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: Wrong Answer)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);

		int n = sc.nextInt();
		int[] x = new int[n];
		int[] y = new int[n];
		int[] h = new int[n];
		int px = 0;
		int py = 0;
		int ph = 0;

		for (int i = 0; i < n; i++) {
			x[i] = sc.nextInt();
			y[i] = sc.nextInt();
			h[i] = sc.nextInt();
			if (h[i] > 0 && ph == 0) {
				px = x[i];
				py = y[i];
				ph = h[i];
			}
		}

		for (int i = 0; i <= 100; i++) {
			loop: for (int j = 0; j <= 100; j++) {
				int cx = i;
				int cy = j;
				int ch = ph + Math.abs(cx - px) + Math.abs(cy - py);

//				System.out.println(cx + ", " + cy + ", " + ch);

				for (int k = 0; k < n; k++) {
//					System.out.print("ch=" + ch + ", k=" + k + ", ");
//					System.out.println(h[k] + Math.abs(cx - x[k]) + Math.abs(cy - y[k]));
					if (ch != h[k] + Math.abs(cx - x[k]) + Math.abs(cy - y[k])) {
						continue loop;
					}
				}
				System.out.println(cx + " " + cy + " " + ch);
				System.exit(0);
			}
		}

		sc.close();
	}

}