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::input;

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

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

    for (a, b) in ab {
        uf.unite(a - 1, b - 1);
    }

    let ans = uf.sizes.iter().max().unwrap();

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

pub struct UnionFind {
    pub parent: Vec<usize>,
    pub sizes: Vec<usize>,
}

impl UnionFind {
    pub fn new(n: usize) -> UnionFind {
        UnionFind {
            parent: (0..n).collect(),
            sizes: vec![1; n],
        }
    }

    pub fn find(&mut self, x: usize) -> usize {
        if x == self.parent[x] {
            x
        } else {
            let x = self.parent[x];
            self.parent[x] = self.find(x);
            self.parent[x]
        }
    }

    pub fn unite(&mut self, x: usize, y: usize) -> bool {
        let mut x = self.find(x);
        let mut y = self.find(y);
        if x != y {
            if self.sizes[x] < self.sizes[y] {
                std::mem::swap(&mut x, &mut y);
            }
            self.parent[y] = x;
            self.sizes[x] += self.sizes[y];
            true
        } else {
            false
        }
    }

    pub fn same(&mut self, x: usize, y: usize) -> bool {
        self.find(x) == self.find(y)
    }

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