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: Time Limit Exceeded)

use proconio::{input};

#[derive(Debug, Clone)]
struct UnionFind {
    vec: Vec<Node>
}

#[derive(Debug, Copy, Clone)]
enum Node {
    Root(u32),
    Vertex(usize),
}

impl UnionFind {
    fn new(n: usize) -> Self {
        UnionFind{
            vec: vec![Node::Root(1); n]
        }
    }

    fn root(&self, x: usize) -> usize {
        match self.vec[x] {
            Node::Root(_) => x,
            Node::Vertex(parent) => self.root(parent),
        }
    }

    fn unite(&mut self, x: usize, y: usize) -> bool {
        let (rx, ry) = (self.root(x), self.root(y));
        if rx == ry {
            return false;
        }
        if let (Node::Root(x_root_size), Node::Root(y_root_size)) = (self.vec[rx], self.vec[ry]) {
            if x_root_size > y_root_size {
                self.vec[ry] = Node::Root(x_root_size + y_root_size);
                self.vec[rx] = Node::Vertex(ry);
            } else {
                self.vec[rx] = Node::Root(x_root_size + y_root_size);
                self.vec[ry] = Node::Vertex(rx); 
            }
            return true;
        } else {
            unreachable!();
        }
    }

    fn size(&self, x: usize) -> u32 {
        if let Node::Root(s) = self.vec[self.root(x)] {
            return s;
        } else {
            unreachable!();
        }
    }
}
 
fn main() {
    input! {
        n: usize,
        m: usize,
        t: [(usize, usize); m],
    }
 
    let mut uf = UnionFind::new(n);
 
    for (a, b) in t {
        uf.unite(a-1, b-1);
    }
    
    println!("{}", (0..n).map(|x| uf.size(x)).max().unwrap());
}