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)

import           Data.List
import           Data.Tuple

main :: IO ()
main = do
    n <- readLn :: IO Int
    case solve n of
        Just (k, mat) -> do
            putStrLn "Yes"
            print k
            putStr.unlines $ map (unwords.map show.((k - 1):)) mat
        Nothing -> putStrLn "No"

solve :: Int -> Maybe (Int, [[Int]])
solve 1 = Nothing
solve n = case find(\k->k*(k-1)==2*n)[1..317]of
    Nothing -> Nothing
    Just k -> Just (k, zipWith (++) tri $ transpose tri ++ [[]])
      where
        tri = snd $ mapAccumL ((swap.).flip splitAt) [1..n] [0..k-1]