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::{input, fastout};

struct UnionFind {
    par: Vec<usize>,
}

impl UnionFind {
    fn new(n: usize) -> Self {
        let mut par = Vec::new();

        for i in 0..n {
            par.push(i);
        }

        Self { par }
    }

    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]
    }

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

        if rx == ry {return;}

        self.par[rx] = ry;
    }

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

    fn greate(&mut self) -> usize {
        let mut counts = vec![0usize; self.par.len()];
        
        for i in 0..self.par.len() {
            self.root(i);
        }
        for &i in self.par.iter() {
            counts[i] += 1;
        }

        *counts.iter().max().unwrap()
    }
}
#[fastout]
fn main() {
    input! {
        n: usize,
        m: usize,
        ab: [(usize, usize); m],
    };

    let mut union = UnionFind::new(n);

    for i in ab {
        union.union(i.0-1, i.1-1);
    }

    //println!("{:?}", union.par);
    println!("{}", union.greate());
}