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 qualified Data.ByteString.Char8 as B
import Data.Maybe (fromJust)
import qualified Data.Map.Strict as M
import qualified Data.Vector.Unboxed as VU

getInts :: IO[Int]
getInts = map (fst . fromJust . B.readInt) . B.words <$> B.getLine


lambda::M.Map Int Int->Int->M.Map Int Int
lambda acc v = foldl (\acc x -> if M.member x acc then M.adjust (+1) x acc else M.insert x 1 acc) acc [v-1,v,v+1]

main = do
  n <- getLine
  an <- getInts
  print $ maximum $ M.elems . VU.foldl lambda M.empty $ VU.fromList an