



'''simple docstring'''

from __future__ import annotations

from math import ceil, floor, sqrt







def 						__UpperCamelCase				(							_lowercase = 200_0000					) ->			int:
	_lowercase					:       list[int]       =		[0]
	_lowercase					:       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
	_lowercase					:       int       =		0
	# the area corresponding to the grid that gives the product closest to target
	_lowercase					:       int       =		0
	# an estimate of b, using the quadratic formula
	_lowercase					:       float
	# the largest integer less than b_estimate
	_lowercase					:       int
	# the largest integer less than b_estimate
	_lowercase					:       int
	# the triangle number corresponding to b_floor
	_lowercase					:       int
	# the triangle number corresponding to b_ceil
	_lowercase					:       int

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

		if abs(target - triangle_b_first_guess * triangle_a					) < abs(
		    target - best_product					):
			_lowercase					:       Optional[Any]       =		triangle_b_first_guess * triangle_a
			_lowercase					:       Union[str, Any]       =		idx_a * b_floor

		if abs(target - triangle_b_second_guess * triangle_a					) < abs(
		    target - best_product					):
			_lowercase					:       Dict       =		triangle_b_second_guess * triangle_a
			_lowercase					:       Optional[Any]       =		idx_a * b_ceil

	return area


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





'''simple docstring'''

from ...configuration_utils import PretrainedConfig
from ...utils import logging


_A				:    Dict     						=logging.get_logger(__name__)

_A				:    Dict     						={
    # See all MEGATRON_BERT models at https://huggingface.co/models?filter=bert
}



class 		lowerCamelCase__      (						A     ):




					'''simple docstring'''



					A_						    =						"""megatron-bert"""




					def __init__(  self				:	int     ,  UpperCamelCase_				:	int=2_9056     ,  UpperCamelCase_				:	Optional[int]=1024     ,  UpperCamelCase_				:	Optional[Any]=24     ,  UpperCamelCase_				:	List[Any]=16     ,  UpperCamelCase_				:	Optional[int]=4096     ,  UpperCamelCase_				:	Optional[Any]="gelu"     ,  UpperCamelCase_				:	List[Any]=0.1     ,  UpperCamelCase_				:	Union[str, Any]=0.1     ,  UpperCamelCase_				:	int=512     ,  UpperCamelCase_				:	Dict=2     ,  UpperCamelCase_				:	Union[str, Any]=0.02     ,  UpperCamelCase_				:	Any=1E-12     ,  UpperCamelCase_				:	Tuple=0     ,  UpperCamelCase_				:	Optional[int]="absolute"     ,  UpperCamelCase_				:	Optional[Any]=True     ,  **UpperCamelCase_				:	Any     ,  )  ->       List[Any]:



						'''simple docstring'''





						super().__init__(pad_token_id=UpperCamelCase_     ,  **UpperCamelCase_					)

						_lowercase					:       Dict       =		vocab_size
						_lowercase					:       Any       =		hidden_size
						_lowercase					:       Union[str, Any]       =		num_hidden_layers
						_lowercase					:       Dict       =		num_attention_heads
						_lowercase					:       Dict       =		hidden_act
						_lowercase					:       Optional[Any]       =		intermediate_size
						_lowercase					:       Optional[int]       =		hidden_dropout_prob
						_lowercase					:       Optional[Any]       =		attention_probs_dropout_prob
						_lowercase					:       Any       =		max_position_embeddings
						_lowercase					:       str       =		type_vocab_size
						_lowercase					:       Optional[Any]       =		initializer_range
						_lowercase					:       List[str]       =		layer_norm_eps
						_lowercase					:       List[Any]       =		position_embedding_type
						_lowercase					:       Optional[Any]       =		use_cache
