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)

import java.io.PrintWriter
import java.util.*
import java.math.*
import java.lang.*

val pw = PrintWriter(System.out)
val MOD: Long = (1e+9 + 7).toLong()

fun main(args: Array<String>) {
    val n = readInt()
    val a = readListOfInt()
    val counts = mutableMapOf<Int, Int>()
    a.forEach { ca ->
        for(i in ca-1..ca+1) {
            counts[i] = if(counts.containsKey(i)) counts[i]!! + 1 else 1
        }
    }
    println(counts.values.max()!!)
    pw.flush()
}

/****** Decrared Functions and Data Structures ******/
// IO
fun read() = readLine()!!
fun readInt() = read().toInt()
fun readLong() = read().toLong()
fun readDouble() = read().toDouble()
fun readListOfString() = read().split(" ")
fun readListOfInt() = readListOfString().map { it.toInt() }
fun readListOfLong() = readListOfString().map { it.toLong() }
fun readListOfDouble() = readListOfString().map { it.toDouble() }

fun Double.format(digits: Int) = String.format("%.${digits}f", this)

fun print(value: Any) { pw.print(value) }
fun println(value : Any) { pw.println(value) }

fun<T> permutations(src: List<T>): List<List<T>> {
    if(src.size == 1) return listOf(src)
    val perms = mutableListOf<List<T>>()
    val insertElement = src[0]
    permutations(src.drop(1)).forEach { perm ->
        for(i in 0..perm.size) {
            val newPerm = perm.toMutableList()
            newPerm.add(i, insertElement)
            perms.add(newPerm.toList())
        }
    }
    return perms
}

// return nCr, if you want nCr, please access v[n][r]
fun combinations(n: Long): List<List<Long>> {
    val v = (0..n).map { (0..n).map{0L}.toMutableList() }.toMutableList()
    for(i in 0 until v.size) {
        v[i][0] = 1L
        v[i][i] = 1L
    }
    for(i in 0 until v.size) {
        for(j in 1 until i) {
            v[i][j] = (v[i-1][j-1] + v[i-1][j] % MOD)
        }
    }
    val rtn = v.map { it.toList() }.toList()
    return rtn 
}

fun gcd(a: Long, b: Long): Long = 
if(b != 0L) a else gcd(b, a % b)

fun lcm(a: Long, b: Long) = 
if(b==0L) a else gcd(b, a % b)

fun sumDigits(num_: Long): Long {
    var num = num_
    var rtn: Long = 0
    while(num != 0.toLong()) {
        val tmp = num % 10
        rtn += tmp
        num /= 10
    }
    return rtn
}

fun isDecimal(v: Double): Boolean = ((v - Math.floor(v)) != 0.0)

// Data Structures
class Stack<T>(private var st: MutableList<T> = mutableListOf<T>()) {
    fun isEmpty() = st.isEmpty()
    fun top(): T = st.last()
    fun push(e: T) { st.add(e) }
    fun pop() { st = st.dropLast(1).toMutableList() }
}

class Queue<T>(private var que: MutableList<T> = mutableListOf<T>()) {
    fun isEmpty() = que.isEmpty()
    fun top(): T = que.first()
    fun push(e: T) { que.add(e) }
    fun pop() { que = que.drop(1).toMutableList() }
}