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 INF 1e7
#define mod 1000000007

using namespace std;
typedef long long int ll;
typedef tuple<int,int,int> tii;
typedef tuple<long long int,long long int,long long int> tll;
typedef tuple<double,double,double> tdd;


int main()
{
    int N; cin >> N;
    bool f = true;
    int k;
    for(k = 1; k*(k-1)/2 <= N; k++) 
    {
        if(k*(k-1)/2 == N) 
        {
            f = false;
            break;
        }
    }
    if(f) 
    {
        cout << "No" << endl;
        return 0;
    }
    else 
    {
        cout << "Yes" << endl;
        cout << k << endl;
    }
    for(int i = 1; i <= k; i++)
    {
        cout << k-1 << " ";
        if(i == 1) 
        {
            for(int j = 1; j*(j-1)/2 + 1 <= N; j++) cout << j*(j-1)/2 + 1 << " ";
            cout << endl;
        }
        else if(i == 2)
        {
            int first = 1;
            for(int j = 1; j <= k-1; j++)
            {
                cout << first << " ";
                first += j+1;
            }
            cout << endl;
        }
        else
        {
            int first = (i-1)*(i-2)/2 + 1;
            for(int j = 1; j <= i-1; j++)
            {
                cout << first << " ";
                first++;
            }
            first--;
            first += i-1;
            for(int j = i; j <= k-1; j++)
            {
                cout << first << " ";
                first += j+1;
            }
            cout << endl;
        }
    }
}