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(non_snake_case, unused)]
use std::io::*;
use std::str::FromStr;
use std::collections::*;

fn main() {
    let cin = stdin();
    let mut sc = Scanner::new(cin.lock());

    let n: usize = sc.next();
    let m: usize = sc.next();
    
    let mut dsu = DSU::new(n);
    for i in 0..m {
	let a: usize = sc.next();
	let b: usize = sc.next();
	let a = a - 1;
	let b = b - 1;
	dsu.unite(a, b);
    }

    let mut ans = 0;
    for i in 0..n {
	ans = ans.max(dsu.get_size(i));
    }

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

pub struct DSU {
    n: usize,
    rank: Vec<usize>,
    parent: Vec<usize>,
    size: Vec<usize>,
}

impl DSU {
    pub fn new(n: usize) -> DSU {
	DSU {
	    n: n,
	    rank: vec![0; n],
	    size: vec![1; n],
	    parent: (0..n).collect()
	}
    }
    pub fn get_rep(&mut self, x: usize) -> usize {
	if self.parent[x] != x {
	    self.parent[x] = self.get_rep(self.parent[x]);
	}
	self.parent[x]
    }

    pub fn unite(&mut self, x: usize, y: usize) {
	let mut p1 = self.get_rep(x);
	let mut p2 = self.get_rep(y);
	if p1 != p2 {
	    if self.rank[p1] < self.rank[p2] {
		std::mem::swap(&mut p1, &mut p2);
	    }
	    if self.rank[p1] == self.rank[p2] {
		self.rank[p1] += 1;
	    }
	    self.parent[p2] = p1;
	    self.size[p1] += self.size[p2];
	}
    }

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

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


// Scanner
struct Scanner<R: std::io::Read> {
    reader: R,
}

#[allow(dead_code)]
impl<R: Read> Scanner<R> {
    fn new(reader: R) -> Scanner<R> {
	Scanner { reader: reader }
    }

    fn read<T: FromStr> (&mut self) -> Option<T> {
	let token = self
	    .reader
	    .by_ref()
	    .bytes()
	    .map(|c| c.unwrap() as char)
	    .skip_while(|c| c.is_whitespace())
	    .take_while(|c| !c.is_whitespace())
	    .collect::<String>();
	if token.is_empty() {
	    None
	} else {
	    token.parse::<T>().ok()
	}
    }

    fn next<T: FromStr>(&mut self) -> T {
	if let Some(s) = self.read() {
	    s
	} else {
	    writeln!(stderr(), "Terminated with EOF").unwrap();
	    std::process::exit(0);
	}
    }

    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
	(0..n).map(|_| self.next()).collect()
    }

    fn char(&mut self) -> char {
	self.next::<String>().chars().next().unwrap()
    }
}