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.to_i
arr = gets.split(" ").map{|x|
	x.to_i
}
memo = {}
arr.each do |x|
	[x, x-1, x+1].each do |n|
		if !memo.has_key?(n) then
			cnt = 0
			arr.each do |y|
				case y 
					when n then
						cnt += 1
					when n-1 then
						cnt += 1
					when n+1 then 
						cnt += 1
					else
				end
			end
			memo.store(n, cnt) 
		end
	end
end

max = 0
memo.each{|key, value|
	if max < value then
		max = value
	end
}
p max