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: Wrong Answer)

import Data.List
import qualified Data.ByteString.Char8 as B

readInt :: B.ByteString -> Int
readInt = maybe undefined fst . B.readInt

readInts :: B.ByteString -> [Int]
readInts = map readInt . B.words

main = do
  getLine
  as <- readInts <$> B.getLine
  print (together as)

together as = succ $ maximum $ (0:) $ map (length . takeWhile (<=2) . scanl1 (+)) $ collectBy (\x y -> x<2&&y<2) ds
  where
    sas = sort as
    ds = zipWith (-) (tail sas) sas

collectBy _ [] = []
collectBy op [x] = [[x]]
collectBy op (x1:x2:xs)
  | op x1 x2 = let (g:gs) = collectBy op (x2:xs) in (x1:g) : gs
  | otherwise = collectBy op (x2:xs)