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 (1.3.71) (judge verdict: Time Limit Exceeded)

import kotlin.math.max

fun main(args: Array<String>) {
    val n = readInt()
    val a = readIntList().sorted()

    var ans = 0
    for (i in 0 until n) {
        var cnt = 0
        var j = 0
        while (i + j < n && a[i + j] in a[i]..a[i] + 1) {
            cnt++
            j++
        }
        j = -1
        while (i + j >= 0 && a[i + j] in a[i] - 1..a[i]) {
            cnt++
            j--
        }
        ans = max(ans, cnt)
    }
    println(ans)
}

// Tools
fun readString() = readLine()!!
fun readInt() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readStringList() = readLine()!!.split(" ")
fun readIntList() = readLine()!!.split(" ").map(String::toInt)