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)


let input = require("fs").readFileSync("/dev/stdin", "utf8")

function main({ input, load, yesno, math_sum }) {

    const [N] = load()
    const A = load(N)

    const Ai_max = 2e5
    const nums = new Array(Ai_max + 1).fill(0)

    for(const a of A) nums[a]++

    for(let i = 1; i <= Ai_max; i++) {
        if(nums[i]) {
            if(nums[i] > 1) nums[i] = 0
            for(let j = i * 2; j <= Ai_max; j += i) {
                nums[j] = 0
            }
        }
    }

    console.log(math_sum(nums))
}

let inputs = input.split(/[\s\n]/)
main({
    input,
    yesno: value => value ? 'Yes' : 'No',
    load(rows = 1, cols = 1, is_number = true) {
        const length = rows * cols
        let result = inputs.splice(0, length)
        if(is_number) result = result.map(Number)
        if(cols > 1) {
            const arrays = new Array(cols)
            for(let col = 0; col < cols; col++) {
                arrays[col] = new Array()
                for(let row = 0; row < rows; row++) {
                    arrays[col].push(result[row * cols + col])
                }
            }
            result = arrays
        }
        return result
    },
    inifinite_loop_preventer() {
        throw new Error("Infinite loop")
    },
    math_sum(numbers) {
        return numbers.reduce((acc, cur) => acc + cur, 0)
    },
})