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.*;
public class make_them_equal
{
	public static void main(String[] args) 
	{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int a[]=new int[n];
		HashSet<Integer> h=new 	HashSet<Integer>();
		for(int i=0;i<n;i++)
		{
			a[i]=sc.nextInt();
		}
		int flag=0;
		Arrays.sort(a);
		for(int i=0;i<n;i++)
		{
			h.add(a[i]);
		}
		int min=a[0];
		int max=a[n-1];
		int req=(max-min)/2;
		if(h.size()>2)
		{
			for(int i=0;i<n;i++)
			{
				if(a[i]==min)
				{
					a[i]+=req;
				}
				else if(a[i]==max)
				{
					a[i]-=req;
				}
			}
			for(int i=0;i<n-1;i++)
			{
				if(a[i]!=a[i+1])
				{
					flag=1;
					break;
				}
			}
			if(flag==1)
			{
				System.out.println("-1");
			}
			else
			{
				System.out.println(req);
			}
		}

		if(h.size()==2)
		{
			if(max%2!=min%2)
			{
				req=max-min;
			}
			System.out.println(req);
		}
		
		if(h.size()==1)
		{
			System.out.println("0");
		}
			

	}
}
