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 vec = vec!(20001; n);
    let mut group: Vec<Vec<usize>> = vec![Vec::new()];
    let mut groupnum = 0;

    for (a, b) in t {
        if vec[a-1] == 20001 && vec[b-1] == 20001 {
            group[groupnum].push(a);
            group[groupnum].push(b);
            vec[a-1] = groupnum;
            vec[b-1] = groupnum;
            groupnum += 1;
            group.push(Vec::new());
        } else {
            if vec[a-1] == 20001 {
                vec[a-1] = vec[b-1];
                group[vec[b-1]].push(a);
            } else if vec[b-1] == 20001 {
                vec[b-1] = vec[a-1];
                group[vec[a-1]].push(b);
            } else if vec[a-1] == vec[b-1] {
                
            } else {
                let mut clonedb = group[vec[b-1]].clone();
                group[vec[a-1]].append(&mut clonedb);
                group[vec[b-1]] = Vec::new();
                for i in &group[vec[b-1]] {
                    vec[*i] = vec[a-1];
                }
            }
        }
    }

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