A. Paint the Numberstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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).InputThe 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.OutputPrint the minimal number of colors to paint all the given numbers in a valid way.ExamplesInput
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
NoteIn 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. 
6
10 2 3 5 4 2

3 
['greedy', 'implementation', 'math', '*800']