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)

#![allow(unused_imports)]
#![allow(unused_variables)]
#![allow(dead_code)]
use proconio::input;
use proconio::marker::*;
use std::cmp::{min, max};
use std::collections::{HashSet, HashMap, BinaryHeap};

struct UnionFind{
    n: usize,
    parent: Vec<usize>,
    size: Vec<usize>,
}

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

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

    fn unite(&mut self, x: usize, y: usize){
        let a = self.root(x);
        let b = self.root(y);
        if a == b{
            return;
        }
        if self.size[a] <= self.size[b]{
            self.parent[b] = a;
            self.size[a] += self.size[b];
        }else{
            self.parent[a] = b;
            self.size[b] += self.size[a];
        }
    }

    fn is_same(&mut self, x: usize, y: usize) -> bool{
        self.root(x) == self.root(y)
    }

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

fn main() {
    input! {
        n: usize,
        m: usize,
        ab: [(Usize1, Usize1); m],
    }
    let mut uf = UnionFind::new(n);

    for i in 0..m{
        let t = ab[i];
        uf.unite(t.0, t.1);
    }
    let mut ans = 0;
    for i in 0..n {
        ans = max(ans, uf.get_size(i));
    }
    let ans = (0..n).map(|i| uf.get_size(i)).max().unwrap();
    println!("{}", ans);
}