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: Accepted)

const [nStr, aStr] = require('fs').readFileSync('/dev/stdin', 'utf8').split(/\n/)
const as = aStr.split(/\s/).reduce((acc, curr) => {
  const num = Number(curr)
  acc[num] = (acc[num] || 0) + 1
  return acc
}, [])
if (as[1] === 1) {
  console.log(1)
} else if (as[1]) {
  console.log(0)
} else {
  for (let i = 2; i < as.length; i++) {
    if (!as[i]) {
      continue
    }
    const until = Math.floor(Math.pow(i, 0.5))
    for (let j = 2; j <= until; j++) {
      if (i % j === 0 && (as[j] || as[i / j])) {
        as[i] = 0
        break
      }
    }
  }
  console.log(as.reduce((a, b) => a + (b === 1 ? b : 0), 0))
}