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;

typedef long long ll;
typedef unsigned long long ull;

int main(){
    int N;
    cin >> N;
    for(ll k=1;k*(k-1)/2<=N;k++){
        if(k*(k-1)/2==N){
            cout << "Yes" << endl << k << endl;
            set<int> ans[1000];
            int l=1,r=2;
            for(int idx=1;idx<=N;idx++){
                ans[l].insert(idx);
                ans[r].insert(idx);
                r++;
                if(r>k){
                    l++;
                    r=l+1;
                }
            }
            for(int i=1;i<=k;i++){
                cout << k-1;
                for(int x:ans[i]) cout << " " << x;
                cout << endl;
            }
            return 0;
        }
    }
    cout << "No" << endl;
    
    return 0;
}