
"""simple docstring"""







from itertools import count
from math import asin, pi, sqrt
def       __UpperCAmelCase		(		a_      :		float					)  ->							float:
   return (
       (1 - 2 * point) * sqrt(point - point**2					) + 2 * point + asin(sqrt(1 - point					)					)
   ) / 4
def       __UpperCAmelCase		(		a_      :		int					)  ->							float:
   _UpperCAmelCase 						=       (circles_number + 1 - sqrt(2 * circles_number					)) / (
       2 * (circles_number**2 + 1)
   )
   _UpperCAmelCase 						=       circles_number * intersection_y

   _UpperCAmelCase 						=       intersection_x * intersection_y / 2
   _UpperCAmelCase 						=       circle_bottom_arc_integral(
       1 / 2					) - circle_bottom_arc_integral(a_					)

   return triangle_area + concave_region_area
def       __UpperCAmelCase		(		a_      :		float = 1 / 10_00					)  ->							int:
   _UpperCAmelCase 						=       (1 - pi / 4) / 4

   for n in count(1					):
      if concave_triangle_area(a_					) / l_section_area < fraction:
         return n

   return -1


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



"""simple docstring"""







from typing import List

import PIL
import torch
from PIL import Image

from ...configuration_utils import ConfigMixin
from ...models.modeling_utils import ModelMixin
from ...utils import PIL_INTERPOLATION






class      __a      (       lowerCAmelCase_					,						lowerCAmelCase_      ):







       def __init__(       self		):



          '''simple docstring'''

          super().__init__()

          self.register_buffer("watermark_image"				,torch.zeros((62, 62, 4)		)		)
          _UpperCAmelCase 						=       None







       def  _snake_case      (       self				,lowerCamelCase_				,lowerCamelCase_=None		):



          '''simple docstring'''

          _UpperCAmelCase 						=       images[0].height
          _UpperCAmelCase 						=       images[0].width

          _UpperCAmelCase 						=       sample_size or h

          _UpperCAmelCase 						=       min(h / sample_size				,w / sample_size		)
          _UpperCAmelCase						,				_UpperCAmelCase 						=       (int(h / coef		), int(w / coef		)) if coef < 1 else (h, w)

          _UpperCAmelCase						,				_UpperCAmelCase 						=       1024**2, img_w * img_h
          _UpperCAmelCase 						=       (Sa / Sa) ** 0.5
          _UpperCAmelCase						,				_UpperCAmelCase						,				_UpperCAmelCase 						=       int(K * 62		), img_w - int(14 * K		), img_h - int(14 * K		)

          if self.watermark_image_as_pil is None:
             _UpperCAmelCase 						=       self.watermark_image.to(torch.uinta		).cpu().numpy()
             _UpperCAmelCase 						=       Image.fromarray(lowerCamelCase_				,mode="RGBA"		)
             _UpperCAmelCase 						=       watermark_image

          _UpperCAmelCase 						=       self.watermark_image_as_pil.resize(
              (wm_size, wm_size)				,PIL_INTERPOLATION["bicubic"]				,reducing_gap=lowerCamelCase_		)

          for pil_img in images:
             pil_img.paste(lowerCamelCase_				,box=(wm_x - wm_size, wm_y - wm_size, wm_x, wm_y)				,mask=wm_img.split()[-1]		)

          return images

