






from __future__ import annotations

from collections import deque
from enum import Enum
from math import atana, degrees
from sys import maxsize
class        __snake_case(					__UpperCamelCase      ):
 lowercase :       int		      =		1
 lowercase :       Optional[Any]		      =		2
 lowercase :       Optional[Any]		      =		3



 def __repr__(	self   :   Any	):

    """simple docstring"""






    return f'''{self.__class__.__name__}.{self.name}'''
def       a__						(  A		,				A		,				A					):
   lowercase__     ,					lowercase__						:	Dict         = point
   return degrees(atana(y - miny		,				x - minx					)					)
def       a__						(  A		,				A		,				A					):
   lowercase__     ,					lowercase__						:	int         = starting
   lowercase__     ,					lowercase__						:	int         = via
   lowercase__     ,					lowercase__						:	Union[str, Any]         = target
   lowercase__						:	int         = degrees(atana(ya - ya		,				xa - xa					)					)
   via_angle %= 360
   lowercase__						:	int         = 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       a__						(  A					):

   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
   lowercase__						:	List[str]         = 0
   lowercase__     ,					lowercase__						:	Any         = maxsize, maxsize
   for i, point in enumerate(A					):
      lowercase__						:	Union[str, Any]         = point[0]
      lowercase__						:	str         = point[1]
      if y < miny:
         lowercase__						:	Union[str, Any]         = y
         lowercase__						:	Tuple         = x
         lowercase__						:	Optional[int]         = i
      if y == miny and x < minx:
         lowercase__						:	int         = x
         lowercase__						:	Union[str, Any]         = i

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

   lowercase__						:	Any         = 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)					)

   lowercase__						:	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.
   lowercase__						:	Optional[Any]         = Direction.left

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

         if next_direction == Direction.left:
            lowercase__						:	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					)










def       a__						(  A					):

   if not isinstance(A		,				A					) or number < 0:
      raise ValueError("""Input must be a non-negative integer"""					)

   lowercase__						:	str         = number & ~(number - 1)
   lowercase__						:	Optional[int]         = 0
   while intermediate:
      intermediate >>= 1
      index += 1
   return index - 1


if __name__ == "__main__":
 import doctest

 doctest.testmod(verbose=True)


