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)

// ABC170
function main(input) {
  var inputs = input.trim().split('\n');
  var N = parseInt(inputs[0], 10);
  var A = typeof(inputs[1]) !== 'undefined' ? inputs[1].split(' ').map(n => parseInt(n, 10)) : [];

  var full = [];
  for (var i = 0; i < 1000001; i++) {
    full.push(0);
  }

  for (var i = 0; i < N; i++) {
    if (full[A[i]] > 1) continue;

    loop = 1;
    while (true) {
      var temp = loop * A[i];
      if (temp > 1000001) {
        break;
      } else {
        if (full[temp] > 1) {
          loop += 1;
          continue;
        } else {
          full[temp] += 1;
          loop += 1;
        }
      }
    }
  }

  var counter = 0;
  for (var n = 0; n < N; n++) {
    if (full[A[n]] === 1) counter += 1;
  }

  console.log(counter);
}

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