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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>

int main(void)
{
	int n, err, i, j, k, l, flag;
	long *x, *y, *h, H, H1;
	err = scanf("%d", &n);
	if ((err!=1) || (n<1)) exit(1);
	x = (long *)malloc(sizeof(long)*n);
	y = (long *)malloc(sizeof(long)*n);
	h = (long *)malloc(sizeof(long)*n);

	for (int i = 0; i < n; ++i)
	{
		err = scanf("%ld%ld%ld", &x[i], &y[i], &h[i]);
		if ((err!=3) || ((x[i]<0) || (x[i]>100)) ||  ((y[i]<0) || (y[i]>100)) || ((h[i]<0) || (h[i]>10e9))) exit(1);
	}

	for (int i = 0; i <= 100; ++i)
	{
		for (int j = 0; j <= 100; ++j)
		{
			l = 0;
			while (h[l] == 0) l++;
			H = h[l] + labs(x[l]-(long)i) + labs(y[l]-(long)j);
			for (int k = 0; k < n; ++k)
			{
				flag = 0;
				H1 = h[k] + labs(x[k]-(long)i) + labs(y[k]-(long)j);
				if (h[k] != 0)
				{
					if (H != H1)
					{
						flag = 1;
						break;
					}
				}else
				{
					if (H > H1)
					{
						flag = 1;
						break;
					}
				}
			}
			if (flag == 0)
			{
				printf("%d %d %ld\n", i, j, H);
				free(x);
				free(y);
				free(h);
				return 0;
			}
		}
	}
	return 0;
}