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)

from collections import deque

N, M = map(int, input().split())
rinsetu = [[] for _ in range(N + 1)]
for i in range(M):
    a, b = map(int, (input().split()))
    rinsetu[a].append(b)
    rinsetu[b].append(a)

grp = 0
color = ["white"] * (N + 1)
color[0] = "black"
for i in range(1, N + 1):
    if color[i] == "white":
        d = deque()
        d.append(i)
        a = []
        a.append(i)
        while (d):
            k = d.popleft()
            color[k] = "black"
            for j in rinsetu[k]:
                if color[j] == "white":
                    d.append(j)
                    a.append(j)
        grp=max(grp,len(a))
print(grp)