




import argparse
import logging
import os
from pathlib import Path
from typing import Any, Dict

import pytorch_lightning as pl
from pytorch_lightning.utilities import rank_zero_info

from transformers import (
    AdamW,
    AutoConfig,
    AutoModel,
    AutoModelForPreTraining,
    AutoModelForQuestionAnswering,
    AutoModelForSeqaSeqLM,
    AutoModelForSequenceClassification,
    AutoModelForTokenClassification,
    AutoModelWithLMHead,
    AutoTokenizer,
    PretrainedConfig,
    PreTrainedTokenizer,
)
from transformers.optimization import (
    Adafactor,
    get_cosine_schedule_with_warmup,
    get_cosine_with_hard_restarts_schedule_with_warmup,
    get_linear_schedule_with_warmup,
    get_polynomial_decay_schedule_with_warmup,
)
from transformers.utils.versions import require_version


a_            =   logging.getLogger(__name__)

require_version('pytorch_lightning>=1.0.4')

a_            =   {
    'base': AutoModel,
    'sequence-classification': AutoModelForSequenceClassification,
    'question-answering': AutoModelForQuestionAnswering,
    'pretraining': AutoModelForPreTraining,
    'token-classification': AutoModelForTokenClassification,
    'language-modeling': AutoModelWithLMHead,
    'summarization': AutoModelForSeqaSeqLM,
    'translation': AutoModelForSeqaSeqLM,
}


# update this and the import above to support new schedulers from transformers.optimization
a_            =   {
    'linear': get_linear_schedule_with_warmup,
    'cosine': get_cosine_schedule_with_warmup,
    'cosine_w_restarts': get_cosine_with_hard_restarts_schedule_with_warmup,
    'polynomial': get_polynomial_decay_schedule_with_warmup,
    # '': get_constant_schedule,             # not supported for now
    # '': get_constant_schedule_with_warmup, # not supported for now
}
a_            =   sorted(arg_to_scheduler.keys())
a_            =   '{' + ', '.join(arg_to_scheduler_choices) + '}'

class        UpperCAmelCase_  (	pl.LightningModule						):
		def __init__(		self							,		UpperCamelCase_							,		UpperCamelCase_=None							,		UpperCamelCase_="base"							,		UpperCamelCase_=None							,		UpperCamelCase_=None							,		UpperCamelCase_=None							,		**UpperCamelCase_							,		)		->   List[Any]:
					super().__init__()
					# TODO: move to self.save_hyperparameters()
					# self.save_hyperparameters()
					# can also expand arguments into trainer signature for easier reading

					self.save_hyperparameters(UpperCamelCase_   )
					__lowercase	:       Tuple				=   0
					__lowercase	:       Optional[int]				=   Path(self.hparams.output_dir   )
					__lowercase	:       Any				=   self.hparams.cache_dir if self.hparams.cache_dir else None
					if config is None:
								__lowercase	:       str				=   AutoConfig.from_pretrained(
								    self.hparams.config_name if self.hparams.config_name else self.hparams.model_name_or_path							,		**({'''num_labels''': num_labels} if num_labels is not None else {})							,		cache_dir=UpperCamelCase_							,		**UpperCamelCase_							,		)
					else:
								__lowercase	:       PretrainedConfig				=   config

					__lowercase	:       Dict				=   ("encoder_layerdrop", "decoder_layerdrop", "dropout", "attention_dropout")
					for p in extra_model_params:
								if getattr(self.hparams							,		UpperCamelCase_							,		UpperCamelCase_   ):
											assert hasattr(self.config							,		UpperCamelCase_   ), F"""model config doesn't have a `{p}` attribute"""
											setattr(self.config							,		UpperCamelCase_							,		getattr(self.hparams							,		UpperCamelCase_   )   )

					if tokenizer is None:
								__lowercase	:       Union[str, Any]				=   AutoTokenizer.from_pretrained(
								    self.hparams.tokenizer_name if self.hparams.tokenizer_name else self.hparams.model_name_or_path							,		cache_dir=UpperCamelCase_							,		)
					else:
								__lowercase	:       PreTrainedTokenizer				=   tokenizer
					__lowercase	:       Optional[Any]				=   MODEL_MODES[mode]
					if model is None:
								__lowercase	:       Union[str, Any]				=   self.model_type.from_pretrained(
								    self.hparams.model_name_or_path							,		from_tf=bool('''.ckpt''' in self.hparams.model_name_or_path   )							,		config=self.config							,		cache_dir=UpperCamelCase_							,		)
					else:
								__lowercase	:       Union[str, Any]				=   model
		def 					_lowerCamelCase    (		self							,		*UpperCamelCase_							,		**UpperCamelCase_   )		->   Optional[int]:
					__lowercase	:       Union[str, Any]				=   self.model_type.from_pretrained(*UpperCamelCase_							,		**UpperCamelCase_   )
		def 					_lowerCamelCase    (		self   )		->   Tuple:
					__lowercase	:       int				=   arg_to_scheduler[self.hparams.lr_scheduler]
					__lowercase	:       int				=   get_schedule_func(
					    self.opt							,		num_warmup_steps=self.hparams.warmup_steps							,		num_training_steps=self.total_steps()   )
					__lowercase	:       int				=   {"scheduler": scheduler, "interval": "step", "frequency": 1}
					return scheduler
		def 					_lowerCamelCase    (		self   )		->   str:
					__lowercase	:       Union[str, Any]				=   self.model
					__lowercase	:       str				=   ["bias", "LayerNorm.weight"]
					__lowercase	:       List[Any]				=   [
					    {
					        "params": [p for n, p in model.named_parameters() if not any(nd in n for nd in no_decay   )],
					        "weight_decay": self.hparams.weight_decay,
					    },
					    {
					        "params": [p for n, p in model.named_parameters() if any(nd in n for nd in no_decay   )],
					        "weight_decay": 0.0,
					    },
					]
					if self.hparams.adafactor:
								__lowercase	:       Union[str, Any]				=   Adafactor(
								    UpperCamelCase_							,		lr=self.hparams.learning_rate							,		scale_parameter=UpperCamelCase_							,		relative_step=UpperCamelCase_   )

					else:
								__lowercase	:       List[Any]				=   AdamW(
								    UpperCamelCase_							,		lr=self.hparams.learning_rate							,		eps=self.hparams.adam_epsilon   )
					__lowercase	:       str				=   optimizer

					__lowercase	:       List[str]				=   self.get_lr_scheduler()

					return [optimizer], [scheduler]
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_							,		UpperCamelCase_   )		->   Union[str, Any]:
					return self.validation_step(UpperCamelCase_							,		UpperCamelCase_   )
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_   )		->   List[str]:
					return self.validation_end(UpperCamelCase_   )
		def 					_lowerCamelCase    (		self   )		->   Optional[int]:
					__lowercase	:       Tuple				=   max(1							,		self.hparams.gpus   )  # TODO: consider num_tpu_cores
					__lowercase	:       Optional[int]				=   self.hparams.train_batch_size * self.hparams.accumulate_grad_batches * num_devices
					return (self.dataset_size / effective_batch_size) * self.hparams.max_epochs
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_   )		->   Any:






					if stage == "test":
								__lowercase	:       Optional[int]				=   len(self.test_dataloader().dataset   )
					else:
								__lowercase	:       Union[str, Any]				=   self.get_dataloader('''train'''							,		self.hparams.train_batch_size							,		shuffle=UpperCamelCase_   )
								__lowercase	:       Any				=   len(self.train_dataloader().dataset   )
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_							,		UpperCamelCase_							,		UpperCamelCase_ = False   )		->   str:
					raise NotImplementedError('''You must implement this for your task'''   )
		def 					_lowerCamelCase    (		self   )		->   List[Any]:
					return self.train_loader
		def 					_lowerCamelCase    (		self   )		->   Union[str, Any]:
					return self.get_dataloader('''dev'''							,		self.hparams.eval_batch_size							,		shuffle=UpperCamelCase_   )
		def 					_lowerCamelCase    (		self   )		->   Optional[int]:
					return self.get_dataloader('''test'''							,		self.hparams.eval_batch_size							,		shuffle=UpperCamelCase_   )
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_   )		->   Dict:
					return os.path.join(
					    self.hparams.data_dir							,		'''cached_{}_{}_{}'''.format(
					        UpperCamelCase_							,		list(filter(UpperCamelCase_							,		self.hparams.model_name_or_path.split('''/'''   )   )   ).pop()							,		str(self.hparams.max_seq_length   )							,		)							,		)
		@pl.utilities.rank_zero_only
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_   )		->   List[str]:
					__lowercase	:       str				=   self.output_dir.joinpath('''best_tfmr'''   )
					__lowercase	:       List[Any]				=   self.step_count
					self.model.save_pretrained(UpperCamelCase_   )
					self.tokenizer.save_pretrained(UpperCamelCase_   )
		@staticmethod
		def 					_lowerCamelCase    (		UpperCamelCase_							,		UpperCamelCase_   )		->   Dict:
					parser.add_argument(
					    '''--model_name_or_path'''							,		default=UpperCamelCase_							,		type=UpperCamelCase_							,		required=UpperCamelCase_							,		help='''Path to pretrained model or model identifier from huggingface.co/models'''							,		)
					parser.add_argument(
					    '''--config_name'''							,		default=''''''							,		type=UpperCamelCase_							,		help='''Pretrained config name or path if not the same as model_name'''   )
					parser.add_argument(
					    '''--tokenizer_name'''							,		default=UpperCamelCase_							,		type=UpperCamelCase_							,		help='''Pretrained tokenizer name or path if not the same as model_name'''							,		)
					parser.add_argument(
					    '''--cache_dir'''							,		default=''''''							,		type=UpperCamelCase_							,		help='''Where do you want to store the pre-trained models downloaded from huggingface.co'''							,		)
					parser.add_argument(
					    '''--encoder_layerdrop'''							,		type=UpperCamelCase_							,		help='''Encoder layer dropout probability (Optional). Goes into model.config'''							,		)
					parser.add_argument(
					    '''--decoder_layerdrop'''							,		type=UpperCamelCase_							,		help='''Decoder layer dropout probability (Optional). Goes into model.config'''							,		)
					parser.add_argument(
					    '''--dropout'''							,		type=UpperCamelCase_							,		help='''Dropout probability (Optional). Goes into model.config'''							,		)
					parser.add_argument(
					    '''--attention_dropout'''							,		type=UpperCamelCase_							,		help='''Attention dropout probability (Optional). Goes into model.config'''							,		)
					parser.add_argument('''--learning_rate'''							,		default=5E-5							,		type=UpperCamelCase_							,		help='''The initial learning rate for Adam.'''   )
					parser.add_argument(
					    '''--lr_scheduler'''							,		default='''linear'''							,		choices=UpperCamelCase_							,		metavar=UpperCamelCase_							,		type=UpperCamelCase_							,		help='''Learning rate scheduler'''							,		)
					parser.add_argument('''--weight_decay'''							,		default=0.0							,		type=UpperCamelCase_							,		help='''Weight decay if we apply some.'''   )
					parser.add_argument('''--adam_epsilon'''							,		default=1E-8							,		type=UpperCamelCase_							,		help='''Epsilon for Adam optimizer.'''   )
					parser.add_argument('''--warmup_steps'''							,		default=0							,		type=UpperCamelCase_							,		help='''Linear warmup over warmup_steps.'''   )
					parser.add_argument('''--num_workers'''							,		default=4							,		type=UpperCamelCase_							,		help='''kwarg passed to DataLoader'''   )
					parser.add_argument('''--num_train_epochs'''							,		dest='''max_epochs'''							,		default=3							,		type=UpperCamelCase_   )
					parser.add_argument('''--train_batch_size'''							,		default=32							,		type=UpperCamelCase_   )
					parser.add_argument('''--eval_batch_size'''							,		default=32							,		type=UpperCamelCase_   )
					parser.add_argument('''--adafactor'''							,		action='''store_true'''   )


class        UpperCAmelCase_  (	pl.Callback						):
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_							,		UpperCamelCase_   )		->   int:






					if (
					    trainer.is_global_zero and trainer.global_rank == 0
					):  # we initialize the retriever only on master worker with RAY. In new pytorch-lightning accelorators are removed.
								pl_module.model.rag.retriever.init_retrieval()  # better to use hook functions.


class        UpperCAmelCase_  (	pl.Callback						):
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_							,		UpperCamelCase_   )		->   Optional[int]:
					__lowercase	:       List[str]				=   trainer.lr_schedulers[0]["scheduler"]
					__lowercase	:       Union[str, Any]				=   {F"""lr_group_{i}""": lr for i, lr in enumerate(lr_scheduler.get_lr()   )}
					pl_module.logger.log_metrics(UpperCamelCase_   )
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_							,		UpperCamelCase_   )		->   Optional[Any]:
					rank_zero_info('''***** Validation results *****'''   )
					__lowercase	:       str				=   trainer.callback_metrics
					# Log results
					for key in sorted(UpperCamelCase_   ):
								if key not in ["log", "progress_bar"]:
											rank_zero_info('''{} = {}\n'''.format(UpperCamelCase_							,		str(metrics[key]   )   )   )
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_							,		UpperCamelCase_   )		->   str:
					rank_zero_info('''***** Test results *****'''   )
					__lowercase	:       Any				=   trainer.callback_metrics
					# Log and save results to file
					__lowercase	:       Dict				=   os.path.join(pl_module.hparams.output_dir							,		'''test_results.txt'''   )
					with open(UpperCamelCase_							,		'''w'''   ) as writer:
								for key in sorted(UpperCamelCase_   ):
											if key not in ["log", "progress_bar"]:
														rank_zero_info('''{} = {}\n'''.format(UpperCamelCase_							,		str(metrics[key]   )   )   )
														writer.write('''{} = {}\n'''.format(UpperCamelCase_							,		str(metrics[key]   )   )   )







def       __UpperCAmelCase      (				__UpperCamelCase					,							__UpperCamelCase					):
			parser.add_argument(
			    '''--output_dir'''					,							default=_UpperCamelCase					,							type=_UpperCamelCase					,							required=_UpperCamelCase					,							help='''The output directory where the model predictions and checkpoints will be written.'''					,							)
			parser.add_argument(
			    '''--fp16'''					,							action='''store_true'''					,							help='''Whether to use 16-bit (mixed) precision (through NVIDIA apex) instead of 32-bit'''					,							)

			parser.add_argument(
			    '''--fp16_opt_level'''					,							type=_UpperCamelCase					,							default='''O2'''					,							help=(
			        '''For fp16: Apex AMP optimization level selected in [\'O0\', \'O1\', \'O2\', and \'O3\'].'''
			        '''See details at https://nvidia.github.io/apex/amp.html'''
			    )					,							)
			parser.add_argument('''--n_tpu_cores'''					,							dest='''tpu_cores'''					,							type=_UpperCamelCase					)
			parser.add_argument('''--max_grad_norm'''					,							dest='''gradient_clip_val'''					,							default=1.0					,							type=_UpperCamelCase					,							help='''Max gradient norm'''					)
			parser.add_argument('''--do_train'''					,							action='''store_true'''					,							help='''Whether to run training.'''					)
			parser.add_argument('''--do_predict'''					,							action='''store_true'''					,							help='''Whether to run predictions on the test set.'''					)
			parser.add_argument(
			    '''--gradient_accumulation_steps'''					,							dest='''accumulate_grad_batches'''					,							type=_UpperCamelCase					,							default=1					,							help='''Number of updates steps to accumulate before performing a backward/update pass.'''					,							)
			parser.add_argument('''--seed'''					,							type=_UpperCamelCase					,							default=42					,							help='''random seed for initialization'''					)
			parser.add_argument(
			    '''--data_dir'''					,							default=_UpperCamelCase					,							type=_UpperCamelCase					,							required=_UpperCamelCase					,							help='''The input data dir. Should contain the training files for the CoNLL-2003 NER task.'''					,							)







def       __UpperCAmelCase      (				__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase=None					,							__UpperCamelCase=True					,							__UpperCamelCase=None					,							__UpperCamelCase=[]					,							__UpperCamelCase=None					,							__UpperCamelCase=None					,							**__UpperCamelCase					,							):
			pl.seed_everything(args.seed					)

			# init model
			__lowercase	:       str				=   Path(model.hparams.output_dir					)
			odir.mkdir(exist_ok=_UpperCamelCase					)

			# add custom checkpoints
			if checkpoint_callback is None:
						__lowercase	:       Optional[Any]				=   pl.callbacks.ModelCheckpoint(
						    filepath=args.output_dir					,							prefix='''checkpoint'''					,							monitor='''val_loss'''					,							mode='''min'''					,							save_top_k=1					)
			if early_stopping_callback:
						extra_callbacks.append(_UpperCamelCase					)
			if logging_callback is None:
						__lowercase	:       Dict				=   LoggingCallback()

			__lowercase	:       Optional[Any]				=   {}

			# TODO: remove with PyTorch 1.6 since pl uses native amp
			if args.fpaa:
						__lowercase	:       Optional[int]				=   16
						# train_params["amp_level"] = args.fp16_opt_level

			if args.gpus > 1:
						__lowercase	:       str				=   "auto"  # "ddp"
						__lowercase	:       str				=   "ddp"

			__lowercase	:       Tuple				=   args.accumulate_grad_batches
			__lowercase	:       int				=   None  # extra_train_kwargs.get("profiler", None) #get unwanted logs
			__lowercase	:       Union[str, Any]				=   "auto"

			__lowercase	:       Optional[Any]				=   pl.Trainer.from_argparse_args(
			    _UpperCamelCase					,							weights_summary=_UpperCamelCase					,							callbacks=[logging_callback] + extra_callbacks + [checkpoint_callback] + [InitCallback()]					,							logger=_UpperCamelCase					,							**_UpperCamelCase					,							)

			if args.do_train:
						trainer.fit(_UpperCamelCase					)

			return trainer









"""simple docstring"""




from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
a_            =   2_0

# Time between time steps in seconds
a_            =   INTERVAL / 1_0_0_0

class        UpperCAmelCase_  :
		def __init__(		self							,		UpperCamelCase_							,		UpperCamelCase_							,		UpperCamelCase_							,		UpperCamelCase_							,		UpperCamelCase_ = 1.0							,		UpperCamelCase_ = 1.0							,		UpperCamelCase_ = "blue"							,		)		->   None:
					__lowercase	:       Optional[int]				=   position_x
					__lowercase	:       List[Any]				=   position_y
					__lowercase	:       Optional[int]				=   velocity_x
					__lowercase	:       List[str]				=   velocity_y
					__lowercase	:       List[Any]				=   mass
					__lowercase	:       Tuple				=   size
					__lowercase	:       Tuple				=   color
		@property
		def 					_lowerCamelCase    (		self   )		->   tuple[float, float]:
					return self.position_x, self.position_y
		@property
		def 					_lowerCamelCase    (		self   )		->   tuple[float, float]:
					return self.velocity_x, self.velocity_y
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_							,		UpperCamelCase_							,		UpperCamelCase_   )		->   None:
					self.velocity_x += force_x * delta_time
					self.velocity_y += force_y * delta_time
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_   )		->   None:
					self.position_x += self.velocity_x * delta_time
					self.position_y += self.velocity_y * delta_time


class        UpperCAmelCase_  :
		def __init__(		self							,		UpperCamelCase_							,		UpperCamelCase_ = 1.0							,		UpperCamelCase_ = 1.0							,		UpperCamelCase_ = 0.0							,		)		->   None:
					__lowercase	:       int				=   bodies
					__lowercase	:       Dict				=   gravitation_constant
					__lowercase	:       List[Any]				=   time_factor
					__lowercase	:       List[str]				=   softening_factor
		def __len__(		self   )		->   int:
					return len(self.bodies   )
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_   )		->   None:
					for bodya in self.bodies:
								__lowercase	:       Optional[Any]				=   0.0
								__lowercase	:       Any				=   0.0
								for bodya in self.bodies:
											if bodya != bodya:
														__lowercase	:       Union[str, Any]				=   bodya.position_x - bodya.position_x
														__lowercase	:       str				=   bodya.position_y - bodya.position_y

														# Calculation of the distance using Pythagoras's theorem
														# Extra factor due to the softening technique
														__lowercase	:       str				=   (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(UpperCamelCase_							,		UpperCamelCase_							,		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       __UpperCAmelCase      (				__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					):
			body_system.update_system(__UpperCamelCase					)

			# Update the positions of the patches
			for patch, body in zip(__UpperCamelCase					,							body_system.bodies					):
						__lowercase	:       List[str]				=   (body.position_x, body.position_y)







def       __UpperCAmelCase      (				__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase = -1					,							__UpperCamelCase = 1					,							__UpperCamelCase = -1					,							__UpperCamelCase = 1					,							):
			__lowercase	:       List[str]				=   plt.figure()
			fig.canvas.set_window_title(__UpperCamelCase					)
			__lowercase	:       List[Any]				=   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
			__lowercase	:       Any				=   [
			    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(__UpperCamelCase					)

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

			__lowercase	:       Tuple				=   animation.FuncAnimation(  # noqa: F841
			    __UpperCamelCase					,							__UpperCamelCase					,							interval=__UpperCamelCase					,							blit=__UpperCamelCase					)

			plt.show()







def       __UpperCAmelCase      (				):
			__lowercase	:       Dict				=   0.9_700_436
			__lowercase	:       Tuple				=   -0.24_308_753
			__lowercase	:       Any				=   0.466_203_685
			__lowercase	:       str				=   0.43_236_573

			__lowercase	:       int				=   [
			    Body(__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					,							size=0.2					,							color='''red'''					),
			    Body(-position_x					,							-position_y					,							__UpperCamelCase					,							__UpperCamelCase					,							size=0.2					,							color='''green'''					),
			    Body(0					,							0					,							-2 * velocity_x					,							-2 * velocity_y					,							size=0.2					,							color='''blue'''					),
			]
			return BodySystem(__UpperCamelCase					,							time_factor=3					)







def       __UpperCAmelCase      (				):
			__lowercase	:       Tuple				=   7.3_476e22
			__lowercase	:       Optional[int]				=   5.972e24
			__lowercase	:       str				=   10_22
			__lowercase	:       Any				=   3_84_39_90_00
			__lowercase	:       Optional[int]				=   6.674e-11

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

			__lowercase	:       Tuple				=   Body(-earth_moon_distance					,							0					,							0					,							__UpperCamelCase					,							__UpperCamelCase					,							10_00_00_00					,							'''grey'''					)
			__lowercase	:       Dict				=   Body(0					,							0					,							0					,							__UpperCamelCase					,							__UpperCamelCase					,							50_00_00_00					,							'''blue'''					)
			return BodySystem([earth, moon]					,							__UpperCamelCase					,							time_factor=1_00_00_00					)







def       __UpperCAmelCase      (				):
			__lowercase	:       Optional[Any]				=   []
			for _ in range(10					):
						__lowercase	:       str				=   random.uniform(-0.5					,							0.5					)
						__lowercase	:       int				=   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					)					,							__UpperCamelCase					,							__UpperCamelCase					,							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(__UpperCamelCase					,							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_3_0_0_0_0_0_0_0,
			    4_3_0_0_0_0_0_0_0,
			    -4_3_0_0_0_0_0_0_0,
			    4_3_0_0_0_0_0_0_0,
			)
			plot('Random system with many bodies', example_a(), -1.5, 1.5, -1.5, 1.5)



