





from __future__ import annotations

from collections.abc import Iterator



class    _SCREAMING_SNAKE_CASE						:







 '''simple docstring'''

 def __init__(self				:   Dict       , UpperCAmelCase_				:   int)       ->None:



   '''simple docstring'''



   lowerCamelCase__:      int			  =value
   lowerCamelCase__:      Node | None			  =None
   lowerCamelCase__:      Node | None			  =None



class    _SCREAMING_SNAKE_CASE						:







 '''simple docstring'''

 def __init__(self				:   Dict       , UpperCAmelCase_				:   Node)       ->None:



   '''simple docstring'''



   lowerCamelCase__:      Union[str, Any]			  =tree

 def 							SCREAMING_SNAKE_CASE_					(self				:   Optional[int]       , UpperCAmelCase_				:   Node | None)       ->int:



   '''simple docstring'''



   if node is None:
     return 0
   return node.value + (
       self.depth_first_search(node.left) + self.depth_first_search(node.right)
   )







 def __iter__(self				:   int)       ->Iterator[int]:



   '''simple docstring'''



   yield self.depth_first_search(self.tree)


if __name__ == "__main__":
     import doctest

     doctest.testmod()


def    a__       (						__UpperCamelCase ):
      if not head:
            return True
      # split the list to two parts
      SCREAMING_SNAKE_CASE_   ,       SCREAMING_SNAKE_CASE_      =     head.next, head
      while fast and fast.next:
            SCREAMING_SNAKE_CASE_      =     fast.next.next
            SCREAMING_SNAKE_CASE_      =     slow.next
      SCREAMING_SNAKE_CASE_      =     slow.next
      SCREAMING_SNAKE_CASE_      =     None  # Don't forget here! But forget still works!
      # reverse the second part
      SCREAMING_SNAKE_CASE_      =     None
      while second:
            SCREAMING_SNAKE_CASE_      =     second.next
            SCREAMING_SNAKE_CASE_      =     node
            SCREAMING_SNAKE_CASE_      =     second
            SCREAMING_SNAKE_CASE_      =     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_      =     node.next
            SCREAMING_SNAKE_CASE_      =     head.next
      return True


def    a__       (						__UpperCamelCase ):
      if not head or not head.next:
            return True

      # 1. Get the midpoint (slow)
      SCREAMING_SNAKE_CASE_      =     SCREAMING_SNAKE_CASE_      =     SCREAMING_SNAKE_CASE_      =     head
      while fast and fast.next:
            SCREAMING_SNAKE_CASE_   ,       SCREAMING_SNAKE_CASE_      =     fast.next.next, slow.next

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

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

      return True





def    a__       (						__UpperCamelCase ):
      if not head or not head.next:
            return True
      SCREAMING_SNAKE_CASE_      =     {}
      SCREAMING_SNAKE_CASE_      =     0
      while head:
            if head.val in d:
                  d[head.val].append(__UpperCamelCase )
            else:
                  SCREAMING_SNAKE_CASE_      =     [pos]
            SCREAMING_SNAKE_CASE_      =     head.next
            pos += 1
      SCREAMING_SNAKE_CASE_      =     pos - 1
      SCREAMING_SNAKE_CASE_      =     0
      for v in d.values():
            if len(__UpperCamelCase ) % 2 != 0:
                  middle += 1
            else:
                  SCREAMING_SNAKE_CASE_      =     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


