sub reachable {
    my ($links, $start, $dest) = @_;
    return 1 if $start eq $dest;
    foreach (keys %{ $links->{$start} }) {
        return 1 if reachable($links, $_, $dest);
    }
    return 0;
}

my %next;
my %prev;
my $ptr;
while(<DATA>) {
    chomp;
    if ($_ eq 'Start') {
        undef $ptr;
        next;
    }

    if (defined $ptr) {
        if (! $next{$ptr}{$_}) {
            for my $parent (keys %{ $prev{$_} }) {
                if (reachable(\%prev, $ptr, $parent)) {
                    delete $prev{$_}{$parent};
                }
            }
            for my $child  (keys %{ $next{$_} }) {
                if (reachable(\%next, $ptr, $child)) {
                    delete $next{$_}{$child};
                }
            }
            $next{$ptr}{$_} = 1;
            $prev{$_}{$ptr} = 1;
        }
    }

    $ptr = $_;
}