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 Data.List
import Data.Ord
main = do
  t <- readLn :: IO Int
  xs <- fmap (map read . words) getLine :: IO [Int]
  print $ maximum $ map (flip g (f xs)) [minimum xs .. maximum xs]
    where
      f xs = map (\x -> (head x, length x)) $ group $ sort xs
      g n = foldl (\acc y -> acc + snd y) 0 . filter (\x -> fst x >= n - 1 && fst x <= n + 1)