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, unused_macros, dead_code)]

macro_rules! min {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| min!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = min!($($ys),*);
        if $x < t { $x } else { t }
    }}
}
macro_rules! max {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| max!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = max!($($ys),*);
        if $x > t { $x } else { t }
    }}
}
macro_rules! ewriteln {
    ($($args:expr),*) => { let _ = writeln!(&mut std::io::stderr(), $($args),*); };
}
macro_rules! trace {
    ($x:expr) => { ewriteln!(">>> {} = {:?}", stringify!($x), $x) };
    ($($xs:expr),*) => { trace!(($($xs),*)) }
}
macro_rules! flush {
    () => {
        std::io::stdout().flush().unwrap();
    };
}
macro_rules! put {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        if let Some(x) = it.next() { print!("{}", x); }
        for x in it { print!(" {}", x); }
        println!("");
    }};
    ($x:expr) => { println!("{}", $x) };
    ($x:expr, $($xs:expr),*) => { print!("{} ", $x); put!($($xs),*) }
}

const M: i64 = 1_000_000_007;

// @set.union_find.rs
#[derive(Debug, Clone)]
enum UF {
    Root(usize),
    Child(usize),
}

#[derive(Debug)]
struct UnionFind {
    table: Vec<UF>,
}
impl UnionFind {
    fn new(n: usize) -> UnionFind {
        UnionFind {
            table: vec![UF::Root(1); n],
        }
    }
    fn root(&mut self, x: usize) -> usize {
        match self.table[x] {
            UF::Root(_) => x,
            UF::Child(parent) => {
                let root = self.root(parent);
                self.table[x] = UF::Child(root);
                root
            }
        }
    }
    fn is_same(&mut self, x: usize, y: usize) -> bool {
        self.root(x) == self.root(y)
    }
    fn size(&mut self, x: usize) -> usize {
        let r = self.root(x);
        match self.table[r] {
            UF::Root(size) => size,
            UF::Child(_) => 0,
        }
    }
    fn merge(&mut self, x: usize, y: usize) {
        let root_x = self.root(x);
        let root_y = self.root(y);
        if root_x != root_y {
            let size_x = self.size(root_x);
            let size_y = self.size(root_y);
            let (i, j) = if size_x > size_y {
                (root_x, root_y)
            } else {
                (root_y, root_x)
            };
            self.table[i] = UF::Root(size_x + size_y);
            self.table[j] = UF::Child(i);
        }
    }
}

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let m: usize = sc.cin();

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

    for _ in 0..m {
        let a = sc.cin::<usize>() - 1;
        let b = sc.cin::<usize>() - 1;
        uf.merge(a, b);
    }

    let ans = (0..n).map(|i| uf.size(i)).max().unwrap();
    put!(ans);
}

use std::collections::VecDeque;
use std::io::{self, Write};
use std::str::FromStr;

struct Scanner {
    stdin: io::Stdin,
    buffer: VecDeque<String>,
}
impl Scanner {
    fn new() -> Self {
        Scanner {
            stdin: io::stdin(),
            buffer: VecDeque::new(),
        }
    }
    fn cin<T: FromStr>(&mut self) -> T {
        while self.buffer.is_empty() {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
        self.buffer.pop_front().unwrap().parse::<T>().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> {
        self.cin::<String>().chars().collect()
    }
    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.cin()).collect()
    }
}