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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

#pragma region Macro
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define FOR(i, m, n) for(int i = m;i < n;i++)
#define SORT(v) sort(v.begin(), v.end())
#define pb(a) push_back(a)
#define eb(a) emplace_back(a)
#define vi vector<int>
#define vvi vector<vector<int>>
#define chmax(x,y) (x = max(x,y))
#define chmin(x,y) (x = min(x,y))

using namespace std;
typedef long long ll;
typedef pair<int, int> P;
#pragma endregion

void solve(){
	#define int ll
	// ここに処理を記述
	// コンパイル時はエイリアス「gpp」--> c++17でコンパイル
	
	int n, m;
	cin >> n >> m;

	set<int> nakama[n];
	rep(i,m){
		int a, b;
		cin >> a >> b;
		a--; b--;
		nakama[a].insert(b);
		nakama[b].insert(a);
	}

	int ans = -1;
	rep(i,n){
		// cout << "pass" << endl;
		int comp = (int)nakama[i].size();
		chmax(ans, comp);
	}

	cout << ans + 1 << endl;

}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	cout << fixed << setprecision(15);
	
	solve();
	return 0;
}