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 <bits/stdc++.h>
#define LOCAL
using namespace std;
template <typename A, typename B>
ostream& operator <<(ostream& out, const pair<A, B>& a) {
out << "(" << a.first << "," << a.second << ")";
return out;
}
template <typename T, size_t N>
ostream& operator <<(ostream& out, const array<T, N>& a) {
out << "["; bool first = true;
for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
return out;
}
template <typename T>
ostream& operator <<(ostream& out, const vector<T>& a) {
out << "["; bool first = true;
for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
return out;
}
template <typename T, class Cmp>
ostream& operator <<(ostream& out, const set<T, Cmp>& a) {
out << "{"; bool first = true;
for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "}";
return out;
}
template <typename U, typename T, class Cmp>
ostream& operator <<(ostream& out, const map<U, T, Cmp>& a) {
out << "{"; bool first = true;
for (auto& p : a) { out << (first ? "" : ", "); out << p.first << ":" << p.second; first = 0;} out << "}";
return out;
}
#ifdef LOCAL
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
#else
#define trace(...) 42
#endif
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
cerr << name << ": " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
const char* comma = strchr(names + 1, ',');
cerr.write(names, comma - names) << ": " << arg1 << " |";
__f(comma + 1, args...);
}
#define rep(i,n) for(int i=0; i<(n); i++)
using ll = long long;
#define int long long
using P = pair<int,int>;
//#########################################
struct UnionFind {
    vector<int> d;
    UnionFind(int n=0): d(n,-1) {}
    int root(int x) {
      if (d[x] < 0) return x;
      return d[x] = root(d[x]);
    }
    bool unite(int x, int y) {
      x = root(x); y = root(y);
      if (x == y) return false;
      if (d[x] > d[y]) swap(x,y);
      d[x] += d[y];
      d[y] = x;
      return true;
    }
    bool same(int x, int y) { return root(x) == root(y);}
    int size(int x) { return -d[root(x)];}
  };
signed main(){
    int n,m;cin >>n >> m;
    UnionFind uf(n);
    rep(i,m){
        int a,b;cin >> a >> b;
        a--;b--;
        uf.unite(a,b);
    }
    int ret = 0;
    rep(i,n)ret = max(ret,uf.size(i));
    cout << ret << endl;
    return 0;
}