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

n=int(input())

if n==1:
    print("Yes")
    print(2)
    print("1 1")
    print("1 1")
    exit()

def sss(n):
    if n==2:
        return [[1,2],[1,3],[2,3]]
    N=n*(n+1)//2
    ss=[[i for i in range(N-n+1,N+1)]]
    j=N-n+1
    for i in sss(n-1):
        i.append(j)
        ss.append(i)
        j+=1

    return ss
    

ok=0
for i in range(1000):
    if n == (i+2)*(i+3)//2:
        ok=1
        k = i+3
        gen = k-1
        break

# n= k+1 C 2


if ok==0:
    print("No")

else:
    print("Yes")
    print(k)
    
    for i in sss(gen):
        print(*([len(i)]+i))