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

public class Sample
{
	public static void main (String[] args) throws java.lang.Exception
	{
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int min = Integer.MAX_VALUE, max = Integer.MIN_VALUE;
        int ar[] = new int[n];
        for(int i = 0; i < n; i++) {
            int num = sc.nextInt();
            ar[i] = num;
            if(num < min) {
                min = num;
            }
            if(num > max) {
                max = num;
            }
        }
        Arrays.sort(ar);
        //System.out.println(min + " " + max);
        boolean flag = true;
        int mi =  Integer.MAX_VALUE;
        for(int i = min; i <= max; i++) {
            if(isValid(ar, n, i)) {
                //System.out.println(i);
                int val1 = i - min;
                int val2 = max - i;
                if(val1 == 0 && val2 < mi) {
                    mi = val2;
                    //System.out.println(val2);
                } else if(val2 == 0 && val1 < mi) {
                    mi = val1;
                    //System.out.println(val1);
                } else if(val1 < mi) {
                    mi = val1;
                    //System.out.println(val1);
                }
                //flag = false;
                //break;
            }
        }
        if(mi == Integer.MAX_VALUE) {
            System.out.println(-1);
        } else {
            System.out.println(mi);
        }
	}
	public static boolean isValid(int ar[], int n, int dest) {
	    int val1 = (dest - ar[0]), val2;
	    for(int i = 1; i < n; i++) {
	        if(ar[i] < dest) {
	            val2 = dest - ar[i]; 
	        } else {
	            val2 = ar[i] - dest;
	        }
	        if(val1 != val2  && val1 != 0 && val2 != 0) {
	            return false;
	        }
	        if(val2 != 0 && val1 == 0) {
	            val1 = val2;
	        }
	    }
	    return true;
	}
}
