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, fastout};
use proconio::marker::Usize1;
use std::collections::HashSet;

pub struct GraphL {
    g: Vec<HashSet<usize>>,
    n: usize,
}
impl GraphL {
    pub fn dfs(&self, s: usize) -> usize {
        let mut stack = Vec::new();
        let mut visit = vec![false; self.n];
        stack.push(s);
        let mut res = 0;
        let mut depth = 1;
        while let Some(&u) = stack.last() {
            visit[u] = true;
            let v = self.g[u].iter().find(|&i| !visit[*i]);
            if let Some(v) = v {
                stack.push(*v);
                depth += 1;
            } else {
                stack.pop();
                res = std::cmp::max(res, depth);
                depth = 0;
            }
        }
        res
    }
}

#[fastout]
fn main() {
    input! {
        n: usize,
        m: usize,
        v: [(Usize1,Usize1);m]
    }
    let mut g = vec![HashSet::new();n];
    for (a,b) in v {
        g[a].insert(b);
        g[b].insert(a);
    }
    let g = GraphL {
        g, n,
    };
    let mut res = 0;
    for i in 0..n {
        res = std::cmp::max(res, g.dfs(i))
    }
    println!("{}", res);
}