





import numpy as np

def 							SCREAMING_SNAKE_CASE__       (  snake_case__  :np.ndarray     )      ->						np.ndarray:
  return 1 / (1 + np.exp(-vector     ))

def 							SCREAMING_SNAKE_CASE__       (  snake_case__  :np.ndarray     )      ->						np.ndarray:
  return vector * sigmoid(snake_case__     )


if __name__ == "__main__":
      import doctest

      doctest.testmod()












from __future__ import annotations

from collections.abc import Generator

def 							SCREAMING_SNAKE_CASE__       (  )      ->						Generator[int, None, None]:
  _lowercase							= {}
  _lowercase							= 2
  while True:
    _lowercase							= factor_map.pop(snake_case__			,							snake_case__     )
    if factor:
      _lowercase							= factor + prime
      while x in factor_map:
        x += factor
      _lowercase							= factor
    else:
      _lowercase							= prime
      yield prime
    prime += 1

def 							SCREAMING_SNAKE_CASE__       (  snake_case__  :float = 1E10     )      ->						int:
  _lowercase							= sieve()

  _lowercase							= 1
  while True:
    _lowercase							= next(snake_case__     )
    if (2 * prime * n) > limit:
      return n
    # Ignore the next prime as the reminder will be 2.
    next(snake_case__     )
    n += 2


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