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: Runtime Error)

def solve(N, M, fridens):
    parents = {}
    groups = {}
    for A, B in friends:
        parents[B] = A
        if A not in groups:
            if A not in parents:
                groups[A] = [A]
            else:
                continue
        groups[A].append(B)

    ans = len(max(groups.values(), key=len))
    print(ans)


if __name__ == "__main__":
    N, M = map(int, input().split())
    friends = []
    for _ in range(M):
        AB = sorted([x - 1 for x in map(int, input().split())])
        if AB not in friends:
            friends.append(AB)
    solve(N, M, friends)