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)

"use strict";

// read lines from stdin
const input = require("fs")
  .readFileSync("/dev/stdin", "utf8")
  .split("\n");

const N = parseInt(input[0], 10);
const points = [];
const outOfBounds = [];

for (let i = 1; i <= N; i++) {
  const line = input[i].split(" ").map((val) => parseInt(val, 10));
  if (line[2] > 0) {
    points.push({ x: line[0], y: line[1], h: line[2] });
  } else {
    outOfBounds.push({ x: line[0], y: line[1], h: line[2] });
  }
}

points.push(...outOfBounds);

for (let x = 0; x <= 100; x++) {
  for (let y = 0; y <= 100; y++) {
    let found = true;
    let estimate = {
      x,
      y,
      h: 0,
    }
    for (let i = 0; i < points.length; i++) {
      const point = points[i];

      if (estimate.h <= 0) {
        estimate.h = estimateTopHeight(point, estimate);
        continue;
      }

      if (!isValidHeight(point, estimate)) {
        found = false;
        break;
      }
    }

    if (found) {
      console.log(`${estimate.x} ${estimate.y} ${estimate.h}`);
      return;
    }
  }
}

function estimateTopHeight(current, top) {
  return current.h + Math.abs(top.x - current.x) + Math.abs(top.y - current.y);
}

function isValidHeight(current, top) {
  return Math.max(top.h - Math.abs(top.x - current.x) - Math.abs(top.y - current.y), 0) === current.h;
}