"""simple docstring"""





from itertools import product

from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
from numpy import dot, exp, mgrid, pi, ravel, square, uinta, zeros


def    lowercase_   (   _lowerCamelCase:	Optional[int]						,   _lowerCamelCase:	Optional[Any]      ) ->      Optional[Any]:



							'''simple docstring'''

							__lowerCamelCase					:		str		   =     k_size // 2
							__lowerCamelCase					:		int		   =     mgrid[0 - center : k_size - center, 0 - center : k_size - center]
							__lowerCamelCase					:		Any		   =     1 / (2 * pi * sigma) * exp(-(square(__lowerCAmelCase      ) + square(__lowerCAmelCase      )) / (2 * square(__lowerCAmelCase      ))      )
							return g


def    lowercase_   (   _lowerCamelCase:	Any						,   _lowerCamelCase:	Dict						,   _lowerCamelCase:	Dict      ) ->      str:



							'''simple docstring'''

							__lowerCamelCase					:		Union[str, Any]		   =     image.shape[0], image.shape[1]
							# dst image height and width
							__lowerCamelCase					:		str		   =     height - k_size + 1
							__lowerCamelCase					:		Optional[int]		   =     width - k_size + 1

							# im2col, turn the k_size*k_size pixels into a row and np.vstack all rows
							__lowerCamelCase					:		Any		   =     zeros((dst_height * dst_width, k_size * k_size)      )
							__lowerCamelCase					:		int		   =     0
							for i, j in product(range(__lowerCAmelCase      )						,   range(__lowerCAmelCase      )      ):
														__lowerCamelCase					:		List[Any]		   =     ravel(image[i : i + k_size, j : j + k_size]      )
														__lowerCamelCase					:		Dict		   =     window
														row += 1

							#  turn the kernel into shape(k*k, 1)
							__lowerCamelCase					:		str		   =     gen_gaussian_kernel(__lowerCAmelCase						,   __lowerCAmelCase      )
							__lowerCamelCase					:		Optional[Any]		   =     ravel(__lowerCAmelCase      )

							# reshape and get the dst image
							__lowerCamelCase					:		Any		   =     dot(__lowerCAmelCase						,   __lowerCAmelCase      ).reshape(__lowerCAmelCase						,   __lowerCAmelCase      ).astype(__lowerCAmelCase      )

							return dst


if __name__ == "__main__":
				# read original image
				__A  =				imread(R'''../image_data/lena.jpg''')
				# turn image in gray scale value
				__A  =				cvtColor(img, COLOR_BGR2GRAY)

				# get values with two different mask size
				__A  =				gaussian_filter(gray, 3, sigma=1)
				__A  =				gaussian_filter(gray, 5, sigma=0.8)

				# show result images
				imshow('''gaussian filter with 3x3 mask''', gaussianaxa)
				imshow('''gaussian filter with 5x5 mask''', gaussianaxa)
				waitKey()
"""simple docstring"""





import math


def    lowercase_   (   _lowerCamelCase:	int      ) ->      bool:



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


def    lowercase_   (   _lowerCamelCase:	int = 10001      ) ->      int:



							'''simple docstring'''

							try:
														__lowerCamelCase					:		Optional[int]		   =     int(_lowerCamelCase      )
							except (TypeError, ValueError):
														raise TypeError("Parameter nth must be int or castable to int."      ) from None
							if nth <= 0:
														raise ValueError("Parameter nth must be greater than or equal to one."      )
							__lowerCamelCase					:		list[int]		   =     []
							__lowerCamelCase					:		Tuple		   =     2
							while len(_lowerCamelCase      ) < nth:
														if is_prime(_lowerCamelCase      ):
																					primes.append(_lowerCamelCase      )
																					num += 1
														else:
																					num += 1
							return primes[len(_lowerCamelCase      ) - 1]


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