Problems and Programmers

A group of N teachers are assigned to solve M programming problems in a teacher professional development program. Every teacher chooses the problems he can solve. Since teachers are always busy, they want to make a possible smallest team to solve the given problems. What is the size of the smallest team that can solve all the problems?

Input specification
The first line of the input contains two integers N (1 ≤ N ≤ 20) and M (1 ≤ M ≤100). Each of the following N lines denotes the problems a teacher can solve with a set of K+1 integers. The first integer (K) is the number of the problems and the following K numbers are the problem IDs.

Output specification
The output contains a single integer that is number of the teachers in the smallest team. If it is not possible to solve all the problems, print the word "impossible".