






from __future__ import annotations

from math import ceil, floor, sqrt






def 				lowerCamelCase__				(_UpperCAmelCase = 200_0000):
   SCREAMING_SNAKE_CASE						= [0]
   SCREAMING_SNAKE_CASE						= 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
   SCREAMING_SNAKE_CASE						= 0
   # the area corresponding to the grid that gives the product closest to target
   SCREAMING_SNAKE_CASE						= 0
   # an estimate of b, using the quadratic formula
   SCREAMING_SNAKE_CASE						= 42
   # the largest integer less than b_estimate
   SCREAMING_SNAKE_CASE						= 42
   # the largest integer less than b_estimate
   SCREAMING_SNAKE_CASE						= 42
   # the triangle number corresponding to b_floor
   SCREAMING_SNAKE_CASE						= 42
   # the triangle number corresponding to b_ceil
   SCREAMING_SNAKE_CASE						= 42

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

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

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

   return area


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












from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


a_		:						List[Any]             =    {
    'configuration_bigbird_pegasus': [
        'BIGBIRD_PEGASUS_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'BigBirdPegasusConfig',
        'BigBirdPegasusOnnxConfig',
    ],
}

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				a_		:						Dict             =    [
				    'BIGBIRD_PEGASUS_PRETRAINED_MODEL_ARCHIVE_LIST',
				    'BigBirdPegasusForCausalLM',
				    'BigBirdPegasusForConditionalGeneration',
				    'BigBirdPegasusForQuestionAnswering',
				    'BigBirdPegasusForSequenceClassification',
				    'BigBirdPegasusModel',
				    'BigBirdPegasusPreTrainedModel',
				]


if TYPE_CHECKING:
				from .configuration_bigbird_pegasus import (
				    BIGBIRD_PEGASUS_PRETRAINED_CONFIG_ARCHIVE_MAP,
				    BigBirdPegasusConfig,
				    BigBirdPegasusOnnxConfig,
				)

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_bigbird_pegasus import (
								    BIGBIRD_PEGASUS_PRETRAINED_MODEL_ARCHIVE_LIST,
								    BigBirdPegasusForCausalLM,
								    BigBirdPegasusForConditionalGeneration,
								    BigBirdPegasusForQuestionAnswering,
								    BigBirdPegasusForSequenceClassification,
								    BigBirdPegasusModel,
								    BigBirdPegasusPreTrainedModel,
								)


else:
				import sys

				a_		:						Tuple             =    _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




