

"""simple docstring"""

def       SCREAMING_SNAKE_CASE							( lowercase__ = 1_0_0_0   )			->						int:
 lowerCAmelCase__   :				Union[str, Any] 			=				-1
 lowerCAmelCase__   :				Optional[Any] 			=				0
 for a in range(1					,					n // 3   ):
  # Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
  lowerCAmelCase__   :				Union[str, Any] 			=				(n * n - 2 * a * n) // (2 * n - 2 * a)
  lowerCAmelCase__   :				Any 			=				n - a - b
  if c * c == (a * a + b * b):
   lowerCAmelCase__   :				Optional[Any] 			=				a * b * c
   if candidate >= product:
    lowerCAmelCase__   :				Dict 			=				candidate
 return product


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









"""simple docstring"""

def       SCREAMING_SNAKE_CASE							( lowercase__   )			->						float:
 return 1_0 - x * x



def       SCREAMING_SNAKE_CASE							( lowercase__					,					lowercase__   )			->						float:
 # Bolzano theory in order to find if there is a root between a and b
 if equation(lowercase__   ) * equation(lowercase__   ) >= 0:
  raise ValueError("Wrong space!"   )

 lowerCAmelCase__   :				Union[str, Any] 			=				a
 while (b - a) >= 0.01:
  # Find middle point
  lowerCAmelCase__   :				int 			=				(a + b) / 2
  # Check if middle point is root
  if equation(lowercase__   ) == 0.0:
   break
  # Decide the side to repeat the steps
  if equation(lowercase__   ) * equation(lowercase__   ) < 0:
   lowerCAmelCase__   :				str 			=				c
  else:
   lowerCAmelCase__   :				List[str] 			=				c
 return c


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    print(bisection(-2, 5))
    print(bisection(0, 6))






