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           Control.Applicative
import           Control.Monad
import           Control.Monad.State

hoge :: [Int] -> State ([Int], Int) ()
hoge []       = return ()
hoge (a : as) = do
  (rs, b) <- get
  let min = if null rs then 0 else minimum rs
  let nrs = a : if (a - min) > 2 then filter (>= (a - 2)) rs else rs
  put (nrs, maximum [b, length nrs])
  hoge as

main = do
  n  <- readLn
  ns <- sort . take n . map (read :: String -> Int) . words <$> getLine
  print $ snd $ execState (hoge ns) ([], 0)