




from copy import deepcopy


class 				UpperCamelCase_    :

    '''simple docstring'''






    def __init__(			self      :	Optional[Any]					, UpperCAmelCase__      :	list[int] | None = None					, UpperCAmelCase__      :	int | None = None)						->None:





           '''simple docstring'''

           if arr is None and size is not None:
                  A__       =    size
                  A__       =    [0] * size
           elif arr is not None:
                  self.init(UpperCAmelCase__)
           else:
                  raise ValueError('''Either arr or size must be specified''')


    def        SCREAMING_SNAKE_CASE							(			self      :	Dict					, UpperCAmelCase__      :	list[int])						->None:





           '''simple docstring'''

           A__       =    len(UpperCAmelCase__)
           A__       =    deepcopy(UpperCAmelCase__)
           for i in range(1					, self.size):
                  A__       =    self.next_(UpperCAmelCase__)
                  if j < self.size:
                         self.tree[j] += self.tree[i]


    def        SCREAMING_SNAKE_CASE							(			self      :	Union[str, Any])						->list[int]:





           '''simple docstring'''

           A__       =    self.tree[:]
           for i in range(self.size - 1					, 0					, -1):
                  A__       =    self.next_(UpperCAmelCase__)
                  if j < self.size:
                         arr[j] -= arr[i]
           return arr


    @staticmethod
    def        SCREAMING_SNAKE_CASE							(			UpperCAmelCase__      :	int)						->int:





           '''simple docstring'''

           return index + (index & (-index))


    @staticmethod
    def        SCREAMING_SNAKE_CASE							(			UpperCAmelCase__      :	int)						->int:





           '''simple docstring'''

           return index - (index & (-index))


    def        SCREAMING_SNAKE_CASE							(			self      :	Union[str, Any]					, UpperCAmelCase__      :	int					, UpperCAmelCase__      :	int)						->None:





           '''simple docstring'''

           if index == 0:
                  self.tree[0] += value
                  return
           while index < self.size:
                  self.tree[index] += value
                  A__       =    self.next_(UpperCAmelCase__)


    def        SCREAMING_SNAKE_CASE							(			self      :	List[str]					, UpperCAmelCase__      :	int					, UpperCAmelCase__      :	int)						->None:





           '''simple docstring'''

           self.add(UpperCAmelCase__					, value - self.get(UpperCAmelCase__))


    def        SCREAMING_SNAKE_CASE							(			self      :	int					, UpperCAmelCase__      :	int)						->int:





           '''simple docstring'''

           if right == 0:
                  return 0
           A__       =    self.tree[0]
           right -= 1  # make right inclusive
           while right > 0:
                  result += self.tree[right]
                  A__       =    self.prev(UpperCAmelCase__)
           return result


    def        SCREAMING_SNAKE_CASE							(			self      :	int					, UpperCAmelCase__      :	int					, UpperCAmelCase__      :	int)						->int:





           '''simple docstring'''

           return self.prefix(UpperCAmelCase__) - self.prefix(UpperCAmelCase__)


    def        SCREAMING_SNAKE_CASE							(			self      :	Union[str, Any]					, UpperCAmelCase__      :	int)						->int:





           '''simple docstring'''

           return self.query(UpperCAmelCase__					, index + 1)





    def        SCREAMING_SNAKE_CASE							(			self      :	Any					, UpperCAmelCase__      :	int)						->int:





           '''simple docstring'''

           value -= self.tree[0]
           if value < 0:
                  return -1

           A__       =    1  # Largest power of 2 <= size
           while j * 2 < self.size:
                  j *= 2

           A__       =    0

           while j > 0:
                  if i + j < self.size and self.tree[i + j] <= value:
                         value -= self.tree[i + j]
                         i += j
                  j //= 2
           return i


if __name__ == "__main__":
  import doctest

  doctest.testmod()








def SCREAMING_SNAKE_CASE				(       lowercase_						)   ->       "list[int]":



       """simple docstring"""

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

       A__       =    [0] * (upper_limit + 1)

       # Base case: C(0) = C(1) = 1
       A__       =    1
       if upper_limit > 0:
              A__       =    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:
      _lowerCamelCase	:		List[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()


