'''simple docstring'''
from itertools import count
from math import asin, pi, sqrt







def 				__UpperCamelCase (					__UpperCAmelCase  :					float			)							->	float:
  return (
      (1 - 2 * point) * sqrt(point - point**2			) + 2 * point + asin(sqrt(1 - point			)			)
  ) / 4







def 				__UpperCamelCase (					__UpperCAmelCase  :					int			)							->	float:
  lowercase				:							Dict									=   (circles_number + 1 - sqrt(2 * circles_number			)) / (
      2 * (circles_number**2 + 1)
  )
  lowercase				:							Optional[int]									=   circles_number * intersection_y

  lowercase				:							Dict									=   intersection_x * intersection_y / 2
  lowercase				:							Optional[Any]									=   circle_bottom_arc_integral(
      1 / 2			) - circle_bottom_arc_integral(__UpperCAmelCase			)

  return triangle_area + concave_region_area







def 				__UpperCamelCase (					__UpperCAmelCase  :					float = 1 / 1_000			)							->	int:
  lowercase				:							Tuple									=   (1 - pi / 4) / 4

  for n in count(1			):
    if concave_triangle_area(__UpperCAmelCase			) / l_section_area < fraction:
      return n

  return -1


if __name__ == "__main__":
 print(f"""{solution() = }""")
'''simple docstring'''
import numpy as np
from PIL import Image







def 				__UpperCamelCase (					__UpperCAmelCase  :					np.array			)							->	np.array:
  lowercase				,      lowercase				,      lowercase				:							Dict									=   rgb[:, :, 0], rgb[:, :, 1], rgb[:, :, 2]
  return 0.2989 * r + 0.5870 * g + 0.1140 * b







def 				__UpperCamelCase (					__UpperCAmelCase  :					np.array			)							->	np.array:
  return (gray > 127) & (gray <= 255)







def 				__UpperCamelCase (					__UpperCAmelCase  :					np.array ,   __UpperCAmelCase  :					np.array			)							->	np.array:
  lowercase				:							str									=   np.zeros_like(__UpperCAmelCase			)
  lowercase				:							Tuple									=   np.zeros(
      (image.shape[0] + kernel.shape[0] - 1, image.shape[1] + kernel.shape[1] - 1)			)

  # Copy image to padded image
  lowercase				:							int									=   image

  # Iterate over image & apply kernel
  for x in range(image.shape[1]			):
    for y in range(image.shape[0]			):
      lowercase				:							str									=   (
          kernel * image_padded[y : y + kernel.shape[0], x : x + kernel.shape[1]]
      ).sum()
      lowercase				:							Tuple									=   int(summation == 5			)
  return output


# kernel to be applied
_A		:      Union[str, Any]						   =np.array([[0, 1, 0], [1, 1, 1], [0, 1, 0]])

if __name__ == "__main__":
 # read original image
 _A		:      Optional[int]						   =np.array(Image.open(r'''..\image_data\lena.jpg'''))
 # Apply erosion operation to a binary image
 _A		:      Optional[int]						   =erosion(grayabinary(rgbagray(image)), structuring_element)
 # Save the output image
 _A		:      int						   =Image.fromarray(output).convert('''RGB''')
 pil_img.save('''result_erosion.png''')