
"""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    ):
										super().__init__()

										self.register_buffer("watermark_image"     ,   torch.zeros((62, 62, 4)    )    )
										lowercase   :    int			=							None

			def       __magic_name__      (      self     ,   _a     ,   _a=None    ):
										lowercase   :    List[str]			=							images[0].height
										lowercase   :    Dict			=							images[0].width

										lowercase   :    Optional[int]			=							sample_size or h

										lowercase   :    int			=							min(h / sample_size     ,   w / sample_size    )
										lowercase		,   lowercase   :    Optional[int]			=							(int(h / coef    ), int(w / coef    )) if coef < 1 else (h, w)

										lowercase		,   lowercase   :    Dict			=							1_024**2, img_w * img_h
										lowercase   :    Tuple			=							(Sa / Sa) ** 0.5
										lowercase		,   lowercase		,   lowercase   :    Optional[Any]			=							int(K * 62    ), img_w - int(14 * K    ), img_h - int(14 * K    )

										if self.watermark_image_as_pil is None:
																	lowercase   :    Dict			=							self.watermark_image.to(torch.uinta    ).cpu().numpy()
																	lowercase   :    Dict			=							Image.fromarray(_UpperCamelCase     ,   mode="RGBA"    )
																	lowercase   :    Union[str, Any]			=							watermark_image

										lowercase   :    Optional[int]			=							self.watermark_image_as_pil.resize(
										    (wm_size, wm_size)     ,   PIL_INTERPOLATION["bicubic"]     ,   reducing_gap=_UpperCamelCase    )

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

										return images




"""simple docstring"""




import math
from collections.abc import Generator


def   __magic_name__     (				__snake_case    :	int  )			->    Generator[int, None, None]:
       lowercase   :    Generator			=							(i for i in range(1					,			(max_n + 1)  ))
       for i in (n for n in numbers if n > 1):
              for j in range(2					,			__snake_case  ):
                     if (i % j) == 0:
                            break
              else:
                     yield i


def   __magic_name__     (				__snake_case    :	int  )			->    Generator[int, None, None]:
       lowercase   :    Generator			=							(i for i in range(1					,			(max_n + 1)  ))
       for i in (n for n in numbers if n > 1):
              # only need to check for factors up to sqrt(i)
              lowercase   :    Dict			=							int(math.sqrt(__snake_case  )  ) + 1
              for j in range(2					,			__snake_case  ):
                     if (i % j) == 0:
                            break
              else:
                     yield i


def   __magic_name__     (				__snake_case    :	int  )			->    Generator[int, None, None]:
       lowercase   :    Generator			=							(i for i in range(1					,			(max_n + 1)					,			2  ))
       # It's useless to test even numbers as they will not be prime
       if max_n > 2:
              yield 2  # Because 2 will not be tested, it's necessary to yield it now
       for i in (n for n in numbers if n > 1):
              lowercase   :    int			=							int(math.sqrt(__snake_case  )  ) + 1
              for j in range(3					,			__snake_case					,			2  ):
                     # As we removed the even numbers, we don't need them now
                     if (i % j) == 0:
                            break
              else:
                     yield i


def   __magic_name__     (				)			->    Tuple:
       from timeit import timeit

       lowercase   :    List[str]			=							"from __main__ import slow_primes, primes, fast_primes"
       print(timeit("slow_primes(1_000_000_000_000)"					,			setup=__snake_case					,			number=100_0000  )  )
       print(timeit("primes(1_000_000_000_000)"					,			setup=__snake_case					,			number=100_0000  )  )
       print(timeit("fast_primes(1_000_000_000_000)"					,			setup=__snake_case					,			number=100_0000  )  )


if __name__ == "__main__":
   _A      :	List[Any]       		=	int(input("""Calculate primes up to:\n>> """).strip())
   for ret in primes(number):
      print(ret)
   benchmark()


