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 Data.Maybe (fromJust)
import Data.List (length, sort, group)
import Data.Array.Unboxed
import Prelude hiding ((!!))

solve :: [Int] -> Int
solve xs = foldr f 0 xs
  where
    (b, e) = (head xs, last xs)
    gs = group xs
    zs = zip (map head gs) (map length gs) ++ [(e+1,0), (e+2,0)]
    aa = accumArray (+) 0 (b, e+2) zs :: UArray Int Int
    f x a = let a' = aa!x + aa!(x+1) + aa!(x+2) in max a a'

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