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)

use proconio::input;
use proconio::marker::Usize1;

fn main() {
    input! {
        n: usize,
        m: usize,
        es: [(Usize1, Usize1); m],
    }

    let mut uf = UnionFind::new(n);
    for (u, v) in es {
        uf.unite(u, v);
    }

    let mut res = 0;
    for i in 0..n {
        res = res.max(uf.count(i));
    }

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

pub trait DisjointSet {
    fn new(len: usize) -> Self;
    fn representative(&mut self, id: usize) -> usize;
    fn equivalent(&mut self, lhs: usize, rhs: usize) -> bool {
        self.representative(lhs) == self.representative(rhs)
    }
    fn unite(&mut self, lhs: usize, rhs: usize) -> bool;
    fn count(&mut self, id: usize) -> usize;
}

struct UnionFind {
    par: Vec<usize>,
    size: Vec<usize>,
}

impl DisjointSet for UnionFind {
    fn new(len: usize) -> Self {
        Self {
            par: (0..len).collect(),
            size: vec![1; len],
        }
    }
    fn representative(&mut self, id: usize) -> usize {
        if self.par[id] != id {
            self.par[id] = self.representative(self.par[id])
        }
        self.par[id]
    }
    fn unite(&mut self, lhs: usize, rhs: usize) -> bool {
        let mut lhs = self.representative(lhs);
        let mut rhs = self.representative(rhs);
        if lhs == rhs {
            return false;
        }
        if self.size[lhs] > self.size[rhs] {
            std::mem::swap(&mut lhs, &mut rhs);
        }
        self.size[rhs] += self.size[lhs];
        self.par[lhs] = rhs;
        true
    }
    fn count(&mut self, id: usize) -> usize {
        let id = self.representative(id);
        self.size[id]
    }
}