Problem:
Score : 300 points

Problem Statement

You are given an integer sequence of length N, a_1,a_2,...,a_N.

For each 1≤i≤N, you have three choices: add 1 to a_i, subtract 1 from a_i or do nothing.

After these operations, you select an integer X and count the number of i such that a_i=X.

Maximize this count by making optimal choices.

Constraints

1≤N≤10^5

0≤a_i<10^5 (1≤i≤N)

a_i is an integer.

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 .. a_N

Output

Print the maximum possible number of i such that a_i=X.

Sample Input 1

7
3 1 4 1 5 9 2

Sample Output 1

4

For example, turn the sequence into 2,2,3,2,6,9,2 and select X=2 to obtain 4, the maximum possible count.

Sample Input 2

10
0 1 2 3 4 5 6 7 8 9

Sample Output 2

3

Sample Input 3

1
99999

Sample Output 3

1

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Monad.Primitive (PrimState)
import qualified Data.Vector.Unboxed as V
import qualified Data.Vector.Unboxed.Mutable as MV
import qualified Data.ByteString.Char8 as B
import Data.Maybe (fromJust)

main :: IO ()
main = do
    _ <- B.getLine
    vs <- V.fromList . map (fst . fromJust . B.readInt) . B.words <$> B.getLine
    let vmin = V.minimum vs
        vmax = V.maximum vs
    mv <- MV.replicate (vmax - vmin + 3) 0 :: IO (MV.MVector (PrimState IO) Int)
    V.forM_ vs $ \i -> do
        MV.unsafeModify mv succ (i - vmin)
        MV.unsafeModify mv succ (i + 1 - vmin)
        MV.unsafeModify mv succ (i + 2 - vmin)
    v <- V.unsafeFreeze mv
    print $ V.maximum v