






"""simple docstring"""


from __future__ import annotations

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






class __a ( snake_case_					):
  __lowercase     :     List[str]       						=       1
  __lowercase     :     List[str]       						=       2
  __lowercase     :     Dict       						=       3



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






def 					a			(  UpperCamelCase_				:					tuple[int, int]  ,						UpperCamelCase_				:					int  ,						UpperCamelCase_				:					int		)	->		float:
 __A     ,       __A						:							Tuple      =						point
 return degrees(atana(y - miny  ,						x - minx		)		)




def 					a			(  UpperCamelCase_				:					tuple[int, int]  ,						UpperCamelCase_				:					tuple[int, int]  ,						UpperCamelCase_				:					tuple[int, int]		)	->		Direction:
 __A     ,       __A						:							List[str]      =						starting
 __A     ,       __A						:							Optional[int]      =						via
 __A     ,       __A						:							Optional[int]      =						target
 __A						:							List[Any]      =						degrees(atana(ya - ya  ,						xa - xa		)		)
 via_angle %= 3_6_0
 __A						:							Optional[int]      =						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 					a			(  UpperCamelCase_				:					list[tuple[int, int]]		)	->		list[tuple[int, int]]:

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

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

 __A						:							List[Any]      =						sorted(UpperCamelCase_  ,						key=lambda UpperCamelCase_		: angle_comparer(UpperCamelCase_  ,						UpperCamelCase_  ,						UpperCamelCase_		)		)
 # 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(UpperCamelCase_		)		):
  while True:
   __A						:							int      =						stack[-2]
   __A						:							int      =						stack[-1]
   __A						:							List[str]      =						sorted_points[i]
   __A						:							List[Any]      =						check_direction(UpperCamelCase_  ,						UpperCamelCase_  ,						UpperCamelCase_		)

   if next_direction == Direction.left:
    __A						:							str      =						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(UpperCamelCase_		)













"""simple docstring"""


import math




def 					a			(  UpperCamelCase_				:					int		)	->		str:
 if number == 0:
  __A						:							Dict      =						'Zero'
  return words
 else:
  __A						:							List[str]      =						math.logaa(UpperCamelCase_		)
  __A						:							Union[str, Any]      =						digits + 1
  __A						:							List[str]      =						{}
  __A						:							int      =						''
  __A						:							Any      =						'One'
  __A						:							Tuple      =						'Two'
  __A						:							Any      =						'Three'
  __A						:							Any      =						'Four'
  __A						:							Optional[Any]      =						'Five'
  __A						:							List[Any]      =						'Six'
  __A						:							List[Any]      =						'Seven'
  __A						:							Dict      =						'Eight'
  __A						:							Union[str, Any]      =						'Nine'

  __A						:							List[Any]      =						{}
  __A						:							Tuple      =						''
  __A						:							List[Any]      =						'Twenty'
  __A						:							Optional[Any]      =						'Thirty'
  __A						:							Any      =						'Forty'
  __A						:							Optional[int]      =						'Fifty'
  __A						:							Dict      =						'Sixty'
  __A						:							Dict      =						'Seventy'
  __A						:							Optional[Any]      =						'Eighty'
  __A						:							Any      =						'Ninety'

  __A						:							int      =						{}
  __A						:							List[str]      =						'Ten'
  __A						:							Optional[Any]      =						'Eleven'
  __A						:							Dict      =						'Twelve'
  __A						:							Union[str, Any]      =						'Thirteen'
  __A						:							Union[str, Any]      =						'Fourteen'
  __A						:							Dict      =						'Fifteen'
  __A						:							str      =						'Sixteen'
  __A						:							str      =						'Seventeen'
  __A						:							Union[str, Any]      =						'Eighteen'
  __A						:							Union[str, Any]      =						'Nineteen'

  __A						:							Optional[Any]      =						{}
  __A						:							Optional[int]      =						'Hundred,'
  __A						:							Union[str, Any]      =						'Thousand,'
  __A						:							Union[str, Any]      =						'Lakh,'
  __A						:							Union[str, Any]      =						'Crore,'

  __A						:							Optional[Any]      =						number
  __A						:							Optional[Any]      =						''
  __A						:							List[str]      =						0
  __A						:							List[str]      =						int(UpperCamelCase_		)
  while counter < digits:
   __A						:							Any      =						temp_num % 1_0
   if counter % 2 == 0:
    __A						:							Optional[Any]      =						''
    if counter in placevalue and current != 0:
     __A						:							Union[str, Any]      =						placevalue[counter]
    if counter == 2:
     __A						:							Dict      =						singles[current] + addition + words
    elif counter == 0:
     if ((temp_num % 1_0_0) // 1_0) == 1:
      __A						:							Any      =						teens[current] + addition + words
      __A						:							int      =						temp_num // 1_0
      counter += 1
     else:
      __A						:							Optional[Any]      =						singles[current] + addition + words

    else:
     __A						:							str      =						doubles[current] + addition + words

   else:
    if counter == 1:
     if current == 1:
      __A						:							List[Any]      =						teens[number % 1_0] + words
     else:
      __A						:							Union[str, Any]      =						''
      if counter in placevalue:
       __A						:							int      =						placevalue[counter]
      __A						:							Optional[Any]      =						doubles[current] + addition + words
    else:
     __A						:							Any      =						''
     if counter in placevalue:
      if current == 0 and ((temp_num % 1_0_0) // 1_0) == 0:
       __A						:							Optional[int]      =						''
      else:
       __A						:							Optional[int]      =						placevalue[counter]
     if ((temp_num % 1_0_0) // 1_0) == 1:
      __A						:							Dict      =						teens[current] + addition + words
      __A						:							Any      =						temp_num // 1_0
      counter += 1
     else:
      __A						:							List[str]      =						singles[current] + addition + words
   counter += 1
   __A						:							Dict      =						temp_num // 1_0
 return words


if __name__ == "__main__":
   import doctest

   doctest.testmod()





