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: Accepted)

<?php

fscanf(STDIN, "%d", $n);
$H = []; $X = []; $Y = [];
for ($i = 0; $i < $n; ++$i) {
    fscanf(STDIN, "%d %d %d", $x, $y, $h);
    $X[] = $x; $Y[] = $y; $H[] = $h;
}

$ans;
for ($cx = 0; $cx <= 100; ++$cx) {
    for ($cy = 0; $cy <= 100; ++$cy) {

        // Hが0になるパターンも含んで列挙する
        $tmp = [];
        for ($i = 0; $i < $n; ++$i) {
            $tmp[] = $H[$i] + abs($X[$i] - $cx) + abs($Y[$i] - $cy);
        }
        $tmp = array_unique($tmp);

        // Hが0になっていないことを検証する
        foreach ($tmp as $hh) {
            // $hh: Hの候補
            $flg = true;
            for ($i = 0; $i < $n; ++$i) {

$tmax = max($hh - abs($X[$i] - $cx) - abs($Y[$i] - $cy), 0);

/* echo "tmax: $tmax, hh: $hh", PHP_EOL; */

                if ($tmax != $H[$i]) {
                    $flg = false;
                    break;
                }
            }
            if ($flg) {
                $ans = $hh;
/* echo "cx: $cx, cy: $cy, arr: " . implode(' ', $tmp), PHP_EOL; */
                break 3;
            }
        }

    }
}

echo sprintf("%d %d %d\n", $cx, $cy, $ans);