



'''simple docstring'''





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									=     1
 lowerCamelCase									=     2
 lowerCamelCase									=     3







 def __repr__(      self  )    ->    Union[str, Any]:
    return F"{self.__class__.__name__}.{self.name}"



def     UpperCAmelCase     (    a_      ,		a_      ,		a_		)   ->       float:



   """simple docstring"""






   A_						,  A_  :		Dict						=					point
   return degrees(atana(y - miny      ,		x - minx		)		)



def     UpperCAmelCase     (    a_      ,		a_      ,		a_		)   ->       Direction:



   """simple docstring"""






   A_						,  A_  :		List[str]						=					starting
   A_						,  A_  :		Optional[int]						=					via
   A_						,  A_  :		Dict						=					target
   A_  :		int						=					degrees(atana(ya - ya      ,		xa - xa		)		)
   via_angle %= 3_6_0
   A_  :		Any						=					degrees(atana(ya - ya      ,		xa - xa		)		)
   target_angle %= 3_6_0
   # 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     UpperCAmelCase     (    a_		)   ->       list[tuple[int, int]]:



   """simple docstring"""






   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
   A_  :		str						=					0
   A_						,  A_  :		Dict						=					maxsize, maxsize
   for i, point in enumerate(a_		):
      A_  :		Dict						=					point[0]
      A_  :		List[str]						=					point[1]
      if y < miny:
         A_  :		Tuple						=					y
         A_  :		Union[str, Any]						=					x
         A_  :		Any						=					i
      if y == miny and x < minx:
         A_  :		Union[str, Any]						=					x
         A_  :		List[str]						=					i

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

   A_  :		Dict						=					sorted(a_      ,		key=lambda a_		: 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)		)

   A_  :		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.
   A_  :		Union[str, Any]						=					Direction.left

   for i in range(3      ,		len(a_		)		):
      while True:
         A_  :		Dict						=					stack[-2]
         A_  :		Dict						=					stack[-1]
         A_  :		Optional[int]						=					sorted_points[i]
         A_  :		List[Any]						=					check_direction(a_      ,		a_      ,		a_		)

         if next_direction == Direction.left:
            A_  :		Union[str, Any]						=					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_		)





'''simple docstring'''





from ..utils import DummyObject, requires_backends


class 							_lowerCAmelCase	(  metaclass=__A							):


 """simple docstring"""

 lowerCamelCase									=     ['''torch''', '''librosa''']







 def __init__(      self					,    *_lowerCamelCase					,    **_lowerCamelCase  )    ->    str:
    requires_backends(self					,    ["""torch""", """librosa"""]  )







 @classmethod
 def       UpperCAmelCase_       (      cls					,    *_lowerCamelCase					,    **_lowerCamelCase  )    ->    Dict:
    requires_backends(cls					,    ["""torch""", """librosa"""]  )







 @classmethod
 def       UpperCAmelCase_       (      cls					,    *_lowerCamelCase					,    **_lowerCamelCase  )    ->    Optional[int]:
    requires_backends(cls					,    ["""torch""", """librosa"""]  )


class 							_lowerCAmelCase	(  metaclass=__A							):


 """simple docstring"""

 lowerCamelCase									=     ['''torch''', '''librosa''']







 def __init__(      self					,    *_lowerCamelCase					,    **_lowerCamelCase  )    ->    Dict:
    requires_backends(self					,    ["""torch""", """librosa"""]  )







 @classmethod
 def       UpperCAmelCase_       (      cls					,    *_lowerCamelCase					,    **_lowerCamelCase  )    ->    str:
    requires_backends(cls					,    ["""torch""", """librosa"""]  )







 @classmethod
 def       UpperCAmelCase_       (      cls					,    *_lowerCamelCase					,    **_lowerCamelCase  )    ->    Dict:
    requires_backends(cls					,    ["""torch""", """librosa"""]  )
