
'''simple docstring'''





def  UpperCamelCase					(							lowerCAmelCase__	):
					'''simple docstring'''
					if upper_limit < 0:
										raise ValueError('''Limit for the Catalan sequence must be ≥ 0'''	)

					lowercase					=		[0] * (upper_limit + 1)

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






class        lowercase	:




							def __init__(       self     ,A__):
												lowercase					=		val
												lowercase					=		None
												lowercase					=		None





							def 				A__   (       self     ,A__):
												if self.val:
																	if val < self.val:
																						if self.left is None:
																											lowercase					=		Node(A__)
																						else:
																											self.left.insert(A__)
																	elif val > self.val:
																						if self.right is None:
																											lowercase					=		Node(A__)
																						else:
																											self.right.insert(A__)
												else:
																	lowercase					=		val



def  UpperCamelCase					(							lowerCAmelCase__				,    lowerCAmelCase__	):
					'''simple docstring'''
					# Recursive traversal
					if root:
										inorder(root.left				,    lowerCAmelCase__	)
										res.append(root.val	)
										inorder(root.right				,    lowerCAmelCase__	)



def  UpperCamelCase					(							lowerCAmelCase__	):
					'''simple docstring'''
					# Build BST
					if len(lowerCAmelCase__	) == 0:
										return arr
					lowercase					=		Node(arr[0]	)
					for i in range(1				,    len(lowerCAmelCase__	)	):
										root.insert(arr[i]	)
					# Traverse BST in order.
					lowercase					=		[]
					inorder(lowerCAmelCase__				,    lowerCAmelCase__	)
					return res


if __name__ == "__main__":
							print(tree_sort([10, 1, 3, 2, 9, 14, 13]))




