALUE,k1=0,k2=0,p=0;
		for(int i=l;i<=r;i++){
			for(int j=0;j<n;j++){
				if(i!=a[j]){
                   if(p==0){
                   	k1 = Math.abs(a[j]-i);
                   	p=1;
                   }
                   else{
                   	k2 = Math.abs(a[j]-i);
                   	if(k1!=k2){
                   		p=-1;
                   		break;
                   	}
                   }
				}
			}
	          if(p!=-1){
	          	min = Math.min(k1,min);
                   
	          }
			p=0;
		}
		if(min!=Integer.MAX_VALUE)
		System.out.println(min);
	    else
	    	System.out.println("-1");

	}
}