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;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.util.HashMap;
import java.util.HashSet;
import java.util.BitSet;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.math.BigInteger;
 
public class codeforces{
 
 public static void main(String[] args) throws NumberFormatException, IOException {
try{
BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
int t=Integer.parseInt(br.readLine());
String[] str=br.readLine().split(" ");
TreeSet<Integer> set=new TreeSet<Integer>();
for(int i=0;i<t;i++){
int k=Integer.parseInt(str[i]);
set.add(k);
}
if(set.size()==1){
  System.out.println(0);
  return;
}

if(set.size()>3){
  System.out.println(-1);
}
else{
  if(set.size()==2){
    int diff=set.last()-set.first();
 if(diff%2==0){
   System.out.println(diff/2);
 }
 else{
  System.out.println(diff);

 }
  }
  else{
    int first=set.first();
    set.remove(first);
    int second=set.first();
    int last=set.last();
    if(second-first==last-second){
      System.out.println(second-first);
    }
    else{
      System.out.println(-1);


    }

  }

}
}



catch(Exception e){
    System.out.println(e);
}
    
}
 
 
}