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: Wrong Answer)

#include <bits/stdc++.h>
#define INF 1000000000
using namespace std;

int main()
{
  int N;
  cin >> N;
  int each_len = 0, num_group, num_part;
  num_part = N * 2;
  for (int i = 1; i * i < 2 * N; ++i)
  {
    if (i * (i + 1) == num_part)
    {
      each_len = i;
      break;
    }
  }
  if (each_len == 0)
  {
    cout << "No" << endl;
    return 0;
  }
  num_group = num_part / each_len;
  vector<vector<int>> graph(each_len);
  int cnt = 1;
  // cout << each_len << ' ' << num_part << ' ' << num_group << endl;
  for (int i = 1; i < each_len + 1; ++i)
  {
    for (int j = 0; j < i; ++j)
    {
      graph.at(i - 1).push_back(cnt);
      cnt += 1;
    }
  }

  vector<vector<int>> ans;
  for (int i = 0; i < each_len; ++i)
  {
    int h = i;
    int w = i;
    vector<int> temp = graph.at(h);
    for (int j = i + 1; j < each_len; ++j)
    {
      temp.push_back(graph.at(j).at(w));
    }
    ans.push_back(temp);
  }
  vector<int> temp;
  for (int i = 0; i < each_len; ++i)
  {
    temp.push_back(graph.at(i).at(i));
  }
  ans.push_back(temp);

  cout << "Yes" << endl;
  cout << ans.size() << endl;
  for (int i = 0; i < ans.size(); ++i)
  {
    for (int j = 0; j < each_len; ++j)
    {
      cout << ans.at(i).at(j) << ' ';
    }
    cout << endl;
  }
  // for (int i = 0; i < each_len; ++i)
  // {
  //   for (int j = 0; j < graph.at(i).size(); ++j)
  //   {
  //     cout << graph.at(i).at(j) << ' ';
  //   }
  //   cout << endl;
  // }
}