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)

open Hashtbl

let id x = x
let n = Scanf.scanf "%d\n" id
let h = create 100

let f n =
  let rec g n' =
    if n' = 0 then ()
    else
      let a = Scanf.scanf "%d " id in
      let v = try find h a with _ -> 0 in
      let v' = try find h (a - 1) with _ -> 0 in
      let v'' = try find h (a + 1) with _ -> 0 in
      replace h a (v + 1) ;
      replace h (a - 1) (v' + 1) ;
      replace h (a + 1) (v'' + 1) ;
      g (n' - 1)
  in
  g n

let () =
  f n ;
  fold (fun _ v tmp -> max v tmp) h 0 |> Printf.printf "%d\n"