

from __future__ import annotations

import random
from collections.abc import Iterable
class 	_A						:

  def __init__(			self	,   _SCREAMING_SNAKE_CASE   ):





        """simple docstring"""







        SCREAMING_SNAKE_CASE_			:					dict[str, bool | None]          =       {literal: None for literal in literals}

  def __str__(			self   ):





        """simple docstring"""







        return "{" + " , ".join(self.literals   ) + "}"

  def __len__(			self   ):





        """simple docstring"""







        return len(self.literals   )

  def 	UpperCAmelCase      (			self	,   _SCREAMING_SNAKE_CASE   ):





        """simple docstring"""







        for literal in self.literals:
              SCREAMING_SNAKE_CASE_			:					str          =       literal[:2]
              if symbol in model:
                    SCREAMING_SNAKE_CASE_			:					Union[str, Any]          =       model[symbol]
              else:
                    continue
              if value is not None:
                    # Complement assignment if literal is in complemented form
                    if literal.endswith('\''   ):
                          SCREAMING_SNAKE_CASE_			:					Union[str, Any]          =       not value
              SCREAMING_SNAKE_CASE_			:					int          =       value



  def 	UpperCAmelCase      (			self	,   _SCREAMING_SNAKE_CASE   ):





        """simple docstring"""







        for literal in self.literals:
              SCREAMING_SNAKE_CASE_			:					List[Any]          =       literal.rstrip('\''   ) if literal.endswith('\''   ) else literal + """'"""
              if symbol in self.literals:
                    return True

        self.assign(_SCREAMING_SNAKE_CASE   )
        for value in self.literals.values():
              if value in (True, None):
                    return value
        return any(self.literals.values()   )

class 	_A						:

  def __init__(			self	,   _SCREAMING_SNAKE_CASE   ):





        """simple docstring"""







        SCREAMING_SNAKE_CASE_			:					int          =       list(_SCREAMING_SNAKE_CASE   )



  def __str__(			self   ):





        """simple docstring"""







        return "{" + " , ".join(str(_SCREAMING_SNAKE_CASE   ) for clause in self.clauses   ) + "}"

def 				A_					(							):
      SCREAMING_SNAKE_CASE_			:					Tuple          =       []
      SCREAMING_SNAKE_CASE_			:					Optional[int]          =       random.randint(1   ,				5					)
      SCREAMING_SNAKE_CASE_			:					Any          =       """A"""
      SCREAMING_SNAKE_CASE_			:					Union[str, Any]          =       0
      while i < no_of_literals:
            SCREAMING_SNAKE_CASE_			:					Dict          =       random.randint(1   ,				5					)
            SCREAMING_SNAKE_CASE_			:					int          =       base_var + str(a					)
            SCREAMING_SNAKE_CASE_			:					int          =       random.randint(0   ,				1					)
            if var_complement == 1:
                  var_name += "'"
            if var_name in literals:
                  i -= 1
            else:
                  literals.append(a					)
            i += 1
      return Clause(a					)

def 				A_					(							):
      SCREAMING_SNAKE_CASE_			:					set[Clause]          =       set()
      SCREAMING_SNAKE_CASE_			:					Optional[int]          =       random.randint(1   ,				1_0					)
      while len(a					) < no_of_clauses:
            clauses.add(generate_clause()					)
      return Formula(a					)

def 				A_					(							a					):
      SCREAMING_SNAKE_CASE_			:					Optional[int]          =       formula.clauses
      SCREAMING_SNAKE_CASE_			:					Optional[int]          =       []
      for clause in formula.clauses:
            for literal in clause.literals:
                  SCREAMING_SNAKE_CASE_			:					List[str]          =       literal[:2]
                  if symbol not in symbols_set:
                        symbols_set.append(a					)
      return clauses, symbols_set

def 				A_					(							a   ,				a   ,				a					):
      SCREAMING_SNAKE_CASE_			:					Union[str, Any]          =       []
      SCREAMING_SNAKE_CASE_			:					dict[str, bool | None]          =       {}
      SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       []

      for clause in clauses:
            if clause.evaluate(a					):
                  continue
            for literal in clause.literals:
                  literals.append(a					)

      for s in symbols:
            SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       s + """'"""
            if (s in literals and sym not in literals) or (
                s not in literals and sym in literals
            ):
                  pure_symbols.append(a					)
      for p in pure_symbols:
            SCREAMING_SNAKE_CASE_			:					Union[str, Any]          =       None
      for s in pure_symbols:
            SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       s + """'"""
            if s in literals:
                  SCREAMING_SNAKE_CASE_			:					Any          =       True
            elif sym in literals:
                  SCREAMING_SNAKE_CASE_			:					str          =       False
      return pure_symbols, assignment

def 				A_					(							a   ,				a					):
      SCREAMING_SNAKE_CASE_			:					Any          =       []
      for clause in clauses:
            if len(a					) == 1:
                  unit_symbols.append(list(clause.literals.keys()					)[0]					)
            else:
                  SCREAMING_SNAKE_CASE_			:					List[Any]          =       0, 0
                  for literal, value in clause.literals.items():
                        if value is False:
                              f_count += 1
                        elif value is None:
                              SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       literal
                              n_count += 1
                  if f_count == len(a					) - 1 and n_count == 1:
                        unit_symbols.append(a					)
      SCREAMING_SNAKE_CASE_			:					dict[str, bool | None]          =       {}
      for i in unit_symbols:
            SCREAMING_SNAKE_CASE_			:					List[Any]          =       i[:2]
            SCREAMING_SNAKE_CASE_			:					Any          =       len(a					) == 2
      SCREAMING_SNAKE_CASE_			:					int          =       [i[:2] for i in unit_symbols]

      return unit_symbols, assignment

def 				A_					(							a   ,				a   ,				a					):
      SCREAMING_SNAKE_CASE_			:					Dict          =       True
      for clause in clauses:
            SCREAMING_SNAKE_CASE_			:					Dict          =       clause.evaluate(a					)
            if clause_check is False:
                  return False, None
            elif clause_check is None:
                  SCREAMING_SNAKE_CASE_			:					Union[str, Any]          =       False
                  continue

      if check_clause_all_true:
            return True, model

      try:
            SCREAMING_SNAKE_CASE_			:					Optional[int]          =       find_pure_symbols(a   ,				a   ,				a					)
      except RecursionError:
            print('raises a RecursionError and is'					)
            return None, {}
      SCREAMING_SNAKE_CASE_			:					Dict          =       None
      if len(a					) > 0:
            SCREAMING_SNAKE_CASE_			:					Any          =       pure_symbols[0], assignment[pure_symbols[0]]

      if p:
            SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       model
            SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       value
            SCREAMING_SNAKE_CASE_			:					int          =       list(a					)
            if p in tmp_symbols:
                  tmp_symbols.remove(a					)
            return dpll_algorithm(a   ,				a   ,				a					)

      SCREAMING_SNAKE_CASE_			:					List[Any]          =       find_unit_clauses(a   ,				a					)
      SCREAMING_SNAKE_CASE_			:					List[str]          =       None
      if len(a					) > 0:
            SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       unit_symbols[0], assignment[unit_symbols[0]]
      if p:
            SCREAMING_SNAKE_CASE_			:					Union[str, Any]          =       model
            SCREAMING_SNAKE_CASE_			:					str          =       value
            SCREAMING_SNAKE_CASE_			:					Optional[int]          =       list(a					)
            if p in tmp_symbols:
                  tmp_symbols.remove(a					)
            return dpll_algorithm(a   ,				a   ,				a					)
      SCREAMING_SNAKE_CASE_			:					Dict          =       symbols[0]
      SCREAMING_SNAKE_CASE_			:					List[Any]          =       symbols[1:]
      SCREAMING_SNAKE_CASE_			:					Tuple          =       model, model
      SCREAMING_SNAKE_CASE_			:					List[str]          =       True, False

      return dpll_algorithm(a   ,				a   ,				a					) or dpll_algorithm(a   ,				a   ,				a					)


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    lowerCAmelCase       :				Union[str, Any]         =					generate_formula()
    print(F'The formula {formula} is', end=' ')

    lowerCAmelCase       ,    lowerCAmelCase       :				Union[str, Any]         =					generate_parameters(formula)
    lowerCAmelCase       ,    lowerCAmelCase       :				Dict         =					dpll_algorithm(clauses, symbols, {})

    if solution:
        print(F'satisfiable with the assignment {model}.')
    else:
        print('not satisfiable.')









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, normalize, rescale, resize, to_channel_dimension_format
from ...image_utils import (
    IMAGENET_STANDARD_MEAN,
    IMAGENET_STANDARD_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


if is_vision_available():
    import PIL


lowerCAmelCase       :				Dict         =					logging.get_logger(__name__)
class 	_A						(					__magic_name__):
  SCREAMING_SNAKE_CASE      : Any    =					['''pixel_values''']

  def __init__(			self	,   _SCREAMING_SNAKE_CASE = True	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = PIL.Image.NEAREST	,   _SCREAMING_SNAKE_CASE = False	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = 1 / 255	,   _SCREAMING_SNAKE_CASE = False	,   _SCREAMING_SNAKE_CASE = True	,   _SCREAMING_SNAKE_CASE = True	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = True	,   **_SCREAMING_SNAKE_CASE	,   ):





        """simple docstring"""







        super().__init__(**_SCREAMING_SNAKE_CASE   )
        SCREAMING_SNAKE_CASE_			:					str          =       size if size is not None else {'height': 346, 'width': 346}
        SCREAMING_SNAKE_CASE_			:					str          =       get_size_dict(_SCREAMING_SNAKE_CASE   )
        SCREAMING_SNAKE_CASE_			:					int          =       crop_size if crop_size is not None else {'height': 289, 'width': 289}
        SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       get_size_dict(_SCREAMING_SNAKE_CASE	,   param_name='crop_size'   )

        SCREAMING_SNAKE_CASE_			:					List[str]          =       do_resize
        SCREAMING_SNAKE_CASE_			:					int          =       size
        SCREAMING_SNAKE_CASE_			:					Tuple          =       resample
        SCREAMING_SNAKE_CASE_			:					int          =       do_center_crop
        SCREAMING_SNAKE_CASE_			:					List[str]          =       crop_size
        SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       do_rescale
        SCREAMING_SNAKE_CASE_			:					Optional[int]          =       rescale_factor
        SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       rescale_offset
        SCREAMING_SNAKE_CASE_			:					Dict          =       do_normalize
        SCREAMING_SNAKE_CASE_			:					str          =       image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
        SCREAMING_SNAKE_CASE_			:					List[str]          =       image_std if image_std is not None else IMAGENET_STANDARD_STD
        SCREAMING_SNAKE_CASE_			:					Union[str, Any]          =       include_top

  def 	UpperCAmelCase      (			self	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE = PIL.Image.NEAREST	,   _SCREAMING_SNAKE_CASE = None	,   **_SCREAMING_SNAKE_CASE	,   ):





        """simple docstring"""







        SCREAMING_SNAKE_CASE_			:					str          =       get_size_dict(_SCREAMING_SNAKE_CASE   )
        if "height" not in size or "width" not in size:
              raise ValueError(f"The size dictionary must have keys 'height' and 'width'. Got {size.keys()}"   )
        return resize(
            _SCREAMING_SNAKE_CASE	,   size=(size['height'], size['width'])	,   resample=_SCREAMING_SNAKE_CASE	,   data_format=_SCREAMING_SNAKE_CASE	,   **_SCREAMING_SNAKE_CASE   )

  def 	UpperCAmelCase      (			self	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE = None	,   **_SCREAMING_SNAKE_CASE	,   ):





        """simple docstring"""







        SCREAMING_SNAKE_CASE_			:					Tuple          =       get_size_dict(_SCREAMING_SNAKE_CASE   )
        if "height" not in size or "width" not in size:
              raise ValueError(f"The size dictionary must have keys 'height' and 'width'. Got {size.keys()}"   )
        return center_crop(_SCREAMING_SNAKE_CASE	,   size=(size['height'], size['width'])	,   data_format=_SCREAMING_SNAKE_CASE	,   **_SCREAMING_SNAKE_CASE   )

  def 	UpperCAmelCase      (			self	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE = True	,   _SCREAMING_SNAKE_CASE = None	,   **_SCREAMING_SNAKE_CASE	,   ):





        """simple docstring"""







        if offset:
              SCREAMING_SNAKE_CASE_			:					Dict          =       (image - 127.5) * scale
              if data_format is not None:
                    SCREAMING_SNAKE_CASE_			:					Tuple          =       to_channel_dimension_format(_SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE   )
              SCREAMING_SNAKE_CASE_			:					int          =       rescaled_image.astype(np.floataa   )
        else:
              SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       rescale(_SCREAMING_SNAKE_CASE	,   scale=_SCREAMING_SNAKE_CASE	,   data_format=_SCREAMING_SNAKE_CASE	,   **_SCREAMING_SNAKE_CASE   )
        return rescaled_image

  def 	UpperCAmelCase      (			self	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE = None	,   **_SCREAMING_SNAKE_CASE	,   ):





        """simple docstring"""







        return normalize(_SCREAMING_SNAKE_CASE	,   mean=_SCREAMING_SNAKE_CASE	,   std=_SCREAMING_SNAKE_CASE	,   data_format=_SCREAMING_SNAKE_CASE	,   **_SCREAMING_SNAKE_CASE   )



  def 	UpperCAmelCase      (			self	,   _SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE=None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = None	,   _SCREAMING_SNAKE_CASE = ChannelDimension.FIRST	,   **_SCREAMING_SNAKE_CASE	,   ):





        """simple docstring"""







        SCREAMING_SNAKE_CASE_			:					List[Any]          =       do_resize if do_resize is not None else self.do_resize
        SCREAMING_SNAKE_CASE_			:					Union[str, Any]          =       resample if resample is not None else self.resample
        SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       do_center_crop if do_center_crop is not None else self.do_center_crop
        SCREAMING_SNAKE_CASE_			:					Optional[int]          =       do_rescale if do_rescale is not None else self.do_rescale
        SCREAMING_SNAKE_CASE_			:					int          =       rescale_factor if rescale_factor is not None else self.rescale_factor
        SCREAMING_SNAKE_CASE_			:					Tuple          =       rescale_offset if rescale_offset is not None else self.rescale_offset
        SCREAMING_SNAKE_CASE_			:					Dict          =       do_normalize if do_normalize is not None else self.do_normalize
        SCREAMING_SNAKE_CASE_			:					str          =       image_mean if image_mean is not None else self.image_mean
        SCREAMING_SNAKE_CASE_			:					List[Any]          =       image_std if image_std is not None else self.image_std
        SCREAMING_SNAKE_CASE_			:					List[Any]          =       include_top if include_top is not None else self.include_top

        SCREAMING_SNAKE_CASE_			:					Optional[int]          =       size if size is not None else self.size
        SCREAMING_SNAKE_CASE_			:					Tuple          =       get_size_dict(_SCREAMING_SNAKE_CASE   )
        SCREAMING_SNAKE_CASE_			:					Any          =       crop_size if crop_size is not None else self.crop_size
        SCREAMING_SNAKE_CASE_			:					Optional[int]          =       get_size_dict(_SCREAMING_SNAKE_CASE	,   param_name='crop_size'   )

        SCREAMING_SNAKE_CASE_			:					List[str]          =       make_list_of_images(_SCREAMING_SNAKE_CASE   )

        if not valid_images(_SCREAMING_SNAKE_CASE   ):
              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 or resample is None:
              raise ValueError('Size and resample 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.'   )

        # All transformations expect numpy arrays.
        SCREAMING_SNAKE_CASE_			:					int          =       [to_numpy_array(_SCREAMING_SNAKE_CASE   ) for image in images]

        if do_resize:
              SCREAMING_SNAKE_CASE_			:					Dict          =       [self.resize(image=_SCREAMING_SNAKE_CASE	,   size=_SCREAMING_SNAKE_CASE	,   resample=_SCREAMING_SNAKE_CASE   ) for image in images]

        if do_center_crop:
              SCREAMING_SNAKE_CASE_			:					str          =       [self.center_crop(image=_SCREAMING_SNAKE_CASE	,   size=_SCREAMING_SNAKE_CASE   ) for image in images]

        if do_rescale:
              SCREAMING_SNAKE_CASE_			:					Tuple          =       [self.rescale(image=_SCREAMING_SNAKE_CASE	,   scale=_SCREAMING_SNAKE_CASE	,   offset=_SCREAMING_SNAKE_CASE   ) for image in images]

        if do_normalize:
              SCREAMING_SNAKE_CASE_			:					Optional[Any]          =       [self.normalize(image=_SCREAMING_SNAKE_CASE	,   mean=_SCREAMING_SNAKE_CASE	,   std=_SCREAMING_SNAKE_CASE   ) for image in images]

        if include_top:
              SCREAMING_SNAKE_CASE_			:					Dict          =       [self.normalize(image=_SCREAMING_SNAKE_CASE	,   mean=[0, 0, 0]	,   std=_SCREAMING_SNAKE_CASE   ) for image in images]

        SCREAMING_SNAKE_CASE_			:					Dict          =       [to_channel_dimension_format(_SCREAMING_SNAKE_CASE	,   _SCREAMING_SNAKE_CASE   ) for image in images]

        SCREAMING_SNAKE_CASE_			:					Any          =       {'pixel_values': images}
        return BatchFeature(data=_SCREAMING_SNAKE_CASE	,   tensor_type=_SCREAMING_SNAKE_CASE   )






