import math
from collections.abc import Generator

def 				UpperCamelCase					(     lowerCAmelCase_ )		->    Generator[int, None, None]:




       '''simple docstring'''






       _A=						(i for i in range(1							,       (max_n + 1) ))
       for i in (n for n in numbers if n > 1):
              for j in range(2							,       lowerCAmelCase_ ):
                     if (i % j) == 0:
                            break
              else:
                     yield i

def 				UpperCamelCase					(     lowerCAmelCase_ )		->    Generator[int, None, None]:




       '''simple docstring'''






       _A=						(i for i in range(1							,       (max_n + 1) ))
       for i in (n for n in numbers if n > 1):
              # only need to check for factors up to sqrt(i)
              _A=						int(math.sqrt(lowerCAmelCase_ ) ) + 1
              for j in range(2							,       lowerCAmelCase_ ):
                     if (i % j) == 0:
                            break
              else:
                     yield i

def 				UpperCamelCase					(     lowerCAmelCase_ )		->    Generator[int, None, None]:




       '''simple docstring'''






       _A=						(i for i in range(1							,       (max_n + 1)							,       2 ))
       # It's useless to test even numbers as they will not be prime
       if max_n > 2:
              yield 2  # Because 2 will not be tested, it's necessary to yield it now
       for i in (n for n in numbers if n > 1):
              _A=						int(math.sqrt(lowerCAmelCase_ ) ) + 1
              for j in range(3							,       lowerCAmelCase_							,       2 ):
                     # As we removed the even numbers, we don't need them now
                     if (i % j) == 0:
                            break
              else:
                     yield i

def 				UpperCamelCase					(     )		->    List[str]:




       '''simple docstring'''






       from timeit import timeit

       _A=						'from __main__ import slow_primes, primes, fast_primes'
       print(timeit('slow_primes(1_000_000_000_000)'							,       setup=lowerCAmelCase_							,       number=1_00_00_00 ) )
       print(timeit('primes(1_000_000_000_000)'							,       setup=lowerCAmelCase_							,       number=1_00_00_00 ) )
       print(timeit('fast_primes(1_000_000_000_000)'							,       setup=lowerCAmelCase_							,       number=1_00_00_00 ) )


if __name__ == "__main__":
      UpperCAmelCase_    		=				int(input('''Calculate primes up to:\n>> ''').strip())
      for ret in primes(number):
            print(ret)
      benchmark()
import numpy as np
from PIL import Image

def 				UpperCamelCase					(     lowerCAmelCase_ )		->    np.array:




       '''simple docstring'''






       _A,      _A,      _A=						rgb[:, :, 0], rgb[:, :, 1], rgb[:, :, 2]
       return 0.2_989 * r + 0.5_870 * g + 0.1_140 * b

def 				UpperCamelCase					(     lowerCAmelCase_ )		->    np.array:




       '''simple docstring'''






       return (gray > 1_27) & (gray <= 2_55)

def 				UpperCamelCase					(     lowerCAmelCase_							,       lowerCAmelCase_ )		->    np.array:




       '''simple docstring'''






       _A=						np.zeros_like(lowerCAmelCase_ )
       _A=						np.zeros(
           (image.shape[0] + kernel.shape[0] - 1, image.shape[1] + kernel.shape[1] - 1) )

       # Copy image to padded image
       _A=						image

       # Iterate over image & apply kernel
       for x in range(image.shape[1] ):
              for y in range(image.shape[0] ):
                     _A=						(
                         kernel * image_padded[y : y + kernel.shape[0], x : x + kernel.shape[1]]
                     ).sum()
                     _A=						int(summation == 5 )
       return output


# kernel to be applied
UpperCAmelCase_    		=				np.array([[0, 1, 0], [1, 1, 1], [0, 1, 0]])

if __name__ == "__main__":
      # read original image
      UpperCAmelCase_    		=				np.array(Image.open(R'''..\image_data\lena.jpg'''))
      # Apply erosion operation to a binary image
      UpperCAmelCase_    		=				erosion(grayabinary(rgbagray(image)), structuring_element)
      # Save the output image
      UpperCAmelCase_    		=				Image.fromarray(output).convert('''RGB''')
      pil_img.save('''result_erosion.png''')