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.*;
// this is terrible

public class Main {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		boolean[] flag = new boolean[101];
		int count = 0;
		int a = -1;
		int b = -1;
		int c = -1;
		int[] nums = new int[3];
		Arrays.fill(nums,-1);
		for( int i = 0; i < n; i++ ) {
			int k = in.nextInt();
			if( !flag[k] ) {
				flag[k] = true;
				count++;
				if( nums[0] == -1) nums[0] = k;
				else if( nums[1] == -1 ) nums[1] = k;
				else if( nums[2] == -1 ) nums[2] = k;
			}
		}
		if( count == 1 ) {
			System.out.println(0);
		} else if ( count == 2 ) {
			if( nums[0] > nums[1] ) {
				if( (nums[0] - nums[1]) % 2 == 0 ) {
					System.out.println((nums[0] - nums[1])/2);
				} else {
					System.out.println( nums[0]-nums[1] );
				}
			} else if ( nums[0] < nums[1] ) {
				if( (nums[1] - nums[0]) % 2 == 0 ) {
					System.out.println((nums[1] - nums[0])/2);
				} else {
					System.out.println( nums[1]-nums[0] );
				}
			}
		} else if ( count == 3 ) {
			Arrays.sort(nums);
			if( nums[2]-nums[1] == nums[1]-nums[0] ) {
				System.out.println( nums[2]-nums[1] );
			} else {
				System.out.println(-1);				
			}
		} else {
			System.out.println(-1);
		}
	}
}