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
//package cc;

import java.util.Scanner;
import java.util.Set;
import java.util.*;

public class abc5 
{
	public static void main(String args[])
	{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		//int a[]=new int[n];
		List<Integer> a=new ArrayList<Integer>(n);
		for(int i=0;i<n;i++)
		{
			a.add(sc.nextInt());
			
		}
		//int max=0;
		NavigableSet<Integer> s=new TreeSet<Integer>();
		s.addAll(a);
		int diff=0;
		int l=s.size();
		
		if(l>3)
			System.out.println("-1");
		else if(l==1)
			System.out.println("0");
		else if(l==2)
		{
			diff=s.last()-s.first();
			if(diff%2==0)
				System.out.println(diff/2);
			else
				System.out.println(diff);
		}
		else
		{
			double diff1=s.last()-s.first();
			s.pollFirst();
			double diff2=s.last()-s.first();
			if(diff1/2==diff2)
				System.out.println((int)diff2);
			else
				System.out.println("-1");
			
		}
		
		/*int i=0,j=l-1;
		double sum=(s.first()+s.last())/2.0;
		int ans=(s.last()-s.first())/2;
		double s1=0.0;
		int c=0;
		
		if(s.size()==2)
		{
			int diff=s.last()-s.first();
			if(diff%2==0)
				System.out.println(diff/2);
			else
				System.out.println(diff);
		}
		else
		{
		while(s.size()>1)
		{
			s1=(s.pollFirst()+s.pollLast())/2.0;
			if(s1!=sum)
				c++;
			
		}
		if(s.size()==1)
		{
			s1=s.pollFirst();
			if(s1!=sum)
				c++;
		}
		
		if(c>0)
			System.out.println("-1");
		else
			System.out.println(ans);
		}*/
	}
}
