


"""simple docstring"""


import re
from typing import Callable, List, Optional, Union

import tensorflow as tf


try:
		from tensorflow.keras.optimizers.legacy import Adam
except ImportError:
		from tensorflow.keras.optimizers import Adam
class snake_case      (  tf.keras.optimizers.schedules.LearningRateSchedule):







		def __init__(					self      :       Tuple    ,   a__      :       float    ,   a__      :       Callable    ,   a__      :       int    ,   a__      :       float = 1.0    ,   a__      :       str = None    ,   )       ->						Optional[int]:





						'''simple docstring'''







						super().__init__()
						_A					  =			initial_learning_rate
						_A					  =			warmup_steps
						_A					  =			power
						_A					  =			decay_schedule_fn
						_A					  =			name







		def __call__(					self      :       Optional[Any]    ,   a__      :       int		)       ->						Dict:





						'''simple docstring'''







						with tf.name_scope(self.name or "WarmUp"		) as name:
										# Implements polynomial warmup. i.e., if global_step < warmup_steps, the
										# learning rate will be `global_step/num_warmup_steps * init_lr`.
										_A					  =			tf.cast(a__    ,   tf.floataa		)
										_A					  =			tf.cast(self.warmup_steps    ,   tf.floataa		)
										_A					  =			global_step_float / warmup_steps_float
										_A					  =			self.initial_learning_rate * tf.math.pow(a__    ,   self.power		)
										return tf.cond(
										    global_step_float < warmup_steps_float    ,   lambda: warmup_learning_rate    ,   lambda: self.decay_schedule_fn(step - self.warmup_steps		)    ,   name=a__    ,   )







		def  a_ (					self      :       Tuple		)       ->						Any:





						'''simple docstring'''







						return {
						    "initial_learning_rate": self.initial_learning_rate,
						    "decay_schedule_fn": self.decay_schedule_fn,
						    "warmup_steps": self.warmup_steps,
						    "power": self.power,
						    "name": self.name,
						}






def      a__ (				__lowercase     ,			__lowercase     ,			__lowercase     ,			__lowercase = 0.0     ,			__lowercase = 0.9     ,			__lowercase = 0.999     ,			__lowercase = 1E-8     ,			__lowercase = None     ,			__lowercase = None     ,			__lowercase = 0.0     ,			__lowercase = 1.0     ,			__lowercase = None     ,			)	->	Union[str, Any]:
				_A					  =			tf.keras.optimizers.schedules.PolynomialDecay(
				    initial_learning_rate=__lowercase     ,			decay_steps=num_train_steps - num_warmup_steps     ,			end_learning_rate=init_lr * min_lr_ratio     ,			power=__lowercase     ,			)
				if num_warmup_steps:
								_A					  =			WarmUp(
								    initial_learning_rate=__lowercase     ,			decay_schedule_fn=__lowercase     ,			warmup_steps=__lowercase     ,			)
				if weight_decay_rate > 0.0:
								_A					  =			AdamWeightDecay(
								    learning_rate=__lowercase     ,			weight_decay_rate=__lowercase     ,			beta_a=__lowercase     ,			beta_a=__lowercase     ,			epsilon=__lowercase     ,			clipnorm=__lowercase     ,			global_clipnorm=__lowercase     ,			exclude_from_weight_decay=["LayerNorm", "layer_norm", "bias"]     ,			include_in_weight_decay=__lowercase     ,			)
				else:
								_A					  =			tf.keras.optimizers.Adam(
								    learning_rate=__lowercase     ,			beta_a=__lowercase     ,			beta_a=__lowercase     ,			epsilon=__lowercase     ,			clipnorm=__lowercase     ,			global_clipnorm=__lowercase     ,			)
				# We return the optimizer and the LR scheduler in order to better track the
				# evolution of the LR independently of the optimizer.
				return optimizer, lr_schedule
class snake_case      (  _UpperCamelCase):







		def __init__(					self      :       Optional[int]    ,   a__      :       Union[float, tf.keras.optimizers.schedules.LearningRateSchedule] = 0.0_0_1    ,   a__      :       float = 0.9    ,   a__      :       float = 0.9_9_9    ,   a__      :       float = 1E-7    ,   a__      :       bool = False    ,   a__      :       float = 0.0    ,   a__      :       Optional[List[str]] = None    ,   a__      :       Optional[List[str]] = None    ,   a__      :       str = "AdamWeightDecay"    ,   **a__      :       Union[str, Any]    ,   )       ->						str:





						'''simple docstring'''







						super().__init__(a__    ,   a__    ,   a__    ,   a__    ,   a__    ,   a__    ,   **a__		)
						_A					  =			weight_decay_rate
						_A					  =			include_in_weight_decay
						_A					  =			exclude_from_weight_decay







		@classmethod
		def  a_ (					cls      :       int    ,   a__      :       Dict		)       ->						int:





						'''simple docstring'''







						_A					  =			{"WarmUp": WarmUp}
						return super(a__    ,   cls		).from_config(a__    ,   custom_objects=a__		)







		def  a_ (					self      :       Any    ,   a__      :       Tuple    ,   a__      :       Dict    ,   a__      :       Any		)       ->						Optional[Any]:





						'''simple docstring'''







						super(a__    ,   self		)._prepare_local(a__    ,   a__    ,   a__		)
						_A					  =			tf.constant(
						    self.weight_decay_rate    ,   name="adam_weight_decay_rate"		)







		def  a_ (					self      :       int    ,   a__      :       Optional[Any]    ,   a__      :       List[str]    ,   a__      :       str		)       ->						str:





						'''simple docstring'''







						_A					  =			self._do_use_weight_decay(var.name		)
						if do_decay:
										return var.assign_sub(
										    learning_rate * var * apply_state[(var.device, var.dtype.base_dtype)]["weight_decay_rate"]    ,   use_locking=self._use_locking    ,   )
						return tf.no_op()







		def  a_ (					self      :       Optional[Any]    ,   a__      :       Dict    ,   a__      :       Any=None    ,   **a__      :       List[str]		)       ->						Tuple:





						'''simple docstring'''







						_A  ,		_A					  =			list(zip(*a__		)		)
						return super(a__    ,   self		).apply_gradients(zip(a__    ,   a__		)    ,   name=a__    ,   **a__		)







		def  a_ (					self      :       Optional[int]    ,   a__      :       Dict    ,   a__      :       Tuple    ,   a__      :       Union[str, Any]		)       ->						List[str]:





						'''simple docstring'''







						if apply_state is None:
										return self._decayed_lr_t[var_dtype], {}

						_A					  =			apply_state or {}
						_A					  =			apply_state.get((var_device, var_dtype)		)
						if coefficients is None:
										_A					  =			self._fallback_apply_state(a__    ,   a__		)
										_A					  =			coefficients

						return coefficients["lr_t"], {"apply_state": apply_state}







		def  a_ (					self      :       List[str]    ,   a__      :       Union[str, Any]    ,   a__      :       Optional[Any]    ,   a__      :       Optional[int]=None		)       ->						Tuple:





						'''simple docstring'''







						_A  ,		_A					  =			self._get_lr(var.device    ,   var.dtype.base_dtype    ,   a__		)
						_A					  =			self._decay_weights_op(a__    ,   a__    ,   a__		)
						with tf.control_dependencies([decay]		):
										return super(a__    ,   self		)._resource_apply_dense(a__    ,   a__    ,   **a__		)







		def  a_ (					self      :       List[Any]    ,   a__      :       List[Any]    ,   a__      :       Union[str, Any]    ,   a__      :       Dict    ,   a__      :       List[Any]=None		)       ->						Optional[int]:





						'''simple docstring'''







						_A  ,		_A					  =			self._get_lr(var.device    ,   var.dtype.base_dtype    ,   a__		)
						_A					  =			self._decay_weights_op(a__    ,   a__    ,   a__		)
						with tf.control_dependencies([decay]		):
										return super(a__    ,   self		)._resource_apply_sparse(a__    ,   a__    ,   a__    ,   **a__		)







		def  a_ (					self      :       Optional[int]		)       ->						int:





						'''simple docstring'''







						_A					  =			super().get_config()
						config.update({"weight_decay_rate": self.weight_decay_rate}		)
						return config







		def  a_ (					self      :       Any    ,   a__      :       List[Any]		)       ->						Union[str, Any]:





						'''simple docstring'''







						if self.weight_decay_rate == 0:
										return False

						if self._include_in_weight_decay:
										for r in self._include_in_weight_decay:
														if re.search(a__    ,   a__		) is not None:
																		return True

						if self._exclude_from_weight_decay:
										for r in self._exclude_from_weight_decay:
														if re.search(a__    ,   a__		) is not None:
																		return False
						return True





class snake_case      (  _UpperCamelCase):







		def __init__(					self      :       Any		)       ->						List[Any]:





						'''simple docstring'''







						_A					  =			[]
						_A					  =			None







		@property
		def  a_ (					self      :       str		)       ->						List[Any]:





						'''simple docstring'''







						if self._accum_steps is None:
										_A					  =			tf.Variable(
										    tf.constant(0    ,   dtype=tf.intaa		)    ,   trainable=a__    ,   synchronization=tf.VariableSynchronization.ON_READ    ,   aggregation=tf.VariableAggregation.ONLY_FIRST_REPLICA    ,   )

						return self._accum_steps.value()







		@property
		def  a_ (					self      :       List[Any]		)       ->						int:





						'''simple docstring'''







						if not self._gradients:
										raise ValueError("The accumulator should be called first to initialize the gradients"		)
						return [gradient.value() if gradient is not None else gradient for gradient in self._gradients]







		def __call__(					self      :       Tuple    ,   a__      :       Optional[Any]		)       ->						int:





						'''simple docstring'''







						if not self._gradients:
										_A					  =			self.step  # Create the step variable.
										self._gradients.extend(
										    [
										        tf.Variable(
										            tf.zeros_like(a__		)    ,   trainable=a__    ,   synchronization=tf.VariableSynchronization.ON_READ    ,   aggregation=tf.VariableAggregation.ONLY_FIRST_REPLICA    ,   )
										        if gradient is not None
										        else gradient
										        for gradient in gradients
										    ]		)
						if len(a__		) != len(self._gradients		):
										raise ValueError(F"""Expected {len(self._gradients		)} gradients, but got {len(a__		)}"""		)

						for accum_gradient, gradient in zip(self._gradients    ,   a__		):
										if accum_gradient is not None and gradient is not None:
														accum_gradient.assign_add(a__		)

						self._accum_steps.assign_add(1		)







		def  a_ (					self      :       str		)       ->						int:





						'''simple docstring'''







						if not self._gradients:
										return
						self._accum_steps.assign(0		)
						for gradient in self._gradients:
										if gradient is not None:
														gradient.assign(tf.zeros_like(a__		)		)



"""simple docstring"""


def      a__ (				__lowercase     ,			__lowercase     ,			__lowercase     ,			__lowercase   )	->	str:
				# Return True if there is node that has not iterated.
				_A					  =			[False] * len(__lowercase   )
				_A					  =			[]
				queue.append(__lowercase   )
				_A					  =			True

				while queue:
								_A					  =			queue.pop(0   )
								for ind in range(len(graph[u]   )   ):
												if visited[ind] is False and graph[u][ind] > 0:
																queue.append(__lowercase   )
																_A					  =			True
																_A					  =			u

				return visited[t]






def      a__ (				__lowercase     ,			__lowercase     ,			__lowercase   )	->	int:
				# This array is filled by BFS and to store path
				_A					  =			[-1] * (len(__lowercase   ))
				_A					  =			0
				while bfs(__lowercase     ,			__lowercase     ,			__lowercase     ,			__lowercase   ):
								_A					  =			float("Inf"   )
								_A					  =			sink

								while s != source:
												# Find the minimum value in select path
												_A					  =			min(__lowercase     ,			graph[parent[s]][s]   )
												_A					  =			parent[s]

								max_flow += path_flow
								_A					  =			sink

								while v != source:
												_A					  =			parent[v]
												graph[u][v] -= path_flow
												graph[v][u] += path_flow
												_A					  =			parent[v]
				return max_flow


a_       							=    [
    [0, 16, 13, 0, 0, 0],
    [0, 0, 10, 12, 0, 0],
    [0, 4, 0, 0, 14, 0],
    [0, 0, 9, 0, 0, 20],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]

a_							,     a_       							=    0, 5




print(ford_fulkerson(graph, source, sink))