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<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<vector>
#define ll long long
#define pb push_back
using namespace std;
const int N=110000;
vector<int> P[N];
int n;
int main()
{
	cin>>n;
	ll k=1;
	for(;k<=n+1;k++)
	{
		if(k*(k-1)!=2ll*n) continue;
		int tot=0;
		for(int i=1;i<=k;i++)
			for(int j=i+1;j<=k;j++)
				P[i].pb(++tot),P[j].pb(tot);
		printf("Yes\n%lld\n",k);
		for(int i=1;i<=k;i++)
		{
			int l=P[i].size();
			printf("%d ",l);
			for(int j=0;j<l;j++) printf("%d ",P[i][j]);
			puts("");
		}
		return 0;
	}
	return puts("No"),0;
}