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
var n=readline();
var arry=readline().split(' ');

function uniqueArr(arr) {
  var output=[];
  
  for (var i = 0; i < arr.length; i++) {
    var counter = 0;
    
    for (var j = 0; j < output.length; j++) {
      if ( arr[i] == output[j] ) {
        counter++;
      }
    }
    
    if (counter == 0) output.push(arr[i]);
  }
  
  for (var x = 0; x < output.length - 1; x++) {
    var minNum = output[x], index = x, old = output[x];
    
    for (var k = x + 1; k < output.length; k++) {
      if (minNum > output[k])  {
        index = k;
        minNum = output[k];
      }
    }
    
    output[x] = minNum;
    output[index] = old;
  }
  
  return output;
}

function findD(arr) {
  arr = uniqueArr(arr);
  
  if (arr.length == 1) {
    return 0;
  }
  
  else if (arr.length == 2) {
    var D = Math.abs( (arr[0] - arr[1])/2 );
    if ( D == Math.floor(D) ) {
      return D;
    }else return Math.abs(arr[0] - arr[1]);
  }
  
  
  else if (arr.length == 3) {
    var D1 = Math.abs(arr[0] - arr[1]), D2 = Math.abs(arr[0] - arr[2]);
    if ( D1 == D2 || 2*D1 == D2) {
      return D1;
    }
    else if (D1 == 2*D2) {
      return D2;
    }
    else return -1;
  }
  
  return -1;
}

print( findD(arry) ) 