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 = {
    val s = new Main()
    s.solve()
    s.out.flush()
  }
}

class Main {
  import java.io._
  import java.util.StringTokenizer

  import scala.collection.mutable
  import scala.util.Sorting
  import math.{abs, max, min}
  import mutable.{ArrayBuffer, ListBuffer}
  import scala.reflect.ClassTag

  val MOD = 1000000007
  val out = new PrintWriter(System.out)

  def solve(): Unit = {
    val N = ni()
    val X, Y, H = Array.ofDim[Int](N)
    rep(N) { i =>
      X(i) = ni()
      Y(i) = ni()
      H(i) = ni()
    }

    if (H forall (_ == 0)) {
      rep(101) { x =>
        rep(101) { y =>
          val b = 0 until N forall { i =>
            X(i) != x || Y(i) != y
          }
          if (b) {
            out.println(s"$x $y 1")
            return
          }
        }
      }
    }

    sealed trait Height
    case class Range(to: Int) extends Height // inclusive
    case class Just(num: Int) extends Height
    def intersect(h1: Height, h2: Height): Option[Height] = {
      (h1, h2) match {
        case (Just(a), Just(b)) if a == b => Some(Just(a))
        case (Range(a), Range(b)) => Some(Range(min(a, b)))
        case (Just(a), Range(b)) if a <= b => Some(Just(a))
        case (Range(b), Just(a)) if a <= b => Some(Just(a))
        case _ => None
      }
    }

    def calcH(x: Int, y: Int): Option[Int] = {
      var height: Height = Range(1e9.toInt)

      rep(N) { i =>
        val d = abs(X(i) - x) + abs(Y(i) - y)
        val cur = if (H(i) == 0){
          Range(d)
        } else {
          Just(H(i) + d)
        }

        intersect(height, cur) match {
          case Some(next) => height = next
          case None => return None
        }
      }

      height match {
        case Just(a) => Some(a)
        case Range(a) if a > 0 => Some(1)
        case Range(a) if a == 0 => None
      }
    }

    rep(101) { x =>
      rep(101) { y =>
        calcH(x, y) match {
          case None =>
          case Some(h) =>
            out.println(s"$x $y $h")
            return
        }
      }
    }
  }


  class InputReader(val stream: InputStream) {
    private val reader = new BufferedReader(new InputStreamReader(stream), 32768)
    private var tokenizer: StringTokenizer = _

    def next(): String = {
      while (tokenizer == null || !tokenizer.hasMoreTokens)
        tokenizer = new StringTokenizer(reader.readLine)
      tokenizer.nextToken
    }

    def nextInt(): Int = next().toInt
    def nextLong(): Long = next().toLong
    def nextChar(): Char = next().charAt(0)
  }
  val sc = new InputReader(System.in)
  def ni(): Int = sc.nextInt()
  def nl(): Long = sc.nextLong()
  def nc(): Char = sc.nextChar()
  def ns(): String = sc.next()
  def ns(n: Int): Array[Char] = ns().toCharArray
  def na(n: Int): Array[Int] = map(n)(_ => ni())
  def nal(n: Int): Array[Long] = map(n)(_ => nl())
  def nm(n: Int, m: Int): Array[Array[Char]] = map(n) (_ => ns(m))
  def rep(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = offset
    val N = n + offset
    while(i < N) { f(i); i += 1 }
  }
  def rep_r(n: Int, offset: Int = 0)(f: Int => Unit): Unit = {
    var i = n - 1 + offset
    while(i >= offset) { f(i); i -= 1 }
  }

  def map[@specialized A: ClassTag](n: Int)(f: Int => A): Array[A] = {
    val res = Array.ofDim[A](n)
    rep(n)(i => res(i) = f(i))
    res
  }

  def sumL(as: Array[Int]): Long = {
    var s = 0L
    rep(as.length)(i => s += as(i))
    s
  }
}