



from __future__ import annotations

from collections import deque
from enum import Enum
from math import atana, degrees
from sys import maxsize


class  _lowercase				(__A ):
    '''simple docstring'''







    lowercase__				  =  1
    lowercase__				  =  2
    lowercase__				  =  3

    def __repr__(	self      ):

         '''simple docstring'''


         return F"""{self.__class__.__name__}.{self.name}"""




def 				_lowerCAmelCase      (_lowerCAmelCase				,		_lowerCAmelCase				,		_lowerCAmelCase):
     UpperCamelCase_											=				point
     return degrees(atana(y - miny				,		x - minx))



def 				_lowerCAmelCase      (_lowerCAmelCase				,		_lowerCAmelCase				,		_lowerCAmelCase):
     UpperCamelCase_											=				starting
     UpperCamelCase_											=				via
     UpperCamelCase_											=				target
     UpperCamelCase_											=				degrees(atana(ya - ya				,		xa - xa))
     via_angle %= 3_60
     UpperCamelCase_											=				degrees(atana(ya - ya				,		xa - xa))
     target_angle %= 3_60
     # t-
     #  \ \
     #   \ v
     #    \|
     #     s
     # via_angle is always lower than target_angle, if direction is left.
     # If they are same, it means they are on a same line of convex hull.
     if target_angle > via_angle:
          return Direction.left
     elif target_angle == via_angle:
          return Direction.straight
     else:
          return Direction.right






def 				_lowerCAmelCase      (_lowerCAmelCase):

     if len(_a) <= 2:
          # There is no convex hull
          raise ValueError("graham_scan: argument must contain more than 3 points.")
     if len(_a) == 3:
          return points
     # find the lowest and the most left point
     UpperCamelCase_											=				0
     UpperCamelCase_											=				maxsize, maxsize
     for i, point in enumerate(_a):
          UpperCamelCase_											=				point[0]
          UpperCamelCase_											=				point[1]
          if y < miny:
               UpperCamelCase_											=				y
               UpperCamelCase_											=				x
               UpperCamelCase_											=				i
          if y == miny and x < minx:
               UpperCamelCase_											=				x
               UpperCamelCase_											=				i

    # remove the lowest and the most left point from points for preparing for sort
     points.pop(_a)

     UpperCamelCase_											=				sorted(_a				,		key=lambda _lowerCAmelCase: angle_comparer(_a				,		_a				,		_a))
     # This insert actually costs complexity,
     # and you should instead add (minx, miny) into stack later.
     # I'm using insert just for easy understanding.
     sorted_points.insert(0				,		(minx, miny))

     UpperCamelCase_											=				deque()
     stack.append(sorted_points[0])
     stack.append(sorted_points[1])
     stack.append(sorted_points[2])
     # In any ways, the first 3 points line are towards left.
     # Because we sort them the angle from minx, miny.
     UpperCamelCase_											=				Direction.left

     for i in range(3				,		len(_a)):
          while True:
               UpperCamelCase_											=				stack[-2]
               UpperCamelCase_											=				stack[-1]
               UpperCamelCase_											=				sorted_points[i]
               UpperCamelCase_											=				check_direction(_a				,		_a				,		_a)

               if next_direction == Direction.left:
                    UpperCamelCase_											=				Direction.left
                    break
               if next_direction == Direction.straight:
                    if current_direction == Direction.left:
                         # We keep current_direction as left.
                         # Because if the straight line keeps as straight,
                         # we want to know if this straight line is towards left.
                         break
                    elif current_direction == Direction.right:
                         # If the straight line is towards right,
                         # every previous points on those straigh line is not convex hull.
                         stack.pop()
               if next_direction == Direction.right:
                    stack.pop()
          stack.append(sorted_points[i])
     return list(_a)





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


UpperCAmelCase				:							Optional[int]								={
    """configuration_realm""": ["""REALM_PRETRAINED_CONFIG_ARCHIVE_MAP""", """RealmConfig"""],
    """tokenization_realm""": ["""RealmTokenizer"""],
}

try:
	if not is_tokenizers_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	UpperCAmelCase				:							Optional[int]								=["""RealmTokenizerFast"""]

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	UpperCAmelCase				:							Union[str, Any]								=[
	    """REALM_PRETRAINED_MODEL_ARCHIVE_LIST""",
	    """RealmEmbedder""",
	    """RealmForOpenQA""",
	    """RealmKnowledgeAugEncoder""",
	    """RealmPreTrainedModel""",
	    """RealmReader""",
	    """RealmScorer""",
	    """load_tf_weights_in_realm""",
	]
	UpperCAmelCase				:							List[str]								=["""RealmRetriever"""]


if TYPE_CHECKING:
	from .configuration_realm import REALM_PRETRAINED_CONFIG_ARCHIVE_MAP, RealmConfig
	from .tokenization_realm import RealmTokenizer

	try:
		if not is_tokenizers_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .tokenization_realm import RealmTokenizerFast

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_realm import (
		    REALM_PRETRAINED_MODEL_ARCHIVE_LIST,
		    RealmEmbedder,
		    RealmForOpenQA,
		    RealmKnowledgeAugEncoder,
		    RealmPreTrainedModel,
		    RealmReader,
		    RealmScorer,
		    load_tf_weights_in_realm,
		)
		from .retrieval_realm import RealmRetriever


else:
	import sys

	UpperCAmelCase				:							str								=_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)
