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 = $stdin.gets.split.map {|i| i.to_i }
AB = []
0.upto(M - 1) do |m|
  a, b = $stdin.gets.split.map {|i| i.to_i }
  if a > b
    a, b = b, a
  end
  AB.push([a, b])
end
AB.sort! do |x, y|
  d = x[0] <=> y[0]
  if d == 0
    d = x[1] <=> y[1]
  end
  d
end

g = 'a'
groups = [g]
counts = { g => 1 }
g = g.succ
same = {}
AB.each do |a, b|
  ga = groups[a - 1]
  gb = groups[b - 1]
  if ga.nil?
    if gb.nil?
      groups[a - 1] = groups[b - 1] = g
      counts[g] ||= 0
      counts[g] += 2
      g = g.succ
    else
      groups[a - 1] = gb
      counts[gb] ||= 0
      counts[gb] += 1
    end
  else
    if gb.nil?
      groups[b - 1] = ga
      counts[ga] ||= 0
      counts[ga] += 1
    elsif ga != gb
      same[ga] ||= []
      same[ga].push(gb)
      same[gb] ||= []
      same[gb].push(ga)
    end
  end
end
c_max = 0
counts.each do |gk, c|
  if s = same[gk]
    s.each do |sk|
      c += counts[sk]
    end
  end
  if c_max < c
    c_max = c
  end
end
puts c_max