sub step {
    my ($dir, $r, $c) = @_;
    if ($dir == N)     {return (--$r, $c)}
    elsif ($dir == NE) {return (--$r, ++$c)}
    elsif ($dir == E)  {return ($r, ++$c)}
    elsif ($dir == SE) {return (++$r, ++$c)}
    elsif ($dir == S)  {return (++$r, $c)}
    elsif ($dir == SW) {return (++$r, --$c)}
    elsif ($dir == W)  {return ($r, --$c)}
    elsif ($dir == NW) {return (--$r, --$c)}
    else {
        die "Inside 'step': invalid param\n"
    }
}