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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <cstdlib>
#include <algorithm>
using namespace std;

int main(){
  long long N;
  cin >> N;

  long long k = 2;
  while(1){
    long long test = k*(k-1);
    if(test == 2*N){
      break;
    }else if(test > 2*N){
      cout << "No" <<"\n";
      return 0;
    }else{
      k++;
    }
  }

  cout << "Yes" << "\n";
  cout << k << "\n";

  int sum[k] = {};
  sum[0]= 1;
  for(int i=1;i<k;i++){
    sum[i] = sum[i-1] + i;
  }

  for(int i=0;i<k-1;i++){
    cout << k-1 << " ";
    for(int j=0;j<i;j++){
      cout << sum[i] + j << " ";
    }
    for(int j=i;j<k-1;j++){
      cout << sum[j] + i;
      if(j != k-2){
        cout << " ";
      }
    }
    cout << "\n";
  }

  cout << k-1 << " ";
  for(int j=0;j<k-1;j++){
    cout << sum[j] + j;
    if(j != k-2){
      cout << " ";
    }
  }
  cout << "\n";

  return 0;
}