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: Accepted)

#include<string.h>
#include<iostream>
#include<vector>
#include<algorithm>
#include<stack>
#include<set>
#define lli long long int
#define ULTRA_INSTINCT ios_base::sync_with_stdio(false); cin.tie(0)
#define fo(i,n) for(int i=0;i<(n);i++)
using namespace std;
const int MAXI = 2e5 + 5;

vector<int >g[MAXI];
int visi[MAXI];
int sz = 0;
void dfs(int node){
    visi[node] = 1;
    sz++;
    for(int to : g[node]){
        if(visi[to] ==0){
            dfs(to);
        }
    }
}

void solve(){

    int  n , m;
    cin>>n>>m;
    int l,r;
    set<pair<int,int > >st;
    fo(i,m){
        cin>>l>>r; --l,--r;
        if(st.find(make_pair(l,r)) == st.end()){
            st.insert(make_pair(l,r));
            st.insert(make_pair(r,l));
            g[l].push_back(r);
            g[r].push_back(l);
        }   
    }
    int ans = 1;
    fo(i,n){
        if(visi[i] == 0){
            sz = 0;
            dfs(i);
            ans = max(ans , sz);
        }
    }
    cout<<ans<<endl;




}

int main(){
    ULTRA_INSTINCT;
    int t =1;
    // cin>>t;
    while(t--){
        solve();
    }

    return 0;
}