


a				:							List[str]					=			float('inf')

class      lowerCamelCase	:

       def __init__(			self	,						a__					):






        '''simple docstring'''






        snake_case   : Any	  =      [0] * n
        snake_case   : int	  =      [0] * n
        snake_case   : Dict	  =      [0] * n
        snake_case   : Dict	  =      [[] for _ in range(a__					)]

       def 				UpperCAmelCase				(			self	,						a__	,						a__	,						a__	,						a__=0					):






        '''simple docstring'''






        self.adj[a].append([b, len(self.adj[b]					), c, 0]					)
        self.adj[b].append([a, len(self.adj[a]					) - 1, rcap, 0]					)

       def 				UpperCAmelCase				(			self	,						a__	,						a__	,						a__					):






        '''simple docstring'''






        if vertex == sink or not flow:
         return flow

        for i in range(self.ptr[vertex]	,						len(self.adj[vertex]					)					):
         snake_case   : List[Any]	  =      self.adj[vertex][i]
         if self.lvl[e[0]] == self.lvl[vertex] + 1:
          snake_case   : Optional[int]	  =      self.depth_first_search(e[0]	,						a__	,						min(a__	,						e[2] - e[3]					)					)
          if p:
           self.adj[vertex][i][3] += p
           self.adj[e[0]][e[1]][3] -= p
           return p
         snake_case   : int	  =      self.ptr[vertex] + 1
        return 0



       def 				UpperCAmelCase				(			self	,						a__	,						a__					):






        '''simple docstring'''






        snake_case  ,					snake_case   : Optional[Any]	  =      0, source
        for l in range(31					):  # noqa: E741  l = 30 maybe faster for random data
         while True:
          snake_case  ,					snake_case   : Tuple	  =      [0] * len(self.q					), [0] * len(self.q					)
          snake_case  ,					snake_case  ,					snake_case   : Optional[Any]	  =      0, 1, 1
          while qi < qe and not self.lvl[sink]:
           snake_case   : List[Any]	  =      self.q[qi]
           qi += 1
           for e in self.adj[v]:
            if not self.lvl[e[0]] and (e[2] - e[3]) >> (30 - l):
             snake_case   : Tuple	  =      e[0]
             qe += 1
             snake_case   : Dict	  =      self.lvl[v] + 1

          snake_case   : Optional[Any]	  =      self.depth_first_search(a__	,						a__	,						a__					)
          while p:
           flow += p
           snake_case   : List[Any]	  =      self.depth_first_search(a__	,						a__	,						a__					)

          if not self.lvl[sink]:
           break

        return flow
a				:							Optional[Any]					=			Dinic(10)
a				:							Optional[Any]					=			0
a				:							Union[str, Any]					=			9
for vertex in range(1, 5):
  graph.add_edge(source, vertex, 1)
for vertex in range(5, 9):
  graph.add_edge(vertex, sink, 1)
for vertex in range(1, 5):
  graph.add_edge(vertex, vertex + 4, 1)

# Now we can know that is the maximum flow(source -> sink)
print(graph.max_flow(source, sink))










from typing import List, Optional, Tuple, Union

from . import logging
from .import_utils import is_torch_available, is_torch_version


if is_torch_available():
  import torch

a				:							Union[str, Any]					=			logging.get_logger(__name__)  # pylint: disable=invalid-name

try:
  from torch._dynamo import allow_in_graph as maybe_allow_in_graph
except (ImportError, ModuleNotFoundError):






  def    _UpperCAmelCase	(   cls       )		->str:


   '''simple docstring'''
   return cls






def    _UpperCAmelCase	(   __lowerCamelCase ,     __lowerCamelCase = None ,     __lowerCamelCase = None ,     __lowerCamelCase = None ,     __lowerCamelCase = None ,     )		->Union[str, Any]:


 '''simple docstring'''
 snake_case   : Union[str, Any]	  =      device
 snake_case   : Any	  =      shape[0]

 snake_case   : Any	  =      layout or torch.strided
 snake_case   : Union[str, Any]	  =      device or torch.device('''cpu'''       )

 if generator is not None:
  snake_case   : Any	  =      generator.device.type if not isinstance(__lowerCamelCase ,     __lowerCamelCase       ) else generator[0].device.type
  if gen_device_type != device.type and gen_device_type == "cpu":
   snake_case   : Optional[int]	  =      '''cpu'''
   if device != "mps":
    logger.info(
        f'''The passed generator was created on \'cpu\' even though a tensor on {device} was expected.'''
        f''' Tensors will be created on \'cpu\' and then moved to {device}. Note that one can probably'''
        f''' slighly speed up this function by passing a generator that was created on the {device} device.'''       )
  elif gen_device_type != device.type and gen_device_type == "cuda":
   raise ValueError(f'''Cannot generate a {device} tensor from a generator of type {gen_device_type}.'''       )

 if isinstance(__lowerCamelCase ,     __lowerCamelCase       ):
  snake_case   : Tuple	  =      (1,) + shape[1:]
  snake_case   : List[Any]	  =      [
      torch.randn(__lowerCamelCase ,     generator=generator[i] ,     device=__lowerCamelCase ,     dtype=__lowerCamelCase ,     layout=__lowerCamelCase       )
      for i in range(__lowerCamelCase       )
  ]
  snake_case   : int	  =      torch.cat(__lowerCamelCase ,     dim=0       ).to(__lowerCamelCase       )
 else:
  snake_case   : Union[str, Any]	  =      torch.randn(__lowerCamelCase ,     generator=__lowerCamelCase ,     device=__lowerCamelCase ,     dtype=__lowerCamelCase ,     layout=__lowerCamelCase       ).to(__lowerCamelCase       )

 return latents






def    _UpperCAmelCase	(   __lowerCamelCase       )		->Tuple:


 '''simple docstring'''
 if is_torch_version('''<''' ,     '''2.0.0'''       ) or not hasattr(__lowerCamelCase ,     '''_dynamo'''       ):
  return False
 return isinstance(__lowerCamelCase ,     torch._dynamo.eval_frame.OptimizedModule       )






