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 = gets.split.map(&:to_i)
AB = readlines.map {|s| s.split.map(&:to_i) }

class Node
  attr_accessor :parent, :rank

  def initialize(n)
    @parent = n
    @rank = 0
  end
end

class UnionFindTree
  def initialize(n)
    @nodes = (0..n).to_a.map { |i| Node.new(i) }
  end

  def find(x)
    return x if @nodes[x].parent == x

    return @nodes[x].parent = find(@nodes[x].parent)
  end

  def unite(a, b)
    a = find(a)
    b = find(b)
    return if a == b

    if @nodes[a].rank < @nodes[b].rank
      @nodes[a].parent = b
    else
      @nodes[b].parent = a
      @nodes[a].rank += 1 if @nodes[a].rank == @nodes[b].rank
    end
  end

  def same?(a, b)
    find(a) == find(b)
  end

  def parents
    @nodes.map(&:parent)
  end
end

g = []

tree = UnionFindTree.new(N-1)

AB.each do |a,b|
  tree.unite(a-1, b-1)
end
n = tree.parents.uniq.size
p n == 1 ? N : N - n