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.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
		int a = N;
		int b = 1;
		string ans = "No";
		while(true){
			a -= b;
			if(a==0){
				ans = "Yes";
				b += 1;
				break;
			} else if(a<0){
				break;
			} else {
				b += 1;
			}
		}
		Console.WriteLine(ans);
		if(ans == "Yes"){
		List<int>[] C = new List<int>[b];
		for(var i=0;i<b;i++){
			C[i] = new List<int>();
		}
		int a1 = 0;
		int ia = 0;
		while(true){
			for(var j=ia+1;j<b;j++){
				C[ia].Add(a1+1);
				C[j].Add(a1+1);
				a1 += 1;
			}
			ia += 1;
			if(a1==N){
				break;
			}
		}
		Console.WriteLine(b);
		for(var i=0;i<b;i++){
			Console.Write(C[i].Count);
			for(var j=0;j<C[i].Count;j++){
				Console.Write(" "+C[i][j]);
			}
			Console.WriteLine();
		}
		}
	}
}