



def      _A				(UpperCamelCase		:      Optional[Any] )  ->Any:



			'''simple docstring'''







			if not head:
						return True
			# split the list to two parts
			lowerCamelCase__							,lowerCamelCase__ :      Union[str, Any]								=		head.next, head
			while fast and fast.next:
						lowerCamelCase__ :      Any								=		fast.next.next
						lowerCamelCase__ :      Tuple								=		slow.next
			lowerCamelCase__ :      Tuple								=		slow.next
			lowerCamelCase__ :      Optional[int]								=		None  # Don't forget here! But forget still works!
			# reverse the second part
			lowerCamelCase__ :      int								=		None
			while second:
						lowerCamelCase__ :      Dict								=		second.next
						lowerCamelCase__ :      int								=		node
						lowerCamelCase__ :      str								=		second
						lowerCamelCase__ :      str								=		nxt
			# compare two parts
			# second part has the same or one less node
			while node:
						if node.val != head.val:
									return False
						lowerCamelCase__ :      List[str]								=		node.next
						lowerCamelCase__ :      int								=		head.next
			return True






def      _A				(UpperCamelCase		:      List[str] )  ->Optional[Any]:



			'''simple docstring'''







			if not head or not head.next:
						return True

			# 1. Get the midpoint (slow)
			lowerCamelCase__ :      Tuple								=		head
			while fast and fast.next:
						lowerCamelCase__							,lowerCamelCase__ :      Union[str, Any]								=		fast.next.next, slow.next

			# 2. Push the second half into the stack
			lowerCamelCase__ :      Dict								=		[slow.val]
			while slow.next:
						lowerCamelCase__ :      int								=		slow.next
						stack.append(slow.val )

			# 3. Comparison
			while stack:
						if stack.pop() != cur.val:
									return False
						lowerCamelCase__ :      Optional[Any]								=		cur.next

			return True






def      _A				(UpperCamelCase		:      str )  ->List[str]:



			'''simple docstring'''







			if not head or not head.next:
						return True
			lowerCamelCase__ :      str								=		{}
			lowerCamelCase__ :      Optional[int]								=		0
			while head:
						if head.val in d:
									d[head.val].append(UpperCamelCase )
						else:
									lowerCamelCase__ :      Tuple								=		[pos]
						lowerCamelCase__ :      int								=		head.next
						pos += 1
			lowerCamelCase__ :      Union[str, Any]								=		pos - 1
			lowerCamelCase__ :      List[Any]								=		0
			for v in d.values():
						if len(UpperCamelCase ) % 2 != 0:
									middle += 1
						else:
									lowerCamelCase__ :      int								=		0
									for i in range(0      ,			len(UpperCamelCase ) ):
												if v[i] + v[len(UpperCamelCase ) - 1 - step] != checksum:
															return False
												step += 1
						if middle > 1:
									return False
			return True








from __future__ import annotations






def      _A				(UpperCamelCase		:      str      ,			UpperCamelCase		:      list[str] | None = None )  ->list[list[str]]:



			'''simple docstring'''







			lowerCamelCase__ :      List[str]								=		word_bank or []
			# create a table
			lowerCamelCase__ :      int								=		len(UpperCamelCase ) + 1

			lowerCamelCase__ :      list[list[list[str]]]								=		[]
			for _ in range(UpperCamelCase ):
						table.append([] )
			# seed value
			lowerCamelCase__ :      Tuple								=		[[]]  # because empty string has empty combination

			# iterate through the indices
			for i in range(UpperCamelCase ):
						# condition
						if table[i] != []:
									for word in word_bank:
												# slice condition
												if target[i : i + len(UpperCamelCase )] == word:
															lowerCamelCase__ :      list[list[str]]								=		[
															    [word, *way] for way in table[i]
															]
															# adds the word to every combination the current position holds
															# now,push that combination to the table[i+len(word)]
															table[i + len(UpperCamelCase )] += new_combinations

    # combinations are in reverse order so reverse for better output
			for combination in table[len(UpperCamelCase )]:
						combination.reverse()

			return table[len(UpperCamelCase )]


if __name__ == "__main__":
				print(all_construct('''jwajalapa''', ['''jwa''', '''j''', '''w''', '''a''', '''la''', '''lapa''']))
				print(all_construct('''rajamati''', ['''s''', '''raj''', '''amat''', '''raja''', '''ma''', '''i''', '''t''']))
				print(
				    all_construct(
				        '''hexagonosaurus''',
				        ['''h''', '''ex''', '''hex''', '''ag''', '''ago''', '''ru''', '''auru''', '''rus''', '''go''', '''no''', '''o''', '''s'''],
				    )
				)



