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(dead_code)]
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}
fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}
#[derive(Debug)]
struct UnionFind {
    par: Vec<usize>,
    sizes: Vec<usize>
}
impl UnionFind {
    fn new(n: usize) -> UnionFind {
        let par = (0..n).collect();
        let sizes = vec![1; n];
        UnionFind{par, sizes}
    }
    fn find(&mut self, x: usize) -> usize {
        if x == self.par[x] { x } else {
            self.par[x] = self.find(self.par[x]);
            self.par[x]
        }
    }
    fn unite(&mut self, x: usize, y: usize) {
        let mut x = self.find(x);
        let mut y = self.find(y);
        if x == y { return; }
        if self.sizes[x] < self.sizes[y] {
            std::mem::swap(&mut x, &mut y);
        }
        self.par[y] = x;
        self.sizes[x] += self.sizes[y];
    }
    fn same(&mut self, x: usize, y: usize) -> bool {
        self.find(x) == self.find(y)
    }
    fn size(&mut self, x: usize) -> usize {
        let t = self.find(x);
        self.sizes[t]
    }
}
fn main() {
    let nm: Vec<usize> = read_vec();
    let mut uf = UnionFind::new(nm[0]);
    for _ in 0..nm[1] {
        let ab: Vec<usize> = read_vec();
        uf.unite(ab[0] - 1, ab[1] - 1);
    }
    let mut ans = 0;
    for i in 0..nm[0] {
        let t = uf.size(i);
        if t > ans { ans = t; }
    }
    println!("{}", ans);
}