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.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        try (Scanner sc = new Scanner(System.in);) {
            new Main().solve(sc);
        }
    }

    void solve(Scanner sc) {
        int n = sc.nextInt();
        Point[] ps = new Point[n];

        for (int i = 0; i < n; i++) {
            int x = sc.nextInt();
            int y = sc.nextInt();
            int h = sc.nextInt();
            if (h == 100) {
                System.out.printf("%d %d %d%n", x, y, h);
                return;
            }
            ps[i] = new Point(x, y, h);
        }

        Arrays.sort(ps, (x, y) -> y.h - x.h);

        for (int x = 0; x <= 100; x++) {
            for (int y = 0; y <= 100; y++) {
                if (n >= 3) {
                    int h1 = ps[0].h + Math.abs(ps[0].x - x) + Math.abs(ps[0].y - y);
                    int h2 = ps[1].h + Math.abs(ps[1].x - x) + Math.abs(ps[1].y - y);

                    if (h1 == h2) {
                        System.out.printf("%d %d %d%n", x, y, h1);
                        return;
                    }
                }
            }
        }
    }
}

class Point {
    int x;
    int y;
    int h;

    Point(int x, int y, int h) {
        this.x = x;
        this.y = y;
        this.h = h;
    }
}