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::*;

fn main() {
    input! {
        n: usize,
        m: usize,
    }
    let mut uf = UnionFind::new(n);
    let mut ans = 0;
    for _ in 0..m {
        input! {
            a: usize,
            b: usize,
        }
        uf.unite(a-1, b-1)
    }
    for r in uf.roots(n).iter() {
        if uf.size(*r) > ans {
            ans = uf.size(*r);
        }
    }
    println!("{}", ans)
}

struct UnionFind {
    root: Vec<usize>,
    rank: Vec<usize>,
    sizes: Vec<usize>,
}

impl UnionFind {
    fn new(n: usize) -> UnionFind {
        let mut vec = vec![0;n];
        for i in 0..n {
            vec[i] = i;
        }
        UnionFind {
            root: vec,
            rank: vec![0;n],
            sizes: vec![1;n],
        }
    }

    fn find(&mut self, x: usize) -> usize {
        if self.root[x] == x { return x }
        self.root[x] = self.find(self.root[x]);
        self.root[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.rank[x] < self.rank[y] {
            self.root[x] = y;
            self.sizes[y] += self.sizes[x];
        } else {
            self.root[y] = x;
            self.sizes[x] += self.sizes[y];
            if self.rank[x] == self.rank[y] {
                self.rank[x] += 1;
            }
        }
    }

    fn same(&mut self, x: usize, y: usize) -> bool {
        self.find(x) == self.find(y)
    }

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

    fn roots(&mut self, n: usize) -> Vec<usize> {
        let mut vec = vec![];
        for i in 0..n {
            if self.root[i] == i {
                vec.push(self.root[i]);
            }
        }
        vec
    }
}