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)

#[allow(unused_imports)]
use {
    proconio::{fastout, input, marker::*},
    std::cmp::*,
    std::collections::*,
    std::ops::*,
};

#[fastout]
fn main() {
    input! {
        n: usize,
        m: usize,
        ab: [(Usize1, Usize1); m]
    }
    let mut uf = UnionFind::new(n);
    for (a, b) in ab {
        uf.unite(a, b);
    }
    let mut ans = 0;
    for i in 0..n {
        if let Some(r) = uf.rank(i) {
            ans = max(ans, r);
        }
    }
    println!("{}", ans);
}

struct UnionFind {
    par: Vec<usize>,
    rank: Vec<usize>,
}
impl UnionFind {
    fn new(size: usize) -> Self {
        UnionFind {
            par: (0..size).collect(),
            rank: vec![1; size],
        }
    }
    fn unite(&mut self, x: usize, y: usize) {
        let rx = self.root(x);
        let ry = self.root(y);
        if rx == ry {
            return;
        }
        if self.rank[x] > self.rank[y] {
            self.par[ry] = rx;
            self.rank[rx] += self.rank[ry];
        } else {
            self.par[rx] = ry;
            self.rank[ry] += self.rank[rx];
        }
    }
    fn same(&mut self, x: usize, y: usize) -> bool {
        self.root(x) == self.root(y)
    }
    fn root(&mut self, x: usize) -> usize {
        if self.par[x] == x {
            x
        } else {
            self.par[x] = self.root(self.par[x]);
            self.par[x]
        }
    }
    fn rank(&mut self, x: usize) -> Option<usize> {
        if x == self.root(x) {
            Some(self.rank[x])
        } else {
            None
        }
    }
}