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 C# (Mono-mcs 6.8.0.105) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;

namespace Contest
{
  class Program
  {
    static void Main(string[] args)
    {
      ABC170.D();
    }
    class ABC170
    {
      public static void A()
      {
        var X = Read.IntN().ToList();
        Console.WriteLine(X.IndexOf(0) + 1);
      }
      public static void B()
      {
        var X = Read.Int();
        var Y = Read.Int();
        Console.WriteLine(X * 2 <= Y && Y <= 4 * X && Y % 2 == 0 ? "YES" : "NO");
      }
      public static void C()
      {
        var X = Read.Int();
        var N = Read.Int();
        var P = new int[0];
        if (N > 0)
        {
          P = Read.IntN();
        }
        var Y = 99999;
        for(int i = -100; i <= 200; ++i)
        {
          if(!P.Contains(i) && Math.Abs(X - Y) > Math.Abs(X - i))
          {
            Y = i;
          }
        }
        Console.WriteLine(Y);
      }
      public static void D()
      {
        var N = Read.Int();
        var A = Read.IntN();
        var freq = Util.Frequency(A);
        int count = 0;
        foreach(var a in A)
        {
          var div = Util.Divisor(a);
          bool ok = true;
          foreach(var d in div)
          {
            var di = (int)d;
            if (freq.ContainsKey(di) && (d != a || freq[di] > 1))
            {
              ok = false;
              break;
            }
          }
          if (ok) { count++; }
        }
        Console.WriteLine(count);
      }
      public static void E()
      {

      }
      public static void F()
      {

      }
    }

    class Util
    {
      public static long[] ASum(long[] array)
      {
        var res = new long[array.Length + 1];
        for (int i = 0; i < array.Length; ++i)
        {
          res[i + 1] = res[i] + array[i];
        }
        return res;
      }
      public static long[,] ASum(long[,] matrix)
      {
        var N = matrix.GetLength(0);
        var M = matrix.GetLength(1);
        var res = new long[N + 1, M + 1];
        for(int i = 0; i < N; ++i)
        {
          for(int j = 0; j < M; ++j)
          {
            res[i + 1, j + 1] = res[i, j + 1] + res[i + 1, j] - res[i, j] + matrix[i, j];
          }
        }
        return res;
      }
      public static Dictionary<T, long> Frequency<T>(T[] array)
      {
        var dict = new Dictionary<T, long>();
        foreach (var a in array)
        {
          if (!dict.ContainsKey(a)) { dict.Add(a, 0); }
          dict[a]++;
        }
        return dict;
      }
      public static HashSet<long> Divisor(long x)
      {
        var div = new HashSet<long>(); for (long p = 1; p * p <= x; ++p) { if (x % p == 0) { div.Add(p); } }
        foreach (var d in div.ToArray())
        {
          if (!div.Contains(x / d)) { div.Add(x / d); }
        }
        return div;
      }

    }
    class Bound
    {
      public static int Lowerbound<T1, T2>(SortedList<T1, T2> list, T1 x) where T1 : IComparable<T1>
      {
        return Lowerbound(list.Keys, x);
      }
      public static int Upperbound<T1, T2>(SortedList<T1, T2> list, T1 x) where T1 : IComparable<T1>
      {
        return Upperbound(list.Keys, x);
      }
      public static int Lowerbound<T>(IList<T> list, T x) where T : IComparable<T>
      {
        int min = 0;
        int max = list.Count;
        while (min < max)
        {
          var mid = (min + max) / 2;
          if (list[mid].CompareTo(x) >= 0)
          {
            max = mid;
          }
          else
          {
            min = mid + 1;
          }
        }
        return max;
      }
      public static int Upperbound<T>(IList<T> list, T x) where T : IComparable<T>
      {
        int min = 0;
        int max = list.Count;
        while (min < max)
        {
          var mid = (min + max) / 2;
          if (list[mid].CompareTo(x) > 0)
          {
            max = mid;
          }
          else
          {
            min = mid + 1;
          }
        }
        return max;
      }
      public static int UpperboundInt(List<int> list, int x)
      {
        int min = 0;
        int max = list.Count;
        while (min < max)
        {
          var mid = (min + max) / 2;
          if (list[mid] > x)
          {
            max = mid;
          }
          else
          {
            min = mid + 1;
          }
        }
        return max;
      }
    }

    static class Read
{
static Queue<string> queue = new Queue<string>();
static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
public static ulong[] ULongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToUInt64(s)).ToArray(); }
public static string[] StrN() { return Console.ReadLine().Split(' '); }
public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
public static long[,] LongMatrix(int r, int c) { var mat = new long[r, c]; for (int i = 0; i < r; ++i) { var x = Read.LongN(); for (int j = 0; j < c; ++j) { mat[i, j] = x[j]; } } return mat; }
public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
{
Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
        for (int i = 0; i < M; ++i) { var ab = Read.IntN(); if (!dict[ab[0]].Contains(ab[1])) { dict[ab[0]].Add(ab[1]); } if (!isDirectional && !dict[ab[1]].Contains(ab[0])) { dict[ab[1]].Add(ab[0]); } }
        return dict;
}
public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
{
Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>(); for (int i = 0; i <= N; ++i) { dict.Add(i, new Dictionary<int, long>()); }
for (int i = 0; i < M; ++i) { var ab = Read.IntN(); dict[ab[0]].Add(ab[1], ab[2]); dict[ab[1]].Add(ab[0], ab[2]); }
return dict;
}
}
    }
}