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)

(* O(n) *)
let kMax = 100000 + 10
let n = Scanf.scanf " %d" @@ (+) 0
let a_s = Array.init n @@ fun _ -> Scanf.scanf " %d" @@ (+) 0
let ns = Array.make (kMax + 1) 0
let f a =
  for i = 0 to 2 do ns.(a + i) <- ns.(a + i) + 1 done
let _ =
  Array.iter f a_s;
  Array.fold_left max 0 ns |> Printf.printf "%d\n"