




def       UpperCAmelCase       (     _snake_case = 100							):
							lowerCAmelCase   =		(n * (n + 1) // 2) ** 2
							lowerCAmelCase   =		n * (n + 1) * (2 * n + 1) // 6
							return sum_cubes - sum_squares


if __name__ == "__main__":
		print(F'''{solution() = }''')









import math

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



def       UpperCAmelCase       (     _snake_case = 3							):
							if isinstance(_snake_case						, _snake_case							):
														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(_snake_case							) != 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).'''							)

							lowerCAmelCase   =		QuantumRegister(_snake_case						, '''qr'''							)
							lowerCAmelCase   =		ClassicalRegister(_snake_case						, '''cr'''							)

							lowerCAmelCase   =		QuantumCircuit(_snake_case						, _snake_case							)

							lowerCAmelCase   =		number_of_qubits

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

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

							# measure all the qubits
							quantum_circuit.measure(_snake_case						, _snake_case							)
							# simulate with 10000 shots
							lowerCAmelCase   =		Aer.get_backend('''qasm_simulator'''							)
							lowerCAmelCase   =		execute(_snake_case						, _snake_case						, shots=10000							)

							return job.result().get_counts(_snake_case							)


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



