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.*;
import java.io.*;
public class A
{
      public static void main(String ar[]) throws Exception
      {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            int n=Integer.parseInt(br.readLine());
            String s1[]=br.readLine().split(" ");
            int a[]=new int[n];
            TreeMap<Integer,Integer> tm=new TreeMap<Integer,Integer>();
            for(int i=0;i<n;i++)
            {
             a[i]=Integer.parseInt(s1[i]);
             if(tm.containsKey(a[i]))
              tm.put(a[i],1+tm.get(a[i]));
             else
              tm.put(a[i],1);
            }
            
            //System.out.println(tm.size());
            if(tm.size()>3)
             System.out.println("-1");
            else if(tm.size()==1)
             System.out.println("0");
            else if(tm.size()==2)
            {
                  int u=tm.firstKey();
                  int v=tm.lastKey();
                  if((v-u)%2==0)
                   System.out.println((v-u)/2);
                  else
                   System.out.println(v-u);
            }
            else
            {
                  int j=0;
                  int b[]=new int[3];
                  for(int i:tm.keySet())
                  { b[j]=i; j++;}
                  if(b[1]-b[0]==b[2]-b[1])
                   System.out.println(b[2]-b[1]);
                  else
                   System.out.println("-1");
            }
      }
}