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.Scanner;
// public class Main {  
//     static int n, s, a, b;  
//     static int f[][];  
//     static int modnum = 100000007; 
    
//     public static void main(String[] args) {
//         Scanner sc=new Scanner(System.in);
//         n=sc.nextInt();
//         s=sc.nextInt();
//         a=sc.nextInt();
//         b=sc.nextInt();
//         f=new int[n][n];
//         f[0][0]=1;
//         System.out.println(c());
//     }

//     private static int c() {
//         if(n==1)
//             return 1;
//         for(int j=1;j<n;j++)
//             for(int i=0;i<n;i++)
//                 f[i][j]=(f[g(i-j*a)][j-1]+f[g(i+j*b)][j-1])% modnum; 
//         return f[g(s)][n-1];
//     }
    
//     private static int g(int v)  
//     {
//         return ((v%n)+n)%n;
//     }
// }package Round552;

import java.util.Arrays;
import java.util.Scanner;

public class B {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        int[] b = new int[3];
        int count = 0;
        for (int i = 0 ; i < n ; i ++) {
            a[i] = sc.nextInt();
        }
        Arrays.sort(a);
        b[0] = a[0];
        for (int i = 1 ; i < n ; i ++) {
            if (b[count]!=a[i]) {
                count++;
                if (count>=3) break;
                b[count] = a[i];
            }
        }
        if (count==0) System.out.println(0);
        else if (count==1) {
            int x = b[1]-b[0];
            if (x%2==0) System.out.println(x/2);
            else System.out.println(x);
        }
        else if (count==2) {
            if ((b[0]+b[2])/2==b[1]&&(b[0]+b[2])%2==0) System.out.println(b[2]-b[1]);
            else System.out.println(-1);
        }
        else System.out.println(-1);
    }
}


