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.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		Point[] arr = new Point[n];
		int zero = 0;
		for(int i=0;i<n;i++){
			
			arr[i] = new Point(sc.nextInt(), sc.nextInt(), sc.nextInt());
			
			if(arr[i].h==0)
			    zero++;
		}
		
		/*if(zero==n){
		    System.out.println("0 0 1");
		}*/
		//else{
			
			Arrays.sort(arr, new Comparator<Point>(){

				@Override
				public int compare(Point arg0, Point arg1) {
					// TODO Auto-generated method stub
					return -Integer.compare(arg0.h, arg1.h);
				}
				
			});
			
    		int h = 0;
    		boolean val=true;
    		L1:for(int x=0;x<=100;x++){
    			for(int y=0;y<=100;y++){
    				val=true;
    				for(int i=0;i<n;i++){
    					if(i==0){
    						h = Math.abs(x-arr[i].x)+Math.abs(y-arr[i].y)+arr[i].h;
    					}
    					else{
    						if(Math.max(h-Math.abs(x-arr[i].x)-Math.abs(y-arr[i].y), 0)!=arr[i].h){
    							val=false;
    							break;
    						}
    					}
    				}
    				if(val && h>=1){
    					System.out.println(x+" "+y+" "+h);
    					break L1;
    				}
    			}
    		}   
		//}
	}
}
class Point{
	int x, y, h;
	Point(int x, int y, int h){
		this.x=x;
		this.y=y;
		this.h=h;
	}
}
/*
4
2 3 5
2 1 5
1 2 5
3 2 5

5
2 3 5
2 1 5
1 2 5
3 2 5
10 20 0

2
47 23 0
10 20 0
*/