



from __future__ import annotations

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

class    _SCREAMING_SNAKE_CASE						(UpperCamelCase			):
     lowerCAmelCase       =      1
     lowerCAmelCase       =      2
     lowerCAmelCase       =      3





     def __repr__(							self			:				Tuple					)->int:
      return F"""{self.__class__.__name__}.{self.name}"""






def 						_lowerCAmelCase    (					__lowerCamelCase :  tuple[int, int]		,						__lowerCamelCase :  int		,						__lowerCamelCase :  int  ):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE							:     Tuple							=						point
 return degrees(atana(y - miny		,						x - minx  )  )






def 						_lowerCAmelCase    (					__lowerCamelCase :  tuple[int, int]		,						__lowerCamelCase :  tuple[int, int]		,						__lowerCamelCase :  tuple[int, int]  ):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE							:     List[str]							=						starting
 __SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE							:     List[Any]							=						via
 __SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE							:     str							=						target
 __SCREAMING_SNAKE_CASE							:     Any							=						degrees(atana(ya - ya		,						xa - xa  )  )
 via_angle %= 360
 __SCREAMING_SNAKE_CASE							:     List[str]							=						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 						_lowerCAmelCase    (					__lowerCamelCase :  list[tuple[int, int]]  ):



 """simple docstring"""





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

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

 __SCREAMING_SNAKE_CASE							:     Optional[Any]							=						sorted(__lowerCamelCase		,						key=lambda __lowerCamelCase  : angle_comparer(__lowerCamelCase		,						__lowerCamelCase		,						__lowerCamelCase  )  )
 # 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)  )

 __SCREAMING_SNAKE_CASE							:     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.
 __SCREAMING_SNAKE_CASE							:     List[Any]							=						Direction.left

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

   if next_direction == Direction.left:
    __SCREAMING_SNAKE_CASE							:     Optional[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(__lowerCamelCase  )














"""simple docstring"""



from __future__ import annotations

import random
from collections.abc import Iterable
from typing import Any, Generic, TypeVar

_UpperCamelCase						:    Optional[int]		=						TypeVar('T', bound=bool)

class 			a	(  Generic[T]      ):







    def __init__(     self				,						_lowerCamelCase			):
      lowercase				       =			value
      lowercase				       =			None
      lowercase				       =			None







    @property
    def      UpperCamelCase_ (     self			):
      return self._value







    @staticmethod
    def      UpperCamelCase_ (     _lowerCamelCase				,						_lowerCamelCase			):
      if not roota:
        return roota

      if not roota:
        return roota

      if roota.value > roota.value:
        lowercase       ,	lowercase				       =			roota, roota

      if random.choice([True, False]			):
        lowercase       ,	lowercase				       =			roota.right, roota.left

      lowercase				       =			RandomizedHeapNode.merge(roota.left				,						_lowerCamelCase			)

      return roota


class 			a	(  Generic[T]      ):







    def __init__(     self				,						_lowerCamelCase = ()			):
      lowercase				       =			None

      if data:
        for item in data:
          self.insert(_lowerCamelCase			)







    def      UpperCamelCase_ (     self				,						_lowerCamelCase			):
      lowercase				       =			RandomizedHeapNode.merge(self._root				,						RandomizedHeapNode(_lowerCamelCase			)			)







    def      UpperCamelCase_ (     self			):
      lowercase				       =			self.top()

      if self._root is None:
        return None

      lowercase				       =			RandomizedHeapNode.merge(self._root.left				,						self._root.right			)

      return result







    def      UpperCamelCase_ (     self			):
      if not self._root:
        raise IndexError('Can\'t get top element for the empty heap.'			)
      return self._root.value







    def      UpperCamelCase_ (     self			):
      lowercase				       =			None







    def      UpperCamelCase_ (     self			):
      lowercase				       =			[]
      while self:
        result.append(self.pop()			)

      return result







    def __bool__(     self			):
      return self._root is not None


if __name__ == "__main__":
    import doctest

    doctest.testmod()


