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 std::*;
use proconio::input;

struct Dsu {
    p: Vec<usize>,
    sz: Vec<u32>,
}

impl Dsu {
    pub fn new(n: usize) -> Self {
        let mut v = vec![0; n];
        for i in 1..n {
            v[i] = i;
        }
        Self {
            p: v,
            sz: vec![1; n]
        }
    }

    fn find(&mut self,mut x: usize) -> usize {
        let mut t = x;
        while self.p[x] != x {
            x = self.p[x];
        }
        
        while self.p[t] != t {
            let tt = self.p[t];
            self.p[t] = x;
            t = tt;
        }
        x
    }

    fn uni(&mut self, mut x: usize, mut y: usize) {
        x = self.find(x);
        y = self.find(y);
        if x == y {
            return;
        }
        self.sz[x] += self.sz[y];
        self.p[y] = x;
    }
}

fn main() {
    input! {
        n: u32,
        m: u32
    }
    let mut dsu = Dsu::new(n as usize + 1);
    for _ in 0..m {
        input! {
            a: usize,
            b: usize
        }
        dsu.uni(a, b);
    }
    let mut ans = 0;
    for i in 1..(n + 1) {
        ans = cmp::max(ans, dsu.sz[i as usize])
    }
    println!("{}", ans);
}