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

def solve(s):
    """
    input is a list s
    """
    allSet = set();
    for i in s:
        if i in allSet:
            continue;
        else:
            allSet.add(i);
        if len(allSet) > 3:
            return -1;
    allValue = [];
    for i in allSet:
        allValue.append(i);
    allValue.sort();
    if (len(allValue) == 1):
        return 0;
    elif (len(allValue) == 2):
        diff = int(allValue[-1] - allValue[0]);
        if diff%2 == 1:
            return int(diff);
        else:
            return int(diff/2);
    else:
        diff = int(allValue[-1] - allValue[1]);
        if ((allValue[0] + allValue[-1])/2 == allValue[1]):
            return int(diff);
        else:
            return -1;

if __name__ == "__main__":
    """the solve(*args) structure is needed for testing purporses"""
    total = int(input());
    a = [int(s) for s in input().split()];
    print(solve(a));