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 "bits/stdc++.h"
using namespace std;
#define Would
#define you
const long long INF = 1e18;
const long long MOD = 1e9 + 7;
const double pi = acos(-1);
const int SIZE = 1 << 17;
int dx[] = { 1,0,-1,0 }, dy[] = { 0,1,0,-1 }, alp[30];
long long fac[100005], finv[100005], inv[100005];

vector<int>v[10005];
int main() {
	int n;
	cin >> n;

	int mon = n, dec = -1, monn = 0;

	for (int i = 1; i < 1005; ++i) {
		if (i*(i - 1) / 2 == n) {
			dec = i;
			break;
		}
	}

	if (dec == -1) {
		cout << "No" << endl;
		return 0;
	}

	cout << "Yes" << endl << dec << endl;
	for (int i = 0; i < dec; ++i) {
		for (int j = i + 1; j < dec; ++j) {
			++monn;
			v[i].push_back(monn);
			v[j].push_back(monn);
		}
	}

	for (int i = 0; i < dec; ++i) {
		cout << v[i].size() << " ";
		for (int j = 0; j < v[i].size(); ++j) {
			cout << v[i][j];
			if (j != v[i].size() - 1) { cout << " "; }
		}
		cout << endl;
	}
}