# Problem K

Is-A? Has-A? Who Knowz-A?

Two familiar concepts in object oriented programming are the
is-a and has-a relationships. Given two classes A and B, we say
that A is-a B if A is a subclass of B; we say A has-a B if one
of the fields of A is of type B. For example, we could imagine
an object-oriented language (call it ICPC++) with code like
that in Figure 1, where the class `Day` is-a
`Time`, the class `Appointment` is both a `DateBook`
and a `Reminder`, and class `Appointment` has-a `Day`.

class Day extends Time class Appointment extends Datebook, Reminder { { ... private Day date; } ... }

These two relationships are transitive. For example if A
is-a B and B is-a C then it follows that A is-a C. This holds
as well if we change all the is-a’s in the last sentence to
has-a’s. It also works with combinations of is-a’s and has-a’s:
in the example above, `Appointment` has-a
`Time`, since it has-a `Day` and `Day` is-a `Time`. Similarly, if class `DateBook` has-a `Year` then
`Appointment` has-a `Year`,
since `Appointment` is-a `DateBook`.

In this problem you will be given a set of is-a and has-a relationships and a set of queries of the form A is/has-a B. You must determine if each query is true or false.

## Input:

Input starts with two integers $n$ and $m$, ($1 \leq n,m \leq 10\, 000$), where $n$ specifies the number of given is-a and has-a relationships and $m$ specifies the number of queries. The next $n$ lines each contain one given relationship in the form $c_1$ $r$ $c_2$ where $c_1$ and $c_2$ are single-word class names, and $r$ is either the string “is-a” or “has-a”. Following this are $m$ queries, one per line, using the same format. There will be at most $500$ distinct class names in the $n+m$ lines, and all class names in the last $m$ lines will appear at least once in the initial $n$ lines. All is-a and has-a relationships between the given classes can be deduced from the $n$ given relationships. Is-a relationships can not be circular (apart from the trivial identity “$x$ is-a $x$”).

## Output

For each query, display the query number (starting at one) and whether the query is true or false.

Sample Input 1 | Sample Output 1 |
---|---|

5 5 Day is-a Time Appointment is-a Datebook Appointment is-a Reminder Appointment has-a Day Datebook has-a Year Day is-a Time Time is-a Day Appointment has-a Time Appointment has-a Year Day is-a Day |
Query 1: true Query 2: false Query 3: true Query 4: true Query 5: true |