





"""simple docstring"""






import math

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

def       __A (     a_  :int = 3)						->						qiskit.result.counts.Counts:
    if isinstance(a_				,    a_):
        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(a_) != number_of_qubits:
        raise ValueError('''number of qubits must be exact integer.''')
    if number_of_qubits > 10:
        raise ValueError('''number of qubits too large to simulate(>10).''')

    __a	:  Optional[int]         =					QuantumRegister(a_				,    '''qr''')
    __a	:  int         =					ClassicalRegister(a_				,    '''cr''')

    __a	:  Optional[Any]         =					QuantumCircuit(a_				,    a_)

    __a	:  Dict         =					number_of_qubits

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

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

    # measure all the qubits
    quantum_circuit.measure(a_				,    a_)
    # simulate with 10000 shots
    __a	:  List[str]         =					Aer.get_backend('''qasm_simulator''')
    __a	:  int         =					execute(a_				,    a_				,    shots=1_00_00)

    return job.result().get_counts(a_)


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






"""simple docstring"""






def       __A (     a_  :int = 1_00_00_00)						->						int:
				__a	:  Tuple         =					[i - 1 for i in range(limit + 1)]

				for i in range(2				,    limit + 1):
								if phi[i] == i - 1:
												for j in range(2 * i				,    limit + 1				,    a_):
																phi[j] -= phi[j] // i

				return sum(phi[2 : limit + 1])


if __name__ == "__main__":
		print(solution())