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 extends App {
	val N = scala.io.StdIn.readInt
	val A = scala.io.StdIn.readLine.split(" ").map(_.toInt)

	val map = scala.collection.mutable.Map[Int,Int]()

	for(x <- A){
		map.put(x - 1, map.getOrElse(x - 1, 0) + 1)
		map.put(x    , map.getOrElse(x    , 0) + 1)
		map.put(x + 1, map.getOrElse(x + 1, 0) + 1)
	}
	println(map.maxBy(_._2)._2)
}