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 OCaml (4.02.3) (judge verdict: Accepted)

let rec upper_bound l r p =
  if r <= 1 + l
  then l
  else let m = (l + r) / 2 in
       if p m 
       then upper_bound m r p
       else upper_bound l m p

let () = Scanf.scanf "%d\n" @@ fun n ->
  let k = upper_bound 0 (n + 2) @@ fun k -> k * (k - 1) / 2 <= n in
  if k * (k - 1) / 2 <> n then
    print_endline "No"
  else begin
    Printf.printf "Yes\n%d\n" k;
    for i = 0 to k - 1 do
      Printf.printf "%d" (k - 1);
      for j = 0 to k - 1 do
        if i + j <> k - 1 then
          let i, j =
            if i + j < k - 1
            then i, j
            else k - j - 1, k - i - 1 in
        Printf.printf " %d" @@ succ @@ (2 * (k - 1) - i + 1) * i / 2 + j
      done;
      print_newline ()
    done
  end