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 C (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>
int a[1000][1000];
int main(void){
    int n;
    scanf("%d", &n);
    for(int i = 3; i < 1000; i++){
        if(i*(i - 1) == 2*n){
            printf("Yes\n");
            printf("%d\n", i);

            //a[][]の生成
            int cnt = 1;
            for(int ii = 0; ii < i - 1; ii++){
                for(int jj = ii; jj < i - 1; jj++){
                    a[ii][jj] = cnt;
                    cnt++;
                }
            }
            cnt = 2;
            for(int ii = 0; ii < i - 1; ii++){
                for(int jj = ii + 1; jj < i; jj++){
                    a[jj][ii] = cnt;
                    cnt++;
                }
            }
            a[i-1][i-2] = 1;


            for(int j = 0; j < i; j++){
                printf("%d ", i - 1);
                for(int k = 0; k < i - 1; k++){
                    printf("%d", a[j][k]);
                    if(k == i - 2){
                        printf("\n");
                    }else{
                        printf(" ");
                    }
                }
            }

            return 0;
        }
    }
    printf("No\n");
    return 0;
}