
'''simple docstring'''







def  snake_case_		(    __SCREAMING_SNAKE_CASE :			int				,				__SCREAMING_SNAKE_CASE :			int							):



						"""simple docstring"""





						lowercase_     :					Optional[Any]													=	1  # To kept the Calculated Value
						# Since C(n, k) = C(n, n-k)
						if k > (n - k):
												lowercase_     :					Any													=	n - k
						# Calculate C(n,k)
						for i in range(__SCREAMING_SNAKE_CASE							):
												result *= n - i
												result //= i + 1
						return result
def  snake_case_		(    __SCREAMING_SNAKE_CASE :			int							):



						"""simple docstring"""





						return binomial_coefficient(2 * node_count				,				__SCREAMING_SNAKE_CASE							) // (node_count + 1)
def  snake_case_		(    __SCREAMING_SNAKE_CASE :			int							):



						"""simple docstring"""





						if n < 0:
												raise ValueError('''factorial() not defined for negative values'''							)
						lowercase_     :					List[str]													=	1
						for i in range(1				,				n + 1							):
												result *= i
						return result
def  snake_case_		(    __SCREAMING_SNAKE_CASE :			int							):



						"""simple docstring"""





						return catalan_number(__SCREAMING_SNAKE_CASE							) * factorial(__SCREAMING_SNAKE_CASE							)


if __name__ == "__main__":
							_lowercase			:  List[Any]   							=	int(input("Enter the number of nodes: ").strip() or 0)
							if node_count <= 0:
														raise ValueError("We need some nodes to work with.")
							print(
							    f"""Given {node_count} nodes, there are {binary_tree_count(node_count)} """
							    f"""binary trees and {catalan_number(node_count)} binary search trees."""
							)





'''simple docstring'''







import qiskit
def  snake_case_		(    __SCREAMING_SNAKE_CASE :			int				,				__SCREAMING_SNAKE_CASE :			int							):



						"""simple docstring"""





						lowercase_     :					List[Any]													=	qiskit.Aer.get_backend('''aer_simulator'''							)

						# Create a Quantum Circuit acting on the q register
						lowercase_     :					Dict													=	qiskit.QuantumCircuit(__SCREAMING_SNAKE_CASE				,				__SCREAMING_SNAKE_CASE							)

						# Map the quantum measurement to the classical bits
						circuit.measure([0]				,				[0]							)

						# Execute the circuit on the simulator
						lowercase_     :					Union[str, Any]													=	qiskit.execute(__SCREAMING_SNAKE_CASE				,				__SCREAMING_SNAKE_CASE				,				shots=1000							)

						# Return the histogram data of the results of the experiment.
						return job.result().get_counts(__SCREAMING_SNAKE_CASE							)


if __name__ == "__main__":
							print(f"""Total count for various states are: {single_qubit_measure(1, 1)}""")



