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::{input, fastout};
use std::cmp::{max};

struct UnionFind {
    parents: Vec<isize>,
}

impl UnionFind {
    fn new(n: usize) -> Self {
        UnionFind { parents: vec![-1; n] }
    }

    fn root(&mut self, x: &usize) -> usize {
        let px = self.parents[*x];
        if px < 0 {
            return *x;
        } else {
            let pp = self.root(&(px as usize));
            self.parents[*x] = pp as isize;
            return pp;
        }
    }

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

    fn join(&mut self, x: &usize, y: &usize) {
        let rx = self.root(x);
        let cx = self.parents[rx];
        let ry = self.root(y);
        if rx == ry { return; }
        self.parents[rx] = ry as isize;
        self.parents[ry] += cx;
    }

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

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

    let mut uf = UnionFind::new(n);
    for (mut a, mut b) in ab {
        a -= 1;
        b -= 1;
        uf.join(&a, &b);
    }
    let mut ans = 0;
    for i in 0..n {
        ans = max(uf.size(&i), ans);
    }
    println!("{}", ans)
}