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)

fn main() {
	let mut s = String::new();
	use std::io::Read;
	std::io::stdin().read_to_string(&mut s).unwrap();
	let mut s = s.split_whitespace();
	let n: usize = s.next().unwrap().parse().unwrap();
	let m: usize = s.next().unwrap().parse().unwrap();
	let mut uf = UnionFind::new(n);
	for _ in 0..m {
		let a: usize = s.next().unwrap().parse().unwrap();
		let a = a - 1;
		let b: usize = s.next().unwrap().parse().unwrap();
		let b = b - 1;
		uf.unite(a, b);
	}
	let mut ans = 0;
	for i in 0..n {
		let s = uf.size(i);
		if ans < s {
			ans = s;
		}
	}
	println!("{}", ans);
}

pub struct UnionFind {
	data: Vec<i32>,
}

impl UnionFind {
	pub fn new(n: usize) -> UnionFind {
		UnionFind { data: vec![-1; n] }
	}

	pub fn unite(&mut self, x: usize, y: usize) -> bool {
		let x = self.find(x);
		let y = self.find(y);
		if x == y {
			false
		} else {
			let (x, y) = if self.data[x] > self.data[y] {
				(y, x)
			} else {
				(x, y)
			};
			self.data[x] += self.data[y];
			self.data[y] = x as i32;
			true
		}
	}

	pub fn find(&mut self, i: usize) -> usize {
		if self.data[i] < 0 {
			i
		} else {
			let p = self.data[i] as usize;
			self.data[i] = self.find(p) as i32;
			self.data[i] as usize
		}
	}

	pub fn size(&mut self, i: usize) -> usize {
		let i = self.find(i);
		(-self.data[i]) as usize
	}
}