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 BS
import Control.Monad
import Data.Maybe (fromJust)
import Data.List
import Data.Array.Unboxed
import Data.Array.ST
import qualified Data.Set as S

ary :: [Int] -> UArray Int Int
ary xs = runSTUArray $ do
    let gs = group xs
        zs = zip (map head gs) (map length gs)
    a <- newArray (head xs, last xs + 2) 0
    forM_ zs $ \(i,n) -> do
        x <- readArray a i
        writeArray a i (x+n)
    return a

solve :: UArray Int Int -> [Int] -> Int
solve a = foldr f 0
  where
    f x mx = let mx' = (a!x) + (a!(x+1)) + (a!(x+2))
              in max mx mx'

fastnub :: [Int] -> [Int]
fastnub = S.toList . S.fromList

main :: IO ()
main = do
    _ <- getLine
    a <- sort . map (fst . fromJust . BS.readInt)
        . BS.words <$> BS.getLine :: IO [Int]
    print $ solve (ary a) (fastnub a)