



'''simple docstring'''




def        lowerCAmelCase_     (			_lowerCamelCase:     int = 10_00      ):
		__SCREAMING_SNAKE_CASE :	List[Any]					 =	-1
		__SCREAMING_SNAKE_CASE :	List[str]					 =	0
		for a in range(1 ,   n // 3      ):
				# Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
				__SCREAMING_SNAKE_CASE :	Optional[Any]					 =	(n * n - 2 * a * n) // (2 * n - 2 * a)
				__SCREAMING_SNAKE_CASE :	str					 =	n - a - b
				if c * c == (a * a + b * b):
						__SCREAMING_SNAKE_CASE :	List[str]					 =	a * b * c
						if candidate >= product:
								__SCREAMING_SNAKE_CASE :	Union[str, Any]					 =	candidate
		return product


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




'''simple docstring'''




import qiskit


def        lowerCAmelCase_     (			_lowerCamelCase:     int = 2      ):
		__SCREAMING_SNAKE_CASE :	Dict					 =	qubits

		# Using Aer's simulator
		__SCREAMING_SNAKE_CASE :	Optional[Any]					 =	qiskit.Aer.get_backend("""aer_simulator"""      )

		# Creating a Quantum Circuit acting on the q register
		__SCREAMING_SNAKE_CASE :	str					 =	qiskit.QuantumCircuit(_lowerCamelCase ,   _lowerCamelCase      )

		# Adding a H gate on qubit 0 (now q0 in superposition)
		circuit.h(0      )

		for i in range(1 ,   _lowerCamelCase      ):
				# Adding CX (CNOT) gate
				circuit.cx(i - 1 ,   _lowerCamelCase      )

		# Mapping the quantum measurement to the classical bits
		circuit.measure(list(range(_lowerCamelCase      )      ) ,   list(range(_lowerCamelCase      )      )      )

		# Now measuring any one qubit would affect other qubits to collapse
		# their super position and have same state as the measured one.

		# Executing the circuit on the simulator
		__SCREAMING_SNAKE_CASE :	str					 =	qiskit.execute(_lowerCamelCase ,   _lowerCamelCase ,   shots=10_00      )

		return job.result().get_counts(_lowerCamelCase      )


if __name__ == "__main__":
						print(f"Total count for various states are: {quantum_entanglement(3)}")