
'''simple docstring'''
from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


lowercase__						       =      {
    "configuration_bloom": ["BLOOM_PRETRAINED_CONFIG_ARCHIVE_MAP", "BloomConfig", "BloomOnnxConfig"],
}
try:
						if not is_tokenizers_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowercase__						       =      ["BloomTokenizerFast"]

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowercase__						       =      [
						    "BLOOM_PRETRAINED_MODEL_ARCHIVE_LIST",
						    "BloomForCausalLM",
						    "BloomModel",
						    "BloomPreTrainedModel",
						    "BloomForSequenceClassification",
						    "BloomForTokenClassification",
						    "BloomForQuestionAnswering",
						]

if TYPE_CHECKING:
						from .configuration_bloom import BLOOM_PRETRAINED_CONFIG_ARCHIVE_MAP, BloomConfig, BloomOnnxConfig

						try:
												if not is_tokenizers_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .tokenization_bloom_fast import BloomTokenizerFast

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_bloom import (
												    BLOOM_PRETRAINED_MODEL_ARCHIVE_LIST,
												    BloomForCausalLM,
												    BloomForQuestionAnswering,
												    BloomForSequenceClassification,
												    BloomForTokenClassification,
												    BloomModel,
												    BloomPreTrainedModel,
												)

else:
						import sys

						lowercase__						       =      _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)




'''simple docstring'''
from __future__ import annotations

from math import ceil, floor, sqrt




def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__ = 200_0000			)  ->							int:


		'''simple docstring'''


		snake_case  :       list[int]     			=						[0]
		snake_case  :       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
		snake_case  :       int     			=						0
		# the area corresponding to the grid that gives the product closest to target
		snake_case  :       int     			=						0
		# an estimate of b, using the quadratic formula
		snake_case  :       float
		# the largest integer less than b_estimate
		snake_case  :       int
		# the largest integer less than b_estimate
		snake_case  :       int
		# the triangle number corresponding to b_floor
		snake_case  :       int
		# the triangle number corresponding to b_ceil
		snake_case  :       int

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

				if abs(target - triangle_b_first_guess * triangle_a			) < abs(
				    target - best_product			):
						snake_case  :       str     			=						triangle_b_first_guess * triangle_a
						snake_case  :       int     			=						idx_a * b_floor

				if abs(target - triangle_b_second_guess * triangle_a			) < abs(
				    target - best_product			):
						snake_case  :       List[Any]     			=						triangle_b_second_guess * triangle_a
						snake_case  :       Any     			=						idx_a * b_ceil

		return area


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


