code: 
  
  
  
  """simple docstring"""
  
  
  
  
  import qiskit
  from qiskit.providers import Backend
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int		,						SCREAMING_SNAKE_CASE__			:		int       ):
  
  
  
  
  
       '''simple docstring'''
  
       _UpperCAmelCase    :			Optional[Any]              =					bin(SCREAMING_SNAKE_CASE__       )[2:], bin(SCREAMING_SNAKE_CASE__       )[2:]  # Remove leading '0b'
  
       # Ensure that both strings are of the same length
       if len(SCREAMING_SNAKE_CASE__       ) > len(SCREAMING_SNAKE_CASE__       ):
            _UpperCAmelCase    :			List[Any]              =					y.zfill(len(SCREAMING_SNAKE_CASE__       )       )
       else:
            _UpperCAmelCase    :			List[Any]              =					x.zfill(len(SCREAMING_SNAKE_CASE__       )       )
  
       # We need (3 * number of bits in the larger number)+1 qBits
       # The second parameter is the number of classical registers, to measure the result
       _UpperCAmelCase    :			Optional[int]              =					qiskit.QuantumCircuit((len(SCREAMING_SNAKE_CASE__       ) * 3) + 1		,						len(SCREAMING_SNAKE_CASE__       ) + 1       )
  
       # We are essentially "not-ing" the bits that are 1
       # Reversed because it's easier to perform ops on more significant bits
       for i in range(len(SCREAMING_SNAKE_CASE__       )       ):
            if x[::-1][i] == "1":
                 circuit.x(SCREAMING_SNAKE_CASE__       )
       for j in range(len(SCREAMING_SNAKE_CASE__       )       ):
            if y[::-1][j] == "1":
                 circuit.x(len(SCREAMING_SNAKE_CASE__       ) + j       )
  
       return circuit, x, y
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		qiskit.QuantumCircuit		,						SCREAMING_SNAKE_CASE__			:		int		,						SCREAMING_SNAKE_CASE__			:		int		,						SCREAMING_SNAKE_CASE__			:		int		,						SCREAMING_SNAKE_CASE__			:		int		,						):
  
  
  
  
  
       '''simple docstring'''
  
       circuit.ccx(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       )
       circuit.cx(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       )
       circuit.ccx(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       )
       circuit.cx(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       )
       circuit.cx(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       )
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int		,						SCREAMING_SNAKE_CASE__			:		int		,						SCREAMING_SNAKE_CASE__			:		Backend = qiskit.Aer.get_backend("aer_simulator"       )		,						):
  
  
  
  
  
       '''simple docstring'''
  
       if vala < 0 or vala < 0:
            raise ValueError("Both Integers must be positive!"       )
  
       # Store the Integers
       _UpperCAmelCase    :			List[Any]              =					store_two_classics(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       )
       for i in range(len(SCREAMING_SNAKE_CASE__       )       ):
            full_adder(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__		,						len(SCREAMING_SNAKE_CASE__       ) + i		,						len(SCREAMING_SNAKE_CASE__       ) + len(SCREAMING_SNAKE_CASE__       ) + i		,						len(SCREAMING_SNAKE_CASE__       ) + len(SCREAMING_SNAKE_CASE__       ) + i + 1       )
            circuit.barrier()  # Optional, just for aesthetics
  
       # Measure the resultant qBits
       for i in range(len(SCREAMING_SNAKE_CASE__       ) + 1       ):
            circuit.measure([(len(SCREAMING_SNAKE_CASE__       ) * 2) + i]		,						[i]       )
  
       _UpperCAmelCase    :			Any              =					qiskit.execute(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__		,						shots=1       ).result()
  
       # The result is in binary. Convert it back to int
       return int(list(res.get_counts()       )[0]		,						2       )
  
  
  if __name__ == "__main__":
   import doctest
  
   doctest.testmod()
  
style_context: 
  
  
  
  """simple docstring"""
  
  
  
  
  _lowerCAmelCase       :      str							=							{
      "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,
  }
  
  _lowerCAmelCase       :      Optional[int]							=							{1_45: 1_45}
  
  _lowerCAmelCase       :      int							=							{
      1_45: 0,
      1_69: 3,
      3_63_01: 3,
      14_54: 3,
      8_71: 2,
      4_53_61: 2,
      8_72: 2,
  }
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int       )						->     int:
  
  
  
  
  
       '''simple docstring'''
  
       if n in CACHE_SUM_DIGIT_FACTORIALS:
            return CACHE_SUM_DIGIT_FACTORIALS[n]
       _UpperCAmelCase    :			Dict              =					sum(DIGIT_FACTORIALS[let] for let in str(SCREAMING_SNAKE_CASE__       )       )
       _UpperCAmelCase    :			Any              =					ret
       return ret
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int		,						SCREAMING_SNAKE_CASE__			:		set | None = None       )						->     int:
  
  
  
  
  
       '''simple docstring'''
  
       _UpperCAmelCase    :			Dict              =					previous or set()
       if n in CHAIN_LENGTH_CACHE:
            return CHAIN_LENGTH_CACHE[n]
       _UpperCAmelCase    :			Dict              =					sum_digit_factorials(SCREAMING_SNAKE_CASE__       )
       if next_number in previous:
            _UpperCAmelCase    :			List[str]              =					0
            return 0
       else:
            previous.add(SCREAMING_SNAKE_CASE__       )
            _UpperCAmelCase    :			str              =					1 + chain_length(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       )
            _UpperCAmelCase    :			str              =					ret
            return ret
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int = 60		,						SCREAMING_SNAKE_CASE__			:		int = 1_000_000       )						->     int:
  
  
  
  
  
       '''simple docstring'''
  
       return sum(1 for i in range(1		,						SCREAMING_SNAKE_CASE__       ) if chain_length(SCREAMING_SNAKE_CASE__       ) == num_terms       )
  
  
  if __name__ == "__main__":
   print(F"{solution() = }")
  