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(unused_imports)]
use itertools::Itertools;
#[allow(unused_imports)]
use num::*;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::collections::*;

pub struct UnionFind {
    n: usize,
    root: Vec<usize>,
    rank: Vec<usize>,
    size: Vec<usize>,
}
impl UnionFind {
    pub fn new(n: usize) -> Self {
        let root = (0..n).collect();
        let rank = vec![0; n];
        let size = vec![1; n];
        Self {
            n,
            root,
            rank,
            size,
        }
    }
    pub fn find(&mut self, x: usize) -> usize {
        if x >= self.n {
            panic!();
        }
        if self.root[x] == x {
            x
        } else {
            let root = self.find(self.root[x]);
            self.root[x] = root;
            root
        }
    }
    pub fn unite(&mut self, x: usize, y: usize) {
        if x >= self.n || y >= self.n {
            panic!();
        }
        let x_root = self.find(x);
        let y_root = self.find(y);
        if x_root == y_root {
            return;
        }
        if self.rank[x_root] < self.rank[y_root] {
            self.root[x_root] = y_root;
            self.size[y_root] += self.size[x_root];
        } else {
            self.root[y_root] = x_root;
            self.size[x_root] += self.size[y_root];
            if self.rank[x_root] == self.rank[y_root] {
                self.rank[x_root] += 1;
            }
        }
    }
    pub fn size(&mut self, x: usize) -> usize {
        if x >= self.n {
            panic!();
        }
        let x_root = self.find(x);
        self.size[x_root]
    }
    pub fn is_same(&mut self, x: usize, y: usize) -> bool {
        if x >= self.n || y >= self.n {
            panic!();
        }
        self.find(x) == self.find(y)
    }
}

pub fn bsearch<F>(ok: i64, ng: i64, pred: F) -> Option<i64>
where
    F: Fn(i64) -> bool,
{
    let orig_ok = ok;
    let mut ok = ok;
    let mut ng = ng;
    while (ok - ng).abs() > 1 {
        let mid = (ok + ng) / 2;
        if pred(mid) {
            ok = mid;
        } else {
            ng = mid;
        }
    }
    if ok == orig_ok {
        None
    } else {
        Some(ok)
    }
}

fn solve() {
    input! {
        n: usize, m: usize,
        abv: [(Usize1, Usize1); m]
    };

    let mut uf = UnionFind::new(n);
    for (a, b) in abv {
        uf.unite(a, b);
    }
    let mut table = HashMap::new();
    for i in 0..n {
        *table.entry(uf.find(i)).or_insert(0) += 1 as i64;
    }
    let mut v = Vec::new();
    for &val in table.values() {
        if val != 1 {
            v.push(val as i64);
        }
    }
    v.sort();
    let mut group = v.len() as i64;
    let all_group = group;
    let mut pos = -1;
    let mut res = 0;
    while pos < all_group - 1 {
        let mut diff = 0;
        for i in pos + 1..all_group {
            let i = i as usize;
            if v[i] <= group - 1 - diff {
                diff += 1;
                pos += 1;
            } else {
                break;
            }
        }
        let i = bsearch(pos, all_group, |x| {
            let x = x as usize;
            v[x] - res <= 0
        });
        if let Some(i) = i {
            group = all_group - i - 1;
            res += group;
            pos = i;
        } else {
            group = all_group - pos - 1;
            res += group;
        }
    }
    println!("{}", res);
}

fn main() {
    std::thread::Builder::new()
        .name("big stack size".into())
        .stack_size(256 * 1024 * 1024)
        .spawn(|| {
            solve();
        })
        .unwrap()
        .join()
        .unwrap();
}