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>
int main(){
  int n;
  scanf("%d",&n);
  int k;
  while(n>(k*(k+1))/2){
    k++;
  }
  if(n==(k*(k+1))/2){
    puts("Yes");
  }else{
    puts("No");
    return 0;
  }
  int ans[k];
  int tmp,i,j;
  printf("%d\n",k+1);
  for(i=0;i<=k;i++){
    printf("%d ",k);
    if(i==0){
      ans[0]=1;
      printf("%d",ans[0]);
      for(j=1;j<k;j++){
        ans[j]=ans[j-1]+j;
        printf(" %d",ans[j]);
      }
      puts("");
    }else if(i==k){
      tmp=1;
      printf("%d",tmp);
      for(j=1;j<k;j++){
        tmp+=j+1;
        printf(" %d",tmp);
      }
      puts("");
    }else{
      tmp=ans[i];
      printf("%d",tmp);
      for(j=1;j<k;j++){
        if(j<=i)tmp+=1;
        else tmp+=j;
        printf(" %d",tmp);
      }
      puts("");
    }
  }
  return 0;
}