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;
use proconio::marker::Usize1;

struct UnionFindTree {
    parent: Vec<usize>,
    size: Vec<usize>,
}

impl UnionFindTree {
    fn new(n: usize) -> Self {
        let parent = (0..n).collect();
        let size = vec![1; n];
        Self { parent, size }
    }

    fn find(&mut self, x: usize) -> usize {
        if self.parent[x] == x {
            x
        } else {
            self.parent[x] = self.find(self.parent[x]);
            self.size[x] = 1;
            self.parent[x]
        }
    }

    fn unite(&mut self, x: usize, y: usize) {
        let x = self.find(x);
        let y = self.find(y);
        if x == y {
            return;
        }

        // if self.size[x] < self.size[y] {
        //     std::mem::swap(&mut x, &mut y);
        // }

        self.parent[y] = x;
        self.size[x] += self.size[y];
    }
}
#[allow(non_snake_case)]
fn main() {
    input! {
        N: usize,
        M: usize,
        AB: [(Usize1, Usize1); M]
    }

    let mut uf = UnionFindTree::new(N);

    for &(a, b) in AB.iter() {
        uf.unite(a, b);
    }

    println!("{:?}", uf.size.iter().max().unwrap());
}