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)

function main(input) {
  var a = input[1].trim().split(" ").map(e => parseInt(e, 10));
  var a_max = 10**6+1;
  var dp = new Array(a_max+1).fill(0);
  for(var i of a){
    dp[i]++;
  }
 
  for(var i=1;i<=a_max;i++){
    if(dp[i]===0){ 
      continue;
    }
    for(var j=i+i;j<=a_max;j+=i){
      if(dp[j]!==0){
        dp[j]=0;
      }
    }
  }
  console.log(dp.filter(function(x){return x===1}).length);
}
main(require('fs').readFileSync('/dev/stdin', 'utf8').trim().split("\n"));