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.

3

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.

4

No