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.*;
public class equal{
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		String[] s = br.readLine().trim().split(" ");
		int[] nums = new int[n];
		for(int i=0;i<n;i++) nums[i] = Integer.parseInt(s[i]);
		Set<Integer> set = new TreeSet<>();
		for(int i=0;i<n;i++){
			set.add(nums[i]);
		}
		//System.out.print(set.size());
		int d =0;
		if(set.size()==2){
			int a=0,b=0,i=0,ans= 101;
			for(int key : set) {
				if(i==0) a= key;
				else b =key;
				i++;
			}
			if((b-a) == 2 *((b-a)/2)) ans = (b-a)/2;

			d = Math.min(Math.abs(a-b),ans);
		}
		else if(set.size()>3) d = -1;
		else if(set.size()==3){
			int a = 0,b=0,c=0,i=0;
			for(int key:set){
				if(i==0) a= key;
				else if(i==1) b= key;
				else c = key;
				i++;
			}
			i =0;
			
			if((c+a) == 2 *((c+a)/2)) i =(c+a)/2;
			//System.out.println(i);
			if(i==b) d = (c-a)/2;
			else d = -1;


		}
		System.out.println(d);


		
	}
}
