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)

module Main where

import Data.List

main :: IO()
main = do
  _ <- getLine
  inputs <- map read . words <$> getLine
  print $ solve inputs

solve :: [Integer] -> Integer
solve = maximum . posibilities . allLists

allLists :: [Integer] -> [[Integer]]
allLists inputs = map (zipWith (+) inputs) adds where
  adds :: [[Integer]]
  adds = sub (length inputs) where
    sub 0 = [[]]
    sub n = concatMap (\l -> [1 : l, 0 : l, -1 : l]) $ sub (n - 1)

posibilities :: [[Integer]] -> [Integer]
posibilities = map (fromIntegral . maximum . map length . group . sort)