




from itertools import count
from math import asin, pi, sqrt



def   lowerCAmelCase						(						_lowerCAmelCase							:				float		):




 """simple docstring"""







 return (
     (1 - 2 * point) * sqrt(point - point**2		) + 2 * point + asin(sqrt(1 - point		)		)
 ) / 4



def   lowerCAmelCase						(						_lowerCAmelCase							:				int		):




 """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(_lowerCAmelCase		)

 return triangle_area + concave_region_area



def   lowerCAmelCase						(						_lowerCAmelCase							:				float = 1 / 1000		):




 """simple docstring"""







 UpperCAmelCase__								=  (1 - pi / 4) / 4

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

 return -1


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











from collections import defaultdict



def   lowerCAmelCase						(						_lowerCAmelCase							:				int = 5		):




 """simple docstring"""







 UpperCAmelCase__								=  defaultdict(_lowerCAmelCase		)
 UpperCAmelCase__								=  0

 while True:
  UpperCAmelCase__								=  get_digits(_lowerCAmelCase		)
  freqs[digits].append(_lowerCAmelCase		)

  if len(freqs[digits]		) == max_base:
   UpperCAmelCase__								=  freqs[digits][0] ** 3
   return base

  num += 1



def   lowerCAmelCase						(						_lowerCAmelCase							:				int		):




 """simple docstring"""







 return "".join(sorted(str(num**3		)		)		)


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





