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 OCaml (4.02.3) (judge verdict: Accepted)

module IntMap = Map.Make (struct
  type t = int
  let compare = compare
end)

let () = 
  let n = Scanf.scanf "%d\n" (fun n -> n) in
  let as_ = Array.init n (fun _ -> Scanf.scanf "%d " (fun a -> a)) in
  Array.fold_left (fun m a ->
    IntMap.add a (1 + try IntMap.find a m with Not_found -> 0) m) IntMap.empty as_
  |> (fun m -> IntMap.fold (fun a n m ->
      IntMap.add (a - 1) (n + try IntMap.find (a - 1) m with Not_found -> 0) m
      |> IntMap.add (a + 1) (n + try IntMap.find (a + 1) m with Not_found -> 0)) m m)
  |> IntMap.bindings
  |> List.map snd
  |> List.fold_left max 0
  |> Printf.printf "%d\n"