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 Scala (2.11.7) (judge verdict: Wrong Answer)

import java.util.Scanner

import scala.collection.mutable

object Main extends App {
  val sc = new Scanner(System.in)
  val n = sc.nextInt
  val xyhs = Seq.fill(n)((sc.nextInt, sc.nextInt, sc.nextInt))
  val h_xys = mutable.Map.empty[(Int, Int), Int]
  xyhs.foreach { case (x, y, h) =>
    for {
      xx <- 0 to 100
      yy <- 0 to 100
    } {
      val hh = Math.abs(x - xx) + Math.abs(y - yy) + h
      val already = h_xys.get((xx, yy))
      if (already.isEmpty) {
        h_xys.update((xx, yy), hh)
      } else if (already.exists(_ != hh)) {
        h_xys.update((xx, yy), -1)
      }
    }
  }
  val center = h_xys.maxBy { case (_, h) => h }
  println(s"${center._1._1} ${center._1._2} ${center._2}")
}