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;

public class AtCoder{
	public static void Main(){
		int n;
		n = int.Parse(Console.ReadLine().Trim());
		bool f = false;
		int k = 0;
		
		for(int i=1; i<1000; i++){
			if(i*(i-1)/2==n){
				f = true;
				k = i;
			}
		}
		
		if(f){
			Console.WriteLine("Yes");
			Console.WriteLine(k);
			int[][] s = new int[k][];
			for (int i=0; i<k; i++){
				s[i] = new int[k-1];
			}
			int c = 1;
			for(int i=k-1; i>0; i--){
				for(int j=0; j<i; j++){
					s[k-1-i][k-1-i+j] = c;
					s[k-1-i+j+1][k-1-i] = c;
					c++;
				}
			}
			for(int i=0; i<k; i++){
				Console.Write(k-1);
				Console.Write(" ");
				for(int j=0; j<k-1; j++){
					Console.Write(s[i][j]);
					Console.Write(" ");
				}
				Console.WriteLine();
			}
		}else{
			Console.WriteLine("No");
		}
	}
}