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: Accepted)

#ruby
#UnionFind

class UnionFind

	def initialize(arr)
		@union_root = {}
		@union_size = {}
		arr.each do |e|
			@union_root[e] = e
			@union_size[e] = 1
		end
	end

	def find(obj)
		if @union_root[obj] == obj
			obj
		else
			find(@union_root[obj])
		end
	end

	def union(obj,targ)
		if issame(obj,targ)
			return
		end
		if size(obj) > size(targ)
			@union_size[find(obj)] += size(find(targ))
			@union_root[find(targ)] = find(obj)
		else
			@union_size[find(targ)] += size(find(obj))
			@union_root[find(obj)] = find(targ)
		end
	end

	def issame(obj,targ)
		find(obj) == find(targ)
	end

	def size(obj)
		@union_size[find(obj)]
	end
end

n,m = gets.chomp.split(" ").map(&:to_i)

uf = UnionFind.new((1..n).to_a)

m.times do
  n1,n2 = gets.chomp.split(" ").map(&:to_i)
  uf.union(n1,n2)
end

max = 0

n.times do |i|
  sz = uf.size(i+1)
  #oy = uf.find(i+1)
  #puts("root:#{oy} size:#{sz}")
  if max < sz
    max = sz
  end
end

p max