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 = gets.chomp.to_i
arr = gets.chomp.split.map(&:to_i).sort
table = {}
arr.each do |ai|
  if table.has_key?(ai)
    table[ai] += 1
  else
    table[ai] = 1
  end
end
# 最頻値の+-1の数とそのtable[+-1]の数を調べる。
# ↑間違い 2 2 2 4 4 5 5 6 6 7 7とか
# なので、出てきたやつを試していく
max_count = 1

table.keys.each do |ai|
  temp = 0
  [-1, 0, 1].each do |i|
    if table.has_key?(ai+i)
      temp+=table[ai+i]
    end
  end
  max_count = [max_count, temp].max
end
puts max_count