POTHOLE  Potholers
A team of speleologists organizes a training in the Great Cave of Byte Mountains. During the training each speleologist explores a route from Top Chamber to Bottom Chamber. The speleologists may move down only, i.e. the level of every consecutive chamber on a route should be lower then the previous one. Moreover, each speleologist has to start from Top Chamber through a different corridor and each of them must enter Bottom Chamber using different corridor. The remaining corridors may be traversed by more than one speleologist. How many speleologists can train simultaneously?
Task
Write a program which:
 reads the cave description from the standard input,
 computes the maximal number of speleologists that may train simultaneously,
 writes the result to the standard output.
Input
The number of test cases t is in the first line of input, then t test cases follow separated by an empty line. In the first line of each test case there is one integer n (2<=n<=200), equal to the number of chambers in the cave. The chambers are numbered with integers from 1 to n in descending level order  the chamber of grater number is at the higher level than the chamber of the lower one. (Top Chamber has number 1, and Bottom Chamber has number n). In the following n1lines (i.e. lines 2,3,...,n) the descriptions of corridors are given. The (i+1)th line contains numbers of chambers connected by corridors with the ith chamber. (only chambers with numbers grater then i are mentioned). The first number in a line, m, 0<=m<=(ni+1), is a number of corridors exiting the chamber being described. Then the following m integers are the numbers of the chambers the corridors are leading to.
Output
Your program should write one integer for each test case. This number should be equal to the maximal number of speleologists able to train simultaneously,
Example
Sample input: 1 12 4 3 4 2 5 1 8 2 9 7 2 6 11 1 8 2 9 10 2 10 11 1 12 2 10 12 1 12 1 12 Sample output: 3
The sample input corresponds to the following cave:
hide comments
xamitksx:
20150808 14:08:15
nice Prob... to start on max flows


kanye west:
20141106 09:08:44
i'm getting wrong answer omg


akulsareen:
20140201 19:57:38
My 50th AC and 1st question on flows. Last edit: 20140201 19:58:16 

:p:
20130703 12:01:29
if there is a direct link from 1st chamber to the nth chamber, then that will be considered as a path or not.??


Codeblooded:
20130614 10:38:45
7sseconds?

Added by:  Piotr Łowiec 
Date:  20040913 
Time limit:  7s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  6th Polish Olympiad in Informatics, stage 2 