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)

use proconio::{input, fastout};
use proconio::marker::Usize1;

pub struct UnionFind {
    p: Vec<usize>,
    rank: Vec<usize>,
}
impl UnionFind {
    pub fn new(n: usize) -> Self {
        UnionFind {
            p: (0..n).collect(),
            rank: vec![1; n],
        }
    }
    pub fn find(&mut self, x: usize) -> usize {
        let p = self.p[x];
        if x != p {
            self.p[x] = self.find(p);
        }
        self.p[x]
    }
    pub 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.rank[x] < self.rank[y] {
            std::mem::swap(&mut x, &mut y);
        }
        self.rank[x] += self.rank[y];
        self.p[y] = x;
        true
    }
    pub fn same(&mut self, x: usize, y: usize) -> bool {
        self.find(x) == self.find(y)
    }
    pub fn size(&mut self, x: usize) -> usize {
        let p = self.find(x);
        self.rank[p]
    }
}

#[fastout]
fn main() {
    input! {
        n: usize,
        m: usize,
        v: [(Usize1,Usize1);m]
    }
    let mut u = UnionFind::new(n);
    for (a,b) in v {
        u.unite(a,b);
    }
    let res = (0..n).map(|x| u.size(x)).max().unwrap();
    println!("{}", res);
}