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;

class Main{
	static final long MOD = 1000000007;

	static int H, W, K;
	static long[][] dp = new long[110][10];
	static int ans = 0;
	static long n = 0;





	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);			//文字の入力
		int n = sc.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] =sc.nextInt();
			y[i] = sc.nextInt();
			h[i] = sc.nextInt();
		}
		for(int cx = 0;cx <= 100;cx++){
			for(int cy = 0;cy <= 100;cy++){
				long H = 0;
				for(int i = 0;i < n;i++){
					if(h[i] != 0){
						H= (long)( h[i] +(long) Math.abs(x[i]-cx) +  Math.abs(y[i]-cy));
						break;
					}
				}


				boolean flag = true;
				for(int i = 0;i < n;i++){
					if(h[i] != 0){
						if(h[i] != H - (long)Math.abs(x[i]-cx) -  Math.abs(y[i]-cy)){
							flag = false;
							break;
						}else{
							if(H - Math.abs(x[i]-cx) -  Math.abs(y[i]-cy)!= 0){
								flag = false;
								break;
							}
						}
					}
				}
				
				if(flag){
					System.out.println(cx + " " + cy + " " + H);
					return;
				}
			}
		}
	}
}







class Pair implements Comparable{
	int from;		//p
	int end;		//y
	int num;
	int bango;
	@Override
	public int compareTo(Object other) {
		Pair otherpair = (Pair)other;

		return end - otherpair.end;
	}
}