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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();        
        sc.close();


        boolean b = false;
        int n1=0, n2=0;
        for(int i=1; i<1000; i++){
            if(i * (i+1) == n * 2){
                b = true;
                n1 = i;
                n2 = i+1;
                break;
            }
        }

        if(!b){
            System.out.println("No");
            return;
        }

        int[][] ans = new int[n2][n1];
        for(int i=0; i<n1; i++){
            ans[0][i] = i+1;
        }
        int c = n1+1;
        for(int i=1; i<n2; i++){
            for(int j=0; j<i; j++){
                ans[i][j] = ans[j][i-1];
            }
            for(int j=i; j<n1; j++){
                ans[i][j] = c;
                c++;
            }
        }

        System.out.println("Yes");
        System.out.println(n2);
        for(int i=0; i<n2; i++){
            System.out.print(n1);
            for(int j=0; j<n1; j++){
                System.out.print(" " + ans[i][j]);
            }
            System.out.println("");
        }

    }
}