





import math
import sys

import cva
import numpy as np






def     lowerCamelCase__			(__lowerCamelCase,       __lowerCamelCase	):
     # For applying gaussian function for each element in matrix.
     _SCREAMING_SNAKE_CASE       :	List[str]						    =							math.sqrt(__lowerCamelCase	)
     _SCREAMING_SNAKE_CASE       :	List[Any]						    =							1 / (sigma * math.sqrt(2 * math.pi	))
     return cons * np.exp(-((img / sigma) ** 2) * 0.5	)






def     lowerCamelCase__			(__lowerCamelCase,       __lowerCamelCase,       __lowerCamelCase,       __lowerCamelCase	):
     _SCREAMING_SNAKE_CASE       :	int						    =							kernel_size // 2
     return img[x - half : x + half + 1, y - half : y + half + 1]






def     lowerCamelCase__			(__lowerCamelCase,       __lowerCamelCase	):
     # Creates a gaussian kernel of given dimension.
     _SCREAMING_SNAKE_CASE       :	List[str]						    =							np.zeros((kernel_size, kernel_size)	)
     for i in range(0,       __lowerCamelCase	):
          for j in range(0,       __lowerCamelCase	):
               _SCREAMING_SNAKE_CASE       :	Optional[int]						    =							math.sqrt(
                   abs(i - kernel_size // 2	) ** 2 + abs(j - kernel_size // 2	) ** 2	)
     return vec_gaussian(__lowerCamelCase,       __lowerCamelCase	)






def     lowerCamelCase__			(__lowerCamelCase,       __lowerCamelCase,       __lowerCamelCase,       __lowerCamelCase,       ):
     _SCREAMING_SNAKE_CASE       :	Optional[Any]						    =							np.zeros(img.shape	)
     _SCREAMING_SNAKE_CASE       :	Dict						    =							get_gauss_kernel(__lowerCamelCase,       __lowerCamelCase	)
     _SCREAMING_SNAKE_CASE    ,			_SCREAMING_SNAKE_CASE       :	Dict						    =							img.shape
     for i in range(kernel_size // 2,       size_x - kernel_size // 2	):
          for j in range(kernel_size // 2,       size_y - kernel_size // 2	):
               _SCREAMING_SNAKE_CASE       :	List[Any]						    =							get_slice(__lowerCamelCase,       __lowerCamelCase,       __lowerCamelCase,       __lowerCamelCase	)
               _SCREAMING_SNAKE_CASE       :	Tuple						    =							img_s - img_s[kernel_size // 2, kernel_size // 2]
               _SCREAMING_SNAKE_CASE       :	Tuple						    =							vec_gaussian(__lowerCamelCase,       __lowerCamelCase	)
               _SCREAMING_SNAKE_CASE       :	str						    =							np.multiply(__lowerCamelCase,       __lowerCamelCase	)
               _SCREAMING_SNAKE_CASE       :	int						    =							np.multiply(__lowerCamelCase,       __lowerCamelCase	)
               _SCREAMING_SNAKE_CASE       :	Any						    =							np.sum(__lowerCamelCase	) / np.sum(__lowerCamelCase	)
               _SCREAMING_SNAKE_CASE       :	Union[str, Any]						    =							val
     return imga






def     lowerCamelCase__			(__lowerCamelCase	):
     _SCREAMING_SNAKE_CASE       :	Optional[Any]						    =							args[1] if args[1:] else "../image_data/lena.jpg"
     _SCREAMING_SNAKE_CASE       :	List[Any]						    =							float(args[2]	) if args[2:] else 1.0
     _SCREAMING_SNAKE_CASE       :	Optional[Any]						    =							float(args[3]	) if args[3:] else 1.0
     if args[4:]:
          _SCREAMING_SNAKE_CASE       :	Union[str, Any]						    =							int(args[4]	)
          _SCREAMING_SNAKE_CASE       :	Union[str, Any]						    =							kernel_size + abs(kernel_size % 2 - 1	)
     else:
          _SCREAMING_SNAKE_CASE       :	int						    =							5
     return filename, spatial_variance, intensity_variance, kernel_size


if __name__ == "__main__":
       UpperCamelCase__ ,     UpperCamelCase__ ,     UpperCamelCase__ ,     UpperCamelCase__      =parse_args(sys.argv)
       UpperCamelCase__      =cva.imread(filename, 0)
       cva.imshow('input image', img)

       UpperCamelCase__      =img / 255
       UpperCamelCase__      =out.astype('float32')
       UpperCamelCase__      =bilateral_filter(out, spatial_variance, intensity_variance, kernel_size)
       UpperCamelCase__      =out * 255
       UpperCamelCase__      =np.uinta(out)
       cva.imshow('output image', out)
       cva.waitKey(0)
       cva.destroyAllWindows()






from __future__ import annotations

UpperCamelCase__      =[True] * 100_0001
UpperCamelCase__      =2
while i * i <= 100_0000:
       if seive[i]:
              for j in range(i * i, 100_0001, i):
                     UpperCamelCase__      =False
       i += 1






def     lowerCamelCase__			(__lowerCamelCase	):
     return seive[n]






def     lowerCamelCase__			(__lowerCamelCase	):
     return any(digit in "02468" for digit in str(__lowerCamelCase	)	)






def     lowerCamelCase__			(__lowerCamelCase = 1000000	):
     _SCREAMING_SNAKE_CASE       :	Optional[Any]						    =							[2]  # result already includes the number 2.
     for num in range(3,       limit + 1,       2	):
          if is_prime(__lowerCamelCase	) and not contains_an_even_digit(__lowerCamelCase	):
               _SCREAMING_SNAKE_CASE       :	List[Any]						    =							str(__lowerCamelCase	)
               _SCREAMING_SNAKE_CASE       :	Optional[Any]						    =							[int(str_num[j:] + str_num[:j]	) for j in range(len(__lowerCamelCase	)	)]
               if all(is_prime(__lowerCamelCase	) for i in list_nums	):
                    result.append(__lowerCamelCase	)
     return result






def     lowerCamelCase__			():
     return len(find_circular_primes()	)


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