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: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>

int find_root(int *a, int x){

    if(a[x] == x)
        return x;
    else
        return find_root(a, a[x]);
}

int main(void){
    int n, m;

    int *g;
    int *size;
    int *root;
    int result;


    int i, j;

    scanf("%d", &n);
    scanf("%d", &m);

    g = (int*)malloc(sizeof(int) * n);
    size = (int*)malloc(sizeof(int) * n);
    root = (int*)malloc(sizeof(int) * n);

    for(i = 0; i < n; i++){
        g[i] = i;
        size[i] = 1;
        root[i] = 1;
    }

    for(i = 0; i < m; i++){
        int a, b, x;
        int root_a;
        int root_b;
        scanf("%d", &a);
        scanf("%d", &b);
        a -= 1;
        b -= 1;

        root_a = find_root(g, a);
        root_b = find_root(g, b);

        if(root_a != root_b){
            g[root_b] = g[root_a];
            size[root_a] += size[root_b];
            root[root_b] = 0;
        }

    }



    result = -1;
    for(i = 0; i < n; i++){
        if(root[i] == 1){
            if(result == -1 || result < size[i])
                result = size[i];
        }

    }



    printf("%d\n", result);





    free(g);



    return 0;
}