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.HashMap;
import java.util.Scanner;

public class B {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] tab = new int[n];
		HashMap<Integer, Integer> hm = new HashMap<Integer, Integer>();
		for(int i=0;i<n;i++) {
			tab[i] = sc.nextInt();
			if(!hm.containsKey(tab[i]))
				hm.put(tab[i], i);
		}
		if(hm.size()>3) {
			System.out.println(-1);
		}else if(hm.size()==2) {
			int min = 0;
			int max = 0;
			for(Integer e:hm.keySet()) {
				min = e;
				max = e;
			}
			for(Integer e:hm.keySet()) {
				if(e>max)
					max = e;
				if(e<min)
					min = e;
			}
			if((max+min)%2==0) {
				System.out.println(max - (max+min)/2);
			}else
				System.out.println(max - min);
		}else if(hm.size()==3) {
			int[] t = new int[3];
			int j = 0;
			for(Integer e: hm.keySet()) {
				t[j] = e;j++;
			}
			j = 0;
			int max = t[j];
			int min = t[j];
			for(int i=1;i<3;i++) {
				if(t[i]<min) min = t[i];
				if(t[i]>max) max = t[i];
			}
			int mo = 0;
			for(int i=0;i<3;i++) {
				if(t[i]!= min && t[i]!= max) mo = t[i];
			}
			if((max+min)%2==0 && ((max+min)/2)==mo)
				System.out.println(max - mo);
			else
				System.out.println(-1);
		}else {
			System.out.println(0);
		}

	}

}