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.ArrayList;
import java.util.Comparator;
import java.util.Scanner;

public class Main {
	public static void main(String args[]){
		int n,k,x,y,z,a[] = new int[105];
		x = y = z = 0;
		Scanner scanner = new Scanner(System.in);
		n = scanner.nextInt();
		int c = 0;
		for(int i = 0;i < n;++i){
			k = scanner.nextInt();
			if(a[k] == 0) ++c;
			if(x == 0 && a[k] == 0) x = k;
			else if(y == 0 && a[k] == 0) y = k;
			else if(z == 0 && a[k] == 0) z = k;
			++a[k];
		}
		if(c > 3) {
			System.out.println(-1);
		}else{
			if(y == 0){
				System.out.println(0);
				return;
			}
			if(z == 0){
				if(x > y){
					int t = x;
					x = y;
					y = t;
				}
				if((y - x) % 2 == 0){
					System.out.println((y-x)/2);
				}else{
					System.out.println((y-x));
				}
				return;
			}
			if(x > y){
				int t = x;
				x = y;
				y = t;
			}
			if(y > z){
				int t = y;
				y = z;
				z = t;
			}
			if(x > y){
				int t = x;
				x = y;
				y = t;
			}
			if(z - y == y - x){
				System.out.println(z-y);
			}else{
				System.out.println(-1);
			}
		}
	}
}
