





"""simple docstring"""





def 					__A  (_SCREAMING_SNAKE_CASE     )   ->str:





  """simple docstring"""


  lowerCAmelCase__     :List[Any]											=				int(_SCREAMING_SNAKE_CASE     )
  if decimal in (0, 1):  # Exit cases for the recursion
    return str(_SCREAMING_SNAKE_CASE     )
  lowerCAmelCase__				,							lowerCAmelCase__     :int											=				divmod(_SCREAMING_SNAKE_CASE	,  2     )
  return binary_recursive(_SCREAMING_SNAKE_CASE     ) + str(_SCREAMING_SNAKE_CASE     )
def 					__A  (_SCREAMING_SNAKE_CASE     )   ->str:





  """simple docstring"""


  lowerCAmelCase__     :str											=				str(_SCREAMING_SNAKE_CASE     ).strip()
  if not number:
    raise ValueError('No input value was provided'     )
  lowerCAmelCase__     :Dict											=				'-' if number.startswith('-'     ) else ''
  lowerCAmelCase__     :int											=				number.lstrip('-'     )
  if not number.isnumeric():
    raise ValueError('Input value is not an integer'     )
  return F"{negative}0b{binary_recursive(int(_SCREAMING_SNAKE_CASE     )     )}"


if __name__ == "__main__":
  from doctest import testmod

  testmod()







"""simple docstring"""




from numpy import exp, pi, sqrt






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       Tuple       ,			_lowercase		:       float = 0.0       ,			_lowercase		:       float = 1.0   )					->int:






	'''simple docstring'''






	return 1 / sqrt(2 * pi * sigma**2   ) * exp(-((x - mu) ** 2) / (2 * sigma**2)   )


if __name__ == "__main__":
		import doctest

		doctest.testmod()


