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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php

$input = trim(fgets(STDIN));
$input = explode(" ", $input);
$n_max = (int) $input[0];

$count = 0;
while (true) {
	$input = trim(fgets(STDIN));
	$input = explode(" ", $input);
	$args[$count] = [
		'x' => (int) $input[0],
		'y' => (int) $input[1],
		'h' => (int) $input[2],
	];
	++$count;
	if ($count >= $n_max) {
		break;
	}
}

for ($x=0; $x <= 100 ; $x++) { 
	for ($y=0; $y <= 100 ; $y++) { 
		$ok = true;
		$check_prev = null;
		for ($n=0; $n < $n_max; $n++) { 
			$tmp = $args[$n];
			if ($tmp['h'] === 0) {
				continue;
			}
			$check = abs($x - $tmp['x']) + abs($y - $tmp['y']) + $tmp['h'];
			if (is_null($check_prev)) {
				$check_prev = $check;
			}else{
				if ($check_prev !== $check) {
					$ok = false;
					break;
				}
			}
		}
		if ($ok) {
			echo $x . ' ' . $y . ' ' . $check;
			exit(0);
		}
	}
}