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)

n = gets.strip.to_i
integers = gets.split(' ').map(&:to_i)

result = {}
count = 0

(1..n).each do |i|
  count = 0
  integers.each do |int|
    if int == i || int + 1 == i || int - 1 == i
      count += 1
    end
  end
  result.store(i,count)
  break if count == n
end

if count == n
  puts n
else
    max = result.max_by {|k,v| v }.last
  if max == 0
    puts 1
  else
    puts max
  end
end