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(dead_code)]
use proconio::input;
use proconio::fastout;
#[macro_use] extern crate text_io;
use proconio::marker::*;
use std::mem::*;
use std::collections::*;
use std::cmp::*;

struct UF{
    par:Vec<usize>,
    rank:Vec<usize>,
}
impl UF{
    fn new(n:usize)->UF{
        let mut v=vec![0;n];
        for i in 0..n{
            v[i]=i;
        }
        UF{
            par:v,
            rank:vec![1;n],
        }
    }
    fn root(&mut self,x:usize)->usize{
        if x==self.par[x]{
            x
        }else{
            let par=self.par[x];
            let res=self.root(par);
            self.par[x]=res;
            res
        }
    }
    fn same(&mut self,a:usize,b:usize)->bool{
        self.root(a)==self.root(b)
    }
    fn unite(&mut self,a:usize,b:usize)->bool{
        let ap=self.root(a);
        let bp=self.root(b);
        if ap==bp{
            return false;
        }
        if self.rank[ap]<self.rank[bp]{
            self.par[bp]=ap;
            self.rank[ap]+=self.rank[bp];
        }else{
            self.par[ap]=bp;
            self.rank[bp]+=self.rank[ap];
        }
        return true;
    }
    fn size(&mut self,a:usize)->usize{
        let ap=self.root(a);
        self.rank[ap]
    }
}
#[fastout]
fn main() {
    input!{
        n:usize,
        m:usize,
        mut v:[[usize;2];m],
    }
    let mut uf:UF=UF::new(n);
    for e in v{
        uf.unite(e[0]-1,e[1]-1);
    }
    let mut ans:usize=0;
    for i in 0..n{
        if ans<uf.size(i){
            ans=uf.size(i);
        }
    }
    println!("{}",ans);
}