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 <iostream>
#include <vector>
#include <algorithm>
#include <set>
#include <map>
#include <queue>
#include <assert.h>
#include <numeric>
#include <math.h>
#include <climits>
#include <stack>
#include <iomanip>
#include <sstream>

using namespace std;

template <typename T>
inline bool sign(T A) {
    return (A>0)-(A<0);
}
#define REP(i, n) for (int i = 0; i < (n); ++i)
#define SREP(i,s,n) for(int i=s; (n-i)*sign(n-s)>0; i+=sign(n-s))
#define all(x) (x).begin(),(x).end()
typedef long long ll;
typedef unsigned long long ull;

template <typename T>
T gcd(T a, T b) {
    if(a < b) gcd(b, a);
    if (b == 1) return 1;
    T r;
    while ((r=a%b)) {
        a = b;
        b = r;
    }
    return b;
}

bool _less(pair<int, int> a, pair<int, int> b) {
    return a.second < b.second;
}

template <template<class,class,class...> class C, typename K, typename V, typename... Args>
V map_get(const C<K,V,Args...>& m, K const& key, const V & defval)
{
    typename C<K,V,Args...>::const_iterator it = m.find( key );
    if (it == m.end())
        return defval;
    return it->second;
}

#define MOD (1'000'000'000+7)

int main(void) {
    int N;
    cin >> N;

    double cM = (-1 + sqrt(1 + 8 * N)) / 2;

    if (floor(cM) != cM) {
        cout << "No" << endl;
        return 0;
    }

    int M = cM;

    vector < vector<int>> c(M + 1, vector<int>(M));
    int b = 1;
    REP(i, M) {
        REP(j, M-i) {
            c[i][i + j] = b+j;
            c[i + j + 1][i] = b + j;
        }
        b += M - i;
    }
    cout << "Yes" << endl;
    cout << M + 1 << endl;
    REP(i, M+1)
    {
        cout << M << " ";
        REP(j, M){
            cout << c[i][j] << " ";
        }
        cout << endl;
    }
    return 0;
}