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 Ruby (2.3.3) (judge verdict: Accepted)

N=readline.to_i

sorted_a = readline.split.map(&:to_i).sort
grouped_a = sorted_a.group_by{|x|x}

count_with_zero = []
(sorted_a.last+1).times do |number|
  numbers = grouped_a[number] || []
  count_with_zero.push(numbers.size);
end

# p count_with_zero

delta_cumulative_count = 
  count_with_zero.map.with_index do |count, i|
    i>0 ? 
      count_with_zero[i-1].to_i + count_with_zero[i].to_i + count_with_zero[i+1].to_i
    :
      count_with_zero[i].to_i + count_with_zero[i+1].to_i
  end

p delta_cumulative_count.max