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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>

using namespace std;

int main()
{
    int n;
    cin >> n;

    long long k = 0;
    for (long long i = 0; i <= n; i++) {
        long long c = i * (i + 1) / 2;
        if (c > n) {
            cout << "No" << endl;
            return 0;
        } else if (c == n) {
            k = i + 1;
            break;
        }
    }

    int num = 1;
    vector<vector<int>> ans(k);
    for (int i = 0; i < k - 1; i++) {
        for (int j = i + 1; j < k; j++) {
            ans[i].emplace_back(num);
            ans[j].emplace_back(num);
            num++;
        }
    }

    cout << "Yes" << endl;
    cout << k << endl;
    for (int i = 0; i < k; i++) {
        cout << ans[i].size() << " ";
        for (int j = 0; j < k - 1; j++) {
            cout << ans[i][j] << (j == k - 2 ? "\n" : " ");
        }
    }

    return 0;
}