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 A552 {

	
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		int[] arr = new int[n];
		for(int i=0; i<n ;i++)
		{
			arr[i] = s.nextInt();
		}
		Arrays.sort(arr);
		int l = arr[0], g = arr[n-1];
		
		if((g-l)%2 == 0)
		{
			int d = (g-l)/2, make = l+d;
			boolean[] a = new boolean[n];
			int x = n;
			for(int i=0;i<n;i++)
			{
				if(arr[i] == make||arr[i]==l||arr[i]==g) {
					x--;
					a[i] = true;continue;
				}
			}
			if(x==0)
			{
				System.out.println(d);return;
			}
		}
		else
		{
			int d = g-l;
			int make = g-d;
			int x = n;
			boolean[] a = new boolean[n];
			for(int i=0;i<n;i++)
			{
				if(arr[i] == make||arr[i]==l||arr[i]==g) {
					x--;
					a[i] = true;continue;
				}
			}
			if(x==0)
			{
				System.out.println(d);return;
			}
		}
			System.out.println(-1);
		
	
	}

}
