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() {
    val n = readLine()!!.toInt()
    val arr = readLine()!!.split(" ").map { it.toInt() }.sorted().toIntArray()
    val s = HashSet<Int>()
    val dup = HashMap<Int,Int>()
    for(d in arr) {
        dup[d] = (dup[d]?:0) + 1
    }
    var ans = 0

    for(i in 0 until n) {
        val v = arr[i]
        var c = v
        val primes = ArrayList<Int>()
        var d = 2
        val cnt = (dup[v]?:0)
        val isDup = cnt > 1

        while(d * d <= v) {
            if(c % d != 0) {
                ++d
                continue
            }
            if(c == 1) break
            while(c % d != 0) {
                c /= d
            }
            primes.add(d)
            ++d
        }

        if(c != 1) {
            primes.add(c)
        }

        fun dfs(idx:Int, v:Int): Boolean {
            if(idx >= primes.size) {
                if(s.contains(v))
                    return true
                return false
            }
            if(dfs(idx + 1, v * primes[idx]) || dfs(idx + 1 , v))
                return true
            return false
        }

        if( !isDup && !dfs(0, 1)) {
            ++ans
        }

        var m = 1
        for(p in primes) {
            m *= p
        }
        s.add(m)
    }
    print(ans)


}