

"""simple docstring"""
import qiskit
from qiskit.providers import Backend







def       UpperCamelCase_					(     lowerCamelCase							:					int     , lowerCamelCase							:					int   )						->     tuple[qiskit.QuantumCircuit, str, str]:



       """simple docstring"""







       __magic_name__       ,							__magic_name__			:		str        =     bin(lowerCamelCase   )[2:], bin(lowerCamelCase   )[2:]  # Remove leading '0b'

       # Ensure that both strings are of the same length
       if len(lowerCamelCase   ) > len(lowerCamelCase   ):
              __magic_name__			:		Optional[int]        =     y.zfill(len(lowerCamelCase   )   )
       else:
              __magic_name__			:		Any        =     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
       __magic_name__			:		Union[str, 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       UpperCamelCase_					(     lowerCamelCase							:					qiskit.QuantumCircuit     , lowerCamelCase							:					int     , lowerCamelCase							:					int     , lowerCamelCase							:					int     , lowerCamelCase							:					int     , )						->     Union[str, Any]:



       """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       UpperCamelCase_					(     lowerCamelCase							:					int     , lowerCamelCase							:					int     , lowerCamelCase							:					Backend = 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
       __magic_name__       ,							__magic_name__       ,							__magic_name__			:		List[str]        =     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]   )

       __magic_name__			:		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()



"""simple docstring"""
import math







def       UpperCamelCase_					(     lowerCamelCase							:					int   )						->     list:



       """simple docstring"""







       if n <= 0:
              raise ValueError('''Only positive integers have prime factors'''   )
       __magic_name__			:		Union[str, Any]        =     []
       while n % 2 == 0:
              pf.append(2   )
              __magic_name__			:		Union[str, Any]        =     int(n / 2   )
       for i in range(3     , int(math.sqrt(lowerCamelCase   )   ) + 1     , 2   ):
              while n % i == 0:
                     pf.append(lowerCamelCase   )
                     __magic_name__			:		Any        =     int(n / i   )
       if n > 2:
              pf.append(lowerCamelCase   )
       return pf







def       UpperCamelCase_					(     lowerCamelCase							:					int   )						->     int:



       """simple docstring"""







       if n <= 0:
              raise ValueError('''Only positive numbers are accepted'''   )
       __magic_name__			:		List[Any]        =     1
       __magic_name__			:		Dict        =     1
       while n % 2 == 0:
              temp += 1
              __magic_name__			:		Dict        =     int(n / 2   )
       div *= temp
       for i in range(3     , int(math.sqrt(lowerCamelCase   )   ) + 1     , 2   ):
              __magic_name__			:		Dict        =     1
              while n % i == 0:
                     temp += 1
                     __magic_name__			:		Union[str, Any]        =     int(n / i   )
              div *= temp
       if n > 1:
              div *= 2
       return div







def       UpperCamelCase_					(     lowerCamelCase							:					int   )						->     int:



       """simple docstring"""







       if n <= 0:
              raise ValueError('''Only positive numbers are accepted'''   )
       __magic_name__			:		int        =     1
       __magic_name__			:		Dict        =     1
       while n % 2 == 0:
              temp += 1
              __magic_name__			:		List[Any]        =     int(n / 2   )
       if temp > 1:
              s *= (2**temp - 1) / (2 - 1)
       for i in range(3     , int(math.sqrt(lowerCamelCase   )   ) + 1     , 2   ):
              __magic_name__			:		Any        =     1
              while n % i == 0:
                     temp += 1
                     __magic_name__			:		Any        =     int(n / i   )
              if temp > 1:
                     s *= (i**temp - 1) / (i - 1)
       return int(lowerCamelCase   )







def       UpperCamelCase_					(     lowerCamelCase							:					int   )						->     int:



       """simple docstring"""







       __magic_name__			:		str        =     n
       for x in set(prime_factors(lowerCamelCase   )   ):
              s *= (x - 1) / x
       return int(lowerCamelCase   )


if __name__ == "__main__":
 import doctest

 doctest.testmod()
