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: Wrong Answer)

module Main where

import Control.Applicative
import Control.Monad
import Data.Function
import Data.List
import Data.Maybe

getK :: Int -> Maybe Int
getK n = get 0
    where get k | ss < 2 * n = get (k + 1)
                | ss == 2 * n = Just k
                | otherwise = Nothing
                where ss = k * (k - 1)

solve :: Int -> Maybe [[Int]]
solve n = getK n >>= gen
    where gen k = Just . map (map snd) . groupBy ((==) `on` fst) $ sort vs
              where is = [i | i <- [1 .. k], j <- [i + 1 .. k]] :: [Int]
                    js = [j | i <- [1 .. k], j <- [i + 1 .. k]] :: [Int]
                    vs = (zip is [1 .. n]) ++ (zip js [1 .. n])

main :: IO ()
main = do
  n <- read <$> getLine
  case (solve n) of
    Just ss -> do putStrLn "Yes"
                  forM_ ss $ \s -> do
                    putStrLn . unwords . map show $ (length s):s
    Nothing -> putStrLn "No"