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.Numerics;
using System.Linq;
using System.Collections.Generic;
using System.Text;
using System.Collections;

namespace debug
{
    class main
    {
        static void Main(string[] args)
        {
            //問題クラスを展開
            ProgramC a = new ProgramC();
            a.main();//実行する

        }

    }

    class ProgramA
    {
        public void main()
        {
            //数値入力する
            string[] s = Console.ReadLine().Split(' ');


            //それぞれの文字列で答えを出す
            if ((int.Parse(s[0]) * int.Parse(s[1])) % 2 == 1)
                Console.WriteLine("Yes");
            else
                Console.WriteLine("No");

        }
    }

    class ProgramB
    {
        public void main()
        {

            //入力
            string input = Console.ReadLine();
            int n = int.Parse(input);

            string[] num = new string[n];


            //char型で読み込み、int型に変換。そこから数を足して、char型に戻す
            for (int i = 0; i < n; i++)
            {
                string s = Console.ReadLine();

                if (num.Contains(s) == true)
                {
                    Console.WriteLine("No");
                    return;
                }

                if (i == 0)
                {
                    num[0] = s;
                }
                else
                {
                    if (num[i - 1][num[i - 1].Length - 1] != s[0])
                    {
                        Console.WriteLine("No");
                        return;
                    }

                    num[i] = s;
                }


            }

            Console.WriteLine("Yes");

        }
    }

    class ProgramC
    {
        public void main()
        {

            //入力
            int n = int.Parse(Console.ReadLine());

            //情報を記録
            List<Pos> info = new List<Pos>();

            //とりあえず情報を記録する
            for (int i = 0; i < n; i++)
            {
                string[] s = Console.ReadLine().Split();
                info.Add(new Pos(int.Parse(s[0]), int.Parse(s[1]), long.Parse(s[2])));
            }

            //この座標が答として高さを仮定する
            for (int i = 0; i <= 100; i++)
                for (int j = 0; j <= 100; j++)
                {
                    long h = info[0].c + Math.Abs(info[0].a -i) + Math.Abs(info[0].b - j);
                    int count = 1;
                    for(int k = 1;k < info.Count;k++)
                    {
                        long h2 = h - Math.Abs(info[1].a - i) - Math.Abs(info[1].b - j);
                        if (h2 == info[1].c)
                            count++;
                    }

                    if (count == n)
                    {
                        Console.WriteLine(i + " " + j + " " + h);
                        return;
                    }
                }

        }
    }

    class Pos
    {
        public int a;
        public int b;
        public long c;
        public Pos(int a, int b, long c)
        {
            this.a = a;
            this.b = b;
            this.c = c;
        }
    }

    class ProgramD
    {
        public void main()
        {

            //入力
            string[] input = Console.ReadLine().Split();
            long n = long.Parse(input[0]);
            long m = long.Parse(input[1]);

            long ans = 1;

            //2変数に分離
            for (int i = 1; i <= Math.Sqrt(m); i++)
            {
                if (m % i == 0)
                {
                    if (m/i >= n)
                    {
                        ans = Math.Max(ans, i);
                        if (i >= n)
                            ans = Math.Max(ans, m / i);
                    }
                }

            }

            //答え出力
            Console.WriteLine(ans);
           

        }
    }




  

}