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>

using namespace std;
typedef long long ll;

ll N;
vector<ll> v[1000];

int main(){
    cin >> N;
    if(N < 3){
        cout << "No" << endl;
        return 0;
    }
    N *= 2;
    ll n = -1;
    for(int i=1;i*i<=N;i++){
        if(N % i != 0) continue;
        if(N / i != i+1) continue;
        n = i;
        break;
    }
    if(n == -1){
        cout << "No" << endl;
        return 0;
    }
    cout << "Yes" << endl;
    cout << n+1 << endl;
    for(int i=0;i<n;i++) v[0].push_back(i+1);
    ll count = n+1;
    for(int i=1;i<n+1;i++){
        for(int j=0;j<i;j++) v[i].push_back(v[j][i-1]);
        for(int j=i;j<n;j++) v[i].push_back(count++);
    }
    for(int i=0;i<n+1;i++){
        cout << n;
        for(int j=0;j<n;j++) cout << " " << v[i][j];
        cout << endl;
    }
    return 0;
}