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)

struct UnionFind {
    dp: Vec<usize>
}

impl UnionFind {
    fn new(length: usize) -> UnionFind {
        return UnionFind { dp: (0..length).collect::<Vec<usize>>() };
    }

    fn find(&mut self, x: usize) -> usize {
        if x == self.dp[x] { return x; }
        self.dp[x] = self.find(self.dp[x]);
        return self.dp[x];
    }

    fn connect(&mut self, a: usize, b: usize) {
        let ra = self.find(a);
        self.dp[ra] = self.find(b);
    }
}

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

    let mut uf = UnionFind::new(n);

    for (a, b) in &ab {
        uf.connect(*a - 1, *b - 1);
    }

    let res = (0..n)
        .fold(std::collections::HashMap::new(), |mut map, index| {
            *map.entry(uf.find(index)).or_insert(0) += 1;
            return map;
        })
        .iter()
        .map(|(_, &count)| count)
        .max()
        .unwrap();

    println!("{}", res);
}