






"""simple docstring"""





from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
from numpy import array, dot, pad, ravel, uinta, zeros






def     A(  snake_case_						,       snake_case_		):
							"""simple docstring"""





							lowercase__:    Optional[int]        =      image.shape
							lowercase__:    int        =      cols - block_size[1] + 1
							lowercase__:    str        =      rows - block_size[0] + 1
							lowercase__:    int        =      zeros((dst_height * dst_width, block_size[1] * block_size[0])		)
							lowercase__:    int        =      0
							for i in range(0						,       snake_case_		):
														for j in range(0						,       snake_case_		):
																					lowercase__:    Optional[Any]        =      ravel(image[i : i + block_size[0], j : j + block_size[1]]		)
																					lowercase__:    List[str]        =      window
																					row += 1

							return image_array






def     A(  snake_case_						,       snake_case_		):
							"""simple docstring"""





							lowercase__:    Optional[Any]        =      image.shape[0], image.shape[1]
							lowercase__:    Optional[int]        =      filter_kernel.shape[0]
							lowercase__:    List[Any]        =      k_size // 2
							# Pads image with the edge values of array.
							lowercase__:    int        =      pad(snake_case_						,       snake_case_						,       mode="edge"		)

							# im2col, turn the k_size*k_size pixels into a row and np.vstack all rows
							lowercase__:    str        =      imacol(snake_case_						,       (k_size, k_size)		)

							#  turn the kernel into shape(k*k, 1)
							lowercase__:    List[Any]        =      ravel(snake_case_		)
							# reshape and get the dst image
							lowercase__:    Tuple        =      dot(snake_case_						,       snake_case_		).reshape(snake_case_						,       snake_case_		)
							return dst


if __name__ == "__main__":
		# read original image
		UpperCamelCase			=      imread(r"""../image_data/lena.jpg""")
		# turn image in gray scale value
		UpperCamelCase			=      cvtColor(img, COLOR_BGR2GRAY)
		# Laplace operator
		UpperCamelCase			=      array([[0, 1, 0], [1, -4, 1], [0, 1, 0]])
		UpperCamelCase			=      img_convolve(gray, Laplace_kernel).astype(uinta)
		imshow("""Laplacian""", out)
		waitKey(0)














"""simple docstring"""





UpperCamelCase			=      {
    """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,
}

UpperCamelCase			=      {1_45: 1_45}

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






def     A(  snake_case_		):
       """simple docstring"""





       if n in CACHE_SUM_DIGIT_FACTORIALS:
              return CACHE_SUM_DIGIT_FACTORIALS[n]
       lowercase__:    Any        =      sum(DIGIT_FACTORIALS[let] for let in str(snake_case_		)		)
       lowercase__:    Optional[Any]        =      ret
       return ret






def     A(  snake_case_						,       snake_case_ = None		):
       """simple docstring"""





       lowercase__:    Optional[int]        =      previous or set()
       if n in CHAIN_LENGTH_CACHE:
              return CHAIN_LENGTH_CACHE[n]
       lowercase__:    Tuple        =      sum_digit_factorials(snake_case_		)
       if next_number in previous:
              lowercase__:    List[Any]        =      0
              return 0
       else:
              previous.add(snake_case_		)
              lowercase__:    Optional[int]        =      1 + chain_length(snake_case_						,       snake_case_		)
              lowercase__:    Any        =      ret
              return ret






def     A(  snake_case_ = 60						,       snake_case_ = 1000000		):
       """simple docstring"""





       return sum(1 for i in range(1						,       snake_case_		) if chain_length(snake_case_		) == num_terms		)


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






