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;
using System.Linq;
using static System.Console;
using static System.Math;

//https://beta.atcoder.jp/contests/abc112/tasks/abc112_c
public class Program_ABC112_C // ←Class名変更！！
{
    public static void Main(string[] args)
    {
        var n = long.Parse(ReadLine());

        var points = new long[n][];
        for (int i = 0; i < n; i++)
        {
            points[i] = Array.ConvertAll(ReadLine().Split(' '), long.Parse);
        }

        //Array.Sort(points, (a, b) => b[2].CompareTo(a[2])); //高さでソート

        var crest = new long[3] { -1, -1, -1 };
        for (var x = 0L; x < 101; x++)
        {
            var xConst = points[0][2] + Abs(x - points[0][0]);
            for (var y = 0L; y < 101; y++)
            {
                var h1 = xConst + Abs(y - points[0][1]);
                var isCrest = true;
                for (int i = 1; i < n; i++)
                {
                    var h2 = points[i][2] + Abs(x - points[i][0]) + Abs(y - points[i][1]);
                    if (points[i][2] > 0)
                    {
                        //座標に高さがあるということは、ピラミッドの一部なので、h1=h2が成り立つ
                        if (h1 != h2)
                        {
                            isCrest = false;
                            break;

                        }
                    }
                    else
                    {
                        //座標の高さが0の場合、ピラミッドの底辺もしくは、ピラミッドの高さとは関係ない座標の2つが考えられる。
                        //ピラミッドの底辺の場合h1=h2となり、無関係な座標で頂点を計算すると、h2<h1となる。
                        if (h1 < h2)
                        {
                            isCrest = false;
                            break;
                        }
                    }
                }

                if (isCrest)
                {
                    crest = new[] { x, y, h1 };
                    break;
                }
            }

        }



        Console.WriteLine($"{crest[0]} {crest[1]} {crest[2]}");

    } // Main
}     // Class