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::{
    fastout, input,
    marker::{Bytes, Chars, Usize1},
};

struct UnionFind {
    size: usize,
    pos: Vec<isize>,
}

impl UnionFind {
    /// UnionFindを作る関数
    fn new(n: usize) -> Self {
        let size = n;
        let pos = vec![-1; n + 1];
        UnionFind { size, pos }
    }

    /// rootを探す関数
    fn find(&mut self, x: usize) -> usize {
        if self.pos[x] < 0 {
            x
        } else {
            let v = self.pos[x] as usize;
            self.pos[x] = self.find(v) as isize;
            self.pos[x] as usize
        }
    }

    fn unite(&mut self, x: usize, y: usize) -> Result<(), ()> {
        let mut x = self.find(x);
        let mut y = self.find(y);

        // x, y共にrootが設定済みで尚且つ
        // rootが同じ時
        if x == y {
            return Err(());
        }
        if self.pos[x] > self.pos[y] {
            std::mem::swap(&mut x, &mut y);
        }
        self.pos[x] += self.pos[y];
        self.pos[y] = x as isize;

        Ok(())
    }

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

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

#[fastout]
fn main() {
    input! {
        n: usize,
        m: usize,
        par: [(Usize1, Usize1); m]
    }
    let mut uf = UnionFind::new(n);
    for &(x, y) in &par {
        uf.unite(x, y).ok();
    }
    let mut ans = 1;
    for i in 0..n {
        ans = std::cmp::max(ans, uf.size(i));
    }
    println!("{}", ans);
}