
'''simple docstring'''





def snake_case_     (					lowercase__		):
  return credit_card_number.startswith(("34", "35", "37", "4", "5", "6")		)







def snake_case_     (					lowercase__		):
  UpperCAmelCase__      :					Optional[Any]				       =							credit_card_number
  UpperCAmelCase__      :					Any				       =							0
  UpperCAmelCase__      :					Optional[int]				       =							len(lowercase__		) - 2
  for i in range(lowercase__   ,       -1   ,       -2		):
    #  double the value of every second digit
    UpperCAmelCase__      :					Optional[int]				       =							int(cc_number[i]		)
    digit *= 2
    # If doubling of a number results in a two digit number
    # i.e greater than 9(e.g., 6 × 2 = 12),
    # then add the digits of the product (e.g., 12: 1 + 2 = 3, 15: 1 + 5 = 6),
    # to get a single digit number.
    if digit > 9:
      digit %= 1_0
      digit += 1
    UpperCAmelCase__      :					List[str]				       =							cc_number[:i] + str(lowercase__		) + cc_number[i + 1 :]
    total += digit

  # Sum up the remaining digits
  for i in range(len(lowercase__		) - 1   ,       -1   ,       -2		):
    total += int(cc_number[i]		)

  return total % 1_0 == 0







def snake_case_     (					lowercase__		):
  UpperCAmelCase__      :					List[Any]				       =							F"""{credit_card_number} is an invalid credit card number because"""
  if not credit_card_number.isdigit():
    print(F"""{error_message} it has nonnumerical characters."""		)
    return False

  if not 1_3 <= len(lowercase__		) <= 1_6:
    print(F"""{error_message} of its length."""		)
    return False

  if not validate_initial_digits(lowercase__		):
    print(F"""{error_message} of its first two digits."""		)
    return False

  if not luhn_validation(lowercase__		):
    print(F"""{error_message} it fails the Luhn check."""		)
    return False

  print(F"""{credit_card_number} is a valid credit card number."""		)
  return True


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      validate_credit_card_number("""4111111111111111""")
      validate_credit_card_number("""32323""")





'''simple docstring'''





import math

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







def snake_case_     (					lowercase__ = 3		):
  if isinstance(lowercase__   ,       lowercase__		):
    raise TypeError("number of qubits must be a integer."		)
  if number_of_qubits <= 0:
    raise ValueError("number of qubits must be > 0."		)
  if math.floor(lowercase__		) != number_of_qubits:
    raise ValueError("number of qubits must be exact integer."		)
  if number_of_qubits > 1_0:
    raise ValueError("number of qubits too large to simulate(>10)."		)

  UpperCAmelCase__      :					Optional[int]				       =							QuantumRegister(lowercase__   ,       "qr"		)
  UpperCAmelCase__      :					List[Any]				       =							ClassicalRegister(lowercase__   ,       "cr"		)

  UpperCAmelCase__      :					List[str]				       =							QuantumCircuit(lowercase__   ,       lowercase__		)

  UpperCAmelCase__      :					Union[str, Any]				       =							number_of_qubits

  for i in range(lowercase__		):
    quantum_circuit.h(number_of_qubits - i - 1		)
    counter -= 1
    for j in range(lowercase__		):
      quantum_circuit.cp(np.pi / 2 ** (counter - j)   ,       lowercase__   ,       lowercase__		)

  for k in range(number_of_qubits // 2		):
    quantum_circuit.swap(lowercase__   ,       number_of_qubits - k - 1		)

  # measure all the qubits
  quantum_circuit.measure(lowercase__   ,       lowercase__		)
  # simulate with 10000 shots
  UpperCAmelCase__      :					Union[str, Any]				       =							Aer.get_backend("qasm_simulator"		)
  UpperCAmelCase__      :					Optional[int]				       =							execute(lowercase__   ,       lowercase__   ,       shots=1_0_0_0_0		)

  return job.result().get_counts(lowercase__		)


if __name__ == "__main__":
      print(
          F'Total count for quantum fourier transform state is: \
    {quantum_fourier_transform(3)}'
      )



