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
(function () {
    var read = {
        number: function () {
            return +readline();
        },
        arr: function (divider) {
            return readline().split(divider ? divider : '');
        },
        arrNumber: function (divider) {
            return readline()
                .split(divider ? divider : '')
                .map(item => +item);
        }
    }

    var n = read.number();
    var a = [...new Set(read.arrNumber(' '))];

    var max = a[0], min = a[0];
    a.forEach(i => {
        if(i > max) max = i;
        if(i < min) min = i;
    });

    mid = min + (max - min)/2

    var midUse = false;
    var minuse = false;
    var maxuse = false
    
    for(var f = 0; f < a.length; f++) {
        var i = a[f]
        if(i === mid) {
            midUse = true;
        }
        else if(i === max) {
            minuse = true;
        }
        else if(i === min) {
            maxuse = true;
        }
        else {
            print(-1);
            return;
        }
    }

    if(midUse) {
        print(max - mid)
    }
    else {
        if((max - min) %2 === 1)
            print(max - min);
        else {
            print((max - min) / 2)
        }
    }
}());
