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::{
    fastout, input,
    marker::{Bytes, Chars, Usize1},
};

struct UnionFind {
    c: std::cell::RefCell<Box<[isize]>>,
}

use std::mem::swap;

impl UnionFind {
    pub fn new(n: usize) -> Self {
        Self {
            c: std::cell::RefCell::new(vec![-1; n].into_boxed_slice()),
        }
    }

    pub fn find(&self, mut x: usize) -> usize {
        let c = &mut *self.c.borrow_mut();
        let mut r = x;
        while c[r] >= 0 {
            r = c[r] as usize;
        }
        while x != r {
            let t = c[x] as usize;
            c[x] = r as isize;
            x = t;
        }
        r
    }

    pub fn unite(&mut self, mut x: usize, mut y: usize) -> (usize, usize) {
        x = self.find(x);
        y = self.find(y);
        let c = &mut *self.c.borrow_mut();
        if x != y {
            if c[x] < c[y] {
                swap(&mut x, &mut y);
            }
            c[x] += c[y];
            c[y] = x as isize;
        }
        (x, y)
    }

    pub fn size(&self, mut x: usize) -> usize {
        x = self.find(x);
        -self.c.borrow()[x] as usize
    }
}

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