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 Python (3.4.3) (judge verdict: Accepted)

import sys
input=lambda: sys.stdin.readline().rstrip()
from collections import defaultdict
n=int(input())
D=defaultdict(int)
i=1
while i*(i+1)//2<=10**5:
  D[i*(i+1)//2]=i
  i+=1
if D[n]==0:
  print("No")
else:
  print("Yes")
  k=D[n]+1
  print(k)
  A=[[0]*(k) for _ in range(k)]
  for i in range(k):
    A[i][0]=k-1
  D=dict()
  D[1]=1*k+1
  for i in range(2,n+1):
    d1,d2=D[i-1]//k,D[i-1]%k
    if d2==k-d1:
      D[i]=(d1+1)*k+1
    else:
      D[i]=d1*k+d2+1
  for i in range(1,n+1):
    d1,d2=D[i]//k,D[i]%k
    A[d1-1][d1+d2-1]=i
    A[d1+d2-1][d1]=i
  for a in A:
    print(*a)