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: Wrong Answer)

use proconio::{input};

fn main() {
    input! {
        n: usize,
        m: usize,
        t: [(usize, usize); m],
    }

    let mut belonging: Vec<Option<usize>> = vec!(None; n+1);
    let mut group: Vec<Vec<usize>> = Vec::new();

    for (a, b) in t {
        if belonging[a] == None && belonging[b] == None {
            let groupnum = group.len();
            group.push(vec![a, b]);
            belonging[a] = Some(groupnum);
            belonging[b] = Some(groupnum);
        } else if belonging[a] == None {
            belonging[a] = belonging[b];
            group[belonging[b].unwrap()].push(a);
        } else if belonging[b] == None {
            belonging[b] = belonging[a];
            group[belonging[a].unwrap()].push(b);
        } else if belonging[a] != belonging[b] {
            let merged_group = belonging[a].unwrap();
            let deleted_group = belonging[b].unwrap();
            for i in &group[deleted_group] {
                belonging[*i] = belonging[a];
            }
            let mut clonedb = group[deleted_group].clone();
            group[merged_group].append(&mut clonedb);
            group[deleted_group] = Vec::new();
        }
    }

    
    let mut answer = 0;
    for g in group {
        if answer < g.len() {
            answer = g.len();
        }
    }
    println!("{:?}", answer);
}