


__lowerCAmelCase									=				{
    '''0''': 1,
    '''1''': 1,
    '''2''': 2,
    '''3''': 6,
    '''4''': 24,
    '''5''': 1_20,
    '''6''': 7_20,
    '''7''': 50_40,
    '''8''': 4_03_20,
    '''9''': 36_28_80,
}

__lowerCAmelCase									=				{1_45: 1_45}

__lowerCAmelCase									=				{
    1_45: 0,
    1_69: 3,
    3_63_01: 3,
    14_54: 3,
    8_71: 2,
    4_53_61: 2,
    8_72: 2,
}




def   snake_case_	(    snake_case	)    ->							int:
       if n in CACHE_SUM_DIGIT_FACTORIALS:
              return CACHE_SUM_DIGIT_FACTORIALS[n]
       lowercase__:  Optional[int]         =  sum(DIGIT_FACTORIALS[let] for let in str(snake_case	)	)
       lowercase__:  Tuple         =  ret
       return ret




def   snake_case_	(    snake_case     ,				snake_case = None	)    ->							int:
       lowercase__:  Optional[Any]         =  previous or set()
       if n in CHAIN_LENGTH_CACHE:
              return CHAIN_LENGTH_CACHE[n]
       lowercase__:  Optional[int]         =  sum_digit_factorials(snake_case	)
       if next_number in previous:
              lowercase__:  str         =  0
              return 0
       else:
              previous.add(snake_case	)
              lowercase__:  int         =  1 + chain_length(snake_case     ,				snake_case	)
              lowercase__:  Optional[int]         =  ret
              return ret




def   snake_case_	(    snake_case = 60     ,				snake_case = 1_00_00_00	)    ->							int:
       return sum(1 for i in range(1     ,				snake_case	) if chain_length(snake_case	) == num_terms	)


if __name__ == "__main__":
 print(F'''{solution() = }''')






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_	(    snake_case	)    ->							List[str]:
       lowercase__:  Any         =  np.array([[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]]	)
       lowercase__:  Optional[Any]         =  np.array([[1, 2, 1], [0, 0, 0], [-1, -2, -1]]	)

       lowercase__:  Optional[int]         =  np.abs(img_convolve(snake_case     ,				snake_case	)	)
       lowercase__:  List[Any]         =  np.abs(img_convolve(snake_case     ,				snake_case	)	)
       # modify the pix within [0, 255]
       lowercase__:  Optional[Any]         =  dst_x * 2_55 / np.max(snake_case	)
       lowercase__:  Dict         =  dst_y * 2_55 / np.max(snake_case	)

       lowercase__:  Tuple         =  np.sqrt((np.square(snake_case	)) + (np.square(snake_case	))	)
       lowercase__:  str         =  dst_xy * 2_55 / np.max(snake_case	)
       lowercase__:  Tuple         =  dst_xy.astype(np.uinta	)

       lowercase__:  List[Any]         =  np.arctana(snake_case     ,				snake_case	)
       return dst, theta


if __name__ == "__main__":
 # read original image
 __lowerCAmelCase									=				imread('''../image_data/lena.jpg''')
 # turn image in gray scale value
 __lowerCAmelCase									=				cvtColor(img, COLOR_BGR2GRAY)

 __lowerCAmelCase			,__lowerCAmelCase									=				sobel_filter(gray)

 # show result images
 imshow('''sobel filter''', sobel_grad)
 imshow('''sobel theta''', sobel_theta)
 waitKey(0)


