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)

def main()
  n = gets.chomp.to_i
  x = gets.chomp.split(' ').map(&:to_i)
  dic = Hash.new(0)
  for i in 0..n-1 do
    dic[x[i]] = dic[x[i]] + 1
    dic[x[i]-1] = dic[x[i]-1] + 1
    dic[x[i]+1] = dic[x[i]+1] + 1
  end
  ans_k,ans_v = dic.max_by{|k,v| v}
  puts ans_v
end

main()