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: Runtime Error)

import scala.math._
object Main {
  def main(args:Array[String]):Unit={
    val N = readInt
    var hP = 0
    var x:Array[Int] = Array()
    var y:Array[Int] = Array()
    var h:Array[Int] = Array()
    for(i <- 0 until N){
      val tmp = readLine.split(" ").map(x => x.toInt)
      x = x:+tmp(0)
      y = y:+tmp(1)
      h = h:+tmp(2)
      if(tmp(2)>0) hP = i
    }
    var flag = true
    for(i <- 0 until N if flag){
      var H = abs(x(i)-x(hP))+abs(y(i)-y(hP)) + h(hP)
      for(a <- 0 until 100 if flag){
        for(b <- 0 until 100 if flag){
          var HH = H-abs(x(i)-a)-abs(y(i)-b)
          HH = max(HH,0)
          if(HH==h(N)) flag = false
          
          if(flag) println(a+" "+b+" "+HH)
        }
      }     
    }
    
  }
}