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.io.BufferedReader;


import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.StringTokenizer;


public class B implements Runnable
{

	static BufferedReader br = null;
	static PrintWriter pw = null;
	static StringTokenizer stk = new StringTokenizer("");

	public static void main(String[] args)
	{
		try
		{
			//br = new BufferedReader(new FileReader("input.txt"));
			//pw = new PrintWriter("output.txt");
			br = new BufferedReader(new InputStreamReader(System.in));
			pw = new PrintWriter(new OutputStreamWriter(System.out));
			
		} catch (Exception e)
		{
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
		(new Thread(new B())).start();
	}

	public void nline()
	{
		try
		{
			stk = new StringTokenizer(br.readLine());
		} catch (IOException e)
		{
			e.printStackTrace();
		}
	}

	public int ni()
	{
		while (!stk.hasMoreTokens())
			nline();
		return Integer.valueOf(stk.nextToken());
	}

	public double nd()
	{
		while (!stk.hasMoreTokens())
			nline();
		return Double.valueOf(stk.nextToken());
	}

	public String nwrd()
	{
		while (!stk.hasMoreTokens())
			nline();
		return stk.nextToken();
	}

	public long nl()
	{
		while (!stk.hasMoreTokens())
			nline();
		return Long.valueOf(stk.nextToken());
	}

	public BigInteger nbi()
	{
		while (!stk.hasMoreTokens())
			nline();
		return new BigInteger(stk.nextToken());
	}

	public char nc()
	{
		while (!stk.hasMoreTokens())
			nline();
		return stk.nextToken().charAt(0);
	}

	public boolean isready()
	{
		try
		{
			return br.ready();
		} catch (IOException e)
		{
			return false;
		}
	}

	String rline()
	{
		try
		{
			return br.readLine();
		} catch (IOException e)
		{
			e.printStackTrace();
		}
		return null;
	}

	public void run()
	{
		solve();
		pw.close();
	}
	public class Hero {
		public long max_health;
		public long regen;
		public Hero(long h, long regen) {
			// TODO Auto-generated constructor stub
			max_health = h;
			this.regen = regen;
		}
	}
	public class Pair implements Comparable<Pair>{
		public long a;
		public long b;
		public Pair( long a, long b) {
			// TODO Auto-generated constructor stub
			this.a = a;
			this.b = b;
		}
		@Override
		public int compareTo(Pair o) {
			// TODO Auto-generated method stub
			if (a != o.a)
				return (int) (a - o.a);
			if (b != o.b)
				return (int) (b - o.b);
			return 0;
		}
		public  String toString() {
			return a + " " + b;
		}
		
	}
	
	
	

	public void solve()
	{
		
		int n = ni();
		HashSet<Integer> hs = new HashSet<Integer>();
		
		for(int i =0; i< n; i++)
			hs.add(ni());
		
		if(hs.size() > 3) {pw.println(-1); return;}
		
		
		Integer[] mas = hs.toArray(new Integer[0]);
		
		Arrays.sort(mas);
		if(mas.length == 2) {
			if ((mas[1] - mas[0]) % 2 ==0 )
				pw.print((mas[1] - mas[0]) / 2);
			else
				pw.print(mas[1] - mas[0]); 
			return;
			
		}
		if(mas.length == 1) {pw.print(0); return;}

		
		if(mas[2] - mas[1] != mas[1] - mas[0])
			pw.print(-1);
		else
			pw.print(mas[2] - mas[1]);
		
		
		
		
		
	}

}