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 Lua (LuaJIT 2.1.0) (judge verdict: Time Limit Exceeded)

local n=io.read("n")
local a={}
local a_map={}
for i=1,n do
    local input=io.read("n")
    a[i]=input
    a_map[input]=(a_map[input] or 0)+1
end

local counter=0
for i=1,n do
    local checker=true
    a_map[a[i]]=a_map[a[i]]-1
    for j=1,math.sqrt(a[i]) do
        local div=math.floor(a[i]/j)
        local ce=(a_map[j] and a_map[j]>0) or (a_map[div] and a_map[div]>0)
        if a[i]%j==0 and ce then
            checker=false
            break
        end
    end
    if checker then
        counter=counter+1
    end
    a_map[a[i]]=a_map[a[i]]+1
end
print(counter)