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: Time Limit Exceeded)

import Control.Monad
import Control.Applicative
import Data.List



getBysplit = map read . words <$> getLine

main :: IO()
main = do
  [n] <- getBysplit :: IO [Int]
  als <- getBysplit :: IO [Int]
  print $ solve als

countBysame :: (Ord a) => [a] -> [(a, Int)]
countBysame [] = []
countBysame lst = let
                    x:xs = sort lst
                    ((e, c), lst') = sameElem x xs 0
                    in (e, c):countBysame lst'
    where
      sameElem :: (Ord a) => a -> [a] -> Int -> ((a, Int), [a])
      sameElem x [] count = ((x, count+1), [])
      sameElem x (y:ys) count
                    | x ==  y = sameElem x ys (count+1)
                    | x /= y = ((x, count+1), y:ys)

solve :: [Int] -> Int
solve lst = let
            list = concatMap (\x -> [x-1, x, x+1]) lst
            list' = countBySame' list
            m = maximum list'
            in m



countBySame' :: [Int] -> [Int]
countBySame' [] = []
countBySame' lst = let x:xs = sort lst  ; (n, list) = (samelist x xs 0) in n : (countBySame' list)
  where
    samelist :: Int -> [Int] ->  Int -> (Int, [Int])
    samelist a [] n = (n+1, [])
    samelist a (x:xs) n
                  | a == x = samelist a xs (n+1)
                  | a /= x = (n+1, x:xs)