Selecting Problems

The college of computer & software is going to hold an ACM contest. N (0<N<=1000) students have registered for the contest, and the teacher LCY has thought up M (0<M<=15) problems numbered from 1 to M. LCY is so familiar with the students that he can forecast the result of every student for the M problems.
Now he will select as many problems as possible from the M problems. And he want at least K (0<=K<=M) students to solve all problems. Will you compute the maximum number of problems he can choose? Output "0" if there is no selection can satisfy the condition.

First line of each case contains three integers: N, M and K. Then N lines follow, and each line has the format:
Name P N1 N2 … NP.
Name (the length won't exceed 20), P (number of problems he/she can solve, 0<=P<=M), then P integers (represent the problems, 1-based).

Output the maximum number of problems.

2 6 2
zl1 6 1 2 3 4 5 6
zl2 5 1 2 3 4 5
2 3 2
zl1 2 2 3
zl2 1 1

5
0

HDU 2009-4 Programming Contest