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)

'use strict';
const main = input => {
  const n = parseInt(input[0]);
  let x = new Array(n), y = new Array(n), h = new Array(n);
  for(let i=0; i<n; i++) {
    let s = input[i+1].split(' ');
    x[i] = parseInt(s[0]);
    y[i] = parseInt(s[1]);
    h[i] = parseInt(s[2]);
  }
  // console.log(n, x, y, h);
  for(let px=0; px<101; px++) {
    for(let py=0; py<101; py++) {
      let height = h[0]+Math.abs(px-x[0])+Math.abs(py-y[0]);
      let tf = 1;
      for(let k=1; k<n; k++) {
        if (height != h[k]+Math.abs(px-x[k])+Math.abs(py-y[k] || height < 1)) {
          tf = 0;
        }
      }
      if (tf==1) {
        console.log(px, py, height);
        return 0;
        
      }
    }
  }
}
main(require("fs").readFileSync("/dev/stdin", "utf8").split('\n'));