






from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
lowercase     :							int	     =			20

# Time between time steps in seconds
lowercase     :							Optional[int]	     =			INTERVAL / 10_00




class 						UpperCAmelCase_  :


						'''simple docstring'''




						def __init__(		self						, _SCREAMING_SNAKE_CASE						, _SCREAMING_SNAKE_CASE						, _SCREAMING_SNAKE_CASE						, _SCREAMING_SNAKE_CASE						, _SCREAMING_SNAKE_CASE = 1.0						, _SCREAMING_SNAKE_CASE = 1.0						, _SCREAMING_SNAKE_CASE = "blue"						, )       -> Any:
								snake_case_ :							Tuple         =				position_x
								snake_case_ :							Optional[int]         =				position_y
								snake_case_ :							Optional[int]         =				velocity_x
								snake_case_ :							List[Any]         =				velocity_y
								snake_case_ :							Dict         =				mass
								snake_case_ :							int         =				size
								snake_case_ :							Dict         =				color






						@property
						def 					_lowerCAmelCase				(		self )       -> Optional[int]:
								return self.position_x, self.position_y






						@property
						def 					_lowerCAmelCase				(		self )       -> Tuple:
								return self.velocity_x, self.velocity_y






						def 					_lowerCAmelCase				(		self						, _SCREAMING_SNAKE_CASE						, _SCREAMING_SNAKE_CASE						, _SCREAMING_SNAKE_CASE )       -> str:
								self.velocity_x += force_x * delta_time
								self.velocity_y += force_y * delta_time






						def 					_lowerCAmelCase				(		self						, _SCREAMING_SNAKE_CASE )       -> Union[str, Any]:
								self.position_x += self.velocity_x * delta_time
								self.position_y += self.velocity_y * delta_time




class 						UpperCAmelCase_  :


						'''simple docstring'''




						def __init__(		self						, _SCREAMING_SNAKE_CASE						, _SCREAMING_SNAKE_CASE = 1.0						, _SCREAMING_SNAKE_CASE = 1.0						, _SCREAMING_SNAKE_CASE = 0.0						, )       -> Dict:
								snake_case_ :							Optional[Any]         =				bodies
								snake_case_ :							List[Any]         =				gravitation_constant
								snake_case_ :							List[Any]         =				time_factor
								snake_case_ :							str         =				softening_factor






						def __len__(		self )       -> Union[str, Any]:
								return len(self.bodies )






						def 					_lowerCAmelCase				(		self						, _SCREAMING_SNAKE_CASE )       -> Tuple:

								for bodya in self.bodies:
										snake_case_ :							Optional[Any]         =				0.0
										snake_case_ :							Tuple         =				0.0
										for bodya in self.bodies:
												if bodya != bodya:
														snake_case_ :							str         =				bodya.position_x - bodya.position_x
														snake_case_ :							str         =				bodya.position_y - bodya.position_y

														# Calculation of the distance using Pythagoras's theorem
														# Extra factor due to the softening technique
														snake_case_ :							int         =				(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(snake_case_						, 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    lowerCAmelCase__		(			_a				:	BodySystem     ,					_a				:	float     ,					_a				:	list[plt.Circle]			):
		body_system.update_system(lowerCamelCase_			)

		# Update the positions of the patches
		for patch, body in zip(lowerCamelCase_     ,					body_system.bodies			):
				snake_case_ :							str         =				(body.position_x, body.position_y)

def    lowerCAmelCase__		(			_a				:	str     ,					_a				:	BodySystem     ,					_a				:	float = -1     ,					_a				:	float = 1     ,					_a				:	float = -1     ,					_a				:	float = 1     ,					):
		snake_case_ :							int         =				plt.figure()
		fig.canvas.set_window_title(lowerCamelCase_			)
		snake_case_ :							Dict         =				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
		snake_case_ :							str         =				[
		    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(lowerCamelCase_			)

		# Function called at each step of the animation
		def update(_a				:	int			) -> list[plt.Circle]:
				update_step(lowerCamelCase_     ,					lowerCamelCase_     ,					lowerCamelCase_			)
				return patches

		snake_case_ :							Optional[int]         =				animation.FuncAnimation(  # noqa: F841
		    lowerCamelCase_     ,					lowerCamelCase_     ,					interval=lowerCamelCase_     ,					blit=lowerCamelCase_			)

		plt.show()

def    lowerCAmelCase__		(			):
		snake_case_ :							Union[str, Any]         =				0.9_700_436
		snake_case_ :							int         =				-0.24_308_753
		snake_case_ :							str         =				0.466_203_685
		snake_case_ :							int         =				0.43_236_573

		snake_case_ :							Union[str, Any]         =				[
		    Body(lowerCamelCase_     ,					lowerCamelCase_     ,					lowerCamelCase_     ,					lowerCamelCase_     ,					size=0.2     ,					color="red"			),
		    Body(-position_x     ,					-position_y     ,					lowerCamelCase_     ,					lowerCamelCase_     ,					size=0.2     ,					color="green"			),
		    Body(0     ,					0     ,					-2 * velocity_x     ,					-2 * velocity_y     ,					size=0.2     ,					color="blue"			),
		]
		return BodySystem(lowerCamelCase_     ,					time_factor=3			)

def    lowerCAmelCase__		(			):
		snake_case_ :							Tuple         =				7.3_476E22
		snake_case_ :							Dict         =				5.972E24
		snake_case_ :							Tuple         =				10_22
		snake_case_ :							str         =				3_84_39_90_00
		snake_case_ :							int         =				6.674E-11

		# Calculation of the respective velocities so that total impulse is zero,
		# i.e. the two bodies together don't move
		snake_case_ :							Tuple         =				earth_mass * velocity_dif / (earth_mass + moon_mass)
		snake_case_ :							Tuple         =				moon_velocity - velocity_dif

		snake_case_ :							Union[str, Any]         =				Body(-earth_moon_distance     ,					0     ,					0     ,					lowerCamelCase_     ,					lowerCamelCase_     ,					10_00_00_00     ,					"grey"			)
		snake_case_ :							List[Any]         =				Body(0     ,					0     ,					0     ,					lowerCamelCase_     ,					lowerCamelCase_     ,					50_00_00_00     ,					"blue"			)
		return BodySystem([earth, moon]     ,					lowerCamelCase_     ,					time_factor=1_00_00_00			)

def    lowerCAmelCase__		(			):
		snake_case_ :							List[str]         =				[]
		for _ in range(10			):
				snake_case_ :							int         =				random.uniform(-0.5     ,					0.5			)
				snake_case_ :							Tuple         =				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			)     ,					lowerCamelCase_     ,					lowerCamelCase_     ,					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(lowerCamelCase_     ,					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)

'''simple docstring'''


from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


snake_case__     :			int      			=  {
    '''configuration_markuplm''': ['''MARKUPLM_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''MarkupLMConfig'''],
    '''feature_extraction_markuplm''': ['''MarkupLMFeatureExtractor'''],
    '''processing_markuplm''': ['''MarkupLMProcessor'''],
    '''tokenization_markuplm''': ['''MarkupLMTokenizer'''],
}

try:
 if not is_tokenizers_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 snake_case__     :			List[str]      			=  ['''MarkupLMTokenizerFast''']

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 snake_case__     :			Dict      			=  [
     '''MARKUPLM_PRETRAINED_MODEL_ARCHIVE_LIST''',
     '''MarkupLMForQuestionAnswering''',
     '''MarkupLMForSequenceClassification''',
     '''MarkupLMForTokenClassification''',
     '''MarkupLMModel''',
     '''MarkupLMPreTrainedModel''',
 ]


if TYPE_CHECKING:
 from .configuration_markuplm import MARKUPLM_PRETRAINED_CONFIG_ARCHIVE_MAP, MarkupLMConfig
 from .feature_extraction_markuplm import MarkupLMFeatureExtractor
 from .processing_markuplm import MarkupLMProcessor
 from .tokenization_markuplm import MarkupLMTokenizer

 try:
  if not is_tokenizers_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_markuplm_fast import MarkupLMTokenizerFast

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_markuplm import (
      MARKUPLM_PRETRAINED_MODEL_ARCHIVE_LIST,
      MarkupLMForQuestionAnswering,
      MarkupLMForSequenceClassification,
      MarkupLMForTokenClassification,
      MarkupLMModel,
      MarkupLMPreTrainedModel,
  )


else:
 import sys

 snake_case__     :			Optional[Any]      			=  _LazyModule(__name__, globals()['''__file__'''], _import_structure)






