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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Data.List

main :: IO ()
main = do
  n <- read <$> getLine :: IO Int
  let (check,k) = notfind 1 n
  if check then putStrLn $ "No"
    else putStrLn "Yes" >> putStrLn (show k) >> subset 0 (k-1) 0 --

notfind :: Int -> Int -> (Bool,Int)
notfind count n = if 2*n == count*(count+1) then (False,count+1)
  else if 2*n < count*(count+1) then (True,count+1)
     else notfind (count+1) n

subset :: Int -> Int -> Int -> IO ()
subset n k iv = do
  if n == (k+1) then return () else do
    putStr $ (show k) ++ " "
    --putStr "loop1-> "
    loop1 n (k-n) (iv+(n*k-(n*(n-1))`div`2)) --iv+Σ(k-i)
    --putStr "loop2-> "
    loop2 n k iv
    putStrLn ""
    subset (n+1) k iv

loop1 n 0 iv = return ()
loop1 n k iv = do
  putStr $ (show (k+iv)) ++ " "
  loop1 n (k-1) iv

loop2 0 k iv = return ()
loop2 n k iv = do
  putStr $ (show (n+iv)) ++ " "
  loop2 (n-1) (k-1) (iv+k)