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 JavaScript (Node.js 12.16.1) (judge verdict: Runtime Error)

const main = (input) => {
  const [, n] = input.trim().split('\n')
  const nums = n.split(' ').map(v => Number(v))

  const max = Math.max(...nums)
  const arr = new Array(max+1).fill(0)

  for (let v of nums) {
    let t = v
    arr[t] = arr[t] + 1

    while (t < max+1) {
      t = t + v
      if (t < max+1) arr[t] = arr[t] + 1
    }
  }

  let ans = 0
  for (let v of nums) {
    if (arr[v] > 1) continue
    ans++
  }
  console.log(ans)
}

process.env.MYTEST ? test() : main(require('fs').readFileSync('/dev/stdin', 'utf8'))