



'''simple docstring'''
import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput






def A__   (					UpperCAmelCase_  ,  UpperCAmelCase_=0.999  ,  UpperCAmelCase_="cosine"  ,  ):
						if alpha_transform_type == "cosine":

												def alpha_bar_fn(UpperCAmelCase_							):
																		return math.cos((t + 0.008) / 1.008 * math.pi / 2							) ** 2

						elif alpha_transform_type == "exp":

												def alpha_bar_fn(UpperCAmelCase_							):
																		return math.exp(t * -12.0							)

						else:
												raise ValueError(f'Unsupported alpha_tranform_type: {alpha_transform_type}'							)

						_UpperCamelCase :		Optional[int]			    =       []
						for i in range(UpperCAmelCase_							):
												_UpperCamelCase :		Dict			    =       i / num_diffusion_timesteps
												_UpperCamelCase :		Tuple			    =       (i + 1) / num_diffusion_timesteps
												betas.append(min(1 - alpha_bar_fn(UpperCAmelCase_							) / alpha_bar_fn(UpperCAmelCase_							)  ,  UpperCAmelCase_							)							)
						return torch.tensor(UpperCAmelCase_  ,  dtype=torch.floataa							)






class 							lowercase__     (							lowercase						, lowercase       ):
	lowercase__      =      [e.name for e in KarrasDiffusionSchedulers]
	lowercase__      =      2





	@register_to_config
	def __init__(			self :    Union[str, Any]			,lowerCamelCase__ :    int = 1000			,lowerCamelCase__ :    float = 0.0_0_0_8_5			,lowerCamelCase__ :    float = 0.0_1_2			,lowerCamelCase__ :    str = "linear"			,lowerCamelCase__ :    Optional[Union[np.ndarray, List[float]]] = None			,lowerCamelCase__ :    str = "epsilon"			,lowerCamelCase__ :    Optional[bool] = False			,lowerCamelCase__ :    Optional[bool] = False			,lowerCamelCase__ :    float = 1.0			,lowerCamelCase__ :    str = "linspace"			,lowerCamelCase__ :    int = 0			,):







							'''simple docstring'''
							if trained_betas is not None:
													_UpperCamelCase :		Dict			    =       torch.tensor(lowerCamelCase__			,dtype=torch.floataa			)
							elif beta_schedule == "linear":
													_UpperCamelCase :		List[Any]			    =       torch.linspace(lowerCamelCase__			,lowerCamelCase__			,lowerCamelCase__			,dtype=torch.floataa			)
							elif beta_schedule == "scaled_linear":
													# this schedule is very specific to the latent diffusion model.
													_UpperCamelCase :		Union[str, Any]			    =       (
													    torch.linspace(beta_start**0.5			,beta_end**0.5			,lowerCamelCase__			,dtype=torch.floataa			) ** 2
													)
							elif beta_schedule == "squaredcos_cap_v2":
													# Glide cosine schedule
													_UpperCamelCase :		List[str]			    =       betas_for_alpha_bar(lowerCamelCase__			,alpha_transform_type='cosine'			)
							elif beta_schedule == "exp":
													_UpperCamelCase :		Union[str, Any]			    =       betas_for_alpha_bar(lowerCamelCase__			,alpha_transform_type='exp'			)
							else:
													raise NotImplementedError(F'{beta_schedule} does is not implemented for {self.__class__}'			)

							_UpperCamelCase :		Dict			    =       1.0 - self.betas
							_UpperCamelCase :		List[Any]			    =       torch.cumprod(self.alphas			,dim=0			)

							#  set all values
							self.set_timesteps(lowerCamelCase__			,lowerCamelCase__			,lowerCamelCase__			)
							_UpperCamelCase :		Any			    =       use_karras_sigmas





	def      UpperCamelCase_  (			self :    Any			,lowerCamelCase__ :    List[str]			,lowerCamelCase__ :    List[Any]=None			):







							'''simple docstring'''
							if schedule_timesteps is None:
													_UpperCamelCase :		Union[str, Any]			    =       self.timesteps

							_UpperCamelCase :		str			    =       (schedule_timesteps == timestep).nonzero()

							# The sigma index that is taken for the **very** first `step`
							# is always the second index (or the last index if there is only 1)
							# This way we can ensure we don't accidentally skip a sigma in
							# case we start in the middle of the denoising schedule (e.g. for image-to-image)
							if len(self._index_counter			) == 0:
													_UpperCamelCase :		int			    =       1 if len(lowerCamelCase__			) > 1 else 0
							else:
													_UpperCamelCase :		List[str]			    =       timestep.cpu().item() if torch.is_tensor(lowerCamelCase__			) else timestep
													_UpperCamelCase :		Optional[Any]			    =       self._index_counter[timestep_int]

							return indices[pos].item()





	@property
	def      UpperCamelCase_  (			self :    Dict			):







							'''simple docstring'''
							# standard deviation of the initial noise distribution
							if self.config.timestep_spacing in ["linspace", "trailing"]:
													return self.sigmas.max()

							return (self.sigmas.max() ** 2 + 1) ** 0.5





	def      UpperCamelCase_  (			self :    Optional[int]			,lowerCamelCase__ :    torch.FloatTensor			,lowerCamelCase__ :    Union[float, torch.FloatTensor]			,):







							'''simple docstring'''
							_UpperCamelCase :		List[str]			    =       self.index_for_timestep(lowerCamelCase__			)

							_UpperCamelCase :		Optional[Any]			    =       self.sigmas[step_index]
							_UpperCamelCase :		List[str]			    =       sample / ((sigma**2 + 1) ** 0.5)
							return sample





	def      UpperCamelCase_  (			self :    str			,lowerCamelCase__ :    int			,lowerCamelCase__ :    Union[str, torch.device] = None			,lowerCamelCase__ :    Optional[int] = None			,):







							'''simple docstring'''
							_UpperCamelCase :		Tuple			    =       num_inference_steps

							_UpperCamelCase :		List[str]			    =       num_train_timesteps or self.config.num_train_timesteps

							# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
							if self.config.timestep_spacing == "linspace":
													_UpperCamelCase :		Any			    =       np.linspace(0			,num_train_timesteps - 1			,lowerCamelCase__			,dtype=lowerCamelCase__			)[::-1].copy()
							elif self.config.timestep_spacing == "leading":
													_UpperCamelCase :		List[Any]			    =       num_train_timesteps // self.num_inference_steps
													# creates integer timesteps by multiplying by ratio
													# casting to int to avoid issues when num_inference_step is power of 3
													_UpperCamelCase :		Dict			    =       (np.arange(0			,lowerCamelCase__			) * step_ratio).round()[::-1].copy().astype(lowerCamelCase__			)
													timesteps += self.config.steps_offset
							elif self.config.timestep_spacing == "trailing":
													_UpperCamelCase :		List[Any]			    =       num_train_timesteps / self.num_inference_steps
													# creates integer timesteps by multiplying by ratio
													# casting to int to avoid issues when num_inference_step is power of 3
													_UpperCamelCase :		Optional[Any]			    =       (np.arange(lowerCamelCase__			,0			,-step_ratio			)).round().copy().astype(lowerCamelCase__			)
													timesteps -= 1
							else:
													raise ValueError(
													    F'{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'.'			)

							_UpperCamelCase :		int			    =       np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5			)
							_UpperCamelCase :		Any			    =       np.log(lowerCamelCase__			)
							_UpperCamelCase :		Dict			    =       np.interp(lowerCamelCase__			,np.arange(0			,len(lowerCamelCase__			)			)			,lowerCamelCase__			)

							if self.config.use_karras_sigmas:
													_UpperCamelCase :		Any			    =       self._convert_to_karras(in_sigmas=lowerCamelCase__			,num_inference_steps=self.num_inference_steps			)
													_UpperCamelCase :		str			    =       np.array([self._sigma_to_t(lowerCamelCase__			,lowerCamelCase__			) for sigma in sigmas]			)

							_UpperCamelCase :		List[str]			    =       np.concatenate([sigmas, [0.0]]			).astype(np.floataa			)
							_UpperCamelCase :		Tuple			    =       torch.from_numpy(lowerCamelCase__			).to(device=lowerCamelCase__			)
							_UpperCamelCase :		Optional[Any]			    =       torch.cat([sigmas[:1], sigmas[1:-1].repeat_interleave(2			), sigmas[-1:]]			)

							_UpperCamelCase :		str			    =       torch.from_numpy(lowerCamelCase__			)
							_UpperCamelCase :		Any			    =       torch.cat([timesteps[:1], timesteps[1:].repeat_interleave(2			)]			)

							if str(lowerCamelCase__			).startswith('mps'			):
													# mps does not support float64
													_UpperCamelCase :		Any			    =       timesteps.to(lowerCamelCase__			,dtype=torch.floataa			)
							else:
													_UpperCamelCase :		List[Any]			    =       timesteps.to(device=lowerCamelCase__			)

							# empty dt and derivative
							_UpperCamelCase :		Optional[int]			    =       None
							_UpperCamelCase :		Union[str, Any]			    =       None

							# for exp beta schedules, such as the one for `pipeline_shap_e.py`
							# we need an index counter
							_UpperCamelCase :		str			    =       defaultdict(lowerCamelCase__			)





	def      UpperCamelCase_  (			self :    Any			,lowerCamelCase__ :    Optional[Any]			,lowerCamelCase__ :    Any			):







							'''simple docstring'''
							# get log sigma
							_UpperCamelCase :		Tuple			    =       np.log(lowerCamelCase__			)

							# get distribution
							_UpperCamelCase :		str			    =       log_sigma - log_sigmas[:, np.newaxis]

							# get sigmas range
							_UpperCamelCase :		Optional[int]			    =       np.cumsum((dists >= 0)			,axis=0			).argmax(axis=0			).clip(max=log_sigmas.shape[0] - 2			)
							_UpperCamelCase :		Optional[int]			    =       low_idx + 1

							_UpperCamelCase :		str			    =       log_sigmas[low_idx]
							_UpperCamelCase :		Any			    =       log_sigmas[high_idx]

							# interpolate sigmas
							_UpperCamelCase :		List[str]			    =       (low - log_sigma) / (low - high)
							_UpperCamelCase :		List[Any]			    =       np.clip(lowerCamelCase__			,0			,1			)

							# transform interpolation to time range
							_UpperCamelCase :		Optional[Any]			    =       (1 - w) * low_idx + w * high_idx
							_UpperCamelCase :		str			    =       t.reshape(sigma.shape			)
							return t





	def      UpperCamelCase_  (			self :    Optional[int]			,lowerCamelCase__ :    torch.FloatTensor			,lowerCamelCase__ :    Tuple			):







							'''simple docstring'''
							_UpperCamelCase :		float			    =       in_sigmas[-1].item()
							_UpperCamelCase :		float			    =       in_sigmas[0].item()

							_UpperCamelCase :		Dict			    =       7.0  # 7.0 is the value used in the paper
							_UpperCamelCase :		Optional[int]			    =       np.linspace(0			,1			,lowerCamelCase__			)
							_UpperCamelCase :		Tuple			    =       sigma_min ** (1 / rho)
							_UpperCamelCase :		str			    =       sigma_max ** (1 / rho)
							_UpperCamelCase :		int			    =       (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
							return sigmas





	@property
	def      UpperCamelCase_  (			self :    Optional[int]			):







							'''simple docstring'''
							return self.dt is None





	def      UpperCamelCase_  (			self :    Union[str, Any]			,lowerCamelCase__ :    Union[torch.FloatTensor, np.ndarray]			,lowerCamelCase__ :    Union[float, torch.FloatTensor]			,lowerCamelCase__ :    Union[torch.FloatTensor, np.ndarray]			,lowerCamelCase__ :    bool = True			,):







							'''simple docstring'''
							_UpperCamelCase :		Tuple			    =       self.index_for_timestep(lowerCamelCase__			)

							# advance index counter by 1
							_UpperCamelCase :		Union[str, Any]			    =       timestep.cpu().item() if torch.is_tensor(lowerCamelCase__			) else timestep
							self._index_counter[timestep_int] += 1

							if self.state_in_first_order:
													_UpperCamelCase :		Dict			    =       self.sigmas[step_index]
													_UpperCamelCase :		Optional[Any]			    =       self.sigmas[step_index + 1]
							else:
													# 2nd order / Heun's method
													_UpperCamelCase :		Optional[Any]			    =       self.sigmas[step_index - 1]
													_UpperCamelCase :		Tuple			    =       self.sigmas[step_index]

							# currently only gamma=0 is supported. This usually works best anyways.
							# We can support gamma in the future but then need to scale the timestep before
							# passing it to the model which requires a change in API
							_UpperCamelCase :		str			    =       0
							_UpperCamelCase :		Dict			    =       sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

							# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
							if self.config.prediction_type == "epsilon":
													_UpperCamelCase :		Tuple			    =       sigma_hat if self.state_in_first_order else sigma_next
													_UpperCamelCase :		Optional[int]			    =       sample - sigma_input * model_output
							elif self.config.prediction_type == "v_prediction":
													_UpperCamelCase :		List[str]			    =       sigma_hat if self.state_in_first_order else sigma_next
													_UpperCamelCase :		List[str]			    =       model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
													    sample / (sigma_input**2 + 1)
													)
							elif self.config.prediction_type == "sample":
													_UpperCamelCase :		Optional[int]			    =       model_output
							else:
													raise ValueError(
													    F'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`'			)

							if self.config.clip_sample:
													_UpperCamelCase :		Optional[int]			    =       pred_original_sample.clamp(
													    -self.config.clip_sample_range			,self.config.clip_sample_range			)

							if self.state_in_first_order:
													# 2. Convert to an ODE derivative for 1st order
													_UpperCamelCase :		Optional[Any]			    =       (sample - pred_original_sample) / sigma_hat
													# 3. delta timestep
													_UpperCamelCase :		str			    =       sigma_next - sigma_hat

													# store for 2nd order step
													_UpperCamelCase :		List[Any]			    =       derivative
													_UpperCamelCase :		Optional[Any]			    =       dt
													_UpperCamelCase :		Dict			    =       sample
							else:
													# 2. 2nd order / Heun's method
													_UpperCamelCase :		Union[str, Any]			    =       (sample - pred_original_sample) / sigma_next
													_UpperCamelCase :		Optional[int]			    =       (self.prev_derivative + derivative) / 2

													# 3. take prev timestep & sample
													_UpperCamelCase :		Union[str, Any]			    =       self.dt
													_UpperCamelCase :		Optional[Any]			    =       self.sample

													# free dt and derivative
													# Note, this puts the scheduler in "first order mode"
													_UpperCamelCase :		int			    =       None
													_UpperCamelCase :		Dict			    =       None
													_UpperCamelCase :		str			    =       None

							_UpperCamelCase :		Any			    =       sample + derivative * dt

							if not return_dict:
													return (prev_sample,)

							return SchedulerOutput(prev_sample=lowerCamelCase__			)





	def      UpperCamelCase_  (			self :    List[str]			,lowerCamelCase__ :    torch.FloatTensor			,lowerCamelCase__ :    torch.FloatTensor			,lowerCamelCase__ :    torch.FloatTensor			,):







							'''simple docstring'''
							# Make sure sigmas and timesteps have the same device and dtype as original_samples
							_UpperCamelCase :		Any			    =       self.sigmas.to(device=original_samples.device			,dtype=original_samples.dtype			)
							if original_samples.device.type == "mps" and torch.is_floating_point(lowerCamelCase__			):
													# mps does not support float64
													_UpperCamelCase :		Optional[Any]			    =       self.timesteps.to(original_samples.device			,dtype=torch.floataa			)
													_UpperCamelCase :		Optional[Any]			    =       timesteps.to(original_samples.device			,dtype=torch.floataa			)
							else:
													_UpperCamelCase :		List[str]			    =       self.timesteps.to(original_samples.device			)
													_UpperCamelCase :		int			    =       timesteps.to(original_samples.device			)

							_UpperCamelCase :		int			    =       [self.index_for_timestep(lowerCamelCase__			,lowerCamelCase__			) for t in timesteps]

							_UpperCamelCase :		Optional[int]			    =       sigmas[step_indices].flatten()
							while len(sigma.shape			) < len(original_samples.shape			):
													_UpperCamelCase :		Tuple			    =       sigma.unsqueeze(-1			)

							_UpperCamelCase :		Tuple			    =       original_samples + noise * sigma
							return noisy_samples





	def __len__(			self :    int			):







							'''simple docstring'''
							return self.config.num_train_timesteps







'''simple docstring'''
class 							lowercase__     :





	def __init__(			self :    List[str]			,lowerCamelCase__ :    List[Any]			,lowerCamelCase__ :    Optional[int]			,lowerCamelCase__ :    Any			):







							'''simple docstring'''
							_UpperCamelCase :		Dict			    =       None
							_UpperCamelCase :		List[Any]			    =       None
							_UpperCamelCase :		int			    =       graph

							self._normalize_graph(lowerCamelCase__			,lowerCamelCase__			)
							_UpperCamelCase :		List[str]			    =       len(lowerCamelCase__			)
							_UpperCamelCase :		Tuple			    =       None





	def      UpperCamelCase_  (			self :    Any			,lowerCamelCase__ :    Optional[Any]			,lowerCamelCase__ :    Any			):







							'''simple docstring'''
							if sources is int:
													_UpperCamelCase :		Optional[int]			    =       [sources]
							if sinks is int:
													_UpperCamelCase :		Union[str, Any]			    =       [sinks]

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

							_UpperCamelCase :		List[str]			    =       sources[0]
							_UpperCamelCase :		str			    =       sinks[0]

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

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

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





	def      UpperCamelCase_  (			self :    List[str]			):







							'''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 :    Any			,lowerCamelCase__ :    Any			):







							'''simple docstring'''
							_UpperCamelCase :		str			    =       algorithm(self			)






class 							lowercase__     :





	def __init__(			self :    List[str]			,lowerCamelCase__ :    Optional[int]			):







							'''simple docstring'''
							_UpperCamelCase :		Optional[Any]			    =       flow_network
							_UpperCamelCase :		List[str]			    =       flow_network.verticesCount
							_UpperCamelCase :		List[str]			    =       flow_network.sourceIndex
							_UpperCamelCase :		Any			    =       flow_network.sinkIndex
							# it's just a reference, so you shouldn't change
							# it in your algorithms, use deep copy before doing that
							_UpperCamelCase :		List[Any]			    =       flow_network.graph
							_UpperCamelCase :		Any			    =       False





	def      UpperCamelCase_  (			self :    str			):







							'''simple docstring'''
							if not self.executed:
													self._algorithm()
													_UpperCamelCase :		Any			    =       True





	def      UpperCamelCase_  (			self :    Any			):







							'''simple docstring'''
							pass






class 							lowercase__     (							lowercase       ):





	def __init__(			self :    Union[str, Any]			,lowerCamelCase__ :    List[str]			):







							'''simple docstring'''
							super().__init__(lowerCamelCase__			)
							# use this to save your result
							_UpperCamelCase :		Tuple			    =       -1





	def      UpperCamelCase_  (			self :    Dict			):







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

							return self.maximum_flow






class 							lowercase__     (							lowercase       ):





	def __init__(			self :    Optional[Any]			,lowerCamelCase__ :    Dict			):







							'''simple docstring'''
							super().__init__(lowerCamelCase__			)

							_UpperCamelCase :		Dict			    =       [[0] * self.verticies_count for i in range(self.verticies_count			)]

							_UpperCamelCase :		Optional[Any]			    =       [0] * self.verticies_count
							_UpperCamelCase :		List[str]			    =       [0] * self.verticies_count





	def      UpperCamelCase_  (			self :    Union[str, Any]			):







							'''simple docstring'''
							_UpperCamelCase :		Dict			    =       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 :		List[str]			    =       [
							    i
							    for i in range(self.verticies_count			)
							    if i != self.source_index and i != self.sink_index
							]

							# move through list
							_UpperCamelCase :		int			    =       0
							while i < len(lowerCamelCase__			):
													_UpperCamelCase :		List[Any]			    =       vertices_list[i]
													_UpperCamelCase :		str			    =       self.heights[vertex_index]
													self.process_vertex(lowerCamelCase__			)
													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(lowerCamelCase__			)			)
																			_UpperCamelCase :		Dict			    =       0
													else:
																			i += 1

							_UpperCamelCase :		Optional[Any]			    =       sum(self.preflow[self.source_index]			)





	def      UpperCamelCase_  (			self :    Union[str, Any]			,lowerCamelCase__ :    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(lowerCamelCase__			,lowerCamelCase__			)

													self.relabel(lowerCamelCase__			)





	def      UpperCamelCase_  (			self :    Tuple			,lowerCamelCase__ :    List[Any]			,lowerCamelCase__ :    List[str]			):







							'''simple docstring'''
							_UpperCamelCase :		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      UpperCamelCase_  (			self :    List[str]			,lowerCamelCase__ :    Optional[int]			):







							'''simple docstring'''
							_UpperCamelCase :		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):
																			_UpperCamelCase :		List[Any]			    =       self.heights[to_index]

							if min_height is not None:
													_UpperCamelCase :		Any			    =       min_height + 1


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

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

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


