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: Accepted)

from collections import defaultdict

N,M = map(int, input().split(' '))

graph = defaultdict(set)
for i in range(M):
    a,b = map(int, input().split(' '))
    graph[a].add(b)
    graph[b].add(a)

ans = 1
vis_set = set()

for start in graph:
    if start in vis_set:
        continue
    count = 0
    stack = [start]
    vis_set.add(start)
    while len(stack) > 0:
        cur = stack.pop()
        count += 1
        for adj in graph[cur]:
            if adj not in vis_set:
                stack.append(adj)
                vis_set.add(adj)

    ans = max(ans, count)

print(ans)