




'''simple docstring'''







from __future__ import annotations

from collections.abc import Iterable


class      _a    :
       def __init__(      self		:      int  ,							lowercase		:      int  ,							lowercase		:      str							):



           '''simple docstring'''

           UpperCAmelCase     			=						float(_SCREAMING_SNAKE_CASE							), float(_SCREAMING_SNAKE_CASE							)
       def __eq__(      self		:      List[str]  ,							lowercase		:      str							):



           '''simple docstring'''

           return self.x == other.x and self.y == other.y
       def __ne__(      self		:      int  ,							lowercase		:      List[Any]							):



           '''simple docstring'''

           return not self == other
       def __gt__(      self		:      List[Any]  ,							lowercase		:      Tuple							):



           '''simple docstring'''

           if self.x > other.x:
               return True
           elif self.x == other.x:
               return self.y > other.y
           return False
       def __lt__(      self		:      Dict  ,							lowercase		:      Optional[int]							):



           '''simple docstring'''

           return not self > other
       def __ge__(      self		:      List[Any]  ,							lowercase		:      Tuple							):



           '''simple docstring'''

           if self.x > other.x:
               return True
           elif self.x == other.x:
               return self.y >= other.y
           return False
       def __le__(      self		:      Optional[Any]  ,							lowercase		:      Optional[int]							):



           '''simple docstring'''

           if self.x < other.x:
               return True
           elif self.x == other.x:
               return self.y <= other.y
           return False
       def __repr__(      self		:      str							):



           '''simple docstring'''

           return f"({self.x}, {self.y})"







       def __hash__(      self		:      Dict							):



           '''simple docstring'''

           return hash(self.x							)






def 		snake_case_				(_a      :				str       ,  ):
    UpperCAmelCase     			=						[]
    if list_of_tuples:
        for p in list_of_tuples:
            if isinstance(_a       ,  _a	):
                points.append(_a	)
            else:
                try:
                    points.append(Point(p[0]       ,  p[1]	)	)
                except (IndexError, TypeError):
                    print(
                        F"Ignoring deformed point {p}. All points"
                        ''' must have at least 2 coordinates.'''	)
    return points





def 		snake_case_				(_a      :				int	):






    if not hasattr(_a       ,  '''__iter__'''	):
        UpperCAmelCase     			=						F"Expecting an iterable object but got an non-iterable type {points}"
        raise ValueError(_a	)

    if not points:
        UpperCAmelCase     			=						F"Expecting a list of points but got {points}"
        raise ValueError(_a	)

    return _construct_points(_a	)





def 		snake_case_				(_a      :				List[str]       ,  _a      :				Optional[Any]       ,  _a      :				List[str]	):
    UpperCAmelCase     			=						(a.x * b.y + b.x * c.y + c.x * a.y) - (a.y * b.x + b.y * c.x + c.y * a.x)
    return det





def 		snake_case_				(_a      :				Union[str, Any]	):
    UpperCAmelCase     			=						sorted(_validate_input(_a	)	)
    UpperCAmelCase     			=						len(_a	)
    UpperCAmelCase     			=						set()

    for i in range(n - 1	):
        for j in range(i + 1       ,  _a	):
            UpperCAmelCase     			=						False
            UpperCAmelCase     			=						True
            for k in range(_a	):
                if k != i and k != j:
                    UpperCAmelCase     			=						_det(points[i]       ,  points[j]       ,  points[k]	)

                    if det_k > 0:
                        UpperCAmelCase     			=						True
                    elif det_k < 0:
                        UpperCAmelCase     			=						True
                    else:
                        # point[i], point[j], point[k] all lie on a straight line
                        # if point[k] is to the left of point[i] or it's to the
                        # right of point[j], then point[i], point[j] cannot be
                        # part of the convex hull of A
                        if points[k] < points[i] or points[k] > points[j]:
                            UpperCAmelCase     			=						False
                            break

                if points_left_of_ij and points_right_of_ij:
                    UpperCAmelCase     			=						False
                    break

            if ij_part_of_convex_hull:
                convex_set.update([points[i], points[j]]	)

    return sorted(_a	)





def 		snake_case_				(_a      :				Optional[int]	):
    UpperCAmelCase     			=						sorted(_validate_input(_a	)	)
    UpperCAmelCase     			=						len(_a	)

    # divide all the points into an upper hull and a lower hull
    # the left most point and the right most point are definitely
    # members of the convex hull by definition.
    # use these two anchors to divide all the points into two hulls,
    # an upper hull and a lower hull.

    # all points to the left (above) the line joining the extreme points belong to the
    # upper hull
    # all points to the right (below) the line joining the extreme points below to the
    # lower hull
    # ignore all points on the line joining the extreme points since they cannot be
    # part of the convex hull

    UpperCAmelCase     			=						points[0]
    UpperCAmelCase     			=						points[n - 1]

    UpperCAmelCase     			=						{left_most_point, right_most_point}
    UpperCAmelCase     			=						[]
    UpperCAmelCase     			=						[]

    for i in range(1       ,  n - 1	):
        UpperCAmelCase     			=						_det(_a       ,  _a       ,  points[i]	)

        if det > 0:
            upper_hull.append(points[i]	)
        elif det < 0:
            lower_hull.append(points[i]	)

    _construct_hull(_a       ,  _a       ,  _a       ,  _a	)
    _construct_hull(_a       ,  _a       ,  _a       ,  _a	)

    return sorted(_a	)





def 		snake_case_				(_a      :				int       ,  _a      :				int       ,  _a      :				List[Any]       ,  _a      :				List[Any]	):






    if points:
        UpperCAmelCase     			=						None
        UpperCAmelCase     			=						float('''-inf'''	)
        UpperCAmelCase     			=						[]

        for p in points:
            UpperCAmelCase     			=						_det(_a       ,  _a       ,  _a	)

            if det > 0:
                candidate_points.append(_a	)

                if det > extreme_point_distance:
                    UpperCAmelCase     			=						det
                    UpperCAmelCase     			=						p

        if extreme_point:
            _construct_hull(_a       ,  _a       ,  _a       ,  _a	)
            convex_set.add(_a	)
            _construct_hull(_a       ,  _a       ,  _a       ,  _a	)





def 		snake_case_				(_a      :				Optional[int]	):
    UpperCAmelCase     			=						sorted(_validate_input(_a	)	)
    UpperCAmelCase     			=						len(_a	)

    UpperCAmelCase     			=						points[:2]
    for i in range(2       ,  _a	):
        UpperCAmelCase     			=						_det(convex_hull[1]       ,  convex_hull[0]       ,  points[i]	)
        if det > 0:
            convex_hull.insert(0       ,  points[i]	)
            break
        elif det < 0:
            convex_hull.append(points[i]	)
            break
        else:
            UpperCAmelCase     			=						points[i]
    i += 1

    for j in range(_a       ,  _a	):
        if (
            _det(convex_hull[0]       ,  convex_hull[-1]       ,  points[j]	) > 0
            and _det(convex_hull[-1]       ,  convex_hull[0]       ,  points[1]	) < 0
        ):
            # The point lies within the convex hull
            continue

        convex_hull.insert(0       ,  points[j]	)
        convex_hull.append(points[j]	)
        while _det(convex_hull[0]       ,  convex_hull[1]       ,  convex_hull[2]	) >= 0:
            del convex_hull[1]
        while _det(convex_hull[-1]       ,  convex_hull[-2]       ,  convex_hull[-3]	) <= 0:
            del convex_hull[-2]

    # `convex_hull` is contains the convex hull in circular order
    return sorted(convex_hull[1:] if len(_a	) > 3 else convex_hull	)





def 		snake_case_				():
    UpperCAmelCase     			=						[
        (0, 3),
        (2, 2),
        (1, 1),
        (2, 1),
        (3, 0),
        (0, 0),
        (3, 3),
        (2, -1),
        (2, -4),
        (1, -3),
    ]
    # the convex set of points is
    # [(0, 0), (0, 3), (1, -3), (2, -4), (3, 0), (3, 3)]
    UpperCAmelCase     			=						convex_hull_bf(_a	)

    UpperCAmelCase     			=						convex_hull_recursive(_a	)
    assert results_bf == results_recursive

    UpperCAmelCase     			=						convex_hull_melkman(_a	)
    assert results_bf == results_melkman

    print(_a	)


if __name__ == "__main__":
   main()








import os

from packaging import version

from .. import __version__
from .accelerate_utils import apply_forward_hook
from .constants import (
    CONFIG_NAME,
    DEPRECATED_REVISION_ARGS,
    DIFFUSERS_CACHE,
    DIFFUSERS_DYNAMIC_MODULE_NAME,
    FLAX_WEIGHTS_NAME,
    HF_MODULES_CACHE,
    HUGGINGFACE_CO_RESOLVE_ENDPOINT,
    ONNX_EXTERNAL_WEIGHTS_NAME,
    ONNX_WEIGHTS_NAME,
    SAFETENSORS_WEIGHTS_NAME,
    TEXT_ENCODER_ATTN_MODULE,
    WEIGHTS_NAME,
)
from .deprecation_utils import deprecate
from .doc_utils import replace_example_docstring
from .dynamic_modules_utils import get_class_from_dynamic_module
from .hub_utils import (
    HF_HUB_OFFLINE,
    _add_variant,
    _get_model_file,
    extract_commit_hash,
    http_user_agent,
)
from .import_utils import (
    BACKENDS_MAPPING,
    ENV_VARS_TRUE_AND_AUTO_VALUES,
    ENV_VARS_TRUE_VALUES,
    USE_JAX,
    USE_TF,
    USE_TORCH,
    DummyObject,
    OptionalDependencyNotAvailable,
    is_accelerate_available,
    is_accelerate_version,
    is_bsa_available,
    is_flax_available,
    is_ftfy_available,
    is_inflect_available,
    is_invisible_watermark_available,
    is_k_diffusion_available,
    is_k_diffusion_version,
    is_librosa_available,
    is_note_seq_available,
    is_omegaconf_available,
    is_onnx_available,
    is_safetensors_available,
    is_scipy_available,
    is_tensorboard_available,
    is_tf_available,
    is_torch_available,
    is_torch_version,
    is_torchsde_available,
    is_transformers_available,
    is_transformers_version,
    is_unidecode_available,
    is_wandb_available,
    is_xformers_available,
    requires_backends,
)
from .logging import get_logger
from .outputs import BaseOutput
from .pil_utils import PIL_INTERPOLATION, numpy_to_pil, pt_to_pil
from .torch_utils import is_compiled_module, randn_tensor


if is_torch_available():
		from .testing_utils import (
		    floats_tensor,
		    load_hf_numpy,
		    load_image,
		    load_numpy,
		    load_pt,
		    nightly,
		    parse_flag_from_env,
		    print_tensor_test,
		    require_torch_a,
		    require_torch_gpu,
		    skip_mps,
		    slow,
		    torch_all_close,
		    torch_device,
		)
		from .torch_utils import maybe_allow_in_graph

from .testing_utils import export_to_gif, export_to_video


lowerCamelCase		=						get_logger(__name__)






def 	lowerCamelCase_       (			_a			):




		"""simple docstring"""






		if version.parse(_a			) < version.parse(_a			):
				if "dev" in min_version:
						lowerCAmelCase__  :     Tuple       	=   (
						    '''This example requires a source install from HuggingFace diffusers (see '''
						    '''`https://huggingface.co/docs/diffusers/installation#install-from-source`),'''
						)
				else:
						lowerCAmelCase__  :     Dict       	=   f'This example requires a minimum version of {min_version},'
				error_message += f' but the version found is {__version__}.\n'
				raise ImportError(_a			)




