A Cactus Problem

Points: 15 (partial)

Time limit: 0.6s

Memory limit: 162M

Problem type

Allowed languages

Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, ~~CommonLisp~~, D, Dart, F#, Forth, Fortran, Go, ~~Groovy~~, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, ~~Nim~~, ~~ObjC~~, OCaml, ~~Octave~~, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig

Given a cactus graph, compute the maximum distance between two vertices.

Constraints

$1 \le N \le 5 \cdot 10^4$ ~1 \le N \le 5 \cdot 10^4~

$0 \le M \le 10^4$ ~0 \le M \le 10^4~

$2 \le K_i \le 10^3$ ~2 \le K_i \le 10^3~

Input Specification

The first line contains two space-separated integers, $N$ ~N~ and $M$ ~M~. There are $N$ ~N~ vertices labeled from $1$ ~1~ to $N$ ~N~.

$M$ ~M~ lines follow. Each line starts with an integer $K_i$ ~K_i~, followed by $K_i$ ~K_i~ space-separated integers. Adjacent integers in each line are connected with an edge. The graph is guaranteed to be a connected cactus.

Output Specification

Output the diameter of the graph.

Sample Input

15 3
9 1 2 3 4 5 6 7 8 3
7 2 9 10 11 12 13 10
5 2 14 9 15 10

Sample Output

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