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)

'use strict';

function Main(input) {
    let tmp = input.trim().split('\n');
    const N = Number(tmp[0]);
    let A = tmp[1].split(' ').map((v) => Number(v)).sort((a, b) => a - b);

    // 1が存在する場合
    if (A[0] === 1) {
        console.log('0');
        return;
    }

    let siftedA = [];
    for (let i = 2; i <= 10**6; i++) {
        if (A[0] !== i) continue;
        const filterA = A.filter(v => v === i);
        if (filterA.length === 1) {
            siftedA = [...siftedA, A[0]];
        }
        A = A.filter(v => v % i !== 0)
        if (A.length === 0) break;
    }

    console.log(String(siftedA.length + A.length));


    return;
}
Main(require('fs').readFileSync('/dev/stdin', 'utf8'));

// Main(`5
// 24 11 8 3 16`); // 3
// Main(`4
// 5 5 5 5`);  // 0
// Main(`10
// 33 18 45 28 8 19 89 86 2 4`);   // 5