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: Patel Rag
import java.util.*;
import java.io.*;
//import javafx.util.*;

public class Main
{

  static class FastReader
  {
    BufferedReader br;
    StringTokenizer st;

    public FastReader(){ br = new BufferedReader(new InputStreamReader(System.in)); }

    String next()
    {
      while (st == null || !st.hasMoreElements())
      {
        try
        {
          st = new StringTokenizer(br.readLine());
        }
        catch (IOException  e)
        {
          e.printStackTrace();
        }
      }
      return st.nextToken();
    }

    int nextInt() { return Integer.parseInt(next()); }

    long nextLong(){ return Long.parseLong(next()); }

    double nextDouble(){ return Double.parseDouble(next()); }

    float nextFloat() { return Float.parseFloat(next());}

    String nextLine()
    {
      String str = "";
      try
      {
        str = br.readLine();
      }
      catch (IOException e)
      {
        e.printStackTrace();
      }
      return str;
    }
  }

  public static void main(String[] args)
  throws IOException
  {
    FastReader fr = new FastReader();
    int n = fr.nextInt();
    HashSet< Integer > set = new HashSet< Integer >();
    for(int  i = 0; i < n; i++) set.add(fr.nextInt());
    if(set.size() > 3)
    {
      System.out.println(-1);
    }
    else
    {
      Integer[] dat = set.toArray(new Integer[set.size()]);
      Arrays.sort(dat);
      if(dat.length == 3)
      {
        if(dat[0]+dat[2] == 2*dat[1]) System.out.println(dat[1]-dat[0]);
        else System.out.println(-1);
      }
      else if(dat.length == 2)
      {
        if((dat[1]-dat[0])%2 == 0) System.out.println((dat[1]-dat[0])/2);
        else System.out.println(dat[1]-dat[0]);
      }
      else
      {
        System.out.println(0);
      }
    }

  }
}
