from ..utils import DummyObject, requires_backends






class 		_lowerCamelCase		(   metaclass=UpperCamelCase_    ):
    __a  =      ["torch", "scipy"]
    def __init__(  self , *lowerCAmelCase , **lowerCAmelCase   )       ->					Any:
     requires_backends(self , ['''torch''', '''scipy''']   )
    @classmethod
    def 						UpperCamelCase_				(  cls , *lowerCAmelCase , **lowerCAmelCase   )       ->					List[str]:
     requires_backends(cls , ['''torch''', '''scipy''']   )



    @classmethod
    def 						UpperCamelCase_				(  cls , *lowerCAmelCase , **lowerCAmelCase   )       ->					Tuple:
     requires_backends(cls , ['''torch''', '''scipy''']   )


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







def 			A__      (	snake_case_ :		Optional[Any]      ):
 if not head or not head.next:
  return True

 # 1. Get the midpoint (slow)
 SCREAMING_SNAKE_CASE__:   List[Any]=      head
 while fast and fast.next:
  SCREAMING_SNAKE_CASE__,	SCREAMING_SNAKE_CASE__:   Any=      fast.next.next, slow.next

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

 # 3. Comparison
 while stack:
  if stack.pop() != cur.val:
   return False
  SCREAMING_SNAKE_CASE__:   Tuple=      cur.next

 return True







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

