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)

// I SELL YOU...! 
#include<iostream>
#include<vector>
#include<algorithm>
#include<functional>
#include<queue>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
signed main(){
  ll n,num=2,v,now,size;
  cin >> n;
  if(n==1){
    cout <<"Yes\n";
    cout <<"2\n";
    cout << "1 1\n";
    cout << "1 1\n";
    return 0;
  }else if(n==2){
    cout <<"No\n";
    return 0;
  }
  v=-1;
  while(v<n){
    v=(num*(num+1))/2;
    num++;
  }
  if(v!=n){
    cout <<"No\n";
    return 0;
  }
  cout <<"Yes\n";
  cout << num<<endl;
  vector<ll> ans[num];
  ans[0].push_back(1);
  ans[0].push_back(2);
  ans[1].push_back(1);
  ans[1].push_back(3);
  ans[2].push_back(2);
  ans[2].push_back(3);
  now = 2;
  size = 2;
  for(int i=3;i<num;i++){
    now = now+size;
    size++;
    for(int j=0;j<size;j++){
      ans[j].push_back(now+j);
    }
    for(int j=0;j<size;j++){
      ans[size].push_back(now+j);
    }
  }
  for(int i=0;i<num;i++){
    cout << ans[i].size()<<" ";
    for(auto j:ans[i]){
      cout << j<<" ";
    }
    cout << endl;
  }
}