





'''simple docstring'''


import math




def       A							(      _UpperCAmelCase   :				int					)  ->				list:


  '''simple docstring'''




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




def       A							(      _UpperCAmelCase   :				int					)  ->				int:


  '''simple docstring'''




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




def       A							(      _UpperCAmelCase   :				int					)  ->				int:


  '''simple docstring'''




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




def       A							(      _UpperCAmelCase   :				int					)  ->				int:


  '''simple docstring'''




  __lowerCAmelCase		:    Tuple			     =  n
  for x in set(prime_factors(_UpperCAmelCase					)					):
    s *= (x - 1) / x
  return int(_UpperCAmelCase					)


if __name__ == "__main__":
    import doctest

    doctest.testmod()












'''simple docstring'''


import numpy as np
import qiskit
from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute




def       A							(      _UpperCAmelCase   :				float = np.pi / 2						,_UpperCAmelCase   :				float = np.pi / 2						,_UpperCAmelCase   :				float = np.pi / 2					)  ->				qiskit.result.counts.Counts:


  '''simple docstring'''




  __lowerCAmelCase		:    Optional[int]			     =  QuantumRegister(3						,'qr'					)  # Define the number of quantum bits
  __lowerCAmelCase		:    Optional[int]			     =  ClassicalRegister(1						,'cr'					)  # Define the number of classical bits

  __lowerCAmelCase		:    List[Any]			     =  QuantumCircuit(_UpperCAmelCase						,_UpperCAmelCase					)  # Define the quantum circuit.

  # Build the circuit
  quantum_circuit.u(_UpperCAmelCase						,_UpperCAmelCase						,_UpperCAmelCase						,0					)  # Quantum State to teleport
  quantum_circuit.h(1					)  # add hadamard gate
  quantum_circuit.cx(
      1						,2					)  # add control gate with qubit 1 as control and 2 as target.
  quantum_circuit.cx(0						,1					)
  quantum_circuit.h(0					)
  quantum_circuit.cz(0						,2					)  # add control z gate.
  quantum_circuit.cx(1						,2					)

  quantum_circuit.measure([2]						,[0]					)  # measure the qubit.

  # Simulate the circuit using qasm simulator
  __lowerCAmelCase		:    List[str]			     =  Aer.get_backend('aer_simulator'					)
  __lowerCAmelCase		:    Optional[Any]			     =  execute(_UpperCAmelCase						,_UpperCAmelCase						,shots=1_0_0_0					)

  return job.result().get_counts(_UpperCAmelCase					)


if __name__ == "__main__":
    print(
        "Total count for teleported state is: "
        F'''{quantum_teleportation(np.pi/2, np.pi/2, np.pi/2)}'''
    )





