
"""simple docstring"""




from __future__ import annotations

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







class 	_lowercase    (							snake_case__					):


     '''simple docstring'''





     _A		    =				1
     _A		    =				2
     _A		    =				3



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





def 				a__			(					lowerCAmelCase						:							Any							,     lowerCAmelCase						:							Tuple							,     lowerCAmelCase						:							Optional[int]		):






     '''simple docstring'''
     UpperCAmelCase__				,						UpperCAmelCase__				:			Tuple							=    point
     return degrees(atana(y - miny							,     x - minx		)		)



def 				a__			(					lowerCAmelCase						:							int							,     lowerCAmelCase						:							int							,     lowerCAmelCase						:							Optional[int]		):






     '''simple docstring'''
     UpperCAmelCase__				,						UpperCAmelCase__				:			List[Any]							=    starting
     UpperCAmelCase__				,						UpperCAmelCase__				:			Dict							=    via
     UpperCAmelCase__				,						UpperCAmelCase__				:			List[str]							=    target
     UpperCAmelCase__				:			Optional[Any]							=    degrees(atana(ya - ya							,     xa - xa		)		)
     via_angle %= 360
     UpperCAmelCase__				:			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__			(					lowerCAmelCase						:							Tuple		):






     '''simple docstring'''

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

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

     UpperCAmelCase__				:			Dict							=    sorted(_SCREAMING_SNAKE_CASE							,     key=lambda lowerCAmelCase		: angle_comparer(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE		)		)
     # 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__				:			str							=    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__				:			Optional[int]							=    Direction.left

     for i in range(3							,     len(_SCREAMING_SNAKE_CASE		)		):
          while True:
               UpperCAmelCase__				:			Tuple							=    stack[-2]
               UpperCAmelCase__				:			List[Any]							=    stack[-1]
               UpperCAmelCase__				:			Optional[Any]							=    sorted_points[i]
               UpperCAmelCase__				:			Any							=    check_direction(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE		)

               if next_direction == Direction.left:
                    UpperCAmelCase__				:			Tuple							=    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(_SCREAMING_SNAKE_CASE		)







"""simple docstring"""
import math







def     _a					(   _SCREAMING_SNAKE_CASE					)     ->					list[int]:
							if not isinstance(_SCREAMING_SNAKE_CASE					,			_SCREAMING_SNAKE_CASE					):
														snake_case_     							=		f"""Input value of [number={number}] must be an integer"""
														raise TypeError(_SCREAMING_SNAKE_CASE					)
							if number < 1:
														snake_case_     							=		f"""Input value of [number={number}] must be a positive integer"""
														raise ValueError(_SCREAMING_SNAKE_CASE					)
							snake_case_     							=		[number]
							while number != 1:
														if number % 2 == 0:
																					snake_case_     							=		math.floor(math.sqrt(_SCREAMING_SNAKE_CASE					)					)
														else:
																					snake_case_     							=		math.floor(
																					    math.sqrt(_SCREAMING_SNAKE_CASE					) * math.sqrt(_SCREAMING_SNAKE_CASE					) * math.sqrt(_SCREAMING_SNAKE_CASE					)					)
														sequence.append(_SCREAMING_SNAKE_CASE					)
							return sequence


if __name__ == "__main__":
				import doctest

				doctest.testmod()



