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: Wrong Answer)

import java.util.Scanner;
public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		boolean ch=false;
		int i=2;
		for(; (i*(i+1))<=n*2; i++){
			if((i*(i+1))==n*2){
				ch=true;
				break;
			}
		}
		int[][] tmp=new int[i][i];
		int count=1;
		for(int j=0; j<i; j++){
			for(int k=0; k<i; k++){
				if(j>=k){
					tmp[j][k]=count++;
				}
			}
		}
		int[][] ans=new int[i+1][i];
		int cc=0;
		int bb=0;
		boolean tk=false;
		for(int j=0; j<i; j++){
			cc=j;
			bb=0;
			tk=false;
			for(int k=0; k<i; k++){
				if(cc==bb || tk){
					ans[j][k]=tmp[cc][bb];
					tk=true;
					cc++;
				}else{
					ans[j][k]=tmp[cc][bb++];
				}
			}
		}
		for(int j=0; j<i; j++){
			ans[i][j]=tmp[j][j];
		}
		if(ch){
			System.out.println("Yes");
			System.out.println(i+1);
			for(int j=0; j<i+1; j++){
				System.out.print(i+" ");
				for(int k=0; k<i; k++){
					System.out.print(ans[j][k]+" ");
				}
				System.out.println();
			}
		}else{
			System.out.println("No");
		}
	}
}