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)

{-# LANGUAGE BangPatterns          #-}

import Control.Monad
import Control.Applicative
import Data.Array.IO

maxNum :: Int
maxNum = 100000

main :: IO()
main = do
    n <- readLn :: IO Int
    a <- map read .words <$> getLine :: IO [Int]
    count <- newArray (0, maxNum + 1) 0 :: IO (IOUArray Int Int)
    forM_ [0..(n - 1)] $ \i -> do
        let v = a!!i
        c1 <- readArray count v
        writeArray count v (c1 + 1)
        if v > 0 then do
            c2 <- readArray count (v - 1)
            writeArray count (v - 1) (c2 + 1)
        else do
            return ()
        if v < maxNum then do
            c3 <- readArray count (v + 1)
            writeArray count (v + 1) (c3 + 1)
        else do
            return ()
    elems <- getElems count
    print $ maximum elems