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: Runtime Error)

#include <stdio.h>
#include <stdlib.h>
int parent[100001],max,component;
int find(int a)
{
    if(parent[a]<0)
        return(a);
    else
    {
        return(parent[a]=find(parent[a]));
    }
}
void _union_(int a,int b)
{
    int pa,pb;pa=find(a);pb=find(b);
    if(pa==pb)
        return;
    else
    {
        if((-parent[pa])<=(-parent[pb]))
        {
          parent[pb]=parent[pa]+parent[pb];parent[pa]=pb;if(max<(-parent[pb]))max=-parent[pb];component--;return;
        }
        if((-parent[pa])>(-parent[pb]))
        {
          parent[pa]=parent[pa]+parent[pb];parent[pb]=pa;if(max<(-parent[pa]))max=-parent[pa];component--;
        }
    }
}
int main()
{
    int j,n,m;scanf("%d %d",&n,&m);
    for(j=0;j<=n;j++)
        parent[j]=-1;
    component=n;max=1;
    for(j=0;j<m;j++)
    {
        int a,b;scanf("%d %d",&a,&b);
        _union_(a,b);
        //printf("%d %d\n",component,max);
    }
    printf("%d\n",max);
    return 0;
}