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.*;
import java.lang.reflect.Array;
import java.util.Arrays;
import java.util.Scanner;

public class cy199 {
	public static void main(String[] args)
	{
		
		Scanner cin = new Scanner(System.in);
		int n;n=cin.nextInt();
		int vis[]= new int[110];
		for(int i=0;i<110;i++) vis[i]=0;
		for(int i=1;i<=n;i++) {
			int tmp;tmp=cin.nextInt();
			vis[tmp]=1;
		}
		int tot=0;
		for(int i=0;i<110;i++) {
			if(vis[i]!=0) tot++;
		}
		if(tot>3) {
			System.out.println("-1");
		}else if(tot==1) {
			System.out.println("0");
		}else if(tot==2) {
			int xx=-1;
			for(int i=0;i<110;i++) {
				if(vis[i]!=0) {
					if(xx==-1) xx=i;
					else {
						if((i-xx)%2==0)
						System.out.println((i-xx)/2);
						else 
						System.out.println(i-xx);
						break;
					}
				}
				
			}
		}else if(tot==3) {
			int x=-1,xx=-1;
			for(int i=0;i<110;i++) {
				if(vis[i]!=0) {
					if(x==-1) {
						x=i;
						continue;
					}
					if(xx==-1) {
						xx=i;
						continue;
					}
					if(i-xx!=xx-x) {
						System.out.println("-1");
					}else {
						System.out.println(i-xx);
					}
					break;
				}
				
			}
		}
	}
}
