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

/*Alone against all
Ahlawy UA07
*/
import java.util.*;
import java.io.*;
import java.math.BigInteger;
import javafx.util.Pair;


public class codeforces {
static BigInteger add(BigInteger A, BigInteger B){return A.add(B);}
static BigInteger multiply(BigInteger A, BigInteger B){return A.multiply(B);}
static BigInteger div(BigInteger A, BigInteger B){return A.divide(B);}
static BigInteger sub(BigInteger A, BigInteger B){return A.subtract(B);}
/* help func */
static boolean prime(long a)
    {
        for(int i=2;i*i<=a;i++)
        {
            if(a%i==0)
                return false;
        }
        return true;
    }
public static int fact(int a)
{
    if(a==0)
        return 1;
    return a*fact(a-1);
}
                  /*main*/
 public static void main(String[] args) {
  Scanner read = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
  PrintWriter out=new PrintWriter(System.out);     
  ArrayList<Pair<Integer,String>> arrofPair=new ArrayList<>();
  Set<Integer> set=new TreeSet<>();
  Stack S=new Stack();
  Map<Character ,Integer>map=new HashMap<>();
  StringBuilder stringBuilder= new StringBuilder(); 
                 /*code*/
 int n=read.nextInt();
for(int i=0;i<n;i++)
{
    set.add(read.nextInt());
}
Integer arr[]=set.toArray(new Integer[set.size()]);
if(arr.length==1)
    out.println(0);
else if(arr.length==2)
{
    if((arr[1]-arr[0])%2==0)
   out.println((arr[1]-arr[0])/2);
    else out.println(arr[1]-arr[0]);
}
else if (arr.length==3)
{
    if(arr[2]-arr[1]==arr[1]-arr[0])
        out.println(arr[2]-arr[1]);
    else
        out.println(-1);
}
else 
    out.println(-1);

    
                 
out.flush();
 
 }

}
