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 collections
import itertools
import sys
from collections import defaultdict, Counter
from math import sqrt, ceil

input = sys.stdin.readline


############ ---- Input Functions ---- ############
def inp():
    return (int(input()))


def inlt():
    return (list(map(int, input().split())))


def insr():
    s = input()
    return (list(s[:len(s) - 1]))


def invr():
    return (map(int, input().split()))


def ds(d):
    for i in range(2, d+1):
        if d%i==0:
            return i

def main():
    n = inp()
    v = inlt()
    d = sorted(set(v))
    if len(d) == 1:
        print(0)
    elif len(d) == 2:
        diff = d[1] - d[0]
        print(diff if diff%2 !=0 else diff//2)
    elif len(d) == 3:
        diff = d[2] - d[0]
        if diff%2 == 0 and d[0]+diff//2 == d[1]:
            print(diff//2)
        else:
            print(-1)
    else:
        print(-1)







if __name__ == "__main__":
    # sys.setrecursionlimit(10 ** 6)
    # threading.stack_size(10 ** 8)
    # t = threading.Thread(target=main)
    # t.start()
    # t.join()
    main()
