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(args: Array<String>) {
    val n = readLine()?.toInt() ?: return
    val a = readLine()?.split(" ")?.map(String::toInt)?.sorted() ?: return
    val count = hashMapOf<Int, Int>()
    fun add(c: java.util.HashMap<Int, Int>, v: Int) {
        if (c.containsKey(v)) {
            c[v] = c[v]!! + 1
        } else {
            c[v] = 1
        }
    }
    a.forEach {
        add(count, it - 1)
        add(count, it)
        add(count, it + 1)
    }
    count.maxBy { it.value }?.let {
        println(it.value.toString())
    }
}