from __future__ import annotations

def   a_					(_lowerCAmelCase  :   Optional[int]       )->				set[int]:
    snake_case:						Optional[int]         =   {1}
    snake_case:						Any         =   [1]
    for _ in range(2			,	depth + 1       ):
        snake_case:						int         =   [*previous_coefficients, 0]
        snake_case:						Optional[Any]         =   [0, *previous_coefficients]
        snake_case:						Tuple         =   []
        for x, y in zip(_lowerCAmelCase			,	_lowerCAmelCase       ):
            coefficients.add(x + y       )
            previous_coefficients.append(x + y       )
    return coefficients

def   a_					(_lowerCAmelCase  :   Tuple       )->				set[int]:
    snake_case:						int         =   set()
    for number in unique_coefficients:
        snake_case:						List[Any]         =   2
        snake_case:						Dict         =   number
        while divisor**2 <= copy_number:
            snake_case:						Any         =   0
            while copy_number % divisor == 0:
                copy_number //= divisor
                multiplicity += 1
            if multiplicity >= 2:
                non_squarefrees.add(_lowerCAmelCase       )
                break
            divisor += 1

    return unique_coefficients.difference(_lowerCAmelCase       )

def   a_					(_lowerCAmelCase  :   Dict = 51       )->				int:
    snake_case:						Union[str, Any]         =   get_pascal_triangle_unique_coefficients(_lowerCAmelCase       )
    snake_case:						List[str]         =   get_squarefrees(_lowerCAmelCase       )
    return sum(_lowerCAmelCase       )


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)


