code: 
  
  
  '''simple docstring'''
  
  
  
  import cva
  import numpy as np
  
  from digital_image_processing.filters.convolve import img_convolve
  from digital_image_processing.filters.sobel_filter import sobel_filter
  
  __lowercase			:		Union[str, Any] =			1_80
  
  
  
  
  
  
  def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     List[str]		,   _SCREAMING_SNAKE_CASE   :     Union[str, Any]     ):
  					__a    : str      					=						k_size // 2
  					__a    : str      					=						np.mgrid[0 - center : k_size - center, 0 - center : k_size - center]
  					__a    : Any      					=						(
  					    1
  					    / (2 * np.pi * sigma)
  					    * np.exp(-(np.square(_SCREAMING_SNAKE_CASE     ) + np.square(_SCREAMING_SNAKE_CASE     )) / (2 * np.square(_SCREAMING_SNAKE_CASE     ))     )
  					)
  					return g
  
  
  
  
  
  
  def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     Optional[int]		,   _SCREAMING_SNAKE_CASE   :     List[str]		,   _SCREAMING_SNAKE_CASE   :     Any     ):
  					__a    : List[Any]      					=						np.zeros(_SCREAMING_SNAKE_CASE     )
  
  					for row in range(1		,   image_shape[0] - 1     ):
  										for col in range(1		,   image_shape[1] - 1     ):
  															__a    : int      					=						gradient_direction[row, col]
  
  															if (
  															    0 <= direction < PI / 8
  															    or 15 * PI / 8 <= direction <= 2 * PI
  															    or 7 * PI / 8 <= direction <= 9 * PI / 8
  															):
  																				__a    : int      					=						sobel_grad[row, col - 1]
  																				__a    : int      					=						sobel_grad[row, col + 1]
  																				if sobel_grad[row, col] >= w and sobel_grad[row, col] >= e:
  																									__a    : List[str]      					=						sobel_grad[row, col]
  
  															elif (
  															    PI / 8 <= direction < 3 * PI / 8
  															    or 9 * PI / 8 <= direction < 11 * PI / 8
  															):
  																				__a    : Optional[int]      					=						sobel_grad[row + 1, col - 1]
  																				__a    : Optional[int]      					=						sobel_grad[row - 1, col + 1]
  																				if sobel_grad[row, col] >= sw and sobel_grad[row, col] >= ne:
  																									__a    : int      					=						sobel_grad[row, col]
  
  															elif (
  															    3 * PI / 8 <= direction < 5 * PI / 8
  															    or 11 * PI / 8 <= direction < 13 * PI / 8
  															):
  																				__a    : List[str]      					=						sobel_grad[row - 1, col]
  																				__a    : str      					=						sobel_grad[row + 1, col]
  																				if sobel_grad[row, col] >= n and sobel_grad[row, col] >= s:
  																									__a    : Optional[Any]      					=						sobel_grad[row, col]
  
  															elif (
  															    5 * PI / 8 <= direction < 7 * PI / 8
  															    or 13 * PI / 8 <= direction < 15 * PI / 8
  															):
  																				__a    : Dict      					=						sobel_grad[row - 1, col - 1]
  																				__a    : str      					=						sobel_grad[row + 1, col + 1]
  																				if sobel_grad[row, col] >= nw and sobel_grad[row, col] >= se:
  																									__a    : List[str]      					=						sobel_grad[row, col]
  
  					return destination
  
  
  
  
  
  
  def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     int		,   _SCREAMING_SNAKE_CASE   :     Dict		,   _SCREAMING_SNAKE_CASE   :     Tuple		,   _SCREAMING_SNAKE_CASE   :     Dict		,   _SCREAMING_SNAKE_CASE   :     Dict		,   _SCREAMING_SNAKE_CASE   :     Any     ):
  					for row in range(1		,   image_shape[0] - 1     ):
  										for col in range(1		,   image_shape[1] - 1     ):
  															if destination[row, col] >= threshold_high:
  																				__a    : Tuple      					=						strong
  															elif destination[row, col] <= threshold_low:
  																				__a    : Optional[Any]      					=						0
  															else:
  																				__a    : int      					=						weak
  
  
  
  
  
  
  def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     Union[str, Any]		,   _SCREAMING_SNAKE_CASE   :     Union[str, Any]		,   _SCREAMING_SNAKE_CASE   :     Optional[int]		,   _SCREAMING_SNAKE_CASE   :     str     ):
  					for row in range(1		,   image_shape[0]     ):
  										for col in range(1		,   image_shape[1]     ):
  															if destination[row, col] == weak:
  																				if 255 in (
  																				    destination[row, col + 1],
  																				    destination[row, col - 1],
  																				    destination[row - 1, col],
  																				    destination[row + 1, col],
  																				    destination[row - 1, col - 1],
  																				    destination[row + 1, col - 1],
  																				    destination[row - 1, col + 1],
  																				    destination[row + 1, col + 1],
  																				):
  																									__a    : List[Any]      					=						strong
  																				else:
  																									__a    : Optional[Any]      					=						0
  
  
  
  
  
  
  def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     Optional[int]		,   _SCREAMING_SNAKE_CASE   :     List[Any]=15		,   _SCREAMING_SNAKE_CASE   :     List[Any]=30		,   _SCREAMING_SNAKE_CASE   :     List[str]=128		,   _SCREAMING_SNAKE_CASE   :     str=255     ):
  					# gaussian_filter
  					__a    : List[str]      					=						img_convolve(_SCREAMING_SNAKE_CASE		,   gen_gaussian_kernel(9		,   sigma=1.4     )     )
  					# get the gradient and degree by sobel_filter
  					__a    : Union[str, Any]      					=						sobel_filter(_SCREAMING_SNAKE_CASE     )
  					__a    : Tuple      					=						PI + np.radadeg(_SCREAMING_SNAKE_CASE     )
  
  					__a    : Tuple      					=						suppress_non_maximum(image.shape		,   _SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE     )
  
  					detect_high_low_threshold(
  					    image.shape		,   _SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE     )
  
  					track_edge(image.shape		,   _SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE		,   _SCREAMING_SNAKE_CASE     )
  
  					return destination
  
  
  if __name__ == "__main__":
  							# read original image in gray mode
  							__lowercase			:		List[str] =			cva.imread(R'../image_data/lena.jpg', 0)
  							# canny edge detection
  							__lowercase			:		int =			canny(lena)
  							cva.imshow('canny', canny_destination)
  							cva.waitKey(0)
  
  
  
  
style_context: 
  
  
  '''simple docstring'''
  
  
  
  import itertools
  
  
  
  
  
  
  def 						lowerCamelCase							(_SCREAMING_SNAKE_CASE   :     int = 1_000_000     ):
  					__a    : str      					=						[1]
  
  					for i in itertools.count(len(_SCREAMING_SNAKE_CASE     )     ):
  										__a    : Dict      					=						0
  										for j in itertools.count(1     ):
  															__a    : int      					=						-1 if j % 2 == 0 else +1
  															__a    : Optional[int]      					=						(j * j * 3 - j) // 2
  															if index > i:
  																				break
  															item += partitions[i - index] * sign
  															item %= number
  															index += j
  															if index > i:
  																				break
  															item += partitions[i - index] * sign
  															item %= number
  
  										if item == 0:
  															return i
  										partitions.append(_SCREAMING_SNAKE_CASE     )
  
  					return 0
  
  
  if __name__ == "__main__":
  	import doctest
  
  	doctest.testmod()
  
  	print(f'''{solution() = }''')
  
  
  
  