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 Common Lisp (SBCL 1.1.14) (judge verdict: Time Limit Exceeded)

(let* ((n (1- (read)))
       (arr (make-array (1+ n) :initial-element 0 :element-type 'fixnum))
       (mem (make-array 100000 :initial-element 0 :element-type 'fixnum)))
  (loop :for a :from 0 :upto n :do(setf (aref arr a) (read)))
  (defun f (k) (if (= 0 (aref mem k))
                   (let ((q (count-if (lambda (a) (< -2 (- k a) 2)) arr)))
                     (setf (aref mem k) q)
                     q)
                   (aref mem k)))
  (princ (loop :for s :across arr :maximize(f s))))