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: Wrong Answer)

const main = (input) => {
  input = input.trim().split('\n')

  const n = input[1].split(' ').map(Number).sort((a, b) => a - b)
  const arr = new Array(parseInt(input[0], 10)+1).fill(false)
  const biggest = n[n.length-1]

  if (Array.from(new Set(n)).length === 1) return console.log(0)

  let ans = 0

  for (let i=0; i<n.length; i++) {
    if ((n[i-1] && n[i-1] === n[i]) || (n[i+1] && n[i+1] === n[i])) {}
    else if (!arr[n[i]]) ans++

    for (let m=2; n[i] * m <= biggest; m++) arr[n[i] * m] = true
  }

  return console.log(ans)
}

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