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: Time Limit Exceeded)

use proconio::{fastout, input};

struct UnionFind {
    set: Vec<i64>,
}

impl UnionFind {
    fn new(n: usize) -> Self {
        let set: Vec<i64> = vec![-1; n];
        Self { set }
    }

    fn root(&self, i: usize) -> usize {
        if self.set[i] < 0 {
            i
        } else {
            self.root(self.set[i] as usize)
        }
    }

    fn unite(&mut self, x: usize, y: usize) -> bool {
        let mut x_root = self.root(x);
        let mut y_root = self.root(y);
        if x_root == y_root {
            false
        } else {
            if x_root > y_root {
                std::mem::swap(&mut x_root, &mut y_root);
            }
            self.set[x_root] += self.set[y_root];
            self.set[y_root] = self.root(x_root as usize) as i64;
            true
        }
    }

    fn size(&self, i: usize) -> usize {
        (self.set[self.root(i)] * -1) as usize
    }
}

#[fastout]
fn main() {
    input! {
        n: usize,
        m: usize,
        a_b_vec: [(usize, usize); m],
    };
    let a_b_vec: Vec<(usize, usize)> = a_b_vec.iter().map(|(a, b)| (a - 1, b - 1)).collect();
    let mut set: UnionFind = UnionFind::new(n);
    for a_b in a_b_vec.iter() {
        set.unite(a_b.0, a_b.1);
    }
    let mut ans = 0;
    for i in 0..n {
        ans = ans.max(set.size(i));
    }
    println!("{}", ans);
}