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
#!python3
"""
I1
a b : D : { a:|a-b|, b:|a-b|, middle: min(a,b) +  abs( (a-b)/2 ) if int }

a b c : c =


Ex
1 4 4 7 4 1
1 4        1,3 4,3
1 4 4
1 4 4 7    4,3
1 4 4 7 4 1

Ex2
2 2 5 2 5
2      (0)
2 2 5   2,3  5,3
2 2 5 2 5
3

Ex3
1 3 3 7
1 3 3    1,2  3,2
1 3 3 7  > -1

"""


def getvariants(variants, x):
    left = []
    for point, diff in variants:
        if (x - diff == point
                or x + diff == point
                or x == point):
            left += [(point, diff)]
    return left


n = int(input('').strip())
A = [int(i) for i in input('').strip().split(' ')]

a = A[0]
variants = None
i = 1
while i < len(A):
    if A[i] != a:
        b = A[i]
        variants = [(a, abs(a - b)), (b, abs(a - b))]
        diff, remainder = divmod(max(a, b) - min(a, b), 2)
        if remainder == 0:
            variants += [(min(a, b)+diff, diff)]
        break
    i += 1

if not variants:
    print(0)
    exit()
else:
    for x in A[i+1:]:
        variants = getvariants(variants, x)
        if not variants:
            break
    if not variants:
        print(-1)
    else:
        print(min(diff for point, diff in variants))
