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;
using System.Linq;//リストの使用
using System.Collections.Generic;
class Program
{
	static void Main()
	{
		long n = long.Parse(Console.ReadLine());
    long memo = 1;//要素数
    long sumMemo = 0;
    bool answer = false;
    long answerMemo = 1;

    while(sumMemo <= n)
    {
      sumMemo += memo;
      if(sumMemo == n)
      {
        answer = true;
        break;
      }
      memo++;
    }

if(answer)
    {
      Console.WriteLine("Yes");
      Console.WriteLine(memo+1);
      long[,] answers = new long[memo+1, memo];

      for(long i = 0; i < memo; i++)
      {
        for(long j = 0; j < memo-i; j++)
        {
          answers[i,i+j] = answerMemo;
          answers[i+j+1,i] = answerMemo;
          answerMemo++;
        }
      }

      for(long i = 0; i < memo+1; i++)
      {
        string ans = memo.ToString();
        for(long j = 0; j < memo; j++)
        {
          ans += " " + answers[i,j].ToString();
        }
        Console.WriteLine(ans);
      }
      
    }
    else Console.WriteLine("No");

    /*
    if(n == 1)
    {
      Console.WriteLine("Yes");
      Console.WriteLine("2");
      Console.WriteLine("1");
      Console.WriteLine("1");
    }
    else if(n == 3)
    {
      Console.WriteLine("Yes");
      Console.WriteLine("3");
      Console.WriteLine("2 1 2");
      Console.WriteLine("2 3 1");
      Console.WriteLine("2 2 3");
    }else Console.WriteLine("No");
    */
    
	}
}