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: Time Limit Exceeded)

fun main(args: Array<String>) {
    var tmpLine = readLine()
    var tmps = tmpLine!!.split("\\s+".toRegex())
    var n = tmps[0].toInt() 

    tmpLine = readLine()
    tmps = tmpLine!!.split("\\s+".toRegex())
    var aarray = tmps.map {it.toInt()}
    var result = 0
    for (i in 0..n-1) {
        var tmpCount = 0
        for (j in 0..n-1) {
            if (i == j) continue
            val ai = aarray[i]
            val aj = aarray[j]
            if (ai % aj == 0) {
                tmpCount++
                break
            }

        }
        if (tmpCount == 0) result++
    }
    println(result)
}