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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import sys
input = sys.stdin.readline
N = int(input())
f = 0
if N <= 2:
  print("No")
  exit(0)
for i in range(1, N + 1):
  if i * (i + 1) == 2 * N:
    f = i + 1
    break
if f:
  print("Yes")
  print(f)
  res = [set() for _ in range(f + 1)]
  table = [0] * (N + 1)
  for i in range(N):
    res[i % f + 1].add(i + 1)
    table[i + 1] = 1
  for i in range(1, f + 1):
    for j in range(f - len(res[i]) - 1):
      for k in res[(i + j) % f + 1]:
        if table[k] < 2:
          res[i].add(k)
          table[k] += 1
          break
    print(len(res[i]), *sorted(res[i]))
else:
  print("No")