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.Maybe

main :: IO ()
main = do
  _ <- getLine
  ls <- fmap read . words <$> getLine :: IO [Int]
  let ls' = foldl solve [] ls
  print $ maximum $ snd <$> ls'

solve :: [(Int,Int)] -> Int -> [(Int,Int)]
solve env val = [(p,p' + 1),(o,o' + 1),(n,n' + 1)] ++ env where
  p = val - 1
  o = val
  n = val + 1
  p' = fromMaybe 0 $ lookup p env
  o' = fromMaybe 0 $ lookup o env
  n' = fromMaybe 0 $ lookup n env