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

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var st = new int[N, 3];
            foreach(var i in Enumerable.Range(0, N))
            {
                var vals = Console.ReadLine().Split(' ').Select(x => Convert.ToInt32(x)).ToArray();
                st[i, 0] = vals[0];
                st[i, 1] = vals[1];
                st[i, 2] = vals[2];
            }

            //可能性のあるxy
            var xy = new Queue<Tuple<int, int>>();
            foreach(var i in Enumerable.Range(0, 101*101))
            {
                xy.Enqueue(new Tuple<int, int>(i / 101, i % 101));
            }


            var limit = xy.Count;
            foreach(var j in Enumerable.Range(0, limit))
            {
                var item = xy.Dequeue();
                var start = 0;
                var tmph = 0;
                foreach(var i in Enumerable.Range(0, N))
                {
                    tmph = st[i, 2] + Math.Abs(st[i, 0] - item.Item1) + Math.Abs(st[i, 1] - item.Item2);
                    if(tmph > 0)
                    {
                        start = i;
                        break;
                    }
                }
                //矛盾を探す
                var conflict = false;
                for (var i = start; i < N; i++)
                {
                    var h = Math.Max(tmph - Math.Abs(st[i, 0] - item.Item1) - Math.Abs(st[i, 1] - item.Item2), 0);
                    if(st[i, 2] != h)
                    {
                        conflict = true;
                        break;
                    }
                }
                if(!conflict)
                {
                    Console.WriteLine($"{item.Item1} {item.Item2} {tmph}");
                    break;
                }
            }
        }
    }
}