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: Wrong Answer)

#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <string.h>
int main()
{
  int n, root, i;
  int count[100000]={0};
  scanf("%d",&n);
  root = (int)sqrt(2*n);
  if(n%2==1){
    puts("Yes");
    printf("%d",(n+1)/2);
    for(i=1;i<=(n+1)/2;i++){
      printf(" %d",i);
    }
    puts("");

    printf("%d",(n+1)/2);
    for(i=(n+1)/2;i<=n;i++){
      printf(" %d",i);
    }
    puts("");

    for(i=1;i<(n+1)/2;i++){
      printf("2 %d %d\n", i, n-i+1);
    }
  } else {
    puts("No");
  }
  /*
  if(2*n != root*(root+1)){
    puts("No");
    return 0;
  }
  */

  return 0;
}