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)

//---------- begin union_find ----------
#[allow(dead_code)]
mod union_find {
    pub struct UF {
        p: Vec<i32>,
    }
    impl UF {
        pub fn new(n: usize) -> UF {
            UF {p: vec![-1; n] }
        }
        pub fn init(&mut self) {
            for p in self.p.iter_mut() {
                *p = -1;
            }
        }
        pub fn root(&self, mut x: usize) -> usize {
            while self.p[x] >= 0 {
                x = self.p[x] as usize;
            }
            x
        }
        pub fn same(&self, x: usize, y: usize) -> bool {
            self.root(x) == self.root(y)
        }
        pub fn unite(&mut self, x: usize, y: usize) -> Option<(usize, usize)> {
            let mut x = self.root(x);
            let mut y = self.root(y);
            if x == y {
                return None;
            }
            if self.p[x] > self.p[y] {
                std::mem::swap(&mut x, &mut y);
            }
            self.p[x] += self.p[y];
            self.p[y] = x as i32;
            Some((x, y))
        }
        pub fn parent(&self, x: usize) -> Option<usize> {
            let p = self.p[x];
            if p >= 0 {
                Some(p as usize)
            } else {
                None
            }
        }
        pub fn get_size(&self, x: usize) -> usize {
            let r = self.root(x);
            (-self.p[r]) as usize
        }
    }
}
//---------- end union_find ----------

use proconio::*;
use proconio::marker::*;

fn run() {
    input! {
        n: usize,
        m: usize,
        e: [(Usize1, Usize1); m],
    }
    let mut u = union_find::UF::new(n);
    for (a, b) in e {
        u.unite(a, b);
    }
    let mut ans = 0;
    for i in 0..n {
        if i == u.root(i) {
            ans = std::cmp::max(ans, u.get_size(i));
        }
    }
    println!("{}", ans);
}

fn main() {
    run();
}