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.HashSet;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int sum = 0;
        int min = 99999;
        int max = -99999;
        ArrayList<Integer> arrayList = new ArrayList<>();
        HashSet<Integer>has = new HashSet<>();
        for (int i = 0; i < n; i++) {
            int x = scanner.nextInt();
            arrayList.add(x);
            has.add(x);
            if (min > x) {
                min = x;
            }
            if (max < x) {
                max = x;
            }
        }
        for(Integer i3 : has){
            sum += i3;
        }
        n = has.size();
            int i = 0;int ss = -1;
            for(;i<arrayList.size();i++){
                if(i == 0){
                    ss = Math.abs(arrayList.get(i) - Math.floorDiv(sum,n));
                }else{
                    if(ss != Math.abs(arrayList.get(i) - Math.floorDiv(sum,n))){
                        break;
                    }
                }
                
            }
            if(i == arrayList.size()){
                arrayList.add(Math.floorDiv(sum,n));
            }else if(sum % n != 0){
                i = 0;ss = -1;
            for(;i<arrayList.size();i++){
                if(i == 0){
                    ss = Math.abs(arrayList.get(i) - Math.floorDiv(sum,n)-1);
                }else{
                    if(ss != Math.abs(arrayList.get(i) - Math.floorDiv(sum,n) -1)){
                        break;
                    }
                }
                
            }
            if(i == arrayList.size()){
                arrayList.add(Math.floorDiv(sum,n)+1);
            }
            }
        
        int equal;
        Collections.sort(arrayList);
        for (Integer i2 : arrayList) {
            equal = i2;
            int same = 0;
            int j = 0;
            for (; j < arrayList.size(); j++) {
                if (arrayList.get(j) > equal) {
                    if (same == 0) {
                        same = arrayList.get(j) - equal;
                    } else if (same != arrayList.get(j) - equal) {
                        break;
                    }
                } else if (arrayList.get(j) < equal) {
                    if (same == 0) {
                        same = equal - arrayList.get(j);
                    } else if (same != equal - arrayList.get(j)) {
                        break;
                    }
                }
            }
            if (j == arrayList.size()) {
                System.out.println(same);
                return;
            }
        }
        System.out.println(-1);
    }
}