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-csc 3.5.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;

public class Test
{
	public static void Main()
	{
		var line0 = Console.ReadLine().Split(new char[]{' '}).Select(c => Int32.Parse(c)).ToArray();
		var n = line0[0];
		var line1 = Console.ReadLine().Split(new char[]{ ' '}).Select(c => Int32.Parse(c)).ToArray();
		var inc = 0;
		for (var i = 0; i < line1.Count(); i++)
		{
			var found = false;
			for (var j = 0; j < line1.Count(); j++)
			{
				if (i != j)
				{
					if (!found)
					{
						if ((line1[i] % line1[j]) == 0)
						{
							found = true;
						}
					}
				}
			}
			if (!found)
			{
				inc++;
			}
		}
		Console.WriteLine(inc);
	}
}