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: Wrong Answer)

#![allow(non_snake_case)]
#![allow(unused_imports)]
use proconio::input;
use std::collections::HashMap;
use std::collections::VecDeque;
use std::cmp::max;
use std::cmp::min;


pub struct UnionFind {
    par: Vec<usize>,
    rank: Vec<usize>,
}

// https://github.com/akiradeveloper/rust-comp-snippets/blob/master/src/union_find.rs
impl UnionFind {
    pub fn new(n: usize) -> UnionFind {
        UnionFind {
            par: (0..n).collect::<Vec<usize>>(),
            rank: vec![1; n],
        }
    }

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

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

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

    pub fn merge(&mut self, x: usize, y: usize) -> bool {
        let mut a = self.root(x);
        let mut b = self.root(y);
        if a == b {
            return false;
        }

        if self.rank[a] < self.rank[b] {
            std::mem::swap(&mut a, &mut b);
        }
        assert!(self.rank[a] >= self.rank[b]);

        self.rank[a] += self.rank[b];
        self.par[b] = a;
        return true;
    }
}


fn main() {
    input! {
        N: usize,
        M: usize,
        tmpABs: [(usize, usize); M],
    }

    // 0-origin
    let mut ABs: Vec<(usize, usize)> = Vec::new();
    for &(a, b) in tmpABs.iter() {
        let tpl: (usize, usize) = (a - 1, b - 1);
        ABs.push(tpl);
    }


    let mut ans = 0;
    let mut uf = UnionFind::new(N);

    for &(a, b) in ABs.iter() {
        uf.merge(a, b);

        ans = max(ans, uf.size(a));
    }

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