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 scan = new Scanner(System.in);
        int N = scan.nextInt();//入力される数
        int[] inx = new int[N];
        int[] iny = new int[N];
        int[] inh = new int[N];
        int H = 0;
        int Cx = 0;
        int Cy = 0;
        int w;
        int temp = 0;
        int flag;

        for(int i = 0;i<N;i++){
            inx[i] = scan.nextInt();
            iny[i] = scan.nextInt();
            inh[i] = scan.nextInt();
        }

        for(int k = 0;k<=100;k++){
            for(int r = 0;r <= 100;r++){
                flag = 1;
                for(int s = 0;s < N;s++){
                    w = getH(inx[s],iny[s],k,r,inh[s]);
                    if(s == 0){
                        temp = w;
                    }else{
                        if(temp != w){
                            flag = -1;
                            break;
                        }
                    }
                }
                if(flag == 1) {
                    Cx = k;
                    Cy = r;
                    H = temp;
                }
            }

        }

        if(H != -1){
            System.out.println(Cx + " " + Cy + " " +H);
        }

    }

    public static int getH(int x,int y,int Cx,int Cy,int h){
        int t = x - Cx > 0 ? x - Cx:Cx - x;
        int u = y - Cy > 0 ? y - Cy:Cy - y;
        int H = h + t + u;
        if(h >= 0){
            return H;
        }else{
            return 0;
        }
    }
}