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 (3.8.2) (judge verdict: Wrong Answer)

N = int(input())

for k in range(N + 1):
    sn = k - 1
    if k * sn != 2 * N:
        continue

    print("Yes")
    print(k)
    s = [[0] * sn for _ in range(sn)]
    for i in range(sn):
        s[i][i] = s[i-1][i-1] + (i + 1)
        for j in range(i + 1, sn):
            s[i][j] = s[i][j-1] + j
            s[j][i] = s[i][j]
    s.append([s[i][i] for i in range(sn)])
    for x in s:
        print(sn, " ".join(map(str, x)))
    break
else:
    print("No")