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 (GCC 5.4.1) (judge verdict: Accepted)

int n;
ans[555][555];
id[555];
main()
{
	scanf("%d",&n);
	int k=1;
	for(;k*(k-1)<n*2;k++);
	if(k*(k-1)!=n*2)
	{
		puts("No");
		return 0;
	}
	printf("Yes\n%d\n",k);
	int p=0,q=1;
	for(int i=1;i<=n;i++)
	{
		ans[p][id[p]++]=i;
		ans[q][id[q]++]=i;
		q++;
		if(q>=k)p++,q=p+1;
	}
	for(int i=0;i<k;i++)
	{
		printf("%d",k-1);
		for(int j=0;j<k-1;j++)printf(" %d",ans[i][j]);
		puts("");
	}
}