




__SCREAMING_SNAKE_CASE      :				Optional[int]				      =float("""inf""")






class      A     :
					"""simple docstring"""

					def __init__(      self					:				Optional[Any]		,					A__					:				Any     )			->    List[Any]:
											lowerCamelCase__ 					=			[0] * n
											lowerCamelCase__ 					=			[0] * n
											lowerCamelCase__ 					=			[0] * n
											lowerCamelCase__ 					=			[[] for _ in range(A__     )]




					def 	__snake_case				(      self					:				Union[str, Any]		,					A__					:				Dict		,					A__					:				str		,					A__					:				Any		,					A__					:				Optional[int]=0     )			->    Any:
											self.adj[a].append([b, len(self.adj[b]     ), c, 0]     )
											self.adj[b].append([a, len(self.adj[a]     ) - 1, rcap, 0]     )




					def 	__snake_case				(      self					:				Tuple		,					A__					:				Dict		,					A__					:				Union[str, Any]		,					A__					:				int     )			->    Optional[int]:
											if vertex == sink or not flow:
																	return flow

											for i in range(self.ptr[vertex]		,					len(self.adj[vertex]     )     ):
																	lowerCamelCase__ 					=			self.adj[vertex][i]
																	if self.lvl[e[0]] == self.lvl[vertex] + 1:
																							lowerCamelCase__ 					=			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
																	lowerCamelCase__ 					=			self.ptr[vertex] + 1
											return 0




					def 	__snake_case				(      self					:				List[str]		,					A__					:				int		,					A__					:				Optional[Any]     )			->    Optional[Any]:
											lowerCamelCase__					,						lowerCamelCase__ 					=			0, source
											for l in range(3_1     ):  # noqa: E741  l = 30 maybe faster for random data
																	while True:
																							lowerCamelCase__					,						lowerCamelCase__ 					=			[0] * len(self.q     ), [0] * len(self.q     )
																							lowerCamelCase__					,						lowerCamelCase__					,						lowerCamelCase__ 					=			0, 1, 1
																							while qi < qe and not self.lvl[sink]:
																													lowerCamelCase__ 					=			self.q[qi]
																													qi += 1
																													for e in self.adj[v]:
																																			if not self.lvl[e[0]] and (e[2] - e[3]) >> (3_0 - l):
																																									lowerCamelCase__ 					=			e[0]
																																									qe += 1
																																									lowerCamelCase__ 					=			self.lvl[v] + 1

																							lowerCamelCase__ 					=			self.depth_first_search(A__		,					A__		,					A__     )
																							while p:
																													flow += p
																													lowerCamelCase__ 					=			self.depth_first_search(A__		,					A__		,					A__     )

																							if not self.lvl[sink]:
																													break

											return flow
__SCREAMING_SNAKE_CASE      :				Dict				      =Dinic(10)
__SCREAMING_SNAKE_CASE      :				List[str]				      =0
__SCREAMING_SNAKE_CASE      :				Optional[int]				      =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))





# Lint as: python3
import sys
from collections.abc import Mapping
from typing import TYPE_CHECKING

import numpy as np
import pyarrow as pa

from .. import config
from ..utils.py_utils import map_nested
from .formatting import TensorFormatter


if TYPE_CHECKING:
      import tensorflow as tf






class      A     (						TensorFormatter[Mapping, "tf.Tensor", Mapping]						):
     """simple docstring"""

     def __init__(      self					:				int		,					A__					:				Tuple=None		,					**A__					:				Tuple     )			->    Dict:
           super().__init__(features=A__     )
           lowerCamelCase__ 					=			tf_tensor_kwargs
           import tensorflow as tf  # noqa: import tf at initialization




     def 	__snake_case				(      self					:				List[Any]		,					A__					:				List[str]     )			->    Dict:
           import tensorflow as tf

           if isinstance(A__		,					A__     ) and column:
                 if all(
                     isinstance(A__		,					tf.Tensor     ) and x.shape == column[0].shape and x.dtype == column[0].dtype for x in column     ):
                       return tf.stack(A__     )
                 elif all(
                     isinstance(A__		,					(tf.Tensor, tf.RaggedTensor)     ) and x.ndim == 1 and x.dtype == column[0].dtype
                     for x in column     ):
                       # only rag 1-D tensors, otherwise some dimensions become ragged even though they were consolidated
                       return tf.ragged.stack(A__     )

           return column




     def 	__snake_case				(      self					:				Tuple		,					A__					:				Optional[int]     )			->    int:
           import tensorflow as tf

           if value is None:
                 return value

           lowerCamelCase__ 					=			{}

           if isinstance(A__		,					(np.number, np.ndarray)     ) and np.issubdtype(value.dtype		,					np.integer     ):
                 lowerCamelCase__ 					=			{'dtype': tf.intaa}
           elif isinstance(A__		,					(np.number, np.ndarray)     ) and np.issubdtype(value.dtype		,					np.floating     ):
                 lowerCamelCase__ 					=			{'dtype': tf.floataa}
           elif config.PIL_AVAILABLE and "PIL" in sys.modules:
                 import PIL.Image

                 if isinstance(A__		,					PIL.Image.Image     ):
                       lowerCamelCase__ 					=			np.asarray(A__     )

           return tf.convert_to_tensor(A__		,					**{**default_dtype, **self.tf_tensor_kwargs}     )




     def 	__snake_case				(      self					:				Optional[int]		,					A__					:				Dict     )			->    List[str]:
           import tensorflow as tf

           # support for torch, tf, jax etc.
           if config.TORCH_AVAILABLE and "torch" in sys.modules:
                 import torch

                 if isinstance(A__		,					torch.Tensor     ):
                       return self._tensorize(data_struct.detach().cpu().numpy()[()]     )
           if hasattr(A__		,					'__array__'     ) and not isinstance(A__		,					tf.Tensor     ):
                 lowerCamelCase__ 					=			data_struct.__array__()
           # support for nested types like struct of list of struct
           if isinstance(A__		,					np.ndarray     ):
                 if data_struct.dtype == object:  # tf tensors cannot be instantied from an array of objects
                       return self._consolidate([self.recursive_tensorize(A__     ) for substruct in data_struct]     )
           elif isinstance(A__		,					(list, tuple)     ):
                 return self._consolidate([self.recursive_tensorize(A__     ) for substruct in data_struct]     )
           return self._tensorize(A__     )




     def 	__snake_case				(      self					:				List[Any]		,					A__					:				dict     )			->    List[str]:
           return map_nested(self._recursive_tensorize		,					A__		,					map_list=A__     )




     def 	__snake_case				(      self					:				Union[str, Any]		,					A__					:				pa.Table     )			->    Mapping:
           lowerCamelCase__ 					=			self.numpy_arrow_extractor().extract_row(A__     )
           lowerCamelCase__ 					=			self.python_features_decoder.decode_row(A__     )
           return self.recursive_tensorize(A__     )




     def 	__snake_case				(      self					:				Optional[Any]		,					A__					:				pa.Table     )			->    "tf.Tensor":
           lowerCamelCase__ 					=			self.numpy_arrow_extractor().extract_column(A__     )
           lowerCamelCase__ 					=			self.python_features_decoder.decode_column(A__		,					pa_table.column_names[0]     )
           lowerCamelCase__ 					=			self.recursive_tensorize(A__     )
           lowerCamelCase__ 					=			self._consolidate(A__     )
           return column




     def 	__snake_case				(      self					:				int		,					A__					:				pa.Table     )			->    Mapping:
           lowerCamelCase__ 					=			self.numpy_arrow_extractor().extract_batch(A__     )
           lowerCamelCase__ 					=			self.python_features_decoder.decode_batch(A__     )
           lowerCamelCase__ 					=			self.recursive_tensorize(A__     )
           for column_name in batch:
                 lowerCamelCase__ 					=			self._consolidate(batch[column_name]     )
           return batch