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: Wrong Answer)

#include <bits/stdc++.h>
#define pb push_back
using namespace std;

int n,m,cnt;

vector<int>a[1000];

int main() {
	scanf("%d",&n);
	
	m=sqrt(2*n);

	for(int i=1;i*(i-1)<=2*n;i++) if(i*(i-1)==n*2) m=i;
	
	if(!m) {
		puts("No");return 0;
	}
	
	puts("Yes");printf("%d\n",m);
	
	for(int i=1;i<=m;i++) for(int j=i+1;j<=m;j++) cnt++,a[i].pb(cnt),a[j].pb(cnt);
	
	for(int i=1;i<=m;i++) {
		printf("%d ",a[i].size());
		for(int j=0;j<a[i].size();j++) printf("%d ",a[i][j]);puts("");
	}
	
	return 0;
}