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CEOI Online Contest - Problems


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Birthday party
Input file: party.in
Output file: party.out
Source code: party.pas/.c/.cpp
100 points
Time limit:
Memory limit:


John's birthday is approaching slowly, and as every year, John is going to organize a great garden party. He wants all his friends to come, but (sadly) he knows, that it is almost impossible. For example Susie left Steve last week, and it will be almost impossible to make both of them come. John spent most of the last week visiting his friends and asking them to come. He got some promises, but even more requests. ('If you invite me, you just have to invite my boyfriend!' exclaimed Veronica. 'If you invite the Burdiliak twins, don't expect me or Joseph to come!' stated Peter.) Suddenly, John realized, that it will be quite hard just to satisfy all the requests he got.

Task

You are given a description of the requests John got from his friends. Your task is to find a group of people such that if John invites the people in this group (and nobody else) to his party, all the requests he got will be satisfied. The requests are described in the following way:

Input description

You can find ten input files, called party1.in to party10.in on the web page. Each of the inputs is worth 10 points.

On the first line of the input file is the number of John's friends F, next F lines contain their names, one per line. On the next line is the number of requests N. Each of the following N lines contains one request.

Output description

For each file partyX.in you have to produce the corresponding output file partyX.out, containing one correct solution. The first line of the output file will be the number K of people John should invite. The following K lines should contain their names, one per line. You may assume that each of the input files has a (not necessarily unique) solution. If there are more possible solutions, you may output any of them.

Submits

Submit the files party*.out using the web interface in the same way you submit your programs for the other tasks.

Example

Input:
3
veronica
steve
dick
3
(veronica => dick)
(steve => -veronica)
(steve & dick)
Output:
2
steve
dick