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)

gets
a = gets.split.map(&:to_i)

table = Hash.new(0)

a.each do |n|
  table[n] += 1
end

nums = table.keys.sort
last_index = nums.length - 1
nums_count = nums.map.with_index do |n, i|
  count = table[n]

  unless i.zero?
    count += table[n - 1] if (n - nums[i - 1]) == 1
  end

  unless i == last_index
    count += table[n + 1] if (nums[i + 1] - n) == 1
  end

  count
end

puts nums_count.max