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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main {
    static MyReader in = new MyReader();

    public static void main(String[] args) {
        int N = in.i();
        int[] x = new int[N * 3];
        for (int i = 0; i < x.length; ) {
            x[i++] = in.i();
            x[i++] = in.i();
            x[i++] = in.i();
        }

        int x0 = 0;
        int y0 = 0;
        int h0 = 0;
        for (int i = 0; i < x.length; ) {
            x0 = x[i++];
            y0 = x[i++];
            h0 = x[i++];
            if (0 < h0) {
                break;
            }
        }

        for (int Cx = 0; Cx <= 100; Cx++) {
            loop: for (int Cy = 0; Cy <= 100; Cy++) {
                int H = h0 + Math.abs(Cx - x0) + Math.abs(Cy - y0);
                for (int i = 0; i < x.length; ) {
                    int h = Math.max(H - Math.abs(Cx - x[i++]) - Math.abs(Cy - x[i++]), 0);
                    if (h != x[i++]) {
                        continue loop;
                    }
                }
                System.out.printf("%d %d %d\n", Cx, Cy, H);
                return;
            }
        }
    }
}

class MyReader extends BufferedReader {
    char[] cbuf = new char[1024];
    int head = 0;
    int tail = 0;

    MyReader() {
        super(new InputStreamReader(System.in));
    }

    char next() {
        if (head == tail) {
            try {
                tail = super.read(cbuf, 0, cbuf.length);
            } catch (IOException e) {
                e.printStackTrace();
            }
            head = 0;
        }
        return cbuf[head++];
    }

    int i() {
        int k = next() - '0';
        boolean minus = k == -3;
        int n = minus ? 0 : k;
        while (0 <= (k = next() - '0') && k <= 9) n = 10 * n + k;
        return minus ? -n : n;
    }

    int[] ii(final int N) {
        int[] a = new int[N];
        for (int j = 0; j < a.length; j++) a[j] = i();
        return a;
    }

    long l() {
        int k = next() - '0';
        boolean minus = k == -3;
        long n = minus ? 0 : k;
        while (0 <= (k = next() - '0') && k <= 9) n = 10 * n + k;
        return minus ? -n : n;
    }

    char[] s(final int N) {
        char[] s = new char[N];
        for (int i = 0; i < N; i++) {
            s[i] = next();
        }
        next();
        return s;
    }

    public int read(char[] cbuf) {
        int i;
        char c;
        for (i = 0; (c = next()) != ' ' && c != '\n'; i++) cbuf[i] = c;
        return i;
    }

    public String readLine() {
        try {
            return super.readLine();
        } catch (IOException e) {
            return null;
        }
    }
}