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 <cctype>
#include <algorithm>
#include <vector>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <utility>
#include <string>
#include <functional>
#include <cctype>
#include <cstring>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <iomanip>
#include <bitset>
#define pb push_back
#define mp make_pair
#define YES cout<<"YES"<<endl
#define Yes cout<<"Yes"<<endl
#define NO cout<<"NO"<<endl
#define No cout<<"No"<<endl
#define INF (1<<30)
#define LLINF (1<<60)
#define MOD 1000000007
#define rep(i, n) for(int i=0;i<n;i++)
using ll = long long;
using namespace std;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int n;
    cin >> n;
    int i = 1;
    while (1) {
        if (i*(i + 1) == n*2)break;
        if (i*(i + 1) > n * 2) {
            cout << "No" << endl;
            return 0;
        }
        i++;
    }
    cout << "Yes" << endl << (i + 1) << endl;
    int num = 1;
    int a[1000][1000] = {};
    int l = i;
    for (int j = 0; j < i; j++) {
        for (int k = 0; k < l; k++) {
            a[j][j + k] = num;
            a[j + 1 + k][j] = num;
            num++;
        }
        l--;
    }
    for (int j = 0; j <= i; j++) {
        cout << i << ' ';
        for (int k = 0; k < i; k++)cout << a[j][k] << ' ';
        cout << endl;
    }
    return 0;
}