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)

use proconio::input;
use proconio::marker::Usize1;
use std::collections::BTreeSet;

fn main() {
    input! {
        n: usize,
        m: usize,
        edges: [(Usize1, Usize1); m], // グラフのエッジを読み込む. Usize1 は 1-origin to 0-origin変換を行う
    }

    let graph = {
        let mut graph = vec![Vec::new(); n];
        for &(u, v) in &edges {
            graph[u].push(v);
            graph[v].push(u)
        }
        graph
    };

    let mut arrived = vec![false; n];

    let mut vec = Vec::new();
    for i in 0..n {
        if !arrived[i] {
            let mut stack = Vec::new();
            stack.push(i);
            let mut set = BTreeSet::new();
            while let Some(j) = stack.pop() {
                arrived[j] = true;
                set.insert(j);
                for &k in graph[j].iter().filter(|&&k| !arrived[k]) {
                    stack.push(k);
                }
            }
            vec.push(set);
        }
    }

    println!("{}", vec.iter().map(|x| x.len()).max().unwrap())
}