from __future__ import annotations

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




class       __lowerCAmelCase     (				a_  ):



 '''simple docstring'''
 _lowerCamelCase  :		List[Any] 			=       1
 _lowerCamelCase  :		Union[str, Any] 			=       2
 _lowerCamelCase  :		Tuple 			=       3

 def __repr__(	self				:						Dict     )       ->							Optional[Any]:
        return f"{self.__class__.__name__}.{self.name}"







def SCREAMING_SNAKE_CASE (   lowercase_:		tuple[int, int]						,  lowercase_:		int						,  lowercase_:		int ):
       _UpperCamelCase  ,					_UpperCamelCase   :				str       =     point
       return degrees(atana(y - miny						,  x - minx ) )


def SCREAMING_SNAKE_CASE (   lowercase_:		tuple[int, int]						,  lowercase_:		tuple[int, int]						,  lowercase_:		tuple[int, int] ):
       _UpperCamelCase  ,					_UpperCamelCase   :				Union[str, Any]       =     starting
       _UpperCamelCase  ,					_UpperCamelCase   :				List[Any]       =     via
       _UpperCamelCase  ,					_UpperCamelCase   :				List[Any]       =     target
       _UpperCamelCase   :				Optional[Any]       =     degrees(atana(ya - ya						,  xa - xa ) )
       via_angle %= 360
       _UpperCamelCase   :				Any       =     degrees(atana(ya - ya						,  xa - xa ) )
       target_angle %= 360
       # 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 SCREAMING_SNAKE_CASE (   lowercase_:		list[tuple[int, int]] ):

       if len(lowercase_ ) <= 2:
              # There is no convex hull
              raise ValueError('graham_scan: argument must contain more than 3 points.' )
       if len(lowercase_ ) == 3:
              return points
       # find the lowest and the most left point
       _UpperCamelCase   :				Optional[int]       =     0
       _UpperCamelCase  ,					_UpperCamelCase   :				str       =     maxsize, maxsize
       for i, point in enumerate(lowercase_ ):
              _UpperCamelCase   :				str       =     point[0]
              _UpperCamelCase   :				List[Any]       =     point[1]
              if y < miny:
                     _UpperCamelCase   :				Union[str, Any]       =     y
                     _UpperCamelCase   :				Union[str, Any]       =     x
                     _UpperCamelCase   :				List[Any]       =     i
              if y == miny and x < minx:
                     _UpperCamelCase   :				Any       =     x
                     _UpperCamelCase   :				Tuple       =     i

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

       _UpperCamelCase   :				List[str]       =     sorted(lowercase_						,  key=lambda lowercase_ : angle_comparer(lowercase_						,  lowercase_						,  lowercase_ ) )
       # 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[tuple[int, int]]       =     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   :				Union[str, Any]       =     Direction.left

       for i in range(3						,  len(lowercase_ ) ):
              while True:
                     _UpperCamelCase   :				Optional[Any]       =     stack[-2]
                     _UpperCamelCase   :				List[str]       =     stack[-1]
                     _UpperCamelCase   :				Union[str, Any]       =     sorted_points[i]
                     _UpperCamelCase   :				int       =     check_direction(lowercase_						,  lowercase_						,  lowercase_ )

                     if next_direction == Direction.left:
                            _UpperCamelCase   :				int       =     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(lowercase_ )




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


UpperCAmelCase							= {'''configuration_nat''': ['''NAT_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''NatConfig''']}


try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 UpperCAmelCase							= [
     '''NAT_PRETRAINED_MODEL_ARCHIVE_LIST''',
     '''NatForImageClassification''',
     '''NatModel''',
     '''NatPreTrainedModel''',
     '''NatBackbone''',
 ]

if TYPE_CHECKING:
 from .configuration_nat import NAT_PRETRAINED_CONFIG_ARCHIVE_MAP, NatConfig

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_nat import (
      NAT_PRETRAINED_MODEL_ARCHIVE_LIST,
      NatBackbone,
      NatForImageClassification,
      NatModel,
      NatPreTrainedModel,
  )

else:
 import sys

 UpperCAmelCase							= _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)



