URI Online Judge | 3012
# Algorithm Teaching

**Timelimit: 6**

By Brazil

The Latin American Beginners Regional Contest is coming, and the University of Byteland wants to prepare a team of newly-admitted students to compete. The university has **N** teachers that can instruct students in the topic of algorithms. Each candidate student must be trained by a single teacher, in a non-empty subset of the algorithms that the teacher knows. For example, if a given teacher knows the two algorithms **PRIM** and **KRUSKAL**, then the teacher can train a student just on **PRIM**, just on** KRUSKAL**, or on both** PRIM** and **KRUSKAL**. As you can see, in this case there are three different options for this particular teacher to train a student. In general, a given teacher that knows **A** different algorithms can train a student in **2 ^{A}**

The university would like to form a team having as many students as possible. However, each pair of students in the final team must be able to cooperate, which means that each one of them must have been trained on an algorithm that the other hasn’t. For example, a student trained on

because the first student is trained on

Given the set of algorithms that each teacher knows, you must determine the maximum number of students in a team in which every student can cooperate with each other. Recall that each student must be trained by a single teacher, while each teacher can train as many students as needed. For example, if there is just one teacher who knows the algorithms

The first line contains an integer **N (1 ≤ N ≤ 100)** indicating the number of teachers. Each of the next **N** lines describes a teacher with an integer **A (1 ≤ A ≤ 10)** representing the number of algorithms the teacher knows, followed by **A** different non-empty strings of at most **10** uppercase letters each, indicating the names of the algorithms that teacher knows.

Output a single line with an integer indicating the maximum number of students in a team in which every student can cooperate with each other.

Input Samples | Output Samples |

1 |
3 |

2 |
8 |

4 |
10 |