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 sys
n, nm, mx, mn, act, same = int(input()), list(), -1, 101, 0, True
an = input().split()
for i in an:
    act = int(i)
    mx = max(mx, act)
    mn = min(mn, act)
    nm.append(act)
    if same and len(nm) > 1 and act != nm[-2]:
        same = False
f1, f2 = (mx-mn)/2, mx-mn
ni1, ni2 = mn+f1, mn+f2
md1, md2 = True, True
# Corto circuitos
if n == 1:
    print(0)
    sys.exit()
if same:
    print(0)
    sys.exit()

if f1 >= 0 and f1 % 1 == 0:
    f1 = int(f1)
    for j in nm:
        if j == ni1:
            continue
        else:
            if j+f1 != ni1 and j-f1 != ni1:
                md1 = False
                break
    if md1:
        print(int(f1))
        sys.exit()
if f2 >= 0 and f2 % 1 == 0:
    for j in nm:
        if j == ni2:
            continue
        else:
            if j+f2 != ni2 and j-f2 != ni2:
                print(-1)
                sys.exit()
    print(int(f2))
else:
    print(-1)


