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;

void solve(long long N){
	map<int,int> mp;
	for(int i = 2; i * (i - 1) / 2 <= N; ++i) {
		if(i * (i - 1) / 2 == N) {
			vector<vector<int>> a(i);
			int cnt = 1;
			for(int j = 0; j < i; ++j) {
				for(int k = j + 1; k < i; ++k) {
					a[j].push_back(cnt);
					a[k].push_back(cnt);
					++cnt;
				}
			}
			cout << "Yes" << endl;
			cout << i << endl;
			for(int j = 0; j < i; ++j) {
				cout << a[j].size();
				for(auto k: a[j]) {
					cout << " " << k;
				}
				cout << endl;
			}
			return;
		}
	}
	cout << "No" << endl;
}

int main(){	
	long long N;
	scanf("%lld",&N);
	solve(N);
	return 0;
}