code: 
  
  
  
  
  
  
  from itertools import count
  from math import asin, pi, sqrt
  
  
  
  
  
  
  
  def 			lowercase__  (				A_		)  ->							float:
  
  
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
         return (
             (1 - 2 * point) * sqrt(point - point**2		) + 2 * point + asin(sqrt(1 - point		)		)
         ) / 4
  
  
  
  
  
  
  
  def 			lowercase__  (				A_		)  ->							float:
  
  
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
         __UpperCAmelCase    							=(circles_number + 1 - sqrt(2 * circles_number		)) / (
             2 * (circles_number**2 + 1)
         )
         __UpperCAmelCase    							=circles_number * intersection_y
  
         __UpperCAmelCase    							=intersection_x * intersection_y / 2
         __UpperCAmelCase    							=circle_bottom_arc_integral(
             1 / 2		) - circle_bottom_arc_integral(A_		)
  
         return triangle_area + concave_region_area
  
  
  
  
  
  
  
  def 			lowercase__  (				A_ = 1 / 1000		)  ->							int:
  
  
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
         __UpperCAmelCase    							=(1 - pi / 4) / 4
  
         for n in count(1		):
                if concave_triangle_area(A_		) / l_section_area < fraction:
                       return n
  
         return -1
  
  
  if __name__ == "__main__":
     print(F"""{solution() = }""")
  
  
  
  
  
style_context: 
  
  
  
  
  
  
  from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
  from numpy import divide, inta, multiply, ravel, sort, zeros_like
  
  
  
  
  
  
  
  def 			lowercase__  (				A_:	int     ,			A_:	Any=3		)  ->							Dict:
  
  
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
         __UpperCAmelCase    							=int(mask / 2		)
         # copy image size
         __UpperCAmelCase    							=zeros_like(A_		)
         for i in range(A_     ,			gray_img.shape[0] - bd		):
                for j in range(A_     ,			gray_img.shape[1] - bd		):
                       # get mask according with mask
                       __UpperCAmelCase    							=ravel(gray_img[i - bd : i + bd + 1, j - bd : j + bd + 1]		)
                       # calculate mask median
                       __UpperCAmelCase    							=sort(A_		)[inta(divide((multiply(A_     ,			A_		))     ,			2		) + 1		)]
                       __UpperCAmelCase    							=median
         return median_img
  
  
  if __name__ == "__main__":
     # read original image
     __A  							=  imread("../image_data/lena.jpg")
     # turn image in gray scale value
     __A  							=  cvtColor(img, COLOR_BGR2GRAY)
  
     # get values with two different mask size
     __A  							=  median_filter(gray, 3)
     __A  							=  median_filter(gray, 5)
  
     # show result images
     imshow("median filter with 3x3 mask", medianaxa)
     imshow("median filter with 5x5 mask", medianaxa)
     waitKey(0)
  
  
  
  
  