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;
class Program{
	static void Main(){
		long n=long.Parse(Console.ReadLine());
		long a=0,b=0;
		for(long i=0;i<=n;i++){
			if(i*(i+1)==n*2){
				a=i;
				b=i+1;
				break;
			}
		}
		if(a==0){Console.WriteLine("No");}
		else{
			Console.WriteLine("Yes");
			Console.WriteLine("{0}",b);
			long[][] arr=new long[b][];
			long k=1;
			for(long i=0;i<b;i++){
				arr[i]=new long[a+1];
				arr[i][0]=a;
				for(long j=1;j<b;j++){
					if(i<j){
						arr[i][j]=k;
						k++;
					}
					else{
						arr[i][j]=arr[j-1][i];
					}
				}
				Console.WriteLine(String.Join(" ",arr[i]));
			}
		}
	}
}