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 sc = new Scanner(System.in);
		int n=sc.nextInt();
		int jou[][]=new int[n][3];

		for(int i=0;i<n;i++) {
			jou[i][0]=sc.nextInt();
			jou[i][1]=sc.nextInt();
			jou[i][2]=sc.nextInt();
		}

		for(int i=0;i<=100;i++) {
			for(int j=0;j<=100;j++) {
				sindan(i,j,n, jou);
			}
		}

	}

	public static void sindan(int x, int y, int n, int[][] jou) {

		int height=0;
		boolean ha = true;
		for(int i=0;i<n;i++) {
			if(jou[i][2]!=0) {
				if(height==0) {
					height= jou[i][2] + zettaichi(jou[i][0]-x) + zettaichi(jou[i][1]-y);
					continue;
				}

				if(height!=jou[i][2] + zettaichi(jou[i][0]-x) + zettaichi(jou[i][1]-y)) {
					ha=false;
				}
			}
		}

		for(int i=0;i<n;i++) {
			if(jou[i][2]==0) {
				if(height>jou[i][2] + zettaichi(jou[i][0]-x) + zettaichi(jou[i][1]-y)) {
					ha=false;
				}
			}
		}

		if(ha)
			System.out.print(x + " " + y + " " + height);

	}



	public static int zettaichi(int x) {
		if(x>=0)
			return x;
		else
			return -x;
	}

}