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)

def solve(n, t)
  arr = (1..n).to_a
  ans = []
  double = []
  arr_select = arr.dup
  t.times do
    arr_select -= ans.flatten.uniq
    next_array = []
    ans.each do |a|
      a -= double
      next_array << a[0]
      double << a[0]
    end
    k = t - next_array.length
    next_array += arr_select[0, k]
    ans << next_array
  end
  ans << arr - double
  ans.map!{ |a| [t] + a }
  ans
end

n = gets.to_i
k = 3
ok = [[3,2]]
c = 3
while k <= 100000
  k += c
  ok << [k,c]
  c += 1
end

if ok.transpose[0].include?(n)
  k = ok.transpose[0].index(n)
  puts 'Yes'
  ans = solve(n, ok[k][1])
  puts ans.size
  puts ans.map{ |a| a.join(' ') }
else
  puts 'No'
end