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::marker::{Bytes, Chars};
use std::collections::*;

fn main() {
    input! {
        n:usize,
        m:usize,
        ab:[(usize,usize);m],
    }
    let ab = ab.iter().map(|&(a, b)| (a - 1, b - 1));

    let mut uf = UnionFind::new(n);
    for (a, b) in ab {
        uf.unite(a, b);
    }

    let ans = uf
        .data
        .iter()
        .filter_map(|&node| match node {
            UFdata::Child(_) => None,
            UFdata::Root(x) => Some(x),
        })
        .max()
        .unwrap();

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

#[derive(Debug, Copy, Clone)]
enum UFdata {
    Child(usize),
    Root(usize),
}
struct UnionFind {
    data: Vec<UFdata>,
}
impl UnionFind {
    pub fn new(n: usize) -> Self {
        UnionFind {
            data: vec![UFdata::Root(1); n],
        }
    }
    fn root(&mut self, x: usize) -> usize {
        match self.data[x] {
            UFdata::Child(p) => {
                let res = self.root(p);
                self.data[x] = UFdata::Child(res);
                res
            }
            UFdata::Root(_) => x,
        }
    }
    pub fn size(&mut self, x: usize) -> usize {
        match self.data[x] {
            UFdata::Root(m) => m,
            UFdata::Child(_) => {
                let r = self.root(x);
                self.size(r)
            }
        }
    }
    pub fn unite(&mut self, x: usize, y: usize) -> bool {
        let (mut u, mut v) = (self.root(x), self.root(y));
        if u == v {
            false
        } else {
            if self.size(u) < self.size(v) {
                std::mem::swap(&mut u, &mut v);
            }
            self.data[u] = UFdata::Root(self.size(u) + self.size(v));
            self.data[v] = UFdata::Child(u);
            true
        }
    }
    pub fn is_same(&mut self, x: usize, y: usize) -> bool {
        self.root(x) == self.root(y)
    }
}