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 PyPy3 (2.4.0) (judge verdict: Accepted)

n = int(input())
import sys

a = 0
s = []
fl = 0
for i in range(1,500):
    a += i
    s.append(a)
    
for i in range(len(s)):
    if s[i] == n:
        fl = 1
        leng = i+1
        
if fl == 0:
    print("No")
    sys.exit()
    
print("Yes")
print(leng+1)
ans = [[] for _ in range(leng)]
a = 0

for i in range(leng):
    while True:
        a += 1
        ans[i].append(a)
        if len(ans[i]) == i+1:
            break
            
for j in range(leng-1,-1,-1):
    a = ans[j][len(ans[j])-1]
    for k in range(leng-1-j):
        a += (k + j + 1)
        ans[j].append(a)
        
sime = s[:leng]
nn = len(ans[0])

for i in range(leng):
    print(nn,*ans[i])
    
print(nn,*sime)