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 Scala (2.11.7) (judge verdict: Accepted)

object Main {
  def main(args: Array[String]): Unit = {
    import scala.io.StdIn.readLine
    val Array(datN) = readLine.split(" ").map(_.toInt)
    val datA = readLine.split(" ").map(_.toInt)

    val scoreA = datA.groupBy(identity).map{ case (k, v) => (k, v.length) }
    val ans = scoreA.keys.map{ a => scoreA.getOrElse(a - 1, 0) + scoreA.getOrElse(a, 0) + scoreA.getOrElse(a + 1, 0)}.max
    println(ans)
  }
}