Problem Description

Given an integer $ N $, determine whether there exists a tuple of subsets $ (S_1, S_2, ..., S_k) $ of $\{1, 2, ..., N\}$ that satisfies the following conditions, and if so, construct one such tuple.

• Each integer from $ 1, 2, ..., N $ is contained in exactly 2 of the subsets $ S_1, S_2, ..., S_k $.
• Any two sets from $ S_1, S_2, ..., S_k $ have exactly 1 element in common.

Input Format

The input is given from the standard input in the following format:

$ N $

Output Format

If no such tuple of subsets exists, output No. If it exists, first output Yes, then output the information of the subsets in the following format. Let $S_i = \{S_{i,1}, S_{i,2}, ..., S_{i,|S_i|}\}$.

If there are multiple valid solutions, you may output any one of them.

$ 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|} $

Sample Input and Output

Sample Input #1

3

Sample Output #1

Yes
3
2 1 2
2 3 1
2 2 3

Sample Input #2

4

Sample Output #2

No

Notes/Hints

Constraints

• $1 \leq N \leq 10^5$
• $ N $ is an integer.

Sample Explanation 1

$(S_1, S_2, S_3) = (\{1, 2\}, \{3, 1\}, \{2, 3\})$ satisfies the conditions.

见题面 Input 部分

见题面 Output 部分