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)

struct UnionFind {
    par: Vec<usize>,
    sizes: Vec<usize>,
}

impl UnionFind {
    fn new(n: usize) -> UnionFind {
        UnionFind {
            par: (0..n).collect(),
            sizes: vec![1; n],
        }
    }

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

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

        if x == y { return; }

        if self.sizes[x] > self.sizes[y] {
            std::mem::swap(&mut x, &mut y);
        }

        self.par[x] = y;
        self.sizes[y] += self.sizes[x];
    }

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

fn main() {
    let (n, m): (usize, usize) = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        let mut iter = buf.split_whitespace();
        (
            iter.next().unwrap().parse().unwrap(),
            iter.next().unwrap().parse().unwrap(),
        )
    };

    let mut uf = UnionFind::new(n);
    for _ in 0..m {
        let (a, b): (usize, usize) = {
            let mut buf = String::new();
            std::io::stdin().read_line(&mut buf).unwrap();
            let mut iter = buf.split_whitespace();
            (
                iter.next().unwrap().parse::<usize>().unwrap() - 1,
                iter.next().unwrap().parse::<usize>().unwrap() - 1,
            )
        };

        uf.unite(a, b);
    }

    let mut ans = 0;
    for i in 0..n {
        ans = std::cmp::max(ans, uf.size(i));
    }
    println!("{}", ans);
}