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: Time Limit Exceeded)

def compress_array_to_hash(array)
  hash = {}
  array.map { |e|
    if hash[e].nil?
      hash[e] = 1
    else
      hash[e] += 1
    end
  }
  hash
end
_n = gets
hash = compress_array_to_hash(gets.split.map(&:to_i))

candidates = []
hash.each do |key, value|
  candidates += [key-1, key, key+1]
  candidates.uniq!
end

max = 0
candidates.each do |candidate|
  count = (hash[candidate-1] || 0) + (hash[candidate] || 0) + (hash[candidate+1] || 0)
  max = [max, count].max
end
puts max