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<cstdio>
#include<cstring>
#include<iostream>
#include<cmath>
#include<algorithm>
#include<set>
#include<map>
#include<vector>
#include<queue>
#define MN 40002
#define MM 5000001
#define ll long long
#define ld long double
#define inf 0x7fffffff
#define clz 1000000007
#define ers(arr,val) memset(arr,val,sizeof(arr));
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define repd(i,b,a) for(int i=(b);i>=(a);i--)
#define repe(i,u) for(int i=h[u];i;i=e[i].nx)
using namespace std;
int n,sum=0,N,p=0;
int ans[3001][3001];
int main(){
	scanf("%d",&n);
	if(n==1) return 0*puts("No");
	for(int i=1;i<=100000;i++){
		sum+=i;
		if(sum==n) {N=i;break;}
		if(sum>n) break;
	}
	if(N){
		rep(i,1,N)rep(j,i,N) ans[i][j]=++p;
		p=0;
		rep(j,1,N)rep(i,j,N) ans[i+1][j]=++p;
		puts("Yes");
		printf("%d\n",N+1);
		rep(i,1,N+1){
			printf("%d ",N); rep(j,1,N) printf("%d ",ans[i][j]);puts("");
		}
	}
	else puts("No");
	return 0;
}