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 input = require("fs").readFileSync("/dev/stdin", "utf8")
let cin = input.split(/ |\n/), cid = 0
const next = () => cin[cid++]
const nexts = (n) => cin.slice(cid, cid+=n).map(i=>parseInt(i))

const N = parseInt(next())
const A = nexts(N).sort((a, b) => a - b)
count = N
for (let i = 0; i < N; i++) {
    if (A[i] == A[i+1]) {
        count--
        continue
    }
    for (let j = 0; j < i; j++) {
        if (i / j < 2) {
            break
        }
        if (A[i] % A[j] == 0) {
            count--
            break
        }
    }
}
console.log(count)