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: Wrong Answer)

function Main(input) {
  input = input.split("\n");
  N = parseInt(input[0]);
  x = new Array(N);
  y = new Array(N);
  h = new Array(N);
  for(i=0;i<N;i++){
    tmp=input[i+1].split(" ");
    x[i]=parseInt(tmp[0]);
    y[i]=parseInt(tmp[1]);
    h[i]=parseInt(tmp[2]);
  }
  for(i=0;i<N;i++){
    if(h[i]!=0){
      var x1=x[i];
      var y1=y[i];
      var h1=h[i];
      break;
        }
  }
  ans=0;
  for(i=0;i<101;i++){
    for(j=0;j<101;j++){
      var H =h1+Math.abs(i-x1)+Math.abs(j-y1);
      var count=0;
      for(k=0;k<N;k++){
        if(h[k]==H-Math.abs(i-x[k])-Math.abs(j-y[k])||h[k]==0){
          count++;
        }
      }

    if(count==x.length){
      ans=i+" "+j+" "+H;
      break;
    }
    }
  }
  console.log('%s', ans);
}
  
// "実行する"ボタンを押した時に実行される関数 (デバッグ用)
function debug(){
  var input = document.getElementById("input").value;
  Main(input);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));