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 LuaJIT (2.0.4) (judge verdict: Accepted)

local n = io.read("*n")
local a = 0
for i = 1, 1000 do
  if i * (i + 1) == n * 2 then
    a = i
    break
  end
end
if a == 0 then
  print("No")
else
  print("Yes")
  print(a + 1)
  local t = {}
  for i = 1, a + 1 do
    t[i] = {}
    for j = 1, a do t[i][j] = 0 end
  end
  local cur = 1
  for i = 1, a do
    for j = i, a do
      t[i][j] = cur + j - i
      t[j + 1][i] = cur + j - i
    end
    cur = cur + a + 1 - i
  end
  for i = 1, a + 1 do
    print(a .. " " .. table.concat(t[i], " "))
  end
end