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>
using namespace std;
using Int = long long;
int PREP = (cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(9), 0);
//int SEGV = getenv("D") || (exit(system("D= SEGFAULT_SIGNALS=all catchsegv ./prog.exe") >> 8), 0);
struct UnionFind {
    vector<int> A;
    UnionFind(int n) : A(n, -1) {}
    int find(int x) {
        if (A[x] < 0) return x;
        return A[x] = find(A[x]);
    }
    void unite(int x, int y) {
        x = find(x), y = find(y);
        if (x == y) return;
        if (A[x] > A[y]) swap(x, y);
        A[x] += A[y];
        A[y] = x;
    }
};
int main() {
    int N, M; cin >> N >> M;
    UnionFind uf(N);
    for (int i = 0; i < M; i++) {
        int a, b; cin >> a >> b; a--, b--;
        uf.unite(a, b);
    }
    int maxsize = 0;
    for (int i = 0; i < N; i++) {
        int t = uf.find(i);
        maxsize = max(maxsize, -uf.A[t]);
    }
    cout << maxsize << endl;
    return 0;
}