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::*;
use proconio::marker::Usize1;

fn main() {
    input!{
        n: usize,
        m: usize,
        ab: [(Usize1, Usize1); m],
    }

    let mut uf = UnionFind::new(n);

    for (a, b) in ab {
        uf.unite(a, b);
    }

    let mut ans = 0;
    for i in 0..n {
        ans = ans.max(uf.size(i));
    }

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

struct UnionFind {
    pub data: Vec<i32>,
}

impl UnionFind {
    pub fn new(n: usize) -> UnionFind {
        UnionFind {
            data: vec![-1; n],
        }
    }

    pub fn unite(&mut self, x: usize, y: usize) -> bool {
        let mut x = self.find(x) as usize;
        let mut y = self.find(y) as usize;
        if x == y {
            return false;
        }
        if self.data[x] > self.data[y] {
            std::mem::swap(&mut x, &mut y);
        }

        self.data[x] += self.data[y];
        self.data[y] = x as i32;
        true
    }

    pub fn find(&mut self, x: usize) -> i32 {
        if self.data[x] < 0 {
            return x as i32;
        }

        let t = self.find(self.data[x] as usize);
        self.data[x] = t;
        t
    }

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