






_lowerCamelCase       :     Tuple           =							[0.3_3, 0.4_4, 0.5_5, 0.4_4, 0.3_3]
_lowerCamelCase       :     str           =							3
_lowerCamelCase       :     Union[str, Any]           =							5

# Buffer Space (with Parameters Space)
_lowerCamelCase       :     list[float]           =							[]
_lowerCamelCase       :     list[float]           =							[]

# Machine Time
_lowerCamelCase       :     Dict           =							0

def     a__  (	UpperCAmelCase							:    Union[str, Any]    )						->		str:
  global buffer_space, params_space, machine_time, K, m, t

  # Choosing Dynamical Systems (All)
  for key, value in enumerate(UpperCAmelCase    ):
    # Evolution Parameter
    UpperCAmelCase :							int								=				float(seed / value    )

    # Control Theory: Orbit Change
    UpperCAmelCase :							Optional[Any]								=				(buffer_space[(key + 1) % m] + e) % 1

    # Control Theory: Trajectory Change
    UpperCAmelCase :							Any								=				(params_space[key] + e) % 1 + 3

    # Modification (Transition Function) - Jumps
    UpperCAmelCase :							int								=				round(float(r * value * (1 - value)    )       ,				10    )
    UpperCAmelCase :							Optional[int]								=				r  # Saving to Parameters Space

  # Logistic Map
  assert max(UpperCAmelCase    ) < 1
  assert max(UpperCAmelCase    ) < 4

  # Machine Time
  machine_time += 1

def     a__  (	)						->		Tuple:
  global buffer_space, params_space, machine_time, K, m, t

  # PRNG (Xorshift by George Marsaglia)
  def xorshift(UpperCAmelCase							:    List[Any]       ,				UpperCAmelCase							:    str    ):
    x ^= y >> 13
    y ^= x << 17
    x ^= y >> 5
    return x

  # Choosing Dynamical Systems (Increment)
  UpperCAmelCase :							int								=				machine_time % m

  # Evolution (Time Length)
  for _ in range(0       ,				UpperCAmelCase    ):
    # Variables (Position + Parameters)
    UpperCAmelCase :							Any								=				params_space[key]
    UpperCAmelCase :							Optional[int]								=				buffer_space[key]

    # Modification (Transition Function) - Flow
    UpperCAmelCase :							Optional[int]								=				round(float(r * value * (1 - value)    )       ,				10    )
    UpperCAmelCase :							Optional[Any]								=				(machine_time * 0.01 + r * 1.01) % 1 + 3

  # Choosing Chaotic Data
  UpperCAmelCase :							Optional[Any]								=				int(buffer_space[(key + 2) % m] * (10**10)    )
  UpperCAmelCase :							List[str]								=				int(buffer_space[(key - 2) % m] * (10**10)    )

  # Machine Time
  machine_time += 1

  return xorshift(UpperCAmelCase       ,				UpperCAmelCase    ) % 0xFF_FF_FF_FF

def     a__  (	)						->		Union[str, Any]:
  global buffer_space, params_space, machine_time, K, m, t

  UpperCAmelCase :							str								=				K
  UpperCAmelCase :							str								=				[0] * m
  UpperCAmelCase :							int								=				0


if __name__ == "__main__":
     # Initialization
     reset()

     # Pushing Data (Input)
     import random

     _lowerCamelCase       :     List[str]           =							random.sample(range(0xf_f_f_f_f_f_f_f), 1_0_0)
     for chunk in message:
          push(chunk)

     # for controlling
     _lowerCamelCase       :     int           =							""

     # Pulling Data (Output)
     while inp in ("e", "E"):
          print(f"""{format(pull(), "#04x")}""")
          print(buffer_space)
          print(params_space)
          _lowerCamelCase       :     int           =							input("(e)exit? ").strip()








from functools import lru_cache

@lru_cache
def     a__  (	UpperCAmelCase							:    int    )						->		int:
  if not isinstance(UpperCAmelCase       ,				UpperCAmelCase    ):
    raise TypeError('''k must be an integer.'''    )
  if k < 0:
    raise ValueError('''k integer must be greater or equal to zero.'''    )
  if k == 0:
    return 0
  elif k == 1:
    return 1
  else:
    return fibonacci(k - 1    ) + fibonacci(k - 2    )

def     a__  (	UpperCAmelCase							:    list       ,				UpperCAmelCase							:    int    )						->		int:
  UpperCAmelCase :							List[str]								=				len(UpperCAmelCase    )
  # Find m such that F_m >= n where F_i is the i_th fibonacci number.
  UpperCAmelCase :							Any								=				0
  while True:
    if fibonacci(UpperCAmelCase    ) >= len_list:
      UpperCAmelCase :							Optional[Any]								=				i
      break
    i += 1
  UpperCAmelCase :							List[Any]								=				0
  while fibb_k > 0:
    UpperCAmelCase :							List[str]								=				min(
        offset + fibonacci(fibb_k - 1    )       ,				len_list - 1    )  # Prevent out of range
    UpperCAmelCase :							Optional[Any]								=				arr[index_k]
    if item_k_1 == val:
      return index_k
    elif val < item_k_1:
      fibb_k -= 1
    elif val > item_k_1:
      offset += fibonacci(fibb_k - 1    )
      fibb_k -= 2
  else:
    return -1


if __name__ == "__main__":
     import doctest

     doctest.testmod()





