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

fscanf(STDIN, "%d", $A);

//$map = array_fil(0, 100, array_fill(0, 100, -1));
$max_p =0;
while($A--){

    fscanf(STDIN, "%d%d%d", $x, $y, $p);
    $map[$x][$y] = $p;
    $max_p = max($max_p, $p);

    if($max_p == $p){
        $max_x = $x;
        $max_y = $y;
    }

}

for($hx = 0; $hx<=100; $hx++){
    for($hy =0;$hy<=100;$hy++){
        if(isset($map[$hx][$hy])){
            $height = $map[$hx][$hy];
        }else{
            $height = -1;
        }
        $k = 1;
        foreach($map as $x => $ydata){
            foreach($ydata as $y => $p){
                if($height == -1){
                    $height = $max_p + abs($hx - $max_x) + abs($hy - $max_y);
//                    if($max_p == 0){
//                        $height = 1;
//                    }
                    if($height > 1000000000){
                        $k = 0;
                        break 2;
                    }
                }
                if (($height != $p + abs($hx - $x) + abs($hy - $y) || $height < $p)) {
                    if($p == 0 && $height - abs($hx-$x) - abs($hy - $y) < 0) {
                        continue;
                    }
                    $k = 0;
                    break 2;
                }

            }
        }
        if($k == 1) {
            echo $hx . " " . $hy . " " . $height;
            exit;
        }
    }
}