






def 	UpperCamelCase	(							snake_case__  : int	):




     '''simple docstring'''






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

     __snake_case      :Any 							=    [0] * (upper_limit + 1)

     # Base case: C(0) = C(1) = 1
     __snake_case      :Optional[Any] 							=    1
     if upper_limit > 0:
          __snake_case      :Union[str, Any] 							=    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(snake_case__	):
               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:
               lowerCamelCase__       		=  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()










def 	UpperCamelCase	(							snake_case__  : float						,snake_case__  : int	):




     '''simple docstring'''






     if digit_amount > 0:
          return round(number - int(snake_case__	)						,snake_case__	)
     return number - int(snake_case__	)


if __name__ == "__main__":
     print(decimal_isolate(1.5_3, 0))
     print(decimal_isolate(3_5.3_4_5, 1))
     print(decimal_isolate(3_5.3_4_5, 2))
     print(decimal_isolate(3_5.3_4_5, 3))
     print(decimal_isolate(-1_4.7_8_9, 3))
     print(decimal_isolate(0, 2))
     print(decimal_isolate(-1_4.1_2_3, 1))
     print(decimal_isolate(-1_4.1_2_3, 2))
     print(decimal_isolate(-1_4.1_2_3, 3))


