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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
	k,n,p,q,i,j:Longint;
	s:array[1..500,1..500]of Longint;
	c:array[1..500]of Longint;
begin
	read(n);
	k:=1;
	while k*(k-1)<n*2 do inc(k);
	if k*(k-1)<>n*2 then begin
		writeln('No');
		exit;
	end;
	writeln('Yes');
	writeln(k);
	p:=1;
	q:=2;
	for i:=1 to n do begin
		inc(c[p]);
		inc(c[q]);
		s[p,c[p]]:=i;
		s[q,c[q]]:=i;
		inc(q);
		if q>k then begin
			inc(p);
			q:=p+1;
		end;
	end;
	for i:=1 to k do begin
		write(k-1);
		for j:=1 to k-1 do write(' ',s[i,j]);
		writeln;
	end;
end.