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 std::io::Read;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

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

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: usize = iterator.next().unwrap().parse().unwrap();
    let m: usize = iterator.next().unwrap().parse().unwrap();

    let mut uf = union_find::UnionFind::new(n);
    for _ in 0..m {
        let ai: usize = iterator.next().unwrap().parse().unwrap();
        let bi: usize = iterator.next().unwrap().parse().unwrap();
        uf.unite(ai - 1, bi - 1);
    }

    let ans = (0..n)
        .map(|i| uf.size(i))
        .max()
        .unwrap();
    ans.to_string()
}

#[allow(dead_code)]
mod union_find {
    pub struct UnionFind {
        parent: Vec<usize>,
        sizes: Vec<usize>,
        len: usize,
    }

    impl UnionFind {
        pub fn new(n: usize) -> UnionFind {
            UnionFind {
                parent: (0..n).map(|i| i).collect(),
                sizes: vec![1; n],
                len: n,
            }
        }

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

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

            if px == py {
                return;
            }

            let (large, small) = if self.sizes[px] < self.sizes[py] {
                (py, px)
            } else {
                (px, py)
            };

            self.parent[small] = large;
            self.sizes[large] += self.sizes[small];
            self.sizes[small] = 0;
            self.len -= 1;
        }

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

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

        pub fn len(&self) -> usize {
            self.len
        }
    }
}