Assigning Work with Penalty Points

Kangho's company has $N$ employees and $M$ jobs to finish. Employees are numbered 1 to $N$, and jobs are numbered 1 to $M$.

Each employee has a fixed list of jobs they can do. Every job is handled by exactly one person, and an employee normally takes only one job from that list. An employee who received $X$ penalty points last month takes at most $X+1$ jobs.

Suppose there are three employees, and last month Minho (employee 1) received 2 points, Jaepil (employee 2) received 1 point, and Juhyun (employee 3) received 0 points. Then Minho takes at most 3 jobs, Jaepil at most 2 jobs, and Juhyun at most 1 job.

No employee knows their own score. Only $K$, the sum of the penalty points over all employees, is known. Kangho uses that: he splits the $K$ points among the employees however he likes, so that as many jobs as possible get done. The points given to one employee form a non-negative integer, and the points sum to exactly $K$.

For example, employee 1 can do jobs 1, 2, 3, 4, 5, employees 2, 3, and 4 can do only job 1, and employee 5 can do jobs 1 and 5. With $K = 2$, giving 1 point to employee 1 and 1 point to employee 5 gets four jobs done. Giving both points to employee 1 instead lets employee 1 take three jobs, so employee 1 takes jobs 2, 3, 4, employee 2 takes job 1, and employee 5 takes job 5, which finishes all five.

Given the job list of every employee and the penalty sum $K$, write a program that finds how many of the $M$ jobs can be done at most.

The first line contains the number of employees $N$, the number of jobs $M$, and the penalty sum $K$, separated by spaces. ($1 \le N, M \le 1000$, $1 \le K \le N$)

Each of the next $N$ lines describes one employee. Line $i$ contains the number of jobs employee $i$ can do, followed by those job numbers, separated by spaces. The count is between 0 and $M$, and no number appears twice on the same line.

Print the largest number of jobs Kangho's company can finish.