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)

import numpy as np
N = int(input())
k = 0
while k*k < 2*N:
    k += 1
if k*(k - 1) != 2*N:
    print('No')
elif N == 1:
    print('Yes')
    print(1)
    print(1, 1)
else:
    print('Yes')
    print(k)
    S = np.zeros([k, k-1], dtype=int)
    max = int(0)
    for i in range(k-1):
        S[i, i:] = list(range(max+1, max+k-i))
        S[i+1:, i] = S[i, i:]
        max += k-i-1
    for i in range(k):
        print(' '.join(map(str, np.insert(S[i], 0, k-1))))