





"""simple docstring"""




def 	a_    (							_lowercase       ):
						if not isinstance(_lowercase	,						_lowercase       ):
												raise TypeError('''Input value must be an \'int\' type'''       )

						_UpperCamelCase      : Optional[Any]         =   0
						while number:
												position += 1
												number >>= 1

						return position


if __name__ == "__main__":
						import doctest

						doctest.testmod()










"""simple docstring"""




def 	a_    (							_lowercase	,						_lowercase       ):
						if discount_rate < 0:
												raise ValueError('''Discount rate cannot be negative'''       )
						if not cash_flows:
												raise ValueError('''Cash flows list cannot be empty'''       )
						_UpperCamelCase      : Optional[int]         =   sum(
						    cash_flow / ((1 + discount_rate) ** i) for i, cash_flow in enumerate(_lowercase       )       )
						return round(_lowercase	,						ndigits=2       )


if __name__ == "__main__":
						import doctest

						doctest.testmod()



