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 <bits/stdc++.h>

using namespace std;
#define _overload3(_1,_2,_3,name,...) name
#define _rep(i,n) repi(i,0,n)
#define repi(i,a,b) for(int i=int(a);i<int(b);++i)
#define rep(...) _overload3(__VA_ARGS__,repi,_rep,)(__VA_ARGS__)

typedef long long ll;
typedef pair<ll, ll> P;
const ll INF = 1LL<<60;

ll gcd(ll a, ll b) {
  if(b == 0) return a;
  return gcd(b, a % b);
}

template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }

ll modpow(ll a, ll n, ll mod) {
  ll res = 1;
  while (n > 0) {
    if (n & 1) res = res * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return res;
}

int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);

  int N;
  cin >> N;

  int ok = false;
  int start = 1;
  for(int i = 2; i <= 10000; i++){
    if(N == start){
      ok = true;
      break;
    }
    if(N < start){
      break;
    }
    start += i;
  }

  if(ok){

    int num = 1;
    vector<vector<int>> ans(2);
    ans[0].push_back(1);
    ans[1].push_back(1);
    for(int i = 2; i < 10000; i++){
      if(num==N){
        break;
      }
      ans.push_back({});
      int ind = 0;
      for(int j = num+1; j <= num + i; j++){
        ans[ind].push_back(j);
        ans[i].push_back(j);
        ind++;
      }
      num += i;
    }

    cout << "Yes" << endl;
    cout << ans.size() << endl;
    rep(i, ans.size()){
      cout << ans[i].size() << " ";
      rep(j, ans[i].size()){
        cout << ans[i][j] << " ";
      }
      cout << endl;
    }

  }else{

    cout << "No" << endl;
  }



  return 0;
}