






from __future__ import annotations

from collections.abc import Iterable





class     __a						:







 def __init__(	self      :     List[str]							,     SCREAMING_SNAKE_CASE      :     List[Any]							,     SCREAMING_SNAKE_CASE      :     Any		):


      '''simple docstring'''






      UpperCamelCase__    :     Optional[Any]        =						float(SCREAMING_SNAKE_CASE		), float(SCREAMING_SNAKE_CASE		)







 def __eq__(	self      :     Any							,     SCREAMING_SNAKE_CASE      :     List[Any]		):


      '''simple docstring'''






      return self.x == other.x and self.y == other.y







 def __ne__(	self      :     Optional[int]							,     SCREAMING_SNAKE_CASE      :     int		):


      '''simple docstring'''






      return not self == other







 def __gt__(	self      :     List[Any]							,     SCREAMING_SNAKE_CASE      :     Dict		):


      '''simple docstring'''






      if self.x > other.x:
           return True
      elif self.x == other.x:
           return self.y > other.y
      return False







 def __lt__(	self      :     List[Any]							,     SCREAMING_SNAKE_CASE      :     str		):


      '''simple docstring'''






      return not self > other







 def __ge__(	self      :     Optional[Any]							,     SCREAMING_SNAKE_CASE      :     Optional[Any]		):


      '''simple docstring'''






      if self.x > other.x:
           return True
      elif self.x == other.x:
           return self.y >= other.y
      return False







 def __le__(	self      :     Union[str, Any]							,     SCREAMING_SNAKE_CASE      :     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      :     List[Any]		):


      '''simple docstring'''






      return F'({self.x}, {self.y})'







 def __hash__(	self      :     Dict		):


      '''simple docstring'''






      return hash(self.x		)







def 	SCREAMING_SNAKE_CASE							(      __lowerCAmelCase      ,					)				->			list[Point]:
     UpperCamelCase__    :     list[Point]        =						[]
     if list_of_tuples:
          for p in list_of_tuples:
               if isinstance(__lowerCAmelCase      ,					__lowerCAmelCase    ):
                    points.append(__lowerCAmelCase    )
               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 	SCREAMING_SNAKE_CASE							(      __lowerCAmelCase    )				->			list[Point]:

     if not hasattr(__lowerCAmelCase      ,					"__iter__"    ):
          UpperCamelCase__    :     Dict        =						f'Expecting an iterable object but got an non-iterable type {points}'
          raise ValueError(__lowerCAmelCase    )

     if not points:
          UpperCamelCase__    :     Tuple        =						f'Expecting a list of points but got {points}'
          raise ValueError(__lowerCAmelCase    )

     return _construct_points(__lowerCAmelCase    )







def 	SCREAMING_SNAKE_CASE							(      __lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase    )				->			float:
     UpperCamelCase__    :     Optional[int]        =						(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 	SCREAMING_SNAKE_CASE							(      __lowerCAmelCase    )				->			list[Point]:
     UpperCamelCase__    :     Union[str, Any]        =						sorted(_validate_input(__lowerCAmelCase    )    )
     UpperCamelCase__    :     int        =						len(__lowerCAmelCase    )
     UpperCamelCase__    :     List[Any]        =						set()

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

                         if det_k > 0:
                              UpperCamelCase__    :     Optional[Any]        =						True
                         elif det_k < 0:
                              UpperCamelCase__    :     List[Any]        =						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__    :     List[Any]        =						False
                                   break

                    if points_left_of_ij and points_right_of_ij:
                         UpperCamelCase__    :     Dict        =						False
                         break

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

     return sorted(__lowerCAmelCase    )







def 	SCREAMING_SNAKE_CASE							(      __lowerCAmelCase    )				->			list[Point]:
     UpperCamelCase__    :     Union[str, Any]        =						sorted(_validate_input(__lowerCAmelCase    )    )
     UpperCamelCase__    :     Optional[int]        =						len(__lowerCAmelCase    )

     # 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__    :     List[str]        =						points[0]
     UpperCamelCase__    :     List[Any]        =						points[n - 1]

     UpperCamelCase__    :     List[Any]        =						{left_most_point, right_most_point}
     UpperCamelCase__    :     Dict        =						[]
     UpperCamelCase__    :     List[Any]        =						[]

     for i in range(1      ,					n - 1    ):
          UpperCamelCase__    :     str        =						_det(__lowerCAmelCase      ,					__lowerCAmelCase      ,					points[i]    )

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

     _construct_hull(__lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase    )
     _construct_hull(__lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase    )

     return sorted(__lowerCAmelCase    )







def 	SCREAMING_SNAKE_CASE							(      __lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase    )				->			None:
     if points:
          UpperCamelCase__    :     str        =						None
          UpperCamelCase__    :     List[Any]        =						float("-inf"    )
          UpperCamelCase__    :     List[Any]        =						[]

          for p in points:
               UpperCamelCase__    :     List[str]        =						_det(__lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase    )

               if det > 0:
                    candidate_points.append(__lowerCAmelCase    )

                    if det > extreme_point_distance:
                         UpperCamelCase__    :     Any        =						det
                         UpperCamelCase__    :     List[str]        =						p

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







def 	SCREAMING_SNAKE_CASE							(      __lowerCAmelCase    )				->			list[Point]:
     UpperCamelCase__    :     Optional[int]        =						sorted(_validate_input(__lowerCAmelCase    )    )
     UpperCamelCase__    :     Any        =						len(__lowerCAmelCase    )

     UpperCamelCase__    :     Optional[Any]        =						points[:2]
     for i in range(2      ,					__lowerCAmelCase    ):
          UpperCamelCase__    :     Union[str, Any]        =						_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__    :     int        =						points[i]
     i += 1

     for j in range(__lowerCAmelCase      ,					__lowerCAmelCase    ):
          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(__lowerCAmelCase    ) > 3 else convex_hull    )







def 	SCREAMING_SNAKE_CASE							(      )				->			Dict:
     UpperCamelCase__    :     Tuple        =						[
         (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__    :     List[Any]        =						convex_hull_bf(__lowerCAmelCase    )

     UpperCamelCase__    :     Tuple        =						convex_hull_recursive(__lowerCAmelCase    )
     assert results_bf == results_recursive

     UpperCamelCase__    :     List[Any]        =						convex_hull_melkman(__lowerCAmelCase    )
     assert results_bf == results_melkman

     print(__lowerCAmelCase    )


if __name__ == "__main__":
 main()








import os
import unittest

from transformers import MPNetTokenizerFast
from transformers.models.mpnet.tokenization_mpnet import VOCAB_FILES_NAMES, MPNetTokenizer
from transformers.testing_utils import require_tokenizers, slow

from ...test_tokenization_common import TokenizerTesterMixin





@require_tokenizers
class     __a						(					A__ ,     unittest.TestCase ):
 _lowerCAmelCase : str 				=				MPNetTokenizer
 _lowerCAmelCase : List[str] 				=				MPNetTokenizerFast
 _lowerCAmelCase : List[Any] 				=				True
 _lowerCAmelCase : Union[str, Any] 				=				True







 def       __lowercase      (	self      :     List[Any]		):


      '''simple docstring'''






      super().setUp()

      UpperCamelCase__    :     List[Any]        =						[
          "[UNK]",
          "[CLS]",
          "[SEP]",
          "[PAD]",
          "[MASK]",
          "want",
          "##want",
          "##ed",
          "wa",
          "un",
          "runn",
          "##ing",
          ",",
          "low",
          "lowest",
      ]
      UpperCamelCase__    :     int        =						os.path.join(self.tmpdirname							,     VOCAB_FILES_NAMES["vocab_file"]		)
      with open(self.vocab_file							,     "w"							,     encoding="utf-8"		) as vocab_writer:
           vocab_writer.write("".join([x + "\n" for x in vocab_tokens]		)		)







 def       __lowercase      (	self      :     Tuple							,     SCREAMING_SNAKE_CASE      :     List[str]		):


      '''simple docstring'''






      UpperCamelCase__    :     List[str]        =						"UNwant\u00E9d,running"
      UpperCamelCase__    :     List[str]        =						"unwanted, running"
      return input_text, output_text







 def       __lowercase      (	self      :     Any		):


      '''simple docstring'''






      UpperCamelCase__    :     str        =						self.tokenizer_class(self.vocab_file		)

      UpperCamelCase__    :     Any        =						tokenizer.tokenize("UNwant\u00E9d,running"		)
      self.assertListEqual(SCREAMING_SNAKE_CASE							,     ["un", "##want", "##ed", ",", "runn", "##ing"]		)
      self.assertListEqual(tokenizer.convert_tokens_to_ids(SCREAMING_SNAKE_CASE		)							,     [9, 6, 7, 12, 10, 11]		)







 @slow
 def       __lowercase      (	self      :     str		):


      '''simple docstring'''






      UpperCamelCase__    :     Union[str, Any]        =						self.tokenizer_class.from_pretrained("microsoft/mpnet-base"		)

      UpperCamelCase__    :     Optional[int]        =						tokenizer.encode("sequence builders"							,     add_special_tokens=SCREAMING_SNAKE_CASE		)
      UpperCamelCase__    :     Optional[int]        =						tokenizer.encode("multi-sequence build"							,     add_special_tokens=SCREAMING_SNAKE_CASE		)

      UpperCamelCase__    :     Tuple        =						tokenizer.build_inputs_with_special_tokens(SCREAMING_SNAKE_CASE		)
      UpperCamelCase__    :     Optional[int]        =						tokenizer.build_inputs_with_special_tokens(SCREAMING_SNAKE_CASE							,     SCREAMING_SNAKE_CASE		)

      assert encoded_sentence == [0] + text + [2]
      assert encoded_pair == [0] + text + [2] + [2] + text_a + [2]