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::marker::*;
use proconio::*;
use std::cmp::max;
use std::cmp::min;

#[derive(Copy, Clone, Debug)]
struct Node {
    g: usize,
    p: usize,
}

fn main() {
    input! {
        n: usize,
        m: usize,
        ab: [(Usize1, Usize1); m],
    };
    let mut par = Vec::with_capacity(m);
    let mut counts = vec![1; n];

    for i in 0..n {
        par.push(i);
    }

    for &(a, b) in &ab {
        unite(min(a, b), max(a, b), &mut par, &mut counts);
    }

    let mut ans = 0;

    for i in 0..n {
        ans = max(ans, counts[i]);
    }

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

fn find(i: usize, p: &mut Vec<usize>, counts: &mut Vec<usize>) -> usize {
    if p[i] == i {
        return i;
    }

    p[i] = find(p[i], p, counts);
    p[i]
}

fn unite(i: usize, j: usize, p: &mut Vec<usize>, counts: &mut Vec<usize>) {
    let x = find(i, p, counts);
    let y = find(j, p, counts);

    if x == y {
        return;
    }
    counts[i] += counts[j];
    counts[j] = 0;
    p[y] = x;
}

fn same(i: usize, j: usize, p: &mut Vec<usize>, counts: &mut Vec<usize>) -> bool {
    find(i, p, counts) == find(j, p, counts)
}