


"""simple docstring"""







import copy
import re




class  UpperCamelCase_	:

	"""simple docstring"""





	snake_case__				:  Dict    					=			"hp"
	snake_case__				:  Optional[int]    					=			{}
	snake_case__				:  Union[str, Any]    					=			None




	@classmethod
	def   UpperCAmelCase_      ( cls			:				Optional[Any]			,			UpperCAmelCase__			:				Dict			,			UpperCAmelCase__			:				Optional[Any]   )       ->	Optional[Any]:
						__SCREAMING_SNAKE_CASE						   =				prefix
						__SCREAMING_SNAKE_CASE						   =				defaults
						cls.build_naming_info()




	@staticmethod
	def   UpperCAmelCase_      ( UpperCAmelCase__			:				Tuple			,			UpperCAmelCase__			:				Optional[Any]   )       ->	Union[str, Any]:
						if len(UpperCAmelCase__   ) == 0:
											return ""
						__SCREAMING_SNAKE_CASE						   =				None
						if any(char.isdigit() for char in word   ):
											raise Exception(F"""Parameters should not contain numbers: '{word}' contains a number"""   )
						if word in info["short_word"]:
											return info["short_word"][word]
						for prefix_len in range(1			,			len(UpperCAmelCase__   ) + 1   ):
											__SCREAMING_SNAKE_CASE						   =				word[:prefix_len]
											if prefix in info["reverse_short_word"]:
																continue
											else:
																__SCREAMING_SNAKE_CASE						   =				prefix
																break

						if short_word is None:
											# Paranoid fallback
											def int_to_alphabetic(UpperCAmelCase__			:				List[Any]   ):
																__SCREAMING_SNAKE_CASE						   =				""
																while integer != 0:
																					__SCREAMING_SNAKE_CASE						   =				chr(ord("A"   ) + integer % 1_0   ) + s
																					integer //= 1_0
																return s

											__SCREAMING_SNAKE_CASE						   =				0
											while True:
																__SCREAMING_SNAKE_CASE						   =				word + "#" + int_to_alphabetic(UpperCAmelCase__   )
																if sword in info["reverse_short_word"]:
																					continue
																else:
																					__SCREAMING_SNAKE_CASE						   =				sword
																					break

						__SCREAMING_SNAKE_CASE						   =				short_word
						__SCREAMING_SNAKE_CASE						   =				word
						return short_word




	@staticmethod
	def   UpperCAmelCase_      ( UpperCAmelCase__			:				Tuple			,			UpperCAmelCase__			:				List[Any]   )       ->	Tuple:
						__SCREAMING_SNAKE_CASE						   =				param_name.split("_"   )

						__SCREAMING_SNAKE_CASE						   =				[TrialShortNamer.shortname_for_word(UpperCAmelCase__			,			UpperCAmelCase__   ) for word in words]

						# We try to create a separatorless short name, but if there is a collision we have to fallback
						# to a separated short name
						__SCREAMING_SNAKE_CASE						   =				["", "_"]

						for separator in separators:
											__SCREAMING_SNAKE_CASE						   =				separator.join(UpperCAmelCase__   )
											if shortname not in info["reverse_short_param"]:
																__SCREAMING_SNAKE_CASE						   =				shortname
																__SCREAMING_SNAKE_CASE						   =				param_name
																return shortname

						return param_name




	@staticmethod
	def   UpperCAmelCase_      ( UpperCAmelCase__			:				Dict			,			UpperCAmelCase__			:				List[Any]   )       ->	List[str]:
						__SCREAMING_SNAKE_CASE						   =				TrialShortNamer.shortname_for_key(UpperCAmelCase__			,			UpperCAmelCase__   )
						__SCREAMING_SNAKE_CASE						   =				short_name
						__SCREAMING_SNAKE_CASE						   =				param_name




	@classmethod
	def   UpperCAmelCase_      ( cls			:				int   )       ->	List[str]:
						if cls.NAMING_INFO is not None:
											return

						__SCREAMING_SNAKE_CASE						   =				{
						    "short_word": {},
						    "reverse_short_word": {},
						    "short_param": {},
						    "reverse_short_param": {},
						}

						__SCREAMING_SNAKE_CASE						   =				list(cls.DEFAULTS.keys()   )

						for k in field_keys:
											cls.add_new_param_name(UpperCAmelCase__			,			UpperCAmelCase__   )

						__SCREAMING_SNAKE_CASE						   =				info




	@classmethod
	def   UpperCAmelCase_      ( cls			:				List[Any]			,			UpperCAmelCase__			:				List[str]   )       ->	Optional[Any]:
						cls.build_naming_info()
						assert cls.PREFIX is not None
						__SCREAMING_SNAKE_CASE						   =				[copy.copy(cls.PREFIX   )]

						for k, v in params.items():
											if k not in cls.DEFAULTS:
																raise Exception(F"""You should provide a default value for the param name {k} with value {v}"""   )
											if v == cls.DEFAULTS[k]:
																# The default value is not added to the name
																continue

											__SCREAMING_SNAKE_CASE						   =				cls.NAMING_INFO["short_param"][k]

											if isinstance(UpperCAmelCase__			,			UpperCAmelCase__   ):
																__SCREAMING_SNAKE_CASE						   =				1 if v else 0

											__SCREAMING_SNAKE_CASE						   =				"" if isinstance(UpperCAmelCase__			,			(int, float)   ) else "-"
											__SCREAMING_SNAKE_CASE						   =				F"""{key}{sep}{v}"""
											name.append(UpperCAmelCase__   )

						return "_".join(UpperCAmelCase__   )




	@classmethod
	def   UpperCAmelCase_      ( cls			:				Union[str, Any]			,			UpperCAmelCase__			:				Dict   )       ->	Any:
						__SCREAMING_SNAKE_CASE						   =				repr[len(cls.PREFIX   ) + 1 :]
						if repr == "":
											__SCREAMING_SNAKE_CASE						   =				[]
						else:
											__SCREAMING_SNAKE_CASE						   =				repr.split("_"   )

						__SCREAMING_SNAKE_CASE						   =				{}

						for value in values:
											if "-" in value:
																__SCREAMING_SNAKE_CASE   ,  __SCREAMING_SNAKE_CASE						   =				value.split("-"   )
											else:
																__SCREAMING_SNAKE_CASE						   =				re.sub("[0-9.]"			,			""			,			UpperCAmelCase__   )
																__SCREAMING_SNAKE_CASE						   =				float(re.sub("[^0-9.]"			,			""			,			UpperCAmelCase__   )   )

											__SCREAMING_SNAKE_CASE						   =				cls.NAMING_INFO["reverse_short_param"][p_k]

											__SCREAMING_SNAKE_CASE						   =				p_v

						for k in cls.DEFAULTS:
											if k not in parameters:
																__SCREAMING_SNAKE_CASE						   =				cls.DEFAULTS[k]

						return parameters




"""simple docstring"""







def    UpperCAmelCase__       (lowerCAmelCase_   ):




					'''simple docstring'''


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

					__SCREAMING_SNAKE_CASE						   =				[0] * (upper_limit + 1)

					# Base case: C(0) = C(1) = 1
					__SCREAMING_SNAKE_CASE						   =				1
					if upper_limit > 0:
										__SCREAMING_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(lowerCAmelCase_   ):
															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__				:							List[str]						=     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()
