




'''simple docstring'''






import math




def 		a_( lowerCamelCase      )				->List[str]:






       '''simple docstring'''




       lowercase  :		Dict						=      0
       if n % 2 == 0:
              count += 1
              while n % 2 == 0:
                     lowercase  :		Optional[Any]						=      int(n / 2      )
    # the n input value must be odd so that
    # we can skip one element (ie i += 2)

       lowercase  :		Optional[int]						=      3

       while i <= int(math.sqrt(lowerCamelCase      )      ):
              if n % i == 0:
                     count += 1
                     while n % i == 0:
                            lowercase  :		Union[str, Any]						=      int(n / i      )
              lowercase  :		Tuple						=      i + 2

       # this condition checks the prime
       # number n is greater than 2

       if n > 2:
              count += 1
       return count


if __name__ == "__main__":
      lowercase	:      int				=       51242183
      print(f'The number of distinct prime factors is/are {exact_prime_factor_count(n)}')
      print(f'The value of log(log(n)) is {math.log(math.log(n)):.4f}')










'''simple docstring'''






import numpy as np
from PIL import Image




def 		a_( lowerCamelCase      )				->np.array:






       '''simple docstring'''




       lowercase,     lowercase,     lowercase  :		Union[str, Any]						=      rgb[:, :, 0], rgb[:, :, 1], rgb[:, :, 2]
       return 0.29_89 * r + 0.58_70 * g + 0.11_40 * b




def 		a_( lowerCamelCase      )				->np.array:






       '''simple docstring'''




       return (gray > 127) & (gray <= 255)




def 		a_( lowerCamelCase   ,				lowerCamelCase      )				->np.array:






       '''simple docstring'''




       lowercase  :		Optional[Any]						=      np.zeros_like(lowerCamelCase      )
       lowercase  :		Any						=      np.zeros(
           (image.shape[0] + kernel.shape[0] - 1, image.shape[1] + kernel.shape[1] - 1)      )

       # Copy image to padded image
       lowercase  :		List[str]						=      image

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


# kernel to be applied
lowercase	:      List[Any]				=       np.array([[0, 1, 0], [1, 1, 1], [0, 1, 0]])

if __name__ == "__main__":
      # read original image
      lowercase	:      Dict				=       np.array(Image.open(r'''..\image_data\lena.jpg'''))
      # Apply erosion operation to a binary image
      lowercase	:      List[str]				=       erosion(grayabinary(rgbagray(image)), structuring_element)
      # Save the output image
      lowercase	:      Optional[Any]				=       Image.fromarray(output).convert('''RGB''')
      pil_img.save('''result_erosion.png''')




