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 self::union_find::UnionFind;
use proconio::input;
use proconio::marker::Usize1;

fn main() {
    input! {
        n: usize,
        m: usize,
        ab: [(Usize1, Usize1); m],
    };
    let mut uf = UnionFind::new(n);
    for &(a_i, b_i) in ab.iter() {
        uf.unite(a_i, b_i);
    }
    let mut max_size = 0;
    for i in 0..n {
        max_size = std::cmp::max(max_size, uf.size(i));
    }
    let ans = max_size;
    println!("{}", ans);
}

mod union_find {
    pub struct UnionFind {
        p: Vec<usize>,
        s: Vec<usize>,
    }

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

        pub fn root(&mut self, x: usize) -> usize {
            if self.p[x] == x {
                return x;
            } else {
                self.p[x] = self.root(self.p[x]);
                self.p[x]
            }
        }

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

        pub fn unite(&mut self, x: usize, y: usize) {
            let rx = self.root(x);
            let ry = self.root(y);
            if rx == ry {
                return;
            };
            if self.s[rx] >= self.s[ry] {
                self.s[rx] += self.s[ry];
                self.p[ry] = rx;
            } else {
                self.s[ry] += self.s[rx];
                self.p[rx] = ry;
            }
        }
    }
}