
from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


UpperCamelCase_   	=	{
    'configuration_nllb_moe': [
        'NLLB_MOE_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'NllbMoeConfig',
    ]
}

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCamelCase_   	=	[
					    'NLLB_MOE_PRETRAINED_MODEL_ARCHIVE_LIST',
					    'NllbMoeForConditionalGeneration',
					    'NllbMoeModel',
					    'NllbMoePreTrainedModel',
					    'NllbMoeTop2Router',
					    'NllbMoeSparseMLP',
					]


if TYPE_CHECKING:
					from .configuration_nllb_moe import (
					    NLLB_MOE_PRETRAINED_CONFIG_ARCHIVE_MAP,
					    NllbMoeConfig,
					)

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_nllb_moe import (
										    NLLB_MOE_PRETRAINED_MODEL_ARCHIVE_LIST,
										    NllbMoeForConditionalGeneration,
										    NllbMoeModel,
										    NllbMoePreTrainedModel,
										    NllbMoeSparseMLP,
										    NllbMoeTopaRouter,
										)


else:
					import sys

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






from __future__ import annotations

from math import ceil, floor, sqrt






def 		_UpperCAmelCase   (	UpperCamelCase:     int = 2_0_0_0_0_0_0  ):






	"""simple docstring"""


	__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(UpperCamelCase  )
		__lowerCAmelCase         =							ceil(UpperCamelCase  )
		__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() = }''')






