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

count :: Int -> [(Int, Int)] -> Int
count n = sum . map snd . filter (\(x, _) -> x == (n-1) || x == n || x == (n+1))

solve :: [Int] -> Int
solve xs =
    let ys = map (\xs -> (head xs, length xs)) . group . sort $ xs
        zs = concatMap (\x -> [x - 1, x, x + 1]) xs
    in maximum . map (flip count ys) $ zs

main = getLine >> map read . words <$> getLine >>= print . solve