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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		long N = long.Parse(Console.ReadLine());
		long[,] A = new long[N,3];
		for(var i=0;i<N;i++){
			string[] str = Console.ReadLine().Split();
			A[i,0] = long.Parse(str[0]);
			A[i,1] = long.Parse(str[1]);
			A[i,2] = long.Parse(str[2]);
		}
		long it = 0;
		long jt = 0;
		while(true){
			long a = Math.Abs(it-A[0,0])+Math.Abs(jt-A[0,1])+A[0,2];
			bool flag = true;
			for(var i=1;i<N;i++){
				if(Math.Abs(it-A[i,0])+Math.Abs(jt-A[i,1])+A[i,2] > a){
					flag = false;
					break;
				} else {
					 a = Math.Min(a,Math.Abs(it-A[i,0])+Math.Abs(jt-A[i,1])+A[i,2]);
				}
			}
			if(flag == true){
				Console.WriteLine(it+" "+jt+" "+a);
				break;
			} else {
				jt += 1;
				if(jt >= 101){
					it += 1;
					if(it >= 101){
						break;
					}
					jt = 0;
				}
			}
		}
	}
}