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 <iostream>
#include <fstream>
#include <vector>
#include <algorithm>
#include <queue>
#include <map>
#include <random>
#include <cstdio>
#include <cstring>
#include <cmath>

using namespace std;
using ll = long long;
using P = pair<ll, ll>;

ll N;

void input() {
    cin >> N;
}


void solve() {
    //    if ((4 * N) % (N + 1)) {
    if (!(N == 1 or N == 3 or N == 6)) {
        cout << "No" << endl;
        return;
    }
    cout << "Yes" << endl;
    
    if (N == 1) {
        cout << 2 << endl;
        cout << 1 << ' ' << 1 << endl;
        cout << 1 << ' ' << 1 << endl;
    } else if (N == 3) {
        cout << 3 << endl;
        cout << 2 << ' ' << 1 << ' ' << 2 << endl;
        cout << 2 << ' ' << 2 << ' ' << 3 << endl;
        cout << 2 << ' ' << 3 << ' ' << 1 << endl;
    } else if (N == 6) {
        cout << 4 << endl;
        cout << 3 << ' ' << 1 << ' ' << 2 << ' ' << 3 << endl;
        cout << 3 << ' ' << 3 << ' ' << 4 << ' ' << 5 << endl;
        cout << 3 << ' ' << 1 << ' ' << 5 << ' ' << 6 << endl;
        cout << 3 << ' ' << 2 << ' ' << 4 << ' ' << 6 << endl;
    }
}


int main() {
    input();
    solve();
    
    return 0;
}