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>) {
        val  numCount = readLine()!!.toInt()
        var numbers = readLine()!!.split(' ').map { it.toInt() }.toIntArray()

        var ans = 0
        numbers.forEachIndexed numLoop@ {i, num ->
            numbers.forEachIndexed checkLoop@ { j, check ->
                if(i == j) return@checkLoop
                if(num % check == 0) {
                    ans++
                    return@numLoop
                }
            }
        }
        println(numCount - ans)
    }