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)

console.log((args=>{
  const [[N],A] = args.trim().split`\n`.map(r=>r.split` `.map(v=>v|0));
  A.sort((a,b)=>a-b);
  const MAX = A[N-1];
  const ex = Array(MAX+1).fill(false);
  let count = 0;
  for ( let i = 0; i < N; i++ ) {
    if ( ex[A[i]] ) continue;
    for ( let j = A[i]; j <= MAX; j+=A[i] ) {
      ex[j] = true;
    }
    if ( A[i] !== A[i+1] ) count++;
  }
  return `${count}`;
})(require('fs').readFileSync('/dev/stdin', 'utf8')));