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)

def main():
	N, M = [int(n) for n in input().split(" ")]
	friends = []
	for i in range(M):
		a, b = [int(x) for x in input().split(" ")]
		m = min([a, b])
		M = max([a, b])
		friends.append({
			"min" : m,
			"max" : M
		})
	friends.sort(key=lambda f: (f["min"], f["max"]))
	group = [-1] * N
	for f in friends:
		M = f["max"]
		m = f["min"]
		if group[m - 1] == group[M - 1] == -1:
			group[m - 1] = m - 1
			group[M - 1] = m - 1
		elif group[m - 1] == -1 and group[M - 1] != -1:
			group[m - 1] = group[M - 1]
		elif group[m - 1] != -1 and group[M - 1] == 1:
			group[M - 1] = group[m - 1]
		else:
			group[M - 1] = group[m - 1]

	group_member = [0] * N
	for i in range(len(group)):
		if group[i] == -1:
			group_member[i] += 1
		else:
			group_member[group[i]] += 1
	print(max(group_member))

main()