




'''simple docstring'''




from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
a_   :	Tuple							   = 20

# Time between time steps in seconds
a_   :	List[str]							   = INTERVAL / 10_00


class 						__UpperCamelCase :






       def __init__(							self,	lowerCAmelCase,	lowerCAmelCase,	lowerCAmelCase,	lowerCAmelCase,	lowerCAmelCase = 1.0,	lowerCAmelCase = 1.0,	lowerCAmelCase = "blue",	):



              """simple docstring"""







              lowerCamelCase_							=position_x
              lowerCamelCase_							=position_y
              lowerCamelCase_							=velocity_x
              lowerCamelCase_							=velocity_y
              lowerCamelCase_							=mass
              lowerCamelCase_							=size
              lowerCamelCase_							=color






       @property
       def   lowercase__  (							self						):



              """simple docstring"""







              return self.position_x, self.position_y






       @property
       def   lowercase__  (							self						):



              """simple docstring"""







              return self.velocity_x, self.velocity_y






       def   lowercase__  (							self,	lowerCAmelCase,	lowerCAmelCase,	lowerCAmelCase						):



              """simple docstring"""







              self.velocity_x += force_x * delta_time
              self.velocity_y += force_y * delta_time






       def   lowercase__  (							self,	lowerCAmelCase						):



              """simple docstring"""







              self.position_x += self.velocity_x * delta_time
              self.position_y += self.velocity_y * delta_time





class 						__UpperCamelCase :






       def __init__(							self,	lowerCAmelCase,	lowerCAmelCase = 1.0,	lowerCAmelCase = 1.0,	lowerCAmelCase = 0.0,	):



              """simple docstring"""







              lowerCamelCase_							=bodies
              lowerCamelCase_							=gravitation_constant
              lowerCamelCase_							=time_factor
              lowerCamelCase_							=softening_factor






       def __len__(							self						):



              """simple docstring"""







              return len(self.bodies						)






       def   lowercase__  (							self,	lowerCAmelCase						):



              """simple docstring"""







              for bodya in self.bodies:
                     lowerCamelCase_							=0.0
                     lowerCamelCase_							=0.0
                     for bodya in self.bodies:
                            if bodya != bodya:
                                   lowerCamelCase_							=bodya.position_x - bodya.position_x
                                   lowerCamelCase_							=bodya.position_y - bodya.position_y

                                   # Calculation of the distance using Pythagoras's theorem
                                   # Extra factor due to the softening technique
                                   lowerCamelCase_							=(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(lowerCAmelCase,	lowerCAmelCase,	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   a_							(   __snake_case							:    BodySystem     , __snake_case							:    float     , __snake_case							:    list[plt.Circle]     )							->		None:



       """simple docstring"""
       body_system.update_system(__snake_case     )

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





def   a_							(   __snake_case							:    str     , __snake_case							:    BodySystem     , __snake_case							:    float = -1     , __snake_case							:    float = 1     , __snake_case							:    float = -1     , __snake_case							:    float = 1     , )							->		None:



       """simple docstring"""
       lowerCamelCase_							=plt.figure()
       fig.canvas.set_window_title(__snake_case     )
       lowerCamelCase_							=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
       lowerCamelCase_							=[
           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(__snake_case     )

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

       lowerCamelCase_							=animation.FuncAnimation(  # noqa: F841
           __snake_case     , __snake_case     , interval=__snake_case     , blit=__snake_case     )

       plt.show()





def   a_							(   )							->		BodySystem:



       """simple docstring"""
       lowerCamelCase_							=0.9_7_0_0_4_3_6
       lowerCamelCase_							=-0.2_4_3_0_8_7_5_3
       lowerCamelCase_							=0.4_6_6_2_0_3_6_8_5
       lowerCamelCase_							=0.4_3_2_3_6_5_7_3

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





def   a_							(   )							->		BodySystem:



       """simple docstring"""
       lowerCamelCase_							=7.34_76e22
       lowerCamelCase_							=5.9_72e24
       lowerCamelCase_							=1022
       lowerCamelCase_							=3_8439_9000
       lowerCamelCase_							=6.6_74e-11

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

       lowerCamelCase_							=Body(-earth_moon_distance     , 0     , 0     , __snake_case     , __snake_case     , 1000_0000     , '''grey'''     )
       lowerCamelCase_							=Body(0     , 0     , 0     , __snake_case     , __snake_case     , 5000_0000     , '''blue'''     )
       return BodySystem([earth, moon]     , __snake_case     , time_factor=100_0000     )





def   a_							(   )							->		BodySystem:



       """simple docstring"""
       lowerCamelCase_							=[]
       for _ in range(10     ):
              lowerCamelCase_							=random.uniform(-0.5     , 0.5     )
              lowerCamelCase_							=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     )     , __snake_case     , __snake_case     , size=0.0_5     , )     )
              bodies.append(
                  Body(
                      random.uniform(-0.5     , 0.5     )     , random.uniform(-0.5     , 0.5     )     , -velocity_x     , -velocity_y     , size=0.0_5     , )     )
       return BodySystem(__snake_case     , 0.0_1     , 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'''




import os
from shutil import copyfile
from typing import List, Optional, Tuple

from tokenizers import processors

from ...tokenization_utils import AddedToken, BatchEncoding
from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import is_sentencepiece_available, logging


if is_sentencepiece_available():
     from .tokenization_mbartaa import MBartaaTokenizer
else:
     a_   :	Tuple							   = None


a_   :	List[Any]							   = logging.get_logger(__name__)

a_   :	Any							   = {"""vocab_file""": """sentencepiece.bpe.model""", """tokenizer_file""": """tokenizer.json"""}

a_   :	Any							   = {
    """vocab_file""": {
        """facebook/mbart-large-50-one-to-many-mmt""": (
            """https://huggingface.co/facebook/mbart-large-50-one-to-many-mmt/resolve/main/sentencepiece.bpe.model"""
        ),
    },
    """tokenizer_file""": {
        """facebook/mbart-large-50-one-to-many-mmt""": (
            """https://huggingface.co/facebook/mbart-large-50-one-to-many-mmt/resolve/main/tokenizer.json"""
        ),
    },
}

a_   :	Dict							   = {
    """facebook/mbart-large-50-one-to-many-mmt""": 10_24,
}

# fmt: off
a_   :	List[str]							   = ["""ar_AR""", """cs_CZ""", """de_DE""", """en_XX""", """es_XX""", """et_EE""", """fi_FI""", """fr_XX""", """gu_IN""", """hi_IN""", """it_IT""", """ja_XX""", """kk_KZ""", """ko_KR""", """lt_LT""", """lv_LV""", """my_MM""", """ne_NP""", """nl_XX""", """ro_RO""", """ru_RU""", """si_LK""", """tr_TR""", """vi_VN""", """zh_CN""", """af_ZA""", """az_AZ""", """bn_IN""", """fa_IR""", """he_IL""", """hr_HR""", """id_ID""", """ka_GE""", """km_KH""", """mk_MK""", """ml_IN""", """mn_MN""", """mr_IN""", """pl_PL""", """ps_AF""", """pt_XX""", """sv_SE""", """sw_KE""", """ta_IN""", """te_IN""", """th_TH""", """tl_XX""", """uk_UA""", """ur_PK""", """xh_ZA""", """gl_ES""", """sl_SI"""]


class 						__UpperCamelCase (				lowerCamelCase__       ):
       lowercase			:					Any   		=VOCAB_FILES_NAMES
       lowercase			:					str   		=PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
       lowercase			:					Dict   		=PRETRAINED_VOCAB_FILES_MAP
       lowercase			:					str   		=['input_ids', 'attention_mask']
       lowercase			:					List[Any]   		=MBartaaTokenizer

       lowercase			:					List[int]   		=[]
       lowercase			:					List[int]   		=[]






       def __init__(							self,	lowerCAmelCase=None,	lowerCAmelCase=None,	lowerCAmelCase=None,	lowerCAmelCase=None,	lowerCAmelCase="</s>",	lowerCAmelCase="</s>",	lowerCAmelCase="<s>",	lowerCAmelCase="<unk>",	lowerCAmelCase="<pad>",	lowerCAmelCase="<mask>",	**lowerCAmelCase,	):



              """simple docstring"""







              lowerCamelCase_							=AddedToken(lowerCAmelCase,	lstrip=lowerCAmelCase,	rstrip=lowerCAmelCase						) if isinstance(lowerCAmelCase,	lowerCAmelCase						) else mask_token

              lowerCamelCase_							=kwargs.get('''additional_special_tokens''',	[]						)
              kwargs["additional_special_tokens"] += [
                  code for code in FAIRSEQ_LANGUAGE_CODES if code not in kwargs["additional_special_tokens"]
              ]

              super().__init__(
                  lowerCAmelCase,	src_lang=lowerCAmelCase,	tgt_lang=lowerCAmelCase,	tokenizer_file=lowerCAmelCase,	eos_token=lowerCAmelCase,	sep_token=lowerCAmelCase,	cls_token=lowerCAmelCase,	unk_token=lowerCAmelCase,	pad_token=lowerCAmelCase,	mask_token=lowerCAmelCase,	**lowerCAmelCase,	)

              lowerCamelCase_							=vocab_file
              lowerCamelCase_							=False if not self.vocab_file else True

              lowerCamelCase_							={
                  lang_code: self.convert_tokens_to_ids(lowerCAmelCase						) for lang_code in FAIRSEQ_LANGUAGE_CODES
              }

              lowerCamelCase_							=src_lang if src_lang is not None else '''en_XX'''
              lowerCamelCase_							=tgt_lang
              lowerCamelCase_							=self.lang_code_to_id[self._src_lang]
              self.set_src_lang_special_tokens(self._src_lang						)






       @property
       def   lowercase__  (							self						):



              """simple docstring"""







              return self._src_lang






       @src_lang.setter
       def   lowercase__  (							self,	lowerCAmelCase						):



              """simple docstring"""







              lowerCamelCase_							=new_src_lang
              self.set_src_lang_special_tokens(self._src_lang						)






       def   lowercase__  (							self,	lowerCAmelCase,	lowerCAmelCase = None						):



              """simple docstring"""







              if token_ids_a is None:
                     return self.prefix_tokens + token_ids_a + self.suffix_tokens
              # We don't expect to process pairs, but leave the pair logic for API consistency
              return self.prefix_tokens + token_ids_a + token_ids_a + self.suffix_tokens






       def   lowercase__  (							self,	lowerCAmelCase,	lowerCAmelCase = "en_XX",	lowerCAmelCase = None,	lowerCAmelCase = "ro_RO",	**lowerCAmelCase,	):



              """simple docstring"""







              lowerCamelCase_							=src_lang
              lowerCamelCase_							=tgt_lang
              return super().prepare_seqaseq_batch(lowerCAmelCase,	lowerCAmelCase,	**lowerCAmelCase						)






       def   lowercase__  (							self						):



              """simple docstring"""







              return self.set_src_lang_special_tokens(self.src_lang						)






       def   lowercase__  (							self						):



              """simple docstring"""







              return self.set_tgt_lang_special_tokens(self.tgt_lang						)






       def   lowercase__  (							self,	lowerCAmelCase						):



              """simple docstring"""







              lowerCamelCase_							=self.convert_tokens_to_ids(lowerCAmelCase						)
              lowerCamelCase_							=[self.cur_lang_code_id]
              lowerCamelCase_							=[self.eos_token_id]

              lowerCamelCase_							=self.convert_ids_to_tokens(self.prefix_tokens						)
              lowerCamelCase_							=self.convert_ids_to_tokens(self.suffix_tokens						)

              lowerCamelCase_							=processors.TemplateProcessing(
                  single=prefix_tokens_str + ['''$A'''] + suffix_tokens_str,	pair=prefix_tokens_str + ['''$A''', '''$B'''] + suffix_tokens_str,	special_tokens=list(zip(prefix_tokens_str + suffix_tokens_str,	self.prefix_tokens + self.suffix_tokens						)						),	)






       def   lowercase__  (							self,	lowerCAmelCase						):



              """simple docstring"""







              lowerCamelCase_							=self.convert_tokens_to_ids(lowerCAmelCase						)
              lowerCamelCase_							=[self.cur_lang_code_id]
              lowerCamelCase_							=[self.eos_token_id]

              lowerCamelCase_							=self.convert_ids_to_tokens(self.prefix_tokens						)
              lowerCamelCase_							=self.convert_ids_to_tokens(self.suffix_tokens						)

              lowerCamelCase_							=processors.TemplateProcessing(
                  single=prefix_tokens_str + ['''$A'''] + suffix_tokens_str,	pair=prefix_tokens_str + ['''$A''', '''$B'''] + suffix_tokens_str,	special_tokens=list(zip(prefix_tokens_str + suffix_tokens_str,	self.prefix_tokens + self.suffix_tokens						)						),	)






       def   lowercase__  (							self,	lowerCAmelCase,	lowerCAmelCase,	lowerCAmelCase,	lowerCAmelCase,	**lowerCAmelCase						):



              """simple docstring"""







              if src_lang is None or tgt_lang is None:
                     raise ValueError('''Translation requires a `src_lang` and a `tgt_lang` for this model'''						)
              lowerCamelCase_							=src_lang
              lowerCamelCase_							=self(lowerCAmelCase,	add_special_tokens=lowerCAmelCase,	return_tensors=lowerCAmelCase,	**lowerCAmelCase						)
              lowerCamelCase_							=self.convert_tokens_to_ids(lowerCAmelCase						)
              lowerCamelCase_							=tgt_lang_id
              return inputs






       def   lowercase__  (							self,	lowerCAmelCase,	lowerCAmelCase = None						):



              """simple docstring"""







              if not self.can_save_slow_tokenizer:
                     raise ValueError(
                         '''Your fast tokenizer does not have the necessary information to save the vocabulary for a slow '''
                         '''tokenizer.'''						)

              if not os.path.isdir(lowerCAmelCase						):
                     logger.error(f'''Vocabulary path ({save_directory}) should be a directory'''						)
                     return
              lowerCamelCase_							=os.path.join(
                  lowerCAmelCase,	(filename_prefix + '''-''' if filename_prefix else '''''') + VOCAB_FILES_NAMES['''vocab_file''']						)

              if os.path.abspath(self.vocab_file						) != os.path.abspath(lowerCAmelCase						):
                     copyfile(self.vocab_file,	lowerCAmelCase						)

              return (out_vocab_file,)




