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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(arg: Array<String>) {
    val N = nextInt()
    val A = listOfInt()
    val M = java.util.HashMap<Int, Int>()
    A.forEach { M[it] = M.getOrElse(it, { 0 }) + 1 }
    var ans = 1
    M.asIterable().forEach {
        val x = it.key
        val c = M.getOrElse(x - 1, { 0 }) +
                M.getOrElse(x + 0, { 0 }) +
                M.getOrElse(x + 1, { 0 })
        if (ans < c) ans = c
    }
    println(ans)
}

fun next() = readLine()!!
fun nextInt(delta: Int = 0) = Integer.parseInt(next()) + delta
fun listOfString() = next().split(" ")
fun listOfInt(D: Int = 0) = listOfString().map { Integer.parseInt(it) + D }
fun listOfInt(vararg deltas: Int) = listOfString().map { Integer.parseInt(it) }.mapIndexed { index, int -> int + deltas[index % deltas.size] }