Speleology

A team of speleologists holds a training session in the Great Cave of the Byte Mountains. During the training, each speleologist explores one route from the Top Chamber to the Bottom Chamber. A speleologist may move downward only: every chamber along a route must lie strictly below the previous one.

In addition, each speleologist must leave the Top Chamber through a different corridor, and each of them must enter the Bottom Chamber through a different corridor. The corridors in between may be used by more than one speleologist. What is the maximum number of speleologists that can train at the same time?

Write a program that:

• reads the description of the cave from standard input,
• computes the maximum number of speleologists that can train simultaneously,
• writes the result to standard output.

The first line contains one integer $n$ ($2 \le n \le 200$), the number of chambers in the cave. The chambers are numbered from $1$ to $n$ from top to bottom: a chamber with a larger number lies lower (at a lower level), the Top Chamber is number $1$, and the Bottom Chamber is number $n$. Every corridor always leads from a lower-numbered chamber to a higher-numbered one, that is, downward.

Each of the next $n-1$ lines (lines $2$ through $n$) describes one chamber: line $i+1$ describes chamber $i$. It begins with an integer $m$ ($0 \le m \le n-i+1$), the number of corridors leaving chamber $i$, followed by the numbers of the $m$ chambers those corridors lead to. All of these numbers are greater than $i$.

Print a single integer on one line: the maximum number of speleologists that can train simultaneously.