Problem:
Score : 400 points

Problem Statement

Given is a number sequence A of length N.

Find the number of integers i \left(1 \leq i \leq N\right) with the following property:

For every integer j \left(1 \leq j \leq N\right) such that i \neq j , A_j does not divide A_i.

Constraints

All values in input are integers.

1 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^6

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N

Output

Print the answer.

Sample Input 1

5
24 11 8 3 16

Sample Output 1

3

The integers with the property are 2, 3, and 4.

Sample Input 2

4
5 5 5 5

Sample Output 2

0

Note that there can be multiple equal numbers.

Sample Input 3

10
33 18 45 28 8 19 89 86 2 4

Sample Output 3

5

Solution in Kotlin (1.3.71) (judge verdict: Wrong Answer)

fun main(args: Array<String>) {
    Program().solve()
}

class Program {
    fun solve() {

        val maxA = 1000000
        val sc = MyScanner()
        val n = sc.nextInt()
        val a = sc.intList()
        val map = mutableMapOf<Int, Int>()
        for (i in 0 until n) {
            map[a[i]] = (map[a[i]] ?: 0) + 1
        }

        var ans = 0
        for (i in 0 until n) {
            if ((map[a[i]] ?: 0) >= 2) continue
            var d = 1
            var flag = true
            while (d * d <= a[i]) {
                if (a[i] % d == 0) {
                    if (map.containsKey(d) || (d != 1 && map.containsKey(a[i] / d))) {
                        flag = false
                        break
                    }
                }
                d++
            }
            if (flag) ans++
        }
        println(ans)
    }
}

class MyScanner {
    private var ptr = 0
    private var l = listOf<String>()

    fun next(): String {
        while (l.size <= ptr) {
            l = readLine()!!.split(' ')
            ptr = 0
        }
        return l[ptr++]
    }

    fun nextInt() = next().toInt()
    fun nextLong() = next().toLong()
    fun nextDouble() = next().toDouble()
    fun nextCharArray() = next().toCharArray()
    fun nextChar() = next()[0]

    fun list(): List<String> {
        ptr = l.size
        return readLine()!!.split(' ')
    }

    fun intList() = list().map { s -> s.toInt() }
    fun longList() = list().map { s -> s.toLong() }
    fun doubleList() = list().map { s -> s.toDouble() }

    fun array() = list().toTypedArray()
    fun intArray() = intList().toIntArray()
    fun longArray() = longList().toLongArray()
    fun doubleArray() = doubleList().toDoubleArray()
}