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::{fastout, input, marker::Usize1};
#[fastout]
fn main() {
    input!(n: usize, m: usize, ab: [[Usize1; 2]; m]);

    let mut unionf = UnionFind::new(n);
    for v in ab {
        unionf.unite(v[0], v[1]);
    }

    println!("{}", (0..n).map(|x| unionf.size(x)).max().unwrap());
}

#[derive(Debug, Clone)]
enum Node {
    Root(usize),
    Child(usize),
}
#[derive(Clone, Debug)]
pub struct UnionFind {
    uf: Vec<Node>,
}

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

    pub fn root(&mut self, target: usize) -> usize {
        match self.uf[target] {
            Node::Root(_) => target,
            Node::Child(par) => {
                let root = self.root(par);
                self.uf[target] = Node::Child(self.root(par));
                root
            }
        }
    }
    pub fn unite(&mut self, x: usize, y: usize) -> bool {
        let rx = self.root(x);
        let ry = self.root(y);
        if rx == ry {
            return false;
        }
        let size_x = self.size(x);
        let size_y = self.size(y);

        let (i, j) = if size_x > size_y { (rx, ry) } else { (ry, rx) };
        self.uf[i] = Node::Root(size_x + size_y);
        self.uf[j] = Node::Child(i);

        true
    }
    pub fn is_same(&mut self, x: usize, y: usize) -> bool {
        self.root(x) == self.root(y)
    }
    pub fn size(&mut self, x: usize) -> usize {
        let root = self.root(x);
        match self.uf[root] {
            Node::Root(size) => size,
            Node::Child(_) => 0,
        }
    }
}