






"""simple docstring"""
import math






def 			lowerCamelCase_    (		_lowerCamelCase							):





 if 1 < number < 4:
  # 2 and 3 are primes
  return True
 elif number < 2 or number % 2 == 0 or number % 3 == 0:
  # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
  return False

 # All primes number are in format of 6k +/- 1
 for i in range(5     ,  int(math.sqrt(UpperCAmelCase_							) + 1							)     ,  6							):
  if number % i == 0 or number % (i + 2) == 0:
   return False
 return True






def 			lowerCamelCase_    (		_lowerCamelCase = 200_0000							):
 return sum(num for num in range(3     ,  UpperCAmelCase_     ,  2							) if is_prime(UpperCAmelCase_							)							) + 2 if n > 2 else 0


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


"""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

_a	:	int=					180
def     __UpperCAmelCase							(       UpperCAmelCase_       :							str     ,				UpperCAmelCase_       :							Tuple    )				->     Union[str, Any]:

	'''simple docstring'''





	__snake_case     :				Optional[Any] 						=					k_size // 2
	__snake_case						,							__snake_case     :				Union[str, Any] 						=					np.mgrid[0 - center : k_size - center, 0 - center : k_size - center]
	__snake_case     :				List[Any] 						=					(
	    1
	    / (2 * np.pi * sigma)
	    * np.exp(-(np.square(UpperCAmelCase_    ) + np.square(UpperCAmelCase_    )) / (2 * np.square(UpperCAmelCase_    ))    )
	)
	return g
def     __UpperCAmelCase							(       UpperCAmelCase_       :							Tuple     ,				UpperCAmelCase_       :							int     ,				UpperCAmelCase_       :							Optional[int]    )				->     List[str]:

	'''simple docstring'''





	__snake_case     :				List[Any] 						=					np.zeros(UpperCAmelCase_    )

	for row in range(1     ,				image_shape[0] - 1    ):
		for col in range(1     ,				image_shape[1] - 1    ):
			__snake_case     :				Any 						=					gradient_direction[row, col]

			if (
			    0 <= direction < PI / 8
			    or 15 * PI / 8 <= direction <= 2 * PI
			    or 7 * PI / 8 <= direction <= 9 * PI / 8
			):
				__snake_case     :				str 						=					sobel_grad[row, col - 1]
				__snake_case     :				str 						=					sobel_grad[row, col + 1]
				if sobel_grad[row, col] >= w and sobel_grad[row, col] >= e:
					__snake_case     :				Union[str, Any] 						=					sobel_grad[row, col]

			elif (
			    PI / 8 <= direction < 3 * PI / 8
			    or 9 * PI / 8 <= direction < 11 * PI / 8
			):
				__snake_case     :				Optional[int] 						=					sobel_grad[row + 1, col - 1]
				__snake_case     :				Optional[Any] 						=					sobel_grad[row - 1, col + 1]
				if sobel_grad[row, col] >= sw and sobel_grad[row, col] >= ne:
					__snake_case     :				Union[str, Any] 						=					sobel_grad[row, col]

			elif (
			    3 * PI / 8 <= direction < 5 * PI / 8
			    or 11 * PI / 8 <= direction < 13 * PI / 8
			):
				__snake_case     :				Union[str, Any] 						=					sobel_grad[row - 1, col]
				__snake_case     :				Optional[int] 						=					sobel_grad[row + 1, col]
				if sobel_grad[row, col] >= n and sobel_grad[row, col] >= s:
					__snake_case     :				int 						=					sobel_grad[row, col]

			elif (
			    5 * PI / 8 <= direction < 7 * PI / 8
			    or 13 * PI / 8 <= direction < 15 * PI / 8
			):
				__snake_case     :				Optional[int] 						=					sobel_grad[row - 1, col - 1]
				__snake_case     :				Union[str, Any] 						=					sobel_grad[row + 1, col + 1]
				if sobel_grad[row, col] >= nw and sobel_grad[row, col] >= se:
					__snake_case     :				List[str] 						=					sobel_grad[row, col]

	return destination
def     __UpperCAmelCase							(       UpperCAmelCase_       :							Tuple     ,				UpperCAmelCase_       :							List[str]     ,				UpperCAmelCase_       :							Optional[Any]     ,				UpperCAmelCase_       :							Optional[Any]     ,				UpperCAmelCase_       :							List[str]     ,				UpperCAmelCase_       :							List[Any]    )				->     Any:

	'''simple docstring'''





	for row in range(1     ,				image_shape[0] - 1    ):
		for col in range(1     ,				image_shape[1] - 1    ):
			if destination[row, col] >= threshold_high:
				__snake_case     :				str 						=					strong
			elif destination[row, col] <= threshold_low:
				__snake_case     :				int 						=					0
			else:
				__snake_case     :				Tuple 						=					weak
def     __UpperCAmelCase							(       UpperCAmelCase_       :							Union[str, Any]     ,				UpperCAmelCase_       :							Tuple     ,				UpperCAmelCase_       :							List[Any]     ,				UpperCAmelCase_       :							int    )				->     List[Any]:

	'''simple docstring'''





	for row in range(1     ,				image_shape[0]    ):
		for col in range(1     ,				image_shape[1]    ):
			if destination[row, col] == weak:
				if 2_55 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],
				):
					__snake_case     :				Tuple 						=					strong
				else:
					__snake_case     :				Tuple 						=					0
def     __UpperCAmelCase							(       UpperCAmelCase_       :							Union[str, Any]     ,				UpperCAmelCase_       :							Any=15     ,				UpperCAmelCase_       :							int=30     ,				UpperCAmelCase_       :							Optional[Any]=1_28     ,				UpperCAmelCase_       :							Dict=2_55    )				->     Optional[Any]:

	'''simple docstring'''





	__snake_case     :				Tuple 						=					img_convolve(UpperCAmelCase_     ,				gen_gaussian_kernel(9     ,				sigma=1.4    )    )
	# get the gradient and degree by sobel_filter
	__snake_case						,							__snake_case     :				str 						=					sobel_filter(UpperCAmelCase_    )
	__snake_case     :				str 						=					PI + np.radadeg(UpperCAmelCase_    )

	__snake_case     :				int 						=					suppress_non_maximum(image.shape     ,				UpperCAmelCase_     ,				UpperCAmelCase_    )

	detect_high_low_threshold(
	    image.shape     ,				UpperCAmelCase_     ,				UpperCAmelCase_     ,				UpperCAmelCase_     ,				UpperCAmelCase_     ,				UpperCAmelCase_    )

	track_edge(image.shape     ,				UpperCAmelCase_     ,				UpperCAmelCase_     ,				UpperCAmelCase_    )

	return destination


if __name__ == "__main__":
	# read original image in gray mode
	_a	:	List[Any]=					cva.imread(R"../image_data/lena.jpg", 0)
	# canny edge detection
	_a	:	Optional[int]=					canny(lena)
	cva.imshow("canny", canny_destination)
	cva.waitKey(0)





