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)

#![allow(dead_code,unused_variables)]
use proconio::{fastout, input};
use proconio::marker::Usize1;
use std::cmp::max;

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

    for e in p{
        // println!("{:?}",e);
        let x;
        let y;
        if e.0 > e.1{
            x = e.1;
            y = e.0;
        }else{
            x = e.0;
            y = e.1;
        }
        uf.unite(x,y);
        // println!("{}",uf.get_size(0));
        // println!("------");
    }

    let mut ans = 0;
    for i in 0..n{
        ans = max(uf.get_size(i),ans);
        // println!("{}",uf.get_size(i));
    }

    println!("{}",ans);

}

struct UnionFind{
    par : Vec<usize>,
    size : Vec<usize>,
}

impl UnionFind{
    pub fn new(n: usize) -> Self{
        let par : Vec<usize>= (0..n).collect();
        UnionFind{
            par,
            size : vec![1;n],
        }
    }

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

        self.par[x] = self.root(self.par[x]);
        self.par[x]
    }

    pub fn unite(&mut self, x: usize, y: usize){
        let rx = self.root(x);
        let ry = self.root(y);

        if rx == ry{
            return;
        }

        if self.size[x] < self.size[y]{
            self.size[y] += self.size[x];
            self.par[x] = y;
        }else{
            self.size[x] += self.size[y];
            self.par[y] = x;
        }
    }

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

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