

'''simple docstring'''

from __future__ import annotations

import random
from collections.abc import Iterable







class lowerCamelCase   :

				def __init__(       self,						lowercase_ )    ->							None:
					snake_case							=					{literal: None for literal in literals}

				def __str__(       self )    ->							str:
					return "{" + " , ".join(self.literals ) + "}"

				def __len__(       self )    ->							int:
					return len(self.literals )

				def 					_lowerCamelCase    (       self,						lowercase_ )    ->							None:
					for literal in self.literals:
						snake_case							=					literal[:2]
						if symbol in model:
							snake_case							=					model[symbol]
						else:
							continue
						if value is not None:
							# Complement assignment if literal is in complemented form
							if literal.endswith('\'' ):
								snake_case							=					not value
						snake_case							=					value






				def 					_lowerCamelCase    (       self,						lowercase_ )    ->							bool | None:
					for literal in self.literals:
						snake_case							=					literal.rstrip('\'' ) if literal.endswith('\'' ) else literal + '\''
						if symbol in self.literals:
							return True

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







class lowerCamelCase   :

				def __init__(       self,						lowercase_ )    ->							None:
					snake_case							=					list(lowercase_ )






				def __str__(       self )    ->							str:
					return "{" + " , ".join(str(lowercase_ ) for clause in self.clauses ) + "}"

def      __magic_name__							(			)      ->		Clause:
	snake_case							=					[]
	snake_case							=					random.randint(1       , 5				)
	snake_case							=					'A'
	snake_case							=					0
	while i < no_of_literals:
		snake_case							=					random.randint(1       , 5				)
		snake_case							=					base_var + str(A				)
		snake_case							=					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      __magic_name__							(			)      ->		Formula:
	snake_case							=					set()
	snake_case							=					random.randint(1       , 1_0				)
	while len(A				) < no_of_clauses:
		clauses.add(generate_clause()				)
	return Formula(A				)

def      __magic_name__							(			A				)      ->		tuple[list[Clause], list[str]]:
	snake_case							=					formula.clauses
	snake_case							=					[]
	for clause in formula.clauses:
		for literal in clause.literals:
			snake_case							=					literal[:2]
			if symbol not in symbols_set:
				symbols_set.append(A				)
	return clauses, symbols_set

def      __magic_name__							(			A       , A       , A				)      ->		tuple[list[str], dict[str, bool | None]]:
	snake_case							=					[]
	snake_case							=					{}
	snake_case							=					[]

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

	for s in symbols:
		snake_case							=					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:
		snake_case							=					None
	for s in pure_symbols:
		snake_case							=					s + '\''
		if s in literals:
			snake_case							=					True
		elif sym in literals:
			snake_case							=					False
	return pure_symbols, assignment

def      __magic_name__							(			A       , A				)      ->		tuple[list[str], dict[str, bool | None]]:
	snake_case							=					[]
	for clause in clauses:
		if len(A				) == 1:
			unit_symbols.append(list(clause.literals.keys()				)[0]				)
		else:
			snake_case			,			snake_case							=					0, 0
			for literal, value in clause.literals.items():
				if value is False:
					f_count += 1
				elif value is None:
					snake_case							=					literal
					n_count += 1
			if f_count == len(A				) - 1 and n_count == 1:
				unit_symbols.append(A				)
	snake_case							=					{}
	for i in unit_symbols:
		snake_case							=					i[:2]
		snake_case							=					len(A				) == 2
	snake_case							=					[i[:2] for i in unit_symbols]

	return unit_symbols, assignment

def      __magic_name__							(			A       , A       , A				)      ->		tuple[bool | None, dict[str, bool | None] | None]:
	snake_case							=					True
	for clause in clauses:
		snake_case							=					clause.evaluate(A				)
		if clause_check is False:
			return False, None
		elif clause_check is None:
			snake_case							=					False
			continue

	if check_clause_all_true:
		return True, model

	try:
		snake_case			,			snake_case							=					find_pure_symbols(A       , A       , A				)
	except RecursionError:
		print('raises a RecursionError and is'				)
		return None, {}
	snake_case							=					None
	if len(A				) > 0:
		snake_case			,			snake_case							=					pure_symbols[0], assignment[pure_symbols[0]]

	if p:
		snake_case							=					model
		snake_case							=					value
		snake_case							=					list(A				)
		if p in tmp_symbols:
			tmp_symbols.remove(A				)
		return dpll_algorithm(A       , A       , A				)

	snake_case			,			snake_case							=					find_unit_clauses(A       , A				)
	snake_case							=					None
	if len(A				) > 0:
		snake_case			,			snake_case							=					unit_symbols[0], assignment[unit_symbols[0]]
	if p:
		snake_case							=					model
		snake_case							=					value
		snake_case							=					list(A				)
		if p in tmp_symbols:
			tmp_symbols.remove(A				)
		return dpll_algorithm(A       , A       , A				)
	snake_case							=					symbols[0]
	snake_case							=					symbols[1:]
	snake_case			,			snake_case							=					model, model
	snake_case			,			snake_case							=					True, False

	return dpll_algorithm(A       , A       , A				) or dpll_algorithm(A       , A       , A				)


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						lowerCAmelCase_     =      generate_formula()
						print(f"The formula {formula} is", end=" ")

						lowerCAmelCase_ ,						lowerCAmelCase_     =      generate_parameters(formula)
						lowerCAmelCase_ ,						lowerCAmelCase_     =      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 (
    get_resize_output_image_size,
    normalize,
    pad,
    rescale,
    resize,
    to_channel_dimension_format,
)
from ...image_utils import (
    IMAGENET_STANDARD_MEAN,
    IMAGENET_STANDARD_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    get_image_size,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, logging
from ...utils.import_utils import is_vision_available


_UpperCAmelCase						:    Optional[Any]      =  logging.get_logger(__name__)


if is_vision_available():
     import PIL




class  __lowerCAmelCase							(				lowerCAmelCase):
       _a			       =    ['''pixel_values''']






       def __init__( self:       Optional[int]							,       _lowerCAmelCase:       bool = True							,       _lowerCAmelCase:       Dict[str, int] = None							,       _lowerCAmelCase:       PILImageResampling = PILImageResampling.BILINEAR							,       _lowerCAmelCase:       bool = True							,       _lowerCAmelCase:       bool = False							,       _lowerCAmelCase:       bool = True							,       _lowerCAmelCase:       bool = True							,       _lowerCAmelCase:       Union[int, float] = 1 / 2_55							,       _lowerCAmelCase:       bool = True							,       _lowerCAmelCase:       Optional[Union[float, List[float]]] = None							,       _lowerCAmelCase:       Optional[Union[float, List[float]]] = None							,       **_lowerCAmelCase:       Dict							,       ):
         super().__init__(**_lowerCAmelCase					)

         lowercase     :Tuple   						=    size if size is not None else {"height": 25_60, "width": 19_20}
         if isinstance(_lowerCAmelCase							,       (tuple, list)					):
           # The previous feature extractor size parameter was in (width, height) format
           lowercase     :Union[str, Any]   						=    size[::-1]
         lowercase     :int   						=    get_size_dict(_lowerCAmelCase					)

         lowercase     :Optional[Any]   						=    do_resize
         lowercase     :int   						=    size
         lowercase     :List[str]   						=    resample
         lowercase     :Any   						=    do_thumbnail
         lowercase     :Optional[int]   						=    do_align_long_axis
         lowercase     :Tuple   						=    do_pad
         lowercase     :Union[str, Any]   						=    do_rescale
         lowercase     :Union[str, Any]   						=    rescale_factor
         lowercase     :Optional[int]   						=    do_normalize
         lowercase     :Dict   						=    image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
         lowercase     :Union[str, Any]   						=    image_std if image_std is not None else IMAGENET_STANDARD_STD






       def        SCREAMING_SNAKE_CASE     ( self:       int							,       _lowerCAmelCase:       np.ndarray							,       _lowerCAmelCase:       Dict[str, int]							,       _lowerCAmelCase:       Optional[Union[str, ChannelDimension]] = None					):
         lowercase						,     lowercase     :int   						=    get_image_size(_lowerCAmelCase					)
         lowercase						,     lowercase     :str   						=    size["height"], size["width"]

         if (output_width < output_height and input_width > input_height) or (
             output_width > output_height and input_width < input_height
         ):
           lowercase     :Any   						=    np.rotaa(_lowerCAmelCase							,       3					)

         if data_format is not None:
           lowercase     :Optional[int]   						=    to_channel_dimension_format(_lowerCAmelCase							,       _lowerCAmelCase					)

         return image






       def        SCREAMING_SNAKE_CASE     ( self:       Optional[int]							,       _lowerCAmelCase:       np.ndarray							,       _lowerCAmelCase:       Dict[str, int]							,       _lowerCAmelCase:       bool = False							,       _lowerCAmelCase:       Optional[Union[str, ChannelDimension]] = None							,       ):
         lowercase						,     lowercase     :Tuple   						=    size["height"], size["width"]
         lowercase						,     lowercase     :Optional[int]   						=    get_image_size(_lowerCAmelCase					)

         lowercase     :List[Any]   						=    output_width - input_width
         lowercase     :Dict   						=    output_height - input_height

         if random_padding:
           lowercase     :List[str]   						=    np.random.randint(low=0							,       high=delta_height + 1					)
           lowercase     :List[Any]   						=    np.random.randint(low=0							,       high=delta_width + 1					)
         else:
           lowercase     :Dict   						=    delta_height // 2
           lowercase     :int   						=    delta_width // 2

         lowercase     :Optional[int]   						=    delta_height - pad_top
         lowercase     :Dict   						=    delta_width - pad_left

         lowercase     :Optional[Any]   						=    ((pad_top, pad_bottom), (pad_left, pad_right))
         return pad(_lowerCAmelCase							,       _lowerCAmelCase							,       data_format=_lowerCAmelCase					)






       def        SCREAMING_SNAKE_CASE     ( self:       str							,       *_lowerCAmelCase:       List[str]							,       **_lowerCAmelCase:       List[str]					):
         logger.info("pad is deprecated and will be removed in version 4.27. Please use pad_image instead."					)
         return self.pad_image(*_lowerCAmelCase							,       **_lowerCAmelCase					)






       def        SCREAMING_SNAKE_CASE     ( self:       Union[str, Any]							,       _lowerCAmelCase:       np.ndarray							,       _lowerCAmelCase:       Dict[str, int]							,       _lowerCAmelCase:       PILImageResampling = PILImageResampling.BICUBIC							,       _lowerCAmelCase:       Optional[Union[str, ChannelDimension]] = None							,       **_lowerCAmelCase:       int							,       ):
         lowercase						,     lowercase     :Any   						=    get_image_size(_lowerCAmelCase					)
         lowercase						,     lowercase     :List[str]   						=    size["height"], size["width"]

         # We always resize to the smallest of either the input or output size.
         lowercase     :Union[str, Any]   						=    min(_lowerCAmelCase							,       _lowerCAmelCase					)
         lowercase     :Any   						=    min(_lowerCAmelCase							,       _lowerCAmelCase					)

         if height == input_height and width == input_width:
           return image

         if input_height > input_width:
           lowercase     :Union[str, Any]   						=    int(input_width * height / input_height					)
         elif input_width > input_height:
           lowercase     :int   						=    int(input_height * width / input_width					)

         return resize(
             _lowerCAmelCase							,       size=(height, width)							,       resample=_lowerCAmelCase							,       reducing_gap=2.0							,       data_format=_lowerCAmelCase							,       **_lowerCAmelCase					)






       def        SCREAMING_SNAKE_CASE     ( self:       int							,       _lowerCAmelCase:       np.ndarray							,       _lowerCAmelCase:       Dict[str, int]							,       _lowerCAmelCase:       PILImageResampling = PILImageResampling.BICUBIC							,       _lowerCAmelCase:       Optional[Union[str, ChannelDimension]] = None							,       **_lowerCAmelCase:       str							,       ):
         lowercase     :Optional[Any]   						=    get_size_dict(_lowerCAmelCase					)
         lowercase     :Optional[Any]   						=    min(size["height"]							,       size["width"]					)
         lowercase     :Tuple   						=    get_resize_output_image_size(_lowerCAmelCase							,       size=_lowerCAmelCase							,       default_to_square=_lowerCAmelCase					)
         lowercase     :Optional[int]   						=    resize(_lowerCAmelCase							,       size=_lowerCAmelCase							,       resample=_lowerCAmelCase							,       data_format=_lowerCAmelCase							,       **_lowerCAmelCase					)
         return resized_image






       def        SCREAMING_SNAKE_CASE     ( self:       Dict							,       _lowerCAmelCase:       np.ndarray							,       _lowerCAmelCase:       Union[int, float]							,       _lowerCAmelCase:       Optional[Union[str, ChannelDimension]] = None							,       **_lowerCAmelCase:       List[Any]							,       ):
         return rescale(_lowerCAmelCase							,       scale=_lowerCAmelCase							,       data_format=_lowerCAmelCase							,       **_lowerCAmelCase					)






       def        SCREAMING_SNAKE_CASE     ( self:       Any							,       _lowerCAmelCase:       np.ndarray							,       _lowerCAmelCase:       Union[float, List[float]]							,       _lowerCAmelCase:       Union[float, List[float]]							,       _lowerCAmelCase:       Optional[Union[str, ChannelDimension]] = None							,       **_lowerCAmelCase:       Dict							,       ):
         return normalize(_lowerCAmelCase							,       mean=_lowerCAmelCase							,       std=_lowerCAmelCase							,       data_format=_lowerCAmelCase							,       **_lowerCAmelCase					)






       def        SCREAMING_SNAKE_CASE     ( self:       Tuple							,       _lowerCAmelCase:       ImageInput							,       _lowerCAmelCase:       bool = None							,       _lowerCAmelCase:       Dict[str, int] = None							,       _lowerCAmelCase:       PILImageResampling = None							,       _lowerCAmelCase:       bool = None							,       _lowerCAmelCase:       bool = None							,       _lowerCAmelCase:       bool = None							,       _lowerCAmelCase:       bool = False							,       _lowerCAmelCase:       bool = None							,       _lowerCAmelCase:       float = None							,       _lowerCAmelCase:       bool = None							,       _lowerCAmelCase:       Optional[Union[float, List[float]]] = None							,       _lowerCAmelCase:       Optional[Union[float, List[float]]] = None							,       _lowerCAmelCase:       Optional[Union[str, TensorType]] = None							,       _lowerCAmelCase:       Optional[ChannelDimension] = ChannelDimension.FIRST							,       **_lowerCAmelCase:       Optional[Any]							,       ):
         lowercase     :Union[str, Any]   						=    do_resize if do_resize is not None else self.do_resize
         lowercase     :Optional[int]   						=    size if size is not None else self.size
         if isinstance(_lowerCAmelCase							,       (tuple, list)					):
           # Previous feature extractor had size in (width, height) format
           lowercase     :List[str]   						=    size[::-1]
         lowercase     :List[str]   						=    get_size_dict(_lowerCAmelCase					)
         lowercase     :Optional[int]   						=    resample if resample is not None else self.resample
         lowercase     :Union[str, Any]   						=    do_thumbnail if do_thumbnail is not None else self.do_thumbnail
         lowercase     :str   						=    do_align_long_axis if do_align_long_axis is not None else self.do_align_long_axis
         lowercase     :int   						=    do_pad if do_pad is not None else self.do_pad
         lowercase     :Optional[Any]   						=    do_rescale if do_rescale is not None else self.do_rescale
         lowercase     :str   						=    rescale_factor if rescale_factor is not None else self.rescale_factor
         lowercase     :int   						=    do_normalize if do_normalize is not None else self.do_normalize
         lowercase     :Dict   						=    image_mean if image_mean is not None else self.image_mean
         lowercase     :str   						=    image_std if image_std is not None else self.image_std

         lowercase     :Any   						=    make_list_of_images(_lowerCAmelCase					)

         if not valid_images(_lowerCAmelCase					):
           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_rescale and rescale_factor is None:
           raise ValueError("Rescale factor must be specified if do_rescale is True."					)

         if do_pad and size is None:
           raise ValueError("Size must be specified if do_pad 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.
         lowercase     :Union[str, Any]   						=    [to_numpy_array(_lowerCAmelCase					) for image in images]

         if do_align_long_axis:
           lowercase     :Union[str, Any]   						=    [self.align_long_axis(_lowerCAmelCase							,       size=_lowerCAmelCase					) for image in images]

         if do_resize:
           lowercase     :Optional[Any]   						=    [self.resize(image=_lowerCAmelCase							,       size=_lowerCAmelCase							,       resample=_lowerCAmelCase					) for image in images]

         if do_thumbnail:
           lowercase     :str   						=    [self.thumbnail(image=_lowerCAmelCase							,       size=_lowerCAmelCase					) for image in images]

         if do_pad:
           lowercase     :List[Any]   						=    [self.pad_image(image=_lowerCAmelCase							,       size=_lowerCAmelCase							,       random_padding=_lowerCAmelCase					) for image in images]

         if do_rescale:
           lowercase     :Optional[Any]   						=    [self.rescale(image=_lowerCAmelCase							,       scale=_lowerCAmelCase					) for image in images]

         if do_normalize:
           lowercase     :Tuple   						=    [self.normalize(image=_lowerCAmelCase							,       mean=_lowerCAmelCase							,       std=_lowerCAmelCase					) for image in images]

         lowercase     :List[str]   						=    [to_channel_dimension_format(_lowerCAmelCase							,       _lowerCAmelCase					) for image in images]

         lowercase     :List[str]   						=    {"pixel_values": images}
         return BatchFeature(data=_lowerCAmelCase							,       tensor_type=_lowerCAmelCase					)



