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 Cf1154B {
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int n,i,j,s=0,temp,p;
		n=sc.nextInt();
		int []arr=new int[3];
		for(i=0;i<n;i++) {
			p=sc.nextInt();
			if(s==4)
				continue;
			else if(s==0) {
				arr[0]=p;
				s++;
			}
			else if(s==1) {
				if(p!=arr[0]) {
					arr[1]=p;
					s++;
				}
			}
			else if(s==2) {
				if(p!=arr[0] && p!=arr[1]) {
					arr[2]=p;
					s++;
				}
			}
			else {
				if(p!=arr[0] && p!=arr[1] && p!=arr[2])
					s=4;
			}
	
		}
		if(s==4)
			System.out.println("-1");
		else if(s==1)
			System.out.println("0");
		else if(s==2) {
			if((arr[1]-arr[0])%2!=0)
				System.out.println(Math.max(arr[0],arr[1])-Math.min(arr[0],arr[1]));
			else
				System.out.println((Math.max(arr[0],arr[1])-Math.min(arr[0],arr[1]))/2);
		}
		else {
			Arrays.sort(arr);
			if(arr[2]-arr[1]==arr[1]-arr[0])
				System.out.println(arr[2]-arr[1]);
			else
				System.out.println("-1");
		}
		sc.close();
	}

}
