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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

#define rep(i, n) for (int i = 0; i < (n); i++)
using namespace std;
typedef long long ll;
const int INF = 1e9;

int main() {
  ll n, ans = 0;
  cin >> n;
  map<ll, ll> mp;
  for (ll i = 2; i <= n; ++i) mp[i * (i - 1) / 2] = i;

  if (mp.count(n)) {
    int m = mp[n], num = 1;
    vector<set<int>> v(m);
    rep(i, m) for (int j = i + 1; j < m; ++j) v[i].insert(num),
        v[j].insert(num++);

    cout << "Yes" << endl;
    cout << m << endl;
    for (auto x : v) {
      cout << x.size() << " ";
      for (auto y : x) cout << y << " ";
      cout << endl;
    }
    return 0;
  }

  cout << "No" << endl;
  return 0;
}