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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

class Main{
	public static void main(String[] $){
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();
		
		if(n==1) {
			System.out.println("Yes\n2\n1 1\n1 1");
			return;
		}
		
		int m=0;
		{
			for(long i=0;i<=n;++i){
				if(i*(i-1)==n*2){
					m=(int)i;
				}
			}
			if(m==0){
				System.out.println("No");
				return;
			}
		}
		System.out.println("Yes\n"+m);

		StringJoiner[] sj=new StringJoiner[m];
		Arrays.setAll(sj,i->new StringJoiner(" "));
		{
			String t=String.valueOf(n*2/m);;
			Arrays.stream(sj).forEach(o->o.add(t));
		}

		int p=1;
		for(int i=0;i<m-1;++i){
			for(int j=i+1;j<m;++j){
				String P=String.valueOf(p);
				sj[i].add(P);
				sj[j].add(P);
				++p;
			}
		}
		Arrays.stream(sj).forEach(System.out::println);
	}
}