"""simple docstring"""
from collections.abc import Callable
class 					a	:



  def __init__(						self :					int       ,		lowerCAmelCase :					Optional[int] = None		)     ->					List[Any]:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_: Optional[Any]     			=[]
     # Stores indexes of each item for supporting updates and deletion.
     SCREAMING_SNAKE_CASE_: List[Any]     			={}
     # Stores current size of heap.
     SCREAMING_SNAKE_CASE_: str     			=0
     # Stores function used to evaluate the score of an item on which basis ordering
     # will be done.
     SCREAMING_SNAKE_CASE_: Dict     			=key or (lambda lowerCAmelCase		: x)



  def 	lowerCamelCase__       (						self :					Union[str, Any]       ,		lowerCAmelCase :					Tuple		)     ->					Union[str, Any]:


     '''simple docstring'''




     return int((i - 1) / 2		) if i > 0 else None



  def 	lowerCamelCase__       (						self :					Optional[int]       ,		lowerCAmelCase :					int		)     ->					Union[str, Any]:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_: Optional[Any]     			=int(2 * i + 1		)
     return left if 0 < left < self.size else None



  def 	lowerCamelCase__       (						self :					List[str]       ,		lowerCAmelCase :					Union[str, Any]		)     ->					int:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_: Optional[int]     			=int(2 * i + 2		)
     return right if 0 < right < self.size else None



  def 	lowerCamelCase__       (						self :					Dict       ,		lowerCAmelCase :					Dict       ,		lowerCAmelCase :					List[str]		)     ->					Optional[Any]:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_			,		SCREAMING_SNAKE_CASE_: Any     			=(
         self.pos_map[self.arr[j][0]],
         self.pos_map[self.arr[i][0]],
     )
     # Then swap the items in the list.
     SCREAMING_SNAKE_CASE_			,		SCREAMING_SNAKE_CASE_: Dict     			=self.arr[j], self.arr[i]



  def 	lowerCamelCase__       (						self :					str       ,		lowerCAmelCase :					Tuple       ,		lowerCAmelCase :					Optional[Any]		)     ->					Union[str, Any]:


     '''simple docstring'''




     return self.arr[i][1] < self.arr[j][1]



  def 	lowerCamelCase__       (						self :					Tuple       ,		lowerCAmelCase :					Optional[int]		)     ->					int:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_: List[str]     			=self._left(_a		)
     SCREAMING_SNAKE_CASE_: List[Any]     			=self._right(_a		)
     SCREAMING_SNAKE_CASE_: Optional[Any]     			=i

     if left is not None and not self._cmp(_a       ,		_a		):
        SCREAMING_SNAKE_CASE_: List[str]     			=left
     if right is not None and not self._cmp(_a       ,		_a		):
        SCREAMING_SNAKE_CASE_: Any     			=right

     return valid_parent



  def 	lowerCamelCase__       (						self :					Dict       ,		lowerCAmelCase :					Dict		)     ->					Tuple:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_: int     			=self._parent(_a		)
     while parent is not None and not self._cmp(_a       ,		_a		):
        self._swap(_a       ,		_a		)
        SCREAMING_SNAKE_CASE_			,		SCREAMING_SNAKE_CASE_: List[Any]     			=parent, self._parent(_a		)



  def 	lowerCamelCase__       (						self :					Dict       ,		lowerCAmelCase :					List[str]		)     ->					List[str]:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_: List[Any]     			=self._get_valid_parent(_a		)
     while valid_parent != index:
        self._swap(_a       ,		_a		)
        SCREAMING_SNAKE_CASE_			,		SCREAMING_SNAKE_CASE_: Optional[int]     			=valid_parent, self._get_valid_parent(_a		)



  def 	lowerCamelCase__       (						self :					Optional[Any]       ,		lowerCAmelCase :					int       ,		lowerCAmelCase :					Optional[int]		)     ->					int:


     '''simple docstring'''




     if item not in self.pos_map:
        return
     SCREAMING_SNAKE_CASE_: List[Any]     			=self.pos_map[item]
     SCREAMING_SNAKE_CASE_: int     			=[item, self.key(_a		)]
     # Make sure heap is right in both up and down direction.
     # Ideally only one of them will make any change.
     self._heapify_up(_a		)
     self._heapify_down(_a		)



  def 	lowerCamelCase__       (						self :					Optional[int]       ,		lowerCAmelCase :					List[str]		)     ->					int:


     '''simple docstring'''




     if item not in self.pos_map:
        return
     SCREAMING_SNAKE_CASE_: Tuple     			=self.pos_map[item]
     del self.pos_map[item]
     SCREAMING_SNAKE_CASE_: Optional[int]     			=self.arr[self.size - 1]
     SCREAMING_SNAKE_CASE_: Any     			=index
     self.size -= 1
     # Make sure heap is right in both up and down direction. Ideally only one
     # of them will make any change- so no performance loss in calling both.
     if self.size > index:
        self._heapify_up(_a		)
        self._heapify_down(_a		)



  def 	lowerCamelCase__       (						self :					int       ,		lowerCAmelCase :					List[str]       ,		lowerCAmelCase :					int		)     ->					str:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_: List[Any]     			=len(self.arr		)
     if arr_len == self.size:
        self.arr.append([item, self.key(_a		)]		)
     else:
        SCREAMING_SNAKE_CASE_: Tuple     			=[item, self.key(_a		)]
     SCREAMING_SNAKE_CASE_: str     			=self.size
     self.size += 1
     self._heapify_up(self.size - 1		)



  def 	lowerCamelCase__       (						self :					Union[str, Any]		)     ->					Tuple:


     '''simple docstring'''




     return self.arr[0] if self.size else None





  def 	lowerCamelCase__       (						self :					Optional[Any]		)     ->					List[str]:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_: str     			=self.get_top()
     if top_item_tuple:
        self.delete_item(top_item_tuple[0]		)
     return top_item_tuple







def      __magic_name__				(							):
   pass


if __name__ == "__main__":
   import doctest

   doctest.testmod()








"""simple docstring"""
def      __magic_name__				(							lowercase ):
   if upper_limit < 0:
      raise ValueError("""Limit for the Catalan sequence must be ≥ 0""" )

   SCREAMING_SNAKE_CASE_: Tuple     			=[0] * (upper_limit + 1)

   # Base case: C(0) = C(1) = 1
   SCREAMING_SNAKE_CASE_: Any     			=1
   if upper_limit > 0:
      SCREAMING_SNAKE_CASE_: List[str]     			=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:
         _UpperCAmelCase     =			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()



