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 math
import re
import sys

def read(type = int):
  return type(raw_input())
  
def read_list(type = int, split = ' ', F = None):
  if F:
    return map(lambda x: F(type(x)), raw_input().split(split))
  return map(type, raw_input().split(split))

def read_list_of_list(N, type = int, split = ' ', F = None):
  return [read_list(type, F = F) for _ in xrange(N)]
  
N = read()
A = sorted(list(set(read_list())))
if len(A)==1:
  print 0
  exit()
if len(A) == 2:
  if (A[1]-A[0])%2==0:
    print (A[1]-A[0])/2
  else:
    print A[1]-A[0]
  exit()
if len(A)>3 or A[2]-A[1] != A[1]-A[0]:
  print -1
  exit()
print A[2]-A[1]
