


from __future__ import annotations

from math import ceil, floor, sqrt




def     UpperCamelCase    (      _a = 2_0_0_0_0_0_0		)					->							int:
     '''simple docstring'''





     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_       :str     =       (-1 + sqrt(1 + 8 * target / triangle_a		)) / 2
          lowercase_       :Tuple     =       floor(_a		)
          lowercase_       :Any     =       ceil(_a		)
          lowercase_       :Tuple     =       triangle_numbers[b_floor]
          lowercase_       :List[Any]     =       triangle_numbers[b_ceil]

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

          if abs(target - triangle_b_second_guess * triangle_a		) < abs(
              target - best_product		):
               lowercase_       :List[str]     =       triangle_b_second_guess * triangle_a
               lowercase_       :Union[str, Any]     =       idx_a * b_ceil

     return area


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





import numpy as np
import torch
import torch.nn as nn
from transformers import CLIPConfig, CLIPVisionModelWithProjection, PreTrainedModel

from ...utils import logging


SCREAMING_SNAKE_CASE       :		int         =				logging.get_logger(__name__)






class      UpperCamelCase					(		lowercase__     ):


   '''simple docstring'''







   lowercase					:	List[str]									=CLIPConfig

   lowercase					:	Tuple									=["""CLIPEncoderLayer"""]
   def __init__(     self   ,							UpperCamelCase_		):
        super().__init__(UpperCamelCase_		)

        lowercase_       :Union[str, Any]     =       CLIPVisionModelWithProjection(config.vision_config		)

        lowercase_       :str     =       nn.Linear(config.vision_config.projection_dim   ,							1		)
        lowercase_       :Optional[int]     =       nn.Linear(config.vision_config.projection_dim   ,							1		)




   @torch.no_grad()
   def 		UpperCamelCase  (     self   ,							UpperCamelCase_   ,							UpperCamelCase_   ,							UpperCamelCase_=0.5   ,							UpperCamelCase_=0.5		):
        lowercase_       :Optional[int]     =       self.vision_model(UpperCamelCase_		)[0]

        lowercase_       :Optional[int]     =       self.p_head(UpperCamelCase_		)
        lowercase_       :List[Any]     =       nsfw_detected.flatten()
        lowercase_       :List[str]     =       nsfw_detected > p_threshold
        lowercase_       :Optional[int]     =       nsfw_detected.tolist()

        if any(UpperCamelCase_		):
             logger.warning(
                 '''Potential NSFW content was detected in one or more images. A black image will be returned instead.'''
                 ''' Try again with a different prompt and/or seed.'''		)

        for idx, nsfw_detected_ in enumerate(UpperCamelCase_		):
             if nsfw_detected_:
                  lowercase_       :str     =       np.zeros(images[idx].shape		)

        lowercase_       :int     =       self.w_head(UpperCamelCase_		)
        lowercase_       :Union[str, Any]     =       watermark_detected.flatten()
        lowercase_       :int     =       watermark_detected > w_threshold
        lowercase_       :int     =       watermark_detected.tolist()

        if any(UpperCamelCase_		):
             logger.warning(
                 '''Potential watermarked content was detected in one or more images. A black image will be returned instead.'''
                 ''' Try again with a different prompt and/or seed.'''		)

        for idx, watermark_detected_ in enumerate(UpperCamelCase_		):
             if watermark_detected_:
                  lowercase_       :Dict     =       np.zeros(images[idx].shape		)

        return images, nsfw_detected, watermark_detected

