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
#!/usr/bin/env python3

import sys

def solve(seq):
    if len(seq) <= 1:
        return 0
    d = abs(seq[1] - seq[0])
    candidates = []
    if d % 2 == 0:
        candidates.append((seq[0] + d // 2, d // 2))
    candidates.extend([(seq[0], d), (seq[1], d)])

    tail = seq[2:]
    for val, dif in candidates:
        for x in tail:
            if x != val and abs(x - val) != dif:
                break
        else:
            return dif
    return -1

def solve2(seq):
    uniq = sorted(set(seq))
    if len(uniq) <= 1:
        return 0
    d = uniq[1] - uniq[0]
    if len(uniq) == 2:
        if d % 2 == 0:
            return d // 2
        else:
            return d
    if len(uniq) == 3:
        if uniq[2] - uniq[1] == d:
            return d
    return -1

n = 0
seq = None

for line in sys.stdin:
    if n == 0:
        n = int(line)
    else:
        seq = list(map(int, line.split()))
        break

print(solve2(seq))
