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.div2;

import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class MakeThemEqual {

    static public void print(int arr[]) {

        HashMap<Integer, Integer> map = new HashMap<>();


        for(int i = 0; i < arr.length; i++) {
            map.put(arr[i], map.getOrDefault(arr[i], 0) + 1);
        }
        if(map.size() == 1) {
            System.out.println(0);
        } else {
            int val = Integer.MAX_VALUE;
            for (int i = 1; i <= 100; i++) {
                map = new HashMap<>();
                for (int j = 0; j < arr.length; j++) {
                    int x = arr[j] + i;
                    int y = arr[j] - i;
                    int z = arr[j];
                    map.put(x, map.getOrDefault(x, 0) + 1);
                    map.put(y, map.getOrDefault(y, 0) + 1);
                    map.put(z, map.getOrDefault(z, 0) + 1);
                }
                boolean flag = false;
                for (Map.Entry<Integer, Integer> entry : map.entrySet()) {
                    if (entry.getValue() == arr.length) {
                        val = Math.min(val, i);
                        flag = true;
                        break;
                    }
                }
                if (flag) {
                    break;
                }
            }


            if (val == Integer.MAX_VALUE) {
                System.out.println("-1");
            } else {
                System.out.println(val);
            }
        }
    }

    public static void main(String []args) {

        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int i = 0;
        int arr[] = new int[n];
        while ( i < n) {
            arr[i++] = sc.nextInt()
;        }
        print(arr);
    }
}
