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## 문제

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 E.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;
}                                 ...
}

Figure E.1: Two ICPC++ classes.

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.

## 입력

Input starts with two integers n and m, (1 ≤ n, m ≤ 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 c1 r c2 where c1 and c2 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”).

## 출력

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

## 예제 입력 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


## 예제 출력 1

Query 1: true
Query 2: false
Query 3: true
Query 4: true
Query 5: true