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.Scanner;

public class Make_Them_Equal {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int[] arr = new int[n];
		int[] abc = new int[3];
		boolean flagA = false;
		boolean flagB = false;
		boolean flagC = false;
		for (int i = 0; i < n; i++) {
			arr[i] = scan.nextInt();
			if (arr[i] != abc[0] && !flagA) {
				abc[0] = arr[i];
				flagA = true;
			} else if (arr[i] != abc[1] && arr[i] != abc[0] && !flagB) {
				abc[1] = arr[i];
				flagB = true;
			} else if (arr[i] != abc[2] && arr[i] != abc[1] && arr[i] != abc[0] && !flagC) {
				abc[2] = arr[i];
				flagC = true;
			} else if(arr[i] != abc[0] && arr[i] != abc[1] && abc[2] != arr[i]) {
				System.out.print(-1);
				System.exit(0);
			}
		}
		Arrays.sort(abc);
		if (abc[0] != 0 && abc[1] != 0 && abc[2] != 0) {
			if (abc[2] - abc[1] != abc[1] - abc[0]) {
				System.out.println(-1);
			} else {
				if (abc[0] == 0 && abc[1] == 0) {
					System.out.print(0);
				} else if (abc[0] == 0) {
					if ((abc[2] - abc[1]) % 2 == 0) {
						System.out.print((abc[2] - abc[1]) / 2);
					} else {
						System.out.print((abc[2] - abc[1]));
					}

				} else {
					System.out.print((abc[2] - abc[0]) / 2);

				}
			}
		} else {
			if (abc[0] == 0 && abc[1] == 0) {
				System.out.print(0);
			} else if (abc[0] == 0) {
				if ((abc[2] - abc[1]) % 2 == 0) {
					System.out.print((abc[2] - abc[1]) / 2);
				} else {
					System.out.print((abc[2] - abc[1]));
				}
			} else {
				System.out.print((abc[2] - abc[0]) / 2);
			}
		}

		scan.close();
	}

}
