import math






def        UpperCamelCase_							(			lowerCAmelCase__  ):



					"""simple docstring"""

					_lowerCAmelCase			:		Optional[int]          = math.loga(math.sqrt(4 * positive_integer + 1  ) / 2 + 1 / 2  )

					return exponent == int(lowerCAmelCase__  )






def        UpperCamelCase_							(			lowerCAmelCase__ = 1 / 1_23_45  ):



					"""simple docstring"""

					_lowerCAmelCase			:		Optional[int]          = 0
					_lowerCAmelCase			:		List[str]          = 0

					_lowerCAmelCase			:		Dict          = 3
					while True:
										_lowerCAmelCase			:		Tuple          = (integer**2 - 1) / 4
										# if candidate is an integer, then there is a partition for k
										if partition_candidate == int(lowerCAmelCase__  ):
															_lowerCAmelCase			:		int          = int(lowerCAmelCase__  )
															total_partitions += 1
															if check_partition_perfect(lowerCAmelCase__  ):
																				perfect_partitions += 1
										if perfect_partitions > 0:
															if perfect_partitions / total_partitions < max_proportion:
																				return int(lowerCAmelCase__  )
										integer += 1


if __name__ == "__main__":
						print(F'''{solution() = }''')








from __future__ import annotations

lowerCamelCase__						=				"#"







class 							lowerCAmelCase__   :

						def __init__(      self					)       ->   None:


								'''simple docstring'''

								_UpperCamelCase         =						{}

						def 			A_					(      self							,				a					)       ->   None:


								'''simple docstring'''

								_UpperCamelCase         =						self._trie
								for char in text:
										if char not in trie:
												_UpperCamelCase         =						{}
										_UpperCamelCase         =						trie[char]
								_UpperCamelCase         =						True

						def 			A_					(      self							,				a					)       ->   tuple | list:


								'''simple docstring'''

								_UpperCamelCase         =						self._trie
								for char in prefix:
										if char in trie:
												_UpperCamelCase         =						trie[char]
										else:
												return []
								return self._elements(a					)







						def 			A_					(      self							,				a					)       ->   tuple:


								'''simple docstring'''

								_UpperCamelCase         =						[]
								for c, v in d.items():
										_UpperCamelCase         =						[""" """] if c == END else [(c + s) for s in self._elements(a					)]
										result.extend(a					)
								return tuple(a					)




lowerCamelCase__						=				Trie()
lowerCamelCase__						=				("depart", "detergent", "daring", "dog", "deer", "deal")
for word in words:
		trie.insert_word(word)


def 				__A(lowerCAmelCase			)		->					tuple:

		"""simple docstring"""






		_UpperCamelCase         =						trie.find_word(lowerCAmelCase			)
		return tuple(string + word for word in suffixes			)


def 				__A()		->					None:

		"""simple docstring"""






		print(autocomplete_using_trie("""de"""			)			)


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		main()



