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 Counter, defaultdict

BS="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
def to_base(s, b):
    res = ""
    while s:
        res+=BS[s%b]
        s//= b
    return res[::-1] or "0"
alpha = "abcdefghijklmnopqrstuvwxyz"
from math import floor, ceil,pi

import re

pattern = r"0+"
"""
n = int(input())

print(3*n+4)
coordList= [["-"]*1000 for _ in range(1000)]

for row in range(2+n):
    if row==0:
        print(f"0 0")
        print("0 1")
        coordList[0][0] = "*"
        coordList[1][0] = "*"
    elif row==2+n-1:
        print(f"{2+n-1} {2+n-1}")
        print(f"{2+n-1} {2+n-2}")
        coordList[2+n-1][2+n-1] = "*"
        coordList[2+n-2][2+n-1] = "*"
    else:
        for j in range(-1,2):
            print(f"{row} {row+j}")
            #print(row+j, row, len(coordList))
            coordList[row+j][row] = "*"
"""




n = int(input())
nums = list(map(int, input().split()))

def check(c, nums):
    mi,ma = min(nums), max(nums)
    poss = [mi,ma, ma-c,mi+c, mi-c, ma+c]
    for j in poss:
        flag = True
        for i in nums:
            if i+c!=j and i-c!=j and i!=j:
                flag = False
                break
        if flag:
            return True

    return False

got = False
for val in range(100):
    if check(val,nums):
        print(val)
        got = True
        break
if not got:
    print(-1)














