code: 
  
  
  UpperCAmelCase      :						int    =		{
      "0": 1,
      "1": 1,
      "2": 2,
      "3": 6,
      "4": 24,
      "5": 1_20,
      "6": 7_20,
      "7": 50_40,
      "8": 4_03_20,
      "9": 36_28_80,
  }
  
  UpperCAmelCase      :						Tuple    =		{1_45: 1_45}
  
  UpperCAmelCase      :						Tuple    =		{
      1_45: 0,
      1_69: 3,
      3_63_01: 3,
      14_54: 3,
      8_71: 2,
      4_53_61: 2,
      8_72: 2,
  }
  
  
  
  
  
  
  def   __lowerCamelCase	(       lowerCamelCase__		:	int			):
  
  
  
  
  
  			'''simple docstring'''
  
  
  
  
  			if n in CACHE_SUM_DIGIT_FACTORIALS:
  						return CACHE_SUM_DIGIT_FACTORIALS[n]
  			lowerCamelCase								=     sum(DIGIT_FACTORIALS[let] for let in str(lowerCamelCase__			)			)
  			lowerCamelCase								=     ret
  			return ret
  
  
  
  
  
  
  def   __lowerCamelCase	(       lowerCamelCase__		:	int     ,       lowerCamelCase__		:	set | None = None			):
  
  
  
  
  
  			'''simple docstring'''
  
  
  
  
  			lowerCamelCase								=     previous or set()
  			if n in CHAIN_LENGTH_CACHE:
  						return CHAIN_LENGTH_CACHE[n]
  			lowerCamelCase								=     sum_digit_factorials(lowerCamelCase__			)
  			if next_number in previous:
  						lowerCamelCase								=     0
  						return 0
  			else:
  						previous.add(lowerCamelCase__			)
  						lowerCamelCase								=     1 + chain_length(lowerCamelCase__     ,       lowerCamelCase__			)
  						lowerCamelCase								=     ret
  						return ret
  
  
  
  
  
  
  def   __lowerCamelCase	(       lowerCamelCase__		:	int = 60     ,       lowerCamelCase__		:	int = 1000000			):
  
  
  
  
  
  			'''simple docstring'''
  
  
  
  
  			return sum(1 for i in range(1     ,       lowerCamelCase__			) if chain_length(lowerCamelCase__			) == num_terms			)
  
  
  if __name__ == "__main__":
  		print(f"""{solution() = }""")
  
  
style_context: 
  
  
  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)}""")
  
  