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 aList = readLine()?.split(" ")?.map { it.toInt() } ?: return

    val map = mutableMapOf<Int, Int>()

    for (a in aList) {
        val a1 = map.putIfAbsent2(a - 1, 0)
        val a2 = map.putIfAbsent2(a, 0)
        val a3 = map.putIfAbsent2(a + 1, 0)

        map[a - 1] = if (a1 != null) a1 + 1 else 1
        map[a] = if (a2 != null) a2 + 1 else 1
        map[a + 1] = if (a3 != null) a3 + 1 else 1
    }

    val max = map.maxBy { it.value }?.value ?: return

    println(max)
}

private fun <K, V> MutableMap<K, V>.putIfAbsent2(key: K, value: V): V? {
    return if (containsKey(key)) {
        get(key)
    } else {
        put(key, value)
    }
}