

class      lowerCamelCase_      :




	def __init__(     self						:     Dict					,      __A						:     int					,      __A						:     Tuple					,      __A						:     List[Any]							):
		__A :			Optional[int]		    =			None
		__A :			Any		    =			None
		__A :			int		    =			graph

		self._normalize_graph(__A					,      __A							)
		__A :			str		    =			len(__A							)
		__A :			Optional[int]		    =			None




	def        lowerCAmelCase_       (     self						:     int					,      __A						:     Any					,      __A						:     Optional[Any]							):
		if sources is int:
			__A :			Dict		    =			[sources]
		if sinks is int:
			__A :			Optional[int]		    =			[sinks]

		if len(__A							) == 0 or len(__A							) == 0:
			return

		__A :			str		    =			sources[0]
		__A :			Dict		    =			sinks[0]

		# make fake vertex if there are more
		# than one source or sink
		if len(__A							) > 1 or len(__A							) > 1:
			__A :			Optional[Any]		    =			0
			for i in sources:
				max_input_flow += sum(self.graph[i]							)

			__A :			List[Any]		    =			len(self.graph							) + 1
			for room in self.graph:
				room.insert(0					,      0							)
			self.graph.insert(0					,      [0] * size							)
			for i in sources:
				__A :			str		    =			max_input_flow
			__A :			Union[str, Any]		    =			0

			__A :			Any		    =			len(self.graph							) + 1
			for room in self.graph:
				room.append(0							)
			self.graph.append([0] * size							)
			for i in sinks:
				__A :			int		    =			max_input_flow
			__A :			Optional[Any]		    =			size - 1




	def        lowerCAmelCase_       (     self						:     Optional[Any]							):
		if self.maximum_flow_algorithm is None:
			raise Exception("""You need to set maximum flow algorithm before."""							)
		if self.source_index is None or self.sink_index is None:
			return 0

		self.maximum_flow_algorithm.execute()
		return self.maximum_flow_algorithm.getMaximumFlow()




	def        lowerCAmelCase_       (     self						:     Optional[Any]					,      __A						:     Dict							):
		__A :			Dict		    =			algorithm(self							)






class      lowerCamelCase_      :




	def __init__(     self						:     Union[str, Any]					,      __A						:     str							):
		__A :			Any		    =			flow_network
		__A :			int		    =			flow_network.verticesCount
		__A :			List[Any]		    =			flow_network.sourceIndex
		__A :			Union[str, Any]		    =			flow_network.sinkIndex
		# it's just a reference, so you shouldn't change
		# it in your algorithms, use deep copy before doing that
		__A :			Optional[int]		    =			flow_network.graph
		__A :			str		    =			False




	def        lowerCAmelCase_       (     self						:     List[Any]							):
		if not self.executed:
			self._algorithm()
			__A :			Any		    =			True




	def        lowerCAmelCase_       (     self						:     List[str]							):
		pass






class      lowerCamelCase_      (	_lowercase	):




	def __init__(     self						:     Any					,      __A						:     List[str]							):
		super().__init__(__A							)
		# use this to save your result
		__A :			str		    =			-1




	def        lowerCAmelCase_       (     self						:     Any							):
		if not self.executed:
			raise Exception("""You should execute algorithm before using its result!"""							)

		return self.maximum_flow






class      lowerCamelCase_      (	_lowercase	):




	def __init__(     self						:     List[Any]					,      __A						:     Dict							):
		super().__init__(__A							)

		__A :			Tuple		    =			[[0] * self.verticies_count for i in range(self.verticies_count							)]

		__A :			Optional[Any]		    =			[0] * self.verticies_count
		__A :			Union[str, Any]		    =			[0] * self.verticies_count




	def        lowerCAmelCase_       (     self						:     int							):
		__A :			Optional[int]		    =			self.verticies_count

		# push some substance to graph
		for nextvertex_index, bandwidth in enumerate(self.graph[self.source_index]							):
			self.preflow[self.source_index][nextvertex_index] += bandwidth
			self.preflow[nextvertex_index][self.source_index] -= bandwidth
			self.excesses[nextvertex_index] += bandwidth

		# Relabel-to-front selection rule
		__A :			List[str]		    =			[
		    i
		    for i in range(self.verticies_count							)
		    if i != self.source_index and i != self.sink_index
		]

		# move through list
		__A :			Dict		    =			0
		while i < len(__A							):
			__A :			List[Any]		    =			vertices_list[i]
			__A :			Optional[Any]		    =			self.heights[vertex_index]
			self.process_vertex(__A							)
			if self.heights[vertex_index] > previous_height:
				# if it was relabeled, swap elements
				# and start from 0 index
				vertices_list.insert(0					,      vertices_list.pop(__A							)							)
				__A :			Any		    =			0
			else:
				i += 1

		__A :			Optional[int]		    =			sum(self.preflow[self.source_index]							)




	def        lowerCAmelCase_       (     self						:     Optional[Any]					,      __A						:     str							):
		while self.excesses[vertex_index] > 0:
			for neighbour_index in range(self.verticies_count							):
				# if it's neighbour and current vertex is higher
				if (
				    self.graph[vertex_index][neighbour_index]
				    - self.preflow[vertex_index][neighbour_index]
				    > 0
				    and self.heights[vertex_index] > self.heights[neighbour_index]
				):
					self.push(__A					,      __A							)

			self.relabel(__A							)




	def        lowerCAmelCase_       (     self						:     Dict					,      __A						:     List[str]					,      __A						:     Optional[Any]							):
		__A :			Union[str, Any]		    =			min(
		    self.excesses[from_index]					,      self.graph[from_index][to_index] - self.preflow[from_index][to_index]					,      )
		self.preflow[from_index][to_index] += preflow_delta
		self.preflow[to_index][from_index] -= preflow_delta
		self.excesses[from_index] -= preflow_delta
		self.excesses[to_index] += preflow_delta




	def        lowerCAmelCase_       (     self						:     Optional[Any]					,      __A						:     Tuple							):
		__A :			Tuple		    =			None
		for to_index in range(self.verticies_count							):
			if (
			    self.graph[vertex_index][to_index]
			    - self.preflow[vertex_index][to_index]
			    > 0
			) and (min_height is None or self.heights[to_index] < min_height):
				__A :			Dict		    =			self.heights[to_index]

		if min_height is not None:
			__A :			Optional[int]		    =			min_height + 1


if __name__ == "__main__":
			UpperCAmelCase_							:					Union[str, Any]		 =   [0]
			UpperCAmelCase_							:					Dict		 =   [3]
			# graph = [
			#     [0, 0, 4, 6, 0, 0],
			#     [0, 0, 5, 2, 0, 0],
			#     [0, 0, 0, 0, 4, 4],
			#     [0, 0, 0, 0, 6, 6],
			#     [0, 0, 0, 0, 0, 0],
			#     [0, 0, 0, 0, 0, 0],
			# ]
			UpperCAmelCase_							:					int		 =   [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

			# prepare our network
			UpperCAmelCase_							:					str		 =   FlowNetwork(graph, entrances, exits)
			# set algorithm
			flow_network.set_maximum_flow_algorithm(PushRelabelExecutor)
			# and calculate
			UpperCAmelCase_							:					int		 =   flow_network.find_maximum_flow()

			print(f"""maximum flow is {maximum_flow}""")













'''simple docstring'''



from typing import Dict, List, Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import (
    center_crop,
    get_resize_output_image_size,
    normalize,
    rescale,
    resize,
    to_channel_dimension_format,
)
from ...image_utils import (
    IMAGENET_STANDARD_MEAN,
    IMAGENET_STANDARD_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    is_valid_image,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


if is_vision_available():
      import PIL


SCREAMING_SNAKE_CASE							=						logging.get_logger(__name__)


def 				lowercase_					(     __A			:							Tuple      )							->   List[List[ImageInput]]:



 """simple docstring"""




 if isinstance(__A       ,   (list, tuple)      ) and isinstance(videos[0]       ,   (list, tuple)      ) and is_valid_image(videos[0][0]      ):
  return videos

 elif isinstance(__A       ,   (list, tuple)      ) and is_valid_image(videos[0]      ):
  return [videos]

 elif is_valid_image(__A      ):
  return [[videos]]

 raise ValueError(F'Could not make batched video from {videos}'      )





class UpperCAmelCase_       (     __A					):




      """simple docstring"""




      UpperCamelCase_             =      ['''pixel_values''']






      def __init__(			self      :		List[Any]  ,   UpperCAmelCase      :		bool = True  ,   UpperCAmelCase      :		Dict[str, int] = None  ,   UpperCAmelCase      :		PILImageResampling = PILImageResampling.BILINEAR  ,   UpperCAmelCase      :		bool = True  ,   UpperCAmelCase      :		Dict[str, int] = None  ,   UpperCAmelCase      :		bool = True  ,   UpperCAmelCase      :		Union[int, float] = 1 / 255  ,   UpperCAmelCase      :		bool = True  ,   UpperCAmelCase      :		Optional[Union[float, List[float]]] = None  ,   UpperCAmelCase      :		Optional[Union[float, List[float]]] = None  ,   **UpperCAmelCase      :		Tuple  ,   )	->	None:


       '''simple docstring'''

       super().__init__(**UpperCAmelCase		)
       lowercase       : Tuple						=size if size is not None else {'''shortest_edge''': 224}
       lowercase       : str						=get_size_dict(UpperCAmelCase  ,   default_to_square=UpperCAmelCase		)
       lowercase       : List[str]						=crop_size if crop_size is not None else {'''height''': 224, '''width''': 224}
       lowercase       : List[Any]						=get_size_dict(UpperCAmelCase  ,   param_name='''crop_size'''		)

       lowercase       : Tuple						=do_resize
       lowercase       : Any						=size
       lowercase       : Optional[Any]						=do_center_crop
       lowercase       : str						=crop_size
       lowercase       : Any						=resample
       lowercase       : List[Any]						=do_rescale
       lowercase       : Dict						=rescale_factor
       lowercase       : List[str]						=do_normalize
       lowercase       : Optional[int]						=image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
       lowercase       : List[Any]						=image_std if image_std is not None else IMAGENET_STANDARD_STD






      def 					A__   (			self      :		Dict  ,   UpperCAmelCase      :		np.ndarray  ,   UpperCAmelCase      :		Dict[str, int]  ,   UpperCAmelCase      :		PILImageResampling = PILImageResampling.BILINEAR  ,   UpperCAmelCase      :		Optional[Union[str, ChannelDimension]] = None  ,   **UpperCAmelCase      :		List[str]  ,   )	->	np.ndarray:


       '''simple docstring'''

       lowercase       : str						=get_size_dict(UpperCAmelCase  ,   default_to_square=UpperCAmelCase		)
       if "shortest_edge" in size:
        lowercase       : int						=get_resize_output_image_size(UpperCAmelCase  ,   size['''shortest_edge''']  ,   default_to_square=UpperCAmelCase		)
       elif "height" in size and "width" in size:
        lowercase       : str						=(size['''height'''], size['''width'''])
       else:
        raise ValueError(f'Size must have \'height\' and \'width\' or \'shortest_edge\' as keys. Got {size.keys()}'		)
       return resize(UpperCAmelCase  ,   size=UpperCAmelCase  ,   resample=UpperCAmelCase  ,   data_format=UpperCAmelCase  ,   **UpperCAmelCase		)






      def 					A__   (			self      :		Any  ,   UpperCAmelCase      :		np.ndarray  ,   UpperCAmelCase      :		Dict[str, int]  ,   UpperCAmelCase      :		Optional[Union[str, ChannelDimension]] = None  ,   **UpperCAmelCase      :		Optional[Any]  ,   )	->	np.ndarray:


       '''simple docstring'''

       lowercase       : List[str]						=get_size_dict(UpperCAmelCase		)
       if "height" not in size or "width" not in size:
        raise ValueError(f'Size must have \'height\' and \'width\' as keys. Got {size.keys()}'		)
       return center_crop(UpperCAmelCase  ,   size=(size['''height'''], size['''width'''])  ,   data_format=UpperCAmelCase  ,   **UpperCAmelCase		)






      def 					A__   (			self      :		int  ,   UpperCAmelCase      :		np.ndarray  ,   UpperCAmelCase      :		Union[int, float]  ,   UpperCAmelCase      :		Optional[Union[str, ChannelDimension]] = None  ,   **UpperCAmelCase      :		Tuple  ,   )	->	List[Any]:


       '''simple docstring'''

       return rescale(UpperCAmelCase  ,   scale=UpperCAmelCase  ,   data_format=UpperCAmelCase  ,   **UpperCAmelCase		)






      def 					A__   (			self      :		Any  ,   UpperCAmelCase      :		np.ndarray  ,   UpperCAmelCase      :		Union[float, List[float]]  ,   UpperCAmelCase      :		Union[float, List[float]]  ,   UpperCAmelCase      :		Optional[Union[str, ChannelDimension]] = None  ,   **UpperCAmelCase      :		int  ,   )	->	np.ndarray:


       '''simple docstring'''

       return normalize(UpperCAmelCase  ,   mean=UpperCAmelCase  ,   std=UpperCAmelCase  ,   data_format=UpperCAmelCase  ,   **UpperCAmelCase		)






      def 					A__   (			self      :		int  ,   UpperCAmelCase      :		ImageInput  ,   UpperCAmelCase      :		bool = None  ,   UpperCAmelCase      :		Dict[str, int] = None  ,   UpperCAmelCase      :		PILImageResampling = None  ,   UpperCAmelCase      :		bool = None  ,   UpperCAmelCase      :		Dict[str, int] = None  ,   UpperCAmelCase      :		bool = None  ,   UpperCAmelCase      :		float = None  ,   UpperCAmelCase      :		bool = None  ,   UpperCAmelCase      :		Optional[Union[float, List[float]]] = None  ,   UpperCAmelCase      :		Optional[Union[float, List[float]]] = None  ,   UpperCAmelCase      :		Optional[ChannelDimension] = ChannelDimension.FIRST  ,   )	->	np.ndarray:


       '''simple docstring'''

       if do_resize and size is None or resample is None:
        raise ValueError('''Size and resample must be specified if do_resize is True.'''		)

       if do_center_crop and crop_size is None:
        raise ValueError('''Crop size must be specified if do_center_crop is True.'''		)

       if do_rescale and rescale_factor is None:
        raise ValueError('''Rescale factor must be specified if do_rescale is True.'''		)

       if do_normalize and (image_mean is None or image_std is None):
        raise ValueError('''Image mean and std must be specified if do_normalize is True.'''		)

       # All transformations expect numpy arrays.
       lowercase       : Dict						=to_numpy_array(UpperCAmelCase		)

       if do_resize:
        lowercase       : Union[str, Any]						=self.resize(image=UpperCAmelCase  ,   size=UpperCAmelCase  ,   resample=UpperCAmelCase		)

       if do_center_crop:
        lowercase       : Optional[Any]						=self.center_crop(UpperCAmelCase  ,   size=UpperCAmelCase		)

       if do_rescale:
        lowercase       : Dict						=self.rescale(image=UpperCAmelCase  ,   scale=UpperCAmelCase		)

       if do_normalize:
        lowercase       : int						=self.normalize(image=UpperCAmelCase  ,   mean=UpperCAmelCase  ,   std=UpperCAmelCase		)

       lowercase       : Optional[Any]						=to_channel_dimension_format(UpperCAmelCase  ,   UpperCAmelCase		)
       return image






      def 					A__   (			self      :		List[str]  ,   UpperCAmelCase      :		ImageInput  ,   UpperCAmelCase      :		bool = None  ,   UpperCAmelCase      :		Dict[str, int] = None  ,   UpperCAmelCase      :		PILImageResampling = None  ,   UpperCAmelCase      :		bool = None  ,   UpperCAmelCase      :		Dict[str, int] = None  ,   UpperCAmelCase      :		bool = None  ,   UpperCAmelCase      :		float = None  ,   UpperCAmelCase      :		bool = None  ,   UpperCAmelCase      :		Optional[Union[float, List[float]]] = None  ,   UpperCAmelCase      :		Optional[Union[float, List[float]]] = None  ,   UpperCAmelCase      :		Optional[Union[str, TensorType]] = None  ,   UpperCAmelCase      :		ChannelDimension = ChannelDimension.FIRST  ,   **UpperCAmelCase      :		Optional[int]  ,   )	->	PIL.Image.Image:


       '''simple docstring'''

       lowercase       : Any						=do_resize if do_resize is not None else self.do_resize
       lowercase       : Union[str, Any]						=resample if resample is not None else self.resample
       lowercase       : Tuple						=do_center_crop if do_center_crop is not None else self.do_center_crop
       lowercase       : List[Any]						=do_rescale if do_rescale is not None else self.do_rescale
       lowercase       : str						=rescale_factor if rescale_factor is not None else self.rescale_factor
       lowercase       : List[str]						=do_normalize if do_normalize is not None else self.do_normalize
       lowercase       : List[str]						=image_mean if image_mean is not None else self.image_mean
       lowercase       : Optional[int]						=image_std if image_std is not None else self.image_std

       lowercase       : Optional[Any]						=size if size is not None else self.size
       lowercase       : Any						=get_size_dict(UpperCAmelCase  ,   default_to_square=UpperCAmelCase		)
       lowercase       : Union[str, Any]						=crop_size if crop_size is not None else self.crop_size
       lowercase       : Optional[int]						=get_size_dict(UpperCAmelCase  ,   param_name='''crop_size'''		)

       if not valid_images(UpperCAmelCase		):
        raise ValueError(
            '''Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, '''
            '''torch.Tensor, tf.Tensor or jax.ndarray.'''		)

       lowercase       : List[str]						=make_batched(UpperCAmelCase		)

       lowercase       : Union[str, Any]						=[
           [
               self._preprocess_image(
                   image=UpperCAmelCase  ,   do_resize=UpperCAmelCase  ,   size=UpperCAmelCase  ,   resample=UpperCAmelCase  ,   do_center_crop=UpperCAmelCase  ,   crop_size=UpperCAmelCase  ,   do_rescale=UpperCAmelCase  ,   rescale_factor=UpperCAmelCase  ,   do_normalize=UpperCAmelCase  ,   image_mean=UpperCAmelCase  ,   image_std=UpperCAmelCase  ,   data_format=UpperCAmelCase  ,   )
               for img in video
           ]
           for video in videos
       ]

       lowercase       : Dict						={'''pixel_values''': videos}
       return BatchFeature(data=UpperCAmelCase  ,   tensor_type=UpperCAmelCase		)



