"""simple docstring"""




def 							SCREAMING_SNAKE_CASE     (			_lowerCamelCase						:       List[Any]=28123	)       ->      Dict:
  _lowerCAmelCase						:       List[str]  			=     [1] * (limit + 1)

  for i in range(2			,int(limit**0.5	) + 1	):
    sum_divs[i * i] += i
    for k in range(i + 1			,limit // i + 1	):
      sum_divs[k * i] += k + i

  _lowerCAmelCase						:       List[Any]  			=     set()
  _lowerCAmelCase						:       Tuple  			=     0

  for n in range(1			,limit + 1	):
    if sum_divs[n] > n:
      abundants.add(_lowerCamelCase	)

    if not any((n - a in abundants) for a in abundants	):
      res += n

  return res


if __name__ == "__main__":
     print(solution())





"""simple docstring"""




import numpy as np
import qiskit





def 							SCREAMING_SNAKE_CASE     (			_lowerCamelCase						:       int = 8			,_lowerCamelCase						:       int | None = None	)       ->      str:
  _lowerCAmelCase						:       int  			=     np.random.default_rng(seed=_lowerCamelCase	)

  # Roughly 25% of the qubits will contribute to the key.
  # So we take more than we need.
  _lowerCAmelCase						:       Tuple  			=     6 * key_len
  # Measurement basis for Alice's qubits.
  _lowerCAmelCase						:       Dict  			=     rng.integers(2			,size=_lowerCamelCase	)
  # The set of states Alice will prepare.
  _lowerCAmelCase						:       Tuple  			=     rng.integers(2			,size=_lowerCamelCase	)
  # Measurement basis for Bob's qubits.
  _lowerCAmelCase						:       Union[str, Any]  			=     rng.integers(2			,size=_lowerCamelCase	)

  # Quantum Circuit to simulate BB84
  _lowerCAmelCase						:       Dict  			=     qiskit.QuantumCircuit(_lowerCamelCase			,name="""BB84"""	)

  # Alice prepares her qubits according to rules above.
  for index, _ in enumerate(_lowerCamelCase	):
    if alice_state[index] == 1:
      bbaa_circ.x(_lowerCamelCase	)
    if alice_basis[index] == 1:
      bbaa_circ.h(_lowerCamelCase	)
  bbaa_circ.barrier()

  # Bob measures the received qubits according to rules above.
  for index, _ in enumerate(_lowerCamelCase	):
    if bob_basis[index] == 1:
      bbaa_circ.h(_lowerCamelCase	)

  bbaa_circ.barrier()
  bbaa_circ.measure_all()

  # Simulate the quantum circuit.
  _lowerCAmelCase						:       int  			=     qiskit.Aer.get_backend("""aer_simulator"""	)
  # We only need to run one shot because the key is unique.
  # Multiple shots will produce the same key.
  _lowerCAmelCase						:       List[str]  			=     qiskit.execute(_lowerCamelCase			,_lowerCamelCase			,shots=1			,seed_simulator=_lowerCamelCase	)
  # Returns the result of measurement.
  _lowerCAmelCase						:       List[Any]  			=     job.result().get_counts(_lowerCamelCase	).most_frequent()

  # Extracting the generated key from the simulation results.
  # Only keep measurement results where Alice and Bob chose the same basis.
  _lowerCAmelCase						:       str  			=     """""".join(
      [
          result_bit
          for alice_basis_bit, bob_basis_bit, result_bit in zip(
              _lowerCamelCase			,_lowerCamelCase			,_lowerCamelCase	)
          if alice_basis_bit == bob_basis_bit
      ]	)

  # Get final key. Pad with 0 if too short, otherwise truncate.
  _lowerCAmelCase						:       List[Any]  			=     gen_key[:key_len] if len(_lowerCamelCase	) >= key_len else gen_key.ljust(_lowerCamelCase			,"""0"""	)
  return key


if __name__ == "__main__":
     print(F"""The generated key is : {bbaa(8, seed=0)}""")
     from doctest import testmod

     testmod()




