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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use proconio::marker::*;
use proconio::{fastout, input};
use std::collections::HashSet;

#[fastout]
fn main() {
    input! {
        n: usize,
        m: usize,
        ar: [(Usize1, Usize1); m],
    }
    let mut ar = ar;
    let res = solve(n, &mut ar);
    println!("{}", res)
}

fn solve(n: usize, ar: &mut [(usize, usize)]) -> usize {
    let mut friends = vec![None; n];
    ar.sort_by(|a, b| a.0.partial_cmp(&b.0).unwrap());
    for a in ar {
        let min = std::cmp::min(a.0, a.1);
        let max = std::cmp::max(a.0, a.1);
        if let Some(pi) = friends[max] {
            if min != pi {
                friends[min] = Some(pi);
            }
            continue;
        }
        let i = {
            let mut t = min;
            loop {
                if let Some(n) = friends[t] {
                    t = n;
                } else {
                    break;
                }
            }
            t
        };
        if max != i {
            friends[max] = Some(i);
        }
    }

    let mut group = vec![1; n];
    for p in friends {
        if let Some(pi) = p {
            group[pi] += 1;
        }
    }

    return group.into_iter().max().unwrap();
}