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: Accepted)

import java.util.Scanner

object Main {
  def main(args: Array[String]): Unit = {
    //nextLineとnextを同時に使ったら死ぬ
    val sc = new Scanner(System.in)

    val n = sc.nextInt()
    val points = Array.fill(n) {
      val x, y, h = sc.nextInt()
      (x, y, h)
    }

    var xx = Array[Int]()
    var yy = Array[Int]()
    var hh = Array[Int]()

    for {
      cx <- 0 to 100
      cy <- 0 to 100
    } {
      val p =
        points
          .map {
            case (x, y, h) =>
              h match {
                case 0 => None
                case _ => Option(h + math.abs(x - cx) + math.abs(y - cy))
              }
          }
          .filter(_.isDefined)
          .map(_.get)
      if (p.foldLeft((true, p.head)) { case ((b, i), n) => (b && i == n, n) }
            ._1) {
        xx = xx :+ cx
        yy = yy :+ cy
        hh = hh :+ p.head
      }

    }

    for (i <- xx.indices) {
      if (points.forall {
            case (x, y, h) =>
              h == math.max(
                0,
                hh(i) - math.abs(x - xx(i)) - math.abs(y - yy(i))
              )
          }) println(s"${xx(i)} ${yy(i)} ${hh(i)}")

    }

  }

  def debug(args: Any*): Unit = {
    Console.err.println(args.mkString(" "))
  }
}