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.io.*;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Iterator;
import java.util.StringTokenizer;

public class Main1154B
{
    public static void main(String[] args) throws IOException
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        HashSet<Integer> hashSet = new HashSet<>();
        int N =Integer.parseInt(br.readLine());
        StringTokenizer st = new StringTokenizer(br.readLine());
        while(st.hasMoreTokens())
        {
            hashSet.add(Integer.parseInt(st.nextToken()));
        }
        if(hashSet.size()==1)
        {
            bw.write("0");
        }
        else if(hashSet.size()==2)
        {
            Iterator<Integer> it = hashSet.iterator();
            int ans = Math.abs(it.next()-it.next());
            if(ans%2==0) ans/=2;
            bw.write(ans+"");
        }
        else if(hashSet.size()==3)
        {
            Iterator<Integer> it = hashSet.iterator();
            int[] arr = new int[3];
            for(int i=0;i<3;++i)
            {
                arr[i] = it.next();
            }
            Arrays.sort(arr);
            if(arr[0]+arr[2]!=2*arr[1])
            {
                bw.write("-1");
            }
            else
            {
                bw.write((arr[2]-arr[1])+"");
            }
        }
        else
            bw.write("-1");
        bw.close();
    }

}
