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: Time Limit Exceeded)

from collections import defaultdict, deque
N, M = [int(a) for a in input().split()]
r = defaultdict(set)
for _ in range(M):
    a, b = [int(a) for a in input().split()]
    r[a].add(b)
    r[b].add(a)

def bfs(r, node):
    q = deque()
    q.append(node)
    visited = set([node])
    while q:
        v = q.popleft()
        for n in r[v]:
            if n not in visited:
                if isinstance(r[v], list):
                    visited = visited | set(r[v])
                else:
                    q.append(n)
                    visited.add(n)
    return list(visited - set([node]))

for i in range(1,N+1):
    r[i] = bfs(r, i)
    # print(r[i])

group = [list(range(1, N+1))]
while 1:
    group.append([])
    completed = False
    for p in group[-2]:
        for f in r[p]:
            if f in group[-2]:
                group[-1].append(f)
                group[-2].remove(f)
    if len(group[-1])==0:
        break

print(len(group)-1)