CF1209A Paint the Numbers

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).

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.

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

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 $ .