


from functools import lru_cache






@lru_cache
def   __lowerCamelCase	(       lowerCamelCase__		:	int			):





			'''simple docstring'''




			if not isinstance(lowerCamelCase__     ,       lowerCamelCase__			):
						raise TypeError("""k must be an integer."""			)
			if k < 0:
						raise ValueError("""k integer must be greater or equal to zero."""			)
			if k == 0:
						return 0
			elif k == 1:
						return 1
			else:
						return fibonacci(k - 1			) + fibonacci(k - 2			)






def   __lowerCamelCase	(       lowerCamelCase__		:	list     ,       lowerCamelCase__		:	int			):





			'''simple docstring'''




			lowerCamelCase								=     len(lowerCamelCase__			)
			# Find m such that F_m >= n where F_i is the i_th fibonacci number.
			lowerCamelCase								=     0
			while True:
						if fibonacci(lowerCamelCase__			) >= len_list:
									lowerCamelCase								=     i
									break
						i += 1
			lowerCamelCase								=     0
			while fibb_k > 0:
						lowerCamelCase								=     min(
						    offset + fibonacci(fibb_k - 1			)     ,       len_list - 1			)  # Prevent out of range
						lowerCamelCase								=     arr[index_k]
						if item_k_1 == val:
									return index_k
						elif val < item_k_1:
									fibb_k -= 1
						elif val > item_k_1:
									offset += fibonacci(fibb_k - 1			)
									fibb_k -= 2
			else:
						return -1


if __name__ == "__main__":
		import doctest

		doctest.testmod()





import math

import qiskit
from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute






def   __lowerCamelCase	(       lowerCamelCase__		:	int = 1     ,       lowerCamelCase__		:	int = 1			):





			'''simple docstring'''




			if isinstance(lowerCamelCase__     ,       lowerCamelCase__			) or isinstance(lowerCamelCase__     ,       lowerCamelCase__			):
						raise TypeError("""inputs must be integers."""			)
			if (bit_a < 0) or (bit_a < 0):
						raise ValueError("""inputs must be positive."""			)
			if (math.floor(lowerCamelCase__			) != bit_a) or (math.floor(lowerCamelCase__			) != bit_a):
						raise ValueError("""inputs must be exact integers."""			)
			if (bit_a > 1) or (bit_a > 1):
						raise ValueError("""inputs must be less or equal to 1."""			)

			# build registers
			lowerCamelCase								=     QuantumRegister(2     ,       """qr"""			)
			lowerCamelCase								=     ClassicalRegister(2     ,       """cr"""			)

			lowerCamelCase								=     QuantumCircuit(lowerCamelCase__     ,       lowerCamelCase__			)

			# entanglement the qubits
			quantum_circuit.h(1			)
			quantum_circuit.cx(1     ,       0			)

			# send the information
			lowerCamelCase								=     str(lowerCamelCase__			) + str(lowerCamelCase__			)

			if c_information == "11":
						quantum_circuit.x(1			)
						quantum_circuit.z(1			)
			elif c_information == "10":
						quantum_circuit.z(1			)
			elif c_information == "01":
						quantum_circuit.x(1			)
			else:
						quantum_circuit.i(1			)

			# unentangled the circuit
			quantum_circuit.cx(1     ,       0			)
			quantum_circuit.h(1			)

			# measure the circuit
			quantum_circuit.measure(lowerCamelCase__     ,       lowerCamelCase__			)

			lowerCamelCase								=     Aer.get_backend("""aer_simulator"""			)
			lowerCamelCase								=     execute(lowerCamelCase__     ,       lowerCamelCase__     ,       shots=1000			)

			return job.result().get_counts(lowerCamelCase__			)


if __name__ == "__main__":
		print(f"""Counts for classical state send: {superdense_coding(1,1)}""")

