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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

def resolve():
  N, M = map(int, input().split(" "))
  checked = [False] * (N + 1)
  # frend_labels = [0] * (N + 1)
  # frend_labels_counter = [0] * (N + 1)
  num_of_friend = [0] * (N + 1)
  friends = []
  for _ in range(N+1):
    friends.append(set())

  maximam_friends = 0
  for _ in range(M):
    A, B = map(int, input().split(" "))
    friends[A].add(B)
    friends[B].add(A)

    if num_of_friend[A] == 0 and num_of_friend[B] == 0:
      num_of_friend[A] += 1
      num_of_friend[B] += 1
    elif num_of_friend[A] == 0:
      num_of_friend[A] = num_of_friend[B]
      num_of_friend[B] += 1
      for friend in friends[B]:
        num_of_friend[friend] += 1
    elif num_of_friend[B] == 0:
      num_of_friend[B] = num_of_friend[A]
      num_of_friend[A] += 1
      for friend in friends[A]:
        num_of_friend[friend] += 1

    if num_of_friend[A] > maximam_friends:
      maximam_friends = num_of_friend[A]

  # for friend in friends:
  #   print(friend)
  print(maximam_friends+1)

if __name__ == "__main__":
  resolve()