




"""simple docstring"""






from __future__ import annotations

from math import ceil, floor, sqrt







def   _snake_case    (       lowercase__ = 2000000	):
				_lowerCamelCase  :    list[int]					=					[0]
				_lowerCamelCase  :    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
				_lowerCamelCase  :    int					=					0
				# the area corresponding to the grid that gives the product closest to target
				_lowerCamelCase  :    int					=					0
				# an estimate of b, using the quadratic formula
				_lowerCamelCase  :    float
				# the largest integer less than b_estimate
				_lowerCamelCase  :    int
				# the largest integer less than b_estimate
				_lowerCamelCase  :    int
				# the triangle number corresponding to b_floor
				_lowerCamelCase  :    int
				# the triangle number corresponding to b_ceil
				_lowerCamelCase  :    int

				for idx_a, triangle_a in enumerate(triangle_numbers[1:]							,					1	):
								_lowerCamelCase  :    int					=					(-1 + sqrt(1 + 8 * target / triangle_a	)) / 2
								_lowerCamelCase  :    int					=					floor(lowercase__	)
								_lowerCamelCase  :    List[Any]					=					ceil(lowercase__	)
								_lowerCamelCase  :    int					=					triangle_numbers[b_floor]
								_lowerCamelCase  :    Tuple					=					triangle_numbers[b_ceil]

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

								if abs(target - triangle_b_second_guess * triangle_a	) < abs(
								    target - best_product	):
												_lowerCamelCase  :    Optional[Any]					=					triangle_b_second_guess * triangle_a
												_lowerCamelCase  :    Optional[int]					=					idx_a * b_ceil

				return area


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





"""simple docstring"""






from dataclasses import dataclass
from typing import List, Optional, Union

import numpy as np
import torch

from ...utils import BaseOutput, OptionalDependencyNotAvailable, is_torch_available, is_transformers_available






@dataclass
class lowerCAmelCase__			(  lowercase		):






			'''simple docstring'''



			lowerCamelCase__   =    42


try:
			if not (is_transformers_available() and is_torch_available()):
						raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
			from ...utils.dummy_torch_and_transformers_objects import *  # noqa F403
else:
			from .pipeline_text_to_video_synth import TextToVideoSDPipeline
			from .pipeline_text_to_video_synth_imgaimg import VideoToVideoSDPipeline  # noqa: F401
			from .pipeline_text_to_video_zero import TextToVideoZeroPipeline