





'''simple docstring'''
def 				lowercase__   (   __lowercase						:  int     ) ->      "list[int]":



       """simple docstring"""






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

       __UpperCamelCase       =  [0] * (upper_limit + 1)

       # Base case: C(0) = C(1) = 1
       __UpperCamelCase       =  1
       if upper_limit > 0:
              __UpperCamelCase       =  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(__lowercase     ):
                     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__							:							Union[str, Any] =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()







'''simple docstring'''
from __future__ import annotations

from typing import Any

class      snake_case     (    __lowerCamelCase       ):




 """simple docstring"""



 pass






class      snake_case     :




 """simple docstring"""



 def __init__(       self       :							List[Any]							,	__A       :							Any	):
        __UpperCamelCase       =  data
        __UpperCamelCase       =  None






 def __iter__(       self       :							Optional[Any]	):
        __UpperCamelCase       =  self
        __UpperCamelCase       =  []
        while node:
               if node in visited:
                      raise ContainsLoopError
               visited.append(__A	)
               yield node.data
               __UpperCamelCase       =  node.next_node






 @property
 def        _lowerCamelCase					(       self       :							List[str]	):
        try:
               list(self	)
               return False
        except ContainsLoopError:
               return True


if __name__ == "__main__":
    a__							:							Dict =Node(1)
    a__							:							Optional[int] =Node(2)
    a__							:							List[str] =Node(3)
    a__							:							Optional[int] =Node(4)
    print(root_node.has_loop)  # False
    a__							:							str =root_node.next_node
    print(root_node.has_loop)  # True

    a__							:							Optional[int] =Node(5)
    a__							:							List[Any] =Node(6)
    a__							:							int =Node(5)
    a__							:							Tuple =Node(6)
    print(root_node.has_loop)  # False

    a__							:							str =Node(1)
    print(root_node.has_loop)  # False
