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: Runtime Error)

import numpy as np
N = int(input().strip('\n'))
k2 = 1+np.sqrt(1+8*N)
if k2%2==0:
    k=int(k2/2)
    print('Yes')
    print(k)
    yel = [1]
    red = [1]
    for i in range(1,k-1):
        yel.append(yel[i-1]+1+i)
        red.append(red[i-1]+i)
    yel = np.array(yel).astype('int16')
    red = np.array(red).astype('int16')
    print(k-1,*yel)
    print(k-1,*red)
    for i in range(1,k-1):
        fs = np.arange(red[i],red[i]+i).astype('int16')
        sc = red[i:]+i
        print(k-1,*fs,*sc)
else:
    print('No')