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 = readInputLine().toInt()
    
    val aList = readInputLine().split(" ").map { it.toInt() }

    val map = mutableMapOf<Int, Int>()
    
    for (i in 0 until n) {
        val noOpNum = map.get(aList[i]) ?: 0
        val plusNum = map.get(aList[i] + 1) ?: 0
        val minusNum = map.get(aList[i] - 1) ?: 0
        
        map.put(aList[i], noOpNum + 1)
        map.put(aList[i] + 1, plusNum + 1)
        map.put(aList[i] - 1, minusNum + 1)
    }
    
    println(map.maxBy { it.value }!!.value)
}
 
fun readInputLine(): String {
    return readLine()!!
}