

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




def       UpperCAmelCase__    (      _A				:			float							):





  '''simple docstring'''







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




def       UpperCAmelCase__    (      _A				:			int							):





  '''simple docstring'''







  a__  =(circles_number + 1 - sqrt(2 * circles_number							)) / (
      2 * (circles_number**2 + 1)
  )
  a__  =circles_number * intersection_y

  a__  =intersection_x * intersection_y / 2
  a__  =circle_bottom_arc_integral(
      1 / 2							) - circle_bottom_arc_integral(_A							)

  return triangle_area + concave_region_area




def       UpperCAmelCase__    (      _A				:			float = 1 / 10_00							):





  '''simple docstring'''







  a__  =(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() = }""")



import os
import unittest

import pytest
from parameterized import parameterized

from transformers.testing_utils import require_torch, require_torch_gpu, slow, torch_device


# skipping in unittest tests

lowerCamelCase									= [(1,)]




def       UpperCAmelCase__    (      ):





  '''simple docstring'''







  a__  =bool(os.getenv('''RUN_SLOW'''     ,				0							)							)
  if run_slow:
    assert True
  else:
    assert False, "should have been skipped"




def       UpperCAmelCase__    (      ):





  '''simple docstring'''







  a__  =bool(os.getenv('''RUN_SLOW'''     ,				0							)							)
  if run_slow and torch_device == "cuda":
    assert True
  else:
    assert False, "should have been skipped"







@require_torch
class 						__magic_name__      (							unittest.TestCase							):

   '''simple docstring'''




   @slow
   @require_torch_gpu
   def 			_UpperCAmelCase			(    self	)							->   Union[str, Any]:






     """simple docstring"""






     check_slow_torch_cuda()



   @require_torch_gpu
   @slow
   def 			_UpperCAmelCase			(    self	)							->   List[str]:






     """simple docstring"""






     check_slow_torch_cuda()



   @parameterized.expand(lowercase_	)
   @slow
   def 			_UpperCAmelCase			(    self,   lowercase_=None	)							->   Tuple:






     """simple docstring"""






     check_slow()





@slow
@require_torch_gpu
def       UpperCAmelCase__    (      ):





  '''simple docstring'''







  check_slow_torch_cuda()




@require_torch_gpu
@slow
def       UpperCAmelCase__    (      ):





  '''simple docstring'''







  check_slow_torch_cuda()




@slow
@pytest.mark.parametrize('''param'''     ,				[1]							)
def       UpperCAmelCase__    (      _A				:			str							):





  '''simple docstring'''







  check_slow()




@pytest.mark.parametrize('''param'''     ,				[1]							)
@slow
def       UpperCAmelCase__    (      _A				:			Tuple							):





  '''simple docstring'''







  check_slow()
