





from __future__ import annotations

import random

from matplotlib import animation
from matplotlib import pyplot as plt

# Frame rate of the animation
UpperCamelCase__          =20

# Time between time steps in seconds
UpperCamelCase__          =INTERVAL / 1000





class 	lowerCAmelCase__:






       '''simple docstring'''


       def __init__(					self			,  __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase = 1.0			,  __lowerCamelCase = 1.0			,  __lowerCamelCase = "blue"			,  )	->   None:
            _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							position_x
            _SCREAMING_SNAKE_CASE				:		List[str]  			=							position_y
            _SCREAMING_SNAKE_CASE				:		Any  			=							velocity_x
            _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							velocity_y
            _SCREAMING_SNAKE_CASE				:		int  			=							mass
            _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							size
            _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							color




       @property
       def 			UpperCamelCase_	(					self							)	->   tuple[float, float]:
            return self.position_x, self.position_y




       @property
       def 			UpperCamelCase_	(					self							)	->   tuple[float, float]:
            return self.velocity_x, self.velocity_y




       def 			UpperCamelCase_	(					self			,  __lowerCamelCase			,  __lowerCamelCase			,  __lowerCamelCase							)	->   None:
            self.velocity_x += force_x * delta_time
            self.velocity_y += force_y * delta_time







       def 			UpperCamelCase_	(					self			,  __lowerCamelCase							)	->   None:
            self.position_x += self.velocity_x * delta_time
            self.position_y += self.velocity_y * delta_time





class 	lowerCAmelCase__:






       '''simple docstring'''


       def __init__(					self			,  __lowerCamelCase			,  __lowerCamelCase = 1.0			,  __lowerCamelCase = 1.0			,  __lowerCamelCase = 0.0			,  )	->   None:
            _SCREAMING_SNAKE_CASE				:		List[str]  			=							bodies
            _SCREAMING_SNAKE_CASE				:		Tuple  			=							gravitation_constant
            _SCREAMING_SNAKE_CASE				:		Dict  			=							time_factor
            _SCREAMING_SNAKE_CASE				:		Dict  			=							softening_factor




       def __len__(					self							)	->   int:
            return len(self.bodies							)







       def 			UpperCamelCase_	(					self			,  __lowerCamelCase							)	->   None:
            for bodya in self.bodies:
                 _SCREAMING_SNAKE_CASE				:		Tuple  			=							0.0
                 _SCREAMING_SNAKE_CASE				:		Any  			=							0.0
                 for bodya in self.bodies:
                      if bodya != bodya:
                           _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							bodya.position_x - bodya.position_x
                           _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							bodya.position_y - bodya.position_y

                           # Calculation of the distance using Pythagoras's theorem
                           # Extra factor due to the softening technique
                           _SCREAMING_SNAKE_CASE				:		List[Any]  			=							(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 			lowerCamelCase__	(__lowerCamelCase,				__lowerCamelCase,				__lowerCamelCase		):
     body_system.update_system(__lowerCamelCase		)

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






def 			lowerCamelCase__	(__lowerCamelCase,				__lowerCamelCase,				__lowerCamelCase = -1,				__lowerCamelCase = 1,				__lowerCamelCase = -1,				__lowerCamelCase = 1,				):
     _SCREAMING_SNAKE_CASE				:		Any  			=							plt.figure()
     fig.canvas.set_window_title(__lowerCamelCase		)
     _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							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
     _SCREAMING_SNAKE_CASE				:		Optional[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(__lowerCamelCase		)

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

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

     plt.show()






def 			lowerCamelCase__	():
     _SCREAMING_SNAKE_CASE				:		int  			=							0.970_0436
     _SCREAMING_SNAKE_CASE				:		Dict  			=							-0.2430_8753
     _SCREAMING_SNAKE_CASE				:		List[str]  			=							0.4_6620_3685
     _SCREAMING_SNAKE_CASE				:		List[Any]  			=							0.4323_6573

     _SCREAMING_SNAKE_CASE				:		int  			=							[
         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__	():
     _SCREAMING_SNAKE_CASE				:		List[str]  			=							7.3476e22
     _SCREAMING_SNAKE_CASE				:		str  			=							5.972e24
     _SCREAMING_SNAKE_CASE				:		int  			=							1022
     _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							384399000
     _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							6.674e-11

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

     _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							Body(-earth_moon_distance,				0,				0,				__lowerCamelCase,				__lowerCamelCase,				10000000,				"grey"		)
     _SCREAMING_SNAKE_CASE				:		Dict  			=							Body(0,				0,				0,				__lowerCamelCase,				__lowerCamelCase,				50000000,				"blue"		)
     return BodySystem([earth, moon],				__lowerCamelCase,				time_factor=1000000		)






def 			lowerCamelCase__	():
     _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							[]
     for _ in range(10		):
          _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							random.uniform(-0.5,				0.5		)
          _SCREAMING_SNAKE_CASE				:		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		),				__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_3000_0000,
           4_3000_0000,
           -4_3000_0000,
           4_3000_0000,
       )
       plot('Random system with many bodies', example_a(), -1.5, 1.5, -1.5, 1.5)






import json
import os
import random
import shutil
import tempfile
import unittest

import numpy as np
import pytest

from transformers import BertTokenizer, BertTokenizerFast
from transformers.models.bert.tokenization_bert import VOCAB_FILES_NAMES
from transformers.testing_utils import require_vision
from transformers.utils import IMAGE_PROCESSOR_NAME, is_vision_available


if is_vision_available():
       from PIL import Image

       from transformers import FlavaImageProcessor, FlavaProcessor
       from transformers.models.flava.image_processing_flava import (
           FLAVA_CODEBOOK_MEAN,
           FLAVA_CODEBOOK_STD,
           FLAVA_IMAGE_MEAN,
           FLAVA_IMAGE_STD,
       )





@require_vision
class 	lowerCAmelCase__(       unittest.TestCase			):






       '''simple docstring'''


       def 			UpperCamelCase_	(					self							)	->   str:
            _SCREAMING_SNAKE_CASE				:		str  			=							tempfile.mkdtemp()

            # fmt: off
            _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							["[UNK]", "[CLS]", "[SEP]", "[PAD]", "[MASK]", "want", "##want", "##ed", "wa", "un", "runn", "##ing", ",", "low", "lowest"]
            # fmt: on
            _SCREAMING_SNAKE_CASE				:		int  			=							os.path.join(self.tmpdirname			,  VOCAB_FILES_NAMES["vocab_file"]							)

            with open(self.vocab_file			,  "w"			,  encoding="utf-8"							) as fp:
                 fp.write("".join([x + "\n" for x in vocab_tokens]							)							)

            _SCREAMING_SNAKE_CASE				:		Any  			=							{
                "image_mean": FLAVA_IMAGE_MEAN,
                "image_std": FLAVA_IMAGE_STD,
                "do_normalize": True,
                "do_resize": True,
                "size": 2_2_4,
                "do_center_crop": True,
                "crop_size": 2_2_4,
                "input_size_patches": 1_4,
                "total_mask_patches": 7_5,
                "mask_group_max_patches": None,
                "mask_group_min_patches": 1_6,
                "mask_group_min_aspect_ratio": 0.3,
                "mask_group_max_aspect_ratio": None,
                "codebook_do_resize": True,
                "codebook_size": 1_1_2,
                "codebook_do_center_crop": True,
                "codebook_crop_size": 1_1_2,
                "codebook_do_map_pixels": True,
                "codebook_do_normalize": True,
                "codebook_image_mean": FLAVA_CODEBOOK_MEAN,
                "codebook_image_std": FLAVA_CODEBOOK_STD,
            }

            _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							os.path.join(self.tmpdirname			,  __lowerCamelCase							)
            with open(self.image_processor_file			,  "w"			,  encoding="utf-8"							) as fp:
                 json.dump(__lowerCamelCase			,  __lowerCamelCase							)




       def 			UpperCamelCase_	(					self			,  **__lowerCamelCase							)	->   List[str]:
            return BertTokenizer.from_pretrained(self.tmpdirname			,  **__lowerCamelCase							)




       def 			UpperCamelCase_	(					self			,  **__lowerCamelCase							)	->   Optional[Any]:
            return BertTokenizerFast.from_pretrained(self.tmpdirname			,  **__lowerCamelCase							)




       def 			UpperCamelCase_	(					self			,  **__lowerCamelCase							)	->   Tuple:
            return FlavaImageProcessor.from_pretrained(self.tmpdirname			,  **__lowerCamelCase							)




       def 			UpperCamelCase_	(					self							)	->   int:
            shutil.rmtree(self.tmpdirname							)




       def 			UpperCamelCase_	(					self							)	->   Optional[int]:
            _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							[np.random.randint(2_5_5			,  size=(3, 3_0, 4_0_0)			,  dtype=np.uinta							)]

            _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							[Image.fromarray(np.moveaxis(__lowerCamelCase			,  0			,  -1							)							) for x in image_inputs]

            return image_inputs




       def 			UpperCamelCase_	(					self							)	->   Any:
            _SCREAMING_SNAKE_CASE				:		Dict  			=							self.get_tokenizer()
            _SCREAMING_SNAKE_CASE				:		Any  			=							self.get_rust_tokenizer()
            _SCREAMING_SNAKE_CASE				:		Dict  			=							self.get_image_processor()

            _SCREAMING_SNAKE_CASE				:		List[Any]  			=							FlavaProcessor(tokenizer=__lowerCamelCase			,  image_processor=__lowerCamelCase							)
            processor_slow.save_pretrained(self.tmpdirname							)
            _SCREAMING_SNAKE_CASE				:		Tuple  			=							FlavaProcessor.from_pretrained(self.tmpdirname			,  use_fast=__lowerCamelCase							)

            _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							FlavaProcessor(tokenizer=__lowerCamelCase			,  image_processor=__lowerCamelCase							)
            processor_fast.save_pretrained(self.tmpdirname							)
            _SCREAMING_SNAKE_CASE				:		int  			=							FlavaProcessor.from_pretrained(self.tmpdirname							)

            self.assertEqual(processor_slow.tokenizer.get_vocab()			,  tokenizer_slow.get_vocab()							)
            self.assertEqual(processor_fast.tokenizer.get_vocab()			,  tokenizer_fast.get_vocab()							)
            self.assertEqual(tokenizer_slow.get_vocab()			,  tokenizer_fast.get_vocab()							)
            self.assertIsInstance(processor_slow.tokenizer			,  __lowerCamelCase							)
            self.assertIsInstance(processor_fast.tokenizer			,  __lowerCamelCase							)

            self.assertEqual(processor_slow.image_processor.to_json_string()			,  image_processor.to_json_string()							)
            self.assertEqual(processor_fast.image_processor.to_json_string()			,  image_processor.to_json_string()							)
            self.assertIsInstance(processor_slow.image_processor			,  __lowerCamelCase							)
            self.assertIsInstance(processor_fast.image_processor			,  __lowerCamelCase							)




       def 			UpperCamelCase_	(					self							)	->   Optional[int]:
            _SCREAMING_SNAKE_CASE				:		Dict  			=							FlavaProcessor(tokenizer=self.get_tokenizer()			,  image_processor=self.get_image_processor()							)
            processor.save_pretrained(self.tmpdirname							)

            _SCREAMING_SNAKE_CASE				:		str  			=							self.get_tokenizer(bos_token="(BOS)"			,  eos_token="(EOS)"							)
            _SCREAMING_SNAKE_CASE				:		List[str]  			=							self.get_image_processor(do_normalize=__lowerCamelCase			,  padding_value=1.0							)

            _SCREAMING_SNAKE_CASE				:		Dict  			=							FlavaProcessor.from_pretrained(
                self.tmpdirname			,  bos_token="(BOS)"			,  eos_token="(EOS)"			,  do_normalize=__lowerCamelCase			,  padding_value=1.0							)

            self.assertEqual(processor.tokenizer.get_vocab()			,  tokenizer_add_kwargs.get_vocab()							)
            self.assertIsInstance(processor.tokenizer			,  __lowerCamelCase							)

            self.assertEqual(processor.image_processor.to_json_string()			,  image_processor_add_kwargs.to_json_string()							)
            self.assertIsInstance(processor.image_processor			,  __lowerCamelCase							)




       def 			UpperCamelCase_	(					self							)	->   Any:
            _SCREAMING_SNAKE_CASE				:		str  			=							self.get_image_processor()
            _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							self.get_tokenizer()

            _SCREAMING_SNAKE_CASE				:		Any  			=							FlavaProcessor(tokenizer=__lowerCamelCase			,  image_processor=__lowerCamelCase							)

            _SCREAMING_SNAKE_CASE				:		int  			=							self.prepare_image_inputs()

            _SCREAMING_SNAKE_CASE				:		List[str]  			=							image_processor(__lowerCamelCase			,  return_tensors="np"							)
            _SCREAMING_SNAKE_CASE				:		str  			=							processor(images=__lowerCamelCase			,  return_tensors="np"							)

            for key in input_feat_extract.keys():
                 self.assertAlmostEqual(input_feat_extract[key].sum()			,  input_processor[key].sum()			,  delta=1E-2							)

            # With rest of the args
            random.seed(1_2_3_4							)
            _SCREAMING_SNAKE_CASE				:		List[Any]  			=							image_processor(
                __lowerCamelCase			,  return_image_mask=__lowerCamelCase			,  return_codebook_pixels=__lowerCamelCase			,  return_tensors="np"							)
            random.seed(1_2_3_4							)
            _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							processor(
                images=__lowerCamelCase			,  return_image_mask=__lowerCamelCase			,  return_codebook_pixels=__lowerCamelCase			,  return_tensors="np"							)

            for key in input_feat_extract.keys():
                 self.assertAlmostEqual(input_feat_extract[key].sum()			,  input_processor[key].sum()			,  delta=1E-2							)




       def 			UpperCamelCase_	(					self							)	->   int:
            _SCREAMING_SNAKE_CASE				:		Any  			=							self.get_image_processor()
            _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							self.get_tokenizer()

            _SCREAMING_SNAKE_CASE				:		int  			=							FlavaProcessor(tokenizer=__lowerCamelCase			,  image_processor=__lowerCamelCase							)

            _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							"lower newer"

            _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							processor(text=__lowerCamelCase							)

            _SCREAMING_SNAKE_CASE				:		List[str]  			=							tokenizer(__lowerCamelCase							)

            for key in encoded_tok.keys():
                 self.assertListEqual(encoded_tok[key]			,  encoded_processor[key]							)




       def 			UpperCamelCase_	(					self							)	->   Tuple:
            _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							self.get_image_processor()
            _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							self.get_tokenizer()

            _SCREAMING_SNAKE_CASE				:		List[Any]  			=							FlavaProcessor(tokenizer=__lowerCamelCase			,  image_processor=__lowerCamelCase							)

            _SCREAMING_SNAKE_CASE				:		Any  			=							"lower newer"
            _SCREAMING_SNAKE_CASE				:		Dict  			=							self.prepare_image_inputs()

            _SCREAMING_SNAKE_CASE				:		List[Any]  			=							processor(text=__lowerCamelCase			,  images=__lowerCamelCase							)

            self.assertListEqual(list(inputs.keys()							)			,  ["input_ids", "token_type_ids", "attention_mask", "pixel_values"]							)

            # add extra args
            _SCREAMING_SNAKE_CASE				:		Tuple  			=							processor(text=__lowerCamelCase			,  images=__lowerCamelCase			,  return_codebook_pixels=__lowerCamelCase			,  return_image_mask=__lowerCamelCase							)

            self.assertListEqual(
                list(inputs.keys()							)			,  [
                    "input_ids",
                    "token_type_ids",
                    "attention_mask",
                    "pixel_values",
                    "codebook_pixel_values",
                    "bool_masked_pos",
                ]			,  )

            # test if it raises when no input is passed
            with pytest.raises(__lowerCamelCase							):
                 processor()




       def 			UpperCamelCase_	(					self							)	->   Dict:
            _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							self.get_image_processor()
            _SCREAMING_SNAKE_CASE				:		str  			=							self.get_tokenizer()

            _SCREAMING_SNAKE_CASE				:		int  			=							FlavaProcessor(tokenizer=__lowerCamelCase			,  image_processor=__lowerCamelCase							)

            _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							[[1, 4, 5, 8, 1, 0, 8], [3, 4, 3, 1, 1, 8, 9]]

            _SCREAMING_SNAKE_CASE				:		Dict  			=							processor.batch_decode(__lowerCamelCase							)
            _SCREAMING_SNAKE_CASE				:		Any  			=							tokenizer.batch_decode(__lowerCamelCase							)

            self.assertListEqual(__lowerCamelCase			,  __lowerCamelCase							)







       def 			UpperCamelCase_	(					self							)	->   Any:
            _SCREAMING_SNAKE_CASE				:		int  			=							self.get_image_processor()
            _SCREAMING_SNAKE_CASE				:		Union[str, Any]  			=							self.get_tokenizer()

            _SCREAMING_SNAKE_CASE				:		Dict  			=							FlavaProcessor(tokenizer=__lowerCamelCase			,  image_processor=__lowerCamelCase							)

            _SCREAMING_SNAKE_CASE				:		Optional[Any]  			=							"lower newer"
            _SCREAMING_SNAKE_CASE				:		Optional[int]  			=							self.prepare_image_inputs()

            _SCREAMING_SNAKE_CASE				:		List[Any]  			=							processor(text=__lowerCamelCase			,  images=__lowerCamelCase							)

            self.assertListEqual(list(inputs.keys()							)			,  processor.model_input_names							)