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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.ArrayList;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int hi = 0;
		ArrayList<Integer> xlist = new ArrayList<Integer>();
		ArrayList<Integer> ylist = new ArrayList<Integer>();
		ArrayList<Integer> hlist = new ArrayList<Integer>();
		for ( int i = 0; i < n; i++ ) {
			xlist.add(in.nextInt());
			ylist.add(in.nextInt());
			hlist.add(in.nextInt());

			if ( hlist.get(i) != 0 ) hi = i;
		}
		in.close();

		for ( int cy = 0; cy <= 100; cy++ ) {
			for ( int cx = 0; cx <= 100; cx++ ) {
				boolean match = true;
				int Height = hlist.get(hi) + Math.abs(xlist.get(hi) - cx) + Math.abs(ylist.get(hi) - cy);
				
				for ( int i = 0; i < hlist.size(); i++ ) {					
					if(hlist.get(i) != 0) {
						int tempH = hlist.get(i) + Math.abs(xlist.get(i) - cx) + Math.abs(ylist.get(i) - cy);
						if ( Height != tempH ) {
							match = false;
							break;
						} else {
							Height = tempH;							
						}						
					}
					
					if(hlist.get(i) == 0 && Height > Math.abs(xlist.get(i) - cx) + Math.abs(ylist.get(i) - cy)) {
						match = false;
						break;
					}
				}
				if ( match ) {
					System.out.println(cx + " " + cy + " " + Height);
					return;
				}
			}
		}
	}
}