Breaking Into Atoms

Problem code: ATOMS

All submissions for this problem are available.

Let X be the set of all integers between 0 and n-1. Suppose we have a collection S1, S2, ..., Sm of subsets of X. Say an atom A is a subset of X such that for each Si we have either A is a subset of Si or A and Si do not have any common elements.

Your task is to find a collection A1, ..., Ak of atoms such that every item in X is in some Ai and no two Ai, Aj with i ? j share a common item. Surely such a collection exists as we could create a single set {x} for each x in X. A more interesting question is to minimize k, the number of atoms.

Input

The first line contains a single positive integer t ? 30 indicating the number of test cases. Each test case begins with two integers n,m where n is the size of X and m is the number of sets Si. Then m lines follow where the i'th such line begins with an integer vi between 1 and n (inclusive) indicating the size of Si. Following this are vi distinct integers between 0 and n-1 that describe the contents of Si.

You are guaranteed that 1 ? n ? 100 and 1 ? m ? 30. Furthermore, each number between 0 and n-1 will appear in at least one set Si.

Output

For each test case you are to output a single integer indicating the minimum number of atoms that X can be partitioned into to satisfy the constraints.

Example

Input:
2
5 2
3 0 1 2
3 2 3 4
4 3
2 0 1
2 1 2
2 2 3

Output:
3
4

Author: friggstad
Date Added: 30-01-2011
Time Limit: 5 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, F#, FORT, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TCL, TEXT, WSPC


Comments

Hello to all, i need codes

mastermind6 @ 28 Mar 2011 07:43 AM

Hello to all, i need codes for thise problem using java language, before march 31, 2011... tnx a lot..

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