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 Java (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.util.Random;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.BitSet;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author AnandOza
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DNotDivisible solver = new DNotDivisible();
        solver.solve(1, in, out);
        out.close();
    }

    static class DNotDivisible {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] a = in.readIntArray(n);
            Util.safeSort(a);
            BitSet composite = new BitSet(n);
            int MAX = Util.max(a);

            int answer = 0;
            for (int i = 0; i < n; i++) {
                int p = a[i];
                if (composite.get(p)) {
                    continue;
                }

                if (!(i + 1 < n && a[i + 1] == a[i]))
                    answer++;

                if (p == 1) {
                    break;
                }

                for (int j = p; j <= MAX; j += p) {
                    composite.set(j);
                }
            }

            out.println(answer);
        }

    }

    static class Util {
        public static int max(int... x) {
            int max = Integer.MIN_VALUE;
            for (int i : x) {
                max = Math.max(i, max);
            }
            return max;
        }

        public static void safeSort(int[] x) {
            shuffle(x);
            Arrays.sort(x);
        }

        public static void shuffle(int[] x) {
            Random r = new Random();

            for (int i = 0; i <= x.length - 2; i++) {
                int j = i + r.nextInt(x.length - i);
                swap(x, i, j);
            }
        }

        public static void swap(int[] x, int i, int j) {
            int t = x[i];
            x[i] = x[j];
            x[j] = t;
        }

        private Util() {
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public int[] readIntArray(int n) {
            int[] x = new int[n];
            for (int i = 0; i < n; i++) {
                x[i] = nextInt();
            }
            return x;
        }

    }
}