code: 
  
  
  """simple docstring"""
  
  
  
  
  
  
  
  import math
  
  import qiskit
  from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute
  def _A		(		lowercase = 1 ,					lowercase = 1	):
  
  
  
  
  
  
  
      """simple docstring"""
      if isinstance(lowercase ,					lowercase	) or isinstance(lowercase ,					lowercase	):
          raise TypeError('''inputs must be integers.'''	)
      if (bit_a < 0) or (bit_a < 0):
          raise ValueError('''inputs must be positive.'''	)
      if (math.floor(lowercase	) != bit_a) or (math.floor(lowercase	) != 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
      a					=QuantumRegister(2 ,					'''qr'''	)
      a					=ClassicalRegister(2 ,					'''cr'''	)
  
      a					=QuantumCircuit(lowercase ,					lowercase	)
  
      # entanglement the qubits
      quantum_circuit.h(1	)
      quantum_circuit.cx(1 ,					0	)
  
      # send the information
      a					=str(lowercase	) + str(lowercase	)
  
      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(lowercase ,					lowercase	)
  
      a					=Aer.get_backend('''aer_simulator'''	)
      a					=execute(lowercase ,					lowercase ,					shots=10_00	)
  
      return job.result().get_counts(lowercase	)
  
  
  if __name__ == "__main__":
         print(F'Counts for classical state send: {superdense_coding(1,1)}')
style_context: 
  
  
  """simple docstring"""
  
  
  
  
  
  
  
  from math import gcd
  def _A		(		lowercase = 1_20_00	):
  
  
  
  
  
  
  
      """simple docstring"""
      a					=0
      for d in range(max_d + 1	):
          for n in range(d // 3 + 1 ,					(d + 1) // 2	):
              if gcd(lowercase ,					lowercase	) == 1:
                  fractions_number += 1
      return fractions_number
  
  
  if __name__ == "__main__":
         print(F'{solution() = }')