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::marker::*;
use proconio::{fastout, input};

#[fastout]
fn main() {
    input! {
        n: usize,
        m: usize,
        ar: [(Usize1, Usize1); m],
    }
    let ar = ar;
    let res = solve(n, &ar);
    println!("{}", res);
}

fn solve(n: usize, ar: &[(usize, usize)]) -> usize {
    let mut uf = UnionFind::new(n);
    for a in ar {
        uf.unite(a.0, a.1);
    }

    let mut max = 0;
    for i in 0..n {
        max = std::cmp::max(max, uf.size(i));
    }
    max
}

struct UnionFind {
    ar: Vec<isize>,
}

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

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

    fn unite(&mut self, x: usize, y: usize) {
        let x = self.root(x);
        let y = self.root(y);
        if x != y {
            self.ar[x] += self.ar[y];
            self.ar[y] = x as isize;
        }
    }

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