





"""simple docstring"""





def 					__A  (_SCREAMING_SNAKE_CASE     )   ->Dict:





  """simple docstring"""


  if not head:
    return True
  # split the list to two parts
  lowerCAmelCase__				,							lowerCAmelCase__     :List[Any]											=				head.next, head
  while fast and fast.next:
    lowerCAmelCase__     :Any											=				fast.next.next
    lowerCAmelCase__     :Any											=				slow.next
  lowerCAmelCase__     :List[Any]											=				slow.next
  lowerCAmelCase__     :Optional[Any]											=				None  # Don't forget here! But forget still works!
  # reverse the second part
  lowerCAmelCase__     :Optional[int]											=				None
  while second:
    lowerCAmelCase__     :Any											=				second.next
    lowerCAmelCase__     :Optional[int]											=				node
    lowerCAmelCase__     :int											=				second
    lowerCAmelCase__     :List[Any]											=				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__     :Optional[Any]											=				head.next
  return True
def 					__A  (_SCREAMING_SNAKE_CASE     )   ->Any:





  """simple docstring"""


  if not head or not head.next:
    return True

  # 1. Get the midpoint (slow)
  lowerCAmelCase__     :str											=				head
  while fast and fast.next:
    lowerCAmelCase__				,							lowerCAmelCase__     :Optional[int]											=				fast.next.next, slow.next

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

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

  return True




def 					__A  (_SCREAMING_SNAKE_CASE     )   ->Optional[Any]:





  """simple docstring"""


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

import random




def    lowerCAmelCase_  (		lowercase:				int	,       lowercase:				float	,       lowercase:				bool = False		)     ->					dict:







 '''simple docstring'''
 _UpperCamelCase:  dict    						=			{i: [] for i in range(lowercase		)}

 # if probability is greater or equal than 1, then generate a complete graph
 if probability >= 1:
  return complete_graph(lowercase		)
 # if probability is lower or equal than 0, then return a graph without edges
 if probability <= 0:
  return graph

 # for each couple of nodes, add an edge from u to v
 # if the number randomly generated is greater than probability probability
 for i in range(lowercase		):
  for j in range(i + 1	,       lowercase		):
   if random.random() < probability:
    graph[i].append(lowercase		)
    if not directed:
     # if the graph is undirected, add an edge in from j to i, either
     graph[j].append(lowercase		)
 return graph




def    lowerCAmelCase_  (		lowercase:				int		)     ->					dict:







 '''simple docstring'''
 return {
     i: [j for j in range(lowercase		) if i != j] for i in range(lowercase		)
 }


if __name__ == "__main__":
  import doctest

  doctest.testmod()