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, marker::Usize1};

fn main() {
    input!(n: usize, friendship: [(Usize1, Usize1)]);

    let mut uf = UnionFind::new(n);
    for (a, b) in friendship {
        uf.unite(a, b);
    }
    let ans = (0..n).map(|i| uf.size(i)).max().unwrap();

    println!("{}", ans);
}

struct UnionFind(Vec<isize>);
impl UnionFind {
    fn new(size: usize) -> Self { Self(vec![-1; size]) }
    fn unite(&mut self, a: usize, b: usize) -> usize {
        let (mut x, mut y) = (self.find(a), self.find(b));
        if x == y {
            return x;
        }
        if -self.0[x] < -self.0[y] {
            std::mem::swap(&mut x, &mut y);
        }
        self.0[x] += self.0[y];
        self.0[y] = x as isize;
        x
    }
    fn find(&mut self, a: usize) -> usize {
        if self.0[a] < 0 {
            return a;
        }
        self.0[a] = self.find(self.0[a] as usize) as isize;
        self.0[a] as usize
    }
    fn size(&mut self, a: usize) -> usize {
        let x = self.find(a);
        -self.0[x] as usize
    }
}