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.io.*;

public class Main{

   
    static void solve(Scanner in, PrintWriter out){
        int n = in.nextInt();
        int[] a = new int[n];
        HashSet<Integer> set = new HashSet<>();
        int mx = Integer.MIN_VALUE;
        int mn = Integer.MAX_VALUE;
        for(int i = 0; i < n; i++){
            a[i] = in.nextInt();
            set.add(a[i]);
            mx = Math.max(mx, a[i]);
            mn = Math.min(mn, a[i]);
        }
        if(set.size() > 3){
            out.println(-1);
            return;
        }
        if(set.size() == 1){
            out.println(0);
            return;
        }
        if(set.size() == 2){
            out.println( (mx - mn)%2 == 0 ? (mx - mn)/2 : mx - mn);
            return;
        }
        // set.size() == 3
        if ((mx - mn) % 2 == 1) {
            out.println(-1);
            return;
        }
        int d = (mx - mn) / 2;
        for(int i = 0; i < n; i++) if(!(mx == a[i] || mn == a[i] || a[i] + d == mx)){
            out.println(-1);
            return;
        }
        out.println(d);
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(new BufferedInputStream(System.in));
        PrintWriter out = new PrintWriter(System.out);
        solve(in, out);
        out.close();
    }
}
