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 Ruby (2.3.3) (judge verdict: Wrong Answer)

require 'pp'
# IS_DEBUG = true
IS_DEBUG = false
def dputs str
	if(IS_DEBUG)
		puts str
	end
end
def dpp str
	if(IS_DEBUG)
		pp str
	end
end

N,_=gets.chomp.split(' ').map{|n| n.to_i}
k = 1
flg = false
while(k*(k+1) <= 100000)
	if(N*2 == k*(k-1))
		flg = true
		break;
	end
	k += 1
end
if(!flg)
	puts "No"
	exit(0)
end
A = Array.new(k){|i| Array.new(k-1)}
numbering = 1
for times in 0..(k-1-1)
	for i in times..(k-1-1)
		# pp [times, i+times]
		# pp [i+times+1, times]
		A[times][i] = numbering
		A[i+1][times] = numbering
		numbering += 1
	end
end
puts "Yes"
puts A.size
A.each{|l|
	print l.size
	print " "
	puts l.join(" ")
}