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A. Paint the Numbers
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a sequence of integers $$$a_1, a_2, \dots, a_n$$$. You need to paint elements in colors, so that:

  • If we consider any color, all elements of this color must be divisible by the minimal element of this color.
  • The number of used colors must be minimized.

For example, it's fine to paint elements $$$[40, 10, 60]$$$ in a single color, because they are all divisible by $$$10$$$. You can use any color an arbitrary amount of times (in particular, it is allowed to use a color only once). The elements painted in one color do not need to be consecutive.

For example, if $$$a=[6, 2, 3, 4, 12]$$$ then two colors are required: let's paint $$$6$$$, $$$3$$$ and $$$12$$$ in the first color ($$$6$$$, $$$3$$$ and $$$12$$$ are divisible by $$$3$$$) and paint $$$2$$$ and $$$4$$$ in the second color ($$$2$$$ and $$$4$$$ are divisible by $$$2$$$). For example, if $$$a=[10, 7, 15]$$$ then $$$3$$$ colors are required (we can simply paint each element in an unique color).

Input

The first line contains an integer $$$n$$$ ($$$1 \le n \le 100$$$), where $$$n$$$ is the length of the given sequence.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 100$$$). These numbers can contain duplicates.

Output

Print the minimal number of colors to paint all the given numbers in a valid way.

Examples
Input
6
10 2 3 5 4 2
Output
3
Input
4
100 100 100 100
Output
1
Input
8
7 6 5 4 3 2 2 3
Output
4
Note

In the first example, one possible way to paint the elements in $$$3$$$ colors is:

  • paint in the first color the elements: $$$a_1=10$$$ and $$$a_4=5$$$,
  • paint in the second color the element $$$a_3=3$$$,
  • paint in the third color the elements: $$$a_2=2$$$, $$$a_5=4$$$ and $$$a_6=2$$$.

In the second example, you can use one color to paint all the elements.

In the third example, one possible way to paint the elements in $$$4$$$ colors is:

  • paint in the first color the elements: $$$a_4=4$$$, $$$a_6=2$$$ and $$$a_7=2$$$,
  • paint in the second color the elements: $$$a_2=6$$$, $$$a_5=3$$$ and $$$a_8=3$$$,
  • paint in the third color the element $$$a_3=5$$$,
  • paint in the fourth color the element $$$a_1=7$$$.