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: Wrong Answer)

# -*- coding: utf-8 -*-
import math
import numpy as np
def solve():
    N = int(input())
    m = int(math.sqrt(1+8*N))
    if 1+8*N == m**2:
        k = (2+m)//2
    elif 1+8*N == (m+1)**2:
        k = (1+m)//2
    else:
        return 'No'
    M = np.arange(k**2, dtype=int).reshape(k,k)-np.array([[(i+1)*i/2] for i in range(k)], dtype=int)-np.arange(k).reshape(k,1)
    M *= (np.arange(k).reshape(1,k)>np.arange(k).reshape(k,1))
    M += M.T
    res = '{}'.format(k+1)
    for a in M:
        t = '\n{} '.format(k)
        t += ' '.join([str(b) for b in a if b > 0])
        res += t 
    return res
    
if __name__ == '__main__':
    print(solve())