Problem:
Score : 500 points

Problem Statement

You are given an integer N. Determine if there exists a tuple of subsets of \{1,2,...N\}, (S_1,S_2,...,S_k), that satisfies the following conditions:

Each of the integers 1,2,...,N is contained in exactly two of the sets S_1,S_2,...,S_k.

Any two of the sets S_1,S_2,...,S_k have exactly one element in common.

If such a tuple exists, construct one such tuple.

Constraints

1 \leq N \leq 10^5

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

If a tuple of subsets of \{1,2,...N\} that satisfies the conditions does not exist, print No.
If such a tuple exists, print Yes first, then print such subsets in the following format:

k
|S_1| S_{1,1} S_{1,2} ... S_{1,|S_1|}
:
|S_k| S_{k,1} S_{k,2} ... S_{k,|S_k|}

where S_i={S_{i,1},S_{i,2},...,S_{i,|S_i|}}.

If there are multiple such tuples, any of them will be accepted.

Sample Input 1

3

Sample Output 1

Yes
3
2 1 2
2 3 1
2 2 3

It can be seen that (S_1,S_2,S_3)=(\{1,2\},\{3,1\},\{2,3\}) satisfies the conditions.

Sample Input 2

4

Sample Output 2

No

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

n = gets.chomp.to_i

if n == 1
  puts 'Yes'
  puts '2'
  puts '1 1'
  puts '1 1'
  exit
end

if n == 3
  puts 'Yes'
  puts '3'
  puts '2 1 2'
  puts '2 3 1'
  puts '2 2 3'
  exit
end

oks = [1]
2.upto(10**5) do |i|
  if i == (oks.last + oks.size + 1)
    oks.push(i)
  end
end

if !oks.include?(n)
  puts 'No'
  exit
end

num = oks.index(n) + 1

ans = Array.new(num + 1) { Array.new }
counts = Array.new(n, 0)

(num + 1).times do |i|
  1.upto(n) do |t|
    next if ans[i].size == num
    if i == 0
      ans[i].push(t)
      counts[t-1] += 1
    else
    i.times do |u|
      if !ans[u].include?(t) && counts[t-1] < 2
        ans[i].push(t)
        counts[t-1] += 1
      end
    end
    end
  end
end
p ans