sub illuminate{
    my $centre_row = shift;
    my $centre_col = shift;
    my $radius     = shift;
    my $insq       = int ($radius / sqrt (2));
    my @ans;

    # inner square
    for my $i ($centre_row - $insq .. $centre_row + $insq) {
        for my $j ($centre_col - $insq .. $centre_col + $insq) {
            push @ans, [$i, $j];
        }
    }

    # outer square
    my $r2 = $radius * $radius;
    for my $i (0 .. $radius) {
        for my $j (0 .. $radius) {
            # Skip already-done inner square
            next if $i < $insq and $j < $insq;
            if ($i * $i + $j * $j < $r2) {
                push @ans,
                    [$centre_row + $i, $centre_col + $j],
                    [$centre_row - $i, $centre_col + $j],
                    [$centre_row + $i, $centre_col - $j],
                    [$centre_row - $i, $centre_col - $j];
            }
        }
    }
    return @ans;
}