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.*;

public class Main {

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

        int k = -1;
        for(int i = 1; i <= n ; i++){
            if((i * (i-1) /2) == n){
                k = i;
                break;
            }
        }

        if(k == -1){
            System.out.println("NO");
            System.exit(0);
        }

        List<Integer>[] ans = new List[k];
        for(int i = 0; i < k;i++){
            ans[i] = new ArrayList<>();
        }
        int num = 1;
        for(int i = 0;i < k;i++){
            for(int j = i+1;j<k;j++){
                ans[i].add(num);
                ans[j].add(num);
                num++;
            }
        }


        System.out.println(k);
        for(int i = 0; i < k;i++){
            System.out.print(ans[i].size() + " ");
            for(int j = 0;j < ans[i].size();j++){
                if(j != 0){
                    System.out.print(" ");
                }
                System.out.print(ans[i].get(j));
            }
            System.out.println("");
        }
    }
}