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: Runtime Error)

#include <iostream>
#include <vector>
#include <stack>
using namespace std;

static const int MAX = 100000;
static const int NIL = -1;

int n;
vector<int> G[MAX];
int color[MAX];
int rsl = 0;

void dfs(int r, int c){
    int cnt = 0;
    stack<int> S;
    S.push(r);
    color[r] = c;
    cnt += 1;
    while(!S.empty()){
        int u = S.top(); S.pop();
        for(int i=0;i<G[u].size();i++){
            int v = G[u][i];
            if(color[v]==NIL){
                color[v] = c;
                cnt += 1;
                S.push(v);
            }
        }
    }
    rsl = max(rsl,cnt);
}

void assignColor(){
    int id = 1;
    for(int i=0;i<n;i++) color[i]=NIL;
    for(int u=0;u<n;u++){
        if(color[u]==NIL) dfs(u, id++);
    }
}

int main(void){
    // Your code here!
    int s,t,m;
    cin >> n >> m;
    for(int i=0;i<m;i++){
        cin >> s >> t;
        s -= 1;t -= 1;
        G[s].push_back(t);
        G[t].push_back(s);
    }

    assignColor();
    cout << rsl << endl;
}