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

from collections import *
def give(a):
    first,second=0,0
    for ind,i in enumerate(a):
        if not ind:
            first=i
        else:
            second=i
            return [first,second]
n=int(input())
a=[int(i) for i in input().split()]
a.sort()
temp=a
a=Counter(a)
# print(a)
if len(a) == 1:
    print(0)
    exit(0)
temp=list(set(temp))
temp.sort()
ab=temp[-1]-temp[0]
# print(temp,ab)
ar,ay=give(a)
if len(a)>3 or (len(a) == 3 and (ar+ab//2)!=ay):
    print(-1)
    exit(0)
if len(a) == 3:print(ab//2 if len(a)== 3 and ab//2 == ab/2 else -1)
else:print(ab//2 if len(a) == 2 and ab&1==0 else ab)




