Problem:
Score: 300 points

Problem Statement

In the Ancient Kingdom of Snuke, there was a pyramid to strengthen the authority of Takahashi, the president of AtCoder Inc.

The pyramid had center coordinates (C_X, C_Y) and height H. The altitude of coordinates (X, Y) is max(H - |X - C_X| - |Y - C_Y|, 0).

Aoki, an explorer, conducted a survey to identify the center coordinates and height of this pyramid. As a result, he obtained the following information:

C_X, C_Y was integers between 0 and 100 (inclusive), and H was an integer not less than 1.

Additionally, he obtained N pieces of information. The i-th of them is: "the altitude of point (x_i, y_i) is h_i."

This was enough to identify the center coordinates and the height of the pyramid. Find these values with the clues above.

Constraints

N is an integer between 1 and 100 (inclusive).

x_i and y_i are integers between 0 and 100 (inclusive).

h_i is an integer between 0 and 10^9 (inclusive).

The N coordinates (x_1, y_1), (x_2, y_2), (x_3, y_3), ..., (x_N, y_N) are all different.

The center coordinates and the height of the pyramid can be uniquely identified.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1 h_1
x_2 y_2 h_2
x_3 y_3 h_3
:
x_N y_N h_N

Output

Print values C_X, C_Y and H representing the center coordinates and the height of the pyramid in one line, with spaces in between.

Sample Input 1

4
2 3 5
2 1 5
1 2 5
3 2 5

Sample Output 1

2 2 6

In this case, the center coordinates and the height can be identified as (2, 2) and 6.

Sample Input 2

2
0 0 100
1 1 98

Sample Output 2

0 0 100

In this case, the center coordinates and the height can be identified as (0, 0) and 100.

Note that C_X and C_Y are known to be integers between 0 and 100.

Sample Input 3

3
99 1 191
100 1 192
99 0 192

Sample Output 3

100 0 193

In this case, the center coordinates and the height can be identified as (100, 0) and 193.

Solution in JavaScript (node.js v5.12) (judge verdict: Accepted)

function main(input){
  const lines = input.split('\n');
  const N = parseInt(lines[0]);
  var vs = [];
  for(var i=0;i<N;i++){
    var line = lines[i+1].split(' ').map(x => parseInt(x));
    vs.push(line);
  }

  if(N==1){
    console.log(vs[0].join(' '));
    return;
  }

  const one_vs = vs.filter(v => v[2]>0);
  if(one_vs.length==1){
    console.log(one_vs[0].join(' '));
    return;
  }


  var candidates = [];
  for(var x=0;x<=100;x++){
    for(var y=0;y<=100;y++){
      var one_v = one_vs[0];
      var height = Math.abs(x - one_v[0]) + Math.abs(y - one_v[1]) + one_v[2]
      candidates.push([x,y,height]);
    }
  }

//console.log(candidates);

  var highest = [0,0,0];
  for(var j=0;j<candidates.length;j++){
    var candidate = candidates[j];
    var detected=true;
    for(var i=0;i<one_vs.length;i++){
      var one_v = one_vs[i];
      var tmp_height = Math.abs(candidate[0] - one_v[0]) + Math.abs(candidate[1] - one_v[1]) + one_v[2];
      if(candidate[2]!=tmp_height){detected=false;}
    }
    if(detected && candidate[2] > highest[2]){highest = candidate}
  }
  console.log(highest.join(' '));
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));