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 sys


def check_mid(arr, D):
    if len(arr)%2 != 0:
        mid = len(arr)//2
    else:
        mid = len(arr)//2 + 1


    if arr[-1]+D == arr[mid]:
        return True
    else:
        return False

     
def main():
    sys.stdin.readline()
    numbers = list(map(int, sys.stdin.readline().split()))
    numbers = set(numbers)
    if len(numbers) == 1:
        sys.stdout.write('0')
        return
    numbers = list(numbers)

    numbers.sort()
    

    x = numbers.pop()
    D = x - max(numbers)
    numbers.append(x)
    numbers.sort(reverse = True)
    x = numbers.pop()
    D_2 = min(numbers) - x
    numbers.append(x)

     
    if abs(D) == abs(D_2):
        if len(numbers) >= 3:
            flag = check_mid(numbers, abs(D))
            if flag:
                if abs(D)%2 == 0 and abs(D)!=2:
                    if numbers[0] - abs(D) == numbers[-1] + abs(D):
                        sys.stdout.write(f'{abs(D)}')
                    else:
                        sys.stdout.write(f'{abs(D)//2}')
                else:
                    sys.stdout.write(f'{abs(D)}')
            else:
                sys.stdout.write(f'{-1}')
        else:
            if abs(D)%2 == 0:
                sys.stdout.write(f'{abs(D)//2}')
            else:
                sys.stdout.write(f'{abs(D)}')
    else:   
        sys.stdout.write(f'{-1}')
     
     
if __name__ == '__main__':
    main()