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
a = gets.chomp.split(' ').map(&:to_i)
a << 10 ** 6
b = [0, 0, 0]
before = nil
max = 0
a.sort.each_with_index { |v, i|
  if v != before
    sum = b.inject(:+) || 0
    max = sum if sum > max
    if before != nil
      (v - before - 1).times {
        b.shift
        b << 0
      }
    end
    b.shift
    b << 1
    before = v
  else
    b[-1] += 1
  end
}

puts max