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.Arrays;
public class eeeee{
public static void main(String[] args){
Scanner in=new Scanner(System.in);
int x=in.nextInt();
int[] y=new int[x];
for(int i=0;i<x;i++)
{y[i]=in.nextInt();}
int[] z=y;
Arrays.sort(z);
int u=-1;
for(int i=0;i<=z[z.length-1];i++)
{int[] a=new int[3];
a[0]=y[0];
a[1]=y[0]+i;
a[2]=y[0]-i;
int t1=1,t2=1,t3=1;
for(int j=1;j<x;j++)
{if(a[0]==y[j]||a[0]==(y[j]+i)||a[0]==(y[j]-i)){t1++;}
if(a[1]==y[j]||a[1]==(y[j]+i)||a[1]==(y[j]-i)){t2++;}
if(a[2]==y[j]||a[2]==(y[j]+i)||a[2]==(y[j]-i)){t3++;}}
if(t1==x||t2==x||t3==x){u=i; break;}}
System.out.print(u);
}}