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.Linq;

public class Program
{
    static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        var piramids = new int[n][];
        var xs = new int[n];
        var ys = new int[n];
        var hs = new int[n];
        for (int i = 0; i < n; i++)
        {
            var input = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
            xs[i] = input[0];
            ys[i] = input[1];
            hs[i] = input[2];
        }

        for (int cy = 0; cy <= 100; cy++)
        {
            for (int cx = 0; cx <= 100; cx++)
            {
                var flag = true;
                var buf = -1;
                for (int i = 0; i < n; i++)
                {
                    var x = xs[i];
                    var y = ys[i];
                    var h = hs[i];
                    var ch = h + Math.Abs(x - cx) + Math.Abs(y - cy);
                    if (buf == -1)
                    {
                        buf = ch;
                    }
                    else
                    {
                        if (buf != ch)
                        {
                            flag = false;
                            break;
                        }
                    }
                }

                if (flag)
                {
                    Console.WriteLine($"{cx} {cy} {buf}");
                }
            }
        }
    }
}