#!/usr/bin/perl

# https://codingcompetitions.withgoogle.com/codejam/round/000000000005
+1635/0000000000104e03

use strict;
use warnings;
use List::Util qw( first shuffle );

my $w;
my $case = 0;

for my $row ( 2 .. 20 )    # testing all sizes, needs change to read i
+nput file
  {
  for my $col ( 2 .. 20 )
    {
    $case++;
    if( $row == 2 && $col < 5 || $row < 5 && $col == 2 ||
      $row == 3 && $col == 3)
      {
      print "Case #$case: IMPOSSIBLE\n";                           # h
+ard coded
      next;
      }
    $w = $col;
    my @pylons = 0;                          # first pylon in upper le
+ft corner
    my @empty = shuffle 1 .. $row * $col - 1;
    while( @empty )
      {
      if( my $try = first { ! conflict($pylons[-1], $_) } @empty )
        {
        push @pylons, $try;
        @empty = grep $_ != $try, @empty;
        }
      else
        {
        push @empty, shuffle splice @pylons, 1;                     # 
+reshuffle
        }
      }
    print "Case #$case: POSSIBLE\n";
    # uncomment next line to print grid locations
    #print +(int 1 + $_ / $w) . ' ' . (1 + $_ % $w) . "\n" for @pylons
+;
    }
  }

sub conflict
  {
  my ($x, $y) = @_;
  my ($r, $c, $rr, $cc) = (int $x / $w, $x % $w, int $y / $w, $y % $w)
+;
  $r == $rr || $c == $cc || $r + $c == $rr + $cc || $r - $c == $rr - $
+cc;
  }
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