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
###########################################
#  Author : Uranux   
#  Created On : Tue Apr 16 2019
#  File : B.py
###########################################

def input_s():
    return raw_input()

def input_i():
    return int(raw_input())

def input_2_i():
    arr = map(int, raw_input().split())
    return arr[0], arr[1]

def input_3_i():
    arr = map(int, raw_input().split())
    return arr[0], arr[1], arr[2]

def input_i_array():
    return map(int, raw_input().split())

def get_presum(n, arr):
    presum = [arr[0]]
    for i in range(1, n):
        presum.append(presum[i - 1] + arr[i])
    return presum

def calc(n, arr):
    ma = max(arr)
    mi = min(arr)
    if ma == mi:
        return 0

    other_vals = set()
    first_other_val = 0
    for i in range(n):
        if arr[i] != ma and arr[i] != mi:
            other_vals.add(arr[i])
            first_other_val = arr[i]

    if len(other_vals) > 1:
        return -1

    if len(other_vals) == 0:
        if (ma - mi) % 2 == 0:
            return (ma - mi) / 2
        return ma - mi

    if ma - first_other_val == first_other_val - mi:
        return ma - first_other_val
    
    return -1

"""
6
1 4 4 7 4 1
"""

n = input_i()
arr = input_i_array()

print calc(n, arr)

