'''simple docstring'''





import itertools






def SCREAMING_SNAKE_CASE__  (				snake_case       :				int = 1_000_000  )   ->				int:







     """simple docstring"""
     a					:							Tuple							= [1]

     for i in itertools.count(len(snake_case  )  ):
          a					:							Dict							= 0
          for j in itertools.count(1  ):
               a					:							Optional[Any]							= -1 if j % 2 == 0 else +1
               a					:							int							= (j * j * 3 - j) // 2
               if index > i:
                    break
               item += partitions[i - index] * sign
               item %= number
               index += j
               if index > i:
                    break
               item += partitions[i - index] * sign
               item %= number

          if item == 0:
               return i
          partitions.append(snake_case  )

     return 0


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      print(f'''{solution() = }''')


'''simple docstring'''





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






def SCREAMING_SNAKE_CASE__  (				snake_case       :				float  )   ->				float:







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






def SCREAMING_SNAKE_CASE__  (				snake_case       :				int  )   ->				float:







     """simple docstring"""
     a					:							List[str]							= (circles_number + 1 - sqrt(2 * circles_number  )) / (
         2 * (circles_number**2 + 1)
     )
     a					:							int							= circles_number * intersection_y

     a					:							List[Any]							= intersection_x * intersection_y / 2
     a					:							List[str]							= circle_bottom_arc_integral(
         1 / 2  ) - circle_bottom_arc_integral(snake_case  )

     return triangle_area + concave_region_area






def SCREAMING_SNAKE_CASE__  (				snake_case       :				float = 1 / 1_000  )   ->				int:







     """simple docstring"""
     a					:							str							= (1 - pi / 4) / 4

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

     return -1


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

