
# Author: OMKAR PATHAK, Nwachukwu Chidiebere

# Use a Python dictionary to construct the graph.
from __future__ import annotations

from pprint import pformat
from typing import Generic, TypeVar

_A     =  TypeVar("T")





class 			_lowerCAmelCase      (			Generic[T] ):




				def __init__(      self       ,       _UpperCamelCase = True  )       ->   None:
							lowerCAmelCase_      			=			{}  # dictionary of lists
							lowerCAmelCase_      			=			directed




				def   __a		(      self       ,       _UpperCamelCase       ,       _UpperCamelCase  )       ->   GraphAdjacencyList[T]:

							if not self.directed:  # For undirected graphs
										# if both source vertex and destination vertex are both present in the
										# adjacency list, add destination vertex to source vertex list of adjacent
										# vertices and add source vertex to destination vertex list of adjacent
										# vertices.
										if source_vertex in self.adj_list and destination_vertex in self.adj_list:
													self.adj_list[source_vertex].append(_UpperCamelCase  )
													self.adj_list[destination_vertex].append(_UpperCamelCase  )
										# if only source vertex is present in adjacency list, add destination vertex
										# to source vertex list of adjacent vertices, then create a new vertex with
										# destination vertex as key and assign a list containing the source vertex
										# as it's first adjacent vertex.
										elif source_vertex in self.adj_list:
													self.adj_list[source_vertex].append(_UpperCamelCase  )
													lowerCAmelCase_      			=			[source_vertex]
										# if only destination vertex is present in adjacency list, add source vertex
										# to destination vertex list of adjacent vertices, then create a new vertex
										# with source vertex as key and assign a list containing the source vertex
										# as it's first adjacent vertex.
										elif destination_vertex in self.adj_list:
													self.adj_list[destination_vertex].append(_UpperCamelCase  )
													lowerCAmelCase_      			=			[destination_vertex]
										# if both source vertex and destination vertex are not present in adjacency
										# list, create a new vertex with source vertex as key and assign a list
										# containing the destination vertex as it's first adjacent vertex also
										# create a new vertex with destination vertex as key and assign a list
										# containing the source vertex as it's first adjacent vertex.
										else:
													lowerCAmelCase_      			=			[destination_vertex]
													lowerCAmelCase_      			=			[source_vertex]
							else:  # For directed graphs
										# if both source vertex and destination vertex are present in adjacency
										# list, add destination vertex to source vertex list of adjacent vertices.
										if source_vertex in self.adj_list and destination_vertex in self.adj_list:
													self.adj_list[source_vertex].append(_UpperCamelCase  )
										# if only source vertex is present in adjacency list, add destination
										# vertex to source vertex list of adjacent vertices and create a new vertex
										# with destination vertex as key, which has no adjacent vertex
										elif source_vertex in self.adj_list:
													self.adj_list[source_vertex].append(_UpperCamelCase  )
													lowerCAmelCase_      			=			[]
										# if only destination vertex is present in adjacency list, create a new
										# vertex with source vertex as key and assign a list containing destination
										# vertex as first adjacent vertex
										elif destination_vertex in self.adj_list:
													lowerCAmelCase_      			=			[destination_vertex]
										# if both source vertex and destination vertex are not present in adjacency
										# list, create a new vertex with source vertex as key and a list containing
										# destination vertex as it's first adjacent vertex. Then create a new vertex
										# with destination vertex as key, which has no adjacent vertex
										else:
													lowerCAmelCase_      			=			[destination_vertex]
													lowerCAmelCase_      			=			[]

							return self




				def __repr__(      self  )       ->   str:
							return pformat(self.adj_list  )





def      lowerCamelCase__       (       __lowerCAmelCase						:						int       ):




			"""simple docstring"""


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

			lowerCAmelCase_      			=			[0] * (upper_limit + 1)

			# Base case: C(0) = C(1) = 1
			lowerCAmelCase_      			=			1
			if upper_limit > 0:
						lowerCAmelCase_      			=			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     =  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()



