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.Scanner;

public class main {

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int num = scanner.nextInt();
		int array[] = new int[num];
		for(int i=0;i<num;i++) array[i]=scanner.nextInt();
		for(int i=0;i<num-1;i++)
			for(int j=0;j<num-i-1;j++) 
				if(array[j]>array[j+1])
				{
					int temp = array[j];
					array[j] = array[j+1];
					array[j+1] = temp;
				}
		int diff=array[num-1]-array[0];
		if(diff%2==0) diff=diff/2;
		int value=array[0]+diff;
		int flag=1;
		for(int i=0;i<num;i++)
		{
			if((array[i]+diff)==value||(array[i]-diff)==value||array[i]==value) flag = 1;
			else {flag=0;break;}
		}
		if(flag==0) System.out.println(-1);
		else System.out.println(diff);
	}

}
