


from __future__ import annotations

from math import ceil, floor, sqrt



def 				UpperCamelCase_(      lowerCamelCase_ = 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[int]      		=		(-1 + sqrt(1 + 8 * target / triangle_a )) / 2
        _lowercase       :							List[str]      		=		floor(lowerCamelCase_ )
        _lowercase       :							Dict      		=		ceil(lowerCamelCase_ )
        _lowercase       :							List[str]      		=		triangle_numbers[b_floor]
        _lowercase       :							List[str]      		=		triangle_numbers[b_ceil]

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


_snake_case     :		Optional[int]       						= logging.get_logger(__name__)

_snake_case     :		Optional[int]       						= {
    'google/vivit-b-16x2-kinetics400': (
        'https://huggingface.co/google/vivit-b-16x2-kinetics400/resolve/main/config.json'
    ),
    # See all Vivit models at https://huggingface.co/models?filter=vivit
}






class 					_UpperCAmelCase   (	lowercase_ ):
					UpperCamelCase      =							'''vivit'''


					def __init__(					self			:Optional[Any]     ,       __UpperCamelCase			:Dict=2_24     ,       __UpperCamelCase			:int=32     ,       __UpperCamelCase			:Union[str, Any]=[2, 16, 16]     ,       __UpperCamelCase			:Optional[Any]=3     ,       __UpperCamelCase			:Optional[Any]=7_68     ,       __UpperCamelCase			:Any=12     ,       __UpperCamelCase			:List[str]=12     ,       __UpperCamelCase			:List[str]=30_72     ,       __UpperCamelCase			:Any="gelu_fast"     ,       __UpperCamelCase			:List[Any]=0.0     ,       __UpperCamelCase			:str=0.0     ,       __UpperCamelCase			:Dict=0.02     ,       __UpperCamelCase			:Optional[Any]=1e-06     ,       __UpperCamelCase			:Dict=True     ,       **__UpperCamelCase			:Tuple     ,       ):
												A		=  hidden_size
												A		=  num_hidden_layers
												A		=  num_attention_heads
												A		=  intermediate_size
												A		=  hidden_act
												A		=  hidden_dropout_prob
												A		=  attention_probs_dropout_prob
												A		=  initializer_range
												A		=  layer_norm_eps

												A		=  image_size
												A		=  num_frames
												A		=  tubelet_size
												A		=  num_channels
												A		=  qkv_bias

												super().__init__(**__UpperCamelCase		)


