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)

function gcd(a,b){while(b)[a,b]=[b,a%b];return a};
console.log(function(args){
  const tmp = args.trim().split('\n')
  const N = tmp[0]|0;
  const A = tmp[1].split(' ').map(v=>v|0).sort((a,b)=>b-a);
  let AA = 1, count = 0;
  for ( let i = 0; i < N-1; i++ ) {
    AA *= A[i];
    if ( AA % A[i+1] ) count++;
    else AA = AA * A[i] / gcd( AA, A[i] );
  }
  return count.toString();
}(require('fs').readFileSync('/dev/stdin', 'utf8')));