Problem:
Score : 400 points

Problem Statement

There are N persons called Person 1 through Person N.

You are given M facts that "Person A_i and Person B_i are friends." The same fact may be given multiple times.

If X and Y are friends, and Y and Z are friends, then X and Z are also friends. There is no friendship that cannot be derived from the M given facts.

Takahashi the evil wants to divide the N persons into some number of groups so that every person has no friend in his/her group.

At least how many groups does he need to make?

Constraints

2 \leq N \leq 2\times 10^5

0 \leq M \leq 2\times 10^5

1\leq A_i,B_i\leq N

A_i \neq B_i

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
\vdots
A_M B_M

Output

Print the answer.

Sample Input 1

5 3
1 2
3 4
5 1

Sample Output 1

3

Dividing them into three groups such as \{1,3\}, \{2,4\}, and \{5\} achieves the goal.

Sample Input 2

4 10
1 2
2 1
1 2
2 1
1 2
1 3
1 4
2 3
2 4
3 4

Sample Output 2

4

Sample Input 3

10 4
3 1
4 1
5 9
2 6

Sample Output 3

3

Solution in Rust (1.42.0) (judge verdict: Accepted)

#![allow(
  non_snake_case,
  unused_variables,
  unused_assignments,
  unused_mut,
  unused_imports,
  dead_code,
  unused_macros
)]
//use proconio::fastout;
use proconio::input;
use proconio::marker::*;
//use std::collections::HashSet;
use petgraph::unionfind::UnionFind;
use std::cmp::*;
use std::collections::*;
macro_rules! debug {
  ($($a:expr),* $(,)*) => {
      #[cfg(debug_assertions)]
      eprintln!(concat!($("| ", stringify!($a), "={:?} "),*, "|"), $(&$a),*);
  };
}
fn main() {
  input! {
     N:usize,
     M:usize,
     AB:[(Usize1, Usize1);M]
  }

  let mut t: UnionFind<usize> = UnionFind::new(N);
  for &(a, b) in AB.iter() {
    t.union(a, b);
  }
  let mut tops = vec![0; N];
  for i in 0..N {
    tops[t.find(i)] += 1;
  }
  let mut ans = 0;
  for i in 0..N {
    ans = max(ans, tops[i]);
  }
  println!("{}", ans);
}