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.Arrays;
import java.util.Comparator;
import java.util.Scanner;
public class Main {//开boolean used[]数组以元素本身值为下标时，注意负数的情况
		public static void main(String args[]) {
			Scanner sc=new Scanner(System.in);
			int n;
			int m;
			n=sc.nextInt();
			Integer a[]=new Integer[n];
			Integer number[]=new Integer[4];
			boolean exist[]=new boolean[220];
			int count=0;//2或者3
			for(int i=0;i<n;i++) {
				a[i]=sc.nextInt();
				
				if(!exist[a[i]]) {//如果这个数是新数
					exist[a[i]]=true;
					number[count++]=a[i];
					if(count>3) {
						System.out.println("-1");
						return;
					}
				}else {
					continue;
				}
			}
			int D;
			Comparator<Integer>cmp=new Comparator<Integer>() {
				@Override
				public int compare(Integer o1, Integer o2) {
					return o2-o1;
				}
			};
			//System.out.println(a[0]+" "+a[1]+" "+a[2]);
			Arrays.sort(number, 0,count, cmp);
			//System.out.println(a[0]+" "+a[1]+" "+a[2]);
			if(count==3) {
				if((number[0]-number[2])%2!=0) {//如果max和min差不是偶数
					//System.out.println("hh");
					System.out.println("-1");
					return;
				}else {
					D=(number[0]-number[2])/2;
					if(number[1]+D==number[0]) {
						System.out.println(D);
					}else {
						System.out.println("-1");
					}
				}
				
			}else if(count==2){
				if((number[0]-number[1])%2!=0) {
					System.out.println(number[0]-number[1]);
				}else {
					D=(number[0]-number[1])/2;
					System.out.println(D);
				}
			}else {//count=1
				System.out.println("0");
			}
			
		}
}
