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.Scanner;

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

        try{
            //入力
            int N = scan.nextInt();
            int[] x = new int[N];
            int[] y = new int[N];
            int[] h = new int[N];
            for(int i = 0; i < N; i++){
                x[i] = scan.nextInt();
                y[i] = scan.nextInt();
                h[i] = scan.nextInt();
            }

            int X = 0;
            int Y = 0;
            int H = 0;
            loop: for(int cx = 0; cx <= 100; cx++){
                for(int cy = 0; cy <= 100; cy++){
                    for(int i = 0; i < N; i++){
                        if(h[i] != 0){
                            H = h[i] + Math.abs(cx-x[i]) + Math.abs(cy-y[i]);
                            break;
                        }
                    }
                    H = getHeight(H, cx, cy, N, h, x, y);
                    if(H != -1){
                        X = cx;
                        Y = cy;
                        break loop;
                    }
                }
            }

            System.out.println(X+" "+Y+" "+H);

        }finally{
            scan.close();
        }
    }

    static int getHeight(int H, int cx, int cy, int N, int[] h, int[] x, int[] y){
        for(int i = 0; i < N; i++){
            if(h[i] != Math.max(H-Math.abs(cx-x[i])-Math.abs(cy-y[i]), 0)){
                H = -1;
            }
        }
        return H;
    }
}