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)

require 'pp'

n = gets.chomp!.to_i
a_n = gets.chomp!.split(" ").map(&:to_i).sort

counter = {}
a_n.each do |a|
    counter[a] ||= 0
    counter[a] += 1
end
# 番兵(counterが3つ以上あることを保証する)
counter[10 ** 8] = 0
counter[10 ** 9] = 0

max = 0
counter.each_cons(3) do |x, y, z|
    count = x[1]
    if x[0] + 1 == y[0]
        count += y[1]
        if y[0] + 1 == z[0]
            count += z[1]
        end
    end

    if max < count
        max = count
    end
end

puts max