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, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};

#[fastout]
fn main() {
    input! {//
        n:usize,m:usize,
        ab:[(Usize1,Usize1);m],
    }
    let mut v = vec![vec![]; n];
    let mut uf = UnionFind::new(n);
    for (a, b) in ab {
        v[a].push(b);
        v[b].push(a);
        uf.unite(a, b);
    }
    let mut st = BTreeSet::new();
    let mut mx = 0;
    for i in 0..n {
        st.insert(uf.par[i]);
        mx = max(mx, uf.size(i));
    }
    // dbg!(mx);
    println!("{}", mx);
}
pub struct UnionFind {
    par: Vec<usize>,
    rank: Vec<usize>,
    size: Vec<usize>,
}
impl UnionFind {
    pub fn new(n: usize) -> UnionFind {
        let mut vec = vec![0; n];
        for i in 0..n {
            vec[i] = i;
        }
        UnionFind {
            par: vec,
            rank: vec![0; n],
            size: vec![1; n],
        }
    }
    pub fn find(&mut self, x: usize) -> usize {
        if x == self.par[x] {
            x
        } else {
            let par = self.par[x];
            let res = self.find(par);
            self.par[x] = res;
            res
        }
    }
    pub fn same(&mut self, a: usize, b: usize) -> bool {
        self.find(a) == self.find(b)
    }
    pub fn unite(&mut self, a: usize, b: usize) {
        let apar = self.find(a);
        let bpar = self.find(b);
        if apar == bpar {
            return;
        }
        if self.rank[apar] > self.rank[bpar] {
            self.par[bpar] = apar;
            self.size[apar] += self.size[bpar];
        } else {
            self.par[apar] = bpar;
            self.size[bpar] += self.size[apar];
            if self.rank[apar] == self.rank[bpar] {
                self.rank[bpar] += 1;
            }
        }
    }
    pub fn size(&mut self, a: usize) -> usize {
        let p = self.find(a);
        self.size[p]
    }
}