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
/**
 * @author PengBorui
 */
import javax.net.ssl.SSLContext;
import java.math.BigDecimal;
import java.util.*;

public class Main
{
    public static void main(String[] args)
    {
        Scanner input = new Scanner(System.in);
        while (input.hasNext())
        {
            int n = input.nextInt();
            int[] data = new int[n];
            int[] busket = new int[200];
            Arrays.fill(busket,0);
            for(int i = 0;i < n;i++)
            {
                data[i] = input.nextInt();
                busket[data[i]]++;
            }
            int type = 0;
            for(int i = 0;i < 200-1;i++)
            {
                if(busket[i] != 0)
                    type++;
            }
            if(type == 1)
            {
                System.out.println("0");
                continue;
            }
            if(type >= 4)
            {
                System.out.println(-1);
                continue;
            }
            if(type == 2)
            {
                int a = data[0];
                int b = data[0];
                for(int i = 0;i < n;i++)
                {
                    if(data[i] != a)
                    {
                        b = data[i];
                        break;
                    }
                }
                int ans = Math.abs(a-b);
                int prv = ans;
                if(Math.max(a,b) - ans == Math.min(a,b) + ans)
                {
                    prv = ans;
                }
                ans /= 2;
                if(Math.max(a,b) - ans == Math.min(a,b) + ans)
                {
                    System.out.println(ans);
                    continue;
                }
                else
                {
                    System.out.println(prv);
                    continue;
                }

            }
            if (type == 3)
            {
                Arrays.sort(data);
                int a,b,c;
                a = data[0];
                b = 0;
                c = 0;
                for(int i = 0;i < n;i++)
                {
                    if(data[i] != a)
                    {
                        b = data[i];
                        break;
                    }
                }
                for(int i = 0;i < n;i++)
                {
                    if(data[i] != a && data[i] != b)
                    {
                          c = data[i];
                          break;
                    }
                }
                int ans = c - b;
                if(a + ans == c - ans)
                    System.out.println(ans);
                else
                    System.out.println("-1");
            }
        }
    }
}