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;

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

  int k = 0;
  for (int i = 1; i < N + 2; i++) {
    if (i * (i - 1) / 2 == N) {
      k = i;
    }
  }
  if (!k) {
    cout << "No" << endl;
    return 0;
  }

  cout << "Yes" << endl;
  cout << k << endl;

  vector<vector<int>> mat(k + 1, vector<int>(k + 1, 0));
  int c = 1;
  for (int i = 1; i < k + 1; i++) {
    for (int j = 1; j < i; j++) {
      mat[i][j] = c++;
    }
  }
  
  for (int i = 1; i < k + 1; i++) {
    set<int> s;
    for (int j = 1; j < k + 1; j++) {
      if(mat[i][j]) s.insert(mat[i][j]);
      if(mat[j][i]) s.insert(mat[j][i]);
    }

    vector<int> v(begin(s), end(s));
    cout << v.size() << ' ';
    for (int j = 0; j < (int)v.size(); j++) {
      cout << v[j] << ( (j == (int)v.size() - 1) ? '\n' : ' ' );
    }
  }

  return 0;
}