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 cp;
import java.io.*;
import java.util.*;
public class Cf_three {
	public static void main(String[] args) throws IOException {	
		PrintWriter out = new PrintWriter(System.out);
		Readers.init(System.in);
		int n=Readers.nextInt();
		int[] a=new int[n];
		HashSet<Integer> set=new HashSet<>();
		for (int i = 0; i < a.length; i++) {
			a[i]=Readers.nextInt();
			set.add(a[i]);
		}
		ArrayList<Integer> ans=new ArrayList<>();
		if(set.size()>3)System.out.println(-1);
		else {
			for(Integer j:set) {
				ans.add(j);
			}
			Collections.sort(ans);
			if(set.size()==3) {
				if(ans.get(2)-ans.get(1)==ans.get(1)-ans.get(0)) {
					System.out.println(ans.get(2)-ans.get(1));
				}
				else System.out.println(-1);
			}
			else if(set.size()==2) {
				if((ans.get(0)+ans.get(1))%2==0) {
					System.out.println((ans.get(1)-ans.get(0))/2);
				}
				else System.out.println(ans.get(1)-ans.get(0));
			}
			else {
				System.out.println(0);
			}
		}
		out.flush();
	}

}
class Readers {

    static BufferedReader reader;

    static StringTokenizer tokenizer;



    /** call this method to initialize reader for InputStream */

    static void init(InputStream input) {

        reader = new BufferedReader(

                     new InputStreamReader(input) );

        tokenizer = new StringTokenizer("");

    }



    /** get next word */

    static String next() throws IOException {

        while ( ! tokenizer.hasMoreTokens() ) {

            //TODO add check for eof if necessary

            tokenizer = new StringTokenizer(

                   reader.readLine() );

        }

        return tokenizer.nextToken();

    }



    static int nextInt() throws IOException {

        return Integer.parseInt( next() );

    }

	

    static double nextDouble() throws IOException {

        return Double.parseDouble( next() );

    }
    
    
    static long nextLong() throws IOException{
    	
		return Long.parseLong(next());
	}

}