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;
use proconio::marker::Usize1;

struct UnionFind {
    n: usize,
    par: Vec<usize>,
    size: Vec<usize>,
}

impl UnionFind {
    fn new(n: usize) -> UnionFind {
        let mut uf = UnionFind {
            n,
            par: Vec::with_capacity(n),
            size: Vec::with_capacity(n),
        };
        for i in 0..n {
            uf.par.push(i);
            uf.size.push(1);
        }
        uf
    }

    fn root(&mut self, x: usize) -> usize {
        if self.par[x] != x {
            self.par[x] = self.root(self.par[x]);
        }
        self.par[x]
    }

    fn unite(&mut self, x: usize, y: usize) -> () {
        if self.root(x) != self.root(y) {
            let rx = self.root(x);
            let ry = self.root(y);
            self.par[rx] = ry;
            self.size[ry] += self.size[rx];
        }
    }

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

    fn is_root(&self, x: usize) -> bool {
        x == self.par[x]
    }
}

#[proconio::fastout]
pub fn main() {
    input! {
        n:usize,
        abs:[(Usize1,Usize1)],
    }
    //let n: usize;
    //let abs: Vec(usize, usize);
    let mut uf = UnionFind::new(n);
    for ab in abs {
        uf.unite(ab.0, ab.1);
    }
    let ans = (0..n)
        .filter(|&i| uf.is_root(i))
        .map(|i| uf.size[i])
        .max().unwrap();
    println!("{:}", ans);
}