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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)


import java.io.PrintWriter;
import java.util.*;

public class Main {
    void run() {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);


        int n = sc.nextInt();
        int m = sc.nextInt();
        UnionFindTree uf = new UnionFindTree(n);
//        debug(uf.parent);
        for (int i = 0; i < m; i++) {
            uf.union(sc.nextInt() - 1, sc.nextInt() - 1);
        }

//        debug(uf.parent);
        int[] size = new int[n];
        for (int i = 0; i < n; i++) {
            int p = uf.parent[i];
            size[p]++;
        }
//        debug(size);
        int max = -1;
        for (int i = 0; i < n; i++) {
            max = Math.max(max, size[i]);
        }

        System.out.println(max);

        // out.println("Hello World");
        out.flush();
    }

    void debug(Object... os) {
        System.err.println(Arrays.deepToString(os));
    }

    public static void main(String[] args) {
        new Main().run();
    }
}


class UnionFindTree {

    int[] parent; //インデックスにとノードを対応させ、そのルートノードのインデックスを格納
    int[] rank; //parentと同様に、木の高さを格納

    public UnionFindTree(int size) {
        this.parent = new int[size];
        this.rank = new int[size];

        for (int i = 0; i < size; i++) {
            makeSet(i);
        }
    }

    public void makeSet(int i) {
        parent[i] = i;
        rank[i] = 0; //集合の高さ
    }

    public void union(int x, int y) {
        int xRoot = find(x);
        int yRoot = find(y);

        //xが属する木の方が大きい場合
        if (rank[xRoot] > rank[yRoot]) {
            parent[yRoot] = xRoot; //yの親をxに更新

        } else if(rank[xRoot] < rank[yRoot]) {
            parent[xRoot] = yRoot;

        } else if (xRoot != yRoot){
            parent[yRoot] = xRoot;
            rank[xRoot]++; //同じ高さの木がルートの子として着くから大きさ++;
        }
    }

    //引数の属する木のルートのidを返す
    public int find(int i) {
        if (i != parent[i]) {
            parent[i] = find(parent[i]);
        }
        return parent[i];
    }

    //同じ木に属しているか
    public boolean same(int x, int y) {
        return find(x) == find(y);
    }
}