
'''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() = }""")



import logging
from dataclasses import dataclass, field
from pathlib import Path
from typing import Optional, Union

from .generation.configuration_utils import GenerationConfig
from .training_args import TrainingArguments
from .utils import add_start_docstrings


__A			:					Optional[Any]						=			logging.getLogger(__name__)





@dataclass
@add_start_docstrings(TrainingArguments.__doc__		)
class 			_SCREAMING_SNAKE_CASE (   __snake_case		):







   '''simple docstring'''




   lowerCamelCase__				=      field(default=__snake_case					,       metadata={"help": "Whether to use SortishSampler or not."}		)
   lowerCamelCase__				=      field(
       default=__snake_case					,       metadata={"help": "Whether to use generate to calculate generative metrics (ROUGE, BLEU)."}		)
   lowerCamelCase__				=      field(
       default=__snake_case					,       metadata={
           "help": (
               "The `max_length` to use on each evaluation loop when `predict_with_generate=True`. Will default "
               "to the `max_length` value of the model configuration."
           )
       }					,       )
   lowerCamelCase__				=      field(
       default=__snake_case					,       metadata={
           "help": (
               "The `num_beams` to use on each evaluation loop when `predict_with_generate=True`. Will default "
               "to the `num_beams` value of the model configuration."
           )
       }					,       )
   lowerCamelCase__				=      field(
       default=__snake_case					,       metadata={
           "help": "Model id, file path or url pointing to a GenerationConfig json file, to use during prediction."
       }					,       )





   def      _snake_case		(       self					:			Union[str, Any]			):
       SCREAMING_SNAKE_CASE										=   super().to_dict()
       for k, v in d.items():
           if isinstance(__lowerCamelCase     , __lowerCamelCase			):
               SCREAMING_SNAKE_CASE										=   v.to_dict()
       return d