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)

class UnionFind
    def initialize(n)
        @parent = []
        @rank = []

        n.times do |i|
            @parent[i] = i
            @rank[i] = 0
        end
    end
    def findSet(x)
        @parent[x] = findSet(@parent[x]) if x != @parent[x]
        @parent[x]
    end
    def same(x, y)
        findSet(x) == findSet(y)
    end
    def link(x, y)
        if @rank[x] > @rank[y] then
            @parent[y] = x
        else
            @parent[x] = y
            @rank[y] += 1 if @rank[x] == @rank[y]
        end
    end
    def unite(x, y)
        link(findSet(x), findSet(y))
    end
    def get_parent()
        return @parent
    end
end

n, m = gets.chomp.split.map(&:to_i)
uf = UnionFind.new(n)
ans = Hash.new(0)
m.times do
    a, b = gets.chomp.split.map(&:to_i)
    uf.unite(a-1, b-1)
end
group = uf.get_parent
group.each do |group_number|
    ans[group_number] += 1
end
puts ans.max{|x, y| x[1] <=> y[1]}[1]