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 Ruby (2.7.1) (judge verdict: Wrong Answer)

N,M,*S = $<.read.split.map &:to_i
A = [[]]*(N+1)
M.times {|i|
  s = S[i+i,2]
  x,y = s.map {|i;j| i=j while (j=A[i]).frozen?; i}.sort
  a,b = [A[x],A[y]].map{_1[0] ? _1 : []}.sort_by{_1.size}
  a.concat(b).push(*s)
  s.each {|i;j| A[i],i = y,j while (j=A[i]).frozen?; A[i]=y; A[y]=a}
}
p A.map{_1.frozen? ? 0 : _1.uniq.size}.max