def    a__       (						__UpperCamelCase = 1_0_0_0 ):
      SCREAMING_SNAKE_CASE_      =     -1
      SCREAMING_SNAKE_CASE_      =     0
      for a in range(1   ,					n // 3 ):
            # Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
            SCREAMING_SNAKE_CASE_      =     (n * n - 2 * a * n) // (2 * n - 2 * a)
            SCREAMING_SNAKE_CASE_      =     n - a - b
            if c * c == (a * a + b * b):
                  SCREAMING_SNAKE_CASE_      =     a * b * c
                  if candidate >= product:
                        SCREAMING_SNAKE_CASE_      =     candidate
      return product


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



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    a__       (						__UpperCamelCase   ,					__UpperCamelCase ):
      SCREAMING_SNAKE_CASE_      =     k_size // 2
      SCREAMING_SNAKE_CASE_   ,       SCREAMING_SNAKE_CASE_      =     mgrid[0 - center : k_size - center, 0 - center : k_size - center]
      SCREAMING_SNAKE_CASE_      =     1 / (2 * pi * sigma) * exp(-(square(__UpperCamelCase ) + square(__UpperCamelCase )) / (2 * square(__UpperCamelCase )) )
      return g


def    a__       (						__UpperCamelCase   ,					__UpperCamelCase   ,					__UpperCamelCase ):
      SCREAMING_SNAKE_CASE_   ,       SCREAMING_SNAKE_CASE_      =     image.shape[0], image.shape[1]
      # dst image height and width
      SCREAMING_SNAKE_CASE_      =     height - k_size + 1
      SCREAMING_SNAKE_CASE_      =     width - k_size + 1

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

      #  turn the kernel into shape(k*k, 1)
      SCREAMING_SNAKE_CASE_      =     gen_gaussian_kernel(__UpperCamelCase   ,					__UpperCamelCase )
      SCREAMING_SNAKE_CASE_      =     ravel(__UpperCamelCase )

      # reshape and get the dst image
      SCREAMING_SNAKE_CASE_      =     dot(__UpperCamelCase   ,					__UpperCamelCase ).reshape(__UpperCamelCase   ,					__UpperCamelCase ).astype(__UpperCamelCase )

      return dst


if __name__ == "__main__":
      # read original image
      A   :     Tuple       =				imread(r"../image_data/lena.jpg")
      # turn image in gray scale value
      A   :     Optional[int]       =				cvtColor(img, COLOR_BGR2GRAY)

      # get values with two different mask size
      A   :     Tuple       =				gaussian_filter(gray, 3, sigma=1)
      A   :     Optional[int]       =				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()


