
'''simple docstring'''



from __future__ import annotations

from math import ceil, floor, sqrt


def A (__lowerCamelCase :int = 2000000						):
						_lowerCAmelCase    		=					[0]
						_lowerCAmelCase    		=					42

						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
						_lowerCAmelCase    		=					0
						# the area corresponding to the grid that gives the product closest to target
						_lowerCAmelCase    		=					0
						# an estimate of b, using the quadratic formula
						_lowerCAmelCase    		=					42
						# the largest integer less than b_estimate
						_lowerCAmelCase    		=					42
						# the largest integer less than b_estimate
						_lowerCAmelCase    		=					42
						# the triangle number corresponding to b_floor
						_lowerCAmelCase    		=					42
						# the triangle number corresponding to b_ceil
						_lowerCAmelCase    		=					42

						for idx_a, triangle_a in enumerate(triangle_numbers[1:]					,      1						):
												_lowerCAmelCase    		=					(-1 + sqrt(1 + 8 * target / triangle_a						)) / 2
												_lowerCAmelCase    		=					floor(__lowerCamelCase						)
												_lowerCAmelCase    		=					ceil(__lowerCamelCase						)
												_lowerCAmelCase    		=					triangle_numbers[b_floor]
												_lowerCAmelCase    		=					triangle_numbers[b_ceil]

												if abs(target - triangle_b_first_guess * triangle_a						) < abs(
												    target - best_product						):
																		_lowerCAmelCase    		=					triangle_b_first_guess * triangle_a
																		_lowerCAmelCase    		=					idx_a * b_floor

												if abs(target - triangle_b_second_guess * triangle_a						) < abs(
												    target - best_product						):
																		_lowerCAmelCase    		=					triangle_b_second_guess * triangle_a
																		_lowerCAmelCase    		=					idx_a * b_ceil

						return area


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







"""simple docstring"""





import contextlib
import importlib
import io
import unittest

import transformers

# Try to import everything from transformers to ensure every object can be loaded.
from transformers import *  # noqa F406
from transformers.testing_utils import DUMMY_UNKNOWN_IDENTIFIER, require_flax, require_tf, require_torch
from transformers.utils import ContextManagers, find_labels, is_flax_available, is_tf_available, is_torch_available


if is_torch_available():
							from transformers import BertForPreTraining, BertForQuestionAnswering, BertForSequenceClassification

if is_tf_available():
							from transformers import TFBertForPreTraining, TFBertForQuestionAnswering, TFBertForSequenceClassification

if is_flax_available():
							from transformers import FlaxBertForPreTraining, FlaxBertForQuestionAnswering, FlaxBertForSequenceClassification


_UpperCamelCase					      =   DUMMY_UNKNOWN_IDENTIFIER
# An actual model hosted on huggingface.co

_UpperCamelCase					      =   'main'
# Default branch name
_UpperCamelCase					      =   'f2c752cfc5c0ab6f4bdec59acea69eefbee381c2'
# One particular commit (not the top of `main`)
_UpperCamelCase					      =   'aaaaaaa'
# This commit does not exist, so we should 404.

_UpperCamelCase					      =   'd9e9f15bc825e4b2c9249e9578f884bbcb5e3684'
# Sha-1 of config.json on the top of `main`, for checking purposes
_UpperCamelCase					      =   '4b243c475af8d0a7754e87d7d096c92e5199ec2fe168a2ee7998e3b8e9bcb1d3'



@contextlib.contextmanager
def 					lowerCAmelCase_      (   ):


							'''simple docstring'''







							print('''Welcome!''' )
							yield
							print('''Bye!''' )



@contextlib.contextmanager
def 					lowerCAmelCase_      (   ):


							'''simple docstring'''







							print('''Bonjour!''' )
							yield
							print('''Au revoir!''' )
class 		SCREAMING_SNAKE_CASE_				(     unittest.TestCase ):
				"""simple docstring"""




				def        __lowercase	(  self	:str      ):
											# If the spec is missing, importlib would not be able to import the module dynamically.
											assert transformers.__spec__ is not None
											assert importlib.util.find_spec('''transformers'''      ) is not None

class 		SCREAMING_SNAKE_CASE_				(     unittest.TestCase ):
				"""simple docstring"""




				@unittest.mock.patch('''sys.stdout'''    ,     new_callable=io.StringIO      )
				def        __lowercase	(  self	:str    ,     __lowercase	:str      ):
											with ContextManagers([]      ):
																		print('''Transformers are awesome!'''      )
											# The print statement adds a new line at the end of the output
											self.assertEqual(mock_stdout.getvalue()    ,     '''Transformers are awesome!\n'''      )




				@unittest.mock.patch('''sys.stdout'''    ,     new_callable=io.StringIO      )
				def        __lowercase	(  self	:Any    ,     __lowercase	:Tuple      ):
											with ContextManagers([context_en()]      ):
																		print('''Transformers are awesome!'''      )
											# The output should be wrapped with an English welcome and goodbye
											self.assertEqual(mock_stdout.getvalue()    ,     '''Welcome!\nTransformers are awesome!\nBye!\n'''      )




				@unittest.mock.patch('''sys.stdout'''    ,     new_callable=io.StringIO      )
				def        __lowercase	(  self	:List[Any]    ,     __lowercase	:Optional[Any]      ):
											with ContextManagers([context_fr(), context_en()]      ):
																		print('''Transformers are awesome!'''      )
											# The output should be wrapped with an English and French welcome and goodbye
											self.assertEqual(mock_stdout.getvalue()    ,     '''Bonjour!\nWelcome!\nTransformers are awesome!\nBye!\nAu revoir!\n'''      )




				@require_torch
				def        __lowercase	(  self	:Tuple      ):
											self.assertEqual(find_labels(__lowercase      )    ,     ['''labels''']      )
											self.assertEqual(find_labels(__lowercase      )    ,     ['''labels''', '''next_sentence_label''']      )
											self.assertEqual(find_labels(__lowercase      )    ,     ['''start_positions''', '''end_positions''']      )
											class 		SCREAMING_SNAKE_CASE_				(     snake_case__ ):
															"""simple docstring"""
															pass

											self.assertEqual(find_labels(__lowercase      )    ,     ['''labels''']      )




				@require_tf
				def        __lowercase	(  self	:str      ):
											self.assertEqual(find_labels(__lowercase      )    ,     ['''labels''']      )
											self.assertEqual(find_labels(__lowercase      )    ,     ['''labels''', '''next_sentence_label''']      )
											self.assertEqual(find_labels(__lowercase      )    ,     ['''start_positions''', '''end_positions''']      )
											class 		SCREAMING_SNAKE_CASE_				(     snake_case__ ):
															"""simple docstring"""
															pass

											self.assertEqual(find_labels(__lowercase      )    ,     ['''labels''']      )




				@require_flax
				def        __lowercase	(  self	:str      ):
											# Flax models don't have labels
											self.assertEqual(find_labels(__lowercase      )    ,     []      )
											self.assertEqual(find_labels(__lowercase      )    ,     []      )
											self.assertEqual(find_labels(__lowercase      )    ,     []      )
											class 		SCREAMING_SNAKE_CASE_				(     snake_case__ ):
															"""simple docstring"""
															pass

											self.assertEqual(find_labels(__lowercase      )    ,     []      )




