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)

n = gets.chomp.to_i

s = 3
d = 3
w = 2
fld = false
while s < 10**5 do
    if s == n then
        flg = true
        break
    end
    s += d
    d += 1
    w += 1
end

if flg then
    puts("Yes")
    h = w + 1
    a = Array.new(h).map{Array.new(w, 0)}

    # ななめ
    num = 1
    add = w
    for j in 0..(w - 1) do
        for i in [j, j+1] do
            a[i][j] = num
        end
        num += add
        add -= 1
    end

    #右上
    for i in 0..(h - 1) do
        for j in i+1..(w - 1) do
            a[i][j] = a[i][j - 1] + 1
        end
    end

    #左上
    for j in 0..(w - 1) do
        for i in (j+2)..(h - 1) do
            a[i][j] = a[i-1][j] + 1
        end
    end

    # 結果の出力
    puts(h)
    for i in 0..(h - 1) do
        print(w.to_s + " ")
        for j in 0..(w - 1) do
            print(a[i][j].to_s + " ")
        end
        print("\n")
    end

    if false then
    for i in 0..(h - 1) do
        for j in 0..(w - 1) do
         print(a[i][j].to_s + " ")
        end
         print("\n")
    end
    end
else
    puts("No")
end