Smallest Student Set Covering All Clubs

Given a list of students along with the clubs they are members of, your task is to select a smallest subset of students such that the union of their clubs covers all unique clubs.

You will be given the input through stdin in a specified format. In particular, the first line contains an integer n denoting the number of students. For each student, you will receive their name on a separate line, followed by a line containing an integer m (the number of clubs the student belongs to), and then m lines listing the club names. It is guaranteed that n ≥ 1.

Your output should list the selected student names sorted in lexicographical order, each printed on a separate line. If there are several valid answers, outputting any one of them is acceptable; however, for deterministic output, please use the following greedy strategy:

• At each step, choose the student who covers the maximum number of yet uncovered clubs. In the event of a tie, choose the student with the lexicographically smallest name.
• Repeat until all clubs are covered.
• Sort the resulting set of chosen student names in lexicographical order and print them.

This problem is analogous to the classic set cover problem and can be solved using a greedy approach.

inputFormat

The input is given from stdin in the following format:

 n
 name1
 m1
 club1
 club2
 ... (m1 lines)
 name2
 m2
 club1
 club2
 ... (m2 lines)
 ...
 nameN
 mN
 club1
 club2
 ... (mN lines)

Where:

• n is the number of students.
• Each student's information consists of the student's name and the list of clubs they belong to.
• Club names may contain spaces.

outputFormat

The output should be printed to stdout and consist of the names of the selected students, one per line, sorted in lexicographical order.

## sample

5
Alice
2
Math Club
Science Club
Bob
2
Science Club
Drama Club
Charlie
2
Math Club
Drama Club
David
1
Art Club
Eve
2
Art Club
Math Club

Alice
Bob
David

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