
"""simple docstring"""




def 						lowercase_      (       A__		)							->							"list[int]":
    """simple docstring"""

    if upper_limit < 0:
        raise ValueError("Limit for the Catalan sequence must be ≥ 0"		)

    snake_case								= [0] * (upper_limit + 1)

    # Base case: C(0) = C(1) = 1
    snake_case								= 1
    if upper_limit > 0:
        snake_case								= 1

    # Recurrence relation: C(i) = sum(C(j).C(i-j-1)), from j = 0 to i
    for i in range(2			,		upper_limit + 1		):
        for j in range(_UpperCAmelCase		):
            catalan_list[i] += catalan_list[j] * catalan_list[i - j - 1]

    return catalan_list


if __name__ == "__main__":
   print("\n********* Catalan Numbers Using Dynamic Programming ************\n")
   print("\n*** Enter -1 at any time to quit ***")
   print("\nEnter the upper limit (≥ 0) for the Catalan number sequence: ", end="")
   try:
      while True:
         _A   =			int(input().strip())
         if N < 0:
            print("\n********* Goodbye!! ************")
            break
         else:
            print(f"The Catalan numbers from 0 through {N} are:")
            print(catalan_numbers(N))
            print("Try another upper limit for the sequence: ", end="")
   except (NameError, ValueError):
      print("\n********* Invalid input, goodbye! ************\n")

   import doctest

   doctest.testmod()



from ....utils import logging


_A   =			logging.get_logger(__name__)







class 					lowerCamelCase		(  A_  ):





     def __init__(self				:   Tuple    ,   _A				:   Optional[int]    ,   _A				:   Tuple=None    ,   _A				:   Union[str, Any]=2_0_4_8       )						->						List[Any]:
         snake_case								= config.__dict__
         snake_case								= modal_hidden_size
         if num_labels:
             snake_case								= num_labels

