



"""simple docstring"""




import math


def 	lowercase__  (      _UpperCAmelCase					)  ->      Any:






      '''simple docstring'''


      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(__SCREAMING_SNAKE_CASE					) + 1					)						,   6					):
            if number % i == 0 or number % (i + 2) == 0:
                  return False
      return True


def 	lowercase__  (      _UpperCAmelCase = 10_00						,   _UpperCAmelCase = 10_00					)  ->      int:






      '''simple docstring'''


      lowercase	:   Dict											= [0, 0, 0]  # length, a, b
      for a in range((a_limit * -1) + 1						,   __SCREAMING_SNAKE_CASE					):
            for b in range(2						,   __SCREAMING_SNAKE_CASE					):
                  if is_prime(__SCREAMING_SNAKE_CASE					):
                        lowercase	:   List[Any]											= 0
                        lowercase	:   Union[str, Any]											= 0
                        while is_prime((n**2) + (a * n) + b					):
                              count += 1
                              n += 1
                        if count > longest[0]:
                              lowercase	:   Optional[int]											= [count, a, b]
      lowercase	:   str											= longest[1] * longest[2]
      return ans


if __name__ == "__main__":
     print(solution(1_0_0_0, 1_0_0_0))


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

_UpperCamelCase:					Tuple     =180



def 	_a  (					__SCREAMING_SNAKE_CASE					:  List[Any]		,				__SCREAMING_SNAKE_CASE					:  int    ):






  """simple docstring"""




  _lowerCAmelCase						=		k_size // 2
  _lowerCAmelCase	,       _lowerCAmelCase						=		np.mgrid[0 - center : k_size - center, 0 - center : k_size - center]
  _lowerCAmelCase						=		(
      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 	_a  (					__SCREAMING_SNAKE_CASE					:  List[str]		,				__SCREAMING_SNAKE_CASE					:  Tuple		,				__SCREAMING_SNAKE_CASE					:  Optional[Any]    ):






  """simple docstring"""




  _lowerCAmelCase						=		np.zeros(__SCREAMING_SNAKE_CASE    )

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

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

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

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

      elif (
          5 * PI / 8 <= direction < 7 * PI / 8
          or 13 * PI / 8 <= direction < 15 * PI / 8
      ):
        _lowerCAmelCase						=		sobel_grad[row - 1, col - 1]
        _lowerCAmelCase						=		sobel_grad[row + 1, col + 1]
        if sobel_grad[row, col] >= nw and sobel_grad[row, col] >= se:
          _lowerCAmelCase						=		sobel_grad[row, col]

  return destination



def 	_a  (					__SCREAMING_SNAKE_CASE					:  Tuple		,				__SCREAMING_SNAKE_CASE					:  List[str]		,				__SCREAMING_SNAKE_CASE					:  Tuple		,				__SCREAMING_SNAKE_CASE					:  Union[str, Any]		,				__SCREAMING_SNAKE_CASE					:  Dict		,				__SCREAMING_SNAKE_CASE					:  List[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:
        _lowerCAmelCase						=		strong
      elif destination[row, col] <= threshold_low:
        _lowerCAmelCase						=		0
      else:
        _lowerCAmelCase						=		weak



def 	_a  (					__SCREAMING_SNAKE_CASE					:  List[Any]		,				__SCREAMING_SNAKE_CASE					:  Optional[int]		,				__SCREAMING_SNAKE_CASE					:  Optional[int]		,				__SCREAMING_SNAKE_CASE					:  Union[str, 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 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],
        ):
          _lowerCAmelCase						=		strong
        else:
          _lowerCAmelCase						=		0



def 	_a  (					__SCREAMING_SNAKE_CASE					:  List[str]		,				__SCREAMING_SNAKE_CASE					:  int=15		,				__SCREAMING_SNAKE_CASE					:  int=30		,				__SCREAMING_SNAKE_CASE					:  Tuple=128		,				__SCREAMING_SNAKE_CASE					:  List[Any]=255    ):






  """simple docstring"""




  _lowerCAmelCase						=		img_convolve(__SCREAMING_SNAKE_CASE		,				gen_gaussian_kernel(9		,				sigma=1.4    )    )
  # get the gradient and degree by sobel_filter
  _lowerCAmelCase	,       _lowerCAmelCase						=		sobel_filter(__SCREAMING_SNAKE_CASE    )
  _lowerCAmelCase						=		PI + np.radadeg(__SCREAMING_SNAKE_CASE    )

  _lowerCAmelCase						=		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
       _UpperCamelCase:					Optional[Any]     =cva.imread(R'../image_data/lena.jpg', 0)
       # canny edge detection
       _UpperCamelCase:					Tuple     =canny(lena)
       cva.imshow('canny', canny_destination)
       cva.waitKey(0)
