


from math import sqrt

def 						_UpperCAmelCase    (      SCREAMING_SNAKE_CASE__      : int    ):

     if 1 < number < 4:
          # 2 and 3 are primes
          return True
     elif number < 2 or number % 2 == 0 or number % 3 == 0:
          # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
          return False

     # All primes number are in format of 6k +/- 1
     for i in range(5      ,					int(sqrt(lowercase_    ) + 1    )      ,					6    ):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True

def 						_UpperCAmelCase    (      SCREAMING_SNAKE_CASE__      : int = 1_00_01    ):
     __UpperCamelCase   							=0
     __UpperCamelCase   							=1
     while count != nth and number < 3:
          number += 1
          if is_prime(lowercase_    ):
               count += 1
     while count != nth:
          number += 2
          if is_prime(lowercase_    ):
               count += 1
     return number


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









from typing import Dict, List, Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import (
    center_crop,
    convert_to_rgb,
    get_resize_output_image_size,
    normalize,
    rescale,
    resize,
    to_channel_dimension_format,
)
from ...image_utils import (
    OPENAI_CLIP_MEAN,
    OPENAI_CLIP_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


_A			=						logging.get_logger(__name__)


if is_vision_available():
   import PIL






class    UpperCAmelCase__	( A_		):



    """simple docstring"""






    UpperCAmelCase__						:		Optional[int]              =  ["pixel_values"]






    def __init__(      self ,       A_ = True ,       A_ = None ,       A_ = PILImageResampling.BICUBIC ,       A_ = True ,       A_ = None ,       A_ = True ,       A_ = 1 / 255 ,       A_ = True ,       A_ = None ,       A_ = None ,       A_ = True ,       **A_ ,       )  ->	None:
         super().__init__(**A_   )
         __UpperCamelCase   							=size if size is not None else {'shortest_edge': 224}
         __UpperCamelCase   							=get_size_dict(A_ ,       default_to_square=A_   )
         __UpperCamelCase   							=crop_size if crop_size is not None else {'height': 224, 'width': 224}
         __UpperCamelCase   							=get_size_dict(A_ ,       default_to_square=A_ ,       param_name='crop_size'   )

         __UpperCamelCase   							=do_resize
         __UpperCamelCase   							=size
         __UpperCamelCase   							=resample
         __UpperCamelCase   							=do_center_crop
         __UpperCamelCase   							=crop_size
         __UpperCamelCase   							=do_rescale
         __UpperCamelCase   							=rescale_factor
         __UpperCamelCase   							=do_normalize
         __UpperCamelCase   							=image_mean if image_mean is not None else OPENAI_CLIP_MEAN
         __UpperCamelCase   							=image_std if image_std is not None else OPENAI_CLIP_STD
         __UpperCamelCase   							=do_convert_rgb






    def _a (      self ,       A_ ,       A_ ,       A_ = PILImageResampling.BICUBIC ,       A_ = None ,       **A_ ,       )  ->	np.ndarray:
         __UpperCamelCase   							=get_size_dict(A_ ,       default_to_square=A_   )
         if "shortest_edge" not in size:
              raise ValueError(f'The `size` parameter must contain the key `shortest_edge`. Got {size.keys()}'   )
         __UpperCamelCase   							=get_resize_output_image_size(A_ ,       size=size['shortest_edge'] ,       default_to_square=A_   )
         return resize(A_ ,       size=A_ ,       resample=A_ ,       data_format=A_ ,       **A_   )






    def _a (      self ,       A_ ,       A_ ,       A_ = None ,       **A_ ,       )  ->	np.ndarray:
         __UpperCamelCase   							=get_size_dict(A_   )
         if "height" not in size or "width" not in size:
              raise ValueError(f'The `size` parameter must contain the keys (height, width). Got {size.keys()}'   )
         return center_crop(A_ ,       size=(size['height'], size['width']) ,       data_format=A_ ,       **A_   )






    def _a (      self ,       A_ ,       A_ ,       A_ = None ,       **A_ ,       )  ->	Union[str, Any]:
         return rescale(A_ ,       scale=A_ ,       data_format=A_ ,       **A_   )






    def _a (      self ,       A_ ,       A_ ,       A_ ,       A_ = None ,       **A_ ,       )  ->	np.ndarray:
         return normalize(A_ ,       mean=A_ ,       std=A_ ,       data_format=A_ ,       **A_   )






    def _a (      self ,       A_ ,       A_ = None ,       A_ = None ,       A_ = None ,       A_ = None ,       A_ = None ,       A_ = None ,       A_ = None ,       A_ = None ,       A_ = None ,       A_ = None ,       A_ = None ,       A_ = None ,       A_ = ChannelDimension.FIRST ,       **A_ ,       )  ->	PIL.Image.Image:
         __UpperCamelCase   							=do_resize if do_resize is not None else self.do_resize
         __UpperCamelCase   							=size if size is not None else self.size
         __UpperCamelCase   							=get_size_dict(A_ ,       param_name='size' ,       default_to_square=A_   )
         __UpperCamelCase   							=resample if resample is not None else self.resample
         __UpperCamelCase   							=do_center_crop if do_center_crop is not None else self.do_center_crop
         __UpperCamelCase   							=crop_size if crop_size is not None else self.crop_size
         __UpperCamelCase   							=get_size_dict(A_ ,       param_name='crop_size' ,       default_to_square=A_   )
         __UpperCamelCase   							=do_rescale if do_rescale is not None else self.do_rescale
         __UpperCamelCase   							=rescale_factor if rescale_factor is not None else self.rescale_factor
         __UpperCamelCase   							=do_normalize if do_normalize is not None else self.do_normalize
         __UpperCamelCase   							=image_mean if image_mean is not None else self.image_mean
         __UpperCamelCase   							=image_std if image_std is not None else self.image_std
         __UpperCamelCase   							=do_convert_rgb if do_convert_rgb is not None else self.do_convert_rgb

         __UpperCamelCase   							=make_list_of_images(A_   )

         if not valid_images(A_   ):
              raise ValueError(
                  'Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, '
                  'torch.Tensor, tf.Tensor or jax.ndarray.'   )

         if do_resize and size is None:
              raise ValueError('Size must be specified if do_resize is True.'   )

         if do_center_crop and crop_size is None:
              raise ValueError('Crop size must be specified if do_center_crop is True.'   )

         if do_rescale and rescale_factor is None:
              raise ValueError('Rescale factor must be specified if do_rescale is True.'   )

         if do_normalize and (image_mean is None or image_std is None):
              raise ValueError('Image mean and std must be specified if do_normalize is True.'   )

         # PIL RGBA images are converted to RGB
         if do_convert_rgb:
              __UpperCamelCase   							=[convert_to_rgb(A_   ) for image in images]

         # All transformations expect numpy arrays.
         __UpperCamelCase   							=[to_numpy_array(A_   ) for image in images]

         if do_resize:
              __UpperCamelCase   							=[self.resize(image=A_ ,       size=A_ ,       resample=A_   ) for image in images]

         if do_center_crop:
              __UpperCamelCase   							=[self.center_crop(image=A_ ,       size=A_   ) for image in images]

         if do_rescale:
              __UpperCamelCase   							=[self.rescale(image=A_ ,       scale=A_   ) for image in images]

         if do_normalize:
              __UpperCamelCase   							=[self.normalize(image=A_ ,       mean=A_ ,       std=A_   ) for image in images]

         __UpperCamelCase   							=[to_channel_dimension_format(A_ ,       A_   ) for image in images]

         __UpperCamelCase   							={'pixel_values': images}
         return BatchFeature(data=A_ ,       tensor_type=A_   )





