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: Time Limit Exceeded)


// A[i]は自分以外すべての要素に対して互いに素である

function main(input) {
    let [N, ...As] = input.trim().split(/[\s\n]/).map(Number)
    
    As.sort((a,b) => a-b)
    
    let dups = []
    for(let i = 0; i < As.length; i++) {
        for(let j = As.length - 1; j > i; j--) {

            if(As[j] === As[i]) {
                dups.push(As[i])
            }

            if(As[j] % As[i] === 0) {
                As.splice(j, 1)
            }
        }
    }
    
    console.log(As.length - new Set(dups).size)
}

main(require("fs").readFileSync("/dev/stdin", "utf8"))