






"""simple docstring"""





from functools import partial
from typing import Any, Callable, Dict, List, Type, TypeVar, Union, overload

import torch
import torch.nn as nn
import torch.types






def 							A(    snake_case_		,  snake_case_		,  snake_case_						):
       """simple docstring"""





       if not inplace:
              lowercase__:							Optional[int]         =     ma + ma
       else:
              ma += ma

       return ma






def 							A(    snake_case_		,  snake_case_						):
       """simple docstring"""





       lowercase__:							str         =     -1 * len(snake_case_						)
       lowercase__:							int         =     list(range(len(tensor.shape[:zero_index]						)						)						)
       return tensor.permute(first_inds + [zero_index + i for i in inds]						)






def 							A(    snake_case_		,  snake_case_						):
       """simple docstring"""





       return t.reshape(t.shape[:-no_dims] + (-1,)						)






def 							A(    snake_case_		,  snake_case_		,  snake_case_		,  snake_case_ = 1E-4						):
       """simple docstring"""





       lowercase__:							List[Any]         =     mask.expand(*value.shape						)
       return torch.sum(mask * value		,  dim=snake_case_						) / (eps + torch.sum(snake_case_		,  dim=snake_case_						))






def 							A(    snake_case_		,  snake_case_ = 2.31_25		,  snake_case_ = 21.68_75		,  snake_case_ = 64						):
       """simple docstring"""





       lowercase__:							Tuple         =     torch.linspace(snake_case_		,  snake_case_		,  no_bins - 1		,  device=pts.device						)
       lowercase__:							Dict         =     torch.sqrt(torch.sum((pts.unsqueeze(-2						) - pts.unsqueeze(-3						)) ** 2		,  dim=-1						)						)
       return torch.bucketize(snake_case_		,  snake_case_						)






def 							A(    snake_case_		,  snake_case_						):
       """simple docstring"""





       lowercase__:							Optional[Any]         =     dicts[0]
       lowercase__:							Optional[int]         =     {}
       for k, v in first.items():
              lowercase__:							Optional[int]         =     [d[k] for d in dicts]
              if isinstance(snake_case_		,  snake_case_						):
                     lowercase__:							Optional[Any]         =     dict_multimap(snake_case_		,  snake_case_						)
              else:
                     lowercase__:							List[str]         =     fn(snake_case_						)

       return new_dict






def 							A(    snake_case_		,  snake_case_						):
       """simple docstring"""





       lowercase__:							Optional[Any]         =     v_bins.view(((1,) * len(x.shape						)) + (len(snake_case_						),)						)
       lowercase__:							List[str]         =     x[..., None] - reshaped_bins
       lowercase__:							Optional[int]         =     torch.argmin(torch.abs(snake_case_						)		,  dim=-1						)
       return nn.functional.one_hot(snake_case_		,  num_classes=len(snake_case_						)						).float()






def 							A(    snake_case_		,  snake_case_		,  snake_case_ = 0		,  snake_case_ = 0						):
       """simple docstring"""





       lowercase__:							List[Union[slice, torch.Tensor]]         =     []
       for i, s in enumerate(data.shape[:no_batch_dims]						):
              lowercase__:							Optional[Any]         =     torch.arange(snake_case_						)
              lowercase__:							Any         =     r.view(*(*((1,) * i), -1, *((1,) * (len(inds.shape						) - i - 1)))						)
              ranges.append(snake_case_						)

       lowercase__:							List[Union[slice, torch.Tensor]]         =     [slice(snake_case_						) for _ in range(len(data.shape						) - no_batch_dims						)]
       lowercase__:							Dict         =     inds
       ranges.extend(snake_case_						)
       # Matt note: Editing this to get around the behaviour of using a list as an array index changing
       # in recent Numpy versions
       return data[tuple(snake_case_						)]


UpperCamelCase					=     TypeVar("""T""")






def 							A(    snake_case_		,  snake_case_		,  snake_case_						):
       """simple docstring"""





       lowercase__:							Dict[Any, Union[dict, list, tuple, Any]]         =     {}
       for k, v in dic.items():
              if isinstance(snake_case_		,  snake_case_						):
                     lowercase__:							Optional[Any]         =     dict_map(snake_case_		,  snake_case_		,  snake_case_						)
              else:
                     lowercase__:							Union[str, Any]         =     tree_map(snake_case_		,  snake_case_		,  snake_case_						)

       return new_dict






@overload
def 							A(    snake_case_		,  snake_case_		,  snake_case_						):
       """simple docstring"""





       ...






@overload
def 							A(    snake_case_		,  snake_case_		,  snake_case_						):
       """simple docstring"""





       ...






@overload
def 							A(    snake_case_		,  snake_case_		,  snake_case_						):
       """simple docstring"""





       ...






@overload
def 							A(    snake_case_		,  snake_case_		,  snake_case_						):
       """simple docstring"""





       ...






def 							A(    snake_case_		,  snake_case_		,  snake_case_						):
       """simple docstring"""





       if isinstance(snake_case_		,  snake_case_						):
              return dict_map(snake_case_		,  snake_case_		,  snake_case_						)
       elif isinstance(snake_case_		,  snake_case_						):
              return [tree_map(snake_case_		,  snake_case_		,  snake_case_						) for x in tree]
       elif isinstance(snake_case_		,  snake_case_						):
              return tuple(tree_map(snake_case_		,  snake_case_		,  snake_case_						) for x in tree						)
       elif isinstance(snake_case_		,  snake_case_						):
              return fn(snake_case_						)
       else:
              print(type(snake_case_						)						)
              raise ValueError("Not supported"						)







UpperCamelCase					=     partial(tree_map, leaf_type=torch.Tensor)














"""simple docstring"""





UpperCamelCase					=     float("""inf""")







class 						_a  :





   '''simple docstring'''






   def __init__(       self					, UpperCAmelCase_)			->   List[str]:




          '''simple docstring'''




          lowercase__:							Optional[Any]         =     [0] * n
          lowercase__:							Dict         =     [0] * n
          lowercase__:							List[Any]         =     [0] * n
          lowercase__:							str         =     [[] for _ in range(UpperCAmelCase_)]





   def __lowercase							(       self					, UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_=0)			->   Optional[int]:




          '''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 __lowercase							(       self					, UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_)			->   Union[str, Any]:




          '''simple docstring'''




          if vertex == sink or not flow:
                 return flow

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





   def __lowercase							(       self					, UpperCAmelCase_					, UpperCAmelCase_)			->   str:




          '''simple docstring'''




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

                        lowercase__:							List[str]         =     self.depth_first_search(UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_)
                        while p:
                               flow += p
                               lowercase__:							Any         =     self.depth_first_search(UpperCAmelCase_					, UpperCAmelCase_					, UpperCAmelCase_)

                        if not self.lvl[sink]:
                               break

          return flow
UpperCamelCase					=     Dinic(10)
UpperCamelCase					=     0
UpperCamelCase					=     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))






