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};

pub struct UnionFind {
    par: Vec<usize>,
    cnt: Vec<i32>,
}

impl UnionFind {
    pub fn new(n: usize) -> UnionFind {
        let mut par: Vec<usize> = Vec::with_capacity(n);
        for i in 0..n {
            par.push(i);
        }
        let cnt: Vec<i32> = vec![1; n];
        UnionFind { par, cnt }
    }
    pub fn find(&mut self, x: usize) -> usize {
        if self.par[x] == x {
            x
        } else {
            let res = self.find(self.par[x]);
            self.par[x] = res;
            res
        }
    }
    pub fn unite(&mut self, x: usize, y: usize) {
        let x_par = self.find(x);
        let y_par = self.find(y);
        if x_par != y_par {
            self.par[x_par] = y_par;
            self.cnt[y_par] += self.cnt[x_par];
            self.cnt[x_par] = 0;
        }
    }
    pub fn same(&mut self, x: usize, y: usize) -> bool {
        self.find(x) == self.find(y)
    }
    pub fn size(&self, x: usize) -> i32 {
        self.cnt[x]
    }
}

#[fastout]
fn main() {
    input! {
        n: usize,
        m: usize,
    }
    let mut uf: UnionFind = UnionFind::new(n);
    for _ in 0..m {
        input! {
            a: usize,
            b: usize,
        }
        uf.unite(a - 1, b - 1);
    }

    let mut ans: i32 = 0;
    for i in 0..n {
        let sz = uf.size(i as usize);
        if ans < sz {
            ans = sz;
        }
    }
    println!("{}", ans);
}