

import math

import numpy as np
import qiskit
from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute
def 							__SCREAMING_SNAKE_CASE     (   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[Any]		    =			QuantumRegister(a__			,"""qr"""       )
	__A :			Optional[int]		    =			ClassicalRegister(a__			,"""cr"""       )

	__A :			Any		    =			QuantumCircuit(a__			,a__       )

	__A :			Optional[Any]		    =			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 :			Union[str, Any]		    =			Aer.get_backend("""qasm_simulator"""       )
	__A :			Dict		    =			execute(a__			,a__			,shots=10000       )

	return job.result().get_counts(a__       )


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








from math import sqrt
def 							__SCREAMING_SNAKE_CASE     (   a__    :   int = 1000000       )					->				int:
	__A :			int		    =			0
	__A :			int		    =			0
	__A :			int

	while num_cuboids <= limit:
		max_cuboid_size += 1
		for sum_shortest_sides in range(2			,2 * max_cuboid_size + 1       ):
			if sqrt(sum_shortest_sides**2 + max_cuboid_size**2       ).is_integer():
				num_cuboids += (
				    min(a__			,sum_shortest_sides // 2       )
				    - max(1			,sum_shortest_sides - max_cuboid_size       )
				    + 1
				)

	return max_cuboid_size


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





