




from __future__ import annotations

from math import ceil, floor, sqrt







def 		lowercase__   (		__A:	int = 2_0_0_0_0_0_0				):





     '''simple docstring'''






     __magic_name__							:	list[int]    							=							[0]
     __magic_name__							:	int

     for idx in range(1							,ceil(sqrt(target * 2				) * 1.1				)				):
          triangle_numbers.append(triangle_numbers[-1] + idx				)

     # we want this to be as close as possible to target
     __magic_name__							:	int    							=							0
     # the area corresponding to the grid that gives the product closest to target
     __magic_name__							:	int    							=							0
     # an estimate of b, using the quadratic formula
     __magic_name__							:	float
     # the largest integer less than b_estimate
     __magic_name__							:	int
     # the largest integer less than b_estimate
     __magic_name__							:	int
     # the triangle number corresponding to b_floor
     __magic_name__							:	int
     # the triangle number corresponding to b_ceil
     __magic_name__							:	int

     for idx_a, triangle_a in enumerate(triangle_numbers[1:]							,1				):
          __magic_name__							:	Optional[int]    							=							(-1 + sqrt(1 + 8 * target / triangle_a				)) / 2
          __magic_name__							:	str    							=							floor(__A				)
          __magic_name__							:	Optional[int]    							=							ceil(__A				)
          __magic_name__							:	Optional[Any]    							=							triangle_numbers[b_floor]
          __magic_name__							:	Any    							=							triangle_numbers[b_ceil]

          if abs(target - triangle_b_first_guess * triangle_a				) < abs(
              target - best_product				):
               __magic_name__							:	List[Any]    							=							triangle_b_first_guess * triangle_a
               __magic_name__							:	str    							=							idx_a * b_floor

          if abs(target - triangle_b_second_guess * triangle_a				) < abs(
              target - best_product				):
               __magic_name__							:	Tuple    							=							triangle_b_second_guess * triangle_a
               __magic_name__							:	Union[str, Any]    							=							idx_a * b_ceil

     return area


if __name__ == "__main__":
 print(F"""{solution() = }""")









import json
import os
import unittest

from transformers.models.blenderbot_small.tokenization_blenderbot_small import (
    VOCAB_FILES_NAMES,
    BlenderbotSmallTokenizer,
)

from ...test_tokenization_common import TokenizerTesterMixin


class    lowerCamelCase    (		_lowerCamelCase				,unittest.TestCase						):






			'''simple docstring'''





			UpperCamelCase__								=BlenderbotSmallTokenizer
			UpperCamelCase__								=False

			def 							UpperCAmelCase__       ( self			:   Union[str, Any]  )						->   str:
								super().setUp()

								__magic_name__							:	Union[str, Any]    							=							['''__start__''', '''adapt''', '''act''', '''ap@@''', '''te''', '''__end__''', '''__unk__''']
								__magic_name__							:	Tuple    							=							dict(zip(lowerCamelCase_       ,						range(len(lowerCamelCase_  )  )  )  )

								__magic_name__							:	Tuple    							=							['''#version: 0.2''', '''a p''', '''t e</w>''', '''ap t</w>''', '''a d''', '''ad apt</w>''', '''a c''', '''ac t</w>''', '''''']
								__magic_name__							:	List[Any]    							=							{'''unk_token''': '''__unk__''', '''bos_token''': '''__start__''', '''eos_token''': '''__end__'''}

								__magic_name__							:	str    							=							os.path.join(self.tmpdirname       ,						VOCAB_FILES_NAMES['''vocab_file''']  )
								__magic_name__							:	List[str]    							=							os.path.join(self.tmpdirname       ,						VOCAB_FILES_NAMES['''merges_file''']  )
								with open(self.vocab_file       ,						'''w'''       ,						encoding='''utf-8'''  ) as fp:
													fp.write(json.dumps(lowerCamelCase_  ) + '''\n'''  )
								with open(self.merges_file       ,						'''w'''       ,						encoding='''utf-8'''  ) as fp:
													fp.write('''\n'''.join(lowerCamelCase_  )  )

			def 							UpperCAmelCase__       ( self			:   List[str]       ,						**lowerCamelCase_			:   Optional[Any]  )						->   List[Any]:
								kwargs.update(self.special_tokens_map  )
								return BlenderbotSmallTokenizer.from_pretrained(self.tmpdirname       ,						**lowerCamelCase_  )

			def 							UpperCAmelCase__       ( self			:   Dict       ,						lowerCamelCase_			:   Union[str, Any]  )						->   Optional[int]:
								__magic_name__							:	Union[str, Any]    							=							'''adapt act apte'''
								__magic_name__							:	Dict    							=							'''adapt act apte'''
								return input_text, output_text

			def 							UpperCAmelCase__       ( self			:   Union[str, Any]  )						->   Any:
								__magic_name__							:	int    							=							BlenderbotSmallTokenizer(self.vocab_file       ,						self.merges_file       ,						**self.special_tokens_map  )
								__magic_name__							:	str    							=							'''adapt act apte'''
								__magic_name__							:	Any    							=							['''adapt''', '''act''', '''ap@@''', '''te''']
								__magic_name__							:	List[str]    							=							tokenizer.tokenize(lowerCamelCase_  )
								self.assertListEqual(lowerCamelCase_       ,						lowerCamelCase_  )

								__magic_name__							:	Union[str, Any]    							=							[tokenizer.bos_token] + tokens + [tokenizer.eos_token]

								__magic_name__							:	List[Any]    							=							[0, 1, 2, 3, 4, 5]
								self.assertListEqual(tokenizer.convert_tokens_to_ids(lowerCamelCase_  )       ,						lowerCamelCase_  )

			def 							UpperCAmelCase__       ( self			:   int  )						->   int:
								__magic_name__							:	Any    							=							BlenderbotSmallTokenizer.from_pretrained('''facebook/blenderbot-90M'''  )
								assert tok('''sam'''  ).input_ids == [1384]
								__magic_name__							:	Dict    							=							'''I am a small frog.'''
								__magic_name__							:	Tuple    							=							tok([src_text]       ,						padding=lowerCamelCase_       ,						truncation=lowerCamelCase_  )['''input_ids''']
								__magic_name__							:	Tuple    							=							tok.batch_decode(lowerCamelCase_       ,						skip_special_tokens=lowerCamelCase_       ,						clean_up_tokenization_spaces=lowerCamelCase_  )[0]
								assert src_text != decoded  # I wish it did!
								assert decoded == "i am a small frog ."


			def 							UpperCAmelCase__       ( self			:   Tuple  )						->   Dict:
								__magic_name__							:	Tuple    							=							BlenderbotSmallTokenizer.from_pretrained('''facebook/blenderbot-90M'''  )
								__magic_name__							:	Any    							=							'''I am a small frog .'''
								__magic_name__							:	List[str]    							=							'''.'''
								__magic_name__							:	Tuple    							=							tok(lowerCamelCase_  )['''input_ids''']
								__magic_name__							:	Optional[Any]    							=							tok(lowerCamelCase_  )['''input_ids''']

								assert encoded[-1] == encoded_dot[0]



