code: import numpy as np
  from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
  
  from digital_image_processing.filters.convolve import img_convolve
  def 		snake_case__  (		lowercase				):
     lowerCAmelCase_:       Union[str, Any]         =  np.array([[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]]				)
     lowerCAmelCase_:       Tuple         =  np.array([[1, 2, 1], [0, 0, 0], [-1, -2, -1]]				)
  
     lowerCAmelCase_:       Optional[int]         =  np.abs(img_convolve(lowercase       ,							lowercase				)				)
     lowerCAmelCase_:       Dict         =  np.abs(img_convolve(lowercase       ,							lowercase				)				)
     # modify the pix within [0, 255]
     lowerCAmelCase_:       List[Any]         =  dst_x * 255 / np.max(lowercase				)
     lowerCAmelCase_:       int         =  dst_y * 255 / np.max(lowercase				)
  
     lowerCAmelCase_:       Union[str, Any]         =  np.sqrt((np.square(lowercase				)) + (np.square(lowercase				))				)
     lowerCAmelCase_:       Dict         =  dst_xy * 255 / np.max(lowercase				)
     lowerCAmelCase_:       List[Any]         =  dst_xy.astype(np.uinta				)
  
     lowerCAmelCase_:       List[Any]         =  np.arctana(lowercase       ,							lowercase				)
     return dst, theta
  
  
  if __name__ == "__main__":
   # read original image
   a     :			Tuple					    =						imread("""../image_data/lena.jpg""")
   # turn image in gray scale value
   a     :			Dict					    =						cvtColor(img, COLOR_BGR2GRAY)
  
   a    ,   a     :			Union[str, Any]					    =						sobel_filter(gray)
  
   # show result images
   imshow("""sobel filter""", sobel_grad)
   imshow("""sobel theta""", sobel_theta)
   waitKey(0)
style_context: import itertools
  def 		snake_case__  (		lowercase				):
     return (
         int("".join(combination[0:2]				)				) * int("".join(combination[2:5]				)				)
         == int("".join(combination[5:9]				)				)
     ) or (
         int("".join(combination[0]				)				) * int("".join(combination[1:5]				)				)
         == int("".join(combination[5:9]				)				)
     )
  def 		snake_case__  (		):
     return sum(
         {
             int("".join(pandigital[5:9]				)				)
             for pandigital in itertools.permutations("123456789"				)
             if is_combination_valid(lowercase				)
         }				)
  
  
  if __name__ == "__main__":
   print(solution())