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

main :: IO ()
main = readLn >>= printRes . solve
    where
        printRes (b, xs)
            | b = putStrLn "Yes" >> (putStrLn . unlines . map (unwords . map show)) xs
            | otherwise = putStrLn "No"

solve :: Int -> (Bool, [[Int]])
solve n
    | b = (b, [k] : map ((k - 1) :) ss)
    | otherwise = (b, [])
    where
        (b, k) = check $ zip [2..] ns
        ns = scanl1 (+) [1..]
        
        check ((k, x) : xs)
            | x == n = (True, k)
            | n < x = (False, k)
            | otherwise = check xs

        ss = build 2 2 [[1], [1]]

        build len c acc
            | k < 3 = acc
            | len == k = acc
            | otherwise = build (len + 1) (c + len + 1) $ add c acc
            where
                add c (x : xs) = (c : x) : add (c + 1) xs
                add c _ = [[(c - len)..(c - 1)]]