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::{cmp::Reverse, collections::*};

#[allow(unused_imports)]
use proconio::{
    fastout, input,
    marker::{Chars, Usize1},
};

#[allow(unused_imports)]
use itertools::Itertools;

#[allow(unused_imports)]
use num::Integer;

#[fastout]
pub fn main() {
    input! {
        n: usize, m: usize,
        p: [(Usize1, Usize1); m],
    }
    let mut ids: Vec<_> = (0..n).collect();
    let mut c_ids: Vec<_> = (0..n)
        .map(|i| {
            let mut t = HashSet::new();
            t.insert(i);
            t
        })
        .collect();
    for (a, b) in p {
        if ids[a] != ids[b] {
            let aid = ids[a];
            let bid = ids[b];
            if c_ids[aid].len() < c_ids[bid].len() {
                let is = c_ids[aid].clone();
                is.iter().for_each(|&i| {
                    ids[i] = bid;
                    c_ids[bid].insert(i);
                });
                c_ids[aid].clear();
            } else {
                let is = c_ids[bid].clone();
                is.iter().for_each(|&i| {
                    ids[i] = aid;
                    c_ids[aid].insert(i);
                });
                c_ids[bid].clear();
            }
        }
    }
    let mut count = HashMap::new();
    ids.iter().for_each(|&id| {
        *count.entry(id).or_insert(0) += 1;
    });
    println!("{}", count.values().max().unwrap());
}