






"""simple docstring"""





from copy import deepcopy
from typing import Optional, Union

import numpy as np

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding
from ...utils import TensorType, is_tf_available, is_torch_available


if is_torch_available():
  import torch

if is_tf_available():
  import tensorflow as tf
class    __lowerCamelCase    (  _a  ):
   a      :				Optional[int] 						=["""image_processor"""]
   a      :				List[Any] 						="""SamImageProcessor"""

   def __init__(					self ,				snake_case_      )		->       Any:
       super().__init__(snake_case_      )
       UpperCamelCase__         =    self.image_processor
       UpperCamelCase__         =    -10
       UpperCamelCase__         =    self.image_processor.size['longest_edge']

   def __call__(					self ,				snake_case_=None ,				snake_case_=None ,				snake_case_=None ,				snake_case_=None ,				snake_case_ = None ,				**snake_case_ ,				)		->       BatchEncoding:
       UpperCamelCase__         =    self.image_processor(
           snake_case_ ,				return_tensors=snake_case_ ,				**snake_case_ ,				)

       # pop arguments that are not used in the foward but used nevertheless
       UpperCamelCase__         =    encoding_image_processor['original_sizes']

       if hasattr(snake_case_ ,				'numpy'      ):  # Checks if Torch or TF tensor
           UpperCamelCase__         =    original_sizes.numpy()

       UpperCamelCase__       ,						UpperCamelCase__       ,						UpperCamelCase__         =    self._check_and_preprocess_points(
           input_points=snake_case_ ,				input_labels=snake_case_ ,				input_boxes=snake_case_ ,				)

       UpperCamelCase__         =    self._normalize_and_convert(
           snake_case_ ,				snake_case_ ,				input_points=snake_case_ ,				input_labels=snake_case_ ,				input_boxes=snake_case_ ,				return_tensors=snake_case_ ,				)

       return encoding_image_processor

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_ ,				snake_case_ ,				snake_case_=None ,				snake_case_=None ,				snake_case_=None ,				snake_case_="pt" ,				)		->       Tuple:
       if input_points is not None:
           if len(snake_case_      ) != len(snake_case_      ):
               UpperCamelCase__         =    [
                   self._normalize_coordinates(self.target_size ,				snake_case_ ,				original_sizes[0]      ) for point in input_points
               ]
           else:
               UpperCamelCase__         =    [
                   self._normalize_coordinates(self.target_size ,				snake_case_ ,				snake_case_      )
                   for point, original_size in zip(snake_case_ ,				snake_case_      )
               ]
           # check that all arrays have the same shape
           if not all(point.shape == input_points[0].shape for point in input_points      ):
               if input_labels is not None:
                   UpperCamelCase__       ,						UpperCamelCase__         =    self._pad_points_and_labels(snake_case_ ,				snake_case_      )

           UpperCamelCase__         =    np.array(snake_case_      )

       if input_labels is not None:
           UpperCamelCase__         =    np.array(snake_case_      )

       if input_boxes is not None:
           if len(snake_case_      ) != len(snake_case_      ):
               UpperCamelCase__         =    [
                   self._normalize_coordinates(self.target_size ,				snake_case_ ,				original_sizes[0] ,				is_bounding_box=snake_case_      )
                   for box in input_boxes
               ]
           else:
               UpperCamelCase__         =    [
                   self._normalize_coordinates(self.target_size ,				snake_case_ ,				snake_case_ ,				is_bounding_box=snake_case_      )
                   for box, original_size in zip(snake_case_ ,				snake_case_      )
               ]
           UpperCamelCase__         =    np.array(snake_case_      )

       if input_boxes is not None:
           if return_tensors == "pt":
               UpperCamelCase__         =    torch.from_numpy(snake_case_      )
               # boxes batch size of 1 by default
               UpperCamelCase__         =    input_boxes.unsqueeze(1      ) if len(input_boxes.shape      ) != 3 else input_boxes
           elif return_tensors == "tf":
               UpperCamelCase__         =    tf.convert_to_tensor(snake_case_      )
               # boxes batch size of 1 by default
               UpperCamelCase__         =    tf.expand_dims(snake_case_ ,				1      ) if len(input_boxes.shape      ) != 3 else input_boxes
           encoding_image_processor.update({'input_boxes': input_boxes}      )
       if input_points is not None:
           if return_tensors == "pt":
               UpperCamelCase__         =    torch.from_numpy(snake_case_      )
               # point batch size of 1 by default
               UpperCamelCase__         =    input_points.unsqueeze(1      ) if len(input_points.shape      ) != 4 else input_points
           elif return_tensors == "tf":
               UpperCamelCase__         =    tf.convert_to_tensor(snake_case_      )
               # point batch size of 1 by default
               UpperCamelCase__         =    tf.expand_dims(snake_case_ ,				1      ) if len(input_points.shape      ) != 4 else input_points
           encoding_image_processor.update({'input_points': input_points}      )
       if input_labels is not None:
           if return_tensors == "pt":
               UpperCamelCase__         =    torch.from_numpy(snake_case_      )
               # point batch size of 1 by default
               UpperCamelCase__         =    input_labels.unsqueeze(1      ) if len(input_labels.shape      ) != 3 else input_labels
           elif return_tensors == "tf":
               UpperCamelCase__         =    tf.convert_to_tensor(snake_case_      )
               # point batch size of 1 by default
               UpperCamelCase__         =    tf.expand_dims(snake_case_ ,				1      ) if len(input_labels.shape      ) != 3 else input_labels
           encoding_image_processor.update({'input_labels': input_labels}      )

       return encoding_image_processor

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_ ,				snake_case_      )		->       List[str]:
       UpperCamelCase__         =    max([point.shape[0] for point in input_points]      )
       UpperCamelCase__         =    []
       for i, point in enumerate(snake_case_      ):
           if point.shape[0] != expected_nb_points:
               UpperCamelCase__         =    np.concatenate(
                   [point, np.zeros((expected_nb_points - point.shape[0], 2)      ) + self.point_pad_value] ,				axis=0      )
               UpperCamelCase__         =    np.append(input_labels[i] ,				[self.point_pad_value]      )
           processed_input_points.append(snake_case_      )
       UpperCamelCase__         =    processed_input_points
       return input_points, input_labels

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_ ,				snake_case_ ,				snake_case_ ,				snake_case_=False      )		->       np.ndarray:
       UpperCamelCase__       ,						UpperCamelCase__         =    original_size
       UpperCamelCase__       ,						UpperCamelCase__         =    self.image_processor._get_preprocess_shape(snake_case_ ,				longest_edge=snake_case_      )
       UpperCamelCase__         =    deepcopy(snake_case_      ).astype(snake_case_      )

       if is_bounding_box:
           UpperCamelCase__         =    coords.reshape(-1 ,				2 ,				2      )

       UpperCamelCase__         =    coords[..., 0] * (new_w / old_w)
       UpperCamelCase__         =    coords[..., 1] * (new_h / old_h)

       if is_bounding_box:
           UpperCamelCase__         =    coords.reshape(-1 ,				4      )

       return coords

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_=None ,				snake_case_=None ,				snake_case_=None ,				)		->       Union[str, Any]:
       if input_points is not None:
           if hasattr(snake_case_ ,				'numpy'      ):  # Checks for TF or Torch tensor
               UpperCamelCase__         =    input_points.numpy().tolist()

           if not isinstance(snake_case_ ,				snake_case_      ) or not isinstance(input_points[0] ,				snake_case_      ):
               raise ValueError('Input points must be a list of list of floating points.'      )
           UpperCamelCase__         =    [np.array(snake_case_      ) for input_point in input_points]
       else:
           UpperCamelCase__         =    None

       if input_labels is not None:
           if hasattr(snake_case_ ,				'numpy'      ):
               UpperCamelCase__         =    input_labels.numpy().tolist()

           if not isinstance(snake_case_ ,				snake_case_      ) or not isinstance(input_labels[0] ,				snake_case_      ):
               raise ValueError('Input labels must be a list of list integers.'      )
           UpperCamelCase__         =    [np.array(snake_case_      ) for label in input_labels]
       else:
           UpperCamelCase__         =    None

       if input_boxes is not None:
           if hasattr(snake_case_ ,				'numpy'      ):
               UpperCamelCase__         =    input_boxes.numpy().tolist()

           if (
               not isinstance(snake_case_ ,				snake_case_      )
               or not isinstance(input_boxes[0] ,				snake_case_      )
               or not isinstance(input_boxes[0][0] ,				snake_case_      )
           ):
               raise ValueError('Input boxes must be a list of list of list of floating points.'      )
           UpperCamelCase__         =    [np.array(snake_case_      ).astype(np.floataa      ) for box in input_boxes]
       else:
           UpperCamelCase__         =    None

       return input_points, input_labels, input_boxes

   @property
   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       Optional[int]:
       UpperCamelCase__         =    self.image_processor.model_input_names
       return list(dict.fromkeys(snake_case_      )      )







   def 						SCREAMING_SNAKE_CASE__ (					self ,				*snake_case_ ,				**snake_case_      )		->       Dict:
       return self.image_processor.post_process_masks(*snake_case_ ,				**snake_case_      )












"""simple docstring"""





from collections import defaultdict
from math import ceil, sqrt







def   lowerCAmelCase_( SCREAMING_SNAKE_CASE = 1_00_00_00 ,	SCREAMING_SNAKE_CASE = 10					)					->	int:
    """simple docstring"""

    UpperCamelCase__         =    defaultdict(SCREAMING_SNAKE_CASE					)

    for outer_width in range(3 ,	(t_limit // 4) + 2					):
        if outer_width * outer_width > t_limit:
            UpperCamelCase__         =    max(
                ceil(sqrt(outer_width * outer_width - t_limit					)					) ,	1					)
        else:
            UpperCamelCase__         =    1

        hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

        for hole_width in range(SCREAMING_SNAKE_CASE ,	outer_width - 1 ,	2					):
            count[outer_width * outer_width - hole_width * hole_width] += 1

    return sum(1 for n in count.values() if 1 <= n <= 10					)


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




