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.*;
import java.math.BigDecimal;

public class Forces{

  static class FastReader{
    BufferedReader br;
    StringTokenizer st;
    FastReader(){
      br=new BufferedReader(new InputStreamReader(System.in));
    }
    String n(){
      while(st==null || !st.hasMoreElements()){
          try{
            st=new StringTokenizer(br.readLine());
          }
          catch(Exception e){
            e.printStackTrace();
          }
      }
      return st.nextToken();
    }

    String nline(){
      String str="";
      try{
        str=br.readLine();
      }
      catch(Exception e){
        e.printStackTrace();
      }
      return str;
    }
    int ni(){
      return Integer.parseInt(n());
    }
    long nl(){
      return Long.parseLong(n());
    }
    double nd(){
      return Double.parseDouble(n());
    }
  }

  public static void main (String args[]) throws IOException{
    FastReader in=new FastReader();
    BufferedOutputStream out=new BufferedOutputStream(System.out);
    StringBuilder sb = new StringBuilder();

    int j,i,n=in.ni();
    int []a=new int[n];
    int sum=0;
    for(i=0;i<n;i++){
      a[i]=in.ni();
    }
    Arrays.sort(a);
    int f=-1,d=-1,ans=(int)(1e9);
    for(i=a[0];i<=a[n-1];i++){
      Set<Integer>set=new TreeSet<Integer>();
      int flag=0;
      for(j=0;j<n;j++){
        if(a[j]!=i)
          set.add((d=Math.abs(a[j]-i)));
        if(set.size()>1){
          flag=-1;
          break;
        }
      }
      if(flag==0){
        f=0;
        if(d<ans)
          ans=d;
        if(set.size()==0){
          ans=0;
          break;
        }
      }
    }
    if(f==-1)
      ans=-1;
    sb.append(ans+"\n");
    out.write(sb.toString().getBytes());
    out.flush();
  }
}
