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)

{-# OPTIONS_GHC -O #-}

import Control.Monad
import Data.List
import Data.Ord
import qualified Data.ByteString.Lazy.Char8 as B
import qualified Data.IntMap as M

readIntLL :: IO [[Int]]
readIntLL = map(unfoldr(B.readInt.B.dropWhile(==' '))).B.lines<$>B.getContents

rsort :: Ord a => [a] -> [a]
rsort = sortBy$flip compare

main=do
    n:as <- readIntLL
    print $ maximum $ map snd $ M.toList
        $ foldl' (\m k -> M.insertWith (+) (k-1) 1 $ M.insertWith (+) (k+1) 1 $ M.insertWith (+) k 1 m) M.empty
        $ head as