'''simple docstring'''

def  _lowerCAmelCase				(				__a      )  ->      int:
     '''simple docstring'''







     if not isinstance(__a			,      __a      ):
          raise ValueError("""double_factorial() only accepts integral values"""      )
     if n < 0:
          raise ValueError("""double_factorial() not defined for negative values"""      )
     return 1 if n <= 1 else n * double_factorial(n - 2      )


if __name__ == "__main__":
      import doctest

      doctest.testmod()




'''simple docstring'''






import qiskit
from qiskit.providers import Backend




def        snake_case_   (	lowerCAmelCase_			,  lowerCAmelCase_						)->						tuple[qiskit.QuantumCircuit, str, str]:





       '''simple docstring'''


       _UpperCAmelCase	,_UpperCAmelCase    :		Optional[Any]     	=					bin(lowerCAmelCase_						)[2:], bin(lowerCAmelCase_						)[2:]  # Remove leading '0b'

       # Ensure that both strings are of the same length
       if len(lowerCAmelCase_						) > len(lowerCAmelCase_						):
              _UpperCAmelCase    :		str     	=					y.zfill(len(lowerCAmelCase_						)						)
       else:
              _UpperCAmelCase    :		int     	=					x.zfill(len(lowerCAmelCase_						)						)

       # We need (3 * number of bits in the larger number)+1 qBits
       # The second parameter is the number of classical registers, to measure the result
       _UpperCAmelCase    :		Any     	=					qiskit.QuantumCircuit((len(lowerCAmelCase_						) * 3) + 1			,  len(lowerCAmelCase_						) + 1						)

       # We are essentially "not-ing" the bits that are 1
       # Reversed because it's easier to perform ops on more significant bits
       for i in range(len(lowerCAmelCase_						)						):
              if x[::-1][i] == "1":
                     circuit.x(lowerCAmelCase_						)
       for j in range(len(lowerCAmelCase_						)						):
              if y[::-1][j] == "1":
                     circuit.x(len(lowerCAmelCase_						) + j						)

       return circuit, x, y




def        snake_case_   (	lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_			,  )->						Dict:





       '''simple docstring'''


       circuit.ccx(lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_						)
       circuit.cx(lowerCAmelCase_			,  lowerCAmelCase_						)
       circuit.ccx(lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_						)
       circuit.cx(lowerCAmelCase_			,  lowerCAmelCase_						)
       circuit.cx(lowerCAmelCase_			,  lowerCAmelCase_						)




def        snake_case_   (	lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_ = qiskit.Aer.get_backend("""aer_simulator"""						)			,  )->						int:





       '''simple docstring'''


       if vala < 0 or vala < 0:
              raise ValueError("""Both Integers must be positive!"""						)

       # Store the Integers
       _UpperCAmelCase	,_UpperCAmelCase	,_UpperCAmelCase    :		Union[str, Any]     	=					store_two_classics(lowerCAmelCase_			,  lowerCAmelCase_						)
       for i in range(len(lowerCAmelCase_						)						):
              full_adder(lowerCAmelCase_			,  lowerCAmelCase_			,  len(lowerCAmelCase_						) + i			,  len(lowerCAmelCase_						) + len(lowerCAmelCase_						) + i			,  len(lowerCAmelCase_						) + len(lowerCAmelCase_						) + i + 1						)
              circuit.barrier()  # Optional, just for aesthetics

       # Measure the resultant qBits
       for i in range(len(lowerCAmelCase_						) + 1						):
              circuit.measure([(len(lowerCAmelCase_						) * 2) + i]			,  [i]						)

       _UpperCAmelCase    :		Optional[int]     	=					qiskit.execute(lowerCAmelCase_			,  lowerCAmelCase_			,  shots=1						).result()

       # The result is in binary. Convert it back to int
       return int(list(res.get_counts()						)[0]			,  2						)


if __name__ == "__main__":
   import doctest

   doctest.testmod()



