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)

N = int(input())
H = list(range(N))
T = []

ctr = 0
L = 0
while ctr < N:
    L += 1
    ctr += L

if ctr != N:
    print('No')
    
else:
    T = [[0 for _ in range(L)] for _ in range(L+1)]
    for i in range(L):
        for j in range(L-i):
            T[i][i+j] = int(i*L-i*(i-1)/2+j+1)
            T[i+j+1][i] = int(i*L-i*(i-1)/2+j+1)
    for i in range(L+1):
        print(L,*T[i])