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: Accepted)

local mfl, mce = math.floor, math.ceil
local n = io.read("*n")
local a = {}
local t = {}
for i = 1, 1000 * 1000 do
  t[i] = 0
end
for i = 1, n do
  a[i] = io.read("*n")
end
local acmp = {}
for i = 1, n do
  local v = a[i]
  if not acmp[v] then acmp[v] = 1
  else acmp[v] = acmp[v] + 1
  end
end
for v, cnt in pairs(acmp) do
  local lim = mfl(1000000 / v)
  for j = 1, lim do
    t[j * v] = t[j * v] + cnt
  end
end
local c = 0
for i = 1, n do
  local v = a[i]
  if t[v] == 1 then
    c = c + 1
  end
end
print(c)