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 Python (3.8.2) (judge verdict: Wrong Answer)

import collections

n,m=map(int,input().split())
par=[i for i in range(n+1)]
rank=[0]*(n+1)

def find(x):
  if par[x]==x:
    return x
  par[x]=find(par[x])
  return par[x]

def union(x,y):
  x=find(x)
  y=find(y)
  if x==y:
    return 0
  if rank[x]<rank[y]:
    par[x]=y
  else:
    par[y]=x
    if rank[x]==rank[y]:
      rank[x]+=1

for i in range(m):
  a,b=map(int,input().split())
  union(a,b)
c=collections.Counter(par)
li=sorted(c.values(),reverse=True)
print(li[0])