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)

object Main {
  def main(args: Array[String]): Unit = {
    solve
  }

  def solve(): Unit = {
    val sc = new java.util.Scanner(System.in)
    val n = sc.nextInt
    val xs = new Array[Long](n)
    val ys = new Array[Long](n)
    val hs = new Array[Long](n)
    for (i <- 0 until n) {
      xs(i) = sc.nextLong
      ys(i) = sc.nextLong
      hs(i) = sc.nextLong
    }

    var result = (0, 0, 0L)
    for (x <- 0 to 100) {
      for (y <- 0 to 100) {
        val ret = check(x, y, n, xs, ys, hs)
        if (ret._1) {
          println(x + " " + y + " " + ret._2)
          return
        }
      }
    }

  }

  private def check(x: Int, y: Int, n: Int, xs: Array[Long], ys: Array[Long], hs: Array[Long]): (Boolean, Long) = {
    var index = 0
    val notZeroIndex: Int = hs.indexWhere(h => h != 0L)
    val H = hs(notZeroIndex) + ((x - xs(notZeroIndex)).abs + (y - ys(notZeroIndex)).abs)
    if (H < 1) return (false, -1)

    while (index < n) {
      val tmpHeight = math.max((H - (((x - xs(index)).abs + (y - ys(index)).abs))).abs, 0)
      if (tmpHeight != hs(index)) {
        return (false, -1)
      }
      index += 1
    }

    (true, H)
  }

}