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: Accepted)

def  nnp1(n)
    a=((n*2)**(0.5)).to_i
    return a*(a+1)==n*2
end

def  nnp(n)
    a=((n*2)**(0.5)).to_i
    return a
end

n=gets.strip.to_i

if nnp1(n) == false 
    puts 'No'
    exit
end
puts 'Yes'
a=nnp(n)
x=Array.new(a+1).map{Array.new(a)}
c=1
puts a+1
(0..a-1).each{|i|
    
    cc=c
    (i..a-1).each{|j|
        x[i][j]=cc
        cc+=1
    }

    cc=c
    (i+1..a).each{|j|
        x[j][i]=cc
        cc+=1
    }
    c=cc
}

x.each do |i|
    print a.to_s + " "
    puts i.join(" ")

end