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 Julia (1.4.0) (judge verdict: Wrong Answer)

using DataStructures
const double = Float64
const int = Int64

parseint(x) = parse(int, x)
readint() = map(parseint, split(readline()))

function main()
  N, M = readint()
  
  G = Vector{Vector{int}}(undef,N)
  for i in 1:N 
    G[i] = Vector{int}(undef,0)
  end
  for i in 1:M
    A,B = readint()
    append!(G[A],[B])
    append!(G[B],[A])
  end
  
  checked = Vector{Bool}(undef,N)
  checked .= false

  Q = Queue{int}()
  smax = 0
  for i in 1:N
    if checked[i]
      continue
    end
    enqueue!(Q,i)
    s = 0

    while true
      if isempty(Q)
        break
      end
      a = dequeue!(Q)
      s += 1

      for b in G[a]
        if ! checked[b]
          enqueue!(Q,i)
          checked[b]=true
        end
      end
    end
    if smax < s
      smax = s
    end
    #println(G)

  end
  println(smax)
  
  

end

main()