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)]
use proconio::{input, fastout};
use proconio::marker::*;
use std::mem::swap;
use nalgebra::{min, max};


#[fastout]
fn main() {
    input! {
    n: usize,
    m: usize,
    ab: [(Usize1, Usize1); m]
    }
    let mut uf = UnionFind{par: vec![], siz: vec![]};
    uf.init(n);
    for i in 0..m {
        uf.unite(ab[i].0, ab[i].1);
    }
    let mut ans = 0;
    for i in 0..n {
        ans = max(ans, uf.size(i));
    }
    println!("{}", ans);
}
#[derive(Default)]
struct UnionFind {
    par: Vec<usize>,
    siz: Vec<usize>,
}

#[allow(dead_code)]
impl UnionFind {
    fn init(&mut self, n: usize) {
        for i in 0..n {
            self.par.push(i);
            self.siz.push(1);
        }
    }

    fn find(&mut self, x: usize) -> usize {
        let ele = self.par[x];
        return if ele == x {
            x
        } else {
            self.par[x] = self.find(ele);
            self.par[x]
        };
    }

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

    fn unite(&mut self, x: usize, y: usize) -> bool {
        let mut x = self.find(x);
        let mut y = self.find(y);
        if x == y {
            return false;
        }
        if self.siz[x] < self.siz[y] {
            swap(&mut x, &mut y)
        }
        self.siz[x] += self.siz[y];
        self.par[y] = x;
        true
    }

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