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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

#!/usr/bin/perl
my ($n) = map { $_ - 0 } split(/\s+/,<STDIN>);
my @d=();
for(my $i=0;$i<$n;$i++){
  my @a = map { $_ - 0 } split(/\s+/,<STDIN>);
  push(@a,0);
  push(@d,\@a);
}
my @dd = sort { $b->[2] <=> $a->[2] } @d;
my $x = $dd[0]->[0];
my $y = $dd[0]->[1];
my @mx = (@{$dd[0]});

my $h = $mx[2] + abs($mx[0] - $x) + abs($mx[1] - $y);
for(my $i=0;$i<$n;$i++){
  $dd[$i]->[3] = abs( $dd[$i]->[2] - &l_h($x,$y,$h,@dd[$i]) );
}

while(1){
  my $chk = 1;
  my $er = dif($x,$y);
  last if $er==0;
  if( $x>0 ){
    if(chk($x-1,$y)){
      $x--;
      next;
    }
  }
  if( $y>0 ){
    if(chk($x,$y-1)){
      $y--;
      next;
    }
  }
  if( $x<100 ){
    if(chk($x+1,$y)){
      $x++;
      next;
    }
  }
  if( $y<100 ){
    if(chk($x,$y+1)){
      $y++;
      next;
    }
  }
}
my $di = $mx[2] + abs($mx[0] - $x) + abs($mx[1] - $y) ;
print "$x $y $di\n";

exit(0);


sub dif {
  my $x = shift;
  my $y = shift;
  my $h = $mx[2] + abs($mx[0] - $x) + abs($mx[1] - $y) ;
  my $er = 0;
  for(my $i=0;$i<$n;$i++){
    $er += abs($dd[$i]->[2] - &l_h($x,$y,$h,$dd[$i]));
  }
  return $er;
}

sub chk {
  my $x = shift;
  my $y = shift;
  my $h = $mx[2] + abs($mx[0] - $x) + abs($mx[1] - $y) ;
  my $rc = 1;
  for(my $i=0;$i<$n;$i++){
    if( $dd[$i]->[3] < abs($dd[$i]->[2] - &l_h($x,$y,$h,$dd[$i])) ){
      $rc = undef;
      last;
    }
  }
  if( $rc ){
    for(my $i=0;$i<$n;$i++){
      $dd[$i]->[3] = abs( $dd[$i]->[2] - &l_h($x,$y,$h,$dd[$i]) );
    }
  }
  return $rc;
}

sub l_h {
  my $x = shift;
  my $y = shift;
  my $h = shift;
  my $r = shift;
  my $k = $h - ( abs($r->[0] - $x) + abs($r->[1] - $y) );
  $k = 0 if $k<0;
  return $k;
}