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(unused_imports)]
use std::io::*;
#[allow(unused_imports)]
use std::str::*;
#[allow(unused_imports)]
use std::mem::*;
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::HashMap;
#[allow(unused_imports)]
use std::collections::VecDeque;
#[allow(unused_imports)]
use std::usize;

#[allow(unused_macros)]
macro_rules! read_cols {
    ($($t:ty),+) => {{
        let mut line = String::new();
        stdin().read_line(&mut line).unwrap();

        let mut it = line.trim()
            .split_whitespace();

        ($(
            it.next().unwrap().parse::<$t>().ok().unwrap()
        ),+)
    }}
}

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let mut line = String::new();
    stdin().read_line(&mut line).unwrap();
    line.trim().to_string().parse().ok().unwrap()
}

#[allow(dead_code)]
fn read_vec<T: FromStr>() -> Vec<T> {
    let mut line = String::new();
    stdin().read_line(&mut line).unwrap();

    line.trim()
        .split_whitespace()
        .map(|s| s.parse().ok().unwrap())
        .collect()
}

fn dfs(adjs: &Vec<Vec<usize>>, g: &mut Vec<bool>, v: usize) -> usize {
    let mut ret = 1;

    g[v] = true;

    for u in &adjs[v] {
        if g[*u] {
            continue
        }

        ret += dfs(adjs, g, *u);
    }

    return ret;
}

fn main() {
    let (n, m) = read_cols!(usize, usize);

    let mut adjs = vec![Vec::new(); n];
    for _ in 0..m {
        let (a, b) = read_cols!(usize, usize);
        adjs[a - 1].push(b - 1);
        adjs[b - 1].push(a - 1);
    }

    let mut ans = 0;
    let mut g = vec![false; n];
    for i in 0..n {
        if !g[i] {
            ans = max(ans, dfs(&adjs, &mut g, i));
        }
    }

    println!("{}", ans);
}