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.*;
import java.math.*;

public class Main3
{ 	

	public static void main(String[] args)throws Exception
	{ 	

	    Reader reader = new Reader();

		reader.readLine();
		int n = reader.readInt(0);

		int freq[] = new int[101];
		reader.readLine();
		List<Integer> unique = new ArrayList<>();
		int uniqueCount = 0;
		boolean valid=true;
		for (int i=0;i < n;++i)
		{
			int v = reader.readInt(i);
			++freq[v];
			if (freq[v] == 1)
			{
				++uniqueCount;
				unique.add(v);
				if (uniqueCount > 3)
				{
					valid = false;
					break;
				}
			}
		}

		if (valid)
		{
			Collections.sort(unique);
			switch (uniqueCount)
			{
				case 1:
					System.out.println(0);
					break;
				case 2:
					int sum = unique.get(0) + unique.get(1);
					System.out.println((sum & 1) == 0 ?unique.get(1)-sum / 2 : unique.get(1) - unique.get(0));
					break;
				case 3:
					int left = unique.get(1) - unique.get(0);
					int right= unique.get(2) - unique.get(1);
					System.out.println(left == right ?left: -1);
					break;
			}
		}
		else
		{
			System.out.println(-1);
		}

		reader.close();
	}
}

class Reader
{     
    private BufferedReader reader; 
    private String line[];     

    public Reader()     
    {         
        reader = new BufferedReader(new InputStreamReader(System.in));     
    }     

    public String[] getLine()     
    {         
        return line;     
    }     

    public boolean readLine()     throws IOException 
    {         
        String str = reader.readLine();
        if (str == null || str.isEmpty())
            return false;
        line = line = str.split(" ");
        return true;
    }    

    public List<Integer> getIntegersList()
    {
        List<Integer> res = new ArrayList<>();
        for (String str:line)
            res.add(Integer.parseInt(str));
        return res;

    }

    public int readInt(int pos)throws IOException     
    {         
        return Integer.parseInt(line[pos]);     
    }     

    public double readDouble(int pos)throws IOException     
    {         
        return Double.parseDouble(line[pos]);     
    }     

    public long readLong(int pos)throws IOException 
    {         
        return Long.parseLong(line[pos]); 
    }     

    public String readString(int pos)throws IOException     
    {         
        return line[pos];     
    }     

    public void close()throws IOException 
    {         
        reader.close();     
    }
}



		