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: Wrong Answer)

use proconio::{fastout, input};

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

    let mut union_found = vec![0; n + 1];
    for item in relations {
        if item.0 < item.1 {
            union_found[item.1] = if union_found[item.1] == 0 {
                item.0
            } else {
                if union_found[item.1] > item.0 {
                    item.0
                } else {
                    union_found[item.1]
                }
            };
        } else {
            union_found[item.0] = if union_found[item.0] == 0 {
                item.1
            } else {
                if union_found[item.0] > item.1 {
                    item.1
                } else {
                    union_found[item.0]
                }
            };
        }
    }

    //println!("{:?}", union_found);
    let mut sum = vec![0; n + 1];
    for i in 0..=n {
        let mut tmp = i;
        while union_found[tmp] != 0 {
            tmp = union_found[tmp];
        }
        sum[tmp] += 1;
    }

    sum.sort();
    println!("{}", sum[sum.len() - 1]);
}