code: 
  
  """simple docstring"""
  
  
  
  
  from __future__ import annotations
  
  import random
  
  from matplotlib import animation
  from matplotlib import pyplot as plt
  
  # Frame rate of the animation
  __A  :					Dict												=	20
  
  # Time between time steps in seconds
  __A  :					Tuple												=	INTERVAL / 10_00
  
  
  
  
  
  class     __UpperCamelCase				:
  
  
  		def __init__(self				:	Tuple  ,  __SCREAMING_SNAKE_CASE				:	float  ,  __SCREAMING_SNAKE_CASE				:	float  ,  __SCREAMING_SNAKE_CASE				:	float  ,  __SCREAMING_SNAKE_CASE				:	float  ,  __SCREAMING_SNAKE_CASE				:	float = 1.0  ,  __SCREAMING_SNAKE_CASE				:	float = 1.0  ,  __SCREAMING_SNAKE_CASE				:	str = "blue"  ,  ):
  							A    =      position_x
  							A    =      position_y
  							A    =      velocity_x
  							A    =      velocity_y
  							A    =      mass
  							A    =      size
  							A    =      color
  
  
  		@property
  		def       SCREAMING_SNAKE_CASE__     (self				:	Tuple):
  							return self.position_x, self.position_y
  
  
  		@property
  		def       SCREAMING_SNAKE_CASE__     (self				:	Union[str, Any]):
  							return self.velocity_x, self.velocity_y
  
  
  		def       SCREAMING_SNAKE_CASE__     (self				:	str  ,  __SCREAMING_SNAKE_CASE				:	float  ,  __SCREAMING_SNAKE_CASE				:	float  ,  __SCREAMING_SNAKE_CASE				:	float):
  							self.velocity_x += force_x * delta_time
  							self.velocity_y += force_y * delta_time
  
  
  		def       SCREAMING_SNAKE_CASE__     (self				:	Any  ,  __SCREAMING_SNAKE_CASE				:	float):
  							self.position_x += self.velocity_x * delta_time
  							self.position_y += self.velocity_y * delta_time
  
  
  
  
  
  class     __UpperCamelCase				:
  
  
  		def __init__(self				:	Tuple  ,  __SCREAMING_SNAKE_CASE				:	list[Body]  ,  __SCREAMING_SNAKE_CASE				:	float = 1.0  ,  __SCREAMING_SNAKE_CASE				:	float = 1.0  ,  __SCREAMING_SNAKE_CASE				:	float = 0.0  ,  ):
  							A    =      bodies
  							A    =      gravitation_constant
  							A    =      time_factor
  							A    =      softening_factor
  
  
  		def __len__(self				:	Optional[Any]):
  							return len(self.bodies)
  
  
  		def       SCREAMING_SNAKE_CASE__     (self				:	str  ,  __SCREAMING_SNAKE_CASE				:	float):
  							for bodya in self.bodies:
  												A    =      0.0
  												A    =      0.0
  												for bodya in self.bodies:
  																	if bodya != bodya:
  																						A    =      bodya.position_x - bodya.position_x
  																						A    =      bodya.position_y - bodya.position_y
  
  																						# Calculation of the distance using Pythagoras's theorem
  																						# Extra factor due to the softening technique
  																						A    =      (dif_x**2 + dif_y**2 + self.softening_factor) ** (
  																						    1 / 2
  																						)
  
  																						# Newton's law of universal gravitation.
  																						force_x += (
  																						    self.gravitation_constant * bodya.mass * dif_x / distance**3
  																						)
  																						force_y += (
  																						    self.gravitation_constant * bodya.mass * dif_y / distance**3
  																						)
  
              # Update the body's velocity once all the force components have been added
  												bodya.update_velocity(__SCREAMING_SNAKE_CASE  ,  __SCREAMING_SNAKE_CASE  ,  delta_time * self.time_factor)
  
  							# Update the positions only after all the velocities have been updated
  							for body in self.bodies:
  												body.update_position(delta_time * self.time_factor)
  
  def      __SCREAMING_SNAKE_CASE		(		lowercase__    ,							lowercase__    ,							lowercase__   ):
  					"""simple docstring"""
  					body_system.update_system(lowercase__   )
  
  					# Update the positions of the patches
  					for patch, body in zip(lowercase__    ,							body_system.bodies   ):
  										A    =      (body.position_x, body.position_y)
  def      __SCREAMING_SNAKE_CASE		(		lowercase__    ,							lowercase__    ,							lowercase__ = -1    ,							lowercase__ = 1    ,							lowercase__ = -1    ,							lowercase__ = 1    ,							):
  					"""simple docstring"""
  					A    =      plt.figure()
  					fig.canvas.set_window_title(lowercase__   )
  					A    =      plt.axes(
  					    xlim=(x_start, x_end)    ,							ylim=(y_start, y_end)   )  # Set section to be plotted
  					plt.gca().set_aspect("equal"   )  # Fix aspect ratio
  
  					# Each body is drawn as a patch by the plt-function
  					A    =      [
  					    plt.Circle((body.position_x, body.position_y)    ,							body.size    ,							fc=body.color   )
  					    for body in body_system.bodies
  					]
  
  					for patch in patches:
  										ax.add_patch(lowercase__   )
  
  					# Function called at each step of the animation
  					def update(lowercase__   ) -> list[plt.Circle]:
  										update_step(lowercase__    ,							lowercase__    ,							lowercase__   )
  										return patches
  
  					A    =      animation.FuncAnimation(  # noqa: F841
  					    lowercase__    ,							lowercase__    ,							interval=lowercase__    ,							blit=lowercase__   )
  
  					plt.show()
  def      __SCREAMING_SNAKE_CASE		(		):
  					"""simple docstring"""
  					A    =      0.9_70_04_36
  					A    =      -0.24_30_87_53
  					A    =      0.4_66_20_36_85
  					A    =      0.43_23_65_73
  
  					A    =      [
  					    Body(lowercase__    ,							lowercase__    ,							lowercase__    ,							lowercase__    ,							size=0.2    ,							color="red"   ),
  					    Body(-position_x    ,							-position_y    ,							lowercase__    ,							lowercase__    ,							size=0.2    ,							color="green"   ),
  					    Body(0    ,							0    ,							-2 * velocity_x    ,							-2 * velocity_y    ,							size=0.2    ,							color="blue"   ),
  					]
  					return BodySystem(lowercase__    ,							time_factor=3   )
  def      __SCREAMING_SNAKE_CASE		(		):
  					"""simple docstring"""
  					A    =      7.3476e22
  					A    =      5.972e24
  					A    =      1_022
  					A    =      384_399_000
  					A    =      6.674e-11
  
  					# Calculation of the respective velocities so that total impulse is zero,
  					# i.e. the two bodies together don't move
  					A    =      earth_mass * velocity_dif / (earth_mass + moon_mass)
  					A    =      moon_velocity - velocity_dif
  
  					A    =      Body(-earth_moon_distance    ,							0    ,							0    ,							lowercase__    ,							lowercase__    ,							10_000_000    ,							"grey"   )
  					A    =      Body(0    ,							0    ,							0    ,							lowercase__    ,							lowercase__    ,							50_000_000    ,							"blue"   )
  					return BodySystem([earth, moon]    ,							lowercase__    ,							time_factor=1_000_000   )
  def      __SCREAMING_SNAKE_CASE		(		):
  					"""simple docstring"""
  					A    =      []
  					for _ in range(10   ):
  										A    =      random.uniform(-0.5    ,							0.5   )
  										A    =      random.uniform(-0.5    ,							0.5   )
  
  										# Bodies are created pairwise with opposite velocities so that the
  										# total impulse remains zero
  										bodies.append(
  										    Body(
  										        random.uniform(-0.5    ,							0.5   )    ,							random.uniform(-0.5    ,							0.5   )    ,							lowercase__    ,							lowercase__    ,							size=0.05    ,							)   )
  										bodies.append(
  										    Body(
  										        random.uniform(-0.5    ,							0.5   )    ,							random.uniform(-0.5    ,							0.5   )    ,							-velocity_x    ,							-velocity_y    ,							size=0.05    ,							)   )
  					return BodySystem(lowercase__    ,							0.01    ,							10    ,							0.1   )
  
  
  if __name__ == "__main__":
  	plot('Figure-8 solution to the 3-body-problem', example_a(), -2, 2, -2, 2)
  	plot(
  	    'Moon\'s orbit around the earth',
  	    example_a(),
  	    -4_30_00_00_00,
  	    4_30_00_00_00,
  	    -4_30_00_00_00,
  	    4_30_00_00_00,
  	)
  	plot('Random system with many bodies', example_a(), -1.5, 1.5, -1.5, 1.5)
  
  
  
  
  
  
style_context: 
  
  """simple docstring"""
  
  
  
  
  from typing import Mapping
  
  from ...configuration_utils import PretrainedConfig
  from ...onnx import OnnxSeqaSeqConfigWithPast
  from ...utils import logging
  
  
  __A  :					List[str]												=	logging.get_logger(__name__)
  
  
  
  
  
  class     __UpperCamelCase				(     _A		):
  		SCREAMING_SNAKE_CASE              =					"mt5"
  		SCREAMING_SNAKE_CASE              =					["past_key_values"]
  
  
  		def __init__(self				:	Optional[Any]  ,  __SCREAMING_SNAKE_CASE				:	Union[str, Any]=2_5_0_1_1_2  ,  __SCREAMING_SNAKE_CASE				:	int=5_1_2  ,  __SCREAMING_SNAKE_CASE				:	Tuple=6_4  ,  __SCREAMING_SNAKE_CASE				:	Union[str, Any]=1_0_2_4  ,  __SCREAMING_SNAKE_CASE				:	Optional[int]=8  ,  __SCREAMING_SNAKE_CASE				:	Any=None  ,  __SCREAMING_SNAKE_CASE				:	Tuple=6  ,  __SCREAMING_SNAKE_CASE				:	int=3_2  ,  __SCREAMING_SNAKE_CASE				:	List[Any]=1_2_8  ,  __SCREAMING_SNAKE_CASE				:	Tuple=0.1  ,  __SCREAMING_SNAKE_CASE				:	Tuple=1E-6  ,  __SCREAMING_SNAKE_CASE				:	List[Any]=1.0  ,  __SCREAMING_SNAKE_CASE				:	Optional[int]="gated-gelu"  ,  __SCREAMING_SNAKE_CASE				:	List[str]=True  ,  __SCREAMING_SNAKE_CASE				:	str=True  ,  __SCREAMING_SNAKE_CASE				:	int="T5Tokenizer"  ,  __SCREAMING_SNAKE_CASE				:	Optional[int]=False  ,  __SCREAMING_SNAKE_CASE				:	Optional[Any]=0  ,  __SCREAMING_SNAKE_CASE				:	Tuple=1  ,  __SCREAMING_SNAKE_CASE				:	List[str]=0  ,  **__SCREAMING_SNAKE_CASE				:	str  ,  ):
  							super().__init__(
  							    is_encoder_decoder=__SCREAMING_SNAKE_CASE  ,  tokenizer_class=__SCREAMING_SNAKE_CASE  ,  tie_word_embeddings=__SCREAMING_SNAKE_CASE  ,  pad_token_id=__SCREAMING_SNAKE_CASE  ,  eos_token_id=__SCREAMING_SNAKE_CASE  ,  decoder_start_token_id=__SCREAMING_SNAKE_CASE  ,  **__SCREAMING_SNAKE_CASE  ,  )
  							A    =      vocab_size
  							A    =      d_model
  							A    =      d_kv
  							A    =      d_ff
  							A    =      num_layers
  							A    =      (
  							    num_decoder_layers if num_decoder_layers is not None else self.num_layers
  							)  # default = symmetry
  							A    =      num_heads
  							A    =      relative_attention_num_buckets
  							A    =      relative_attention_max_distance
  							A    =      dropout_rate
  							A    =      layer_norm_epsilon
  							A    =      initializer_factor
  							A    =      feed_forward_proj
  							A    =      use_cache
  
  							A    =      self.feed_forward_proj.split("-")
  							A    =      act_info[-1]
  							A    =      act_info[0] == "gated"
  
  							if len(__SCREAMING_SNAKE_CASE) > 1 and act_info[0] != "gated" or len(__SCREAMING_SNAKE_CASE) > 2:
  												raise ValueError(
  												    F"""`feed_forward_proj`: {feed_forward_proj} is not a valid activation function of the dense layer."""
  												    "Please make sure `feed_forward_proj` is of the format `gated-{ACT_FN}` or `{ACT_FN}`, e.g. "
  												    "'gated-gelu' or 'relu'")
  
  							# for backwards compatibility
  							if feed_forward_proj == "gated-gelu":
  												A    =      "gelu_new"
  
  
  		@property
  		def       SCREAMING_SNAKE_CASE__     (self				:	List[Any]):
  							return self.d_model
  
  
  		@property
  		def       SCREAMING_SNAKE_CASE__     (self				:	Optional[int]):
  							return self.num_heads
  
  
  		@property
  		def       SCREAMING_SNAKE_CASE__     (self				:	Optional[int]):
  							return self.num_layers
  
  
  
  
  
  class     __UpperCamelCase				(     _A		):
  
  
  		@property
  		# Copied from transformers.models.t5.configuration_t5.T5OnnxConfig.inputs
  		def       SCREAMING_SNAKE_CASE__     (self				:	int):
  							A    =      {
  							    "input_ids": {0: "batch", 1: "encoder_sequence"},
  							    "attention_mask": {0: "batch", 1: "encoder_sequence"},
  							}
  							if self.use_past:
  												A    =      "past_encoder_sequence + sequence"
  												A    =      {0: "batch"}
  												A    =      {0: "batch", 1: "past_decoder_sequence + sequence"}
  							else:
  												A    =      {0: "batch", 1: "decoder_sequence"}
  												A    =      {0: "batch", 1: "decoder_sequence"}
  
  							if self.use_past:
  												self.fill_with_past_key_values_(__SCREAMING_SNAKE_CASE  ,  direction="inputs")
  
  							return common_inputs
  
  
  		@property
  		# Copied from transformers.models.t5.configuration_t5.T5OnnxConfig.default_onnx_opset
  		def       SCREAMING_SNAKE_CASE__     (self				:	Union[str, Any]):
  							return 1_3
  
  
  		@property
  		def       SCREAMING_SNAKE_CASE__     (self				:	int):
  							return 5E-4
  
  
  
  
  
  