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: Accepted)


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    private static int dfs(int current, Set<Integer>[] graph, boolean[] visited){
        visited[current] = true;
        int count = 1;
        if(graph[current] != null){
            for(int next : graph[current]){
                if(!visited[next]){
                    visited[next] = true;
                    count += dfs(next, graph, visited);
                }
            }
        }
        return count;
    }
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb = new StringBuilder();
        // code goes here
        int[] in = nextIntArray(br, 2);
        int n = in[0];
        int m = in[1];
        Set<Integer>[] graph = new HashSet[n];
        for(int i = 0; i < m; i++){
            int[] arr = nextIntArray(br, 2);
            if(graph[arr[0] - 1] == null) graph[arr[0] - 1] = new HashSet<>();
            if(graph[arr[1] - 1] == null) graph[arr[1] - 1] = new HashSet<>();
            graph[arr[0] - 1].add(arr[1] - 1);
            graph[arr[1] - 1].add(arr[0] - 1);
        }
        boolean[] visited = new boolean[n];
        int ans = 0;
        for(int i = 0; i < n; i++){
            if(!visited[i]){
                ans = Math.max(ans, dfs(i, graph, visited));
            }
        }
        sb.append(ans);
        System.out.print(sb.toString());
    }

    private static int nextInt(BufferedReader br) throws IOException{
        return Integer.parseInt(br.readLine());
    }

    private static int[] nextIntArray(BufferedReader br, int n) throws IOException{
        StringTokenizer st = new StringTokenizer(br.readLine());
        int[] arr = new int[n];
        for(int i = 0; i < n; i++){
            arr[i] = Integer.parseInt(st.nextToken());
        }
        return arr;
    }

    static class Pair<A, B>{
        A first;
        B second;
        public Pair(A first, B second){
            this.first = first;
            this.second = second;
        }
    }
}