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.lang.*;
import java.io.*;

public class Ideone
{
	static final int MAX = 100 + 10;
	static int[] arr = new int[MAX];
	static int min = 101;
	static int max = 0;
	static int n;
	static int m;
	
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner e = new Scanner(System.in);
		
		n = e.nextInt();
		for(int i = 1; i <= n; i++)
		{
			arr[i] = e.nextInt();
			min = Math.min(arr[i], min);
			max = Math.max(arr[i], max);
		}
		
		int mid = max - min;
		if(mid % 2 != 0)
		{
			for(int i = 1; i <= n; i++)
			{
				if(arr[i] != min && arr[i] != max)
				{
					System.out.println("-1");
					return;
				}
			}
			
			System.out.println(mid);
		}
		else
		{
			mid >>= 1;
			int aux = min + mid;
			for(int i = 1; i <= n; i++)
			{
				if(arr[i] != min && arr[i] != max && arr[i] != aux)
				{
					System.out.println("-1");
					return;
				}
			}
			System.out.println(mid);
		}
	}
}