
'''simple docstring'''
class 			SCREAMING_SNAKE_CASE__      :







				def __init__(       self						,				A_						,				A_						,				A_     )->		Any:







											'''simple docstring'''






											UpperCamelCase   			=     None
											UpperCamelCase   			=     None
											UpperCamelCase   			=     graph

											self._normalize_graph(A_						,				A_     )
											UpperCamelCase   			=     len(A_     )
											UpperCamelCase   			=     None







				def 						UpperCAmelCase_    (       self						,				A_						,				A_     )->		Tuple:







											'''simple docstring'''






											if sources is int:
																		UpperCamelCase   			=     [sources]
											if sinks is int:
																		UpperCamelCase   			=     [sinks]

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

											UpperCamelCase   			=     sources[0]
											UpperCamelCase   			=     sinks[0]

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

																		UpperCamelCase   			=     len(self.graph     ) + 1
																		for room in self.graph:
																									room.insert(0						,				0     )
																		self.graph.insert(0						,				[0] * size     )
																		for i in sources:
																									UpperCamelCase   			=     max_input_flow
																		UpperCamelCase   			=     0

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







				def 						UpperCAmelCase_    (       self     )->		Optional[Any]:







											'''simple docstring'''






											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 						UpperCAmelCase_    (       self						,				A_     )->		Any:







											'''simple docstring'''






											UpperCamelCase   			=     algorithm(self     )


class 			SCREAMING_SNAKE_CASE__      :







				def __init__(       self						,				A_     )->		Dict:







											'''simple docstring'''






											UpperCamelCase   			=     flow_network
											UpperCamelCase   			=     flow_network.verticesCount
											UpperCamelCase   			=     flow_network.sourceIndex
											UpperCamelCase   			=     flow_network.sinkIndex
											# it's just a reference, so you shouldn't change
											# it in your algorithms, use deep copy before doing that
											UpperCamelCase   			=     flow_network.graph
											UpperCamelCase   			=     False







				def 						UpperCAmelCase_    (       self     )->		Dict:







											'''simple docstring'''






											if not self.executed:
																		self._algorithm()
																		UpperCamelCase   			=     True







				def 						UpperCAmelCase_    (       self     )->		Dict:







											'''simple docstring'''






											pass


class 			SCREAMING_SNAKE_CASE__      (     snake_case_):







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







											'''simple docstring'''






											super().__init__(A_     )
											# use this to save your result
											UpperCamelCase   			=     -1







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







											'''simple docstring'''






											if not self.executed:
																		raise Exception('You should execute algorithm before using its result!'     )

											return self.maximum_flow


class 			SCREAMING_SNAKE_CASE__      (     snake_case_):







				def __init__(       self						,				A_     )->		Optional[Any]:







											'''simple docstring'''






											super().__init__(A_     )

											UpperCamelCase   			=     [[0] * self.verticies_count for i in range(self.verticies_count     )]

											UpperCamelCase   			=     [0] * self.verticies_count
											UpperCamelCase   			=     [0] * self.verticies_count







				def 						UpperCAmelCase_    (       self     )->		Tuple:







											'''simple docstring'''






											UpperCamelCase   			=     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
											UpperCamelCase   			=     [
											    i
											    for i in range(self.verticies_count     )
											    if i != self.source_index and i != self.sink_index
											]

											# move through list
											UpperCamelCase   			=     0
											while i < len(A_     ):
																		UpperCamelCase   			=     vertices_list[i]
																		UpperCamelCase   			=     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_     )     )
																									UpperCamelCase   			=     0
																		else:
																									i += 1

											UpperCamelCase   			=     sum(self.preflow[self.source_index]     )







				def 						UpperCAmelCase_    (       self						,				A_     )->		Dict:







											'''simple docstring'''






											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 						UpperCAmelCase_    (       self						,				A_						,				A_     )->		str:







											'''simple docstring'''






											UpperCamelCase   			=     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 						UpperCAmelCase_    (       self						,				A_     )->		List[str]:







											'''simple docstring'''






											UpperCamelCase   			=     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):
																									UpperCamelCase   			=     self.heights[to_index]

											if min_height is not None:
																		UpperCamelCase   			=     min_height + 1


if __name__ == "__main__":
						lowerCAmelCase					:    int           = [0]
						lowerCAmelCase					:    Tuple           = [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],
						# ]
						lowerCAmelCase					:    List[str]           = [[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

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

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











from dataclasses import dataclass
from enum import Enum
from typing import List, Optional, Union

import numpy as np
import PIL
from PIL import Image

from ...utils import BaseOutput, is_torch_available, is_transformers_available


@dataclass
class       __lowerCAmelCase					(       _UpperCamelCase      ):


	'''simple docstring'''





	_A													=				42
	_A													=				42


if is_transformers_available() and is_torch_available():
			from .pipeline_semantic_stable_diffusion import SemanticStableDiffusionPipeline


