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 count[] = new int[n];
        for (int i = 0;i < 315;++i){
            if((i * i + i) / 2 == n){
                int res[][] = new int[i + 1][i];
                int field[] = new int[n];
                for (int j = 0;j < n;++j){
                    field[j] = -1;
                }
                for (int j = 0;j < i;++j){
                    res[0][j] = j;
                    field[j] = 0;
                    ++count[j];
                }
                for (int j = 1; j < i + 1;++j){
                    boolean ps[] = new boolean[i + 1];
                    int c = 0;
                    for (int k = 0;k < n;++k){
                        if(count[k] == 2)continue;
                        if(field[k] >= 0){
                            if(ps[field[k]])continue;
                            res[j][c] = k;
                            ps[field[k]] = true;
                            field[k] = j;
                            ++count[k];
                            ++c;
                        }
                        else{
                            res[j][c] = k;
                            field[k] = j;
                            ++count[k];
                            ++c;
                        }
                        if(c == i)break;
                    }
                }
                System.out.println("Yes");
                System.out.println(i + 1);
                StringBuilder sb = new StringBuilder();
                for (int j = 0;j < i + 1;++j){
                    sb.append(i);
                    sb.append(' ');
                    for (int k = 0;k < i;++k){
                        sb.append(res[j][k] + 1);
                        if(k + 1 != i)sb.append(' ');
                        else sb.append('\n');
                    }
                }
                System.out.println(sb);
                return;
            }
        }
        System.out.println("No");
    }




}