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 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <string.h>
int main(void)
{
  int n;
  int root_2n;
  int i, j, k;
  int num[550][550];

  scanf("%d",&n);
  root_2n = (int)sqrt(2*n);
  if(n==root_2n*(root_2n+1)/2) {
    puts("Yes");
    printf("%d\n",root_2n+1);
    for(i=1;i<=root_2n;i++){
      for(j=1;j<=i;j++){
        num[i][j] = i*(i-1)/2 + j;
      }
    }

    printf("%d",root_2n);
    for(i=1;i<=root_2n;i++) {
      //group[k][i] = num[i][i];
      printf(" %d",num[i][i]);
    }
    printf("\n");

    for(k=1;k<=root_2n;k++) {
      printf("%d",root_2n);
      for(j=1;j<=k;j++) {
        //group[k][j] = num[k][j];
        printf(" %d",num[k][j]);
      }
      for(i=k+1;i<=root_2n;i++) {
        //group[k][i] = num[i][k];
        printf(" %d",num[i][k]);
      }
      printf("\n");
    }
  } else {
    puts("No");
  }

  return 0;
}