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: Accepted)

n = int(input())

k = int((n * 2) ** 0.5) + 1
if k * (k - 1) != 2 * n:
    print('No')
else:
    print('Yes')
    print(k)
    arr = [list() for _ in range(k)]

    num = 1
    tar1, tar2 = 0, 1
    while True:
        arr[tar1].append(num)
        arr[tar2].append(num)
        if num == n:
            break
        else:
            num += 1
        if len(arr[tar1]) == k - 1:
            tar1 += 1
            tar2 = tar1 + 1
        else:
            tar2 += 1
    for i in range(k):
        print(k - 1, *arr[i])