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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;

namespace tenka1_2018_d
{
	class Program
	{
		static void Main(string[] args)
		{
			int n = int.Parse(Console.ReadLine());
			int sum = 0; int k = 0;
			for (; sum < n; k++) sum += k;
			k--;
			if (sum == n)
			{
				Console.WriteLine("Yes");
				Console.WriteLine(k + 1);
				int[,] ret = new int[k + 1, k];
				int count = 1;
				for (int i = 0; i < k; i++)
				{
					for (int j = 0; j < k - i; j++)
					{
						ret[i, i + j] = count + j;
						ret[i + j + 1, i] = count + j;
					}
					count += k - i;
				}
				for (int i = 0; i <= k; i++)
				{
					Console.Write(k);
					for (int j = 0; j < k; j++) Console.Write(" " + ret[i, j]);
					Console.WriteLine();
				}
			}
			else Console.WriteLine("No");
		}
	}
}