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::{input, fastout, marker::Usize1};
use std::collections::HashMap;

#[derive(Debug)]
struct UnionFind {
    parent: Vec<usize>,
    rank: Vec<usize>,
    size: Vec<usize>,
}

impl UnionFind {
    fn new(n: usize) -> Self {
        let mut p = vec![0; n];
        for (i, v) in p.iter_mut().enumerate() {            
            *v = i;
        }
        Self {
            parent: p,
            rank: vec![0; n],
            size: vec![1; n],
        }
    }

    fn root(&mut self, x: usize) -> usize {
        if x == self.parent[x] {
            x
        } else {
            self.parent[x] = self.root(self.parent[x]);
            self.parent[x]
        }
    }

    fn unite(&mut self, a: usize, b:usize) {
        let ra = self.root(a);
        let rb = self.root(b);
        if self.rank[ra] > self.rank[rb] {
            self.parent[rb] = ra;
            self.size[ra] += self.size[rb];
        } else if self.rank[ra] < self.rank[rb] {
            self.parent[ra] = rb;
            self.size[rb] += self.size[ra];
        } else if ra != rb {
            self.parent[rb] = ra;
            self.size[ra] += self.size[rb];
            self.rank[ra] += 1;
        }
    }

    // fn size (&mut self, x: usize) -> usize {
    //     let rx = self.root(x);
    //     self.size[rx]
    // }

    // fn same(&mut self, a: usize, b: usize) -> bool {
    //     self.root(a) == self.root(b)
    // }

}

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

    let mut uf = UnionFind::new(n);
    for (a, b) in ab {
        uf.unite(a, b);
    }

    let mut map = HashMap::new();

    for i in 0..n {
        *map.entry(uf.parent[i]).or_insert(0) += 1;
    }

    let ans = map.iter().map(|(_, &val)| val).max().unwrap();

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